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Dianzuo Wang
Flotation Reagents: Applied Surface Chemistry on Minerals Flotation and Energy Resources Beneficiation Volume 1: Functional Principle
Flotation Reagents: Applied Surface Chemistry on Minerals Flotation and Energy Resources Beneficiation
Dianzuo Wang
Flotation Reagents: Applied Surface Chemistry on Minerals Flotation and Energy Resources Beneficiation Volume 1: Functional Principle
123
Dianzuo Wang General Research Institute for Nonferrous Metals (GRINM) Chinese Academy of Engineering Beijing China
ISBN 978-981-10-2028-5 DOI 10.1007/978-981-10-2030-8
ISBN 978-981-10-2030-8
(eBook)
Jointly published with Metallurgical Industry Press, Beijing, China ISBN: 978-7-5024-7145-3 Metallurgical Industry Press, Beijing, China Library of Congress Control Number: 2016945949 © Metallurgical Industry Press, Beijing and Springer Science+Business Media Singapore 2016 This work is subject to copyright. All rights are reserved by the Publishers, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Science+Business Media Singapore Pte Ltd.
Preface
The development of minerals processing over one hundred years has shown flotation a predominant process of materials separation. Nowadays, flotation is widely used in minerals separation, treatments of slag and wastes, materials separation, and valuables recovery in metallurgical, coal, and chemical engineering. Flotation reagents have played vital roles in the progress of flotation process. The development and application of the reagents have made it possible for more and more traditional refractory ores and materials to be treated by flotation process with high efficiency. Several books on flotation principles and reagents have been published, however, for further improvement of current minerals processing performance and for the treatment and recovery of refractory and nontraditional mineral and energy resources, scientists need to develop new reagents and innovative processes. The author of this book took up investigation of flotation reagents in the 1960s. The fundamentals and approaches of surface chemistry have been applied in the round to discuss the structure, performance of the reagents, and the interaction between the reagents and minerals, as well as to set up theoretical criteria for collector performance. Molecular orbit method incorporating with molecular design was used to have obtained quantum chemistry parameters, steric configuration, HOMO, and LUMO surface of various reagents. This book has summarized the results that the author has achieved on functional principle of flotation reagents in the last 50 years. The Chinese edition of this book was published in 1982 and reprinted in 1994 by Metallurgical Industry Press. This English edition, on the basis of Chinese edition, has incorporated the new findings on the topic in particular the molecular design of reagents achieved by the author and his research group. This book is intended for worldwide university teachers, researchers, R&D engineers, and graduate students in minerals processing, extractive metallurgy, and resources utilization who wish to explore innovative reagents and technologies that lead to more energy efficient and environmentally sustainable solutions.
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Preface
In time of publication of the English edition, I would like to acknowledge cooperation and contributions to the contents of this book from my colleagues and graduate students. A special acknowledgment is warranted to Dr. Guihong Han, who completed the onerous translation of this book with his dedication and persistence. I give my sincere thanks to Prof. Tao Jiang, who undertook the proposal for the publication and helped to review the first draft. Thanks also to Mr. Xiaofeng Liu (editor of Metallurgical Industry Press), who encouraged and helped to complete this project. Beijing, China December 2015
Dianzuo Wang
Contents
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Interaction Between Minerals and Reagents . . . . . . . . . . . . . . . . . . . 2.1 Various Theories on Interaction Between Collectors and Minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Main Interactions Between Collector and Mineral . . . . . 2.1.2 Adsorption Models of Collector on Mineral . . . . . . . . . 2.2 Adsorption Equation of Flotation Reagent on Mineral Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Adsorption Isotherm Model . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Adsorption Isotherm of Flotation Reagent on Mineral Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Adsorption Kinetics Equation of Flotation Reagent on Mineral Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Brief History of Research and Application of Flotation and Reagents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Classification and Significance of Flotation Reagents . . . . . 1.2.1 Classification of Flotation Reagents According to Their Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Classification of Flotation Reagents According to Their Roles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Classification of Flotation Reagents According to Their Structures . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4 Classification of Flotation Reagents According to Their Chemical Constituents . . . . . . . . . . . . . . . 1.2.5 Classification of Flotation Reagents According to Characteristics of Coordination Chemistry . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9 9 10 18 18 21 27
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2.3
Structure of Adsorption Film and Flotation Behavior of Mineral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Structure of Adsorbed Layer . . . . . . . . . . . . . . . . . . . . . 2.3.2 Relationship of Collector Adsorption and Mineral Flotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Mineral Structure, Bonding Characteristics, and the Reaction of Reagents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Geochemical Classification of Mineral Elements and Their Interaction With reagent . . . . . . . . . . . . . . . . 2.4.2 Structure and Valence Bond of Mineral and Their Reactions with Reagents . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Structure and Property of Polar Group of Collector . . . . . . . . . . . . 3.1 Structural Characteristics of Collector Molecule and Independent Effect of Chemical Groups Belong to Surface Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Effect of Polar Group Structure on Dissociation of Reagent and Adsorption in Electrical Double Layer of Mineral Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Dissociation of Collector and Its Flotation Function . . . 3.2.2 Zero Charge Point of Mineral and Dissociation Constant of Collector, and Their Interrelation in Flotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Adsorption of Amphoteric Collector in Electric Double Layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Effect of Polar Group Structure on Dissociation of Collector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Molecular Structure of Nonionic Reagent and Adsorption by van der Waals Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 van der Waals Force Between Collector Molecules . . . . 3.3.2 Relation between Reagent Molecular Structure and van der Waals Force . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Hydrogen Bonding Adsorption of Reagent . . . . . . . . . . 3.4 Polar Group Structure and Chemisorption . . . . . . . . . . . . . . . . . 3.4.1 Common Solidophilic Atoms in Polar Group . . . . . . . . 3.4.2 Bonding Capability of Solidophilic Atoms . . . . . . . . . . 3.5 Inductive Effect in Polar Group of Collector . . . . . . . . . . . . . . . 3.5.1 Introduction of Inductive Effect . . . . . . . . . . . . . . . . . . . 3.5.2 Inductive Effect in Xanthate Molecule . . . . . . . . . . . . . . 3.5.3 Inductive Effect in Thionocarbamates Molecule as Collector [9] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.4 Inductive Effect in Aerofloat Collector Molecule . . . . . .
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Contents
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3.5.5
Comparison of Inductive Effect in Xanthate, Dithiocarbamate, and Aerofloat . . . . . . . . . . . . . . . 3.5.6 Inductive Effect in Collector of Nonsulfide Minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Conjugative Effect in Polar Group of Collector . . . . . . . . . 3.6.1 Introduction of Conjugative Effect . . . . . . . . . . . . . 3.6.2 Conjugative Effect in Xanthate Molecule . . . . . . . 3.6.3 Conjugative Effect in Aromatic Collector . . . . . . . 3.7 Polar Group of Coordinating Collector . . . . . . . . . . . . . . . . 3.7.1 Major Features of Coordinating Collector . . . . . . . 3.7.2 Structure and Property of Polar Group of Coordinating Collector . . . . . . . . . . . . . . . . . . . 3.7.3 Functional Mechanism of the Coordinating Collector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.4 Classification of the Coordinating Collector . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
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Structure and Property of Nonpolar Group of Collector . . . . . 4.1 Role of Nonpolar Group of Collector . . . . . . . . . . . . . . . . . 4.2 Structure, Solubility, and Surface Activity of Nonpolar Group for Flotation Reagent . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Solubility of Organic Liquid in Water . . . . . . . . . . 4.2.2 Surface Activity and Solubility of Organic Liquid in Water . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Solubility and Surface Activity of Heteropolarity Organic Solid Matter . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Comparison of Hydrophobic Association Energy of Nonpolar Group and Electrostatic Interaction Energy of Collector During Double Electric Layer Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Normal Alkyl Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Isoalkyl Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Unsaturated Hydrocarbon Chain . . . . . . . . . . . . . . . . . . . . . 4.6 Aromatic Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Other Kinds of Nonpolar Groups . . . . . . . . . . . . . . . . . . . . 4.7.1 Cycloalkyl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7.2 Alkoxyl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Structure Relationship Between Polar and NonPolar Group in Collector Molecule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.1 Correlation Between Size of NonPolar Group and Variety of Polar Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.2 Relationship Between Number and Position of Polar Group and NonPolar Group . . . . . . . . . . . . . . . . . . . . . 130
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5.2.1
Two or More of Polar Groups in a Collector Molecule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.2.2 Two or More of NonPolar Groups in Collector Molecule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.2.3 Position of Polar Group in Collector Molecule . . . . . . . 131 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6
Theoretical Criteria and Calculation for Collector Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Solubility Product Theory of Reaction of Flotation Reagent and Related Calculation . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Solubility Product Theory of Collector Reaction . . . . . . 6.1.2 Calculation for the Optimum Conditions of Interaction Between Collector and Mineral Using Solubility Product . . . . . . . . . . . . . . . . . . . . . . . . 6.1.3 Diagram of Solubility Product Calculation . . . . . . . . . . 6.1.4 Comparison and Discussion of Computational Methods of Solubility Product . . . . . . . . . . . . . . . . . . . . 6.1.5 Research on Structure and Performance of Reagent via Solubility Product Calculation . . . . . . . . 6.2 Critical Micelle Concentration and Related Calculation for Flotation Reagent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Critical Micelle Concentration (CMC) and Related Calculation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 General Relation Between CMC and Structure of Reagent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Application of CMC to Predict Reagent Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Hydrophile-Lipophile Balance (HLB) for Flotation Reagent . . . . 6.3.1 Hydrophile-Lipophile Balance (HLB) and Related Calculation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Relationship Between HLB and Other Physical Property Values of Reagents . . . . . . . . . . . . . . . . . . . . . 6.3.3 Application of Molecular Fragment Method to Calculate Hydrophile-Lipophile Property for Flotation Reagent . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.4 The Prediction of Uses of Reagent . . . . . . . . . . . . . . . . 6.4 Electronegativity and Related Calculation for Flotation Reagent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Electronegativity and Related Calculations . . . . . . . . . . 6.4.2 Calculation of Group Electronegativity of Flotation Reagent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.3 Relation Between Group Electronegativity and Physical and Chemical Properties of General Surfactant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Relationship Between Group Electronegativity and Properties of Flotation Reagents . . . . . . . . . . . . . . . 6.4.5 Uses of Group Electronegativity to discuss the Structure—Performance of Flotation Reagent . . . . . 6.4.6 Uses of Group Electronegativity to Hydrophilicity– Hydrophobicity Balance of Polar and Non-polar Groups in a Reagent Molecule . . . . . . . . . . . . . . . . . . . 6.4.7 Application of Group Electronegativity to Classification and Uses of Flotation Reagents . . . . . . Steric Size of Collector Molecule and Its Flotation Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 General Relation Between Steric Size of Reagents and Their Collector Performance . . . . . . . . . . . . . . . . . . 6.5.2 Rough Calculation for Steric Size of Collector Molecule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.3 Relation between Steric Size of Polar Group and Selectivity of Collector . . . . . . . . . . . . . . . . . . . . . . 6.5.4 Relationship Between Steric Size of Non-polar Group and Selectivity of Collector . . . . . . . . . . . . . . . . 6.5.5 Selectivity of Flotation Reagents—xg Calculation and Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Molecular Orbital Approach of Reagent Performance . . . . . . . . . 6.6.1 Introduction of Molecular Orbital Approach (HMO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.2 Application of HMO to Calculate Orbit Energy and Electron Density Distribution . . . . . . . . . . . . . . . . . 6.6.3 Application of HMO to calculate Theoretical Index . . . 6.6.4 Application of HMO to calculation of flotation reagent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.5 Application of Electron Density to Discuss the Structure—Performance of Polar Group . . . . . . . . . 6.6.6 Application of Valence Theory and HMO to Discuss the Bonding Property and Mechanism of Reagents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.7 Application of HMO and Synergism of BackDonation Bond to Discuss the Bonding and Selectivity of Reagent . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.8 Application of HMO to Discuss the Structure— Performance of Non-polar Group . . . . . . . . . . . . . . . . . 6.6.9 Application of HMO to Discuss and Compare Several Collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6.7
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Comprehensive Applications of Various Theoretical Criteria . . . 6.7.1 Characteristic of the Sulfide Collector . . . . . . . . . . . . . . 6.7.2 Characteristic of the Nonmetal Oxide Collector. . . . . . . 6.7.3 Characteristic of the Rare and Ferrous Metal Oxide Collector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7.4 Characteristic of Organic Depressant . . . . . . . . . . . . . . . 6.7.5 Characteristic of Frother . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Structure and Performance of Frother . . . . . . . . . . . . . . . . . . . 7.1 Classification of Frothers and Their Structure Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Role of Frother in Mineral Flotation . . . . . . . . . . . . . . . . . . 7.2.1 Criteria for Frother Performance . . . . . . . . . . . . . . 7.2.2 Relation Between Solution Concentration and Surface Tension, Frothing Capability of Frother . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 Interaction Between Frother and Other Reagent . . 7.3 Effect of Polar Group Structure on Frothing Performance . 7.3.1 Effect of Polar Group on Solubility of Frother . . . 7.3.2 Effect of Polar Group on Dissociation Degree of Frother . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Effect of Hydratability and Cross Section of Polar Group on Frother Performance . . . . . . . . 7.3.4 Effect of Chemical Properties of Polar Group on Frother Performance . . . . . . . . . . . . . . . . . . . . . 7.3.5 Effect of Quantity and Position of Polar Group . . . 7.4 Effect of Nonpolar Group Structure on Flotation Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Effect of n-Alkyl . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.2 Effect of Aryl and Alkylaryl . . . . . . . . . . . . . . . . . 7.4.3 Effect of Isoalkyl and Unsaturated Aliphatic Hydrocarbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.4 Effect of Alkoxy . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Prediction of Frothing Performance via Reagent Structure and Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.1 Concept and Calculation of Parachor . . . . . . . . . . . 7.5.2 Application of Parachor to Prediction of Frother Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.3 Application of HLB to Prediction of Frother Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Structure and Performance of Organic Depressant . . . . . . . . . . . . . 8.1 Classification of Organic Depressants and Their Functions in Flotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.1 Classification of Organic Depressants . . . . . . . . . . . . . . 8.1.2 Functional Mechanism of Organic Depressants . . . . . . . 8.2 Structure and Performance of LMW Organic Depressant . . . . . . 8.2.1 Comparison of Organic Acids in the Application of Depressing the Quartz Activated by Cu Ion . . . . . . . 8.2.2 Comparison of Organic Depressants in the Application of Depressing Fluorite and Barite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.3 Application of Group Electronegativity and HLB to the Discussion of Depressant Structure and Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.4 Summary for the Relation Between Depressant Structure and Performance . . . . . . . . . . . . . . . . . . . . . . . 8.3 Structure and Performance of HMW Organic Depressant . . . . . . 8.3.1 Classification and Characteristic of Macromolecular Organic Depressants . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Structure and Performance of Natural Starch . . . . . . . . . 8.3.3 Structure and Performance of Dextrine . . . . . . . . . . . . . 8.3.4 Structure and Performance of Other Modified Starchs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.5 Structure and Performance of Tannins . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
307
Structure and Performance of Flocculant . . . . . . . . . . . . . . . . . . . . . 9.1 Classification of Flocculants and Their Functions in Flotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.1 Functions of Flocculant . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.2 Classification and Characteristic of Macromolecular Organic Depressants . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Component and Performance of Inorganic Electrolyte Coagulant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Structure and Performance of Organic Flocculant . . . . . . . . . . . . 9.3.1 Effect of Polar Group on the Performance of Flocculant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.2 Effect of Molecular Weight and Hydrocarbon Chain Structure on the Performance of Flocculant . . . . . . . . . . 9.4 Flotation Application of Various flocculants . . . . . . . . . . . . . . . . 9.4.1 Demand for Molecular Weight and Dissociation Degree of Flocculant . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.2 Demand for Adsorption Rate of Flocculant and Necessary Agitation . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
337
307 307 308 313 314
316
319 322 323 323 325 327 330 332 336
337 337 339 340 344 344 349 351 351 352 355
xiv
Contents
10 Molecular Design of Reagents for Mineral Processing . . . . . . . . . . . 10.1 Energy Criterion for Reactivity of Reagents . . . . . . . . . . . . . . . . 10.2 Application of Energy Criterion to Discuss the Relationship of Polar Groups of Reagents and Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1 Relationship of Polar Groups of Flotation Reagents and Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.2 Relationship of Polar Groups of Humic Substances-Based Binder and Performance . . . . . . . . . . 10.3 Application of Energy Criterion to Discuss the Relationship of Nonpolar Groups of Reagents and Performance . . . . . . . . . . . 10.3.1 Relationship of Nonpolar Groups of Flotation Reagents and Performance . . . . . . . . . . . . . . . . . . . . . . . 10.3.2 Relationship of Nonpolar Groups of Humic Substances-Based Binder and Performance . . . . . . . . . .
357 357
361 361 365 373 373 379
Chapter 1
Introduction
1.1
Brief History of Research and Application of Flotation and Reagents
Flotation is one of the mineral processing methods according to the difference of surface hydrophobicity and hydrophilicity of minerals. Although part of ores can be beneficiated based on their natural hydrophobicity, most of them need the addition of various reagents into the ore pulp for selectively controlling the hydrophobicity and flotation behaviors of minerals and for achieving satisfactory separation results. Therefore, flotation reagents are important for the application and the development of flotation technology. The application of flotation technique and reagents in the mineral processing can date back to ancient times. The early flotation process was quite simple and was mainly film flotation based on natural hydrophilicity or flotability of minerals. Taking the beneficiation of talc and kaolin for example, there were four major steps such as washing, sinking, floating, and pouring. Those steps include not only gravity separation but film flotation. The record on this kind of processes can be found from the book “Heavenly Creations,” written by Ying-Hsing Sung, a famous scholar of Ming dynasty of China in sixteenth century. The book described the flotation process of cinnabar as follows: (1) Firstly, grinding the ore into fine powders in a large metal trough; (2) Secondly, soaking fine powders with clear water in a water tank; (3) Then for three days, the suspension called second-class cinnabar were poured from water tank to another one; (4) Finally, sedimented particles called top-class cinnabar were dried. Later on, people utilized flotation reagents alike with these used today, which may be unconscious in the beginning. There were numerous examples for the application of various reagents to mineral flotation. In the processing and purifying of painting pigments (covellite, cinnabar, and so on), for instance, animal glue was added to the ore suspension to improve the adhesivity. The protein, amino acid, and their polymers in animal glue can act as collector, depressant, and flocculant, and © Metallurgical Industry Press, Beijing and Springer Science+Business Media Singapore 2016 D. Wang, Flotation Reagents: Applied Surface Chemistry on Minerals Flotation and Energy Resources Beneficiation, DOI 10.1007/978-981-10-2030-8_1
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1
Introduction
therefore affect the process of “grinding, soaking, floating, and sinking.” For another instance, medicinal plants were often added into the minerals pulp and cooked together before elutriation in the processing and purifying of mineral medicinal substances (realgar, orpiment, talc, cinnabar, etc.). In the process, organic acids, organic bases, alcohols, and various oils coming from those plants could perform as flotation reagents. These examples were common occurrences in the “Compendium of Medica,” which was written by Shizhen Li in Ming Dynasty. The book recorded the flotation processing of ruddle and realgaras in detail. Since ancient times, a process called “scratching gold by goose feather” was used in the beneficiation of gold from placer gold. In the course of panning placer gold, the goose feather was dipped with plant oil for bonding fine gold particles. In fact, this was the special flotation with oils and fats as collectors. There was also description about the so-called oil agglomeration of fine particles in the book of “Heavenly Creations.” When golden foil ornaments were worn out and broken, they were scraped off and burned in the fire and the gold particles would be in ashes. Adding water and some drops of oil, the oil agglomerates with gold formed and fell in the bottom and were put to the metallurgical furnaces. This is probably the earliest description about selective agglomeration for fine gold particles. According to records, William Haynes in 1860s patented a process for separating sulfide and gangue minerals using oil and it was called bulk oil flotation. The modern froth flotation process was invented in the late 1900s [1, 2]. Froth flotation technology was used initially for treating lead–zinc ore and then expanded into the treatment of other nonferrous metal, rare metals, iron ore, and nonmetallic minerals. Statistics show that flotation accounts for the greatest share among currently used methods in mineral processing. And the share will increase in the future. In addition to the beneficiation of ores, flotation technology has been gradually adopted for treating various industrial wastes and applied in the areas of agriculture and light industry. The research and the application of flotation reagents continue to advance with the development of flotation technology. In briefly, the development of flotation reagents mainly includes three stages. The first stage is the period of oil reagents. In the beginning of flotation industrialization, various mineral oils and plant oils, such as coal tar and paper tar, were used as flotation reagents. These flotation reagents consist of hydrocarbon oils, fatty oils, and some organic matters. Because of being water-insoluble and weak interaction with minerals, those reagents were used in high dosage. Subsequently, people began to process oils to improve the properties of oil reagents. The early so-called processing oil means that coal tar oil is thermally treated with sulfur, acids, or alkali, or treated with carbon disulfide, or sulfur monochloride. Because of containing a given mass of water-soluble organic sulfides, phenolates, and pyridinium salts, the processed oil owns better flotation performance than the crude oil. For example, the sulfurated anthracene oil once used as the substitute for xanthate in China is a typical representative of processed oils. Then flotation scientists began to realize that the crude oil is not the excellent reagents. But the water-soluble “impurity” (organic compounds containing nitrogen or sulfur) usually performs
1.1 Brief History of Research and Application of Flotation and Reagents
3
excellent collecting property. That may be the earliest knowledge about the structure and performance of flotation reagents. The second stage is the period of artificial synthesis of water-soluble flotation reagents. The water-soluble frothers were firstly applied in 1909. Fatty acid soaps were used in the flotation of nonsulfide minerals in 1924. Xanthates were used as collector in 1925. Cyanide, acids, and alkali were utilized as regulators in succession from 1922 to 1929. These reagents are all artificial synthesis or modified products of natural products. Because of a higher proportion of water-soluble active ingredients, the utilization of these reagents has turned flotation into a process of low consumption, low cost, high efficiency, and wide application. Meantime, the theory of flotation reagents was much improved. The flotation reagents had been classified in accordance with their different roles. Various theories, hypotheses about flotation reagents were proposed to guide or improve flotation processes and search for new reagents. Among these theories and hypothesis, the solubility product hypothesis proposed by Taggart produced a great impact. As for searching for reagents, the hypothesis can be briefly described as follows: Reagents which can form low solubility product compound with mineral component, and at the same time possesses the structure characteristic of flotation reagent, may act as collectors and depressants. Although this hypothesis is imperfect, it is still used not only for the analysis of flotation phenomenon but also as one of criteria searching for new reagents. The third stage is characterized by further expansion of reagent variety and raw material source for production of new reagents. The development of mining industry and the requirement of science and technology for mineral raw materials make new demands on types and quantity of flotation reagents. Meantime, the development of petroleum industry provided various structural and cheap, wide raw materials for reagent development, resulting in diversification of flotation reagents. For example, xanthate, including n-alkanol ethyl xanthate, n-alkanol butyl xanthate, was extended to isopropyl xanthate, isobutyl xanthate, isoamyl xanthate, and so on. Lots of special-purpose and high efficiency reagents were developed and used in order to treat various rare metal ores, polymetallic ores, low grade and fine ores, and oxidized ores, which include all kinds of collectors, depressants, and high selectivity flocculants. Frothers are also gradually used from petroleum products, which in past were main terpene alcohols made from natural plants. It is worth mentioning that water-insoluble and high effective oily collectors were also developed in recent years. For example, these collectors involve thionocarbamates, xanthate esters, and dithiophosphates. And these reagents possess the characteristic of low dosage (1/5–1/10 dosage of xanthate) and high efficiency. The theory of flotation and reagent was improved much more in this period. Because of the application of various testing techniques and advancement of modern physical chemistry, surface chemistry, electrical chemistry, structural chemistry, and quantum chemistry, many flotation fundamentals associated with reagents were well elucidated. Recent years, the advances in the areas of material molecular design pave a way for development of new flotation reagents. The theory of molecular design may
4
1
Introduction
provide the scheme and quantitative basis for the manufacture of materials with specific performance in the fields of plastic and rubber polymer. Based on the research of quantitative structure–activity relationships (QSAR), drug design science has been built, and a series of problems have been resolved. Chinese scientists also have made great achievements in the basic theory of structural chemistry. These achievements include the studies of inductive effect and linear rules of chemical homolog, bond parameter function, electronegativity calculation, and molecular orbital approach, which provide inspiration and elements for the development of flotation theory. And the theory about the structure-performance and development of flotation reagents will catch up and satisfy the actual need.
1.2
Classification and Significance of Flotation Reagents
There are lots of flotation reagents in many companies. Meantime, applications, mechanisms, sources, and raw materials of reagents are diverse from each other. In order to find the general character and individuality among them, it is necessary to categorize reagents. Because of different perspectives, there are many classifications which are of great help for us to understand and use reagents [1–3].
1.2.1
Classification of Flotation Reagents According to Their Uses
For guiding the application of flotation reagents, the categories of flotation reagents according to their functions are listed in Table 1.1.
Table 1.1 Categories of flotation reagents according to their functions Reagent
Use
Example
(1) Collector
Sulfide mineral collector Oxide mineral collector Nonpolar mineral collector General frother Frother with collecting capability Activator Depressant pH regulator Flocculant and dispersant
Xanthate, aerofloat, and dixanthogen Fatty acids, fatty amines Nonpolar oils Terpenol, alcohols Heavy pyridine, fatty acids
(2) Frother
(3) Regulator
Metal ion salts, inorganic acids, and alkali organic and inorganic chemicals Inorganic acids, alkali Inorganic acids, alkali, salts, and polymers
1.2 Classification and Significance of Flotation Reagents
1.2.2
5
Classification of Flotation Reagents According to Their Roles
The categories of flotation reagents according to their roles are listed in Table 1.2. The categories can illustrate the basic behavior of flotation reagents in the flotation process.
1.2.3
Classification of Flotation Reagents According to Their Structures
The categories of flotation reagents according to their structures are listed in Table 1.3. This classification shows the relationship between structure and performance of flotation reagents.
1.2.4
Classification of Flotation Reagents According to Their Chemical Constituents
The categories of flotation reagents according to their chemical constituents are listed in Table 1.4. This classification shows the manufacturing processes and raw material characteristics of reagents. Table 1.2 Categories of flotation reagents according to their roles Reacting interphase
Role of reagent
Example
(1) On mineral surface
Changing the surface property of mineral
Collector, frother
(2) Gas–water interface (3) Liquid phase
Increasing mineral hydrophobicity and adhesion to air bubble Changing the adsorption capability of collector Changing the assembling Making particles grow state of mineral particles larger Preventing agglomeration of particles Changing the surface tension of pulp solution and adjusting froth Reacting with ions in Controlling the pulp to control the composition of solution composition of solution and pH
Activator, depressant Flocculant, collector Dispersant
Frother Collector, regulator, and depressant
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1
Introduction
Table 1.3 Categories of flotation reagents according to their structure Category of reagents
Structural characters
Uses
(1) Nonpolar reagents (2) Polar reagents
Nonpolar cyclane armotic and fatty hydrocarbon
Synergetic collector, solvent Depressant, activator, and pH regulator Collector, frother, and depressant Activator, collector Collector Collector, frother Collector, depressant
Anionic reagents
Cationic reagents Amphoteric reagents Nonionic reagents
(3) Polymer compound
Anionic reagents Cationic reagents Amphoteric reagents
Inorganic salts, acids, and alkali Organic acids and their salts containing O, S, N, P, As, etc. Soluble salts containing metal ions Amines and their salts Pyridines and their salts Amino acids Others Alcohols, ethers, aldehydes, and ketones Esters containing S, N, P, As, Cl, and Br Other organics Every polymers and natural compounds
Frother Collector Collector, depressant, and frother Flocculant, collector, and depressant
Table 1.4 Categories of flotation reagents according to their chemical constituents Reagents
Chemical constituents
Application
(1) Inorganics
Acids Alkalis Salts Organic acids and their salts, esters
Depressant, activator, and pH regulator
(2) Organics
Carbonic acids and their derivatives Carboxylic acids and their derivatives
Thiocarbonates Thiocarbonate esters Fatty acids
Substituted acids Amino acids Thiocarbamic acids
Collector
Collector, depressant, and frother Collector, depressant
(continued)
1.2 Classification and Significance of Flotation Reagents
7
Table 1.4 (continued) Reagents
Chemical constituents Sulfonates, sulfate
Other organic acids and salts
Organic alkalis and their salts
Other organics
(3) Polymer compound
Natural polymer compounds Synthetic macromolecular compounds
Amines and their salts
Pyridines and quinolines Alkaloids Alcohol, ethers, and ester and alkalean Starches Celluloses Gums Polymer Condensation compound Mixed-type compound
1.2.5
Application Alkyl sulfonates Alkyl sulfates Sulfamates Sulfonated fatty acids Alkyl arsonic acids Alkyl phosphoric acids and phosphates Thiophosphates Hydroximic acid and salts Primary amine, secondary amine Quaternary amine Aniline, naphthylamine Derivatives with side chains
Collector, frother Collector
Collector
Collector
Frother, solvent Collector, frother Depressant Collector, frother, and solvent Depressant, flocculant
Polyacrylamide, etc. Urea– formaldehyde resins, etc. Polyacrylonitrile, etc.
Depressant, flocculant
Classification of Flotation Reagents According to Characteristics of Coordination Chemistry
This classification can enable us to study the reagents in terms of coordination chemistry. The categories of flotation reagents according to chemical characteristics of their complex compounds are listed in Table 1.5.
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1
Introduction
Table 1.5 Categories of flotation reagents according to chemical characteristics | of their complex compound Category
Structure characteristics
Uses
(1) Complex
Monocomplex
Aliphatic amines
Collector
Amines
Depressant, activator
Cyanides Multicomplex
Depressant
The bonding atom is SS
Four-membered ring
The bonding atom is SN
Four-membered ring
Xanthates
Collector
Aerofloats Rhodanides Diphenyl-thiourea
Collector, depressant
Thiocarbamate
Collector
Five-membered ring Five-membered ring
o-aminobenzenethiol
Collector
Thiosalicylic acid
Collector
Four-membered ring
Fatty acid soaps
Collector
Five-membered ring
Hydroximic acids
Multimembered ring
Tannins
Depressant
The bonding atom is NN
Five-membered ring
Nickel reagents
Collector
Multimembered ring
Polyamidoamine
Flocculant
The bonding atom is NO
Four-membered ring
Hydroximic acids
Collector
Five-membered ring
8-oxyquinoline
The bonding atom is SO The bonding atom is OO
Polyacid ion
Dichromates, phosphates, and silicates
Depressant
p-complex
Alkenes, acetylides
Flocculant
(2) Noncomplex
References 1. A.M. Gaudin, Flotation 2nd edn. (McGraw-Hill Book Company, Inc., New York Toronto London, 1957), pp. 232, 182, 285 2. K.L. Sutherland, I.W. Wark, Principles of Flotation (Australian institude of mining and metallurgy (INC), Melbourne, 1955), pp. 84, 98, 278, 302, 319 3. K. Yamasaki, dorff Nanjou: Min. Soc. Japan 10, 644 (1970)
Chapter 2
Interaction Between Minerals and Reagents
As well known, mechanisms of reagents in the flotation process are very complicated. Much progress on interaction between collectors and mineral surface has been made using modern testing methods. However, there are still many problems to be solved. There have been many books and papers related to the mechanism of flotation reagents. Considering that the interaction mechanism of flotation reagents is not the key content of this book and also it is difficult to clearly illustrate the subject in one chapter, this chapter just briefly introduces a few significant theories and the related research results to this book. And collector is mainly concerned with this chapter. Other reagents will be introduced in the following chapters.
2.1 2.1.1
Various Theories on Interaction Between Collectors and Minerals Main Interactions Between Collector and Mineral
Main interactions between collector and mineral include [1, 2]: (1) Physical adsorption The adsorption heat or energy (0.01–0.1 eV/mol) of physical adsorption is very low. The distance between adsorption molecules and mineral surface is large. Meantime, the adsorption forces include van der Waals force and electrostatic force. There are not shared electrons or electron transfer between reagent and mineral. It is not selective adsorption and is easy to desorption. Usually, the adsorption capability decreases with increasing temperature.
© Metallurgical Industry Press, Beijing and Springer Science+Business Media Singapore 2016 D. Wang, Flotation Reagents: Applied Surface Chemistry on Minerals Flotation and Energy Resources Beneficiation, DOI 10.1007/978-981-10-2030-8_2
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2 Interaction Between Minerals and Reagents
(2) Chemical adsorption The adsorption heat or energy (1 eV/mol) is high. The distance between adsorption molecules and mineral surface is small. Meantime, the adsorption force is essentially the chemical force. The adsorption between reagent and mineral involves bonding force of electrons. It is selective adsorption and is hard to desorption. Adsorption capability increases with increasing temperature. (3) Surface chemical reaction The further development of chemical adsorption often leads to chemical reaction on the mineral surface. The difference between surface chemical reaction and chemical adsorption lies in the production of new independent phase of product on the mineral surface of the former.
2.1.2
Adsorption Models of Collector on Mineral
The main adsorption models of collector on mineral are as follows: (1) Physical adsorption of nonpolar molecule It refers to the adsorption of various nonpolar hydrocarbon oils onto mineral. The adsorption force is dipolar force or London force. According to research results, the adsorption of nonpolar oil occurs at the three-phase wetting interface when the bubble adheres to mineral surface. (2) Adsorption theory of electric double layer If the mineral surface is charged, then there must be a corresponding excess of oppositely charged ions (counterions) to maintain electrical neutrality. The combined system of surface charge and the excess charge is known as the electrical double layer and its inside is called interlayer and the outside is expand layer. A fundamental concept in electric double layer is that there is a plane of shear (stern layer), which separates the fixed and mobile charge. The electric potential at the plane of shear is universally known as the zeta potential and given the symbol f. The adsorption of collector and other ions is able to change the zeta potential with the help of electrostatic force. When the concentration value of collector is low, the adsorption of collector occurs in form of ions. When the concentration value of collector is high, the adsorption of collector occurs in form of semi-micelle and ion– molecule reaction [3–5]. If collector ions are able to enter into the inner of stern layer (IHP), superfluous compensating ions in the solution can make the charge reverse. Specific adsorption forms at the interface of mineral and reagent under such circumstances. And specific adsorption is a very important method for destabilization of charged mineral particles. A conceptual picture of the collector adsorption onto mineral surface is shown in Fig. 2.1.
2.1 Various Theories on Interaction Between Collectors and Minerals
(a)
(b)
(c)
Mineral
Mineral
11
Mineral
Fig. 2.1 A conceptual picture of sodium laurate adsorption onto hematite. a dilute solution, single-ion adsorption; b concentrate solution, semi-micelle adsorption; c ion–molecule coadsorption
(3) Exchange adsorption of isonym ions The experimental results of Gaudin (MIT) revealed that the concentration of sulfur-bearing ion increase with decrease of anion concentration of residual xanthate in the solution system of xanthate and sulfide mineral. Based on the results as above, the model of exchange adsorption is given by the following [6]: Cu2 S
A
þ X ! Cu2 S
X
þ A
ð2:1Þ
where X− refers to the xanthate anion, A− refers to the anionic from mineral. Wark and Cox also proposed another model, which is similar to Eq. 2.1. The model becomes following [7]: Mþ
Mþ
MN N þ X ! MN X þ N
ð2:2Þ
where X− refers to the xanthate anion; M+ refers to the cation, and N− refers to the anion from mineral. According to their results, collector’s effective style is its ions and occur competitive adsorption with OH− in water on mineral surface. For studying the critical condition of flotation occurring, Wark et al. (Melbourne University) reported that the collector concentration and the solution pH of sulfide mineral showed a relationship. Taking the adsorption of potassium ethyl xanthate onto galena, for example, the relationship between reagent concentration and solution pH is presented by the following:
12
2 Interaction Between Minerals and Reagents
Concentration of KEX (mg/L) pH C [H+]
625
500
100
25
5
12.5 1.3 10−15
11.9 4.2 10−15
11.4 2.7 10−15
10.4 6.7 10−15
9.1 2.7 10−14
where C [H+] is the product value of two factors (reagent concentration C and solution H+). From above results, Barsky found that the product value of reagent concentration and solution pH is a constant value under the flotation critical condition. The results are explained by people in favor of ionic theory as follows. The dissociation constant of xanthic acid is Ka = 10−5–10−3; the ion concentration is approximately equal to the reagent concentration in alkali solution, that is, [X−] = C, and [X−] [H+] = constant. Under alkaline conditions, [H+][OH−] = 10−14, the following equation can be drawn based on these relations: ½X ¼K ½OH
ð2:3Þ
The Eq. (2.3) is called Barsky relation—the famous concept in flotation research history. To the adsorption of potassium ethyl xanthate on galena, Ka = 10−1–1 is the quantitative relation of competitive adsorption between OH− and collector anion. It can be concluded that xanthic acid ion is an effective fraction of reagent. In fact, [OH−] is not in direct ratio to [X−]. The actual relation between [OH−] and [X−] is as follows: ½X ¼ K ½OH y This problem will be discussed further in Chap. 7. (4) Molecular adsorption Cook et al. (University of Utah) gave another explanation about the adsorption of potassium ethyl xanthate with galena [8]. Although the adsorption of negative xanthate ion is decreased owing to the resistance of negatively charged sulfide mineral, there is no resistance of the adsorption of xanthate molecule by hydrolysis on the mineral surface. For xanthate, the dissociation equation is as follows: Ka ¼
½H þ ðC ½HXÞ ½HX
Ka is far greater than [H+] in alkaline solution. Therefore, it can be drawn by the following:
2.1 Various Theories on Interaction Between Collectors and Minerals
½HX ¼
13
½H þ C Ka
where Ka is the dissociation constant of xanthic acid; C is the reagent concentration. Thus, it can be seen that [HX] is also a constant on the basis of C [H+] reported by Wark et al. This is an excellent proof that that xanthate molecule is the effective fraction of reagent. Thus, Barsky relation expression can be given by the following: ð1 hÞ þ ½HX ¼ h Therefore, 1 h ¼K ½HX 1 h
ð2:4Þ
where h is the proportion of collector coverage on mineral surface. Although the theories of ion adsorption and molecular adsorption are on the basis of the same experimental results, there also is contradiction between them for some time. For enhancing the interactions of xanthate and mineral, ore pulp pH should be increased in order to [X−] increasing according to ion adsorption theory. The pH of ore pulp should be decreased in order to increase [HX] according to molecular adsorption theory. However, the competitive adsorption of OH− increases with increase of solution pH. And it is not conducive to the adsorption of X−. The decomposing rate of xanthate increases with decrease of solution pH. And it is also not good for the selectivity of collector toward different minerals. However, it is worth mentioning that, the calculated experimental data about the ion adsorption and the molecular adsorption agree with each other in a particular alkaline solution. We shall not go into details here. The details will be discussed further in Chap. 7. (5) Chemical adsorption The interaction between collector and mineral involves electron transfer, that is, chemical adsorption. Taggart (Columbia University) proposed the solubility product theory, which is used to explain the behavior of chemical adsorption and flotation. But there is distinction between flotation process and chemical reaction in solution. The distinctions are as follows: (1) Mineral flotation takes place at solid– liquid interface; (2) The concentration ratio of collector to metal ion is over that of chemical reaction in solution. Someone, however, insist that the data of solubility product does not conform to actual condition. For instance, the solubility product of lead xanthate is bigger than that of lead sulfide. But chemical adsorption of xanthate still occurs on the surface of galena. Someone, thus, proposes that the solubility product value of surface reaction may be smaller than that of solution reaction.
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2 Interaction Between Minerals and Reagents
In addition, the mineral is not pure one in the flotation processing. For example, after surface oxidation, the surface of galena is not component of PbS. But the calculation of the solubility product of reaction is still adopted at present. The reason is that it is helpful to explain the role of flotation reagent in many cases. Taking the adsorption of galena and xanthate, for example, the process of dissociation of lead xanthate formed on the surface of galena can be given as follows: K1 ¼ Pb2 þ ðX Þ ¼ LPbX2
PbX2 , Pb2 þ þ 2X ;
ð2:40 Þ
And then the adsorption reaction of Pb2+ with OH− becomes following: 1 K2 ¼ 2 þ ¼ 1=LPbðOHÞ2 ½OH 2 Pb
Pb2 þ þ 2OH , PbðOHÞ2 ;
From above two-step reactions, it can be given as follows: PbX2 þ 2OH , PbðOHÞ2 þ 2X The equilibrium constant of reaction is as follows [9] (L refers to solubility product): K 0 ¼ K1 K2 ¼
½X 2 2
½OH
¼
LPbX2 LPbðOHÞ2
or K¼
pffiffiffiffiffi ½X K0 ¼ ½OH
where LPbðOHÞ2 ¼ 4:2 1015 ; For isopropyl xanthate, LPbX2 ¼ 1:58 1018 , Kisopropyl ¼ 1:9 102 ; For ethyl xanthate, LPbX2 ¼ 1:7 1017 , Kethyl ¼ 1:2 101 . For the adsorption of galena and xanthate, meantime, the reaction process and K 00 were expressed in another way by Kakovski. The new expression for reaction and K 00 become the following: PbðOHÞ2 þ 2X , PbX2 þ 2OH ½OH ¼ 10 K 00 ¼ ½X
2.1 Various Theories on Interaction Between Collectors and Minerals
15
It suggests that the value of [X−]/[OH−] is 10−1. By comparing this value with that calculated value of Barsky (C [H+] = 10−15, and [H+]/[OH−] = 10−14), while, it can be found that the value of [X−]/[OH−] acquired by both of them is same with each other. To sum up, although those theories analyze the results from different aspects, they can reflect the actual conditions of flotation process and reagent to some extent. In most cases, the interaction between coordination collector and mineral involves chemical adsorption [8]. Taking the flotation of chrysocollite with salts of hydroximic acid, for example, the interaction is attributed to chemical adsorption. In fact, coordination chemistry theory is the application and development of solubility product theory. Based on this theory, dissociation constant of complex Ka is closely related to its stability. The stability of coordination increases with decrease of Ka. Therefore, Ka may serve as a criterion for chemical adsorption and chemical reactivity of flotation reagent. (6) Adsorption of reaction product The interaction between mineral and reagent is not as simple as it seems. There is a series of complicated reactions in the flotation process. Mineral reacts with not only air (or oxygen) but also with impurities in pulp. And it leads to changes of the surface properties. There are side reactions occurring such as oxidation-reduction reaction, catalystic reaction, and some other special reactions. Among these side reactions, reaction product adsorption influences the flotation performance remarkably. Lots of reaction products of xanthate with sulfide mineral are studied [10–13]. Research shows that the adsorption products of xanthate with sulfide surface include usually dixanthogen (X2) and its existent, and quantity is relationship with mineral flotation. The interpretations of this relation are varied. One of those interpretations is based on the scanning potential study by R. Woods. The electrode reaction of xanthate occurs on the surface of sulfide mineral and the xanthate is further oxidized to dixanthogen. The expression for electrode reaction of xanthate is given by the following: 2ROCSS þ 1=2 O2 þ 2H þ ! ðROCSSÞ2 þ H2 O The anodic oxidation reaction is as follows: 2ROCSS ! ðROCSSÞ2 þ 2e The cathodic reduction reaction is as follows: 1= O2 þ 2H þ þ 2e ! H2 O 2
16
2 Interaction Between Minerals and Reagents
Sulfide mineral acted as a catalyst of these reactions. The anodic oxidation reaction and the cathodic reduction reaction can be expressed as follows: PbS þ 2ROCSS ! PbðROCSSÞ2 þ S þ 2e R. Woods reports that, under the condition of the concentration of potassium ethyl xanthate 6.25 10−4 and solution pH 7, the reversible potential of dixanthogen in which xanthate is oxidized to dixanthogen is 0.13 V. The rest potentials of various minerals such as pyrite, chalcopyrite, covellite, bornite, and galena are 0.22, 0.14, 0.05, 0.06, and 0.06 V, respectively. It is reported that dixanthogen product can improve the flotation performance of mineral. For example, under the condition of low pH, electrode oxidation of xanthate starts first, and the oxidation of mineral itself is followed. Under the condition of high pH, electrode oxidation of xanthate does not occur. The flotation tests show that the flotability of mineral is good at low pH but bad at high pH. Another interpretation is that the adsorption of dixanthogen to mineral can improve the flotation performance of mineral on condition that xanthate ion is preferentially oxidized to dixanthogen. The reaction process can be given by the following: 1 O2 þ H2 O ! X2 þ 2OH 2 jPbS þ X2 !jPbS surface compound 2X þ
Someone proposes that the reaction of dixanthogen with mineral can also be given by the following: PbS þ X2 ! PbX2 þ S It is experimentally reported that the reaction product of xanthate with sulfide exists of dixanthogen and it is the main adsorption product especially on the surface of chalcopyrite, covellite, pyrite, and so on. (7) Surface chemical reaction The chemical adsorption of reagent on mineral surface should result in surface chemical reaction. Through testing the reaction product of xanthate with sulfide, it can be found that the crystals of metal salts xanthate are found on the surface of mineral. Taking the reaction product of fatty acid with oxidized ore, for example, it can be found that metal salt of fatty acid can be dissolved in some solvents. There are some differences among chemical adsorption, surface chemical reaction, and solution chemical reaction. Taking the adsorption of dithiophosphate on copper mineral, for example, the differences can be given by the following [14]:
2.1 Various Theories on Interaction Between Collectors and Minerals
17
Chemical adsorption Cu DTP
Cu
Cu DTP
Cu
Surface chemical reaction Cu
DTP
Precipitate in solution
The effect of the occurrence of surface chemical reaction on flotation behavior has been unknown now. Someone insist that surface chemical reaction is bad for flotation because the surface chemical reaction does not lead to nonpolar group of reagent in hydrophobic-oriented arrangement. However, someone insist that the product of surface chemical reaction is necessary for flotation. For instance, the presence of dixanthogen is good for flotation. From above results, it can be seen that those theories and hypothesis are proposed from different conditions (minerals, reagents, and reaction environments), research methods, and reaction stages. In fact, there may be some relation among those reactions in flotation. The practical results also indicate that collector exists in the form of free molecule, ion, and the reaction product on the surface of mineral. According to Dewey, after a longtime reaction of chalcocite with high concentrate potassium amyl xanthate, the reaction products dissolved in methanal, acetone, and ether extract are given by the following: Cu2 ½SSCOC5 H11 2 ; Cu2 S Cu2 ½SSCOC5 H11 2 ; ½SSCOC5 H11 2 Therefore, the reactions may be given by the following: Exchange adsorption:
½Cu2 SA þ X ! ½Cu2 SX þ A
18
2 Interaction Between Minerals and Reagents
Surface oxidation of chalcocite: xCu2 S yCuS þ
1 O2 þ H2 O ! ðx 2ÞCu2 S ðy þ 2ÞCuS þ 2Cu2 þ þ 2OH 2
Reaction of copper ion with xanthate ion: 2Cu2 þ þ 2X ! Cu2 X2 # 2Cu2 þ þ 4X ! Cu2 X2 # þ X2 Reaction of chalcocite with dixanthogen: 2Cu2 S þ X2 ! 2CuS þ Cu2 X2
2.2
Adsorption Equation of Flotation Reagent on Mineral Surface
The adsorption process of reagent on mineral surface can be described by various adsorption equations in surface chemistry. At first, some typical adsorption isotherm models and adsorption kinetics equations are introduced in this section. Subsequently, the adsorption equations of flotation reagent on mineral surface are derived.
2.2.1
Adsorption Isotherm Model
(1) Langmuir model It has been found that the monolayer adsorption of gas molecules on solid surface can be expressed by Langmuir equation. The following gives a rough deduce for Langmuir adsorption of flotation reagent on mineral surface: jM þ A , jMA where M is mineral surface; A is reagent; MA is adsorption product; CA is the reagent concentrate; CM is the proportion of residual active site in which mineral surface is not covered by reagent; CMA is the proportion of active site in which mineral surface is covered by reagent. When the adsorption reaches to reaction equilibrium, the equilibrium constant (K) is given by the following:
2.2 Adsorption Equation of Flotation Reagent on Mineral Surface
K¼
19
CMA CM CA
It is obvious that the value of CMA is same as that of adsorption amount (C). Because of CM + CMA = 1, a modified equation is as follows: C¼
KCA 1 þ KCA
ð2:5Þ
The equation above can be further modified, and Langmuir equation is as follows: C b 1 ¼ Cþ C a a
ð2:50 Þ
Langmuir equation shows that it is a linear relation between C/C and C. (2) Freundlich model Freundlich equation, as an empirical model, is base on the multilayer adsorption of reagent. The following gives a rough deduce for Freundlich adsorption of flotation reagent on mineral surface: jM þ nA , jMAn KCAn C¼ 1 þ KCAn When the values of K and CAn both are small, the equation above can be further modified, and Freundlich equation is as follows: C ¼ KCAn
ð2:6Þ
log C ¼ a þ n log C
ð2:60 Þ
Freundlich equation indicates that it is a linear relation between Log C and log C. Under the condition of mineral reacting with two or more reagents, the rough deduce process is given by the following: jM þ nA , jMAn ; jM þ mB , jMBm CMA ¼ KA CAn CM ; CMB ¼ KB CAm CM That is: CA Cn ¼ K mA CB CB
ð2:7Þ
20
2 Interaction Between Minerals and Reagents
As shown in Eq. 2.7, there exists competitive adsorption between reagent A and reagent B on mineral. If one of the adsorption amounts of reagents keeps unchanged and n = m, Eq. 2.7 can be given as follows: log C ¼ a þ b log
CA CB
ð2:70 Þ
(3) Temkin model Temkin equation applies to the situation that the reagent adsorption changes with surface coverage. With increase of adsorption density, the interaction of adsorbing particulate gradually diminishes. The relationship between adsorption energy and adsorption amount is as follows: DE ¼ að1 bCÞ where a and b refer to constants, respectively. When the adsorption reaches to reaction equilibrium, the adsorption and the desorption processes are given by the following: KA CM CA ¼ KB CMA e
að1bCMA Þ RT
að1bCMA Þ RT
CMA e CA ¼ K CM
When the value of CMA is close to CA, that is, coverage is 0.5. The expression of CA is given by the following: a
CA ¼ eRT e
abCMA RT
K
The equation above can be further modified, and Temkin equation is as follows: C ¼ a þ b log C
ð2:8Þ
1 RT RT ln K; and b is equivalent to . b ab ab It can be found that it is a linear relation between C and Log C. Under the condition of mineral reacting with two reagents, Temkin equation can be given by the following: where a is equivalent to
C ¼ a þ b log
CA CB
ð2:80 Þ
2.2 Adsorption Equation of Flotation Reagent on Mineral Surface
2.2.2
21
Adsorption Isotherm of Flotation Reagent on Mineral Surface
As mentioned before, the interactions of flotation reagent with mineral include physical adsorption by van der Waals force, electric double layer adsorption, chemical adsorption, and surface chemical reaction. There have been lots of reports on the experimental data and mathematical relations of interactions. Adopting various adsorption isotherm models, the analysis on main interactions between reagent and mineral are given by the following: (1) Monolayer physical adsorption The process of various reagents adsorption on the mineral surface can be adequately described with monolayer Langmuir equation, under the condition of low concentration of reagent. Under the condition of high concentration of reagent, however, Langmuir equation is not adaptable for describing the adsorption process. The reason lies in that multilayer adsorption and chemical adsorption are hard to occur under the condition of low concentration of reagent. Usually, the adsorption of flocculant with mineral is in conformity with Langmuir equation. (2) Electric double layer adsorption Electric double layer adsorption includes the adsorption of counterions in diffusion layer, the adsorption of surface-active ion and electrolyte in stern layer, and specific ion adsorption. 1. Adsorption of counterions in diffusion layer Counterions is called inactive (indifferent) electrolyte. The monolayer coverage decides the maximum adsorption density of counterions. The most famous equation in electric double layer theory, Gouy-Chapman Equation, is given as follows: 0
C ¼ kC 1=2 ek f1
ð2:9Þ
where k and k0 refers to a constant, respectively; C is the concentration of counterions; f is the zeta potential of mineral surface. Equation 2.9 is same with Freundlich equation (Eq. 2.6) in form. It indicates the adsorption of counterions in diffusion layer is a multilayer adsorption process. It is in accordance with the desorption theory of electric double layer. The thickness of the diffusion layer is larger than the diameter of monolayer ions. 2. Adsorption of surface-active ion and electrolyte in stern layer The adsorption of surface-active ion and electrolyte in stern layer can be described with Stern-Grahame Equation, which is important for explaining the adsorption process.
22
2 Interaction Between Minerals and Reagents
Firstly, we assume that the chemical potentials of reagent and mineral surface are, respectively, li and lsi . The values of li and lsi can be obtained by the following: li ¼ loi þ RT ln ai s lsi ¼ loi þ RT ln asi where loi and ai are, respectively, the standard chemical potential and the activity of s and asi are, respectively, the standard chemical reagent of the solution; loi potential and the activity of mineral surface; R is the gas constant (J (mol T)−1); T is the absolute temperature. When the adsorption reaches to reaction equilibrium (that is, li ¼ lsi ), the equation above is given by the following: s ls loi asi ¼ exp i ai RT If the value of ai is same as that of solution concentration (C), the adsorption standard free energy DGoads (J/mol) can be obtained by the following: s DGoads ¼ loi loi Cd ¼ 2rCeDGads =RT o
ð2:10Þ
DGoads ¼ DGoelec þ DGoChem þ DGoCH2 þ DGCH2 where Cd is the adsorption density in stern layer (mol/cm−2); r is the effective diameter of the adsorbed ion (cm); asi ¼ Cd =2r; DGoelec (J/mol) is the free energy of electrostatic adsorption; DGoChem (J/mol) is the free energy of chemical adsorption; DGoCH2 (J/mol) is the free energy of hydrocarbon chain association in nonpolar group; DGCH2 (J/mol) is the free energy of association between nonpolar group and mineral. When the adsorption is actuated by the electrostatic force, the standard adsorption free energy DGoads (J/mol) can be obtained by the following: DGoads ¼ DGoelec ¼ vFwd where m is the valence of the adsorbed ion; F is the faraday constant; Wd is the surface potential of a certain distance (d) from mineral surface. For the n-alkyl, the free energy DGoCH2 (J/mol) can be obtained by the following: DGoCH2 ¼ nU
2.2 Adsorption Equation of Flotation Reagent on Mineral Surface
23
where n is the number of –CH2–; U is the free energy of each –CH2– (2.50– 4.184 kJ/mol). DGochem means the chemical bond energy of reagent and mineral. In general, the value of DGochem is about several tens kJ/mol. It was reported that the adsorption heat of hexyl mercaptan on the ZnO or ZnSiO4 surface is 42 kJ/mol; the adsorption heat of ethyl xanthate on the PbS surface is 83 kJ/mol; the adsorption heat of Cu2+ on the ZnS surface is 63 kJ/mol. Specific adsorption includes the chemical adsorption and molecular chain association adsorption except the electrostatic adsorption. The free energy of specific adsorption DGospec (J/mol), hence, can be given by the following: DGospec ¼ DGochem þ DGoCH2 From those equations above, it can be found that Eq. (2.10) is similar to Eq. (2.6). Both equations belong to the type of Freundlich model. If the adsorption is confined to the reaction between mineral and indifferent electrolyte, DGospec only includes DGoelec . If the adsorption is extended to the reaction between mineral and active reagent, DGospec includes DGoelec and DGochem . But DGochem and DGoCH2 are seldom displayed under the condition of low reagent concentration. Taking the adsorption of sodium dodecylsulphonate on alumina, for example, the adsorption isotherm can be divided into three regions. In the first region (reagent concentration < 10−5 mol), the collector just act as counterion, and DGoads ¼ DGoelec . In the second region (10−5 < reagent concentration < 3 10−4 mol), the absorption amount increases remarkably as increasing collector concentration; the hydrocarbon chain association reaction occurs, that is, DGoads ¼ DGoelec þ DGoCH2 ; the free energy of each –CH2– (U) is 2.51 kJ/mol. When the reagent concentration (C) is 5 10−5 mol and the monolayer coverage is 1/10, the semi-micelle adsorption takes place. In the third region (reagent concentration > 310−4 mol), the abundant absorption of the collector anion makes the zeta potential of mineral reverse (from positive potential to negative potential); the free energy of each –CH2– (U) is 2.929 kJ/mol; the electrostatic force becomes a repulsion force of antiadsorption at this case. According to the testing of de Bruyn, the adsorption equation of lauryl amine hydrochloride on quartz can be presented by the following: C ¼ 8:1 109 C1=2 , when 10−7 < reagent concentration (C) < 2 10−4 mol or C ¼ 2:2 106 C 1:16 , when reagent concentration (C) > 2 10−4 mol The lauryl amine ion absorbs on the quartz in the form of semi-micelle. Although the exponents of two equations vary, the adsorptions of reagents both in diffusion layer and stern layer are in line with the Freundlich model. 3. Adsorption of potential-determining ion in stern layer The special role of the crystal lattice ions is recognized by referring to them as the potential-determining ions in electric double layer theory. Based on actual
24
2 Interaction Between Minerals and Reagents
results, the half-logarithm equation of the adsorption of potential-determining ion in stern layer is given by the following: C ¼ a b ln C It shows the adsorption of potential-determining ion in stern layer is in accordance with the Temkin model (Eq. 2.8). That is, the adsorption of potential-determining ions in stern layer affects the electrical properties of mineral surface. (3) Chemical adsorption Xanthate collectors adsorb on the surface of sulfide ore mainly via multilayer chemical adsorption. The adsorption equation of these reagents, thus, is in line with the Freundlich model in most circumstances. For instance, the exponent (n) of Freundlich equation of xanthate adsorbing on sphalerite in the solution of potassium ethyl xanthate is 0.203 (from M Tokorozawa Liming). According to the report by Mukai, the Freundlich equation of xanthate adsorbing on sulfide ore is given by the following: C ¼ a½X 1=n For MoS2 : a ¼ 4:96 105 ; 1=n ¼ 0:28; HgS: a ¼ 2:12 105 ; 1=n ¼ 0:32; PbS: a ¼ 5:24 105 ; 1=n ¼ 0:33; FeS2 : a ¼ 2:58 106 ; 1=n ¼ 0:38; Sb2 S3 : a ¼ 3:98 105 ; 1=n ¼ 0:45; According to de Bruyn’s results, the Freundlich equation of hexyl mercaptan adsorbing on gold ore is given by the following: C ¼ 1:68 106 C 0:52 According to study results from Plaksin, the Freundlich equation of tridecylamine adsorbing on oxidized ore is given by the following: C ¼ kC1=n where 1/n, hubnerite: 0.51; wolframite: 0.58; quartz: 0.47; fluorite: 0.60; spar: 1.07. The adsorption of tridecylamine on the inactive quartz, fluorite, and calcite may belong to multilayer physical adsorption. The adsorption of tridecylamine on the wolframite may belong to chemical adsorption. In the course of studying the flotation of wolframite with 8-hydroxyquinoline as collector, the adsorption isotherm was obtained and shown in Fig. 2.2 [15]. By comparing with five types of adsorption isotherms in surface chemistry, the
2.2 Adsorption Equation of Flotation Reagent on Mineral Surface
25
Fig. 2.2 Adsorption isotherm of 8-hydroxyquinoline on wolframite
adsorption isotherm of 8-hydroxyquinoline on the wolframite is similar to type II. It indicates that there is no obvious point of saturated adsorption. But the point B is equivalent to point of saturated monolayer adsorption. By data processing using those adsorption isotherm equations, the adsorption of 8-hydroxyquinoline on the wolframite is in accordance with Freundlich and BET equations rather than Langmuir equation. And Fig. 2.3 shows that the adsorption isotherm accords with Freundlich equation much more. The results indicate that the adsorption of collector on the mineral is mainly multilayer adsorption of uneven distribution. Based on the analysis of adsorbate components, the adsorption includes physical and chemical adsorption. Under the condition of pH 8.5, they are almost competitive equally. But the chemical adsorption plays a decisive role in improving the mineral flotation. (4) Competitive adsorption of two reagents Based on experimental results, when competitive adsorption occurs between collector and depressant, the adsorption of reagent on the mineral is in accordance with Freundlich equation. Considering the effect of the concentrations of collector and depressant on the adsorption amount of collector, the adsorption of collector on mineral is given by the following: log C ¼ a þ b log
½ A ½D
where C is the adsorption amount of collector; [A] is concentration of collector; [D] is the concentration of depressant. If the concentration of collector is fixed, the following equation can be obtained: log C ¼ a b log½D
26
2 Interaction Between Minerals and Reagents
Fig. 2.3 Adsorption isotherms of 8-hydroxyquinoline on wolframite. a Freundlich isotherm, b BET isotherm
And if [D] is [H+] or [OH−], therefore log C ¼ a bpH According to the experimental determination by Mitrofanov, the half-logarithm equation of competitive adsorption is expressed as follows: C ¼ a þ b log
½ A ½D
According to the discussions above, the competitive adsorption occurs between collector and depressant is in accordance with Temkin model.
2.2 Adsorption Equation of Flotation Reagent on Mineral Surface
27
(5) Surface chemical reaction If the surface chemical reaction belongs to double decomposition reaction, the equilibrium constant can be calculated by the following equation: K¼
La1 C1c ¼ Lb2 C2d
where K is the equilibrium constant; C1 and C2 are the reagent concentrations; L1 and L2 are the solubility products; a, b, c, and d are the reaction constants. This equation is in accordance with the equation of solubility product theory (2.4′).
2.2.3
Adsorption Kinetics Equation of Flotation Reagent on Mineral Surface
The adsorption amount of reagent varies with time. And the adsorption kinetics equation, usually, can be expressed by the following form: C ¼ at1=n where t is the adsorption time; a and n are constants. For example, 1/n is 0.1–1.02 when sodium sulfide reacts with oxidized ores by Mitrofanov. According to the experimental determination by Gaudin, the adsorption kinetics equation of Cu2+ adsorbing on sphalerite can be expressed by the following: C ¼ 0:82 þ 0:165 t1=2 The adsorption rate, usually, is very fast. For instance, the time of the adsorption equilibrium is from 10−11 to several seconds. The report shows that reagent molecule keeps to-and-fro motion at the interface when the adsorption equilibrium is reached, the motion of which could last for about 10−9 s [16].
2.3 2.3.1
Structure of Adsorption Film and Flotation Behavior of Mineral Structure of Adsorbed Layer
There have been many determination and opinions on the structure and composition of the adsorbed layer on mineral surface. As far as we know, the adsorption is multilayer in general. Based on the study on the adsorption of fatty acid on hematite and cassiterite, the single adsorbed layer can reach to 70 layers. The adsorbed reagent is in the form of molecule, ion, semi-micelle, and surface chemical reaction products.
28
2 Interaction Between Minerals and Reagents
The combination and arrangement of the adsorbed reagent on the mineral is not clear now. It is an accepted fact that the nearest layer of the adsorbed reagent is the product of chemical adsorption and then is the physical adsorption to minerals. For electrostatic adsorption in electric double layer, the adsorption of potential-determining ion occurs in inner layer; the adsorption of counterions occurs in the outer diffusion layer. The ratio of chemical and physical adsorption is different under different conditions. The chemical adsorption increases with increasing activity of mineral. Experimental result in our laboratory shows that the proportion of chemical to physical adsorption is 4:1 for the adsorption of xanthate on galena surface, 1:1 for the adsorption of 8-hydroxyquinoline on wolframite, and 1:(3–4) for the adsorption of fatty acid on hematite. For the arrangement of the adsorbed collector on the mineral, nonpolar groups direct outward in order to improve the hydrophobicity of mineral. However, flotation is depressed under the condition of too high reagent concentration. The explanation is that outward of polar groups of reagent molecule in adsorption outermost layer leads to increase of hydrophilicity. The reasons for heterogeneous distribution of the adsorbed collector include mainly two aspects as follows: First, there is crystal defect, impurity, surface chemical reaction, and electrochemistry on the mineral surface; second, the differences in crystalline properties and residual chemical bonds on broken faces lead to the adsorption variation of reagent on the high-energy or low-energy zones of mineral. According to reports by isotopic analysis, the adsorbed collector is in the form of fascicles; the adsorption density at edge and corner of mineral is bigger than that in other zones. In addition, there is a relation between distribution of the adsorbed collector and lattice structure of mineral.
2.3.2
Relationship of Collector Adsorption and Mineral Flotation
Within a certain range of reagent concentration, the flotation recovery is improved with increasing reagent concentration and increasing adsorption amount. If the reagent concentration reaches a fixed value, however, the recovery rate varies not significantly with increasing reagent concentration and adsorption amount. When the reagent concentration reaches a higher value, adsorption amount increases and the flotation recovery decreases on the contrary. Corton and Bogdanov had found these similar results. The following Fig. 2.4 is the common relation between reagent concentration and adsorption amount of ethyl xanthate on the galena. And Fig. 2.5 is the relation between adsorption density of ethyl xanthate and flotation recovery of galena (from Gaudin and Bogdanov). As shown in Fig. 2.5, the flotation recovery rate of galena reaches a maximum when the monolayer coverage of ethyl xanthate is 40 %. The study of Gaudin
2.3 Structure of Adsorption Film and Flotation Behavior of Mineral
29
1
2
Fig. 2.4 Relation between reagent concentration and adsorption amount of ethyl xanthate on the galena (from Gaudin)
Fig. 2.5 Relation between adsorption density of ethyl xanthate and flotation recovery of galena (from Bogdanov)
showed that, however, the flotation recovery rate of mineral reaches a maximum when the monolayer coverage of reagent is 70 %. The following Fig. 2.6 is the relation between reagent concentration and adsorption amount and flotation recovery rate of 8-hydroxyquinoline on wolframite surface (By Wang).
2 Interaction Between Minerals and Reagents
100
10
2
Recovery rate (%)
B 80
8
1
60
6
40
4
20
2
Adsorption amount (mol/g ×10-6)
30
0 100
200
300
400
Reagent concentration (mg/L) Fig. 2.6 Relation between reagent concentration and adsorption amount and flotation recovery of 8-hydroxyquinoline on wolframite surface
It can be shown in Fig. 2.6 that, within a certain range of reagent concentration, the flotation recovery rate and the adsorption amount increase consistently with reagent concentration. The adsorption amount increases all along when the reagent concentration reaches a higher value (point B). However, the flotation recovery rate decreases with reagent concentration. The point B is equivalent to the whole monolayer coverage. The following Fig. 2.7 is the relation between solution pH and adsorption amount and flotation recovery rate of 8-hydroxylquiloninato on wolframite surface. It can be shown in Fig. 2.7 that, within a certain range of solution pH, the flotation recovery rate and the adsorption amount increase similarly with solution pH. When the pH reaches a higher value, however, the adsorption amount and the flotation recovery rate decreases with solution pH, respectively. The variation trends have also been found in other documents. The following Fig. 2.8 is the relation between solution pH and adsorption amount and flotation recovery rate of butyl and benzyl xanthate on galena surface. Chemical adsorption, as the most important adsorption, affects the flotation behavior of mineral markedly. FT-IR results of Wadsworth showed that [3, 4] around wavelength of 5.8 lm assigned physical adsorption of oleic acid molecule; around wavelength of 6.4 lm is chemical adsorption of calcium oleate. The adsorption between oleic acid and fluorite is presented in following Figs. 2.9 and 2.10.
31
10
100
Recovery rate (%)
1 8
80
2 60
6
40
4
20
2
4
6
8
Adsorption amount (mol/g ×10-6)
2.3 Structure of Adsorption Film and Flotation Behavior of Mineral
10
pH Fig. 2.7 Relation between solution pH and adsorption amount and flotation recovery of 8-hydroxylquiloninato on wolframite surface
Fig. 2.8 Relation between solution pH and adsorption amount and flotation recovery of butyl and benzyl xanthate on galena surface
The flotation behaviors of fluorite show that the flotation recovery rate is small at low pH; while the flotation recovery rate becomes better under the condition of high pH. Chemical adsorption of reagent increases with increasing pH. Meantime, the effect of chemical adsorption on flotation behavior of mineral is bigger than that of physical adsorption. It is reasonable that the flotation recovery rate increases with increasing pH.
2 Interaction Between Minerals and Reagents
Adsorption amount (mg/g )
32
pH
Adsorption amount (mg/g )
Fig. 2.9 Adsorption of oleic acid on fluorite. 1 Chemical adsorption; 2 Physical adsorption
Reagent concentration (mol/L×105) Fig. 2.10 Chemical adsorption of oleic acid on fluorite (by Wadsworth)
We have studied the relationship of chemical adsorption and flotation behavior by means of the flotation of wolframite with 8-hydroxylquiloninato as collector. The Fig. 2.11 is the critical curve for wolframite flotation with 8-hydroxylquiloninato. The results show that the critical curve for flotation is in line with the critical curve for chemical adsorption of collector. That is, the flotation behavior of mineral is strongly linked to the chemical adsorption.
33
Collector concentration (mg/L)
2.4 Mineral Structure, Bonding Characteristics and the Reaction of Reagents
pH Fig. 2.11 The critical curve for wolframite flotation with 8-hydroxylquiloninato [17]. -occurrence of chemical adsorption and contact of bubble and mineral; ○-not occurrence of chemical adsorption and contact of bubble and mineral
2.4 2.4.1
Mineral Structure, Bonding Characteristics, and the Reaction of Reagents Geochemical Classification of Mineral Elements and Their Interaction With reagent
According to electronic structure, chemical affinity, and characteristic geochemical, the classifications of mineral elements are as follows: (1) Lithophile elements Lithophile elements refer to the main elements in the rocks. Electronic structure of their cation is similar to that of inert gaseous element. The number of outer shell electron is 2 or 8. If lithophile elements are ionized, they lose s or p electrons. For instance: Electronic structure of 1s2: Li+, Be2+ Electronic structure of 1s22s22p6: Na+, Mg2+ Electronic structure of 3s23p6: K+, Ca2+
He model Ne model Ar model
Other elements such as Al, Ba, rare elements and anions such as O, Cl, F, P, Si, and B belong to lithophile elements, too. These elements, as the principal part of pegmatite, mainly formed in the late stage of magmatism. These elements are prone
34
2 Interaction Between Minerals and Reagents
to combine with O and Cl and further form ionic bonding compounds of large electronegative difference (Dx). Those compounds are characterized by stable chemical properties, widespread, and long-term preservation. Usually, physical adsorption (including electric double layer adsorption) of flotation collector occurs on the mineral which are comprised of these elements. Chemical adsorption only occurs on the minerals which are comprised of those elements with large atomic number or high valence number (such as Ca and Ba and so on). (2) Chalcophile elements Chalcophile elements include the elements of heavy nonferrous metals and precious metals. Their cation possesses electronic structure of d10 or d10s2, such as Cu2+, Zn2+, Ag+, Cd2+, Au+, Hg2+, As3+, Sn2+, Sb3+, Pb2+, Bi3+, and so on. Nonmetallic anion includes S and Se. These elements, as the principal part of polymetallic ore, mainly formed in the hydrothermal stage. These elements are prone to combine with S and further form covalent bond compounds of small electronegative difference. Because of unstable chemical properties, those compounds are more easily weathered away into secondary mineral deposit. In general, chemical adsorption of flotation collector occurs on the minerals which are comprised of these elements. (3) Siderophile elements Siderophile elements include the elements of transition metals. Their cation possesses electronic structure of dx (x, 0–8), such as Ti, V, Cr, Mn, Zr, Ta, Nb, Fe, Co, Ni, Mo, and rare precious metals. Nonmetal includes C and P. These elements mainly formed in the early stage of magma. These elements are prone to combine with C, P, and N and further form compounds of medial electronegative difference. In general, both chemical and physical adsorptions of flotation collector occur on the minerals which are comprised of these elements.
2.4.2
Structure and Valence Bond of Mineral and Their Reactions with Reagents
Considering the flotation process and variety of reagents, minerals are divided into two classes by flotation scientists: sulfide minerals and nonsulfide minerals. Sometimes, nonsulfide minerals are also called oxidized minerals, although nonsulfide minerals contain some salineoxy acid of nonoxides or various saline minerals that do not contain oxygen. The flotability of sulfide minerals are good, in general. For example, adopting low dosage of selective thio-organic collector, the multimetal polymetallic sulfide
2.4 Mineral Structure, Bonding Characteristics and the Reaction of Reagents
35
ore can be separated effectively. Although nonsulfide minerals are divided into many types, nonsulfide minerals (except for a few nonpolar minerals such as sulfur, coal, talc, and mica) own bad flotability. For example, using a large reagent dosage of carboxylic acids or amines as collector, sulfide ore cannot be separated well. From the view of geochemical classification of mineral elements, sulfide minerals are mainly comprised of chalcophile elements (or some siderophile elements such as Fe, Co, and Ni); nonsulfide minerals are mainly comprised of lithophile and siderophile elements. As for those minerals in secondary oxide deposits such as cerussite, smithsonite, and malachite, they are product oxidized from sulfide minerals. First, presulfurization of secondary oxide minerals is applied in the flotation process. Subsequently, secondary oxide minerals are separated by adopting selective thio-organic collector. That is, flotation reagents for these secondary oxide minerals are still same as those for sulfide minerals. Valence bond properties of minerals have been mentioned. On the whole, the oxide minerals are ionic bonding; the sulfide minerals are covalent bond. Crystal structure properties of minerals are strongly linked to their natural flotability and the reaction of flotation reagent. It is listed in Table 2.1. Crystal structure can affect the crushing behavior of minerals, hydrophilicity or hydrophobicity of surface, and accumulation mode of mineral elements. For example, molybdenite is one of the sulfide minerals with covalent bond of Mo–S. But nonpolar bond of S–S is exposed to the cleavage plane of molybdenite due to its stratiform crystal lattice. The natural flotability of molybdenite is so good that it can be floated by using hydrocarbon oil as collector. Because of the occurrence of nonpolar bond on the cleavage plane, some oxide minerals including talc and mica own good natural flotability. They can be separated even though frother is only used in flotation. Meantime, the impurities and defect of minerals also make influence on the crystal structure and flotability of minerals. For example, the presence of various impurities such as Fe, Mn, and Cd in sphalerite leads to the changes of ionic fraction and lattice parameter. As is well known, the flotability of marmatite with large ionic fraction is worse than that of pure sphalerite. And the content of Fe also affects the ionic fraction and lattice parameter. The following are the flotation results of sphalerites with single bubble flotation tube. It shows that there is a relation between lattice parameter and flotability of minerals. Lattice parameter of ZnS (Å) Results of flotation (%)
5.4234 8.0
5.4187 0.0
5.4139 30.0
36
2 Interaction Between Minerals and Reagents
Table 2.1 Crystal structure of minerals and their flotation behavior Crystal structure
Valence bond
Typical mineral
Interaction with reagent and flotability
Needle-like, schistic
Covalent bond
Cleavage along the van der Waals force direction; Nonpolar cleavage plane; Having natural flotability and can be floated by hydrocarbon oil; Physical adsorption g between reagent and mineral
Diamond type
Covalent bond
Se element: needle-like, atomic separation in needle: d = 2.32 Å, Atomic separation between needles: d = 3.46 Å; Graphite: schistic, atomic separation in sheet: d = 1.42 Å, atomic separation between sheets: d = 3.40 Å; Molybdenite: atomic separation in sheet: S–S, d = 2.98 Å, S–Mo, d = 2.35 Å; Atomic separation between sheets: S–S, d = 3.66 Å Diamond, C–C tetrahedron, d = 1.54 Å
Metallic crystal
Metallic bond
Natural gold, silver, copper; Cu: d = 2.55 Å
Semi-metallic crystal
Covalent bond Metallic bond
Silicates
Covalent bond Ionic bond
Nonferrous metals sulfide ores such as: galena: metallic bond Pb–Pb, d = 4.18 Å; S–S, d = 5.93 Å; Pb–S, d = 2.96 Å; Sphalerite: 50 % ionicity, Zn–Zn, d = 3.83 Å; Pyrite: S appearing covalent double ion, d = 2.14 Å; Fe–S, d = 2.26 Å; Fe–Fe, d = 3.83 Å The fundamental structure appearing in forms of silicon– oxygen tetrahedron; Si–O ionicity 40 %; (1) orthosilicates, tetrahedron, example: olivine (2) polysilicate, ditetrahedron, example: akermanite (3) metasilicate, free ring, example: beryl (4) metasilicates, single stranded, example: diopside (5) metasilicates, duplex, example, tremolite
No cleavage; Having natural flotability and can be floated by hydrocarbon oil; Physical adsorption between reagent and mineral Floated by thio-organic collector; Chemical adsorption Having cleavage; Weak polarity; Having natural flotability and can be floated by Thio-organic collector; Chemical adsorption
Flotated by fatty acid or amine, or activation flotation; Physical adsorption (1) imperfect cleavage, polarity, no natural flotability; (2) imperfect cleavage, polarity, no natural flotability; (3) appearing cleavage, polarity, no natural flotability; (continued)
References
37
Table 2.1 (continued) Crystal structure
Valence bond
Typical mineral
Interaction with reagent and flotability
(6) layer silicates, example, talcum (7) framework, silicates, example: quartz
(4) appearing cleavage, polarity, no natural flotability; (5) appearing cleavage, polarity, no natural flotability; (6) appearing cleavage, no polarity, natural flotability; (7) no cleavage, polarity, no natural flotability; Appearing cleavage, polarity, And can be floated by fatty acid; Physical and chemical adsorption Appearing cleavage, polarity; And can be floated by fatty acid; Physical and chemical adsorption
Metallic oxide
Ionic bond
Corundum, rutile, hematite
Complex ion crystal
Ionic bond
Simple ion crystal
Ionic bond
Oxysalts such as CO32−, PO32−, and SO32−; The inner of complex ion appearing covalent bond, anion-cation is electrovalent bond; Example: CaSO4 S–O, d = 1.56 Å; Ca–Ca, d = 3.11 Å; Ca–S, d = 3.48 Å; Ca–O, d = 2.42 Å Halide salts
Appearing cleavage, polarity; And can be floated by fatty acid; Physical adsorption
References 1. P. Somasundaran, AICHE 71(150) (1975) 2. H.S. Hanna, P. Somasundaran, Flotation AM Gaudin Memorial Volume, vol. I. (1976), p. 197 3. F.F. Aplan, D.W. Fuerstenau, Forth Flotation 50th Anniversary Volume (AIME, INC., New York, 1962), p. 170 4. D.W. Fuerstenau, Flotation foundation (notes): central and south mining and metallurgy college intelligence document (1979) 5. D.W. Fuerstenau et al., XIIth IMPC (1977), p. 6 6. A.M. Gaudin, Flotation 2nd edn. (McGraw-Hill Book Company, Inc., New York, Toronto, London, 1957), pp. 232, 182, 285 7. K.L. Sutherland, I.W. Wark, Principles of Flotation (Australian Institude of Mining and Metallurgy (INC), Melbourne, 1955), pp. 84, 98, 278, 302, 319 8. M.A. Cook, J.C. Nixon, J. Phy. Chem. 445 (1950) 9. B.O. Kondo, Surface Chemistry (1962), p. 73
38 10. 11. 12. 13. 14. 15. 16. 17.
2 Interaction Between Minerals and Reagents P.J. Harris, XIth IMPC (1975), p. 35 B.O. Kondo, Surface Chemistry (1962), p. 73 M.C. Prasad, IXth IMPC (1970), p. 149 N.P. Finkelstein, J. South Afr. Inst. Min. Met. 72, 328 (1972) S. Chander, et al., Intern. J. Min. Proc. 2, 333 (1975) D. Wang, J. Central-South Inst. Min. Met. 11 (1963) J. Davies, E.K. Rideal, Interfacial Phenomena, pp. 86, 154, 189 A.M. Gaudin, D.W. Fuerstenau, Trans. AIME 202, 958 (1955)
Chapter 3
Structure and Property of Polar Group of Collector
3.1
Structural Characteristics of Collector Molecule and Independent Effect of Chemical Groups Belong to Surface Chemistry
The fundamental characteristics of collector are supposed to include two aspects as follows. The first one is that collector is able to interact and attach with mineral surface. The second one is that the hydrophobicity of mineral surface can be improved after the adsorption of collector. Except for auxiliary collector such as nonpolar hydrocarbon oils, all ionic and nonionic collectors are comprised of polar groups which can be absorbed on mineral surface and consist of nonpolar groups which make mineral surface showing hydrophobicity. That is why a collector is divided into polar groups and nonpolar groups in textbooks. Polar groups are further divided into the solidophilic atoms (or called the bonding atoms) and the linking atoms. Taking ethyl xanthate for example, categories of groups or atoms are presented as follows:
H
Non-polar group
H
H
C
C
H
H
S O
C
S
Na
Polar group linking atoms
Centronucleus atoms
Solidophile atoms
Dissociation atom
anion
cation
Ion with collecting ability
Ion without collecting ability
© Metallurgical Industry Press, Beijing and Springer Science+Business Media Singapore 2016 D. Wang, Flotation Reagents: Applied Surface Chemistry on Minerals Flotation and Energy Resources Beneficiation, DOI 10.1007/978-981-10-2030-8_3
39
40
3 Structure and Property of Polar Group of Collector
According to the principle of independent effect of chemical groups in surface chemistry, the whole activity of surfactant molecule is a summation of the activity of each group. The total surface energy of the molecule is given as follows: U ¼ n1 s1 r1 þ n2 s2 r2 þ where U refers to the total surface energy of molecule; n means the number of a group in molecule; s refers to the surface area of the corresponding group; and r refers to the surface energy of each group. Therefore, it is used to simplify the study on the relationship between molecular structure and property of complex reagent molecule by studying the structure and property of each group in the molecule. Generally speaking, the affinity of reagent and mineral depends on the polar groups of reagent. The influences of polar groups on the affinity of reagent are mainly manifested in terms of the changes of chemical property and physical property of reagent (such as adsorption capability, chemical reaction, dissociation property, and solubility). Meantime, the steric size is also an important factor that decides the property of reagent. Because the sectional area of polar groups is much larger than that of nonpolar groups, the steric size of polar groups becomes a determining factor of the whole steric size and property of reagent molecule. The hydrophobicity depends on the nonpolar groups of reagent. The influences of nonpolar groups on the hydrophobicity of reagent are mainly manifested in terms of the changes of solubility and surface activity. However, the hydrophilicity or hydrophobicity of reagent is also influenced by the degree of hydration and polarity of polar groups. Meantime, the surface activity of nonpolar groups not only influences directly the affinity of reagent but also influence indirectly the effect of polar groups. Structural factors of reagent include bonding factor, hydrophilicity or hydrophobicity and steric factor. According to classification of structural factors, the polar group influences the bonding factor of reagent; the nonpolar group influences the hydrophilicity or hydrophobicity of reagent; these two above factors influence the steric factor of reagent. Table 3.1 shows a general describing for structural factors of reagents and their performance. The structural factors of reagent will be further discussed in the following Chap. 6.
3.2
3.2.1
Effect of Polar Group Structure on Dissociation of Reagent and Adsorption in Electrical Double Layer of Mineral Surface Dissociation of Collector and Its Flotation Function
The dissociation of collector decides not only the molecular or ionic state but also the adsorption capability in electrical double layer. Strong electrolyte collectors can be completely dissociated into ions and react with mineral in the form of ions state.
Chemical reaction
Weak, R2NCSS−
Nonionic Strong, RSO3−
Weak, RCOO− Strong, RSO3−
R2NCSSNa
(ROCSS)2
RNHCSOR
RSO3Na
RCOONa
RCOONa
RSO3Na
RNH2
RNH2(CH2)2COOH
Aminosulfate (dialkyldithio dithiocarbate)
Dixanthogen
Dialkyl thiocarbanate
Sodium sulfonate
Stearate soap
Fatty acid soap
Sodium sulfonate
Primary amine
Amino acid Amphoteric
Weak, RNH+
Weak, RCOO−
Nonionic
Weak, (RO)2PSS−
(RO)2PSSNH4
Aerofloat (dialkyl dithiosphonate)
Weak, ROCSS−
Soluble
Soluble
Soluble
Soluble
Soluble
Soluble
Insoluble
Insoluble
Soluble
Soluble
Soluble
Polar
Polar
Strong polar
Polar
Polar
Strong polar
Polar
Polar
Polar
Polar
Polar
Reacting with heavy metal ion to generate complex
Reacting with alkaline-earth or heavy metal ion to generate insoluble compound
Reacting with metal ion to generate insoluble compound
Alkyl
Alkyl
Alkyl
Alkyl
Alkyl, alkyl
Alkenyl
Alky, i-alky
Alky, alkyl
Alkyl
Alkyl, tolyl
n-alky, ialky
Surface factor Polarity
Category of nonpolar group
Water solubility
Bonding factor Dissociation property
ROCSSNa
Molecular formula
Xanthate (alkyl dithiocarbonate)
(一) collector
Reagent
Table 3.1 Structural factors of various common flotation reagents Steric factor
5.2
C8–C18
5.2
C10–C20
3.7
5.9
C12–C25
C12–C18
8.7
C2–C5
5.9
10.1
C2–C5
C12–C25
7.0
C2–C5
5.2
7.3
C2–C5
C17
7.0
Diameter of cross section of polar group
C2–C5
Chain length of nonpolar group
(continued)
Long linear chain
Long linear chain
Winding long linear chain
Long linear chain
Long linear chain
Two short linear chains
Two short linear chains
Two short linear chains
Two short linear chains or benzene ring
Short linear chain or branched chain
Shape of nonpolar group
3.2 Effect of Polar Group Structure on Dissociation … 41
CnH2n+2
Diesel fuel
R(OCnH2n)nOH
Poly (vinyl alcohol)
Anionic Anionic
(C6H9O5)nCH2COONa
–
(C6H10O5)n
Carboxymethylcellulose
Sulfonated lignin
Starch Nonionic
Anionic
HOOC–COOH
Weak anionic
Nonionic
Oxalic acid
(三) depressant
R
C10H17OH
Terpineol
OH
Nonionic
CnH2n+1OH Nonionic
Nonionic
CnH2n+1OH
Nonionic
n-alkanol
Phenols
Chemical reaction
Insoluble
Soluble
Soluble
Soluble
Soluble in alkali
Small solubility
Insoluble
Polar
Polar
Nonpolar
No activity
–
Reacting with metal ion to generate water-soluble complex
No surface activity
No surface activity
No surface activity
No surface activity
No surface activity
No activity
Pyranose
Aryl
Pyranose
No nonpolar group
Aryl
Alkoxy
Terpenyl
i-alky
Alkyl
Hydrocarbon
Surface factor Polarity
Category of nonpolar group
Water solubility
Bonding factor Dissociation property
Iso-alkanol
(二) Frother
Molecular formula
Reagent
Table 3.1 (continued)
n = 200– 1000
MW: 800– 10000
n = 450– 500
2.8
–
5.2
5.2
2.8
2.8
C8–C9 Phenyl
2.8
2.8
Hexacyclic group
2.8
C6–C8 C6–C8
4.0
C10–C20
Steric factor Diameter of cross section of polar group
Chain length of nonpolar group
Long chain
Polyphenyl chain
Long chain
Benzene ring
Linear chain
Terpenyl
Branched chain
Linear chain
Long linear chain
Long linear chain
Shape of nonpolar group
42 3 Structure and Property of Polar Group of Collector
3.2 Effect of Polar Group Structure on Dissociation …
43
For instance, besides the occurring of hydrolysis and chemical reactions, alkyl sulfonates or alkyl sulfates are mainly dissociated into ions and evenly distributed in the water. Weak electrolyte collectors can be partly dissociated into ions. The proportion of molecular state to ionic state depends on the dissociation constant of collector and solution pH. Taking anionic collector for example, its dissociation process can be presented as follows: HA H þ + A The dissociation constant Ka is expressed as follows: Ka ¼
½H þ ½A ½H þ ½A ½H þ ðC ½HAÞ ¼ ¼ ½HA ½HA ðC ½A Þ
and ½A ¼
Ka C Ka þ ½H þ
or
½HA ¼
C ½H þ Ka þ ½H þ
where C refers to the concentration of anionic collector; [A–] and [HA] refer to the concentration of anion and molecule, respectively The relationships between [A–] and [HA], as well C, are illustrated as follows: (1) When Ka [H+], or pKa pH: log ½A = log C pKa þ pH; log ½HA ¼ log C; (2) When Ka [H+], or pKa pH: log ½A = log C; log ½HA ¼ log C þ pKa pH; (3) When Ka = [H+], or pKa = pH: ½A ¼ ½HA log ½A = log C log ðKa þ ½H þ Þ þ log Ka ; log ½HA] = log C þ log ½H þ log ðKa þ ½H þ Þ For anionic collector, pH pKa = log
½A ½HA
44
3 Structure and Property of Polar Group of Collector
Table 3.2 Dissociation constants Ka of various alkyl xanthic acids Alkyl xanthic acid
Ka
Potassium methyl xanthic acid Potassium ethyl xanthic acid Potassium propyl xanthic acid Potassium butyl xanthic acid Potassium amyl xanthic acid Potassium i-propyl xanthic acid Ethyl xanthic acid Ethyl xanthic acid Amyl xanthic acid Ethyl xanthic acid Amyl xanthic acid Xanthic acid Ethyl xanthic acid Propyl xanthic acid Butyl xanthic acid Amyl xanthic acid
3.4 2.9 2.5 2.3 1.9 2.0
Ref. or measuring method
10−2 10−2 10−2 10−2 10−2 10−2
0.02 ± 0.001 3.0 10−3 1.0 10−6 5.2 10−4 2.5 10−5 3.0 10−2 3.4 10−2 3.4 10−2 3.4 10−2 3.4 10−2
By Hong Mashima, ultraviolet spectroscopy
By Yan Iwasaki, ultraviolet spectroscopy By Last, ultraviolet spectroscopy By Nixon, potential method By von Halben (from A.M. Gaudin) By M.C. Fuerstenau
when pKa = pH, the proportion of [A–] is 50 %; when pH – pKa = 0.5, the proportion of [A–] is 76 %; when pH – pKa = 1, the proportion of [A–] is 91 %. From here, we can see that the dissociation constant Ka is useful to illustrate the mechanism and the activity controlling of the reagent. The dissociation constant Ka of xanthic acid is listed in Table 3.2. Because xanthic acid can easily resolve, Ka of xanthic acid is difficult to measure. The result varies with the change of test method. According to the structural features of xanthic acid, a small value (for 10−5 example) is reliable. Meantime, the value decreases gradually with nonpolar hydrocarbon chain lengthening. The dissociation constants Ka of fatty acids are listed in Table 3.3. Taking cationic collector dodecylamine anionic collector for another example, its dissociation process in alkaline solution is given as follows: RNH2ðaqÞ þ 2H2 O RNH3þ þ OH The dissociation constant Kb is expressed as follows: Kb =
½RNH3þ ½OH ¼ 4:3 104 ½RNH2ðaqÞ
3.2 Effect of Polar Group Structure on Dissociation …
45
Table 3.3 Dissociation constants Ka of various fatty acids Fatty acid
Ka
HCOOH CH3COOH C2H5COOH C3H7COOH C4H9COOH C5H11COOH
2.10 1.83 1.32 1.50 1.56 1.40
10−5 10−5 10−5 10−5 10−5 10−5
Fatty acid
Ka
C4H13COOH C7H16COOH C8H15COOOH C12H23COOH Oleic acid
1.30 1.41 1.10 0.51 1.00
10−5 10−5 10−5 10−6 10−6
If including: RNH2ðsÞ RNH2ðaqÞ Ksl ¼ ½RNH2ðaqÞ ¼ 2 105 Here, this Ksl refers to the solubility of collector. For solid dodecylamine, its dissociation process is given as follows: RNH2ðsÞ þ 2H2 O RNH3þ þ OH KsO ¼ ½RNH3þ ½OH ¼ 8:6 109 ¼ ðKb Ksl Þ It can be obtained that [RNH3+] = [RNH2](a, q) under the condition of pH = 10.65. The dissociation process of dodecylamine in acid solution is given as follows: RNH3þ RNH2 þ H þ The dissociation constant Ka is expressed as follows: Ka ¼
½RNH2 ½H þ ½RNH3þ
The relation between Kb and Ka is as follows: Kb ¼
1014 Ka
The dissociation constant of aliphatic amine is listed in Table 3.4.
46
3 Structure and Property of Polar Group of Collector
Table 3.4 Dissociation constants Ka of various alkyl amines Fatty amine
Ka
Nonyl amine Decyl amine Undecylamine Dodecylamine Tridecylamine Tetradecylamine
4.4 4.4 4.4 4.3 4.3 4.2
3.2.2
10−4 10−4 10−4 10−4 10−4 10−4
Fatty amine
Ka
Pentadecylamine Cetylamine Octadecylamine Cetylpyridine bromide N-methyl dode cylamine Dimethyl dode cylamine
4.1 10−4 4.0 10−4 4.0 10−4 30.0 10−4 10.2 10−4 0.6 10−4
Zero Charge Point of Mineral and Dissociation Constant of Collector, and Their Interrelation in Flotation
The electrostatic force between collector and mineral, as well as the physical adsorption of neutral molecule, is discussed in this section. Because of hydration, the surface of oxide mineral is covered by hydroxyl ions (–OH), and simultaneously adsorb or dissociation hydrogen (H+). Therefore, –OH or H+ often behaves as the potential-determining ion in the electrical double layer. Oxide surface can undergo the reaction with –OH or H+ depending on the solution pH. The relation between surface electric property of oxide and solution pH is expressed as follows [1]: þ þ MOH2ðsÞ
MOHðsÞ þ HðaqÞ þ MOHðsÞ MO ðsÞ þ HðaqÞ
where M refers to the cation in oxide mineral, such as Al in alumina and Si in þ quartz; MOH(s) refers to the neutral surface of oxide; MOH2ðsÞ refers to the positive
+ þ surface of oxide; MO ðsÞ refers to the negative surface of oxide; Hða qÞ refers to H in water solution. The point of zero electricity (PZC) is the pH where the surface potential of mineral is equal to zero and the sign of pHPZC or pH0 is used to show this point. The pHPZC of some common minerals are listed in Table 3.5. Under the condition of OH− or H+ behaving as the potential-determining ion, the surface potential of mineral W0 can be expressed as follows:
w0 ¼
RT ½H þ RT ½OH ln þ ¼ ln F ½H 0 F ½OH 0
3.2 Effect of Polar Group Structure on Dissociation …
47
Table 3.5 pHPZC of various minerals Mineral category
Mineral
pHPZC
Mineral category
Mineral
pHPZC
Insoluble salt mineral
Scheelite (CaWO4) Calcite (CaCO3) Fluorite (CaF2) Fluorapatite (Ca5(PO4)3(FOH)) Hydroxylapatite (Ca5(PO4)3(OH)) Magnesite (MgCO3) Silica gel (SiO2) a-quartz (SiO2)
10.2 9.5 6.2 6.0
Silicate
Forsterite (Mg2SiO4) Olivine ((Mg,Fe)2SiO4) Zircon (ZrSiO2) Kyanite (Al2SiO5)
4.1 4.1 5.8 7.8, 6.2, 6.9 2.6
Cassiterite (SnO2)
4.5
Zircon (ZrO2)
4
Rutile (TiO2)
5.8– 6.7
Goethite (FeOOH)
6.8
Corundum (Al2O3)
9.1
Magnesium oxide (MgO) Synthetical hematite (Fe2O3) Natural hematite (Fe2O3)
12.0
Oxide mineral
7.0 6.5 1–2 2–3
8.3– 9.0 5.4– 8.7
Spodumene (LiAl (SiO3)2) Rhodonite (MnSiO3) Beryl (Be3Al(Si5O18)) Riebeckite (Na2Fe″3 Fe″’ 2 Al(Si8O22)(OH)) Kaolinite (Al4(Si4O10) (OH)8) Talcum (Mg6(Si8O20) (OH)4) Muscovite (K2Al4(Al2Si6O20) (OH,F)4) Chrysotile (Mg6(Si4O10) (OH)8) Microcline (K (AlSi3O8) Orthoclase (K (AlSi3O8) Albite Na(AlSi3O8) Quartz (SiO2)
2.8 3.2, 3.4 3.3 3.4 3.6 1.0
12.4 1.7–1.9 1.4–1.7 1.9, 2.3 2, 2.2, 3.1 3.7, 4.0
and w0 ¼ 2:3
RT ðpHPZC pH) F
ð3:1Þ
where R is absolute temperature; F refers to the Faraday constant; [H+]0 and [OH–]0 mean the concentration of H+ and OH– under the condition of PZC, respectively. For the situation that OH− or H+ is not the potential-determining ion, the surface potential of mineral can also be influenced by solution pH or other ions. The adsorption via electrostatic force takes place in the electrical double layer only if the collector owns the opposite ion with mineral. Based on this interaction theory, the anionic collector should be used in the mineral flotation under the condition of pH < pHPZC; the cationic collector should be applied for the flotation
48
3 Structure and Property of Polar Group of Collector
under the condition of pH > pHPZC. Figure 3.1 displays the flotation results under different pH conditions. The results further confirm the interaction theory above. This is a much more useful guide in practice. We can evaluate the effect of reagent on mineral in a certain solution pH according to the pHPZC of mineral and the pKa of reagent. Under the condition of pH pKa, weak electrolyte anionic collector can be mainly dissociated into ions. Providing that pH < pHPZC at the same time, the surface potential of mineral is positive. As noted above, under the condition of pKa pHPZC, the adsorption of collector on mineral surface can occur in the electrical double layer. For cationic collector, the adsorption of collector on mineral surface only takes place in the electrical double layer under the condition of pKa pHPZC. Practical test results, however, show that the functions of pHPZC of mineral and pKa of collector in flotation are not as obvious as shown in Fig. 3.1. The main reasons involve the following three aspects. The first one is that the effective concentration of collector has wide fluctuations in flotation. Sometimes, the adsorption of collector on mineral occurs even at a quite low dosage of collector. The second one is that the coadsorption of nonionic molecule leads to the occurrence of mineral flotation but not via completely electrostatic force. The last one is
ζ potential (mV)
1. 10-4 M NaCl 2. 10-3 M NaCl 3. 10-2 M NaCl
1
2
60
3
40 20 0 -20 -40
Recovery rate (%)
-60
80 60
× RSO4Na O RSO3Na RNH3Cl
40 20 0
2
4
6
8
10
12
pH Fig. 3.1 Effects of f potential of limonite and electric charge of collector ion on recovery rate of mineral (From Iwasaki)
3.2 Effect of Polar Group Structure on Dissociation … Fig. 3.2 The contact angle of surface via dodecylamine salt concentration (From de Brugn) [1]
49
30˚
Reagent concentration (mol/L)
10-2
40˚
20˚
50˚ 70˚ 60˚
10-3
80˚
10˚
10-4
10-5
— contact angle --- adsorption monolayer 5~7% 4
8
12
pH
that the special adsorption such as strong chemical adsorption of reagent molecule results in flotation independent of electrostatic force. According to de Brugn, the flotation result of quartz using dodecylamine is presented in Fig. 3.2. The contact angle result shows that under the condition of pH < pHPZC(=2), mineral flotation does not occur because the surface potential of mineral is positive; under the condition of pH > 12, mineral flotation also does not occur because of the complete hydrolysis of collector. When the value of pH is large, the surface potential of mineral is negative. Mineral flotation takes place at a low dosage of collector. For instance, under the condition of reagent concentration of 5 10−5 and pH 12, mineral flotation occurs. Mineral flotation, sometimes, can occur at high dosage of collector under the condition of low pH. The reason is that the association force of hydrocarbon chain can overcome electrostatic force even though collector and mineral have similar electric charges. Under the condition of a low proportion of opposite charges between reagent and mineral, the occurring of mineral flotation results from the coadsorption of nonionic molecules and ions in many cases. The adsorption of a few ions on mineral surface, instead, offers the optimum condition for the association of hydrocarbon chain in nonionic molecule. Because the coadsorption of nonionic molecules is very important for flotation, it is illustrated by the following from different adsorption stages. When the charges of reagent ions and mineral are opposite, the adsorption of ions becomes very easy; the adsorption capability of nonionic molecule is weaker than that of ions. When the surface charges of mineral are neutralized by the
50
3 Structure and Property of Polar Group of Collector
adsorbed reagent ions, and then, the electrostatic force between mineral and reagent becomes weak, the adsorption capability of ions starts decreasing, but the adsorption capability of nonionic molecule does not decrease. When the charges of reagent ions and mineral are the same, the adsorption of collector ions receives the resistance of electrostatic force; the adsorption capability of nonionic molecule becomes stronger than that of ions. Thus, it can be seen that the coadsorption of nonionic molecules enlarges the pH range for mineral flotation. When the solution pH is near the pHPZC of mineral, the coadsorption of nonionic molecules is more marked. But it also decreases the selectivity of electrostatic interaction between collector and mineral. The effect of weak electrolyte collector on mineral separation is stronger that of strong electrolyte at a low concentration. For example, the pHPZC value of corundum is about 9. When solution pH = 6, the charges of mineral are positive. Anionic collector is effective in flotation. When solution pH = 11, the charges of mineral are negative and the cationic collector is effective in flotation. However, it manifests a better flotation index in the system of weak electrolyte collector. The reason lies in the coadsorption of nonionic molecules.
3.2.3
Adsorption of Amphoteric Collector in Electric Double Layer
General form of amphoteric collector is as follows: R1 X1 R2 X2 where R1 refers to the alkyls with long chain; R2 refers to the alkyls with short chain in usual; X1 means the cationic groups such as –NH–, –AsH–,
P
N
, –NH4,
As
,
, –PH4; and X2 means the anionic groups such as –COOH, –
SO3H, –SH, –SO4H, –PO(OH)2, and –AsO(OH)2. The dissociation of amphoteric collector depends on acidic or alkaline medium. Taking amino acid for an example, the dissociation process is given as follows: RNHCH(CH3 ÞCH2 COOH þ OH RNHCH(CH3 ÞCH2 COO þ H2 O RNHCH(CH3 ÞCH2 COOH þ H þ RNH2þ CH(CH3 ÞCH2 COOH Amino acid is dissociated into anion in alkaline solution, but cation in acidic solution. And it keeps anion–cation balance at the appropriate pH value.
3.2 Effect of Polar Group Structure on Dissociation … Table 3.6 pHPZC of common amphoteric collectors
51
Reagent
pHPZC
(1) (2) (3) (4) (5) (6) (7)
4.5 4.1 4.3 3.7 About 1.0 6.3–6.6 6.3–6.6
Cetyltrimethyl aminoacetic acid N-coconut oil-b-aminobutyric acid N-dodecyl-b-lactamine N-dodecyl-b-secondary diaminopropane N-myristyl aminoethanesulforic acid Sulfamic acid stearate Sulfamic acid oleate
R1 X1þ R2 X2 This value of pH at the balance point is also called pHPZC, or pH0. The solubility and the degree of dissociation are the smallest at pHPZC (Table 3.6). Because the dissociation of amphoteric collector changes at pHPZC, correspondingly, the flotation behavior of collector also alters at pHPZC. The following picture shows the dissociation and the flotation behavior of amphoteric collector changing with pH [2, 3].
Under the condition of (A), the pH0R of collector is smaller than pH0M of mineral. Providing pH0R < pH < pH0M, the charges of mineral and collector ions are opposite. The electrostatic interaction between mineral and collector is easy to take place. Under the condition of (B), the pH0R of collector is larger than pH0M of mineral. Providing pH0R > pH > pH0M, the ionic adsorption of collector on mineral is easy to take place. It can be concluded that the range of pH can be expressed as the difference between pH0R and pH0M (pH0R–pH0M). When the difference is positive value, mineral flotation is easy to take place if pH > pH0M . When the difference is negative value, mineral flotation is easy to take place if pH < pH0M. Figure 3.3 further shows the flotation behavior of amphoteric collector under different conditions. As shown in Fig. 3.3, the pH0M of N-dodecyl-b-lactamine, hematite, muscovite, calcite, and quartz is 4.3, 6.7, 1.0, 9.7, and 1-4, respectively. As noted above, the occurrence of hematite and calcite flotation lies in the adsorption of anionic collector on the positive mineral surface. The occurrence of muscovite flotation lies in the adsorption of cationic collector on the negative mineral surface; the flotation decreases with increasing pH; the reason for the
3 Structure and Property of Polar Group of Collector
Recovery rate (%)
52
Collector: C12H25NHCH2CH2COOH, pH=4.3
pH
Fig. 3.3 Flotation behavior of amphoteric collector under different conditions (By Wrobel)
decrease of flotation is that N-dodecyl-b-lactamine gradually changes into anions at a higher pH. The appearance of quartz flotation lies in the adsorption of cationic or nonionic collector on the negative mineral surface.
3.2.4
Effect of Polar Group Structure on Dissociation of Collector
As for those organic acids, that is anionic collectors, when polar group is comprised of large electronegativity atoms such as the halogens and oxygen element, the degree of dissociation is often high. In addition, the degree of dissociation of oxyacid increases with increasing oxygen atom in polar group. The pKa of different inorganic oxygen acids are listed in Table 3.7. Table 3.7 shows that the degree of dissociation of inorganic oxygen acid increases with an increase in electronegativity of atoms and quantity of oxygen atoms.
3.3
Molecular Structure of Nonionic Reagent and Adsorption by van der Waals Force
Providing the adsorption of nonionic molecule via van der Waals force and hydrogen bond, the relation between molecular structure and adsorption capability is introduced in this section.
3.3 Molecular Structure of Nonionic Reagent and Adsorption …
53
Table 3.7 pKa of different inorganic oxygen acids pKa
Acidity
Acid in III group
Acid in IV group
Acid in V group
Acid in VI group
Acid in VII group
H2SO4 (N S>O O > N (for elements with more d-orbital electrons) N > O (for elements with less d-orbital electrons)
For those atoms of nitric group Lithophile elements: N P > As Chalcophile elements: N P < As For those atoms of oxygenic group Lithophile elements: O S > Se > Te Chalcophile elements: O S * Se * Te For those atoms of halogens Lithophile elements: F Cl > Br > I Chalcophile elements: F < Cl < Br I
Notes appended: the solubilitydata of low MW Ca, Mg, and Ag fatty compounds (By Berger) Ca(C2H5COO)2 H2O Ca(C4H9COO)2 H2O Ca(C6H14COO)2 H2O
3.6 10−1 1.7 10−1 1.8 10−2
C2H5COOAg C4H9COOAg C6H9COOAg
4.26 10−3 1.26 10−2 2.23 10−3
listed in Table 3.11. Table 3.12 shows the recent reports on the data of solubility products of various metal fatty acid compounds [7].
62
3 Structure and Property of Polar Group of Collector
Table 3.11 Solubility products of various alkyl sulfonates Sulfonate
Na+ 25 °C
C12 C14 C16 C18
0.2530 0.0410 0.0073 0.0010
60 °C
Mg2+ 25 °C
48.0000 38.8000 6.4900 0.1310
0.0330 0.0350 0.0012 0.0010
60 °C
Ca2+ 25 °C
60 °C
48.0000 0.0160 0.0600 0.0030
0.0110 0.0014 0.0050 0.0060
0.0330 0.0050 0.0013 0.0007
Table 3.12 The negative logarithm of solubility products of metallic salts of fatty acids (From M. C. Fuerstenau: Flotation A.M. Gaudin Memorial Volume V.16/P.143) The number of C atoms in hydrocarbon chain
The negative logarithm of solubility product pL Sr2+ Ba2+ La2+ Mg2+
12 14 16 18
10.48 13.08 15.77 18.33
11.02 13.37 16.16 18.60
11.46 14.15 17.11 19.60
23.91 27.14 31.03 34.30
Notes appended: solubility of calcium fatty acid and calcium sulfonate C8
C9
C10
C11
C12
C13
C14
C16
C18
Ca (RCOO)2
6.57
8.10
14.66 15.00 13.54
19.69
–
12.16 12.10 10.33
17.42
–
10.90 10.66 –
13.30
Ca (RSO3)2
9.32 9.42 8.07
15.80
–
–
It can be concluded that the solubilities of alkyl sulfonates are similar with those of metal fatty acids. Under the condition of high molecular weight, the solubilities of metallic compounds of reagent and mineral may be very small. The data also show that there exists special relation between bonding capability and kind of the solidophilic atoms. It also can be found from the solubility products of metallic compounds and flotation characteristics of reagents; the collecting property of collector increases with decrease in solubility product. However, if bonding capability of the solidophilic atom is too strong, the selectivity of collector will be influenced. These trends can be found from the flotation results using xanthate or aerofloat as collector. Therefore, the solubility product is not only used for judging the collecting property of collector but also the selectivity. Meantime, someone proposed that the ratio of solubility products of reagent and metallic compound can act as the criteria for reagent application for selective flotation process of two minerals [8].
3.4 Polar Group Structure and Chemisorption
63
(2) Electronegativity According to valence bond theory, lithophile elements can bond with O and further form ionic bond. The reason is that the small metal ions with high positive charges are prone to bond with those small atoms with high negative charges. The bonding capability of lithophile element can be measured as follows: Z2 =r where Z refers to the valence of ion; r means the radius of ion. Because Z2/r is related to electronegativity, the electronegativity difference (Dx) can become the criteria of collector: Dx ¼ x1 x2 where x1 refers to the electronegativity of the bonding atom in polar group of reagent molecule; x2 refers to the electronegativity of metal ion. According to Pauling, the electronegativity indicates the ability of attracting electron of an atom in molecule. In general, the ionicity of chemical bond increases with an increase in the electronegative difference (Dx). For chalcophile elements, they can bond with S and further form covalent bonds (including ordinary covalent and coordination bond). The bonding capability of chalcophile element increases with the decrease in the electronegativity difference (Dx). According to the calculation of Pauling, when Dx = 1.7, the ionicity of bond is 50 %; when Dx < 1.7, the covalent bond is dominant; when Dx > 1.7, the ionic bond is dominant. Z2/r of metal atom with the solidophilic atom is listed in Table 3.13. For those collectors for nonsulfide minerals such as fatty acids and sulfonates, the solidophilic atom is O. Because O can bond with various metal ion and form strong polar ionic bond, the solubility of metallic compound is not too low. Only if the molecular weight of nonpolar is very large, its hydrophobic interaction can make product less solubility. For those collectors of sulfide mineral such as xanthate, the solidophilic atom is S which can bond with various metal ion and form weak polar covalent bond, so the metallic compound has lower solubility. In this condition, even though the molecular weight of nonpolar is very low, a small solubility product can be obtained. Therefore, for different metallic compounds, Table 3.13 The negative logarithm of solubility products of metallic salts of fatty acids S
O
N
S
Siderophile element
Dx
N
Chalcophile element
Dx
O
O
N
S
1.67
2.5
2.0
1.5
Cu
1.6
1.1
0.6
Ti
2.0
1.5
1.0
Na
1.05
2.6
2.1
1.6
Zn
1.9
1.4
0.9
Mn
2.0
1.5
1.0
K
0.75
2.7
2.2
1.7
Ag
1.6
1.1
0.6
Fe
1.7
1.2
0.7
Mg
6.2
2.3
1.8
1.3
Cd
1.8
1.3
0.8
Nb
1.9
1.4
0.9
Ca
4.0
2.5
2.0
1.5
Au
1.1
0.6
0.1
Cr
1.9
1.4
0.9
Ba
2.9
2.6
2.1
1.6
Hg
1.0
1.1
0.6
Lithophile element
Z2/r
Li
Dx
64
3 Structure and Property of Polar Group of Collector
there are obvious differences in terms of solubility products. That is, the property of metal influences the solubility product obviously. For fatty acids and sulfonates, however, the property of metal influences the solubility product slightly. In other words, the small solubility products of low molecular weight collector for sulfide mineral are affected by valence bond; the small solubility products of high molecular weight collector for oxides mineral are determined by the molecular weight of nonpolar groups, which is called “addition effect.” Figure 3.4 shows the relation between pL(solubility product constant pKsp) and electronegativity difference (Dx). It is shown in Fig. 3.4 that for the collector of sulfide mineral, pL varies obviously with Dx. For the collector of nonsulfide mineral, pL varies slightly with Dx. Therefore, the hydrocarbon chain for the collector of sulfide mineral is usually shorter and the minerals can also be selectively separated. For the collector of nonsulfide mineral, only if the hydrocarbon chain is longer enough, all minerals can be floted without selectivity.
3.5
Inductive Effect in Polar Group of Collector
There are interactions between atoms in molecule of flotation reagent. The interaction mainly includes the following: inductive effect, conjugative effect, and steric effect. Inductive effect and conjugative effect are first introduced in following sections. Steric effect will be expounded in Chap. 6.
3.5.1
Introduction of Inductive Effect
Because of different attracting electron capabilities of the bonding atoms, the electron cloud starts to shift and is further passed down by electrostatic attraction that is so-called inductive effect. As H atom as standard, providing that the atom X has larger capability of attracting electrons, the electron cloud turns toward X, and it is called negative effect (−I), on the contrary is positive (+I). The structural formula can be expressed as follows: R ! CH2 ! X Inductive effect can influence the physicochemical property of reagent. The inductive effect and conjugative effect often coexist. And the conjugative effect will be further discussed in Sect. 3.6.
3.5.2
Inductive Effect in Xanthate Molecule
Xanthate derivatives refer to alkyl thiocarbonates. Alkyl dithiocarbonates (also called xanthates) are most widely used in the derivatives. In addition, alkyl
3.5 Inductive Effect in Polar Group of Collector Fig. 3.4 a Relation between pL of metal salt of xanthate and Dx, b Relation between pL of metal salt of aerofloat and Dx, c Relation between pL of metal salt of palmitic acid and Dx
65
66
3 Structure and Property of Polar Group of Collector O (1)
R
O
C
S
H(Me)
S
H(Me)
S
H(Me)
S
(2)
R
O
C
S (3)
R
S
C
monothiocarbonates and trithiocarbonates are used in the flotation of sulfide ores. Their general formulae can be expressed as follows: In the three formulae above, inductive effect of the linking atoms toward the solidophilic atom (S) includes the following two aspects. The first one is O or S . The second one is –O← or –S←. Because the electronegativity of O is larger than that of S (xO = 3.5, xS = 2.5), the inductive effect of O in formula (1) is larger than that of S in formula (2). That is, the bond energy of S–H in formula (1) is weaker than that of S–H in formula (2). In other words, the solid-affinity of S atom in formula (1) is weaker than in formula (2). Flotation results show the collecting capability of alkyl monothiocarbonates is weaker than that of alkyl dithiocarbonates. Because the inductive effect of –S← in formula (3) is lower than that of –O← in formula (2), the collecting capability of alkyl trithiocarbonates is stronger than that of alkyl dithiocarbonates [6]. The solubility products of lead thiocarbonates are presented as follows: ðC2 H5 OCOSÞ2 Pb
L ¼ 1:5 108
ðC2 H5 OCSSÞ2 Pb
L ¼ 1:7 1017
The results also show that the bonding capabilities of alkyl monothiocarbonates are weaker than those of alkyl dithiocarbonates.
3.5.3
Inductive Effect in Thionocarbamates Molecule as Collector [9]
Polar group of thionocarbamates is as follows: S O
C
NH
3.5 Inductive Effect in Polar Group of Collector
67
A famous flotation reagent Z-200 belongs to thionocarbamates, and its molecular formula is as follows: S CH3 CH
O
C
CH2
NH
CH3
CH3
The influence of electron-donating group or electron-accepting group on the property of reagent can be explained according to inductive effect. Structure and property of some derivatives of reagent are listed in Table 3.14 [9]. It can be seen that the electron-accepting groups (or called negative inductive effect) including –COC6H5 and –C6H5 can weaken the electron density and the protophilia of S in C=S. Thionocarbamates can undergo the following transmutations at different pH: S R
O
C
S NHR'
R
O
C
NR'
It can be concluded that the introduction of electron-accepting groups can make H of S–H easier to dissociate, and the acidity becomes stronger for this reason. The introduction of electron-donating groups can make H of S–H harder to dissociate, and the acidity becomes weaker. Flotation results of copper sulfide ore with thionocarbamates are listed in Table 3.15. Because of the introduction of electron-accepting groups, the interaction of S atom and Fe ion decreases. But the interaction of Cu still retains, and the selectivity of collector is good. For example, using O–butyl–S–phenyl dithiocarbonate as collector, copper mineral flotation is selectively separated from pyrite. For the introduction of electron-donating groups, however, the activities of S atom toward both Fe and Cu ions remain the same. Therefore, the selectivity of collector becomes worse. For example, using butyl xanthate as collector, copper mineral flotation cannot be effectively selectively separated from pyrite.
3.5.4
Inductive Effect in Aerofloat Collector Molecule
Aerofloat refers to dialkyl dithiophosphate or monothiophosphate. The solubility product of lead aerofloat and the effect of aerofloat on the contact angle of galena are listed in Table 3.16 [10].
O-butyl-N-phenyl thiocarbamate
O-isopropyl-N-ethyl thiocarbamate
O-butyl-N-phenmethyl thiocarbamate
O-butyl-N-ethyl thiocarbamate
O-butyl-N-ethoxyl thiocarbamate
O-butyl-S-phenacyl dithiocarbamate
(2)
(3)
(4)
(5)
(6)
(7) C4H9
C4H9
C4H9
i
C4H9
C4H9
C4H9
O
O
O
C3H7
O
O
O
Structure
C
S
C
S
C
S
C
S
O
C
S
C
S
NH
NH
C6H5
C6H5
C6H5
C6H5
C2H4OH
C2H5
CH2C6H5
C
O
C
NH
NH
NH
C
S
NH
S
O
–
12.70
12.70
12.10
11.53
11.05
7.45
pKa
Where, r* (called Taft constant) is a criterion for inductive effect; kmax means the largest ultraviolet absorption wavelength
O-butyl-N-phenacyl thiocarbamate
(1)
Thiocarbamate
Table 3.14 Structure and property of thiocarbamate collectors
–
−0.10
−0.10
+0.22
–
+0.60
+2.34
r*
kmax
–
245
243
246
–
272
266
68 3 Structure and Property of Polar Group of Collector
3.5 Inductive Effect in Polar Group of Collector
69
Table 3.15 Flotation results of copper ore (pyrite 2.7 %) with thionocarbamates Thiocarbamate
Dosage (g/t)
Cu (%) of concentrate
Recovery of copper (%)
(1) (2) (7) (8)
35 24 38 25
26.40 25.10 30.82 18.02
82.80 80.56 80.87 83.00
Table 3.16 Solubility product of lead aerofloat and the effect of aerofloat on contact angle of galena
Aerofloat
(1)
Solubility product of lead aerofloat
Contact angle of galena (1 mM/L solution) Ethyl Butyl
Soluble
45°
53
5.9 10−5
51°
67
2.2 10−10
69°
86
O
C2H5O P
O
C2H5O
K
(2)
S
C2H5O P
O
C2H5O
K
(3) S
C2H5O P C2H5O
S
K
As shown in Table 3.16, comparing reagent (1) with reagent (2), the solidophilic atom and the core atom are the same. Because the inductive effect of the linking atom (═S and ═O) is different, the effect of reagent on the contact angle of galena varies. The difference of contact angle is Dh° = 6°. Comparing reagent (2) with reagent (3), the linking atom is the same. Because the inductive effect of the solidophilic atoms (S and O) is different, the effect of reagent on the contact angle of galena also varies. The difference of contact angle is Dh° = 18°. Comparing reagent (1) with reagent (3), the effect of reagent on the contact angle of galena varies much more. The difference of contact angle is Dh° = 24°.
70
3.5.5
3 Structure and Property of Polar Group of Collector
Comparison of Inductive Effect in Xanthate, Dithiocarbamate, and Aerofloat
Comparison of inductive effect in three types of flotation reagents (xanthate, dithiocarbamate, and aerofloat) is discussed in this section. These reagents have the same solidophilic atoms, but have different core or linking atoms. The condensed formulas of reagents are given as follows: (1)
Xanthate
S R
O
R
O
C S
(2)
H (Fe)
Aerofloat
S P
(3)
R
O
R
O
S
O
Dithiocarbamate
S N
R
H (Fe)
P S
H (Fe)
Comparing xanthate with aerofloat, the first difference lies in the core atoms. The core atom of xanthate is C, but aerofloat atom is P. The electronegativity of P ðxP ¼ 2:1Þ is smaller than that of C ðxC ¼ 2:5Þ. Therefore, the inductive effect of P in aerofloat is smaller than that of C in xanthate. The second difference between xanthate and aerofloat lies in the linking atoms. There are two –O– in aerofloat. But there is only one –O– in xanthate. The inductive effect of –O– in aerofloat is bigger than that of –O– in xanthate. The third difference between xanthate and aerofloat lies in the R group. There are two R– in aerofloat, and there is only one R– in xanthate. The positive inductive effect of two R– in aerofloat is bigger than that of one R– in xanthate. But because of the long distance between R– and –SH, the inductive effect of polar group in both xanthate and aerofloat is influenced slightly by R–. It can be concluded that the mineral-philic capability of S in aerofloat is smaller than that of S atom in xanthate. Although the molecular weight of aerofloat is higher than that of xanthate, the solubility of metal salt of aerofloat remains bigger than that metal salt of xanthate. That is why the collecting capability of aerofloat is lower than that of xanthate. Comparing xanthate with dithiocarbamate, the first difference lies in the linking atoms. It is O atom in xanthate molecule, but in dithiocarbamate is N. The electronegativity of N in aerofloat is smaller than that of O in xanthate. Therefore, the negative inductive effect of N in aerofloat is smaller than that of O in xanthate. The second difference between xanthate and dithiocarbamate lies in the R–. There are two R– linked with the N in aerofloat. But there is only one R–linked with O in xanthate. The positive inductive effect of R– in aerofloat is bigger than that of R– in xanthate.
3.5 Inductive Effect in Polar Group of Collector Table 3.17 Solubility products of silver salts of sulfide collectors
71
Nonpolar group
Silver alkyl thiocarbonate
Ethyl Propyl Butyl Amyl
4.4 2.1 4.2 1.8
10−19 10−19 10−20 10−20
Silver dialkyl dithiophosphate 1.2 6.5 5.2 5.1
Silver dialkyl dithiocarbamate
10−16 10−18 10−19 10−20
4.2 3.7 5.3 9.4
10−21 10−22 10−23 10−24
It can be concluded that the mineral-philic capability of S in dithiocarbamate is larger than that of S in xanthate. The solubility of metal salt of dithiocarbamate is smaller than that of metal salt of xanthate. Comparison of solubility products between xanthate and dithiocarbamate is listed in Table 3.17. The results show that the collecting capability and the selectivity of dithiocarbamate are better than those of xanthate.
3.5.6
Inductive Effect in Collector of Nonsulfide Minerals
The common collectors for nonsulfide minerals include alkyl sulfonates, alkyl phosphonic acids, alkyl arsonic acids, fatty acids, and alkyl hydroxamic acids. Their characteristics such as structure, dissociation capability, and solubility product value are as follows [2, 4]: Alkyl sulfonate acid structure
Alkyl phosphonic acid
O R
S
Alkyl arsonic acid
O OH
O
R
P OH
or
Fatty acid
O
O OH
R
As
OH
R
C
S
O OH
C NH
R
O
OH R
OH
O
pKa pL of calcium salt pL of ferric salt
*1.5 7–9
2.6–2.9 –
OH
or
O R
Alkyl hydroxamic acid
3.7–4.7 –
*5 6-11
*9 –
9–11
6–11
*15
C
N
OH
72
3 Structure and Property of Polar Group of Collector
As a common tendency, the dissociation capacity of organic acids and the ionic bonding of their metal salts will be dependent on the increase in the number of O in polar group. The collector with low degree of dissociation, by contrast, owns a stronger protophilia, which results in the production of strong covalent bond. It can be concluded that when the dissociation constant Ka of collector is comparatively large, the electrostatic force of electric double layer and the ion adsorption easily take place between collector and mineral surface. When the Ka of collector is comparatively small, chemical adsorption easily takes place between collector and mineral surface. Protophilia is also expressed by the protonation constant in coordination chemistry. The expression of protonation constant can be given as follows: 1 Ka Kb H K ¼ KW KH ¼
or
where Ka refers to the dissociation constant of acid; Kb refers to the dissociation constant of alkali; and Kw refers to the ion product of water. In general, the surface electric property of mineral has an obvious influence on the collecting behavior of alkyl sulfonates, but the chemical reactivity has an unconspicuous influence. For fatty acids, the chemical reactivity of mineral has an obvious influence on the collecting behavior, and the surface electric property of mineral also plays subordinate sometimes. Owning the same nonpolar groups, the collecting property of sulfonate is low relatively. For example, sulfonates with 10 carbon atoms are usually used as frother instead of collector. But fatty acids with 10 carbon atoms are usually used as collector. Comparison of solubility products of calcium alkyl sulfonate and calcium fatty acid is listed in Table 3.18 [7, 11]. As shown in Table 3.18, for reagents with same long-chain hydrocarbon, the solubility product of calcium alkyl sulfonate is larger than that of calcium fatty acid. When the nonpolar group is benzyl or the alkyl of C6–C8, phosphonic acid and arsonic acid owns good collecting capability, respectively. The solubility product of
Table 3.18 Solubility products of calcium salts of fatty acids and alkyl sulfonates
The number of C atoms in alkyl
Solubility product (RCOO)2Ca (RSO3)2Ca
8 9 10 11 12 14 16 18
6.2 7.5 8.5 2.8 4.7 2.9 1.6 3.6
10−9 10−19 10−19 10−19 10−11 10−14 10−16 10−15
2.7 8.0 3.8 2.2 8.0 1.0 1.6 4.0
10−4 10−9 10−10 10−11 10−13 10−15 10−16 10−18
3.5 Inductive Effect in Polar Group of Collector
73
benzyl arsonic acid (10−9–10−11) is small relatively. It shows the chemical adsorption on mineral surface has an obvious influence on their collecting behavior. For reagent molecule with many polar groups, take chloroacid for example: R
COOH
CH Cl
Because of the intense inductive effect of Cl, the degree of dissociation of carboxyl and the adsorption of electrostatic force in electric double layer all will be larger. Meantime, collector is easy to dissolve. Facts have shown that the saturated fatty acids with long hydrocarbon chain are solid at normal temperatures, but their chloroacid is liquid. Therefore, chloroacid is able to be used in the mineral pulp of low temperature. Various second groups are introduced to a-position of hexadecyl carboxylic acid, for example: R
CH
COOH
X
where X refers to –OH, –SH, –Br, –SO3H, –NH2, –Cl, and so on. The effects of various second groups on the dissociation constant of hexadecyl carboxylic acid are shown in Table 3.19. Table 3.19 shows the change in dissociation constant of the first group (Ka1) is consistent with the electron-accepting capability of the second group. Because of the strong dissociation capability of SO3 has the positive inductive effect on –COOH and leads to the decrease of dissociation of carboxyl. The effects of various second groups on the flotation behavior of carboxylic acid are shown in Table 3.20. Flotation results show that the flotation performance of reagent is improved with the introduction of various second groups in most cases. The alkalinity of amines depends on the inductive effect of the alkyl which is linked with the N atom of polar group. Therefore, the alkalinity of primary amine
Table 3.19 Effects of various second groups on the dissociation constant of hexadecyl carboxylic acid
Sulfocarboxylic acid Carboxylic acid Hydroxycarboxylic acid Sulfydrylcarboxylic acid Bromocarboxylic acid Chlorcarboxylic acid Amidocarboxylic acid
Ka1 (COOH)
pKa1 (COOH)
Ka2 (second group)
pKa2 (second group)
7.08 1.75 1.48
*6.0 4.75 3.83
3.78 – –
– – –
2.1
3.68
4.0
10.40
1.26
2.90
–
–
1.4
2.86
–
–
4.47
2.35
–
9.78
150
100 20.0
Calcite
Barite Hematite
0.382 0.066
0.493
mol/t
0.082 0.410
25.0 125
wolframite Cassiterite
Oleate
g/t
Mineral
mol/t
17.96
– 0.018
– 5.0
0.144 7.184
5000
40.0 2000
g/t
Palmitate
– 5– 10
150
25.0 400
g/t
– 0.014– 0.025
0.421
0.070 1.121
mol/t
Bromopalmitate g/t
– 5–10
50.0
25.0 150.0
mol/t
– 0.015– 0.03
1.151
0.076 4.450
50.0 120–150
150 No flotability 2500 0.131 0.32–0.39
0.39 No flotability 6.58
Sulfydrylpalmitate Hydroxypalmitate g/t mol/t
Table 3.20 Effects of various second groups on the flotation behavior of hexadecyl carboxylic acid
Bad flotability – 700
900 2000
Bad flotability – 2.04
2.63 5.84
Sulfopalmitate Chlorpalmitate g/t mol/t
g/t
– 20
250
20 250
mol/t
– 0.070
0.880
0.070 0.880
74 3 Structure and Property of Polar Group of Collector
3.5 Inductive Effect in Polar Group of Collector
75
with one alkyl group is larger than that of secondary amine with two alkyl groups. However, the alkalinity of tertiary amine with one alkyl group is smaller than that of tertiary amine because of steric hindrance. Quaternary amine belongs to strong base. Alkyl, as electron-donating group, plays a part in the positive inductive effect. On the contrary, phenyl and ethylene group, as electrophilic groups, play a part in the negative inductive effect. The explanation can be given as follows: the C atom of alkyl is sp3 hybridization; the C atom of phenyl and ethylene group is sp2 hybridization; the electron cloud of s-hybrid orbital is much closer to atomic core than that of p-hybrid orbital; because of more s-hybrid orbitals, the electron cloud of sp2 is much closer to atomic core than that of sp3; the electronegativity of sp2 is larger than that of sp3. Therefore, the pKb of fatty amine and phenylamine is about 6 and 9.4, respectively. And the pKb of pyridine is 8.8. The conclusion above can be confirmed by the flotation of quartz with various amines. According to the results of Schubert, the collecting performances of various amines are given as follows: C n > C n '''
>
C n > C n ' > Cn '' > C n
where the above symbols are as follows: Cn Cn''
CnH2n+1NH3Cl Cn'
CnH2n+1(CH3)NH2Cl
,
CnH2n+1(CH3)2NHCl Cn''' ,
CnH2n+1(CH3)3NCl CH2
CH2
CH2
CH2
C nH 2n+1N
Cn
, ,
O Cl
,
Cn
CnH2n+1 N
Br
and n are, respectively, 12 and 18.
3.6 3.6.1
Conjugative Effect in Polar Group of Collector Introduction of Conjugative Effect
Conjugative effect is caused by the conjugated p bond which includes p–p conjugation, p–p conjugation, and r–p conjugation. The significance of these types of p bonds is briefly introduced by the following.
76
3 Structure and Property of Polar Group of Collector
(1) p–p conjugation Compound is comprised of alternated single and double bonds, such as 1, 3-butadiene. Four carbon atoms of 1, 3-butadiene are linked with r bond of sp2 hybrid orbitals. There is one p electron on each carbon atom and those p electrons could form p bonds in C1C2, C3C4 as perpendicular to r bond. It can be expressed as follows:
The p–p conjugation is caused by two p bonds. It leads to the asymmetry of distribution of electron cloud density in the conjugated double bond of the asymmetry of the structure. The effect of p–p conjugation on electron cloud density is indicated by winding arrow given as follows:
(2) p–p conjugation The p–p conjugation of p electron and adjacent p electron occurs when the atoms have lone pair electrons near the double bond. For instance, chloroethylene (CH2=CH–Cl), nitrobenzene (C6H5NO2), aminoethylene (CH2=CH–NH2), and amide (R–CO–NH2) contain p–p conjugation bond. Taking carboxylic acid for example, the lone pair electrons of O in carboxyl conjugate with p bond electron of the O in carbonyl. The p–p conjugation is expressed as follows: O R C
O
H
The p–p conjugation makes electrons of the O in hydroxyl disperse into molecule and weakens the O–H bond. Meantime, it results in that the H atom is easy to dissociate. (3) r–p conjugation If the effect of p bond electron of O in carbonyl acts on the C atom, the electron cloud of r bond inclines to the O atom. The effect leads to the increase of polarity and the improvement of reactivity of the C atom. That is so-called r–p conjugation. The r–p conjugation of ketone is expressed as follows:
3.6 Conjugative Effect in Polar Group of Collector R
77
O
C R
Except r–p conjugation, there is r–r conjugation, p–r conjugation, p–p conjugation, and so on. But they are not expounded in this section. The type of p bond is usually expressed by the following: Pm n where m refers to the number of electrons in p bond; n refers to the number of atoms in p bond. In addition, the interaction between alkyl group and p bond in r–p conjugation is called super conjugation, symbolized as P.
3.6.2
Conjugative Effect in Xanthate Molecule
The C atom in xanthate molecule is bonded with –OR, –SH, and ═S via r bond of sp2 hybrid orbital. And there is also p bond in the C=S bond. Because the principal quantum numbers and the orbital energies of C and S atoms are different, the C–S bond is weaker than C–O bond in carbonic acid. Compared with carbonic acid, therefore, thiocarbonic acid is much more instable. The lone pair electron p of O and S atoms which are linked with C via single bond conjugates with r electron of C═S bond to form P64 type of p–p conjugated system. Because of the occurrence of electronic delocalization, the S–H bond is weakened and further dissociated into anion as follows:
.. O
R
S -
S C
..
R
S
O
+H+
C
H
S
Due to the electronic delocalization, the negative charges of sulfhydryl are apportioned equally to disulfide atoms. Therefore, the capability of xanthate anion is improved. That is, the anion of xanthate is equivalent to a P64 type conjugated system which is comprised of the lone pair electron of O, the single electron of C, S, S, and a negative charge of anion. Because the pKa is about 3–5, short-chain dithiocarbonic acids can keep enough capability in alkaline medium. When xanthate anion reacts with heavy metal ion, four-membered chelate forms via covalent coordination bond. The two S atoms have the same effect on the reaction. The structure of divalent metal ion compound can be seen as follows. S R
O
S Me
C S
C S
O
R
78
3 Structure and Property of Polar Group of Collector
The conjugate action in aerofloat is similar with that in xanthate. Conjugate action in aerofloat belongs to P85 type conjugated system. Research shows the bonding atoms of dithiocarbamate (R2NCSSH) is SS but not SN. Conjugate action in the dithiocarbamate chelates is also P64 -type of p–p conjugated system. Inductive effects in three thiocarbonate derivatives were studied in Sect. 3.5. Conjugative effect of the bonded atoms toward the bonding atom (S) is expounded as follows. (1)
S R
O
(2)
C
S
H
S
H
S
H
O R
O
(3)
C S
R
S
C
According to structural theory of organic chemistry, the negative conjugative effect (–C) increases with an increase in the electronegativity of atom of the same period; the positive conjugative effect (+C) decreases with an increase in the electronegativity of atom of the same period; when the orbital energy of atom is closer to another one of the same group, the positive conjugative effect (+C) is more obvious. Compare formula (1) with formula (2), because the negative conjugative effect of C=O in formula (2) is larger than that of C=S in formula (1). The bonding capability of S–H in formula (2) is weaker than that of S–H in formula (1). Compare formula (2) with formula (3), because the positive conjugative effect of R–O in formula (2) is smaller than that of R–S in formula (3), and the bonding capability of S–H in formula (2) is weaker than that of S–H in formula (3). According to flotation results, the collecting performance of trithiocarbonates is stronger than that of thiocarbonates. It indicates the direction of conjugative effect is same with that of inductive effect. Comparing R2NCSSH with ROCSSH, the positive conjugative effect and the negative conjugative effect of C=S and C–SH in R2NCSSH are same with those of C=S and C–SH in ROCSSH. Meantime, the direction of conjugative effects is same with that of inductive effect. However, the positive conjugative effect of R2N in R2NCSSH is stronger than that of R–O in ROCSSH. The direction of positive conjugative effect is same with that of inductive effect. Therefore, the bonding capability of S atom in R2NCSSH is stronger than that of S atom in ROCSSH.
3.6 Conjugative Effect in Polar Group of Collector
3.6.3
79
Conjugative Effect in Aromatic Collector
(1) Comparison of two kinds of benzomercaptan collectors The structures of benzothiazolemercaptan (a) and benzoimidazolemercaptan (b) are presented as follows: N
N C
S
C
H
S
H
N H
S
(a)
(b)
The conjugative effect of –N═ in benzothiazolemercaptan(a) is same with that of – N═ in benzimidazolemercaptan(b). However, the positive conjugative effect of – NH– in molecule (b) is stronger than that of –S– in (a). For benzothiazolemercaptan, flotation results show that it is mainly used as the collector for sulfide ores. Meantime, it has good collecting capability in the flotation of pyrite, pyrite-bearing gold, and lead oxide ore. The benzimidazolemercaptan (b) is used as the collector of copper sulfide and oxide ore, and it can react with nonferrous ion to form insoluble compound. (2) Comparison of two kinds of thiophenol collectors Various thiophenols are used as collector in the flotation of sulfide minerals. The values of pKa and solubility products of various silver salts of thiophenol are given as follows: Thiophenol
p-methylthiophenol
m-methylthiophenol
o-xylenethiophenol
pKa
6.61
6.82
6.66
6.99
Benzyl thiophenol 9.4
LAgA
2.4 10−21
2.8 10−22
2.0 10−21
2.3 10−21
3.9 10−23
The structures of p-methylthiophenol and benzyl thiophenol are presented as follows: CH3
..
SH
CH2
SH
As seen from the data and formulas above, the molecular weight of p-methylthiophenol is same with that of benzyl thiophenol. The S atom in p-methylthiophenol is directly linked with benzyl to form p–p conjugation. But the S atom in benzyl thiophenol is indirectly linked to benzyl through –CH2–. There is no conjugated system between S atom and benzyl. Therefore, benzyl thiophenol has a smaller acidity and a stronger bonding capability toward metal ion.
80
3 Structure and Property of Polar Group of Collector
For thiophenol and methylthiophenol, because of the positive conjugative effect and the positive inductive effect, methylthiophenol has a smaller acidity and a stronger bonding capability. For three isomerism methylthiophenols, because the conjugative effect of p-methylthiophenol is stronger than that of m-methylthiophenol, the pKa of p-methylthiophenol is larger than that of m-methylthiophenol. Besides for the conjugative effect, there also exists the effect of steric size in o-xylenethiophenol. Thus, the pKa of o-xylenethiophenol is larger than other two isomerism methylthiophenols. (3) Comparison of several thiophenol derivative collectors For collector (a) and collector (b), –OH and –NH2 produce the positive conjugative effect, and the bonding capability of S atom is improved. For collector (c) and collector (d), –NO2 and –COOH produce the negative conjugative effect, and the bonding capability of S atom decreases. The structures of several thiophenol derivative collectors are presented as follows: SH
..
OH
(a)
SH
SH
SH
NH2
NO2
COOH
(b)
(c)
(d)
It is reported that the collecting capability of the molecule (b) and naphthaline is better than common thiophenol. The reason lies in the introduction of –NH2. Carboxyl thiophenol is effectively used for the flotation of galena, but not very strong for the flotation of chalcopyrite and pyrite. That is, the introduction of – COOH weakens the collecting capability of thiophenol. (4) Comparison of arsonic acid collectors For methylbenzene arsonic acid and benzyl arsonic acid, because of the conjugation effect between polar group and methylbenzene, acidity of methylbenzene arsonic acid is stronger than that of benzyl arsonic acid. The structures of methylbenzene arsonic acid and benzyl arsonic acid are presented as follows:
CH3
pKa1
3.70
CH2
AsO3H2
AsO3H2
4.43
For m-methylbenzene arsonic acid and o-methylbenzene arsonic acid, the values of pKa of them are the same. There may be another reason.
3.7 Polar Group of Coordinating Collector
3.7
81
Polar Group of Coordinating Collector
In recent years, various complexing agents are used as the effective flotation reagents. For example, 8-hydroxylquiloninato is employed in the flotation of formanite, wolframite, and lead zinc ore [12, 13]; cupferron is employed in the flotation of formanite, wolframite, and copper ore; dimethylglyoxime is used to flotate nickel ore; hydroxamic acid is used in the flotation of iron ore, copper oxide ore, and rare earth ores. Correspondingly, complex chemistry promotes the development of flotation reagent.
3.7.1
Major Features of Coordinating Collector
According to the number of the bonding atoms, coordinating agents are further divided into unit coordinating agent and multiunit coordinating agent (or called chelator). Chelator can react with metal ion to form ring-shaped compound. Taking 8-hydroxylquiloninato for example, the reaction product of 8-hydroxylquiloninato and zinc ion is presented as follows: O
N
Zn
N
O
The bonding atoms of chelator include SS, NN, OO, SN, SO, and NO. Meantime, the bonding atoms are also comprised of at least two atoms. Unit coordinating agent, such as fatty amines, cannot form ring-shaped compound. The reason is that there is only one N atom in the polar group. Usually, the stability of chelator is better than that of common coordinating agent. Although the molecular weight of chelator is not very high, chelator can react with metal ion to form the product with low solubility. The product of unit coordinating agent is water miscible coordination complex in general. Only when the molecular weight is high relatively, the product of unit coordinating agent becomes insoluble. The widely used flotation reagents such as xanthate, aerofloat, and fatty acids also belong to coordinating agent. Because of the existence of P64 type of p–pconjugated system in carboxylic acid molecule, the bond length of carbonyl in carboxylic is longer than that of common C=O, and the bond length of hydroxy in carboxylic is shorter than that of common C–O. For example, the conjugative structure of formic acid is given as follows:
82
3 Structure and Property of Polar Group of Collector
. 1.08A H
122o
. 1.22A
C
125o
O
.
o
107
0.96A
. 1.41A
O
H
The bond length of two C–O in carboxylic ion are both 1.27 Å, and the bond angle of O–C–O is 124º. When formic acid reacts with metal ion, the two O atoms both play a role in the bonding atom. The same happens to xanthate, aerofloat, and amino dithioformicates. For example, xanthate reacts with metal ion to form coordinate product. The product contains a four-membered ring which is comprised of S, S, C, and metal ion. Providing the metal is divalent element, the product is called as two-/ four-membered ring chelator.
3.7.2
Structure and Property of Polar Group of Coordinating Collector
(1) Classification and property of the bonding atom For divalent metal, the valence band between the bonding atom and metal ion in coordinating collector can be expressed as follows:
O
O
O
N
N
N
O
N
S
O
N
S
S
N
O
S
S
S M
M
M
M
M
M O
N
O
N
S
S
(Electrovalent) lectrovalent) (E (Electrovalent (Electrovalent (Electrovalent (C (Covalent ovalent)) (C (Covalent ovalent)) and covalent covalent)) and covalent covalent)) and covalent covalent))
According to the coordination number and the steric structure of bond, classifications of valence bond are as follows: (1) Electrovalent bond The electron-donating atoms are with negative charge, so the atoms with the same charge push away from each other and four/six groups take the metal ion as the center and form a tetrahedron/octahedron. (2) Covalent bond The oriented distribution of groups depends on the angle of the bonding orbit. The most common distribution of groups includes tetrahedron of sp3 hybrid
3.7 Polar Group of Coordinating Collector
83
orbital, octahedron of d2sp3 hybrid orbital, and square planar structure of dsp2 hybrid orbital. The mineral elements which are able to form tetrahedron by coordinating with collector include Be, Si, Cu, Zn, As, Sn, Pt, Cd, and Hg. The mineral elements are able to form octahedron by coordinating with collector include Al, Cr, Mn, Fe, Co, Sn, Pb, Zn, and As. According to the classification of the bonding atom, the application field and the selectivity of coordinating collector can be inferred. If the coordination bond is electrovalent one, the coordinating collector is effective in the flotation of those minerals which are comprised of lithophile elements. If the coordination bond is covalent one, the coordinating collector is effective in the flotation of those minerals which are comprised of chalcophile elements. The properties of aerofloat with different boding atoms are listed in Table 3.21 [10]. The results in Table 3.21 show that for chalcophile metal elements such as Pb and Cu, the reaction products of SS bond types of coordinating collectors have small solubility products. Meantime, sulfide minerals acquire a large relatively contact angle. For lithophile elements and siderophile elements such as Ca and Fe, the reaction products of OO bond types of coordinating collectors also have small solubility products. Sulfide minerals acquire a large relatively contact angle, too. (2) Size of ring The intrinsic bond angle between atoms and interior angle decides the stability of polycyclic structure. In general, four-membered, five-membered, and six-membered rings are stable relatively. For the ring containing saturated bonds, five-membered ring is more stable. For the ring containing two or more double bonds, six-membered ring is more stable. For example, xanthate, aerofloat, and carboxylic acids are constructed from four-membered ring; 8-hydroxylquiloninato consists of five-membered ring; hydroxamic acids are comprised of four-/five-membered ring. A larger ring structure is given as follows: CH2
CH2
NH2
CH2
CH2
NH2
NH2
CH2
CH2
CH2
CH2
Cu CH2
CH2
CH2
NH2 NH2
NH2
CH2
CH2
CH2
NH2
CH2
CH2
CH2
Cu CH2
CH2
CH2
NH2
If the ring is too large, the structure is also instable. Therefore, two bonding atoms of polar group in chelant cannot directly contact with each other. And it is appropriate that the members of the ring are less six. (3) Quantity of ring The following picture shows several chelants with different quantities of ring. As seen from the picture, the chelant which is produced by the reaction of
(RO)2PSSK h˚ (ethyl)
69 69 36 44
Mineral
PbS CuFeS2 FeS2 CaCO3
86 60 54 40
h˚ (butyl) 51 68 27 50
2.2 10−10 9.6 10−10 – Soluble 67 63 40 38
(RO)2PSOK h˚ (ethyl) h˚ (butyl)
Ksp 5.9 10−5 5.4 10−10 – 6.5
Ksp 45 55 46 53
53 61 56 39
(RO)2POOK h˚ (ethyl) h˚ (butyl)
Table 3.21 Properties of aerofloats with different boding atoms (reagent concentration 0.001 g/L; pH = 5.6–5.8)
– – – 8.4 10−10
Ksp
84 3 Structure and Property of Polar Group of Collector
3.7 Polar Group of Coordinating Collector
85
cyclo-calcichrome and calcium ion is comprised of six-membered rings. Researches show that the stability of chelant increases with an increase in the quantity of ring.
O
O Cu
HC
N
N
CH3
CH3
CH
O
O Cu HC
N
N
CH2
CH2
CH
O
O Cu
N
N
HC
CH
SO3H
SO3H
N
OH
N SO3H
HO3S
N N HO
HO3S
Ca
OH N
N
SO3H
86
3 Structure and Property of Polar Group of Collector
(4) Effect of the second polar group Taking the reaction product of salicylaldehyde aniline and copper ion for an example, the effect of the second polar group on the stability of chelant is as follows: O
O
Cu HC
A1
–NO2
–SO3Na
E1/2
0.03
0.09
N
N
A
A
0.10
CH
–H
–CH3
–OH
–OCH3
0.12
0.15
0.17
0.21
A is –OCH3
O Cu1/2 N
HC
O CH3
A is –NO2
O Cu1/2 N
HC
N O
O
3.7 Polar Group of Coordinating Collector
87
In general, if the second polar group is electron-donating group, the electron density and the bonding capability of the bonding atom in the first group are both improved. If the second polar group is electron-accepting group, the electron density and the bonding capability of the bonding atom in the first group both decrease. (5) Steric size of polar group Each polar group appears to have steric size. The effect of steric size of polar group on the property of collector will be specially expounded in Chap. 6. However, it should be pointed out that the coordinating collector only reacts with metal ion of a given size. For instance, the steric size of hydroximic is 2.5 Å. The structure of hydroximic is as follows: NOH C
C
OH
The coordinating collector with hydroximic only reacts with the transition metal ions of which the radius is less than 0.8 Å. If the radius of metal ions increases, the product becomes instable. Taking cyclo-calcichrome as another example, the cage structure of polar group limits the size of the entered ion. By comparing the radius of alkaline earth metals, the radius of Ca2+ is smallest among them. That is why cyclo-calcichrome has special selectivity toward Ca2+.
Radius (Å)
3.7.3
Ca2+ 0.99
Sr2+ 1.13
Ba2+ 1.13
Functional Mechanism of the Coordinating Collector
When xanthate is used as collector in the mineral flotation of covellite and galena, the recovery of minerals is concerned with the solution pH; the yields of copper xanthate and lead xanthate which are measured by means of UV adsorption spectrum method are also related to the solution pH. By comparison, the changing trends of the flotation recovery of minerals are consistent with those of the yields of products of copper xanthate and lead xanthate. The results show that chemical adsorption and surface reaction have an influence on the occurrence of flotation. From the flotation of wolframite with 8-hydroxylquiloninato as collector, it can also be found that there is significant correlation between the flotation behavior of wolframite and the formation conditions of manganese chelate [12]. Meantime, Rinelli [13] also proposed that the flotation of smithsonite and cerussite depends on the chemical adsorption of 8-hydroxylquiloninato.
88
3 Structure and Property of Polar Group of Collector
In recent years, there are some reports on the interaction between alkylhydroxamic acid and oxide minerals. One opinion on the interaction is based upon the adsorption of the OO bonding atoms and mineral [14, 15]. The adsorption can be expressed as follows: SixOy
SixOy +OH- + HO
Cu
Mineral surface
Fe
OH
HO
C
C
O
N
R + H2O
SixOy
Solution
+
O Cu
R
N
O
SixOy
C
Mineral surface
Fe
R
O
C
O
N
Solution R + H2O
N
O
Solution
Mineral surface
Mineral surface
Solution
Some people pointed out that the interaction lies in the adsorption of the NO bonding atoms and mineral. According to the measured results, the solubility of Ti chelate and Fe chelate is 2.8 10−5 and 3 10−5, respectively. The structures of Fe and Ti chelates can be expressed as follows: OH
+
+
OH
O
N
N
R
O
Ti
C
C
Fe
C
R
R N
O
O OH
Barbery [8] had researched the interaction between malachite and salicylaldoxime. It appears the adsorption bands at 1195 and 915 cm−1 in the FTIR. The results indicate the formation of Cu bissalicylaldoxime. The reaction process and pKa can be given as follows: Cu2 þ þ L CuL þ CuL þ þ L CuL2
K1 ¼ 1012 K1 ¼ 1022
where the structure of L is presented as follows: OH CH
N
OH
In order that the reagent is prior to bond with heavy metal ions (Cu2+, Pb2+, and Zn ) but not with gangue minerals (Ca2+, Mg2+), the precondition of flotation separation lies in that there is a certain gap between the stability constants of the 2+
3.7 Polar Group of Coordinating Collector
89
above two types of metals. The gap of the stability constants of the above two types of metals can be expressed as follows: Dlog K ¼ 5 Meantime, it can be found that the bonding of H+ and chelant anion is consistent with that of metal cation and chelant anion. The acid dissociation constant pKa of the coordinating collector parallels to the stability y constant pKs of chelant. Therefore, the pKa of the coordinating collector is often used to assess the bonding capability of the coordinating collector.
3.7.4
Classification of the Coordinating Collector
The categories of the coordinating collectors according to their structural features are listed in Table 3.22 [8, 16, 17].
Table 3.22 Categories of the coordinating collectors The bonding atom
Polar group
The bonded metal atom
Application example
N
–N═
Siderophile and chalcophile elements
Fatty amine, alkyl pyridine: oxide collector
Ni, Pd
Nickel reagent: floating nickel sulfide and copper sulfide
Zn
Diphenylguanidine: floating nickel and zinc sulfide
Cu, Fe
Cupferron: floating copper ore;
Co, Zr, U
a-nitroso-b-naphthol: floating wolframite
Co, Zr, Cd, Ta
8-oxyquinoline: floating wolframite
Fe, Cd, Co, Ni, rare earth metals
Hydroxamic acid: floating iron oxide ore, copper oxide ore, and rare earth minerals
Most metals
Amino acid: floating iron oxide ore and wolframite
Cu, Pb, and so on, the chalcophile and most siderophile elements
Xanthate: sulfide collector
NN HO
C
C
N
N
OH
C
NH
HN
NH
NO
N
OH
N
O
C
C OH
OH
C
C N
OH C O
C NOH COOH
n(H2C)
NH2
SS
S O
C SH
(continued)
90
3 Structure and Property of Polar Group of Collector
Table 3.22 (continued) The bonding atom
Polar group
The bonded metal atom
Application example
Cu, Pb
Aerofloat: sulfide collector
Cu, Pb, Cd, Hg, Bi and Ti and so on
Dithiocarbamate: sulfide collector
Cu, Cd, Hg, Ti, Pb, Bi
Hydroxyl benzothiazole: sulfide collector
Sn, Bi, Mo, W, Cu
Dithiol: sulfide collector
Cu
Dixanthogen: floating deposited copper
SH
Hg, Ag, Cu, Pb, Bi, Cd, As, Sb, Sn
Sulfydryl benzimidazole: oxidized nonferrous metal ore
S
Hg, Ag, Cu, Pb, Bi, Cd, As, Sb, Sn
Thiocarbamate: sulfide collector
Bi, Rm, Os and so on
2-N-phenyl thiourea, sulfide minerals, Dithizon, sulfide minerals
Cu, Pb, Bi, Cd, Fe, U, As, Sb, Sn
Aminothiophenol, sulfide minerals
Cu, Pb, Bi, Cd, Fe, U, As, Sb, Sn
Hydroxyl thiophenol: sulfide collector
Au, Pb, Bi, Cd, Fe, U, As, Sb, Sn
Carboxyl thiophenol: sulfide collector
Alkaline earth metals heavy metals
Fatty acid soap: sulfide collector
Zr, Hf, Nb, Ta, Ti, Sn
p-methyl phenylene-arsonic acid: collecting cassiterite
Zr, Hf, Nb, Ta, Ti, Sa
Alkyl phosphoric acid: collecting cassiterite
Ti, Zr, Th
Alizarine: collecting cassiterite
S
O P
SH
O
S C
N
SH S C
SH
N C
C
SH
SH
C
S
S
SN
HN
C
HN
N
SO
C
C
N
C
C
HN
SN
C
C
HO
SH C
C
SH
C HO
O O
OO C
OH
OH
1
O
As OH
OH
1
O
P OH
OH O
References
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
D.W. Fuerstenau et al., in XIIth IMPC (1977), p. 6 S.H. Wrobel, Min. Min. Eng. 6, 35 (1970) S.H. Wrobel, Min. Min. Eng. 6, 43 (1970) G.X. Xu, Material Structure (People Education Press), p. 92 Gackt: Quantum Chemistry, p. 568 du Rietz: Progress in Mineral Pressing 1958 p. 417. XI. IMPC, 1957, p. 375 M.C. Ferstenau et al., Flotation A. M. Gaudin Memorial Volume, vol. I, (1976), p. 148 C. Barbery, J.L. Cecile, in XIIth IMPC, vol. II, (1977), p. 19 O.S. Bogdanov et al., in XIIth IMPC (1977), p. 2 K. Sakada, D. Nanjou, K. Yamasaki, Min. Soc. Japan 80, 992 (1970) M.C. Fuerstenau, Trans. AIME 238, 153 (1967) A.M. Gaudin, D.W. Fuerstenau, Trans. AIME 202, 958 (1955) G. Rinelli, A.M. Marabini, in X th IMPC (1973), p. 20 H.M. Fetson, M.C. Fuerstenau, Trans. AIME 232, 288 (1965) M.C. Fuerstenau, J.D. Miller, Trans. AIME 238, 200 (1967) J.F. Flagg: Organic Reagents Beshall: Theory and Practice of Emulsion. Science Press. pp. 164, 169
91
Chapter 4
Structure and Property of Nonpolar Group of Collector
According to the different polar group and collectors used, the structures of nonpolar groups are diverse. Therefore, the relation between structure and property of nonpolar group of collector is expounded in this chapter. The categories of nonpolar groups of collector according to their structural features are listed in Table 4.1.
4.1
Role of Nonpolar Group of Collector
The effects of nonpolar group on the flotation performance of collector are as follows: (1) Nonpolar groups of collector direct outward when the collector adsorbs on the mineral surface. The floatability of mineral, therefore, is greatly promoted due to the enhancement of surface hydrophobicity. It can be concluded that the structure of nonpolar group directly influences the surface hydrophobicity of mineral. (2) Interaction between nonpolar groups of collector includes the association of hydrocarbon chain which is caused by not only van der Waals force, but also the electrostatic force, hydrogen bond force, and association of other groups when the collector is adsorbed on the mineral surface. Besides for the bonding force of polar group, therefore, those forces produced by nonpolar groups also must be overcome when desorption of collector from the mineral surface occurs. In other words, the structure of nonpolar group also influences the bonding capability of collector with mineral. (3) Nonpolar groups can indirectly influence the adsorption capability of polar groups by inductive effect, conjugative effect, and steric effect in same time. The above actions are drawn as in Fig. 4.1.
© Metallurgical Industry Press, Beijing and Springer Science+Business Media Singapore 2016 D. Wang, Flotation Reagents: Applied Surface Chemistry on Minerals Flotation and Energy Resources Beneficiation, DOI 10.1007/978-981-10-2030-8_4
93
94
4 Structure and Property of Nonpolar Group of Collector
Table 4.1 Categories of nonpolar groups of collector Category
Structural features
Example
Straight chain saturation alkyl
normal alkyl CH3CH2CH2…CH2 iso-alkyl CH3CH2CH2…CH
Butyl xanthate; Stearic acid; i-butyl xanthate
Straight chain unsaturation alkyl
Alkyl radical containing single double bond: cis-form:
CH3
H
C
(C H 2)nC H 3
H
C
(C H 2)nC H 3
Cis-oleic acid; trans-oleic acid; cis-linoleic acid; trans-linoleic acid; tearolic acid
trans-form: CH3
(C H 2)n
C
H
C
(C H 2)n
; H
Alkyl radical containing poly-double bond (including double bond of conjugate and nonconjugate); Alkyl radical containing triple bond:
CH3(CH2)nC Aryl Fatty-aryl
Cycloalkyl Alkoxy
C
(CH2)n
Aryl with single ring; Aryl with poly-rings; Straight chain saturation aryl with single ring; Straight chain saturation aryl with poly-rings; Straight chain unsaturation aryl Five/six-member rings CH3(CH2)n–O– RO–(OC2H4)n–OCH2–
Thiophenol; Thionaphthol; p-methyl-phenylene arsonic acid; alkyl naphthalene sulfonate; cinnamyl xanthate; sodium alkyl benzene sulfonate Petroleum naphthenic acid Alkoxyxanthate ether acid, ether amine;
A simple and convenient way is discussion of the homolog reagents. The changing trend of the surface activity of heteropolarity homologous molecule was studied widely. Traube proposed in 1984 that the surface activity of alkyl fatty acid is multiplied 3.2 times with increasing one –CH2– [1]. The empirical formula for the Traube rule is expressed by the following: Dr ¼ r0 r where Dr refers to the variation of surface tension; r refers to the surface tension of solution; and r0 refers to the surface tension of pure substance.
4.1 Role of Nonpolar Group of Collector
95
Fig. 4.1 Actions of nonpolar group with mineral. 1 interaction between polar group and mineral; 2 interaction between polar group and nonpolar group; 3 interaction between nonpolar groups; 4 interaction between polar groups
3
4
1
2
The variation of surface tension ðDrÞ is concerned with the solution concentration (C). According to Szyszkowski equation, the relation between Dr and solution concentration can be given as follows: Dr ¼ a Inð1 þ bcÞ; where a refers to the characteristic parameter of polar group; b refers to the surface activity coefficient for nonpolar group. For homologs, a is a constant. For the homologs with the same polar group and adjacent two different alkyl nonpolar groups, the value of b is 0.313. The flotation performances of homologous collectors with different nonpolar groups were studied by Wark et al. [2]. As shown in Table 4.2, the results were considered that the contact angle value of the mineral surface absorbed with collector only depended on the structure of nonpolar group. That is, various nonpolar groups have their own contact angles and increase only with the increase of their atomic weights.
Table 4.2 Effect of nonpolar group of reagent on contact angle of the mineral surface absorbed with collector Reagent
Contact angle of the mineral surface (h˚) Methyl Ethyl Butyl Phenmethyl
Dithiocarbamate Mercaptan Xanthate Aerofloat
50 – 50 –
60 60 60 59
77 74 74 76
– 71 72 –
Phenyl
Cycloalkyl
– 70 – –
68 69–71 71–75 –
96
4 Structure and Property of Nonpolar Group of Collector
Table 4.3 Contact angles of various structural n-alkyls Alkyl
Measured h˚
Calculated h˚
Alkyl
Measured h˚
Calculated h˚
Propyl Butyl Amyl
68 74 80
68 74 79
Hexyl Heptyl
90 94
87 91
The relation between structure of nonpolar group of collector and contact angle value of mineral surface was studied by many scientists later. According to gas equation and Young’s equation, the expression of contact angle can be given as follows: 1 þ cos h C ¼ 1 cos h f where h refers to the contact angle; C is a constant; and f refers to van der Waals force between hydrocarbon chain s. For each –CH2–, f = 0.2174C is obtained by the computation on the basis of the known contact angles. Having derived the fundamental formula, the contact angles of various structural alkyls can be obtained from Table 4.3. It is worth mentioning that the above discussion is just based on the early results. Lots of flotation tests show that, however, their collecting capabilities are still diverse although different types of collectors have the same nonpolar groups. For example, comparing ethyl dithiocarbonate with ethyl monothiocarbonate, although they have the same nonpolar groups and similar polar groups, there is a great deal of difference between their collecting capabilities. Comparing diethyl dithioposphoric acid with diethyl monothiophosphoric acid, there is also a lot of differences between their collecting capabilities although they have the same nonpolar groups. Not to mention the difference of ethyl xanthogenate and fatty acid soap. The former can be used as an effective collector for sulfide ore, but the latter has nothing collecting capability for any minerals.
4.2
Structure, Solubility, and Surface Activity of Nonpolar Group for Flotation Reagent
Effects of structure of nonpolar group on the solubility and the surface activity of collector are discussed in this section. In addition, the relation between solubility and surface activity of collector is expounded according to Traube law.
4.2 Structure, Solubility, and Surface Activity of Nonpolar …
4.2.1
97
Solubility of Organic Liquid in Water
The dissolution process of organic liquid in water includes two changes of evaporation-free energy and hydration-free energy. The dissolution energies can be expressed as follows:
DG1 ¼ DGvap þ DGh
where DG1 refers to the total dissolution free energy change; DGvap refers to the evaporation-free energy change; DGh refers to the change of hydration-free energy including the free energy of polar group DGp and the free energy of nonpolar group DGa . Because of having the same polar groups in organic homologs, DGp is a constant. With the increase of –CH2– in homologs, the solubility decreases and the surface activity increases. The variation of dissolution energies is as follows:
DG2 ¼ 96:23 J=mol is n, the relation between solubility (Sn) When the number of –CH2– in nonpolar and standard free energy change DGn is expressed as follows:
DGn ¼ RT In Sn
When the number of –CH2– is n + 1, the standard free energy change DGn þ 1 is as follows:
D Gn þ 1 ¼ RT
The difference DG
In Sn þ 1
between DGn þ 1 and DGn can be given by the following:
DG ¼ DGn þ 1 DGN ¼ RT In
Sn ¼ DGvap þ DGa þ DG2 Sn þ 1
That is, RT In
Sn ¼ 3585:6 J=mol Sn þ 1
or Sn ¼ 4:25 Sn þ 1
98
4 Structure and Property of Nonpolar Group of Collector
It shows the solubility difference of the two adjacent alkyls with –CH2– group. For random homologs, the solubility difference of the two adjacent alkyls can be obtained as follows: Sn þ a ¼
Sn Sn 1=a or ¼ 4:25 ð4:25Þa Sn þ 1
where a refers to the number of hydrocarbon chain. By logarithmic transformation, the above-mentioned equation can be expressed by the following: log Sn ¼ b 0:6284 n log Sn þ a ¼ Sn 0:6284a where b is a constant for homologs. For n-alkane, n-alcohols, and n-mercaptans, it can be obtained as follows: log S ¼ 0:185 0:6284 n log S ¼ 2:543 0:6284a log S ¼ 0:31 0:6284n The solubilities of some organic collectors can be found in Table 4.4. Based on these data, the solubilities of their homologs can be deduced. For instance, the solubility of ethyl dixanthogen is 10−5. Therefore, the solubility of butyl dixanthogen can be calculated as follows: S ¼ 105 =ð4:25Þ4 ¼ 3 108
Table 4.4 Solubilities of some organic collectors Reagent
Molecular formula
Solubility (mol/L)
Reagent
Molecular formula
Solubility (mol/L)
Butane
C4H10
0.0020
(C2H5OCSS)2
10−5
Butyl alcohol
C4H9OH
1.0700
[(C2H5O)2PSS]2
5 10−7
Butyric acid
C4H9COOH
0.3450
C6H5CH2SH
0.0022
Butyl mercaptan Diethyl thioether Dibutylamine
C4H9SH
0.0065
Ethyl dixanthogen Ethyl diaerofloat Benzyl mercaptan Thiophenol
C6H5SH
0.0040
(C2H5)2S
0.0050
CH3C6H4SH
0.00035
(C4H9)2NH
0.0250
p-methyl thiophenol
4.2 Structure, Solubility, and Surface Activity of Nonpolar …
4.2.2
99
Surface Activity and Solubility of Organic Liquid in Water
Adsorption of organic compound is the atomophilic process of hydrocarbon group at air/water interface. Therefore, the change of free energy can be expressed by the evaporation-free energy. The surface activity (A) of organic liquid in water can be expressed as follows: RT In
An þ 1 ¼ 2949:6 J/mol An An þ 1 ¼ 3:29 An
The result is in accordance with the reported value of Traube law (3.2). Meantime, the relation between solubility (Sn) and surface activity (A) is expressed as follows: RT In
An þ 1 ¼ 705; An
RT In
Sn ¼ 857 Sn þ 1
or An þ 1 705 Sn Sn 0:823 In ¼ RT ¼ RT In RT In 857 Sn þ 1 An Sn þ 1 The expression above shows that the surface activity of collector varies inversely with the solubility to the 0.823th power. Based on the data of solubility and surface activity of a collector, the data of homologs can also be deduced.
4.2.3
Solubility and Surface Activity of Heteropolarity Organic Solid Matter
The dissolution of solid is described as a process in which one solid substance melts; a fluid permeates or is dissolved by water. Therefore, the solubility of the solid collector is smaller than that of the liquid one. Unlike inorganic salt, the organic compound comprised of heteropolarity collector and metal ion is characterized by low melting point, small dipole moment (1.7–1.8 D), and high solubility in nonpolar organic solvent. The molar solubility of homologs is proportional to the number of –CH2– groups.
100
4 Structure and Property of Nonpolar Group of Collector
When the dissolved solid collector is further dissociated into ion, the process of dissolution and dissociation can be given as follows: MAðsolidÞ ! MAðliquidÞ
DG ¼ RT ln S
MAðliquidÞ ! MA þ þ A
DG ¼ RT ln Ka
The two mathematical equations above can be consolidated as follows: MAðsolidÞ ! M þ þ A
DG ¼ RT ln S Ka ¼ RT ln L
where S refers to the solubility; Ka refers to the dissociation constant; and L refers to the solubility product. The equation above indicates that total dissolved solid depends on the solubility product of collector, but not the solubility. Therefore, the change of free energy in dissolution process can be presented as follows: DG ¼ RT ln L The effect of each –CH2– group on the solubility, hence, can be calculated according to the solubility products of two compounds. Take silver n-xanthate for example, when the numbers of –CH2– groups are, respectively, 2 and 10, the solubility products are, respectively, 44 10−19 and 5.4 10−24. The calculation process of free energy is as follows:
L2 L10
1 102
¼ 4:11
Take zinc n-xanthate for another example, when the numbers of –CH2– groups are, respectively, 2 and 8, the solubility products are, respectively, 4.9 10−9 and 1.5 10−16. So the effect of each –CH2– group on the solubility is 4.23. Based on lots of measurements, the average value is 4.19; so the DGº in the dissolution process is about 3552 J/mol. Therefore, the general relation between the number of –CH2– and the solubility product can be given as follows:
Ln Ln þ a
1=a ¼ 4:19 or Ln þ a ¼
Ln ð4:19Þa
Usually, collector ion has a valence and heavy metal ion has two valences or more. The solubility product of the organic compound comprised of heteropolarity collector and metal ion is as follows: L ¼ M M þ ½A m For high-valent metal compound, the equivalent amounts of reagent must be considered to evaluate the chemical activity of reagent with mineral. Therefore, the free energy of high-valent metal compound is given by the following:
4.2 Structure, Solubility, and Surface Activity of Nonpolar …
DG ¼ RT ln L1=m ¼
101
RT ln L m
where L1/m is called as the unit solubility product, which refers to the relative affinity between high-valent metal and reagent. Take xanthate (X), respectively, reacting with of Zn2+ and Ti2+ for example, and 1/1 LZnX2 and LTiX are, respectively, 4.9 10−9 and 2.9 10−8. But L1/2 ZnX2 and LTiX −5 −8 + are, respectively, 7.0 10 and 2.9 10 . Therefore, Ti can react with not only potassium xanthate (KX), but also ZnX2. The reaction between Ti+ and ZnX2 is given as follows: 2Ti þ þ ZnX2 ¼ 2TiX þ Zn2 þ The reaction equilibrium constant is given as follows: 2 K ¼ 2:4 103 ¼ 5:8 106
4.2.4
Comparison of Hydrophobic Association Energy of Nonpolar Group and Electrostatic Interaction Energy of Collector During Double Electric Layer Adsorption
When the interaction of collector and mineral belongs to double electric layer adsorption, the adsorption amount then depends on the hydrophobic association force of nonpolar group and electrostatic force (see Eq. 2.10). The adsorption amount (Г ) can be given as follows: C ¼ 2rc expð
Þ
vFf þ nU RT
where U refers to the free energy of each –CH2– (2.50–4.184 kJ/mol); v refers to the valence of collector ion; F refers to the Faraday constant; f refers to the surface potential of mineral. The value of U varies with the reagent concentration (C) and the adsorption amount. For the homolog collectors with different number of –CH2– (n), under the condition of the same adsorption amounts, the reagent concentration when the surface potential (f) of mineral is zero can be given as follows: ln C ¼ In
C U n 2r RT
Therefore, the value of U can be determined based on the slopes of lines (ln C * n) at different adsorption amounts. For example, the adsorption results of quaternary ammonium hydrochloride on the surface of quartz are as follows:
102
4 Structure and Property of Nonpolar Group of Collector
Г
Adsorption density (monolayer %)
U (J/mol)
7.5 10−8 15 10−8 30 10−8
20 40 80
1363.5 1944.2 2272.5
The magnitude of hydrophobic association energy of –CH2– in nonpolar groups was discussed in this chapter and Chap. 2. The related results about hydrophobic association energy of –CH2– at different conditions are concluded as follows: Researcher
Testing condition
kT
U (J/mol)
Langmuir Traube Schefer Shinoda Fuestanuo etc. Dhahran etc. Glembotski Kakovski
Water/gas and water/oil interfaces Water/gas interface Water/gas and water/oil interfaces Critical micelle concentration (CMC) All kinds of conditions Adsorption and flotation Evaporation-free energy Calculation of solubility product Calculation of solubility product
1.08–1.2 1.16 1.36 1.08 0.6–2.0 1.0 1.18 1.43 1.43
2720–3012 2929 3410 2720 1506–5021 2510 (f = 0) 2950 3598 3586
4.3
Normal Alkyl Chain
N-alkyl chain is a common nonpolar group in collectors. According to organic structural chemistry, n-alkyl chain appears in the form of planar zigzag. As shown in Fig. 4.2, the bond angle of C–C–C is 109.5°, and the separation of adjacent C atoms is 1.54 Å. Based on the diameter of C atom (1.54 Å), it can be calculated that alkyl chain increases by 1.26 Å with each additional –CH2–. According to X-ray spectrographic
Fig. 4.2 Structure of n-alkyl chain
4.3 Normal Alkyl Chain
103
analysis, the separation of adjacent C atoms in C29H60 is 2.54 Å; the section width of alkyl chain is 4 Å. Because the adjacent C atoms are linked via r-bond of sp3 hybrid orbital, each C atom can rotate freely. The effect of –CH2– in alkyl chain on the solubility and the surface activity of collector had been discussed in the previous section. The effect of –CH2– on the flotation behavior of collector is mainly discussed in the following section. Based on lots of flotation research, a well linear correlation is found between the solubility product (PL) and the carbon number of alkyl chain. For example, the relation between PL of metal salts of aerofloat and the carbon number (n) of alkyl chain is as follows [3]: PL ¼ 10:77 þ 12 log n PL ¼ 10:77 þ 39:61 log n PL ¼ 20:54 þ 40:96 log n
For copper salt of aerofloat For ferric salt of aerofloat For nickel salt of aerofloat
The solubility products of metal salts of aerofloat are listed in Table 4.5. But it is also worth pointing out that these data may be distinct from the data mentioned before (such as Kakovski) due to different testing conditions. The following Fig. 4.3 shows the relation between pL of metal salts of xanthate and the carbon number (n) of alkyl chain. The results also display that the solubility product (pL) is linear to the carbon number of alkyl chain. When alkyl xanthates and fatty acids with carbon chains are used in the flotation of galena, the changing trend of recovery rate with reagent dosage is displayed in Fig. 4.4 from A. Gaudin. It is shown in Fig. 4.4 that the collecting capability of collector varies regularly with increasing the number of carbon atoms of alkyl chain within a certain range. For instance, when fatty acids with different carbon chains
Table 4.5 Solubility products of aerofloat metal salts Nonpolar group
Dimethyl Diethyl Dipropyl Dibutyl Diamyl Dihexyl Diheptyl Dioctyl
Metal ion Cu2+ Measured value 10.87 14.38 16.71 18.48 – – – –
Calculated value
Fe3+ Measured value
10.77 14.56 16.77 18.35 19.60 20.70 21.60 22.30
– – – 13.67 – 21.00 – 26.55
Calculated value
Ni+ Measured value
Calculated value
–10.07 1.85 8.82 13.77 17.66 20.75 23.40 25.70
– – – – – 11.33 – 16.45
–20.54 –8.21 –1.00 4.12 8.13 11.33 14.07 16.45
104
4 Structure and Property of Nonpolar Group of Collector
13 1.7 12
1.6
11
pLZnX2
pKa
pKa
pL 10 1.5 9
8 1
2
3
4
5
The number of C atoms
Fig. 4.3 Relationship between pL of metal salts of xanthate and the carbon number (n) of alkyl chain
are used in the flotation of calcite, the relation between the collecting capability and the number of carbon atoms of alkyl chain is shown obviously. As shown in Fig. 4.5, when recovery rate of mineral is 80 %, the needed reagent concentration and the number of carbon atoms of alkyl chain are semilog straight line correlation. According to the research results of Somasundaran etc., a well semilog straight line correlation is also found between the needed reagent dosage and the number of carbon. The relation is shown in Figs. 4.6 and 4.7, respectively. The explanation for the relation is that the association of hydrocarbon chain has a good additivity with the increase of –CH2–. Based on the points discussed above, the correlation between molecular weight of nonpolar group and property of collector is in line with that of surfactant. It can be concluded that the collecting capability of collector increases with the increase of the number of carbon atoms of alkyl chain within a certain range. When the number of carbon atoms of alkyl chain is too large, the collecting capability of collector will decrease as a result of its lower solubility in water. As discussed earlier, the selectivity of collector usually decreases with the increase of collecting capability. As shown in Fig. 4.6b, the flotation critical pH increases with the increase of alkyl chain. The reason lies in the association of alkyl chain only depends on the length and the structure of alkyl chain, but not on the polar group of reagent.
4.3 Normal Alkyl Chain
(a) 100
isopentyl xanthate ethyl xanthate
80
Recovery rate (%)
Fig. 4.4 a Changing trend of recovery rate of galena with xanthate dosage; b changing trend of recovery rate of galena with fatty acid dosage
105
butyl xanthate
60
propyl xanthate
methyl xanthate
40 20 0 0.0
22.7
45.4
68.1
90.8
113.5
Xanthate dosage (g/t)
(b)
C13 C12
Recovery rate (%)
100
C11
C10
C9
C8
80 60 C7
40 20 0 0.0
45.4
90.8 136.2 181.6 227.0 272.4 317.8
Fig. 4.5 Correlation between the number of carbon atoms of alkyl chain of fatty acids and the needed reagent concentration when flotation recovery of calcite is 80 % (from M. Fuerstenau)
-logC
Fatty acid dosage (g/t)
8
9
10
11
12
The number of C atoms in hydrocarbon chain
4 Structure and Property of Nonpolar Group of Collector
Critical concentration (mol/L)
106
Critical concentration (mol/L)
The number of C atoms in hydrocarbon chain
pH Fig. 4.6 a Relation between critical concentration of primary amine and the number (n) carbon in alkyl chain for quartz flotation (from P. Somasundaran); b relation between critical concentration of primary amine and the number (n) carbon in alkyl chain for quartz flotation (from D.W. Fuerstenau)
107
Fig. 4.7 Relation between the needed reagent concentration and the number of carbon when zeta potential of quartz is zero (from P. Somasundaran et al.)
Critical concentration (mol/L)
4.4 Isoalkyl Group
The number of C atoms in hydrocarbon chain
4.4
Isoalkyl Group
When aliphatic hydrocarbon chain is comprised of three or more C atoms, there has usually existed the phenomenon of the existence of isomers. The isomers with the same atoms are bonded in the same ways but differ in their three-dimensional configurations. The number of isomers increases with increasing the length of hydrocarbon chain. Take alkyl xanthate for example, propyl xanthate has two isomers, and butyl xanthate has four isomers. The structures of alkyl xanthate isomers are given as follows: Propyl xanthic acid
(I) n-propyl xanthic acid (II) i-propyl xanthic acid
CH3
CH2
CH2
OCSSH
CH3 CH2
OCSSH
CH3
Butyl xanthic acid
(I) n-butyl xanthic acid (II) i-butyl xanthic acid
CH3–CH2–CH2–CH2OCSSH CH3 CH
CH2
OCSSH
CH3
(III) sec-butyl xanthic acid
CH3
CH2
CHOCSSH CH3
(IV) tertiary butyl xanthic acid
CH3 CH3
C
OCSSH
CH3
Compared with n-alkanes, the structural features of iso-alkanes include the following two aspects: (1) The atoms are bonded more closely in molecule, but the molecules cannot touch closely with each other because of the effect of branched chain; (2) the total length of molecule is shorter than that of n-alkanes, but the sectional area of molecule is more larger than that of n-alkanes. Because of these
108
4 Structure and Property of Nonpolar Group of Collector
differences in the structural features, there are also obvious differences in flotation behavior between n-alkanes and iso-alkanes. The differences in the collecting behavior can be summarized by the following: (1) The van der Waals force between hydrocarbon chains is weak because of the effect of branched chain; compared with n-alkanes, iso-alkanes are characterized by low melting point, high solubility, and large critical micelle concentration (CMC). (2) The steric hindrance effect of branched chain can weaken the bonding capability of reagent on mineral surface. (3) For the collectors with short hydrocarbon chains, the positive inductive effect of methyl on the polar group in iso-alkanes is larger than that in n-alkanes. Therefore, the bonding capability of polar group is improved. Take isopropyl xanthate for example: H3C
CH OCSSH
CH3
Two methyl groups are directly linked with a–C atom in its molecule. But only one methyl group is directly linked with b–C atom in the molecule of n-propyl xanthate. Therefore, the bonding capability of polar group in isopropyl xanthate is stronger than that in n-propyl xanthate. That is why isopropyl xanthate has a better collecting capability. (4) The hydrophobic coverage of each reagent with iso-alkanes is large relatively because of a larger-sectional area of molecule. And this can lead to the decrease of selectivity and the increase of foam capability of the reagent. According to the analysis of the aspects mentioned above, it can be concluded that for the collector with short hydrocarbon chain, the positive inductive effect is obvious relatively. For example, the flotation behavior of isomeric xanthate or aerofloat is usually better than that of normal one. The contact angles of galena surface in the solution of normal and isomeric xanthate are presented in Fig. 4.8 [2]. Moreover, the flotation behavior of isomeric xanthate will be worse than that of normal one when the number of C atoms is more larger. The reason mainly lies in the following two aspects. The first one is that the proportion of the positive inductive effect is small when the hydrocarbon chain becomes too large. Another one is that van der Waals force decreases and the steric hindrance effect caused by branched chain increases with increasing the number of C in chain. The relationships between chain structure and performance of xanthates can be discussed by the data of solubility of zinc xanthate in Table 4.6. We can see that isopropyl xanthate with short hydrocarbon chain has a better collecting capability
109
Contact angle (˚)
4.4 Isoalkyl Group
The number of C atoms in hydrocarbon chain
Fig. 4.8 Contact angles of galena in the solution of normal and isomeric xanthates (From Sutherland and Wark)
Table 4.6 Solubility of zinc xanthate with various structures Xanthate
Structure
Solubility (mol/L)
n-propyl xanthic acid i-propyl xanthic acid
CH3–CH2–CH2–OCSSH
4.4 10−4 3.8 10−4
CH3 CH2
OCSSH
CH3
n-butyl xanthic acid i-butyl xanthic acid
CH3–CH2–CH2–CH2OCSSH CH3
CH
CH2CH2OCSSH
CH3
CH2
2.1 10−4 1.9 10−4
CH3
Sec-butyl xanthic acid
CH
CH2OCSSH
2.9 10−4
CH3
Amyl xanthic acid a-methyl butyl xanthic acid
CH3–CH2–CH2–CH2–CH2OCSSH CH3
CH
CH2CH2OCSSH
CH3
CH2
0.73 10−4 0.92 10−4
CH3
a-methyl butyl xanthic acid [1]
CH
CH2OCSSH
1.34 10−4
CH3
2,2-dimethyl propyl xanthic acid
1.37 10−4
CH3 CH3
C
CH2OCSSH
CH3
a-methyl butyl xanthic acid [3]
CH3
CH
CH
CH3
CH3
Amyl xanthic acid [2]
CH3CH2CH2CHOCSSH
Amyl xanthic acid [3]
CH3CH2
OCSSH
1.38 10−4 1.54 10−4
CH3 CHOCSSH
1.60 10−4
CH3CH2
(continued)
110
4 Structure and Property of Nonpolar Group of Collector
Table 4.6 (continued) Xanthate
Structure
Solubility (mol/L)
n-hexyl xanthic acid i-hexyl xanthic acid
CH3–CH2–CH2–CH–CH2–CH2OCSSH
3.15 10−5 4.0 10−5
n-heptyl xanthic acid i-heptyl xanthic acid
CH3–(CH2)5–CH2OCSSH
CH3CHCH2CH2CH2OCSSH CH3
CH3
CH
(CH2)3
CH2OCSSH
1.5 10−5 2.2 10−5
CH3
than n-propyl xanthate. Isobutyl xanthate also owns a better collecting capability than n-butyl xanthate, but sec-butyl xanthate possesses a worse collecting capability than n-butyl xanthate. Amyl xanthate also has a better collecting capability than n-amyl xanthate. The effects of branched chain on the property of long-chain fatty acids have been studied rarely. The effects can be summarized by the following: (1) the solubility may increase with the increase of branched chains; (2) the van der Waals force between hydrocarbon chains and hydrophobicity of molecule decreases with the increase of branched chains; (3) the sectional area of molecule increases with increase of branched chains, and this can result in the decrease of selectivity. In addition, for the fatty acids with the branched chains around carboxyl group, the acidity of reagent becomes weak because of the steric hindrance caused by the interaction of reagent ion and water molecule. The surface activity of myristic acid derivatives can be seen in Table 4.7. As shown in Table 4.7, the increase of branched chains leads to the decrease of the van der Waals force between hydrocarbon chains and the increase of CMC value. The flotation results of apatite and hematite using oxidized paraffin soap which is prepared from high molecular weight soft wax or paraffin (n > 15) are shown in Fig. 4.9. The results display that isopropyl fatty acid with long hydrocarbon chain
Table 4.7 Surface activities of myristic acid derivatives with branch chains [4] Physical and chemical properties
Myristic acid
Solubilizer 0.10 N 182.0 0.25 N 248.0 29.0 Surface tension 0.10 % 30 °C, 10−3 N/m 0.3 % 28.3 Equivalent conductance 117.0 0.10 % 0.30 % 137.0 CMC (%) – *Dissolving of dimethylbenzene(g) in 100
a-methyl myristic acid
a-propyl myristic acid
a-i-propyl myristic acid
201.0 272.0 35.8
288.0 326.0 50.5
248.0 304.0 48.7
33.0 121.0
37.1 132.0
34.3 122.6
138.0 142.9 0.2 0.3 ml soap solution at 30 °C
141.0 0.3
4.4 Isoalkyl Group
111
100
1 3
2
42
60
40
40
5
Concentrate grade (%)
Recovery rate (%)
80
4 38
20
36
0 100
200
300
Fatty acid dosage
Fig. 4.9 Flotation results of apatite and hematite using oxidized paraffin soap which is prepared from high molecular weight soft wax or paraffin (n > 15) (from A. Eigeles). 1, 4 Floating apatite with isomeric oxidized paraffin acid; 2, 5 Floating apatite with isomeric oxidized paraffin and normal fatty acid (1:1); 3 Floating hematite with isomeric oxidized paraffin soap
has a better collecting capability than normal one. Therefore, the concentrate grade is improved when reagent is used with isopropyl fatty acid and normal one at the same time. Another research which the blended isomeric oxidized paraffin was used in the flotation of ilmenite, zircon, feldspar, quartz, and apatite was carried on. The blended isomeric oxidized paraffin is not only comprised of isomeric fatty acid, but oxyacid with hydroxyl. The results display that the collecting capability of isomeric oxidized paraffin is better than that of oleic acid. But the selectivity of isomeric oxidized paraffin is worse than that of oleic acid. Thus, it can be seen that the flotation behavior of oxidized paraffin can be improved by the preparation of the blended isomeric oxidized paraffin which contains a given mass of isomeric fatty acid.
4.5
Unsaturated Hydrocarbon Chain
The property of unsaturated hydrocarbon chain depends on the unsaturated bonds. Unsaturated hydrocarbonyl such as alkenyl is very common in the flotation reagent, but alkynyl is also found in the collectors for sulfide minerals in recent years. Compared with saturated hydrocarbon, the adjacent C atoms in unsaturated alkenes are linked via r-bond of sp2 hybrid orbital and a perpendicular p-bond; the adjacent
112
4 Structure and Property of Nonpolar Group of Collector
C atoms in unsaturated alkynes are linked via r-bond of sp hybrid orbital and two p-bonds. The properties of unsaturated bonds are shown in Table 4.8. Compared with the same type of saturated organic compounds, the unsaturated organic compounds are usually characterized by low melting point, high solubility, large CMC, high activity, and large cross-sectional area. The basic properties mentioned above of fatty acids are shown in following Table 4.9. Besides for the difference in saturation, there is also a difference in the position of the double bond in the unsaturated organic compounds. Meantime, if two more alkenyl groups exist in organic compounds, the double bond is further divided into isolated double bond and conjugated double bond, or into cis-form and trans-form in terms of steric configuration. These differences above can lead to the difference of property of reagent. The effect of the position of double bond on the melting point of octadecenoic acid can be found in Table 4.10. When there is double bond in aliphatic hydrocarbon, the reasons for the change of flotation behavior of reagent can be deduced by the following: (1) Energy factor. As shown in Table 4.8, the bond energy of double bond or tripe bond is far smaller than the sum of two single bonds. And the hydrophilicity and the water solubility of the unsaturated bonds are better than those of the saturated bonds. According to the study on the CMC of surfactant, comparing the saturated hydrocarbon chain with the same number of C atoms, the CMC increases when a double bond exists in hydrocarbon chain [5]. Based on the report on the solubility product (L) of metal xanthates, the solubility product of zinc propyl xanthate and zinc propenyl xanthate is 8.8 10−9 and 3.4 10−10, respectively. Therefore, the ratio of equivalent solubility product can be shown as follows: Lunsat 1=2 Da ¼ ¼ 5:1 Lsat It is clear that the hydrophobicity of reagent decreases when a double bond exists in hydrocarbon chain. And the effect of increasing by a double bond is equivalent to that of decreasing by a –CH2– group.
Table 4.8 Properties of unsaturated bonds Bond
Bond length (Å)
Bond energy (kJ/mol)
Bond angle a, b
Steric configuration
Motion of carbon atom
C–C
1.54
345.6
109° 28′
Freely rotation
C=C
1.34
606.7
122°, 116°
Regular tetrahedron Plane
CC
1.20
778.2
180°
Straight line
No freely rotation No freely rotation
CH3(CH2)15COOH CH3(CH2)7CH=CH(CH2)7COOH CH3(CH2)7CH=CH(CH2)7COOH CH3(CH2)4CH=CHCH2CH=CH (CH2)2COOH CH3(CH2)4CH=CHCH2CH=CH (CH2)2COOH CH3(CH2CH=CH)3CH2(CH2)6COOH CH3(CH2CH=CH)3CH2(CH2)6COOH
Stearic acid Oleic acid Elaidic acid Linoleic acid
Linolenic acid Trans-linolenic acid Eleostearic acid Castor oil acid Trans-castor oil acid
Trans-linoleic acid
Molecular formula
Fatty acid
Table 4.9 Properties of unsaturated fatty acids
17.4 12.4 14.3 12.4 – 12.2 – – – –
– 0.2000 – – – –
pLCaA2 (20°)
0.00045 0.0012 0.0015 0.1500 g/L
CMC (mol/L)
12.5 – 39 – –
–
65 16.3 43.7 –
Melting point (°C)
68.2 60.0 – 109.4 79.7
53.3
24.4 56.6 48.5 59.9
Sectional area of alkyl (Å2)
4.5 Unsaturated Hydrocarbon Chain 113
(2, (3, (4, (6, (9,
Cis Cis Cis Cis Cis
3) 4) 5) 7) 10)
Position of double bond
Octadecenoic acid
59 56–57 52–53 45.5 a 13.4, b 16.3
Melting point (°C) Cis Trans Trans Trans Trans
Octadecenoic acid (12, 13) (5, 6) (6, 7) (7, 8) (8, 9)
Position of double bond
Table 4.10 Effect of position of double bond on melting point of octadecenoic acid
9.8–10.4 47.5 53 45.5 53
Melting point (°C) Trans Trans Trans Trans
Octadecenoic acid
(9, 10) (10, 11) (11, 12) (12, 13)
Position of double bond
43.7 42 39 39.7–40.1
Melting point (°C)
114 4 Structure and Property of Nonpolar Group of Collector
4.5 Unsaturated Hydrocarbon Chain
115
For the short-chain collectors for sulfide minerals, the nonpolar groups are usually alkyl groups of which the number of C atoms ranges from 2 to 6. The collecting capabilities of these collectors are very good. For example, the water solubility and the bonding capability of xanthate and aerofloat are all good. Therefore, further improving the solubility and chemical activity of them has no actual meaning. But decreasing hydrophobicity of them possesses practical significance. The flotation results of copper ore by unsaturated xanthate and saturated xanthate are drawn in Fig. 4.10 [6]. The results show that the collecting capability of butyl xanthate with saturated nonpolar group is good. The collecting capability of benzyl xanthate is similar with that of butyl xanthate. Although the molecular weight of cinnamyl xanthate is larger than that of benzyl xanthate, the collecting capability of cinnamyl xanthate is worse than those another two xanthates. The reason lies in the following aspects: The extra part is unsaturated propenyl; the double bond in unsaturated propenyl can form conjugated large p-bond with benzene ring; the increase of polarity also can lead to the decrease of collecting capability of reagent. It can be concluded that the collecting capability of the unsaturated short-chain collector is worse than that of saturated one in general. For the long-chain collectors for oxide minerals, the nonpolar groups are usually aliphatic groups of which the number of C atoms ranges from 10 to 20. For example, the water solubility and the bonding capability of fatty acid as one of these collectors are usually very bad. Therefore, further improving the solubility and the chemical activity of these collectors possesses practical significance. In general, the water solubility of these collectors increases when a double bond exists in hydrocarbon chain. Take fatty acids for example, the collecting capability of unsaturated one is better than that of saturated one. The flotation behavior of oleic acid is better than that of saturated octadecanoic acid. Meantime, the distillation tar oil which consists of unsaturated octadecanoic acid can also be used as a good collector for oxide minerals. However, the selectivity of reagent decreases when the degree of
Recovery rate (%)
Fig. 4.10 Flotation results of galena with various structural xanthates [6]
1. benzyl xanthate; 2. butyl xanthate; 3.cinnamyl anthate.
pH
116
4 Structure and Property of Nonpolar Group of Collector
Table 4.11 Flotation results of minerals with various fatty acids Mineral
Orders of collecting performance of reagents
Document
Hematite
Oleic acid > elaidic acid > linoleic acid > linolenic acid > stearic acid Oleic acid > dodecoic acid > myristic acid > palmitic acid Linolenic acid > linoleic acid > oleic acid > stearic acid Linolenic acid > oleic acid > linoleic acid Linolenic acid > linoleic acid > oleic acid > elaidic acid > stearic acid
[7]
Hematite Ilmenite Phosphorite Quartz
[8] [9]
unsaturation becomes too large. The flotation results of various minerals with various unsaturated and saturated fatty acids are briefly summarized in Table 4.11. For the flotation of oxide minerals containing quartz, the researches show that the flotation index of recovering iron ore from quartz is good when the iodine value of is smaller than 110; the flotation index of recovering quartz from iron ore is good when the iodine value of is bigger than 110 [10, 11]. Based on these, some opinions are put forward as follows: The degree of unsaturation, if too high, weakens the flotation index of the mineral-bearing metal-cation; the degree of unsaturation, if too low, weakens the flotation index of mineral which does not contain metal-cation. For example, when unsaturated fatty acid is used as collector in the flotation of quartz activated by Ca2+, the interaction between the unsaturated double bond and mineral surface leads the reagent to slant across or lie on the mineral surface for improving the adsorption of reagent. Therefore, when there are too little double bonds, the collecting capability of reagent decreases. For hematite flotation, the adsorption of reagent ion takes place in the electric double layer of mineral. The hydrophobic association of nonpolar groups and the chemical adsorption of polar group can make the reagent arrange on the mineral surface. But the hydrophilicity of double bond weakens the hydrophobic association of nonpolar groups. Therefore, when there are too many double bonds, the collecting capability of reagent also decreases. (2) Steric factor. The bond angle of unsaturated bond is bigger than that of saturated single bond. Meantime, because the p-electron bond of double bond is asymmetric with bond shaft and cannot rotate freely. Because of a larger-sectional area of unsaturated hydrocarbon chain, the coverage of reagent becomes also a higher value. The flotation results of calcite with various structural fatty acids are briefly drawn in Fig. 4.11. As shown in Fig. 4.11, there is an obvious difference in the flotation behavior among various fatty acids. Table 4.10 shows that the melting point of octadecenoic acid increases with decreasing the distance between double bond and carboxyl. The water solubility of reagent increases with increasing the distance between double bond and polar group. The two C atoms of double bond appear cis-form and trans-form in terms of steric configuration. The cis-form and trans-form configuration is given as follows:
4.5 Unsaturated Hydrocarbon Chain
Recovery rate (%)
Fig. 4.11 Collecting performances of different structural unsaturated fatty acids for calcite flotation (from Gaudin and Hausen). 1 oleic acid (25 °C); 2 cis-docosyl olefine acid (65 °C); 3 cis-docosyl olefine acid (25 °C); 4 stearic acid (70 °C); 5 hendecyl olefine acid; 6 elaidic acid (70 °C); 7 stearic acid (25 °C); 8 elaidic acid (25 °C)
117
Fatty dosage (g/t)
Cis-form: a
a C
C
b
b
a
b
Trans-form:
C
C
a
b
The alkylene which the H atoms are located in the same side of double bond is called cis-form. And the H atoms are located in the different sides, which is called trans-form. The schematic diagram of different configurational gadoleic acids is presented by the following: Cis-form: H
C
(CH2)n
CH3
H
C
(CH2)n
CH3
Trans-form: CH3
(CH2)n H
C
H
C
(CH2)n
COOH
Usually, unsaturated fatty acid is in form of cis-form. The modified and oxidation fatty acid appears as trans-form. Compared with the trans-form fatty acid, the cis-form one is usually characterized by low melting point, high solubility, high activity, and large cross-sectional area.
118
4 Structure and Property of Nonpolar Group of Collector
The following Fig. 4.11 shows the collecting performances of different structural unsaturated organic acids. It shows that the cis-form oleic acid has a better collecting capability than the trans-form oleic acid. The reason that the collecting capability of oleic acid decreases after leaving alone for a long time lies in the occurrence of chemical reaction, as well as the producing of the trans-form oleic acid. For those organic compounds with two or more alkenyl groups, besides for the difference in steric configuration, there is also a difference in terms of isolated double bond and conjugated double bond. The p–p conjugated double bond can increase the polarity and hydrophilicity of nonpolar group. It is obviously that the sinuosity and the coverage of reagent increase with increasing the degree of unsaturation. And these lead to the decrease of the selectivity of reagent. The related results can be found in following Table 4.12 which shows the flotation of oxide iron ore using different structural fatty acids [7]. Based on comprehensive analysis and judgment, the effects of structure parameters on the flotation behavior of reagent are listed in following Table 4.13. However, it should be pointed out that those results are just based upon chemical structure theory. The combination property of reagent finally depends on the crucial factor. The reasons for the unsaturated hydrocarbon used as the solidophilic group can be explained by p-bond theory in complex chemistry. Transition metal complex with unsaturated hydrocarbon such as ligand was developed early in the fields of complex chemistry and catalytic chemistry. The structure of the famous Zeise salt [PtCl3(C2H4)]H2O is given as follows: H
H
Cl Cl
C
Pt C
H
Cl H
Table 4.12 Flotation results of hematite with various fatty acids (from I. Iwasaki) Fatty acid
Structure
Concentrate quality (HCl insoluble matter, %) 25 °C 70 °C
Linoleic acid Linolelaidic acid Linoleic acid Linolelaidic acid Linolenic acid Linolenic acid Linolenic acid
Non conjugated cis–cis Non conjugated trans–trans Conjugated cis–trans Conjugated trans–trans Non conjugated cis–cis–cis Conjugated cis–cis–cis Conjugated trans–trans–trans
42.85 16.55 13.45 13.14 37.55 – –
20.52 5.50 4.39 3.05 18.34 Full floating Full floating
Increasing the number of double bond Close to polar group
Position of double bond Far from polar group
Melting point − + − Dispersity + − + Sectional area + − + Selectivity − + − Collecting capability + − + Where the sign “+” refers to that the effects of structure parameters on the flotation behavior of reagent structure parameters on the flotation behavior of reagent are not obvious
Activity
Table 4.13 Effects of structure parameters on the flotation behavior of reagent
+ − − + − to that the effects of
Conjugate character of double bond Conjugated Nonconjugated
− + − + − + + − + − + − + − + are obvious; the sign “−” refers
Steric configuration Cis Trans
4.5 Unsaturated Hydrocarbon Chain 119
120
4 Structure and Property of Nonpolar Group of Collector
[PtCl3(C2H4)]H2O is prepared via the reaction of K2PtCl4 and ethylene. According to the study, there are four ligands which appear in the form of foursquare around central Pt2+. Three of the four ligands are Cl; the remaining one is ethylene. The C=C of ethylene is perpendicular to the plane of PtCl3–. Therefore, the complex of Pt and C2H4 is in the shape of side group. The central Pt2+ is d8 electronic configuration. The feedback p-bond is formed via the dxz electron orbit connecting with the p* antibonding orbital of ethylene. The transitional metals with d electrons such as Cu+, Hg2+, and Ag+ are all capable of bonding with C2H4. When there is no vacant d orbit, the s or p orbit also accepts the electron pair of C2H4. Acetylene is similar with C2H4, but the r–p bond can form in its molecule. The reported collectors with alkene or alkyne as the solidophilic group of collectors are as follows [12]: (a) 1-butoxyl-2-ethyleneoxyethane (C2H9O–CH2–CH2–O–CH=CH) The mixture of 1-butoxyl-2-ethyleneoxyethane and that of methyl isobutyl methanol (1:1) are used for flotation of galena from Cu–Pb sulfide ore. (b) Isobutenyl acetenyl methanol (C2H6–C=CH–O–CH(OH)–CCH) It is used for flotation of galena from Zn–Pb sulfide ore. (c) Acetenyl methanol (CHC–CH2–OH) It is used as collector for sulfide ore. (d) Other ethers and alcohols with alkene, alkyne groups, such as: R' CH2
R
O
CH
O
C
CH
R' C
(RO)2
CH
CH2
(RO)2
CH
C
C
C
C
CH
CH CH
CH3
The interaction of these collectors and sulfide minerals may attribute to the following two aspects. The first one is the chemical adsorption or the surface chemical reaction which takes place between p-bond of complex and mineral surface. The other one is the van der Waals force adsorption of neutral molecules and the hydrogen-binding adsorption.
4.6
Aromatic Group
Phenyl is often used as flotation reagent. Although benzene ring is comprised of 6 C atoms, the bond energy and the steric property of phenyl are not directly compared with those of the aliphatic hydrocarbon which contains the same number of C atoms. Total length and thickness of benzene ring are 2.84 and 1.85 Å, respectively.
4.6 Aromatic Group
121
Because of the existence of big p-bond, the chemical activity and the hydrophilicity of benzene ring are better than those of butyl alkyl including six carbon atoms. According to the reports about surfactants of sulfurnate [5], the effect of a phenyl on the CMC of nonpolar group is equivalent to 3.5 times of –CH2–. Comparison of the solubilities between zinc phenyl xanthates and zinc alkyl xanthates is given as follows: Zinc benzyl xanthate Zinc n-butyl xanthate Zinc n-amyl xanthate
C6H5–CH2–OCSSZn1/2 CH3CH2CH2CH2OCSSZn1/2 CH3(CH2)3CH2OCSSZn2/1
S = 1.5 10−4 S = 2.1 10−4 S = 0.73 10−4
It shows that the chemical activity of benzene ring is better than that of n-amyl, but worse than that of n-butyl or in other words a benzene group is equivalent to propyl. Flotation results display that the collecting capability of cresol aerofloat is no better than that of butyl aerofloat. It indicates that the hydrophobicity of phenyl is equivalent to ethyl or propyl. Results in Fig. 4.9 also show that the collecting capability of benzyl xanthate is equivalent to butyl xanthate. It further confirms that the hydrophobicity of phenyl is equivalent to ethyl or propyl. Under the condition of the existence of aliphatic and aromatic groups, the position of aromatic group in molecule influences the property of reagent. The properties of various structural collectors containing—SH are listed in Table 4.14 [13]. With increasing number of –CH2–, the dissociation constant Ka of reagent with alkyl as nonpolar group decreases, but the collecting capability increases. When the sulfhydryl is linked directly with phenyl, the dissociation constant Ka of reagent is enhanced obviously and the chemical activity of reagent decreases. The reason is that the interaction between S atom and the big p-bond of benzene ring makes the bonding capability of S atom to decrease. For benzyl mercaptan with intervening –CH2–, however, the dissociation constant Ka of reagent is not changed obviously. For the long-chain collectors for oxide minerals, take sodium alkyl benzene sulfonate for example, the solubility of reagent can be improved if phenyl exists in the nonpolar group. Besides for the phenyl, the collectors with naphthyl such as naphthyl thiazole mercaptan, alkyl naphthalene sulfonate, alkyl pyridines, and 8-hydroxy quinoline are also applied in the flotation industry.
Table 4.14 Properties of various collectors containing –SH Reagent
pKa
Butyl mercaptan C4H9SH Ethyl mercaptan C2H5SH Benzyl mercaptan C6H5CH2SH Tolyl mercaptan CH3C6H5SH Phenyl mercaptan C6H5SH
10.7 10.6 9.4 6.8 6.5
Collecting performance (floating ZnS)
decreasing
122
4.7 4.7.1
4 Structure and Property of Nonpolar Group of Collector
Other Kinds of Nonpolar Groups Cycloalkyl
The collectors with cycloalkyl such as petroleum naphthenic acid and cycloalkyl xanthate are usually reported. The petroleum naphthenic acid is a carboxylic acid which contains monocyclic ring, dual ring, or alkyl side chain. The property of petroleum naphthenic acid is similar to that of fatty acid. In general, the water solubility and the selectivity of petroleum naphthenic acid are better than those of oleic acid. But the collecting capability of petroleum naphthenic acid is worse than that of oleic acid. The property of cycloalkyl xanthate is also similar to that of alkyl xanthate. According to X-ray spectrographic analysis, the length of a six-ring cycloalkyl is 2.84 Å. The value lies between those two values of ethyl and phenyl. The steric size is similar to that of phenyl. Because the six-ring cycloalkyl is comprised of various saturated bonds, the hydrophobicity is better than that of phenyl in conjugated system.
4.7.2
Alkoxyl
Alkoxyl organic substances such as alkoxy xanthate and alkoxy aerofloat have been used as frother or collector in mineral flotation. It has been discovered that the bubbling capability of alkoxy xanthate is stronger than that of alkyl xanthate [14]. Alkoxyl carboxylic acid is also applied recently. The molecular formula of ether alkyl carboxylic acid (ECA) is given as follows: Rn1 ðOC2 H4 Þn2 OCH2 COOH where R means the linear alkyl or alkenyl of which the number of carbon atoms ranges from 8 to 18; n1 and n2 refers to the number of carbon atoms of which the oxyethylene ranges from 0 to 16. The existence of ether in long-chain nonpolar group can improve the solubility of reagent. In addition, because of the inductive effect between ether and carboxyl, the acidity and the value of Ka increase. Meantime, the solubility of metal salt of alkoxyl reagent also becomes larger. Compared with oleic acid, the characteristics of alkoxyl acid are presented by the following: (a) The solubility of alkoxyl acid is largely relative. When n1 is 10, 12, 14, and 17, and n2 is 10, 20, and 30, the alkoxyl acid owns a strong hard water tolerance. That is, the ether acid cannot react with Ca2+or Mg2+ to form insoluble salt. (b) It is able to be used in the flotation of mineral-bearing calcium, beryl, and chalcopyrite at a lower pH (6). (c) The adsorption of alkoxyl acid on mineral is desorpted easily by water. So it has a better selectivity than oleic acid.
4.7 Other Kinds of Nonpolar Groups
123
The effects of the structure of nonpolar group can be concluded as follows: The collecting capability of reagent increases with the increase of the value of n1. Take the flotation of fluorite with ECA for example, under the condition of 50 % recovery rate of mineral, the needed reagent dosage decreases with increasing of the value of n1. As shown in Fig. 4.12, there is a straight linear relationship between reagent dosage and the value of n1. However, the collecting performance of reagent increases first but decreases with the increase of the value of n2. For example, the collecting capability of 12-alkyl-10-ethyoxyl ether acid is better than that of 12-alkyl carboxylic acid. But the collecting capabilities of 12-alkyl-20-ethyoxyl ether acid and 12-alkyl-30-ethyoxyl ether acid are, respectively, worse than that of 12- alkyl carboxylic acid. As shown in Fig. 4.13, there is also a straight linear relationship between reagent dosage and the value of n2. Under the condition of 50 % recovery rate of fluorite, however, the needed reagent dosage increases with increasing of the value of n2. Besides for ether alkyl carboxylic acids, oxyalkyl reagents also include polyoxyethylene phosphonic acids and etheramines [15]. Their structures and properties are similar with each other. The structures of polyoxyethylene phosphonic acids are given as follows [16]: OH RO
(CnH2nO)m
P
O
OH
RO
(CnH2nO)m
O P
Fig. 4.12 Relationship between reagent concentration and the value of n1 under the condition of 50 % flotation of calcium fluorite mineral
(CnH2nO)m
OH
Reagent concentration (mg/L)
RO
n1
4 Structure and Property of Nonpolar Group of Collector
Fig. 4.13 Relationship between reagent concentration and the value of n2 under the condition of 50 % flotation of calcite mineral
Reagent concentration (mg/L)
124
n2
It was reported by J. Leja that a series of oxyethylene reagents are prepared from epoxy ethane and other materials. For example, the reaction of epoxy ethane and mercaptan is as follows: RSH þ nðC2 H4 OÞ ! RSðC2 H4 OÞn H The condensation reaction: RNH2+n(C2H4O)
(C2H4O)nH NR (C2H4O)nH
RCONH2+n(C2H4O)
RCON[(C2H4O)nH]2
Some of these reagents are used as frother or collector. The applications of these reagents used as frother will be expounded in Chap. 7.
References 1. N.P. Peskov, Colloid Chemistry Tutorial (Higher Education Press, 1953) 2. K.L. Sutherland, I.W. Wark, Principles of Flotation Australian Institute of Mining and Metallurgy (INC) Melbourne 1955, pp. 84, 98, 278, 302, 319 3. E. Stamboliadis et al., Trans. AIME 260, 3 (1976) 4. T. Goha et al., Indian. J. Appl. Chem. 21, 223 (1958) 5. K. Shinoda et al. Colloidal Surfactants, p. 42 6. D.Z. Wang, Nonferrous Metals (1964), p. 25 7. I. Iwasaki, S.R.B. Cooke, Trans. AIME 217, 237 (1960)
References
125
8. S.A. Falconer, Trans. AIME 217, 207 (1960) 9. P. Kivalo, E. Lehmusvaara, in Progress in Mineral Pressing (1958) p. 417. XI. IMPC (1957), p. 577 10. F.F. Aplan, D.W. Fuerstenau, in Forth Flotation 50th Anniversary Volume (AIME Inc., New York, 1962), p. 170 11. D.W. Fuerstenau, Flotation foundation (notes): Central and South Mining and metallurgy college intelligence document (1979) 12. P.M. Solozhenkin, C.A.88, 156356 (1978) 13. J. Steininger, Trans. AIME 238, 251 (1971) 14. J.M. Wechuizen et al., in XIth IMPC (1975), p. 121 15. I.G. Pattison et al., Austr. Inst. Min. Met. 250, 25 (1974) 16. C.H.G. Bushell et al., Can. Min. Met. Bull. 51, 137 (1958)
Chapter 5
Structure Relationship Between Polar and NonPolar Group in Collector Molecule
5.1
Correlation Between Size of NonPolar Group and Variety of Polar Group
It is frequently seen that, for the collectors with various polar groups, there is a great difference in the size of nonpolar group. For different polar groups, the problem that what size of nonpolar group makes reagent own enough collecting capability is still not solved. For example, C.I. Mitrofanov proposed the minimum size of nonpolar group for common reagents, and the data are listed in Table 5.1. It can be seen that the results about the size of nonpolar group are not in agreement with the actual data. Especially for the collectors for oxide minerals, the discrepancy is more obvious. For the purpose of establishing the relationship between molecular weight of nonpolar group and variety of polar group, the related theory calculations of polar and nonpolar groups such as CMC, hydrophile–lipophile balance (HLB), and electronegativity will be carried on in the next Chapter. These calculations are not only based on the surface energy of groups but also on the hydrophilicity of mineral. The most basic condition of mineral being enough hydrophobicity after the adsorption of reagent, in fact, lies in that the surface energy of nonpolar group is larger than that of polar group. The following Tables 5.2 and 5.3 display the surface energies of various groups and metal ions at different conditions [1]. These data are only used to show the variation trend of the surface energy of various groups but can not be used to evaluate quantificationally flotation reagent.
© Metallurgical Industry Press, Beijing and Springer Science+Business Media Singapore 2016 D. Wang, Flotation Reagents: Applied Surface Chemistry on Minerals Flotation and Energy Resources Beneficiation, DOI 10.1007/978-981-10-2030-8_5
127
O
O
–SH
O
S
S
P
C
SMe
S
SMe
S
Category of polar group
4
2
1 2
1
1
2 2
Aromatic ring number
C atoms number in alkyl
–NH2
ONa
O
C
SO3Na
C
N SMe
S
Category of polar group
Table 5.1 Ideal size of nonpolar group for common reagents from C.I. Mitrofanov
8
2 3
2
C atoms number in alkyl
–
1 –
2
Aromatic ring number
128 5 Structure Relationship Between Polar and NonPolar Group …
W air/water
W oil/water
–COOH 4330 6820 –OH 24.6 3347.2 104.1 –NH2 2133.8 –CONH2 –CO– Where, W refers to the surface energy; eW refers to energy of –CH2–
Group
1255.2
–SO42− 7531.2
7531.2
W oil/water
7322
2092
eW
Alkyl oil nitrobenzene Air (weak solution) Air (strong solution)
–CH2– in water phase
3389 2448 2510 2920
Ф
3974.8 –N(CH3)+3 the surface energy of the adsorption of monovalent ion in electric double layer; Ф refers to the surface
1255.2
W air/water
–SO4
Group
Table 5.2 Adsorption energies of various groups on different interfaces from Davies (J/mol)
5.1 Correlation Between Size of NonPolar Group and Variety of Polar Group 129
5 Structure Relationship Between Polar and NonPolar Group …
130 Table 5.3 Adsorption energies of metal ions on different surfaces
5.2 5.2.1
Adsorption system Adsorption Adsorption Adsorption Adsorption Adsorption Adsorption Adsorption
of of of of of of of
Li+ on phosphate surface Na+ on phosphate surface K+ on phosphate surface Mg2+ on carboxylic acid surface Ca2+ on carboxylic acid surface Ag+ on phosphate surface Cu2+ on carboxylic acid surface
W/kT 3.6 2.6 HMC, the adsorption of reagent is in the form of semimicelle adsorption. The adsorption amount and the recovery rate increase obviously with increasing C. The surface potential of the mineral gradually reaches zero. 3) When C reaches a higher level, the sign of electric charge changes. Electrostatic force becomes a repulsion force. The adsorption amount and the recovery rate increase slightly with increasing C. Based on the structures and properties of semimicelle and micelle, the relation between CMC and HMC can be expounded. CMC always increases with increasing action of polar group. But the effect of polar group on HMC varies with the change in the surface electrical property of the mineral. When reagent ion and mineral have the different sign of electric charge, HMC is positively correlated with the action of polar group. When reagent ion and mineral have the same sign of electric charge, HMC is negatively correlated with the action of polar group. In the flotation process, the strong electrostatic repulsion between reagent ion and mineral rarely happens. Thus, it is very common that CMC is smaller than HMC in mineral flotation. The distance between CMC and HMC increases with the increase in the zeta potential of the mineral. When the zeta potential of the mineral is zero, there is no electrostatic force. It was reported by Somasundaran that the adsorption amount and the recovery rate increase obviously with increasing reagent concentration in the flotation of quartz with fatty quaternaries. Keeping the zeta potential of the mineral as zero, the
6.2 Critical Micelle Concentration and Related Calculation …
163
needed concentration (equal to HMC) of fatty quaternaries is about 1/10–1/100 CMC. The related results are listed as follows: The number of C atoms in quaternary amine acetate C10 6 10−4 4 10−2
HMC CMC
C12 1 10−4 1.3 10−2
C14 3 10−5 4 10−3
C16 8 10−6 8 10−4
It is well known that the flotation index decreases when the reagent concentration is above a critical value. In general, the critical value is called critical depression concentration (CDC). It is reported that CDC and CMC are of a certain percentage of media relations [14]. For example, CDC is about 4 times of CMC when fatty acid soap is used in the flotation of calcite. The related results are listed as follows:
CHM CMC
Fatty acid soap Sodium Sodium oleate linoleate
Sodium linolenate
Sodium ricinoleate
Oil soap
0.75 1.00
0.20 0.90
0.45 2.00
0.50 2.00
0.15 0.60
(3) Application of CMC to estimate the relationship between polar and non-polar groups In the study of new flotation reagent, it is demanded that some polar or non-polar groups should be introduced to the material which can be further synthesized into a good reagent. CMC can help us to predict the relationship between polar and non-polar groups in reagent. Taking RCOOK for example, when the number of C atoms in R (n) is 15, it can be calculated that logCMC = −2.72. Then, based on the CMC, the number of C atoms in other reagents can be calculated. The number of C atoms that correlate with the CMC is given as follows:
n
RCOOK
RSO3Na
RSO4Na
RNH3Cl
RN(CH3)Br
RCH(COOK)2
15
14.6
14.1
15.3
15.6
19.4
Based on the discussions above, it can be seen that the calculation of CMC can be used to study the reagent performance. Especially, the calculation of CMC can provide quantitative result for the long-chain collector for oxide mineral.
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6 Theoretical Criteria and Calculation for Collector Performance
6.3
Hydrophile-Lipophile Balance (HLB) for Flotation Reagent
6.3.1
Hydrophile-Lipophile Balance (HLB) and Related Calculation Methods
Hydrophile-lipophile balance (HLB) is another criterion for the performance of surfactant. For heteropolarity surfactant, it comprises both hydrophilic polar group and hydrophobic non-polar group. Because the sorts and quantity of groups are diverse, the values of HLB of different molecules are also diverse. The HLB of surfactant can be measured and calculated, respectively. And HLB is usually used to study the performance of the surfactant. The testing methods for HLB are very complex. Some common computational methods are given by the following [15–18]. (1) The group addition method The base addition method (also called Davies equation) is the most common computational method of HLB. Its expression is given as follows: HLB ¼
X
ðhydropilicgroupsvalueÞ
X
ðlyophobigroupsvalueÞ þ 7
ð6:3Þ
The HLB values of common groups of surfactants are found in Table 6.13. Meantime, the HLB values of common surfactants are calculated according to Table 6.13, and the results are listed in Table 6.14. The HLB values of the reagent which are calculated by Davies equation have additivity. That is, the HLB of two mixture reagents (HLB0) is the summation of that of single component (HLBA) and (HLBB). For example, when reagent A is mixed with reagent B in different proportions by weight, the calculation process of HLB0 of the mixture can be given by the following:
Table 6.13 HLB values of common groups in surfactants Hydrophilic group Group –SO4Na –COOK –COONa –N (quaternary ammonium) –NH2 –OH Ester
Hydrophilic group HLB 38.7 21.1 19.1 9.4 1.6 1.9 6.8
Group –O– –COOH –SO3H –PO3H –AsO3H Na+
Lyophobic group HLB 1.3 2.1 4.5 1.1 0.6 17
Group –CH2– –CH3 C=C –CH2–CH2–O–
HLB 0.475 0.475 −0.475 0.33
6.3 Hydrophile-Lipophile Balance (HLB) for Flotation Reagent
165
Table 6.14 HLB values of common reagents according to Davies equation Reagent
HLB
Reagent
HLB
Octadecanoic acid Capric acid Cetylamine Octylamine Docosane sulfonic acid Myristyl sulfonic acid Pentadecane phosphonic acid Octyl phosphonic acid Myristyl arsonic acid Heptyl arsonic acid Methyl isobutyl methanol Alcohol with C6–C8 Butyl alcohol
1.0 4.8 1.0 4.8 1.0 4.8 1.0 4.3 1.0 4.3 5.9 5.6 6.9
Polypropylene glycol ether Terpene alcohol Potassium oleate Sodium oleate Sodium dodecyl sulfate Terephthalic acid Oxalic acid Acidum lacticum Citric acid Starch Carboxymethylcellulose Tannin
5.9 4.6 20.0 18.0 40.0 8.4 11.2 10.0 13.8 11.3 12.3 12.0
HLBO ¼
ðWA HLBA Þ þ ðWB HLBB Þ WA þ WB
It can be seen that the group addition method is very simple and convenient for the calculation of HLBo. (2) The ratio method The ratio method is also called Ryohei Odai method. The expression of HLB is given as follows: P ðorganic group valueÞ HLB ¼ P k ðinorganic group valueÞ
ð6:4Þ
where k refers to a constant (10). The HLB of polar and non-polar groups in surfactants are found in Table 6.15. The HLB of common surfactants is also calculated according to Table 6.15, and the results are listed in Table 6.16. (3) The HLB calculation for fatty acid esters The calculation method for the HLB of fatty acid esters was proposed by Griffin. For polyol fatty acid esters, HLB calculation is expressed by the following:
S HLB ¼ 20 1 A where S refers to the saponification value of ester; A refers to the acid value of fatty acid.
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6 Theoretical Criteria and Calculation for Collector Performance
Table 6.15 HLB value of common groups according to ratio method Inorganic group
HLB
Inorganic group
HLB
Organic and inorganic group
Light metal salts Heavy metal salts, NH4+ –AsO3H, – AsO2H – SO2NHCON=N– NH2 –SO3H –SO2NH– –CONHCO ¼N–OH ¼N–NH– –CONH–
>500 >400
–Hg –NH–NH–
95
>SO2 –SCN
40 70
110 80
300
–O–CO–O–
80
–NCS
70
75
260
–NH2, –NHR, –NR2
70
–NO2
70
70
250 240 230 220 210 200
65 60 60 30 20 155
–CN –NO –ONO2 –NC –NCO –I
40 50 60 40 30 60
70 50 40 40 30 20
–CSSH– –CSOH–COSH –COOH lactone –CO–O–CO–
180 160 150 120 110
>CO –COOR >C=NH –N=N– >O Anthryl, phenanthryl Naphthyl Benzene ring Tribond Double bond Non-aromatic ring
40 20 80 100 80
20 20 150 260 160
–OH
100
–Br, –SH, –S– –Cl, –P –OCSSH >O2PSSH >NCSSH
85 15 3 2 20
–CH2–
Organic HLB
Inorganic HLB
20
For turpentine, beeswax, and lanolinum, the calculation method of HLB is expressed by the following: HLB ¼
EþP 5
where E refers to the percentage of (C2H4O); P refers to the percentage of polyol. For the products that only contain C2H4O, and the polymers of fatty alcohols and C2H4O, the computational method of HLB is expressed by the following: HLB ¼
E 5
6.3 Hydrophile-Lipophile Balance (HLB) for Flotation Reagent
167
Table 6.16 HLB values of common reagents according to ratio method Reagent
HLB
Reagent
HLB
Octanoic acid Capric acid Lauric acid Myristic acid Palmitic acid Octadecanoic acid Oleic acid Decyl sulfonic acid Myristyl sulfonic acid Octadecyl sulfonic acid Docosane sulfonic acid Cerul sulfonic acid Triacontyl sulfonic acid Octylamine Decyl amine Laurylamine Tetradecylamine Ethyl xanthic acid Propyl xanthic acid Butyl xanthic acid
10.7 8.3 6.8 5.7 5.0 4.4 4.5 12.4 9.0 7.0 5.7 4.8 4.2 4.4 3.5 2.9 2.5 12.4 10.8 9.3
Amyl xanthic acid Diethyl phosphorodithioic acid Phenmethyl aerofloat Butyl aerofloat Diethyl dithiocarbamic acid Dipropyl dithiocarbamic acid Dibutyl dithiocarbamic acid Amyl alcohol Hexyl alcohol Heptanol Octanol Oxalic acid Acidum lacticum Gallic acid Starch Sodium oleate Sodium laurate Sodium myristyl sulfonate Sodium octadecyl sulfonate
8.4 14.4 12.3 10.0 10.0 8.0 6.7 10.0 8.3 7.1 6.2 75 62 37 36 19 27 27 21
(4) The HLB calculation for nonionic surfactant According to Kawakami, the calculation method for the HLB of nonionic surfactant can be expressed as follows: HLB ¼ 7:11:7 log
MW MO
where MW refers to the molecular weight of hydrophilic group; MO refers to the molecular weight of lipophilic group. (5) The HLB calculation for nonionic surfactant The calculation method for the HLB of polyoxyethylene surfactants can be expressed as follows: H unit number of EO 100 ¼ L number of C atoms in lipophilic group where EO refers to C2H4O.
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6 Theoretical Criteria and Calculation for Collector Performance
There are some other calculation methods for HLB of surfactants, but here we will not go into them. The simplest Davies equation will be emphatically introduced in the following sections.
6.3.2
Relationship Between HLB and Other Physical Property Values of Reagents
(1) Relationship between HLB and CMC There are some correlations between HLB and CMC. For the reagent with non-polar hydrocarbon chain, the general relation between HLB and CMC can be expressed as follows: log CMC ¼ a þ bðHLBÞ Based on the Davies equation, the expression can be changed to: i X ðhydrophilic groupsÞ ðlyophobicgroupsÞ þ 7 hX i B a¼Ab ðhydropilicgroupÞ þ 7 ; b ¼ 0:475
log CMC ¼ a þ b
hX
where A and B refer to the constants which were mentioned in the equation of CMC. For RCOONa, A = 2.41 and B = 0.341, that is, a = −16.33 and b = 0.718. Therefore, the general relation between HLB and CMC can be expressed as follows: log CMC ¼ 16:33 þ 0:718ðHLBÞ Based on the general relation, the relationship between HLB and CMC for different sodium soaps can be expressed as follows: CMC R9COONa R11COONa R13COONa R15COONa R17COONa
1.0 2.4 4.4 9.0 1.8
HLB 10−10 10−2 10−3 10−4 10−4
21.83 20.88 19.93 18.98 18.03
(2) Relationship between HLB and solubility (S) of reagents There also exist some correlations between HLB and solubility (S). For example, the values of HLB and S of fatty acids are found in Table 6.17.
6.3 Hydrophile-Lipophile Balance (HLB) for Flotation Reagent
169
Table 6.17 Values of HLB and S of fatty acids Fatty acid
S
HLB
Fatty acid
S
R4COOH R5COOH R6COOH R7COOH R8COOH R9COOH R10COOH
0.37 8.3 1.9 4.7 1.7 8.7 5.0
7.2 6.7 6.3 5.8 5.3 4.8 4.3
R11COOH R12COOH R13COOH R14COOH R15COOH R16COOH R17COOH
2.7 1.5 8.8 5.0 2.8 1.5 1.0
10−2 10−2 10−3 10−3 10−4 10−4
HLB
10−4 10−4 10−5 10−5 10−5 10−5 10−5
3.8 3.4 2.9 2.4 2.0 1.5 1.0
The general relationship between HLB and S can be expressed as follows: HLB ¼ a þ b log S where a and b are both constants. Based on one of the values of HLB and S, hence, the other value can be inferred. For example, the values of HLB and S for different primary amines can be expressed as follows:
C10H21NH2 C12H25NH2 C14H29NH2
S (mol/L)
HLB
5.0 10−4 2.0 10−5 1.0 10−6
4.8 3.8 2.9
However, there is no clear quantitative relationship in many instances. For industrial application, the relationship between HLB and the dispersibility based on the measurement and calculation of properties of reagent can be found by the following: Scope of HLB
The dispersibility of reagent
1–4 3–6 6–8 8–10 10–13 >13
There is no dispersibility Bad dispersibility Milky dispersoid Stable dispersoid Transparent dispersoid Diaphanous dispersoid
170
6 Theoretical Criteria and Calculation for Collector Performance
(3) Relationship between HLB and surface tension (r) It is reported that the relation between HLB and surface tension (r) can be expressed by the following: HLB ¼
ab or r ¼ aHLB þ b a
where a and b are both constants. As reported, a = 2.36 and b = 45.3. For the values of HLB calculated by the ratio method, however, a = 2.36 and b = 45.3. (4) Relation between HLB and partition coefficient (K) in oil and water phases The partition coefficient (K) of reagent in oil and water phases is as follows: K ¼ Co =Cw Hence, one of the relations of HLB and K can be expressed by the following: HLB ¼ 26
K 2:6
The other relations of HLB and K can be expressed by the following:
0:45 RT Cw HLB ¼ ln 7 800 Co where Cw refers to the concentration of reagent in water; CO refers to the concentration of reagent in oil.
6.3.3
Application of Molecular Fragment Method to Calculate Hydrophile-Lipophile Property for Flotation Reagent
CMC and HLB can just be used to roughly reflect the hydrophile-lipophile property of flotation reagents. The researches demonstrated that element types, bond types, and interactions between polar atoms also had an important effect on the hydrophile-lipophile property of surfactant. Molecular fragment method is a more accurate way to judge the hydrophilelipophile property of flotation reagents. Distribution constant (P) is introduced in molecular fragment method, which reflects the ratio values of equilibrium concentrations of compounds between organic solvent (n-octyl alcohol) and water. Generally, lgP is used as the criterion of the hydrophile-lipophile property for
6.3 Hydrophile-Lipophile Balance (HLB) for Flotation Reagent
171
flotation reagents. The molecular fragment method is established based on the linear free energy relationship (LFER) of Hammett equation. One compound can be further divided into small fragments including atoms and functional groups. When the standard free energy of one compound transferred from water phase to organic solvent phase is ΔGo, the contribution of one fragment (i) to ΔGo can be expressed as f 0i . According to the principle of LFER, all the fragments (n) to ΔGo can be given by the following: DGo ¼
n X
f 0i
i¼1
C oct P¼ w C where Coct and Cw are the equilibrium concentrations of compounds in organic solvent (n-octyl alcohol) and water, respectively. The relationship between ΔGo and P can be expressed as follows: DGo ¼ RT lnP Therefore, the distribution constant P can be given as follows: lgP ¼
n X
f 0i
i¼1
The equation above indicates that the distribution constant P of flotation reagents can be calculated by adding the contributions of their fragments. Considering the effects of structural factors including deflection of non-polar chain, conjugation effect, unsaturation degree, branched chain, intramolecular hydrogen bond, interaction between polar groups, and charged nature on hydrophobic property of organic compounds, the distribution constant P can be expanded as follows: lgP ¼
n X i¼1
fi þ
n X
fj
j¼1
where fj is the contribution of one structural factor (j) to the distribution constant P. The classification of fragments is very important to the calculation of molecular fragment method. The compounds consist of single atom or polyatom fragments. Single-atom fragments include two classes: (1) The isolated carbon atom IC. The isolated carbon atoms should possess four single bonds, but without two of single bonds connecting heteroatom. Alternately, the isolated carbon atoms can form multiple bonds with other carbon atoms. For example, –C– in CH4 molecule and =C< in H2C=CH2 molecule belong to isolated carbon atoms.
172
6 Theoretical Criteria and Calculation for Collector Performance
(2) The hydrogen atom is connected to IC or heteroatoms connecting all the bonds of IC. For example, H in H–C C–H molecule belongs to single-atom fragments. The polyatom fragments consist of non-isolated carbon (NIC) atoms, hydrogen atom, and heteroatoms. The bonds of a whole polyatom fragments should be linked to IC. The examples for double-atom fragments are as follows: O
O
C
S
C
C
N,
,
N
SH,
,
,
NH
The examples for three-atom fragments are as follows: O
NH2,
SCN,
O
The following examples belong to multiatom fragments: O
O O
C OH ,
NHC
NH2,
POH ,
NH
N
CH
,
NH NH
In general, organic group in reagent molecule is a fragment unit. The other parts of molecule including alkyls, unsaturated alkyls, ring alkyls, and heterocyclic atoms can be further divided into smaller fragments. Fragment constants of common atoms and groups are listed in Table 6.18. The fU is the hydrophobic constant value when fragment is connected to one aromatic group. The fU refers to the hydrophobic constant value corresponding to the fragment connected to the left side of aromatic group, when the fragment has two bonds outward. The f1/U refers to the hydrophobic constant value corresponding to the fragment connected to the right side of aromatic group. The fUU is the hydrophobic constant value when the fragment is connected to two aromatic groups. The f1R is the hydrophobic constant value when the fragment is connected to benzyl group. The fx is the hydrophobic constant value when the fragment is connected to aromatic group with electron-withdrawing substituent. The fx1 refers to the hydrophobic constant value when the inductive effect value (rI) of electron-withdrawing substituent is from 0.3 to 0.6. The fx2 refers to the hydrophobic constant value when rI is bigger than 0.6.
−2.18
–S– H –NH –OH –SH –NH2
OP(O)O2
–NO –NO2 –O– –S(O)– –SO2
−0.79 0.23 −2.15 −1.64 −0.23 −1.54
0.11 −1.16 −1.82 −3.01 −2.67 −2.29
−0.93
0.06 −0.38 0.59
–Cl –F –I
N
0.94 0.37 1.35
0.20
–Br
−0.03 0.23 −1.03 −0.44 0.62 −1.00
−0.03 −0.61 −2.12 −2.17 −1.71
1.09
f
Fragment
fU
−0.09
0.77
0.53 −1.62 −1.28
−1.13
fUU = 0.48
fx1 = −0.23 f1R = −1.35
fx1 = −0.37 fx1 = 0.32 f1R = −1.34
fx1 = −1.50
f = 0.09 fx1 = −0.22 fx2 = 0.17
x2
f1R = −1.76
f
1R
Special type
Table 6.18 Fragment constants of common atoms and groups
CON
–NHCONH2
NCONH2
–CO2H –CH=NOH –CONH2 –NHCONH–
–C(O)– –CO2– –CO(−) 2 –CH=N– –CONH– –OCONH– –COH
–CF3 –CN
C
Fragment
−2.18
−1.11 −1.02 −2.18 −21.8
−2.71 −1.79 −1.10
−1.90 −1.49 −5.19
−1.27 −3.04
0.20
f
−1.07
0.03 −0.15 −1.26 −1.57 −2.25
−1.09 −0.56 −4.13 −1.03 −1.81 −1.4 −0.42
1.11 −0.34 −2.80
0.20
fU
−0.82 −2.15
−1.84 −1.06
−0.50 −0.09
−1.93
fUU
fx1 = −0.82 f1R = −1.99
f1R = −1.03
f1/U = −1.51 f1/U = −0.91
fx1 = −0.83 f1R = −1.77 fx1 = −0.36 f1R = −1.38
f1R = −0.88 f1/U = −2.20
Special type
6.3 Hydrophile-Lipophile Balance (HLB) for Flotation Reagent 173
174
6 Theoretical Criteria and Calculation for Collector Performance
Table 6.19 Fragment constants of atoms and groups in common aromatic ring Fragment N
fU
Fragment
fU
−1.12
C
0.13
−1.60 N
−0.56
Φ
o
0.225 (aromatic ring connected to carbon atom)
* C
0.44 (aromatic ring connected to heteroatom)
C
N
−2.14
CH
0.355
−3.46
–C(O)–
−0.59
−0.08 0.36 −2.08
–OC(O)– –CH=N–NH– –N=CH–NH–
−1.40 −0.47 −0.79
Se
0.45
–NHC(O)–
−2.00
NH
0.65
–N=CH–O–
−0.71
–N=CH–S–
−0.29
N
N
N O O S O S
The fU refers to the hydrophobic constant value of fragment for lgP calculation of aromatic ring and aromatic ring compounds. Fragment constants of common atoms and groups in common aromatic ring are listed in Table 6.19. Distribution constant of flotation reagent can be calculated by fragment method. For example, Palmitic acid C15H31COOH lg PPalmitic acid ¼ 15f C þ 31f H þ ð15 1ÞFb þ f COOH ¼ 15 0:2 þ 31 0:23 þ ð15 1Þ ð0:12Þ þ ð1:11Þ ¼ 7:34 a-Bromo palmitic acid C14H29CH(Br)COOH lg Pabromo palmitic acid ¼ lgPpalmitic acid þ f Br f H þ Fb þ FHSP ¼ 7:34 þ 0:2 þ ð0:23Þ þ ð0:12Þ þ 0:85 ¼ 8:04 Toluene arsonic acid CH3C6H4AsO3H2
6.3 Hydrophile-Lipophile Balance (HLB) for Flotation Reagent
175
lgPToluene arsonic acid ¼ 7f C þ 7f H þ ð6 1ÞFb þ 3F/ð¼Þ þ ð2 1ÞFb þ f /AsO3 H2 ¼ 7 0:2 þ 7 0:23 þ ð6 1Þ ð0:09Þ þ 3 ð0:42Þ þ 2 ð0:12Þ þ ð1:90Þ ¼ 0:74 Hydrophobic constant values of structure factors are found in Table 6.20. Hydrophobic constant values of halogenate factor are listed in Table 6.21. Fragment constants and chain factor of various ammonium salts are listed in Table 6.22. Molecular fragment method can not only be used to calculate the hydrophobic property of whole compounds, but also be used for the calculation of atoms or groups. Compared to the calculation of CMC and HLB, molecular fragment method can be used to calculate the more complicated flotation reagents. Comprehensive comparison of lgP, CMC, and HLB values for common reagents are given in Table 6.23.
Table 6.20 Hydrophobic constant values of structure factors Structure factors
Hydrophobic constant Fð¼Þ
−0.55
Connected U
FU ð¼Þ
−0.42
Connected to two U
U FU ð¼Þ
−0.00
FðÞ
−1.42
U FU ð¼Þ
−0.00
Fb Fb FbYN FbYP FcBr FgBr
−0.12(n −0.09(n −0.20(n −0.31(n −0.13 −0.22
Double bond
Triple bond Connected to two U Chain Loop chain Amine chain Phosphate ester chain Branched chain Group branched chain Interactions between polar groups In the chain
Alicyclic groups
Hydrogen bond
FP1 FP2 FP3 FP1 FP2
In aromatic ring
FU P1
N–P O–P
FU P2 FHBN FHBO
− − − −
1) 1) 1) 1)
P 0:42 f 1 þ f 2 P 0:26 f 1 þ f 2 P 0:10 f 1 þ f 2 P 0:32 f 1 þ f 2 P 0:20 f 1 þ f 2 P 0:16 f 1 þ f 2 P 0:08 f 1 þ f 2 0.60 1.0
176
6 Theoretical Criteria and Calculation for Collector Performance
Table 6.21 Hydrophobic constant values of halogenate factor Fragment
Number of a-F atoms 1
–CO2H –C(O)OAlk –C(O)Alk –C(O)Ar –CH2CO2H –S–Ar –S–Ar –C(O)–NH–Ar –C(O)–NH–Alk –C(O)–NH2 –SO2–Ar
2
3
0.89
Number of a-Cl atoms 1 2 3
Number of a-Br atoms 1 2 3
0.90
0.85 0.85
0.98
1.20
1.07 0.87 1.17
0.86 0.68
0.91 0.97
1.31 1.49
1.47 1.71 1.65 1.70 2.01 2.78
0.76 0.91 1.05
1.15 1.33
1.28 1.61
0.91 0.92
1.09
1.06
Table 6.22 Fragment constants and chain factor of various ammonium salts Compound
Primary ammonium salt
Secondary ammonium salt
Tertiary ammonium salt
Quaternary ammonium salt
f
fN3:4 þ H3 Cl
fN3:86 þ H2 Cl
fN3:63 þ HCl
fN3:05 þ I
Fb+1 (first bond) Fb+2 (second bond) Fb+3 (third bond) Fb+4 (forth bond) Fb+5 (fifth bond) Fb+6 (sixth bond)
−0.68
−0.68
−0.76
−0.90
−0.40
−0.40
−0.48
−0.59
−0.26
−0.26
−0.34
0.45
−0.19
−0.19
−0.27
−0.35
−0.12
−0.12
0.20
−0.31
−0.12
−0.12
−0.20
−0.27
Remarks fN/þ Br ¼ 4:07 when fragment is connected to benzene ring fNP þ Br ¼ 5:02 when fragment is in pyridine fNQþ Br ¼ 5:78 when fragment is connected to quinoline
6.3 Hydrophile-Lipophile Balance (HLB) for Flotation Reagent
177
Table 6.23 Comprehensive comparison of lgP, CMC, and HLB values for common reagents
Lauric acid Palmitic acid Stearic acid Sodium oleate Lauryl sodium sulfate Sodium hexadecyl sulfate Sodium dodecyl sulfate Sodium dodecyl benzene sulfonate Toluene arsonic acid Benzyl arsonic acid Heptyl arsonic acid Octylamine Lauryl amine Cetylamine Hexadecylpyridinium bromide Isooctyl alcohol Terpene alcohol Oxalic acid Tannin Starch
6.3.4
Flotation reagents
CMC (mol/L)
C11H23COOH C15H31COOH C17H35COOH C17H33COONa C12H25OSO3Na C16H33OSO3Na C12H25SO3Na C12H25C6H4SO3Na
2.4 9.0 1.8 2.1 8.2 2.1 9.8 1.2
CH3C6H4AsO3H2 C6H5CH2AsO3H2 C7H15AsO3H2 C8H17NH2 C12H25NH2 C16H33NH2 C18H37C5H5NBr C8H17OH C10H17OH (COOH)2 C6H2(OH)3COOH C6H9O4OH
10−2 10−4 10−4 10−3 10−3 10−4 10−3 10−3
1.3 10−2 8.3 10−4 9.0 10−4
HLB
lgP
3.9 2.0 1.0 18.0
5.18 7.34 8.42 2.92 1.60 3.76 0.96 2.86
22.8 24.2 8.6 8.6 4.3 4.8 2.9 1.0 6.1 4.6 11.2 12.0 11.3
0.31 0.31 1.13 2.57 4.41 6.25 2.75 3.02 2.54 −0.29 −0.06 −2.98
The Prediction of Uses of Reagent
(1) Application of HLB to predict reagent category In general, the value of HLB of collector is smallest. The value of HLB of depressant is largest. And the value of HLB of frother falls in between collector and depressant. Therefore, the HLB can be used to predict the reagent uses. According to the calculated values of HLB of various reagents, the categories of various reagents can be concluded as follows:
178
6 Theoretical Criteria and Calculation for Collector Performance
Reagent category
Scopes of HLB The base addition method
The ratio method
Collector for oxide minerals Collector for sulfide minerals Frother Depressant
1–4 4–7 5–7 >10
3–7 8–15 6–10 >35
The flotation reagents used in industries usually are comprised of a number of ingredients. By using the HLB calculation of group addition method, hence, it is convenient to predict the reagent uses. Taking a complex reagent with 50 % octadecanoic acid and 50 % heptylic acid for example, the value of HLB of octadecanoic acid is 1.0, and the value of HLB of heptylic acid is 5.7. The value of HLB of the complex reagent can be calculated via the base addition method as follows: HLBO ¼
1:0 0:5 þ 507 0:5 ¼ 3:35 0:5 þ 0:5
The result shows that this complex reagent can be used as collector. And its collecting capability may be equivalent to that of lauric acid. Providing the complex reagent comprising 30 % octadecanoic acid and 70 % heptylic acid, the value of HLB of the complex reagent is 5.7. The complex reagent can be used as frother. Meantime, it also has a certain collecting capability. (2) Application of HLB to predict the usage of reagent Aiming at improving the flotation behavior of reagent, it is necessary to make reagent disperse and dissolve completely in pulp. It has been mentioned that there exists a relation between HLB and solubility of reagent. Therefore, the solubility of reagent can be inferred according to the HLB. If the HLB of reagent system is bigger than 10, it can directly dissolve in the solution. If the HLB of reagents is smaller than 10, however, it cannot directly dissolve in the solution. Therefore, some methods must be considered to improve the solubility of reagent. The methods can be given as follows: 1) When the reagent can be neutralized or saponified, sodium salt can be added to the solution to improve the solubility. The reason lies in that
6.3 Hydrophile-Lipophile Balance (HLB) for Flotation Reagent
179
the HLB of Na+ is large according to the base addition method. That is, sodium salt is able to improve the solubility of the reagent with small HLB. 2) Based on the calculation of HLB, it is helpful to choose the emulsifier, solubilizer, and wetting agent to dilute the reagent. The reference value of HLB for the possible application of reagent can be concluded as follows:
Scope of HLB
The possible application of reagent
1–3 3–6 7–9 8–18 13–15 15–18
Defoamer W/O emulsifier Wetting agent O/W emulsifier Wetting agent Solubilizer
The flotation performance of reagent is successfully enhanced when an emulsifier or a wetting agent is applied to the flotation process. For instance, alkyl sulfonate is used to disperse kerosene collector in the flotation of molybdenite. Lignosulfonate is applied as wetting agent to the flotation process of mineral using insoluble white drug (thiourea). (3) Application of HLB to predict the proportion of polar group and non-polar group For the aliphatic hydrocarbon of C8–C10, provided that the proportion of C8, C9, and C10 is the same, it can be calculated that the value of HLBO of fatty acid of C7–C9 is 5.3. This fatty acid does not have enough collecting capability and has bad selectivity. If one –OH is added to the fatty acid, the value of HLBO of fatty acid becomes 7.2, and it can act as a frother. If one –SO3H is added to the fatty acid, the value of HLBO of fatty acid becomes 9.8, and fatty acid starts to exhibit depressing capability. If two –SO3H are added to the fatty acid, the fatty acid can act as a typical depressant. During the chemical synthesis of alkylphosphonic acid, it can be calculated that the value of HLB of collector must be above 4. For n-alkyl, the value of HLB of amyl is able to make the reagent possess the mere collecting capability. Therefore, only when the material containing hydrocarbon chain is equivalent to amyl, the synthetical reagent is able to act as a good collector.
180
6.4 6.4.1
6 Theoretical Criteria and Calculation for Collector Performance
Electronegativity and Related Calculation for Flotation Reagent Electronegativity and Related Calculations
Electronegativity is an orbital indicating non-metallic property of an element atom. Many calculations related to electronegativity were proposed by L. Pauling, Mulliken, Sanderson, Gordy, Allred-Rochow, Jaffè, Allen, etc. [19–21]. According to Pauling, electronegativity is a measure of the relative capability of an atom to attract electrons in molecule A–B. When the electronegativity difference of two atoms (A–B) is large, the valence electrons are toward the atom of large electronegativity to form polar bond. In general, chemical bond is intermediate between the pure covalent bond (A:B) and pure ionic bond (A+B−). Assuming that the bond energy of the theoretical covalent bond (DAB) is the arithmetic mean of that of the same atoms (DAA and DBB), the actual bond energy of the covalent bond is above the arithmetic mean. The difference between the actual bond energy and its theoretical value (DE), hence, can be expressed as follows: 1 DE ¼ DAB ðDAA þ DBB Þ 2 It was accepted by Pauling that DE is concerned with the electronegativity difference of A and B atoms (Dx). The empiric formula for the relation between DE and Dx can be given by the following: 23Dx2 ¼ DE or rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 jxA xB j ¼ 0:208 DAB ðDAA þ DBB Þ 2 Based on the electronegativity of H atom xH = 2.1, the electronegativity of other atoms can be calculated. Afterward, thermochemistry electronegativity was proposed by Pauling. The relation between DE´ and xP can be given by the following: DE0 ¼ DAB ðDAA þ DBB Þ2 1
and
pffiffiffiffiffiffiffiffi Dx ¼ 0:182 DE 0
6.4 Electronegativity and Related Calculation for Flotation Reagent
181
According to Mulliken Mark, the electronegativity of atom is based on the ionization potential (I) and the electron affinity (E). The calculation method of xM can be given by the following: 1 xM ¼ ðI þ EÞ 2 The relation between xM and xP can be expressed as follows: xM 2:7xP However, the coefficient can also be 2.3 or 3.1 proposed by some other ones. According to Gordy Mark, the electronegativity of atom is based on the effective charge (Z*) and the radius of covalent bond (r). The calculation method of xG can be given by the following: xG ¼ a
Z þb r
where a and b refer to the constants, respectively. The Pauling electronegativity has the features of practicability. The Pauling electronegativity of the common element is given by the following. The electronegativity difference can express the polarity of chemical bond. According to Pauling, the ionicity percentage is given by the following:
182
6 Theoretical Criteria and Calculation for Collector Performance
1 u% ¼ 100½1 exp ðxA xB Þ2 4
ð6:5Þ
where u refers to the ionicity percentage. When u is 50 %, Δx is j1:7j. According to Hannay, the ionicity percentage is given by the following: u% ¼ 16ðDxÞ þ 3:5ðDxÞ2
ð6:6Þ
Wilmshurst proposed that the ionic character can express the polarity of molecule. The ionic character is given by the following: I% ¼ jxA xB j=ðxA þ xB Þ
6.4.2
Calculation of Group Electronegativity of Flotation Reagent
Because the electronegativity of an atom located in molecule is influenced by the adjacent or the spaced atoms, the electronegativity of the atom will change. For different groups, the same atoms have different electronegativities. In general, group electronegativity is to characterize the feature of group. Some calculation methods of group electronegativity and related results are found in Tables 6.24 and 6.25 [22–27].
Table 6.24 Calculation methods of group electronegativity Calculation formula
Symbolic meaning
Ref.
x ¼ 0:31ðn þ 1=rÞ þ 0:5 xA xA n ¼ ðN pÞ þ m 2þs xA þ xB xA þ xB
x—group electronegativity; n*—the number of effective valence electrons in AB group; r—covalent radius; N—the number of valence electrons of A atom; P—the number of bonded electrons by B atom; m—the number of bonded electrons; s—the number of resonators;
[28]
x—group electronegativity; n*—the number of effective valence electrons of A; r*—effective radius; n—the bond number difference between A and B; m —the number of bonded electrons in B atom; P—the number of unbonded electrons in B atom; a— isolation coefficient (2.7);
[29]
x ¼ n =r
n ¼ nþ2
X
xA 1 X xB xA m þ p xA þ xB xA xB a
(continued)
6.4 Electronegativity and Related Calculation for Flotation Reagent
183
Table 6.24 (continued) Calculation formula 2 z xi ¼ a i þ bz i þ C ni N X xA d¼N 2 xA þ xB i¼1 2 jdj½ðxr Þi ðxA Þi 3 2 ðxg Þi ðxA Þi jdj½ðxr Þi ðxl Þi 3 m X xB ð þ mqÞ ¼ xB ðoÞ þ q Dxiþ
ðxg Þi ¼ ðxA Þi þ
i¼1
xB ðnqÞ ¼ xA ðoÞ þ q
m X
Dx i
i¼1
ri fxB þ 1 ðoÞ xB ðoÞg 1 rk r j Dx fxA ðoÞ xA1 ðoÞg i ¼ 1 rk
Dxiþ ¼
Symbolic meaning
Ref.
xi—atom orbit electronegativity; zi*—the number of effective valence electrons of A; N—e the number of bonded electrons between A and B; ni*—the principal quantum number of i orbit; m— the number of bonded electrons in B atom; (xg)i— group electronegativity of i orbit; (xr)i, (xl)i—group electronegativity of i orbit of other atoms;
[30]
xB(o), xA(o)—group electronegativity of free A and B; xA(−nq), xB(+mq)—group electronegativity of bonded A and B; n, m—oxidation number; q—the motion of electric charge; Dx+i , Dx−j —the change of x because the motion of electric charge;
[31]
Table 6.25 Group electronegativity calculated according to various methods Group
Calculation method (Ref.) Wilmshurst
Hinze
Muller
Clifford
Daily
Zhang
Yuan
Me. Domel [34]
Wang (Author)
[28]
[30]
[30]
[32]
[33]
[30]
[29]
OH
3.98
3.82
3.45
3.10
3.51
3.84
3.58
3.60
3.9
SH
2.61
2.83
–
–
2.45
2.24
2.60
3.20
2.6
CN
3.17
–
3.20
2.60
2.52
3.2
2.90
3.30
3.04
NH2
3.40
2.96
3.00
–
2.99
3.01
3.09
–
3.7
COOH
2.84
–
2.85
–
2.57
2.90
3.13
–
4.1
NO2
3.45
–
–
3.20
–
–
–
–
3.8
Because the group structure of flotation reagent is more complex than that in Table 6.25, the group electronegativity of reagent is not characterized by the existing methods. Based on the structural features of reagent and various concepts of inductive effect index and the ratio of charge, a modified method is applied to calculate the group electronegativity of reagent. The modified method can be expounded as follows: The structure of flotation reagent is as follows:
A
B 0
where A refers to the bonding atom.
D
C 1
2
184
6 Theoretical Criteria and Calculation for Collector Performance
As mentioned above, Gordy Mark proposed that the electronegativity of atom can be expressed as Z*/r. Z*/r is called the atom potential and is a measure of the capability of an atom to attract a pair of electrons at covalent radius. Usually, the computational method of Z* is as follows: Z ¼ Z r where r refers to the screening constant. Based on the proposition of Gordy, the value of r of the valence electron is 0.5; the value of r of the inner layer electron is 1.0. Therefore, G.X. Xu proposed a modified computational method for Z*, and the expression can be given as follows: Z ¼ Z ½ðZ nÞ ðn 0:5Þ ¼ 0:5n It shows that the number of effective charges is connected with the number of effective valence electrons. Hence, if the number of effective valence electrons in molecule is expressed as n*, the group electronegativity of reagent can be given by the following: xg ¼ a þ b
n r
where xg refers to the group electronegativity; a and b refer to a constant, respectively. Adopting the calculation method of Pauling electronegativity, the above formula can be changed to:
n þ 1 xg ¼ 0:31 þ 0:5 r
ð6:7Þ
For the calculation of n*, the number of unbonded electrons of the bonding atom and related correction parameters can be given by the following: (1) The number of unbonded electrons of the bonding atom is equal to N P where N refers to the number of valence electrons of A atom; P refers to the number of bonded electrons by B atom. (2) The proportion of electron pairs of A–B of the A atom is as follows: X
where m0 refers to the 0-bond.
2mo
xA xA þ xB
6.4 Electronegativity and Related Calculation for Flotation Reagent
185
(3) The inductive effect of unbonded electrons (s0) of the B atom is as follows: X xB xA s0 xB þ xA (4) The proportion of electrons of B–C of the B atom is as follows: 1X xB 2m1 a xc þ xB where a refers to the isolation coefficient (a = 2.7). (5) The inductive effect of unbonded electrons (s1) of the C atom is as follows: 1X xC x B 2s1 a xC þ xB A For ease of writing, make e0 ¼ xB xþA xA ; d0 ¼ xxBB x þ xA
e1 ¼
xB xC xB ; d1 ¼ xB þ xA xC þ xB
To facilitate the calculation, it can be assumed that those atoms after B atom meet the following criteria: e = d. Hence, the number of the effective valence electrons (n*) in molecule can be expressed as follows: n ¼ ðN PÞ þ
X
2m0 e0 þ
X
s 0 d0 þ
X 2mi þ si ai
di
ð6:70 Þ
where i refers to the atomic number difference. The values of e and d are given as follows. e value xS =xS þ xC ¼ 0:500 d value xS xC =xS þ xC ¼ 0 e value xO =xO þ xS ¼ 0:583 d value xO xS =xO þ xS ¼ 0:166 e value xO =xO þ xN ¼ 0:538 d value xO xN =xO þ xN ¼ 0:077 e value xC =xC þ xH ¼ 0:541 d value xC xH =xC þ xH ¼ 0:087
xO =xO þ xC ¼ 0:583 xS =xS þ xP ¼ 0:543 xO xC =xO þ xC ¼ 0:166 xS xP =xS þ xP ¼ 0:087
xO =xO þ xP ¼ 0:625
xO =xO þ xAS ¼ 0:635
xO xP =xO þ xP ¼ 0:250 xO xAS =xO þ xAS ¼ 0:272
xN =xN þ xC ¼ 0:545
xN =xN þ xH ¼ 0:410
xN xN =xP þ xC ¼ 0:091 xN xH =xN þ xH ¼ 0:176
xN =xN þ xP ¼ 0:583
xAS =xAS þ xC ¼ 0:443
xN xP =xN þ xP ¼ 0:176 xC xAS =xC þ xAS ¼ 0:111
The calculation process of the group electronegativity for xanthate and aerofloat is, respectively, given by the following: (a) The calculation process of the group electronegativity for xanthate S S
O
C 0
1
C 2
3
186
6 Theoretical Criteria and Calculation for Collector Performance
8 6 2 n ¼ ðN PÞ þ 2eSC þ dOC þ dOC þ 2 dOC ¼ 6:37 a a a
n þ1 xg ¼ 0:31 þ 0:5 ffi 2:7 r (b) The calculation process of the group electronegativity for aerofloat S
S C
P
C
O 0
1
C 2
3
8 12 4 dOP þ 2 dCO ¼ 7:37 n ¼ ðN PÞ þ 2ePS þ dSP þ a a a
n þ1 xg ¼ 0:31 þ 0:5 ffi 3:0 r The group electronegativities of the other reagents are found in Table 6.26.
Table 6.26 Group electronegativity of various collectors Collector
Molecular formula
xg
Fatty alcohol Mercaptan Xanthic acid Thiocarbonic acid
R–OH R–S(H) R–OCSS(H) R–OCOS(H) R–OCSO(H) R–SCSS(H) (RO)2PSS(H) (RO)2POS(H) (RO)2PSO(H) (RO)2POO(H) R2–NCSS(H)
3.9 2.6 2.7 2.8 3.4 2.6 3.0 3.2 3.4 3.6 2.6 2.6
Trithiocarbonic acid Dithiophosphoric acid Thiophosphoric acid Dialkyl phosphoric acid Dithiocarbamic acid Benzothiazole mercaptan
S C
S(H)
C
S(H)
N
Benzimidazole mercaptan
2.7
HN N
(continued)
6.4 Electronegativity and Related Calculation for Flotation Reagent
187
Table 6.26 (continued) Collector
Molecular formula
Benzoxazolyl mercaptan
xg 2.7
O C
S(H)
N
Benzoyloxy mercaptan
3.3
S(H) COOH
Diphenylthiourea Thiocarbamate Dixanthogen Xanthic acid ester Dithiophosphoramidic acid Dialkyl thiophosphoryl chloride Fatty acid Hydroxy acid Alkyl sulfonic acid Hydroximic acid Alkyl arsonic acid Alkyl phosphoric acid Fatty amine
(C6H5NH)2CS R–NHC(S)O–R′ R–OCS(S)–(S)SSCO–R R–OC(S)S–R′ (RNH)2PSS(H) (RO)2PSCl R–COO(H) R–CH(OH)COO(H) R–SO3(H) R–C(OH)NO(H) R–AsO(OH)2 R–PO(OH)2 R–NH2
2.9 2.9 2.8 3.2 4.1 4.2 4.3 3.8 4.3 4.3 3.7
Table 6.27 Group electronegativity and maximum absorption wavelength (kmax) of various sulfide collectors Reagent
Molecular formula
xg
kmax (lm)
Thiocarbonic acid Dithiocarbonic acid Trithiocarbonic acid Dixanthogen Dithiocarbamate Thiocarbamate Alkyl phosphoric acid Thiophosphoric acid Dithiophosphoric acid Benzothiazole mercaptan
R–OCOSH, R–OCSOH R–O–CSSH R–SCSSH (R–OCSS)2 R2–NCSSH R–NHCSOR′ (R–O)2POOH (R–O)2POSH, (R–O)2PSOH (R–O)2PSSH
3.4 2.7 2.8 2.9 2.6 2.8 3.6 3.4 3.1 2.6
222 301 330 280 280.5 242 13
Chalcopyrite (xg−xzn)2 pH
pH 1.7 0.81 0.64
Sphalerite (xg−xzn)2
3.5 10.5 10.5
pH
1.4 0.64 0.49
Pyrite (xg−xzn)2
9.4 11.8 >13
pH
194 6 Theoretical Criteria and Calculation for Collector Performance
6.4 Electronegativity and Related Calculation for Flotation Reagent
195
14
Fig. 6.9 Linear relationship between Dx2 and critical pH
Critical pH
12 10 8 Δ—FeS2 —PbS —CuFeS2
6 4 0.0
0.5
1.0 Δx 2
1.5
2.0
Based on the calculation of the data above, the linear relationship between Dx2 and critical pH is shown in Fig. 6.9.
6.4.5
Uses of Group Electronegativity to discuss the Structure—Performance of Flotation Reagent
(1) Application of group electronegativity to discuss reagent performance Based on the data of Table 6.26, collectors can be divided into the following three categories: Criterion
(I) sulfide collector
(II) transition metal oxide collector
(III) oxide collector
xg xg – xH u% (Hanny Mark) u% (Pauling Mark) xM xg – xM u% (Hanny Mark) u% (Pauling Mark)
2.5–3.3 0.4–1.2 7.0–24 4.0–31 1.8–2.4 0.1–1.5 2.0–30 0.3–43
3.7–3.9 1.6–1.8 30–40 47–55 1.5–1.8 1.9–2.4 37–46 59–70
4.0–4.2 1.9–2.1 45–50 59–66 0.9–1.5 2.5–3.3 50–65 79–93
where xg refers to the electronegativity of reagent; xM refers to the electronegativity of metal; and xH refers to the electronegativity of hydrogen atom; u refers to the ionicity percentage of chemical bond.
196
6 Theoretical Criteria and Calculation for Collector Performance
For the sulfide collectors of type I, the interaction of collector and mineral is governed by chemical adsorption and surface chemical reaction. The valence bond between reagent and mineral metal is covalent bond. The bonding atom usually is S atom. Because of the small values of group electronegativity, the collector containing the bonding S atom can easily react with those metals of large group electronegativity. That is, those collectors of type I are more prone to react with the chalcophile or sulfophilic elements such as copper (Cu), lead (Pb), and zinc (Zn). In general, the bond covalency increases with decreasing Dx or Dx2; the collecting capability of reagent increases with the decrease of Dx. For the oxide collectors of type III, the bonding atom usually is O atom. Because of the large group electronegativity, the oxide collector can easily react with those metals of small values of group electronegativity. That is, those collectors of type III are more prone to react with the lithophilic-oxophilic elements such as calcium (Ca), magnesium (Mg), and Barium (Ba). In general, the interaction of these collectors and mineral is governed by electric double layer adsorption and ionic bond chemical adsorption. Therefore, the collecting capability of reagent increases with the increase of Dx. For the transition metal oxide collectors of type II, the bonding atom usually is O or N atom. Because of the intermediate value of group electronegativity, those collectors of type III are more prone to react with the siderophile elements such as Ti, Cr, Mn, and Fe. The sulfide containing the siderophile elements can be collected with the sulfide collector. The oxide ores containing the ironophilic elements can be collected with the oxide collector. But the transition metal oxide collector such as hydroxamic acid has the stronger collecting capability and selectivity. As mentioned above, when the collecting capability of reagent is too strong, the selectivity of reagent may decrease. For the same type of reagents, hence, the collecting capability of reagent may decreases with increasing Dx, but the selectivity increases. For example, compared xanthate with aerofloat, the value of Dx of aerofloat is relatively large, and the collecting capability of aerofloat is relatively small, but the selectivity is relatively better. (2) Application of electronegativity to discuss the activity of flotation reagent on mineral surface J.H. Chen et al. proposed that the interaction energy between flotation reagent and mineral surface can be expressed as follows: DE ¼ DE1 þ DE2 þ DE3 þ DE4
ðaÞ
where DE1 is the energy dissipation of the water molecules out from polar groups of flotation reagent; DE2 is the energy dissipation of the water molecules out from mineral surface; DE3 is the energy dissipation of reagent adsorbed on mineral surface; DE4 is the energy dissipation between water molecules.
6.4 Electronegativity and Related Calculation for Flotation Reagent
197
According to Pauling and Pritchard, the relationship between the interaction energy and electronegativity can be expressed as follows: 1 DE ¼ DAB ðDAA þ DAB Þ 2 And 23Dx2 ¼ DE Hence,
1=2 1 jxA xB j ¼ 0:208 DAB ðDAA þ DBB Þ 2 9 pffiffiffi DE1 ¼ 23K n xg xH ðxO xH Þ > > > pffiffiffi > DE2 ¼ 23K nðxA xB ÞðxO xH Þ = pffiffiffi > DE3 ¼ 23K nðxA xB Þ xg xH > > > pffiffiffi ; DE4 ¼ 23K nðxO xH ÞðxO xH Þ
ðbÞ
According to the electronegativity calculated by D.Z. Wang, the comparison between results of energy calculated by the way of GPT equation and by Eqs. (a) and (b) is listed in Table 6.29. As shown in Table 6.29, the order of the energies calculated using Eqs. (a) and (b) is in agreement with that of GPT equation. (a) Effects of polarity of mineral surface on interactive energy of flotation reagents Supposing that polarity of minerals is continuous, the derivative of Eq. (b) can be given as follows:
Table 6.29 Comparison between results of energy calculated by the way of quantum chemistry and by Eq. (b) Polar group
R–SCSSH R2–NCSSH R–OCSSH R–OCSOR R–NHCSO–R′ R–OCSS–R′ (RO)2PS (OR′)
Chalcopyrite energy Calculated by Eqs. (a) and (b) /(kJ mol−1)
GPT method /a. u.
165.6 165.6 147.2 128.8 128.8 110.4 55.2
2.01 1.65 1.47 1.13 1.3 0.71 0.85
Pyrite energy Calculated by Eqs. (a) and (b) /(kJ mol−1) 144.9 144.9 128.8 112.7 112.7 96.6 48.3
GPT method /a. u. 0.36 0.28 0.31 0.27 0.21 0.17 0.12
198
6 Theoretical Criteria and Calculation for Collector Performance
pffiffiffi dDE ¼ 23K n DxgH DxH2 O dxAB The critical value of xg is 3.5 when dDE=dxAB becomes zero. Therefore, the interactive energy (ΔE) of polar groups of flotation reagents with mineral surface increases with decreasing polarity of mineral surface when the value of xg is less than 3.5. The interactive energy (ΔE) of polar groups of flotation reagents with mineral surface increases with increasing polarity of mineral surface when the value of xg is bigger than 3.5. (b) Effects of polarity of polar groups of reagents on interactive energy of flotation reagents Supposing that xg is continuous, the derivative of Eq. (b) can be given as follows: pffiffiffi dDE ¼ 23K nðDxAB DxH2 O Þ dxg The polarity of mineral A–B bond is less than that of water. For metal sulfide (MS), ðDxAB DxH2 O Þ < 0, the interactive energy (ΔE) of polar groups of flotation reagents with mineral surface increases with decreasing value of xg. For metal oxide, ðDxAB DxH2 O Þ > 0, the interactive energy (ΔE) of polar groups of flotation reagents with mineral surface increases with increasing value of xg. The effects of polarity of polar groups of reagents on interactive energy of flotation reagents are given in Tables 6.30, 6.31, and 6.32.
Table 6.30 Adsorption concentration of ethyl xanthate on different mineral surface Mineral
Polarity (xA − xB)
Adsorptive concentration (mg m−2)
Calculated ΔE (kJ mol−1)
Fluorite 3.0 0.75 −294.4 Quartz 2.1 0.79 −147.2 Malachite 1.96 1.39 −103.5 Hematite 1.70 1.58 −55.2 Sphalerite 0.90 3.57 92 Pyrite 0.82 4.06 105.8 Galena 0.70 7.55 128.8 Chalcopyrite 0.6 11.2 147.2 Note 1 Concentration of ethyl xanthate is 5.0 10−4 mol/L, and mass of all mineral is 2 g; 2 data of element electronegativity come from reference [37], and electronegativity of group is calculated by reference
6.4 Electronegativity and Related Calculation for Flotation Reagent
199
Table 6.31 Adsorption concentration of dodecyl sulfonic acid sodium salt on a different mineral surface Mineral
Polarity (xA − xB)
Calculated ΔE (kJ mol−1)
Adsorptive concentration (mg m−2)
Calcite 2.86 6.78 Quartz 2.2 4.57 Hematite 1.7 4.27 Sphalerite 0.90 3.39 Pyrite 0.82 3.18 Chalcopyrite 0.6 2.65 Note 1 Concentration of sodium dodecyl sulfosalt is 100 mg/L, and electronegativity of group is calculated by reference Table 6.32 Wetting heat of rutile in organic liquid of different polarization
257.6 147.2 55.2 −92.0 −105.8 −147.2 mass of all mineral is 2 g; 2
Organic liquid
Radicals
Electronegativity
Wetting heat /(J m−2)
Butyl amine Butyl alcohol Butyl acid
–NH2 –OH
3.7 3.9
0.33 0.41
–COOH
4.1
0.502
(3) Application of group electronegativity calculation for the discussion of effect of polar group structure on the reagent performance The effects of polar group structure on the reagent performance can be expounded according to the group electronegativity. Taking xanthate and aerofloat for example, the effects of chemical bond of polar group on the value of n* can be given as follows (from the Sect. 6.4.2 of this book, the calculation of inductive effect n* in formula 6.7′): S
Xanthate:
0.0 +1.0
S
C
+0.37
O
-0.046
C......
S +0.26
Aerofloat:
+1.09
S
P(
+0.55
O
-0.046
C ...... )2
It can be seen that the differences of the effects of polar group structure on the reagent performance can be concluded as follows: (a) The effect of S–P bond of aerofloat on n* is larger than that of S–C of xanthate. That is, compared with the C atom of xanthate, the P atom of aerofloat makes the group electronegativity higher.
200
6 Theoretical Criteria and Calculation for Collector Performance
(b) The effect of S=P bond of aerofloat on n* is larger than that of S=C of xanthate. Thus, the group electronegativity of aerofloat is larger than that of xanthate. (c) The effect of two S–O bonds of aerofloat on n* is larger than that of single C–O of xanthate, which results in that the group electronegativity of aerofloat is larger than that of xanthate. (d) The effect of –CH2– bonds of aerofloat on n* is smaller than that of –CH2– of xanthate, which leads to that the group electronegativity of aerofloat is smaller than that of xanthate. Based on the discussion above, it can be found that the value of group electronegativity of aerofloat is larger than that of xanthate. However, the collecting capability of aerofloat is worse than that of xanthate. The reason mainly lies in that the electronegativity of P atom in aerofloat is smaller than that of C atom in xanthate. In other words, the polarity of P–S and O–P bonds in aerofloat molecule is larger than that of C–S and O–C bonds in xanthate. According to the calculation, it can be found that the collecting capability of dialkyl dithiocarbamate is better than that of xanthate. The reason mainly lies in that the electronegativity of N atom in dialkyl dithiocarbamate is smaller than that of O atom in xanthate. For the groups with the structure of –A–B–C–, we come to a conclusion that the A atom (the bonding atom) decides the specialized for applied range and ability of reagent; the linking B or C atom influences indirectly the strength of interaction between reagent and mineral of A atom. The group electronegativity of reagent decreases with the increase of electronegativity of linking B atom. The group electronegativity of reagent, however, increases with the increase of electronegativity of linking C atom. Taking fatty acid and alkyl sulfonate for example, their structure can be expressed as follows: O
Fatty acid:
O C
R
O O C
R
Sulfonate O
It can be seen that the bonding atoms (A) of fatty acid and alkyl sulfonate are both O atoms. The linking atom of fatty acid and alkyl sulfonate is, respectively, C and S atoms. Because the C atom of fatty acid is linked with two = O and xC = xS, the electronegativity of alkyl sulfonate is larger than that of fatty acid. (4) Uses of group electronegativity for the discussion of effect of non-polar group structure on the polar group The effects of non-polar group can be concluded by the following two aspects: (1) the hydrophobic effect of itself and (2) the effect of non-polar group on the polar group. The first one of the effect of non-polar group will be discussed in the
6.4 Electronegativity and Related Calculation for Flotation Reagent
201
following section. The second one of the effect of non-polar group is expounded according to the calculation of group electronegativity in this section. As mentioned above, the addition of –CH2– group can make the value of n* to decrease. That is, the effect of –CH2– group on the bonding atom of polar group belongs to the positive inductive effect. For the n-alkyl, the positive inductive effect increases with the increase of –CH2– group. For the isoalkyl, the positive inductive effect increases more obviously because the –CH3 is more close to the polar group. For alkyl organics, the effect of each –CH3 on the total positive inductive effect (I) is presented as follows: Ethyl group
CH3CH2X
1 I ¼ I 0 2:7 ¼ 0:37I 0
Normal-propyl group
CH3CH2CH2X
1 0 I ¼ I 0 ð2:7Þ 2 ¼ 0:14I
Isomal-propyl group
CH3
1 I ¼ 2I 0 2:7 ¼ 0:74I 0
CHX CH3
Normal-butyl group
CH3CH2X
1 0 I ¼ I 0 ð2:7Þ 3 ¼ 0:05I
Isomal-butyl group
CH3
1 0 I ¼ 2I 0 ð2:7Þ 2 ¼ 0:28I
CHCH2X CH3
Secondary butyl group
1 0 1 0 I ¼ I 0 ð2:7Þ 2 þ I 2:7 ¼ 0:51I
CH3CH2CHX CH3
where I´ refers to the positive inductive effect of each –CH3; 1/(2.7)i refers to the “isolating action” of the separated atoms, and the i refers to the number of separated atoms. The following data are about the values of I of various alkyl groups and the solubility products of related salt of xanthates with zinc and silver ions from Glembosky.
Alkyl group
Structure
L Zinc salt
Ethyl group
CH3–CH2X
I′
position of methyl a
Silver salt
4.9 10−9
4.4 10−19
0.37
−10
2.1 10−19
0.14
b 2a
n-propyl group
CH3–CH2–CH2X
3.4 10
i-propyl group
CH3
2.1 10−10
1.2 10−19
0.74
3.7 10−11
4.2 10−20
0.05
c
1.6 10−20
0.28
2b
CHX CH3
n-butyl group i-butyl group
CH3–CH2CH2CH2X CH3
CHCH2X
2.75 10
−11
CH3
(continued)
202
6 Theoretical Criteria and Calculation for Collector Performance
(continued) Alkyl group Secondary butyl group
Structure CH3
L
CH2CHX
I′
position of methyl
–
0.51
ab
Zinc salt
Silver salt
9.8 10−11 1.55 10−12
CH3
n-amyl group 3-methyl butyl group
CH3–CH2CH2CH2CH2X CH3
CHCH2CH2X
1.8 10−20
0.02
h
−12
6.0 10−21
0.1
2c
9.6 10−12
2.7 10−20
0.19
bc
1.0 10−11
1.0 10−20
0.42
3b
1.65 10−11
2.7 10−20
0.28
2b
1.45 10−11
9.1 10−20
0.42
ac
1.05 10−11
4.8 10−20
0.51
a2b
1.25 10−13
2.65 10−21
0.007
2.55 10−13
–
0.028
1.35 10−14
9.8 10−22
0
4.25 10−14
–
0.014
3.1 10
CH3
2-methyl butyl group
CH3
CH2CHCH2X CH3
2,2-dimethyl propyl group
CH3 CH3
CHCH2X CH3
i- amyl group
CH3
CH2 CHX
Secondary amyl group
CH3
CH2
CH3
CH2CH2CHX CH3
i-3-methyl butyl group
CH3
CH
CHX
CH3
CH3
n-hexane group
CH3– CH2CH2CH2CH2CH2X
5-methyl amyl group
CH3
CHCH2CH2CH2X CH3
n-heptyl group
CH3– CH2CH2CH2CH2CH2CH2X
6-methyl hexane group
CH3
CHCH2CH2CH2CH2X CH3
It should be pointed out that the solubility product is influenced not only by inductive effect but also by hydrophobic association between hydrocarbon chains, weighting effect of molecular weight and steric effect of isomer. Through the comparison of inductive effect above, the conclusion can be given as follows: (a) Compared with n-alkyl, the positive inductive effect is the lead in the simple short-chain isoalkyl such as isopropyl. Therefore, the activity of isoalkyl reagent is stronger than that of n-alkyl reagent.
6.4 Electronegativity and Related Calculation for Flotation Reagent
203
(b) Compared with n-alkyl, the positive inductive effect is also the lead in the complex short-chain isoalkyl such as isobutyl. The activity of isoalkyl reagent is usually stronger than that of n-alkyl reagent. However, when –CH3 is too close to the polar group, for example secondary alcohol, the existing steric effect becomes over the inductive effect. Therefore, although the positive inductive effect of isosecondary alcohol reagent is larger than that of n-alkyl reagent, the solubility product of isosecondary alcohol reagent is smaller than that of n-alkyl reagent. (c) When the number of –CH2– is greater than 6, the positive inductive effect becomes unimportant.
6.4.6
Uses of Group Electronegativity to Hydrophilicity– Hydrophobicity Balance of Polar and Non-polar Groups in a Reagent Molecule
When the collector adsorbs onto the mineral surface from aqueous solution, the chemical potential of collector can be shown as follows: lb = l0b þ RT ln Cb ls = l0s þ RT ln Cs where µb refers to the chemical potential of collector in solution; µs refers to the chemical potential of collector on the mineral surface; l0b refers to the standard chemical potential of collector in solution; l0s refers to the standard chemical potential of collector on the mineral surface; Cb refers to the concentration of collector in solution; and Cs refers to the concentration of collector on the mineral surface. When the reaction reaches adsorption equilibrium, that is, µb = µs, the relation between Cb and Cs can be expressed by the following: 0
Cs l l0s DGo ¼ exp b ¼ exp Cb RT RT where DGo refers to the standard free energy of adsorption reaction. DG° includes the free energy of polar group ðDGop Þ and the free energy of polar group ðDGon Þ. Therefore, DGo can be expressed by the following: DGo = DGop DGon If DGon is weighted with фn, and DGop is weighted with Dx2 , the relation between Cb and Cs can be further expressed by the following:
204
6 Theoretical Criteria and Calculation for Collector Performance
Cs Dx2 þ kn/ ¼ exp RT Cb where k refers to the constant coefficient. When Cb = Cs, hence, the following equation can be obtained: Dx2 ¼ k/n The equation above shows the precondition of collector possessing hydrophobicity lies in that the hydrophobicity of non-polar group is over the hydrophilicity of polar group. Besides for the hydrophilicity of collector itself, the collector also must overcome the hydrophilicity of mineral in the flotation process. If the hydrophilicity of mineral is also weighted with Dx2, the requirement on non-polar group can be given as follows: k/n ¼ Dx2R þ Dx2M
ð6:8Þ
2 where Dx2R refers to xg xM , which is the square of the electronegative difference between reagent (xg) and mineral (xM); Dx2M refers to ðxA xB Þ2 , which is the square of the polarity standard between mineral (A) and mineral (B). Under the condition of k = 1 and ф = 1, the balance relation between polar and non-polar groups is roughly estimated using the Eq. 6.8, and the results are listed in Table 6.33. According to the data in Table 6.33, the relationship between polar and non-polar groups of collector is shown in Fig. 6.10. The results show that the estimated value is in accordance with that of actual value. The hydrophobicity and hydrophilicity of salts of anionic of collectors and metallic ion of mineral depend on the size of non-polar group and the bond polarity between metal and the bonding atom of polar group. For the sulfide collector, the effect of non-polar group is small because of the small proportion of non-polar groups. For the oxide collector, the effect of non-polar group is large. That is why the sulfide collector has a better selectivity than the oxide collector.
6.4.7
Application of Group Electronegativity to Classification and Uses of Flotation Reagents
The flotation reagents include collector, frother, and depressant. The proportional relations of polar and non-polar groups are various in different types of reagents. The calculation of group electronegativity can also be used for the classification of reagents. For example, according to (xg − xH)2 and n values, the criterion for the classification of reagents is given in Eq. 9
6.4 Electronegativity and Related Calculation for Flotation Reagent
205
Table 6.33 Proportional relationship between polar and non-polar groups in collector molecule Dx2R Metal (xM)
Reagent
Value
Xanthate (2.7)
Pb (1.8)
0.81
Aerofloat (3.0)
Pb
1.44
Mercaptan (2.6) Dithiocarbamic acid (2.6) Fatty acid (4.1)
Pb Pb Ca (1.0) Fe (1.8) Ca Fe Na (0.9) Fe Si (1.8) Fe Ti (1.5) Sn (1.8) Fe
Alkyl sulfonic acid (4.3) Fatty amine (3.7)
Hydroximic acid (3.8) Alkyl arsonic acid (4.3) Alkyl phosphoric acid (4.3)
0.64 0.64 9.61 5.29 10.89 6.25 7.84 3.61 3.61 4.00 5.29 6.25 6.25
Dx2M Mineral
Value
PbS PbO PbS PbO PbS PbS CaO FeO CaO FeO Na2O FeO SiO2 FeO TiO2 SnO2 FeO
0.49 2.89 0.49 2.89 0.49 0.49 6.25 2.89 6.30 2.89 6.76 2.89 2.89 2.89 4.00 2.89 2.89
Related n 1.3 (methyl-ethyl) 3.7 (propyl-butyl) 1.9 (ethyl) 4.3 (butyl-amyl) 1.1 (methyl) 1.1 (methyl) 15.8 (cetyl) 8.1 (octyl) 17.1 (heptadecyl) 9.1 (nonyl) 14.6 (pentadecyl) 6.5 (heptyl) 6.5 (heptyl) 6.8 (heptyl) 9.3 (nonyl) 9.0 (nonyl) 9.0 (nonyl)
24
R20SO3 H-Ca ore 20
R18 COOH-Ca ore R14SO3 H-Be ore
n
16
R18 COOH-Ba ore
12
R12NH2 -Fe ore
R8 ONHON-Fe ore R8 ONHON-Cu ore
8
R8PO3H2 -Sn ore R7 AsO3H2 -Sn ore
EP-PbS 4
EX-ZnS
EX-PbS EX -Pb
EP -Zn
EX-ZnS
0 0
2
4
6
8
10
12
Δx +Δx 2 R
2 M
Fig. 6.10 Relation between polar and non-polar groups of collector
14
16
18
206
6 Theoretical Criteria and Calculation for Collector Performance
Table 6.34 Classification of reagent according quality number i Collector
i1
i2
Frother
i1
i2
Depressant
i1
i2
C2H5OCSSH
0.18
18.4
C7H15OH
0.46
16.2
(HOOC)2
8.0
28.0
(C2H5O) PSSH
0.20
16.8
C6H13OH
0.54
17.2
CH3CH2OHCOOH
3.6
25.2
C9H19COOH
0.44
14
C10H17OH
0.32–0.46
13.2
C6H10O5
2.7
30.0
C17H35COOH
0.24
7
C7H8OH
0.54–1.08
7.2
C6H2(OH)3COOH
2.3–4.6
27.6
i1 ¼
2 P xg xH P n/
or i2 ¼
X
ðDxÞ2
X
n/ þ K
ð6:9Þ
where i refers to the specific ratio of flotation reagent; R refers to the summation of groups; and K refers to the empirical constant and the u = 1 in the above equation. According to Eq. 6.9, the calculation results of some typical reagents are listed in Table 6.34. It can be seen that the classification of reagent can be deduced according to the value of i.
6.5 6.5.1
Steric Size of Collector Molecule and Its Flotation Selectivity General Relation Between Steric Size of Reagents and Their Collector Performance
It had been observed that there exist some general relations between steric size and flotation performance. Taking the activation of sphalerite with Cu2+ for example, A. Gaudin studied the relation between the steric size of Cu2+ and the size of s crystal lattice of sphalerite and distance of Zn atoms. Taking the adsorption of xanthate onto galena for example, Gaudin studied the relation between the absorption density of xanthate and the size of galena mineral crystal lattice [8]. These results above indicate that the adsorption interaction is prone to take place when the steric size of reagent is close to that of mineral. When the steric size of reagent is far from that of mineral, the reagent absorbs onto mineral in the shape of loosen state. And the adsorption interaction between reagent and mineral becomes weak. When the reagent absorbs onto mineral via chemical adsorption or surface chemical reaction, the effect of the steric size of reagent becomes very obvious. The reason lies in that the chemical bonding force proposes a strict requirement for the steric size of reagent and the interatomic distance. As described in Eq. 2.10 which is the stern-Graham formula in Chap. 2, the steric size of reagent also influences the adsorption process even though the reagent absorbs onto mineral by electrostatic
6.5 Steric Size of Collector Molecule and Its Flotation Selectivity
207
force. The explanation for the effect of steric size of reagent on adsorption can be summarized as follows: (1) Firstly, reagent acts as the compensating ion in electric double layer. The adsorption density decreases with the increase in the cross section of polar group of reagent. That is, the capability of compressing electric double layer decreases with increasing cross section of polar group. (2) When reagent absorbs in the stern outer layer of mineral surface, zeta potential of mineral changes if the steric size of polar group exceeds the thickness of intrinsic stern layer. (3) When reagent enters into the stern inner layer of mineral, reagent starts to act as the potential-determining ion. In fact, most of the potential-determining ions comprise various mineral ions. Therefore, the adsorption interaction is prone to occur only if the steric size of reagent is close to that of mineral ion. Because the lattice structure of soluble salt is simple and typical, the relation between the size of crystal lattice of the soluble salt and the steric size of polar group in collector molecule had been widely researched [38]. Some proposed that the polar group of amine collector was embedded in the crystal lattice of mineral to improve the collecting capability. The schematic diagram of the flotation of salt mineral with amine as collector is presented in Fig. 6.11. The adsorption interaction occurs when the steric size of amine is less than or equal to that of the crystal lattice of mineral. When the steric size of reagent is bigger than that of mineral, the adsorption interaction is hard to take place. The radii of various ions are listed as follows: ˚ rCl ¼ 1:81 A; ˚ rNa ¼ 0:95 A; ˚ rNH3 ¼ 1:43 A; ˚ rSO4 ¼ 2:40 A ˚ rK ¼ 1:35 A; It can be seen from the above data the potassium chloride mineral (sylvine) can be floated with alkyl amine (the radius of primary amine is about 1.8 Å) as collector. But the sodium chloride mineral cannot be applied to float sylvine. If the alkyl sulfonate is used as collector (the radius of polar group is 2.9 Å), the minerals cannot be floated. The flotation results of various soluble salt minerals with aliphatic amines as collectors are found in Table 6.35. Fig. 6.11 Schematic diagram of the flotation of soluble salt mineral with amine collectors
Table 6.35 Flotation results of various salt mines with aliphatic amine Anion −
F Cl− Br− I−
Li+
Na+
K+
Rb+
Cs+
8.1 13.2 15.2 17.9
10.7 15.8 17 20.9
14.2 19.7 21.7 24.9
15.9 21.6 23.9 27.1
17.7 23.9 26.0 29.4
NH4+ 21.1 23.1 26.2
Flotation results Useless Efficient
208
6 Theoretical Criteria and Calculation for Collector Performance
Someone also proposed that there was a certain difference between the steric size of reagent and the size of crystal lattice of mineral (such as 20 %).
6.5.2
Rough Calculation for Steric Size of Collector Molecule
The value of steric size of surfactants had been determined by the methods of surface film and X-ray spectrometry. Meantime, they also can be roughly calculated according to bond angle, bond length, van der Waals radius, and covalent radius. Based on the calculation for steric size, the models for some collector molecules are given in Fig. 6.12. In the study on biochemistry for works of Hansch and Fujita, the sterimol parameter is used as the criterion for the steric size of reagents [39]. For instance, the schematic diagram for –CHFCl group is given by the following:
where L refers to the length of bond shaft; B1, B2, B3, and B4 refer to the projected widths of four vertical plane of bond shaft, respectively. The steric parameters of various groups are found in Table 6.36. Another criterion is van der Waals volume which is calculated according to van der Waals radius. Assuming that the atoms are linked in the shape of sphere in the molecule, van der Waals volume is the sum of each steric volume of sphere excluding the overlaps and the volume has additivity. The van der Waals radii (rb) Fig. 6.12 The steric size of polar group of fatty acid and aerofloat
6.5 Steric Size of Collector Molecule and Its Flotation Selectivity Table 6.36 Steric parameters of various groups
209
Group
L
B1
B2
B3
B4
H Cl Br CH3 C2H5 n-C3H7 n-C4H9 i-C4H9 n-C5H11 i-C5H11 n-C6H13 CH2OH COOH COOCH3 CONH2 C6H5 OH SH SCN NH2 N+(CH3)3
2.06 3.52 3.83 3.00 4.11 5.05 6.17 5.05 7.11 6.17 8.22 3.97 3.91 4.85 4.06 6.28 2.74 3.74 4.08 2.93 4.02
1.00 1.80 1.95 1.52 1.52 1.52 1.52 1.52 1.52 1.52 1.52 1.52 1.60 1.90 1.60 1.70 1.85 1.70 1.70 1.50 2.56
1.00 1.80 1.95 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.60 1.90 1.60 1.70 1.35 1.70 1.70 1.50 2.80
1.00 1.80 1.95 1.90 1.90 1.90 1.90 3.16 1.90 3.16 1.90 1.90 2.36 2.36 2.42 3.11 1.35 1.70 1.70 1.84 2.80
1.00 1.80 1.95 2.04 2.97 3.49 4.42 4.21 4.49 4.42 5.87 2.70 2.66 3.36 3.07 3.11 1.93 2.33 4.45 1.84 2.90
of various elements and the volumes (VW) of various elements are listed in Table 6.37. And the correction values for VW of various covalent bonds are listed in Table 6.38. Based on the data in Tables 6.37 and 6.38, the van der Waals volumes (VW) of polar group can be calculated. For example, the calculation for VW of xanthic acid can be expressed as follows: ˚ VW ¼ ðVO þ VC þ 2VS þ VH Þ ðVC¼O þ VC¼S þ VCS þ VSH Þ ¼ 62:1 A
Table 6.37 van der Waals radius and volume of element
Element
rb (Å)
VW (Å)
Element
rb (Å)
VW (Å)
C
1.7
0.206
Cl
1.8 (1.61)
0.244
H
1.1 (0.95)
0.056
Br
1.9 (1.80)
0.287
N
1.5 (1.40)
0.141
I
2.1 (2.03)
0.388
O
1.4 (1.23)
0.115
B
2.1
0.388
S
1.8 (1.54)
0.244
He
1.2
0.072
F
1.4
0.115
P
1.9
0.287
210
6 Theoretical Criteria and Calculation for Collector Performance
Table 6.38 Correction values for VW of various covalent bonds Bond
Bond length
−DVW (Å3 102)
Bond
Bond length
−DVW (Å3 102)
C–C C–H C–N C–O C–S C–Cl C–P N–H N–N N–O N–S N–P O–H O–S O–P
1.5 1.1 1.4 1.4 1.8 1.8 1.8 1.0 1.4 1.4 1.6 1.5 1.7 1.7 1.6
0.078 0.043 0.065 0.056 0.066 0.066 0.076 0.038 0.050 0.042 0.061 0.075 0.046 0.046 0.058
S–S S–P P–Cl C=C C=N C=O C=S N=O P=O S=O P=S CC CO CN C=C (aromatic ring)
2.0 2.1 2.0 1.3 1.3 1.2 1.6 1.2 1.4 1.5 1.9 1.2 1.4 1.2 1.4
0.062 0.064 0.071 0.094 0.072 0.068 0.081 0.053 0.071 0.057 0.079 0.101 0.086 0.079 0.086
S–H
1.3
0.040
The van der Waals volumes (VW) of various polar groups are found in Table 6.39. For the adsorption surface, the cross section of polar group is more important than the volume. Therefore, the calculation for the cross section of polar group by means of the bond angle, bond length, van der Waals radius, and covalent radius of reagent molecule is discussed in the following. The schematic diagram for van der Waals radius and covalent radius of reagent molecule is given in Fig. 6.13.
Table 6.39 van der Waals volumes (VW) of various polar groups Group
Molecular formula
VW
Group
Molecular formula
VW
Xanthic acid Thiocarbonic acid Trithiocarbonic acid Thiophosphoric acid Phosphorodithioic acid Carboxylic acid
–OCSSH –OCOSH –SCSSH ¼O2POSH ¼O2PSSH
62.1 50.0 74.1 63.9 79.8
–NH2 –SH (OCSS)2 –NHC(S)O– –C(O)NHOH
18.0 26.0 115 52.2 43.0
–COOH
32.2
–P(O)(OH)2
46.1
Sulfonic acid
–SO3H
43.9
Amine Thiol Dixanthogen Thiocarbamate Hydroximic acid Phosphonic acid Ethyl
CH3CH2–
39.8
6.5 Steric Size of Collector Molecule and Its Flotation Selectivity
211
Fig. 6.13 Schematic diagram of van der Waals radius and covalent radius of reagent molecule a covalent radius; b van der Waals radius
The van der Waals radii (rb) of various elements are mentioned in Table 6.37. The covalent radii (ra) of various elements are listed in Table 6.40. In addition, the van der Waals radii (rW) of –CH3 and –C6H5 are, respectively, 2.0 and 1.85 Å. Based on the calculation, the bond angles of various groups are listed in Table 6.41. As shown in Table 6.41, the regularity of the bond angle of organics can be concluded as follows: (a) Bond type: C
Y
X
The bond angle of X–C–Y is 90°. (b) Bond type: C=C–X The bond angle of C–C–X is 120°–125°.
Table 6.40 Covalent radii (ra) of various elements (Å)
Bond
Single bond
H B C N O F Si P S Cl Ge As Se Br Sn Sb Te I
0.30 0.88 0.77 0.70 0.66 0.64 1.17 1.10 1.04 0.99 1.22 1.21 1.17 1.14 1.40 1.41 1.37 1.33
Double bond
Triple bond
0.76 0.67 0.61 0.55
0.68 0.60 0.55
1.07 1.00 0.94
1.00 0.93 0.87
1.11
212
6 Theoretical Criteria and Calculation for Collector Performance
Table 6.41 Bond angles of various groups Bond type
X
C
Bond angle
Example
Bond type
Bond angle
Example
109°
Methinehalide
C–C=O
121°
(CH3)2CO
120°
C2H4
124°
CH3COOH
127°
CH3NO2 CH3ONO
Y
C=C–H C=C–C
124°
O
C
O
O
N
O
i-C4H8
C=C=C
180°
C3H4
O–N–O
180°
CC–X
180°
Halogeno-acetylene
C–S–H
95°
–
109°
(CH3)2NH
C–S–C
100°
–
107°
–
C–P–C
100°
(CH3)3P
106°
CH3OH
C–O–C
111°
(CH3)3O
C
N
C
C
N
H
C–O–H
(c) Bond type: CC–X and C=C=C The bond angle of C–C–C is 180°. (d) When the central atom contains unshared electron pair, the bond angle is 90°–109°. For the calculation of steric size of collector, examples are as follows: Xanthate ion: O C
R
S α S
Under the condition of a = 120°, raC = 0.77 Å, raS = 1.04 Å, and rbS = 1.85 Å, the calculation process of the steric size of xanthate ion (dS–S) can be given as follows: ˚ dSS ¼ 2½ðraC þ raS Þ sin 60 þ rbS 6:9 A If raC = 0.72 Å and raS = 1.71 Å, then the average value dS–S 6.7 Å. Aerofloatation: R O
b S α P S O b R
6.5 Steric Size of Collector Molecule and Its Flotation Selectivity
213
Under the condition of a = 110°, b = 110°, raP = 1.1 Å, raO = 0.66 Å, rbR = 2.0 Å, raC = 0.77 Å, raS = 1.04 Å, and rbS = 1.85 Å, the calculation process can be given as follows: ˚ dSS ¼ 2½ðraR þ raS Þ sin 55 þ rbS 7:2 A h i1=2 ˚ þ 2rbR 10:4 A dRR ¼ 2 ðraC þ raO Þ2 þ ðraO þ raP Þ2 2ðraC þ raO ÞðraO þ raP Þ cos 110
Fatty acid ion: R
C
O α O
Under the condition of a = 124°, raO = 0.66 Å, rbO = 2.0 Å, and raC = 1.04 Å, the calculation process can be given as follows: ˚ dOO ¼ 2½ðraO þ raC Þ sin 62 þ rbO 5:3 A If raO = 0.66 Å, then dO–O 5.1 Å. It should be pointed out that the R group is considered as –CH3 in the above calculation of the steric size of collector. The roughly calculated values for the steric sizes of other collectors (dg) are found in Table 6.42.
Table 6.42 Calculated values for the steric sizes of collectors (dg) Collector
dg (Å)
Collector
dg (Å)
Primary amine Fatty acid Sulfonic acid Phosphonic acid Arsonic acid Hydroximic acid Dithiocarbonic acid Thiocarbonic acid Trithiocarbonic acid Xanthate ester
3.6 dO−O 5.1–5.3 dO−O 5.8 dO−O 6.0 dO−O 6.4 dO−O 6.5 dS−S 6.7–6.9 dS−O 5.8 dS−S 6.7–6.9 dS−S 7.0 dR−R 9.0 dS−S 10.4 dR−R 12.6
Benzothiazole mercaptan Benzimidazole mercaptan Thiambutosine
dS−N 6.2 dS−S 6.9 dS−N 6.2 dR−R 10.4 dS−S 6.2 dR−R 10.4 dS−O 6.3 dS−S 6.9 dR−R 5.0 dS−N 6.2 dR−R 8.7 dS−O 8.2 dS 3.7
Dixanthogen
Dithiophosphate Thiophosphate Dithiocarbamic acid Thiocarbamate Benzoyloxy mercaptan Mercaptan
214
6.5.3
6 Theoretical Criteria and Calculation for Collector Performance
Relation between Steric Size of Polar Group and Selectivity of Collector
Practice shows that the selectivity of collector is in connection with the steric size of polar group. It is shown in Table 6.42 the selectivity of sulfide collector performs better when the steric size of polar group increases. Excepting the mercaptan, the van der Waals volume of sulfide mineral collectors usually is above 50 Å. The cross section of sulfide collectors ranges from 6.2 to 12 Å. Compared with sulfide mineral collector, the selectivity of oxide mineral collectors is bad. The reason lies in that the cross section and the volume of oxide collector are smaller than those of sulfide collectors. The van der Waals volume of oxide collectors usually is less than 50 Å. The cross section of sulfide collector ranges from 3.6 to 6.5 Å. For the same type of collectors such as primary amine, fatty acid, alkyl sulfonate, phosphonic acid, and arsonic acid, the selectivity of collector also increases with the increase in steric size of polar group. For sulfide mineral collectors, examples for the relation between selectivity of collector and steric size of polar group are as follows. (1) Comparison of xanthate and aerofloat In general, the selectivity of aerofloat is better than that of xanthate. Besides for the valence bond factor and surface factor, the main reason lies in that the steric size of aerofloat is bigger than that of xanthate. (2) Comparison of xanthic acid and xanthogenate S
Xanthic acid:
R
O
C
S H
S
Xanthogenate:
R
O
C
S R`
The bonding atoms of xanthic acid and xanthogenate are the same. But the steric sizes of xanthic acid and xanthogenate are diverse. Because the bonding S atom of xanthogenate occupies a middle ground between two hydrocarbonyls, the cross section of xanthogenate is bigger than that of xanthic acid. When xanthic acid and xanthogenate are, respectively, used in the flotation of sphalerite, chalcopyrite, and pyrite, the selectivity can be weighted by the flotation recovery ratio of two minerals [40, 41]. The expression of the selectivity index, hence, can be given as follows: S1 ¼
RZnS ; RFeS2
S2 ¼
RCuFeS2 RFeS2
For s1: isopropyl xanthate propenyl ester > ethyl xanthate propenyl ester > isopropyl aerofloat > butyl xanthate propyl ester > butyl xanthate;
6.5 Steric Size of Collector Molecule and Its Flotation Selectivity
215
For s2: isopropyl xanthate propenyl ester > butyl xanthate propenyl ester > butyl xanthate propyl ester > ethyl xanthate propenyl ester > butyl xanthate. The arrangements show that the selectivity of xanthogenate is better than that of xanthic acid; the selectivity of xanthogenates which contain the branched chain of large cross section is better than that containing linear chains of small cross section; when R′ is an unsaturated hydrocarbon radical, the reagent performs a better selectivity because the cross section of unsaturated hydrocarbon radical is bigger than that of saturated hydrocarbon radical. The reagent sometimes performs a better selectivity when R is a high molecular weight hydrocarbon radical. It indicates that the effect of the steric size of reagent has exceeded the influences of valence bond and surface reaction. (3) Comparison of xanthate and dixanthogen The structure of dixanthogen can be expressed by the following: S R
O
C
S C
S S
R
O
It is reported that the flotation selectivity of dixanthogen is better than that of xanthate. The main reason lies in that the steric size of dixanthogen is bigger than that of xanthate. The dixanthogens are also common flotation collectors for sulfide minerals and sediment metals and their bonding properties in flotation reaction are same like xanthate. According to the report in application, the flotation selectivity of dixanthogens is better than that of xanthates. For example, compared with the poor flotation result of chalcopyrite and galena by xanthate-K2Cr2O7 depressant, the separative results are much better as using dixanthogen-K2Cr2O7 depressant. (4) Comparison of aerofloat and related ester of aerofloat The structures of aerofloat and related aerofloat ester can be expressed by the following: R
S
O P
aerofloat :
R R
SH,
O
S
O P
aerofloat ester:
R
O
S
R'
The selectivity of aerofloat ester is better than that of aerofloat because the steric size of aerofloat ester is bigger. The structure of the ester of aerofloat can be given as follows:
216
6 Theoretical Criteria and Calculation for Collector Performance
R
S
O P
R
S(CH)n
O
R''
R'
where R refers to the alkyl of which the number of C atoms is less than six; R′ refers to the H atom or –CH3; R″ refers to the methyl, ethyl, propyl, butyl, amyl, hexyl, alkenyl, and aromatic groups. It is reported that (C2H5O)2P(S)SCH2SC2H5 is used as selective collector of unactivated flotation sphalerite in separating Zn–Pb sulfide minerals. (5) Comparison of thionocarbamate and xanthate The famous reagent Z-200 is thionocarbamate collector. The structure of Z-200 can be expressed as follows: S R
NH
C
O
R'
where R is similar to dithiocarbamate acid radical; R′ is similar to xanthic acid radical. The section width of thionocarbamate collector is about 8.7 Å. Therefore, the reagent performs a good selectivity. It was reported that the selectivity of thionocarbamate collector is better than that of xanthate [42]. For example, the comparison of O-methyl-N-isopropyl-thionocarbamates and xanthates as collectors for separation flotation of Cu, Fe, Mo, and sulfide minerals is listed in Table 6.43. The sign of s1 and s2 in Table 6.43 refers to the Gaudin’s selectivity index, respectively. (6) Comparison of mercaptans The structures of mercaptan and dimercaptan can be expressed as follows: Mercaptan : RSH
Dimercaptan : HSRSH
Table 6.43 Gaudin’s selectivity indexes of thionocarbamate and xanthate Reagent and dosage
Pulp pH
Gaudin’s selectivity index Cu/Fe (s1)
Gaudin’s selectivity index Mo/Fe (s2)
O-methyl-N-isopropyl-thionocarbamate (25 +11 g/t)
6.8
3.3
11.9
8.2
4.0
14.5
9.7
5.3
15.4
6.8
3.0
9.7
8.2
2.8
10.2
9.7
2.8
9.6
Butyl xanthate (25 + 10 g/t)
6.5 Steric Size of Collector Molecule and Its Flotation Selectivity
217
The selectivity of mercaptan collector is worse than that of xanthate. It is reported that the dimercaptan has stronger collectivity for sphalerite flotation, but is weaker for pyrite. According to the molecular structure, the dimercaptan should be used as depressant for sulfide minerals. (7) Flotation property of thiosalicylic acid The molecule of thiosalicylic acid exists in two polar groups: SH COOH
The section width of thiosalicylic acid is about 8.2 Å. According to the flotation of galena, chalcopyrite, and pyrite (Fig. 6.14) [43], thiosalicylic acid as a collector has a good selectivity. (8) Comparison of fatty acid and polycarboxylic acid The structures of dicarboxylic and tricarboxylic acid can be expressed as follows: COOH
dicarboxylic acid:
R
(DCA)
CH COOH COOH
tridicarboxylic acid: (TCA)
R
C
COOH
COOH
where R refers to the alkyl of which the number of C atoms ranges from 10 to 19.
(b)
Recovery rate (%)
1—PbS 2—CuFeS2 3—FeS2
Recovery rate (%)
(a)
1—PbS 2—CuFeS2
pH
Reagent concentration (mg/L)
Fig. 6.14 a Selectivity of thiosalicylic acid in the flotation of galena, chalcopyrite, and pyrite (reagent concentration 30 mg/L); b selectivity of thiosalicylic acid in the flotation of galena and chalcopyrite (pH = 9.4–9.6)
218
6 Theoretical Criteria and Calculation for Collector Performance
Table 6.44 Flotation results of cassiterite and tourmaline using dicarboxylic acid and tridicarboxylic acid Collector
The range of pH (100 mg/L)
The optimum pH of cassiterite
Flotation results of quartz at optimum pH (%)
Flotation results of tourmaline at optimum pH (%)
DCA-10 DCA-12 DCA-19 TCA-10 TCA-12
2.5–9.0 3.0–9.0 2.5–10.0 3.5–11.0 2.0–11.0
3.0–4.0 3.0–4.0 3.0–5.0 4.0–5.5 3.5–4.5
20 20 10 30 60
65 70 75 96 95
It is well known that fatty acid performs a bad selectivity in the flotation of oxide minerals. It was reported that however, dicarboxylic acid and tridicarboxylic acid have a relatively good selectivity. The results of dicarboxylic acid and tridicarboxylic acid in the flotation of cassiterite and tourmaline are found in Table 6.44.
6.5.4
Relationship Between Steric Size of Non-polar Group and Selectivity of Collector
When polar and non-polar groups are, respectively, located at the end of reagent molecule, and the non-polar group is normal alkyl, the cross section of polar group is bigger than that of non-polar group. Therefore, the cross section of the reagent molecule depends on the steric size of polar group. When non-polar group comprises branched chains, the cross section of non-polar group also becomes big. When two or more polar groups are in the middle of molecule, the steric size of reagent molecule will increase. The steric sizes of various fatty acids are shown in Table 6.45. It is shown in Table 6.45 that the steric size of various fatty acids increases with enlarging hydrocarbon chain. Comparing to isoalkyl with n-alkyl, the difference in the steric size lies in that the cross section of isoalkyl increases with increase in branched chain. The related results had been discussed in Chap. 4. Because the cross section of non-polar linear alkyl is smaller than that of polar group, the steric size of non-polar group only depends on its length. However, the steric size of non-polar isomerous or unsaturated alkyl depends on the size and Table 6.45 Steric sizes of various fatty acids (Å) Fatty acid
Number of C atoms
d1 (length)
d2
d3
d1 (alkyl)
Capric acid Dodecanoic acid Myristic acid Palmitic acid Stearic acid Docosanoic acid
10 12 14 16 18 22
23.2 27.0 32.2 34.7 38.7 47.8
– 4.11 4.12 4.08 4.05 4.10
– 3.68 3.72 3.65 3.62 3.66
– – – – C17 24.3 C18 25.9
6.5 Steric Size of Collector Molecule and Its Flotation Selectivity
219
shape of cross section. The relation between steric size of isomerous or unsaturated alkyl and selectivity of collector is briefly introduced by the following: (a) For the isomerous alkyl as non-polar group, Compared with normal collector, isomerous collector has a higher solubility and a lower hydrophobicity. For a short-chain collector, there is no obvious difference in the steric size between normal collector and isomerous collector. For a long-chain collector, isomerous collector will have lower associate force between chains and higher CMC value. (b) For the unsaturated alkyl as non-polar group, In brief, the selectivity of collector decreases with increasing cross section of the unsaturated alkyl. The reason lies in that coverage of non-selective non-polar group on the mineral surface increases with the increase in cross section of the unsaturated alkyl.
6.5.5
Selectivity of Flotation Reagents—xg Calculation and Diagram
(a) Selectivity of flotation reagents—Relationship between group electronegativity and steric size of collector The studies by Wang and Deng [44] show that the selectivity of flotation reagent decreases with the decrease in steric size of polar groups. But the interactive activity of flotation reagent increases with decreasing its selectivity. This phenomenon is generally called as “wedge effect.” The relationship between flotation selectivity and section size of polar groups of flotation reagent can be shown by the following: u=
d2 1 DE or S ¼ = 2 u DE d
where ΔE is the interactive activity of polar groups of flotation reagents; d is the section size of polar groups; S (or 1/u) is the interactive energy of flotation reagent on unit surface of mineral, that is “wedge effect.” The derivative of the equation above can be given as follows: 2Dd ¼
d DðDEÞ DE
ðiÞ
According to the electronegativity calculated by J.H Chen in Sect. 6.4.2, the interactive energy of flotation reagent on mineral surface can be described as follows:
220
6 Theoretical Criteria and Calculation for Collector Performance
pffiffiffi DE = 23K nðxAB xH2 O Þ xg xO
ðiiÞ
Hence, d Dd=Dxg = xg xO 2 When Dd=Dxg [ d2 xg xO , the section size ðD dÞ of polar groups is the main influencing factor for the selectivity of flotation reagent; when d Dd=Dxg \ 2 xg xO , the electronegativity of polar groups is the main influencing factor for the selectivity of flotation reagent. According to the calculation results by J.Z. Wang et al., the selectivity of some flotation reagents is listed in Table 6.46 (Table 6.47, 6.48 and 6.49). Table 6.46 Electronegativity of ethoxycarbonyl thionocarbamates Ethoxy carbonyl sulfur ammonia ester collectors
Electronegativity
The order of selectivity of flotation reagents
AECTC EECTC IBECTC NBECTC IPECTC
3.4417 3.4298 3.4631 3.4401 3.4562
EECTC > NBECTC > AECTC > IPECTC > IBECTC
Table 6.47 Electronegativity of Y-89 and butyl xanthate Reagent
Electronegativity
Relationship between selectivity and Electronegativity
Conclusion
Y-89 Butyl xanthate
3.078 3.084
3.0 < xg < 3.5, copper and zinc, sulfur R12/xg Butyl xanthate
Table 6.48 Electronegativity and polar group diameters of COBA and HOBA Reagent code
Section size ðD dÞ of polar groups [11]
Electronegativity
Conclusion
COBA HOBA
87 73
5.10, 4.50 4.64, 4.42
COBA > HOBA
Table 6.49 Molecular formula and electronegativity of RO-12 and R-12 Reagent code
Molecular formula
Electronegativity
Conclusion
RO-12 R-12
R-CONHCH2COOH R-NHCH2COOH
xg-COOH = 4.73, xg-NH = 4.92 xg-COOH = 4.67, xg-NH = 4.91
RO-12 > R-12
6.5 Steric Size of Collector Molecule and Its Flotation Selectivity
221
(2) The diagram method The relation between group electronegativity (xg) and group diameter (dg) of collector is shown in Fig. 6.15. The relation between electronegativity difference (Dx) and radius sum of mineral ions is shown in Fig. 6.16. The electronegativity and ionic radius are calculated according to the data of Pauling. As shown in Figs. 6.15 and 6.16, the reagents and minerals are, respectively, divided into two parts. The part on the upper left of diagonal line involves the sulfide minerals and related collectors, respectively. The group on the lower right of diagonal line involves the oxide minerals and related collectors, respectively. For the sulfide minerals which are characterized by large ionic radius or small electronegativity difference, all sulfide collectors can be used in the flotation process. But the collector that is characterized by large group electronegativity (xg) and group diameter (dg) performs a better selectivity. For the sulfide minerals characterized by small ionic radius or large electronegativity difference, only the collector that is characterized by small group electronegativity (xg) and group diameter (dg) can be applied in the flotation process. In addition, the mineral needs to be activated. For example, ZnS and NiS must be activated with Cu2+; Sb2S3 must be activated with Pb2+. For the secondary oxide mineral of copper or lead, collector that is characterized by small group electronegativity (xg) and group diameter (dg) can be applied in the flotation after the oxide mineral has been vulcanized. For the mineral that contains lithophile element, oxide collector characterized by large group electronegativity (xg) can be applied in the flotation process. For the mineral that contains transition siderophile metal, all oxide collectors can be applied in the flotation process. But the oxide collector characterized by large group electronegativity (xg) and group diameter (dg) performs a better selectivity.
(C6 H 5 NH)2 CS
(ROCSS)2
ROCSSR
dg
R2 NCSSH ROCSSH C6 H 4 NSCSH C6 H 4 NNHCSH
RNHCSOR C6 H 4 COOHSH (RO)2 PSSH RONHOH
(RO)2 POSH
RAsO3 H 2 RPO3 H 2
ROCOSH
RSO3 H
RCOOH RSH
RNH 2
xg
Fig. 6.15 Relation between group electronegativity (xg) and group diameter (dg) of collector
6 Theoretical Criteria and Calculation for Collector Performance
r++r –
222
Δx Fig. 6.16 Relationship between electronegativity difference (Dx) and radius sum of mineral ions
Based on Figs. 6.15 and 6.16, the flotation behavior of reagent can be predicted in the unknown reagent–mineral system. Examples for the prediction of reagent performance are given by the following: (a) Flotation separation of Cu–Pb–Zn–Fe sulfides It is shown in Fig. 6.16 the flotation priority for Cu–Pb–Zn–Fe sulfides will be usually Pb–Cu–Zn–Fe. The collectors characterized, respectively, by small group electronegativity (xg) and large group diameter (dg) can be orderly used in the flotation separation of Pb and Cu sulfides. Those above collectors mainly include xanthate, aerofloat, and thionocarbamate of high selectivity. For the flotation separation of Zn and Fe sulfides, the collector characterized by small group electronegativity (xg) and small group diameter (dg) can be used in the flotation process. (b) Flotation separation of Bi-Pb and Bi-Cu sulfides Flotation separation of Bi-Pb and Bi-Cu sulfides is hard to achieve. It is shown in Fig. 6.16 the flotation behavior of Bi is close to that of Pb. In principle, Bi sulfide should be firstly floated. Meantime, the difference in the flotation behavior of Bi and Pb sulfides should be enlarged. That is, the collector characterized by small group electronegativity (xg) and large group diameter (dg) may be used in the flotation separation of Bi and Pb sulfides. For the flotation separation of Bi and Cu sulfides, the collector characterized by large group diameter (dg) can be used in the flotation process. Bi sulfide is firstly floated, and Cu sulfide is depressed on this condition. (c) Flotation separation of Cu-As sulfides Flotation separation of Cu-As sulfides is harder to achieve. Based on Figs. 6.15 and 6.16, the flotation behavior of Cu is close to that of As. If As exists in the form of single sulfide, the collector characterized by large group
6.5 Steric Size of Collector Molecule and Its Flotation Selectivity
223
electronegativity (xg) and large group diameter (dg) can be firstly used in the flotation of Cu sulfide. The collectors characterized by small group electronegativity (xg) and small group diameter (dg) can also be firstly used in the flotation of As sulfide. If As occurs mainly in iron sulfide (pyrite) mineral, the collector characterized by large group diameter (dg) such as thionocarbamate can be firstly used in the flotation of Cu sulfide. And Fe sulfide is depressed on this condition. (d) Flotation of secondary oxidized minerals of sulfide ore For the flotation separation of secondary Pb, Zn, and Cu oxidized minerals, the collectors characterized by small group electronegativity (xg) and small group diameter (dg) can be used in the flotation process. But it is necessary of presulfidation by sodium sulfide.
6.6
Molecular Orbital Approach of Reagent Performance
Molecular orbital approach and related calculations for reagent performance are mainly discussed in this section [19, 29–31, 45–49].
6.6.1
Introduction of Molecular Orbital Approach (HMO)
Molecular orbital approach (MO) can be divided into single MO, semiempirical MO, and non-empirical MO. Their features are given as follows: Approximation method
Treated electron
Repulsion of electron
Single MO
Hückel method (HMO) Extended Hückel method
− −
Semiempirical MO
Pariser–Parr–Pople method Complete neglect of differential overlap method
p electron Complete electron p electron Complete electron Complete electron
Non-empirical MO
+ + +
The so-called complete electron refers to the inner layer electron. The HMO theory, as the simplest calculation method, was proposed by Hückel in 1931. First, the orbit energy can be calculated according to Schrodinger equation. Schrodinger equation can be expressed as follows:
224
6 Theoretical Criteria and Calculation for Collector Performance
r2 w +
8p2 m ðE VÞw = 0 h2
where ∇ refers to the Laplace operator; w refers to the wave function; m refers to the particle mass; h refers to the Planck’s constant; E refers to the total energy of particle; V refers to the potential energy. Operator of Schrodinger equation can be given by the following: Hw = Ew where H refers to the Hamilton operator. It can be seen from the operator of Schrodinger equation the motion state of electron can be described by the wave function.
6.6.2
Application of HMO to Calculate Orbit Energy and Electron Density Distribution
When the two sides of Schrodinger equation are, respectively, multiplied by w, it can be obtained: wHw = wEw The integral representation of the above equation can be given as follows: Z
Z wHwds = E
wwds
Hence, R wHwds E¼ R 2 w ds
ð6:10Þ
Taking benzene for example, the calculation process of orbit energy can be given by the following: wi ¼ Ci1 x1 þ Ci2 x2 þ þ Ci6 x6 where i refers to the orbit serial number; C refers to the orbit coefficient of atom.
6.6 Molecular Orbital Approach of Reagent Performance
225
When the above equation is put into Eq. 6.10, it can be obtained: R ðC1 v1 þ C2 v2 þ C3 v3 þ þ C6 v6 ÞH ðC1 v1 þ C2 v2 þ C3 v3 þ þ C6 v6 Þds E¼ R ðC1 v1 þ C2 v2 þ C3 v3 þ þ C6 v6 ÞC1 v1 þ C2 v2 þ C3 v3 þ þ C6 v6 Þds R R R R C12 v1 Hv1 ds þ þ C62 v6 Hv6 ds þ C1 C2 v1 Hv2 ds þ þ C2 C1 v2 Hv1 ds þ R R R R ¼ C12 v21 ds þ þ C62 v26 ds þ C1 C2 v1 v2 ds þ þ C2 C1 v2 v1 ds þ ¼
C12 a1 þ þ C62 a6 þ C1 C2 b12 þ þ C2 C1 b21 þ C12 þ þ C62 þ C1 C2 S12 þ þ C2 C1 S21 þ
where Z a1 ¼ b12 ¼
Z Z
S12 ¼
v1 Hv1 ds v1 Hv2 ds v1 v2 ds
where a1 refers to the Coulomb integral which is equivalent to the atomic energy in molecule; b12 refers to the exchange integral; S12 refers to the overlap integral. According to the assumption of Hückel: (a) The Coulomb integrals of all atoms are the same. That is, a1 = a2 = a3 ¼ a6 = a: (b) The exchange integrals of adjacent atoms are the same. The exchange integrals of non-adjacent atoms are zero. That is, b12 = b23 = ¼ b61 = b b13 = b14 = ¼ b64 ¼ 0 (b) The overlap integrals of different atoms are zero. That is, Sij ¼ 0 ði 6¼ jÞ;
Sij ¼ 1ði ¼ jÞ:
The expression of E can be given by the following: 2 C1 þ C22 þ C32 þ þ C62 a þ 2ðC1 C2 þ C2 C3 þ þ C6 C1 Þb E¼ C12 þ C22 þ C32 þ þ C62
ð6:11Þ
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6 Theoretical Criteria and Calculation for Collector Performance
When each C is dealt with partial differential, @E = 0; @C1
@E ¼ 0; @C2
A group of simultaneous equations, then, can be given as follows: 9 C1 ða EÞ þ C2 b þ C6 b ¼ 0 > > = C1 b þ C2 ða EÞ þ C3 b ¼ 0 > > ; C1 b þ C2 b þ C6 ða EÞ ¼ 0
ð6:12Þ
These simultaneous equations are also called as “secular equation.” The necessary and sufficient condition to has nonzero solutions of the secular equation is that the related coefficient determinant becomes zero. The coefficient determinant, so-called secular determinant, is as follows: aE b 0 0 0 b
b aE b 0 0 0
0 b aE b 0 0
0 0 b aE b 0
0 0 0 b aE b
b 0 0 ¼0 0 b aE
If E = a + kb, that is k = (E − a)/b, Eq. 6.12 can be changed into: 9 C1 k ¼ C2 þ C6 > > > > > C2 k ¼ C1 þ C3 > > > > C k ¼ C þC = 3
2
4
ð6:13Þ
C4 k ¼ C3 þ C5 > > > > > C5 k ¼ C4 þ C6 > > > > C k ¼ C þC ; 6
1
5
0 0 1 k 1 0
0 0 0 1 k 1
And, k 1 0 0 0 1
1 k 1 0 0 0
0 1 k 1 0 0
1 0 0 ¼0 0 1 k
6.6 Molecular Orbital Approach of Reagent Performance
227
The above equation is a unary sextic equation of E. The roots of this equation are as follows: E1 ¼ a þ 2b; E2 ¼ a þ b; E3 ¼ a þ b; E4 ¼ a b; E5 ¼ a b; E6 = a 2b Because the values of a and b are negative, the energy level of E1, E2, and E3 is, respectively, lower than a of atomic orbit. But the energy level of E4, E5, and E6 is, respectively, higher than a of atomic orbit. For the molecular orbital ui of Ei, u1, u2, and u3 are, respectively, the bonding molecular orbitals; u4, u5, and u6 are, respectively, the antibonding molecular orbitals. Based on these results, the p-electron energy-level diagram of benzene is drawn as follows: E6 E 4, E 5 E 2, E 3 E1
It can be seen that E1 = a + 2b is the lowest energy level. The value of Ci can be obtained by putting the E values of Eq. 6.13 into the Eq. 6.12. According to the normalization condition of molecular orbital u, then, the absolute value of Ci can be obtained. The normalization condition of molecular orbital u is as follows: Z u2 ds ¼ C12 þ C22 þ þ C62 ¼ 1 Based on Eq. 6.12, the relation between coefficients of atomic orbital (C11, C12, …, C16) can be obtained as follows: C11 ¼ C12 ¼ ¼ C16 According to Eq. 6.13, 1 C11 ¼ C12 ¼ ¼ C16 ¼ pffiffiffi 6 Thus, it can be obtained: 1 u1 ¼ pffiffiffi ðv1 þ v2 þ þ v6 Þ 6 Using the same principle and calculation, u2, u3, u4, u5, and u6 are obtained by the following:
228
6 Theoretical Criteria and Calculation for Collector Performance
1 u2 ¼ pffiffiffiffiffi ð2v1 þ v2 v3 2v4 v5 þ v6 Þ 12 1 u3 ¼ pffiffiffi ðv2 þ v3 v5 v6 Þ 4 1 u4 ¼ pffiffiffi ðv2 v3 þ v5 v6 Þ 4 1 u5 ¼ pffiffiffiffiffi ð2v1 v2 v3 þ 2v4 v5 v6 Þ 12 1 u6 ¼ pffiffiffi ðv1 v2 þ v3 v4 þ v5 v6 Þ 6 Therefore, the value of Ei can also be obtained on the basis of the value of ui.
6.6.3
Application of HMO to calculate Theoretical Index
Various theoretical indexes of HMO are usually used to explain the reaction types and the physical and chemical properties of reagent in the applied quantum chemistry theory. Therefore, various theoretical indexes are expounded in this section. (1) Molecular orbit energy The calculation process of molecular orbit energy had been expounded by taking benzene for example. In general, the value of Ei can be expressed with a and b. Taking butadiene as another example, its structure and secular determinant are given as follows: CH2 ¼ CHCH¼CH2 k 1 0 0 1 k 1 0 ¼0 0 1 k 1 0 0 1 k The four roots of secular determinant are as follows: k1 ¼ 1:6180; k2 ¼ 0:6180; k3 ¼ 1:6180; k4 ¼ 0:6180
6.6 Molecular Orbital Approach of Reagent Performance
229
Hence, the four p-orbit energies of butadiene can be expressed as follows: E4 E3 E2 E1
¼ a 1:6180 b ¼ a 0:6180b ¼ a þ 0:6180b ¼ a þ 1:6180b
Because the values of a and b are both negative, E1 = a + 1.6180b is the lowest energy level. E1 = a – 1.6180b is the highest energy level. It should be pointed out that a and b refer to the Coulomb integral and the exchange integral of butadiene or benzene, respectively. However, the values of a and b of benzene are prone to be taken as those of various organic matters. In fact, there exist some differences in the values of a and b between organic matters. For example, the values of a and b of benzene are, respectively, a = –7.2 eV and b = –3.0 eV; the values of a and b of aromatic compound are, respectively, a = –7.06 eV and b = –2.49 eV; the values of a and b of saturated aliphatic compound are, respectively, a = –5.85 eV and b = –6.36 eV [47]. For those atoms such as N and O atoms, the values of a or b can be dealt with adding a correction factor. (2) Bond energy The Coulomb integral of r atom can be given as follows: Z vr Hvr ds = ar = a For benzene, a1 = a2 = = a6. The Coulomb integral refers to the attraction energy between p-electron and r atom. In general, the value of a is smaller than that of b. As mentioned above, orbit energy of u1, u2, and u3 are, respectively, smaller than a of atomic orbit; orbit energy of u4, u5, and u6 are, respectively, bigger than a of atomic orbit. The difference between a and E is defined as bond energy. For benzene, E1 = a + 2b, therefore, the bond energy of the molecular orbit u1 can be calculated by the following: a ða + 2b) = 2( b) Assuming that the six p-electrons are, respectively, owned by six C atoms, molecular orbit energy is 6a. Hence, the bond energy (WB) can be expressed as follows: WB ¼ 6a W ¼ 8ðbÞ where W refers to the total bonding energy.
230
6 Theoretical Criteria and Calculation for Collector Performance
(3) Electron density For conjugated system, p-electrons distribute in the whole molecule. Electron density is concerned with the chemical reaction and molecular polarity. p-electron density is used as the criterion for the reactivity of conjugated compound. For the molecular orbit i, ui ¼ Ci1 x1 þ Ci2 x2 þ þ Cin xn Z Z Z 2 2 2 2 ui ds ¼ Ci1 v1 ds þ þ Cin v2n ds ¼ 1 Through normalizing atomic orbital, it can be obtained: 2 2 2 Ci1 þ Ci2 þ þ Cin ¼
n X
2 Cin ¼1
r¼1
The electron density q(i) r of r atom in i orbit can be expressed as follows: qrðiÞ ¼ Cir2 If the number of molecular orbits is un, and there are two p-electrons in each orbit, the total electron density qr can be expressed by the following: m m X 2 X 2 2 qr ¼ 2 C1r þ C2r þ þ Cmr 2Cir2 ¼ 2qrðiÞ ¼ i¼1
i¼1
or qr ¼
occ X
vi Cir2
i
where occ refers to that all the electron orbits are occupied; vi refers to the number of electrons in i orbit. (4) Net charge Net charge refers to the electrons of p-system which are donated by r atom. The expression of net charge can be given as follows: Qr = Nr qr where Qr refers to the number of net charges; Nr refers to the number of effective charges.
6.6 Molecular Orbital Approach of Reagent Performance
231
(5) Bond order Bond order refers to the probability of electrons in r–s bond. It represents the bonding degree. Meantime, it can be used as the criterion for the reactivity of r–s. The expression of bond order can be given as follows: prs =
0cc X
vi Cir Cis
i
where r and s are the adjacent atoms. (6) Ionization potential Ionization potential (IP) refers to the needed energy which a molecule becomes a positive ion by losing an electron. The expression of ionization potential can be given as follows: IP ¼ Eho where Eho refers to the highest occupied orbital energy. (7) Electron affinity Electron affinity (EA) refers to the released energy which a molecule becomes a negative ion by getting an electron. The expression of electron affinity can be given as follows: EA = Elu where Elu refers to the lowest unoccupied orbital energy. (8) Electronegativity According to the definition by Mulliken, the expression of electronegativity (xM) can be given as follows: xM =
EA + Ip 2
The relation between Mulliken electronegativity and Pauling electronegativity (xP) can be given as follows: xM ¼ 2:3xp or xM ¼ 2:7xp
232
6 Theoretical Criteria and Calculation for Collector Performance
(9) Frontier electron density Frontier electron refers to the electron which is in the highest occupied orbit (HOMO) and the lowest unoccupied orbit (LUMO). And frontline electron density is used as the theoretical index of HMO. For electrophilic reaction, it depends on the ðEÞ frontline electron density of HOMO. The frontline electron density ðfr Þ can be expressed as follows: 2 frðEÞ ¼ 2 Crho where (E) refers to the theoretical index of electrophilic reaction; Crho refers to the HOMO coefficient of r atom. For nucleophilic reaction, it depends on the frontline electron density of LUMO. ðNÞ The frontier electron density ðfr Þ can be expressed by the following: 2 frðNÞ ¼ 2 Crlu where (N) refers to the theoretical index of nucleophilic reaction; Crlu refers to the LUMO coefficient of r atom. (10) Reactivity index (Superdelocalizability) Sr Reactivity index also is called as superdelocalize capability. The reactivity index (Sr) for electrophilic reaction and nucleophilic reaction can be, respectively, expressed by the following: SðEÞ r ¼2 SrðNÞ ¼ 2
occ X ðCir Þ2 i unocc X i
ki ðCir Þ2 ki
where occ refers to the occupied orbit; unocc refers to the unoccupied orbit; (E) refers to the electrophilic reaction; (N) refers to nucleophilic reaction; and k refers to the HMO parameter. It can be seen that reactivity index can be used as the criterion for intramolecular reaction, as well as intermolecular reaction. (11) Population analysis Population analyses mainly include atomic orbital population (AOP), atom population (AP), atom orbital bond population (AOBP), and atom bond population (ABP).
6.6 Molecular Orbital Approach of Reagent Performance
233
AOP: Nr ¼ 2
occ X X
Cir Cis Srs
s
i
AP: ony X
My ¼
Nr
r
AOBP: Nrs ¼ 4
occ X
Cis Cis Srs
i
ABP: Myz ¼
ony X onz X r
6.6.4
Nrs
s
Application of HMO to calculation of flotation reagent
Taking xanthate for example, the application of HMO to the calculation of flotation reagent is expounded by the following. The conjugated system of xanthate is P64 type. The serial numbers of O, C, S, and S atoms are given as follows: O(1)
C (2)
S(3) S(4)
The orbital function of O, C, S, and S atoms is x1, x2, x3, and x4. According to LCAO MO, the molecular orbit of electron is the linear combination of all atomic orbits: ui ¼ Ci1 v1 þ Ci2 v2 þ Ci3 v3 þ Ci4 v4 then, Ei ¼
2 2 2 2 Ci1 aO þ Ci2 aC þ Ci3 aS3 þ Ci4 aS4 þ 2Ci2 Ci2 bCO þ 2Ci3 Ci4 bCS3 þ 2Ci2 Ci4 bCS4 2 þ C2 þ C2 þ C2 Ci1 i2 i3 i4
234
6 Theoretical Criteria and Calculation for Collector Performance
where R aO ¼ v1 Hv1 ds called Coulomb integral of oxygen atom, R aC ¼ v2 Hv2 ds called Coulomb integral of carbon atom, R aS3 ¼ v3 Hv3 ds called Coulomb integral of sulfur (3) atom, R aS4 ¼ v4 Hv4 ds called Coulomb integral of sulfur (4) atom, R bCO ¼ v2 Hv1 ds called exchange integral of carbon and oxygen, R bCS3 ¼ v2 Hv3 ds called exchange integral of carbon and sulfur (3), R bCS4 ¼ v2 Hv4 ds called exchange integral of carbon and sulfur (4). Adopting the assumption of Hückel, @Ei ¼ 0; @Ci1
@Ei ¼ 0; @Ci2
@Ei ¼ 0; @Ci3
@Ei ¼0 @Ci4
The empirical coefficients of a and b: bCO ¼ 0:6 b; bCS3 ¼ bCS4 ¼ 1:2b; bCC ¼ b; aO ¼ aC þ 2b; aS3 ¼ aS4 ¼ aC þ 0:9b The secular equation and determinant can be, respectively, obtained as follows: 9 ð2 ki ÞCi1 þ 0:6Ci1 ¼ 0 > > = 0:6i1 kCi2 þ 1:2Ci3 þ 1:2Ci4 ¼ 0 1:2Ci2 þ ð0:9 kC ÞCi3 ¼ 0 > > ; 1:2Ci2 þ ð0:9 ki ÞCi4 ¼ 0 2 ki 0:6 0 0
0:6 2 ki 1:2 1:2
0 1:2 0:9 ki 0
0 1:2 ¼0 0 0:9 ki
The roots of secular determinant are as follows: k1 ¼ 1:37349; k2 ¼ 0:90000; k3 ¼ 1:76785; k4 ¼ 2:50564 Based on these results, the electron energy-level diagram of xanthate is drawn as follows: E1 ¼ a 1:373490b E¼a E2 ¼ a þ 0:90000b E3 ¼ a þ 1:76785 b E4 ¼ a þ 2:50564 b
6.6 Molecular Orbital Approach of Reagent Performance
235
Various theoretical indexes of reagent can be further calculated according to the above results. For example, p-electron density and net charge of xanthate are given by the following: -0.6495
1.6495 1.9601 0.7409
C
O
S
S
+0.0399 +0.2591
O
1.6495
C
-0.6495
S
S
By utilizing the computer technology, various theoretical indexes of some typical collectors are calculated and the results are presented by the following: (i) Coulomb integral of displacing group ax = aC + ab; (ii) Coulomb integral of adjacent C atoms aadj = aC + bb; (iii) Exchange integral of c–x b = lb; The values of a, b, and l are listed as follows: Exchange integral
a
b
l
Exchange integral
a
b
l
–F –Cl –Br –I –O
2.1 1.8 1.4 1.2 2
0.2 0.18 0.14 0.12 0.2
–NH2 ¼S –S– –SH –OCH3
0.4 0.9 0.9 0.55 0.5
0 0.1 0.1 0 0
0.06 1.2 0.5 0.6 0.6
–O– –OH ¼N–
2 0.6 0.6 1
0.2 0 0.1 0.1
1.25 0.8 0.7 0.6 pffiffiffi 2 0.6 0.7 1 1
–CH3 P+5 (P)–O (P)=S
3 −1 2 0.8
−0.1
1
N
0.6 0.85
The structure and secular determinants of various collectors are as follows: (a) Dithiocarbonic acid: Structure: O (R)
O
C
S
(H)
Secular determinant: 2 k 0:6 0 0
0:6 k 1:2 1:2
0 1:2 0:9 k 0
0 1:2 ¼0 0 0:9 k
236
6 Theoretical Criteria and Calculation for Collector Performance
(b) Monothiocarbonic acid: Structure: S O
(R)
C
S
(H)
Secular determinant: 2k 0:6 0 0
0:6 k pffiffiffi 2 1:2
0 1:2 ¼0 0 0:9 k
0 1:2 2k 0
(c) Trithiocarbonic acid: Structure: S S
(R)
C
(H)
S
Secular determinant: 0:9 k 0:5 0 0
0:5 k 1:2 1:2
0 1:2 ¼0 0 0:9 k
0 1:2 0:9 k 0
(d) Dithiocarbamate: Structure: S (R)
N
C
S
(H)
Secular determinant: 1 k 0:6 0 0
1 k 1:2 1:2
0 1:2 0:9 k 0
0 1:2 ¼0 0 0:9 k
6.6 Molecular Orbital Approach of Reagent Performance
237
(e) Phosphorodithioic acid: Structure: (R)
O
(R)
O
S P S
(H)
Secular determinant: 2k 0:6 0 0 0
0:6 1 k 0:6 0:85 0:85
0 0:6 2k 0 0
0 0:85 ¼0 0 0 0:8 k
0 0:85 0 0:8 k 0
(f) Diamino phosphorodithioic acid: Structure: (R)
NH
(R)
HN
S P
Secular determinant: 0:4 k 0:6 0 0 0
0:6 1 k 0:6 0:85 0:85
S
0 0:6 0:4 k 0 0
(H)
0 0:85 0 0:8 k 0
0 0:85 ¼0 0 0 0:8 k
(g) Thionocarbamate: Structure: S (R) NH
C
O
(R` )
Secular determinant: 0:4 k 0:6 0 0
0:6 k 1:2 0:6
0 1:2 0:9 k 0
0 0:6 ¼0 0 2 k
238
6 Theoretical Criteria and Calculation for Collector Performance
(h) Thionocarbamate: Structure: S(H) (R)
N
C
O
(R` )
Secular determinant: 1 k 0:6 0 0
1 k 0:6 0:6
0 0:6 0:55 k 0
0 0:6 ¼0 0 2k
(i) Benzothiazole mercaptan: Structure: (C) N
C
S
(H)
S (C)
Secular determinant: k 1 0 0
1 k 0:6 0:5
0 0:6 0:55 k 0
0 0:5 ¼0 0 0:9 k
(j) Imidazole mercaptan: Structure: (C) N
C
S
(H)
NH (C)
Secular determinant: k 1 0 0
1 k 0:6 0:6
0 0:6 0:55 k 0
0 0:6 ¼0 0 0:6 k
6.6 Molecular Orbital Approach of Reagent Performance
239
(k) Oxazole mercaptan: Structure: (C) N
C
S
(H)
O (C)
Secular determinant: k 1 0 0
1 k 0:6 0:6
0 0:6 ¼0 0 2k
0 0:6 0:55 k 0
(l) Carboxylic acid: Structure: O (R)
C
O
(H)
Secular determinant: k pffiffiffi 2 pffiffiffi 2
pffiffiffi 2 2k 0
(R)
C
pffiffiffi 2 ¼0 0 2k
(m) Hydroxamic acid: Structure: N
O
(H)
OH
Secular determinant: k 0:7 0 0
0:7 0:6 k 0 0
1 0 0:6 k 0:7
0 0:6 ¼0 1 0:6 k
240
6 Theoretical Criteria and Calculation for Collector Performance
(n) Hydroxamic acid: Structure: (R)
C
NH
O
(H)
O
Secular determinant: k pffiffiffi 2 1 0
pffiffiffi 2 2k 0 0
1 0 0:4 k 0:7
0 0 ¼0 0:6 0:6 k
The various theoretical indexes of the above collectors are found in Table 6.50.
6.6.5
Application of Electron Density to Discuss the Structure—Performance of Polar Group
(1) Discussion of the position of the bonding atom As mentioned above, the negative charges of xanthate ion are mostly centrally distributed on the S atoms. Thus, it can be seen that the interaction between xanthate ion and mineral surface is via the bonding of S atoms. The results of electron density also indicate that the states and electron densities of the two S atoms are the same because of delocalization. Therefore, the structure of xanthate ion can be expressed as follows: S O
-
C S
When xanthate ion reacts with metal ion, the two S atoms coordinate with metal to form complex with four-membered ring.
S
S1 = 0.97, S2 = 0.32 S3 = 1.42, S4 = 1.42
S1 = 0.028, S2 = 0.91 S3 = 0.25, S4 = 0.25
f1 f2 f3 f4
f1 f2 f3 f4
Superdelocalizability S(E) r
S(N) r
Frontal electron density f(E) r
f(N) r
= = = =
= = = =
= = = =
Q1 Q2 Q3 Q4
Net charge Qr
0.04 1.25 0.34 0.34
0 0 0.99 0.99
0.0398 0.2588 −0.6493 −0.6493
1.9601 0.7412 1.6493 1.6493
= = = =
q1 q2 q3 q4
Electron density qr
− 1.3734 ß + 0.90000 ß + 1.7678 ß + 2.5056 ß
(4)
E1 E2 E3 E4
a a a a
C
(2)
Orbital energy E
= = = =
(1)
O (H)
dithiocarbonic acid S(3)
= = = =
Q1 Q2 Q3 Q4
S (4)
− 1.3462 ß + 1.2338 ß + 1.9999 ß + 3.0124 ß
0.0430 0.3368 −0.7612 −0.6185
1.9570 0.6632 1.7612 1.6185
a a a a
C (2)
f1 f2 f3 f4
f1 f2 f3 f4 = = = =
= = = = 0.04 1.33 0.23 0.38
0.06 0.11 0.38 1.44
S1 = 0.03, S2 = 0.99 S3 = 0.17, S4 = 0.78
S1 = 0.96, S2 = 0.27 S3 = 0.81, S4 = 1.22
= = = =
= = = =
q1 q2 q3 q4
E1 E2 E3 E4
(1)
O
thiocarbonic acid O(3)
Table 6.50 Various HMO theoretical indexes of common collectors
(H)
= = = =
= = = =
= = = =
S (4)
− 1.3755 ß + 0.8999 ß + 0.9000 ß + 2.2755 ß
0.0602 0.2466 −0.6533 −0.6533
1.9398 0.7534 1.5533 1.5533
a a a a
C (2)
f1 f2 f3 f4
f1 f2 f3 f4
= = = =
= = = =
0.05 1.24 0.34 0.34
0.05 0 1.06 1.06
S1 = 0.04, S2 = 0.90 S3 = 0.25, S4 = 0.25
S1 = 0.65, S2 = 0.33 S3 = 1.45, S4 = 1.45
Q1 Q2 Q3 Q4
q1 q2 q3 q4
E1 E2 E3 E4
(1)
S (H)
trithiocarbonic acid S(3)
= = = =
= = = =
= = = =
S (4)
− 1.5608 ß + 0.8999 ß + 0.9737 ß + 2.4870 ß
0.1874 0.2285 −0.7078 −0.7078
1.8126 0.7715 1.7078 1.7078
a a a a
C (2)
f1 f2 f3 f4
f1 f2 f3 f4
= = = =
= = = =
0.18 1.22 0.29 0.29
0 0 0.99 0.99
(H)
(continued)
S1 = 0.12, S2 = 0.81 S3 = 0.18, S4 = 0.18
S1 = 1.64, S2 = 0.31 S3 = 1.56, S4 = 1.56
Q1 Q2 Q3 Q4
q1 q2 q3 q4
E1 E2 E3 E4
(1)
N
dithiocarbamic acid S(3)
6.6 Molecular Orbital Approach of Reagent Performance 241
C
E1 E2 E3 E4 E5
q1 q2 q3 q4 q5
Q1 Q2 Q3 Q4 Q5
Orbital energy E
Electron density qr
Net charge Qr
= = = = =
= = = = =
= = = = =
(2)
P
− 1.7568ß + 0.8000ß + 1.2501ß + 2.0000ß + 2.3066ß
0.0402 0.5723 0.0402 −0.8262 −0.8262
1.9598 0.4277 1.9598 1.8262 1.8262
a a a a a
(3)
O
(1)
O
(5)
S
(4)
S
dithiophosphoric acid
(H)
3.00
2.83
Electronegativity xp
10.17
= = = = = = = = = = = = = = =
E1 E2 E3 E4 E5 q1 q2 q3 q4 q5 Q1 Q2 Q3 Q4 Q5
S (4)
(H)
P (2)
− 1.8613ß + 0.7999ß + 0.5106ß + 0.7999ß + 1.5506ß
0.1047 0.4872 −0.1047 −0.8482 −0.8482
1.8953 0.5128 1.8953 1.8482 1.8482
a a a a a
(3)
H N
(1)
H N
(5)
S
(4)
S (H)
dithiophosphoramidic acid
(2)
C
thiocarbonic acid O(3) (1)
O
3.80
(H)
3.67
(4)
S
9.35
(2)
Ionization potential Ip
(1)
O
dithiocarbonic acid S(3)
Electron affinity EA
Table 6.50 (continued)
2.80
3.70
9.35
(1)
S
Q1 Q2 Q3 Q4
q1 q2 q3 q4
E1 E2 E3 E4
(2)
C
= = = =
0.2085 0.2766 −0.5333 −0.0483
1.7915 0.7234 1.5333 1.9517
− 1.0847ß + 0.4857ß + 1.5773ß + 2.3212ß
(4)
a a a a
O
C
(1) (2)
N
= = = = = = = =
(H)
thiocatbamate H S(3)
(4)
S
trithiocarbonic acid S(3)
2.70
3.20
9.34
C (2)
S
= = = = = = = = = = = =
q1 q2 q3 q4 Q1 Q2 Q3 Q4
(1)
N
O
(2) (4)
(H)
(continued)
−0.6282 0.3410 −0.7701 0.0575
1.6292 0.6590 1.7701 1.9425
a − 0.8991ß a + 0.6462ß a + 1.5236ß 2.2792ß
C
(3)
(4)
thiocatbamate S (H)
E1 E2 E3 E4
(1)
N
dithiocarbamic acid S(3)
242 6 Theoretical Criteria and Calculation for Collector Performance
(2)
P
S
(5)
S
(4)
f1 = f 3 = 0.04, f f4 = f5 = 0.17
9.1
2.7
2.6
f(N) r
Ionization potential Ip
Electron affinity EA
Electronegativity xp
(H)
E1 E2 E3 E4
q1 q2 q3 q4
Orbital energy E
Electron density qr
= = = =
= = = =
(1)
N
(H)
− 1.1777ß + 0.3630ß + 0.7793ß + 1.4852ß
1.2409 0.9470 1.8730 1.9390
a a a a
S (2) (3)
S (4)
C
thiazole mercaptan
= 1.57
f1 = f 3 = 0, f 2 = 0 f 4 = f 5 = 0.99
Frontal electron density f(E) r 2
S1 = 0.02, S2 = 0.89 S3 = 0.02, S4 = S5 = 0.09
S1 = 0.95, S2 = 0.26 S3 = 0.95, S4 = S5 = 1.88
(3)
O
(1)
O
dithiophosphoric acid
S(N) r
Superdelocalizability
S(E) r
Table 6.50 (continued)
P (2)
S
(5)
S
(4)
4
1
=f =f 5
3
= 0.99, f =0
2.3
2.45
8.09
= = = = = = = =
E1 E2 E3 E4 q1 q2 q3 q4
(1)
(H)
− 1.2204ß + 0.3179ß + 0.5760ß + 1.4765ß
(4)
1.2913 0. 9445 1.8787 1.8853
a a a a
S (2) (3)
N(H)
C
q1 q2 q3 q4
E1 E2 E3 E4
= = = =
= = = =
(1)
3
1
= 0.33, f = 1.61, f
2.9
4.8
8.7
(H)
(continued)
− 1.1740ß + 0.3756ß + 1.1186ß + 2.2297ß 1.2291 0.9375 1.8713 1.9620
a a a a
S
4
2
= 0.04 = 0.008 f1 = 0.36, f2 = 1.30 f3 = 0.22, f4 = 0.05
f f
(2) (3)
O(4)
C
O
(2) (4)
(3)
S1 = 0.41, S2 = 1.46 S3 = 0.25, S4 = 0.06
N
2.7
4.4
8.3
f1 = 0.21, f2 = 1.27 f3 = 0.46, f4 = 0.05
f1 = 1.67, f 2 = 0.03 f 3 = 0.28, f 4 = 0.005
S1 = 0.19, S2 = 1.17 S3 = 0.42, S4 = 0.04
C
S1 = 1.32, S2 = 0.39 S3 = 2.50, S4 = 0.96
(1)
N
= 1.48
=0
(4)
S1 = 3.51, S2 = 0.43 S3 = 1.32, S4 = 0.97
O
C
(1) (2)
N
N
thiocatbamate S (H)
oxazol mercaptan
2
2
(H)
thiocatbamate H S(3)
imidazole mercaptan
f1 = f 3 = 0.10, f f4 = f5 = 0.15
f f
S1 = S3 = 0.05, S2 = 0.79 S4 = S5 = 0.08
S1 = S3 = 4.07, S2 = 0.36 S4 = S5 = 2.09
(3)
H N
(1)
H N
dithiophosphoramidic acid
6.6 Molecular Orbital Approach of Reagent Performance 243
7.9
f1 = 0.75, f2 = 1.05 f3 = 0.12, f4 = 0.05
8.0
4.2
2.6
E1 = a − 1.2360ß E2 = a + 2ß E3 = a + 3.2360ß
f(N) r
Ionization potential Ip
Electron affinity EA
Electronegativity xp
Orbital energy E
C (1) O (3)
O(2) (H)
carboxylic acid
f1 = 0.70, f2 = 1.05 f3 = 0.12, f4 = 0.11
f1 = 0.76, f2 = 0.10 f3 = 1.04, f4 = 0.08
Frontal electron density f(E) r
(1) (3)
(4)
E1 E2 E3 E4
= = = =
(2)
O a a a a
− 1.0423ß + 0.1793ß + 0.8983ß + 1.7647ß
(H)
hydroxamic acid C N O (H)
2.6
4.1
f1 = 0.89, f2 = 0.09 f3 = 0.60, f4 = 0.41
S1 = 0.58, S2 = 0.86 S3 = 0.099, S4 = 0.093
S1 = 3.09, S2 = 0.86 S3 = 3.74, S4 = 3.42
S1 = 0.64, S2 = 0.89 S3 = 0.10, S4 = 0.05
−0.2913 0.0555 −0.8787 0.1147
S(N) r
= = = =
S1 = 2.51, S2 = 0.89 S3 = 3.74, S4 = 2.27
Q1 Q2 Q3 Q4
(4)
N(H)
(2) (3)
Superdelocalizability S(E) r
−0.2406 0.0530 −0.8730 0.0610
(1)
Q1 Q2 Q3 Q4
= = = =
S (4)
(2) (3)
(H)
= = = =
S (2) (3)
−0.2291 0.0625 −0.8713 0.0038
O(4)
C
(H)
(1) (3)
(4)
E1 E2 E3 E4
= = = =
a a a a
(2)
O
(continued)
− 1.2996ß + 0.14406ß + 1.3178ß + 2.8378ß
hydroxamic acid (H) C N O (H)
2.7
4.17
8.02
f1 = 0.76, f2 = 1.05 f3 = 0.12, f4 = 0.03
f1 = 0.70, f2 = 0.09 f3 = 1.17, f4 = 0.01
S1 = 0.65, S2 = 0.90 S3 = 0.11, S4 = 0.03
S1 = 2.32, S2 = 0.90 S3 = 3.74, S4 = 1.03
Q1 Q2 Q3 Q4
(1)
N
(1)
S
oxazol mercaptan
C
N
(H)
imidazole mercaptan
S
N
C
thiazole mercaptan
Net charge Qr
Table 6.50 (continued)
244 6 Theoretical Criteria and Calculation for Collector Performance
f1 = 0 f2 = f3 = 0.99
Frontal electron density f(E) r
= = = =
= = = = 0.0895 −0.8028 −0.3969 0.1096
0.9105 1.8026 1.3969 1.8903
(H)
(4)
4.5 2.6
4.0
3.5
Electronegativity xp
7.5
12.1
f1 = 1.08, f2 = 0.19 f3 = 0.60, f4 = 0.11
f1 = 0.18, f2 = 0.52 f3 = 0.34, f4 = 0.94
S1 = 1.04, S2 = 0.19 S 3 = 0.57, S 4 = 0.10
S1 = 1.56, S2 = 4.23 S3 = 2.56, S4 = 6.13
Q1 Q2 Q3 Q4
q1 q2 q3 q4
(2)
O
Electron affinity EA
(H)
(1) (3)
hydroxamic acid C N O (H)
Ionization potential Ip
f1 = 1.44 f2 = f3 = 0.27
S1 = 1.17 S2 = S3 = 0.22
S(N) r
(N) r
S1 = 0.17 S2 = S 3 = 0.72
Superdelocalizability S(E) r
f
Q1 = 0.4473 Q2 = −0.7236 Q3 = −0.7236
Net charge Qr
O (3)
q1 = 0.5527 q2 = 1.7236 q3 = 1.7236
C (1)
O(2)
carboxylic acid
Electron density qr
Table 6.50 (continued)
= = = =
Q1 Q2 Q3 Q4
0.1561 −0.7876 0.5562 −0.9244
0.8439 1.7876 1.4438 1.9244
(4)
2.5
3.8
7.5
f1 = 1.15, f2 = 0.21 f3 = 0.55, f4 = 0.07
f1 = 0.30, f2 = 0.17 f3 = 0.45, f4 = 1.06
S1 = 0.89, S2 = 0.16 S3 = 0.43, S4 = 0.05
S1 = 2.31, S2 = 1.87 S3 = 3.85, S4 = 8.08
= = = =
q1 q2 q3 q4
(2)
O
(1) (3)
hydroxamic acid (H) C N O (H)
6.6 Molecular Orbital Approach of Reagent Performance 245
246
6 Theoretical Criteria and Calculation for Collector Performance
According to the data of electron density, the bonding atoms of aerofloat and dithiocarbamate can be deduced. The structures and electron densities of tetrathiocarbonic acid and phosphorodithioic acid are as follows: qr
Qr
Electron of tetrathiocarbonic acid
-0.7078 S
1.7078
S 1.8125 0.7715
N
+0.1874+0.2258
C
N
1.7078
C
S
Electron of phosphorodithioic acid:
1.8268
1.9598
O
S
0.4277
+0.0402
- 0.8262 S
+0.0402
- 0.8262 S
O +0.5723 P
P 1.8268
1.9598
O
-0.7078 S
O
S
Thus, it can be seen that the bonding atoms of aerofloat and dithiocarbamate are both S atoms. Therefore, the reason for the flotation performance difference of these three reagents does not lie in the bonding atom, but lies in the difference of the bonded atoms, join ways, and non-polar groups. Based on the results of AP, ABP, and AOBP which are calculated from the adsorption of xanthate on mineral, the following opinions were obtained by Takahashi: (a) When the Coulomb integral of mineral metal (such as Pb) is small, the electron density of S atom in xanthate decreases obviously because the electron of S atom shifts to the metal surface. The bonding orbital between metal and xanthate includes 3s and 3p orbital; (b) When the Coulomb integral of mineral metal (such as Na) is large, the electron density of S atom in xanthate decreases slightly because the S atom of xanthate cannot bond with metal surface. But the value of s6 − x1 is large. It indicates the S atom of mineral may bond with xanthate; (c) The interaction between xanthate and mineral metal is mainly via r bond, with partly p bond. The interaction model between xanthate and mineral (MX) proposed by Takahashi is as follows: X H7
H8
2.962
S6 M 2.962
X-1
C4
1.685
105o
124.5o C
1.345
2
113.5o
S1
1.685
118.5o
O3
1.465
1.54
1.09
H6
C5 H11
H10
6.6 Molecular Orbital Approach of Reagent Performance
247
The M of MX in the model refers to the metal with 3s23p2. The X refers to the S atom with 3s23p4. The interatomic distance can be expressed as M − X = 2.962 Å. The distance between xanthate and mineral is 2 Å. (2) Discussion of the interaction of atoms in polar group The interaction of atoms in polar group can be discussed by comparison with monothiocarbonic acid, dithiocarbonic acid, tridithiocarbonic acid, and tetrathiocarbonic acid. The electron densities of dithiocarbonic acid and tetrathiocarbonic acid had been given. The electron densities of monothiocarbonic acid and tridithiocarbonic acid are given by the following: qr
Qr
Monothiocarbonic acid
-0.7612 O
1.7612
O
1.9570 0.6632
O
C
+0.0430
1.6185
O
Tridithiocarbonic acid
C +0.3368
S
-0.6533 S
1.6533 1.9398 0.7534
S
C
-0.6185 S
S
+0.0602
1.6533
S
S
C
+0.2466
-0.6533 S
It can be seen that the orders of electron densities (qS) of these four reagents are as follows: Monothiocarbonic acid < dithiocarbonic acid < tridithiocarbonic acid < dithiocarbamic acid Flotation results show that the orders of collecting capability of these four reagents are same with those of qS. The bonding atoms of reagents are the same (S atom). It can be concluded that other atoms in polar group may influence the qS of the bonding atom to cause the difference of reagent performance. Firstly, the adjacent C atom can directly influence the qS of the bonding atom. The orders of qC of these four reagents are also same with those of qS. It further confirms that the performance difference of S atoms in four polar groups lies in the effects of other atoms. For monothiocarbonic acid, the C atom of polar group connects with two O atoms with electron-withdrawing capability. The electron densities (qO) of the two O atoms are relatively bigger. Therefore, electron density of the adjacent S atom weakens. For dithiocarbonic acid, the C atom of polar group connects with one O atom with electronwithdrawing capability. Therefore, the effect of O atom on electron density of the adjacent S atom is relatively weak. For tridithiocarbonic acid, the C atom of polar group connects with two S atoms. Therefore, the electron density of the bonding S atom is relatively big. For dithiocarbamic acid, the C atom of polar group connects with one –NH2 group with electron-donating capability. Therefore, electron densities of the C and S atoms become strong.
248
6 Theoretical Criteria and Calculation for Collector Performance
AP and ABP of these four reagents were calculated by Takahashi. As listed below, the results also support the above opinions. 0.824
H7
H8
0.774 7.424
O6
C4
ethyl thiocarbonic acid
0.870
0.424 3.760 0.710
0.662 0.610
C2
4.798 C5
O3
0.810
0.811
7.025
2.313
H9
H11
0.901
H10
0.876
S1 6.881
0.821
H7
H8
0.777
6.805
S6
C4
0.436
0.986
ethyl dithiocarbonic acid
C2
0.582
3.761
0.870 0.710
C 4.400 5
O3
0.811
7.084
2.891
H9
0.810
H11
0.970
H10
0.876
S1 6.832
0.840
H7
H8
0.757
6.851
S6
C4
ethyl trithiocarbonic acid
3.761
0.867
0.911
C2
0.864
0.880 0.652 4.371 C5
O3
0.817
5.791
3.511
H11
0.901
0.878
S1 6.867
0.874
H7
H8
0.807
6.821
S6
C4
0.658
0.962
dithiocarbamic acid
C2
3.230
0.795
4.073
0.806
H9
N3
0.874
5.738
0.962
S1
H12
4.073 C5
0.806 0.874
H10 0.874
H11
H9
0.824
H10
6.6 Molecular Orbital Approach of Reagent Performance
249
Table 6.51 Relations between various theoretical indexes (q, Q, S, and f) and solubility product (L) of silver salt of reagent Reagent
qs
Qs
S(N) s
f(N) s
S(E) s
f(E) s
x
L
Thiocarbonic acid Dithiocarbonic acid Trithiocarbonic acid Dithiocarbamic acid Phosphorodithioic acid Dithiophosphoramidic acid Oxazole
1.618 1.649 1.653 1.708 1.826 1.848 1.871 – 1.873 – 1.878 – 1.533
–0.818 –0.649 –0.653 –0.708 –0.826 –0.848 –0.871 – –0.873 – –0.878 – –0.533
0.78 0.25 0.25 0.18 0.09 0.08 0.11 – 0.10 – 0.099 – 0.42
0.38 0.34 0.34 0.29 0.17 0.15 0.12 – 0.12 – 0.12 – 0.46
1.22 1.42 1.45 1.56 1.88 2.09 3.74 – 3.74 – 3.74 – 1.32
1.44 0.99 0.87 0.99 0.99 0 0.12 – 1.04 – 0.60 – 0.28
3.0 2.8 2.8 2.7 2.6 2.3 2.7 – 2.6 – 2.6 – 2.7
– 4.4 – 4.4 1.4 – 5.3 2.0 2.0 2.4 3.1 1.6 –
Thiazole mercaptan Imidazole mercaptan Thiocarbamate
10−19 10−21 10−16
10−22 10−19 10−22 10−20 10−22 10−20
The relation between various theoretical indexes and reagent performance had been expounded above. Meantime, the effects of various theoretical indexes on the reagent performance are found in Table 6.51. As shown in Table 6.51, there exist some special relations between various theoretical indexes (q, Q, S, and f) and solubility product of silver salt of reagent.
6.6.6
Application of Valence Theory and HMO to Discuss the Bonding Property and Mechanism of Reagents
The selectivity of collector is discussed via valence theory and electronegativity (xP) calculated by HMO in this section. (1) Soft–hard acid and basic (SHAB) theory According to the soft–hard acid and basic (SHAB) theory of Lewis, the interaction between reagent and mineral metal can be expressed as follows: M þ L ! ML where M refers to the mineral metal; L refers to the reagent. Metal M acts as the acceptor of electron. Reagent L acts as the donor of electron. Therefore, metal M and reagent L can be, respectively, considered as acid and base. Meantime, acid and base can be further divided into two groups: “soft” and “hard.” Hard acid metal is characterized by high positive charges, small volume, low deform capability, and small electronegativity. Soft acid is characterized by low
250
6 Theoretical Criteria and Calculation for Collector Performance
positive charges, large volume, high deform capability, and large electronegativity. Hard base reagent is characterized by small volume, low deform capability, and large electronegativity. Soft base is characterized by large volume, high deform capability, and small electronegativity. According to SHAB, hard acid is prone to react with hard base; soft acid is prone to react with soft base. The hard acid metals include alkali metals, alkaline earth metals, rare earth metals, IIIA metals, and some transition metals of before d5. The soft acid metals include some d10 transition metals. Interim metals refer to d6−9 transition metals. The groups of hard base usually comprise –COO–, –OH–, –O–, –SO42–, –SO32–, F–, Cl–, –CO3–, –PO4–, –NH2, =NH, –N+R3, etc. The groups of hard base usually comprise –S–, –SH, –SCN–, –OCSS–, =O2PSS–, –NCSS–, –NOH, etc. The groups of interim base usually comprise –AsO3H, –PO3H, –NO2−, –Br, etc. It can be seen that SHAB theory is related to the electronegativity of reagent and metal. Thus, SHAB theory accompanied with electronegativity can be used as the criterion for the interaction between reagent and mineral. The calculation method for electronegativity had been mentioned above. Therefore, we shall not go into detail here. (2) Inner–outer orbital theory According to the coordination bond theory of Pauling, outer orbital complex ion often forms when the electronegativity difference between metal ion and the bonding atom of reagent is large; inner orbital complex ion forms when the electronegativity difference between metal ion and the bonding atom of reagent is small. Taking Fe2+ for example, the electronic shell structure can be expressed by the following: Fe2+ 3d
4s
4p
4d
It can be seen that the electronic structure of Fe2+ is 1s22s22p63s23p63d6; there is no electron in the outermost 3s23p63d6. When Fe2+ forms inner orbital coordination ion, such as one Fe2+ and six H2O molecules forming a Fe(H2O)2+, six coordination bonds form at the same time. The electronic structure of Fe(H2O)2+ can be expressed by the following: Fe(H2O)62+ 3d
4s
4p
sp3d2 outer hybrid orbital
4d
6.6 Molecular Orbital Approach of Reagent Performance
251
The electronic shell structure of Fe2+ appears in the form of is 3s23p63d6 outer hybrid orbital in the Fe(H2O)2+. Metal ions with sp3d2 outer hybrid orbital also contain Al3+, Sn4+, Pb4+, etc. Metal ions with sp3 outer hybrid orbital contain Zn2+, Cd2+, Hg2+, etc. When Fe2+ forms outer orbital coordination ion, such as one Fe2+ and six CN– ions forming a Fe(CN)2+ 6 , six coordination bonds also form. The electronic structure of Fe(CN)2+ can be expressed by the following: 6 Fe(CN)644p
4s
3d
4d
d2sp3 outer hybrid orbital
The electronic shell structure of Fe2+ appears in the form of is d2sp3 inner hybrid 2 3 orbital in the Fe(CN)2+ 6 . Metal ions with d sp inner hybrid orbital also contain 2+ 2 Co , etc. Metal ions with dsp inner hybrid orbital contain Cu2+, Ag+, Au+, Ni2+, etc. Metal ions with d4sp3 inner hybrid orbital contain Mo4+, W4+, etc. In general, the bonding atoms with large electronegativity, such as O and F atom, are prone to form outer orbital complex ion. For those bonding atoms with small electronegativity (such as S, P, and As atom), they are prone to form inner orbital complex ion. Meantime, inner orbital complex ion is prone to form when the electronegativity of metal is large. Thus, it can be seen that inner–outer orbital theory combined with electronegativity is helpful to explain the interaction between reagent and mineral. The electronegativity difference had been used to discuss the reagent performance in former section. A supplement to the discussion is as follows. According to ion parameter (u) of Pauling: 2
u ¼ 100½1 e1=4ðxA xB Þ Taking monothiocarbonic acid, dithiocarbonic acid, tridithiocarbonic acid, and carboxylic acid for example, the ion parameters of their metal compounds can be given by the following:
u%
Cu Zn Ca
Monothiocarbonic acid
Dithiocarbonic acid
Tridithiocarbonic acid
Carboxylic acid
43 56 76
15 26 52
12 23 48
70 80 91
252
6 Theoretical Criteria and Calculation for Collector Performance
It can be seen that the ion parameters of Cu dithiocarbonic acid and Cu tridithiocarbonic acid are both very small. That is, Cu dithiocarbonic acid and Cu tridithiocarbonic acid are both soft acid–soft base type. Because the ion parameter of soft acid type of Cu monothiocarbonic acid is relatively large, the bonding capability of monothiocarbonic acid is weak. Because carboxylic acid is hard base type, the ion parameter of Cu carboxylic acid is 50 %. It indicates the bonding capability of carboxylic acid is not very good. The hard acid type of Ca can bond with carboxylic acid to form ionic bond. However, compared with carboxylic acid, the ion parameter of Ca xanthic acid is 55 %. It indicates that the ionic bond between Ca and carboxylic acid is not very strong. The electronegativity of Zn or Fe is smaller than that of Cu, but bigger than that of Ca. Although xanthate can be used as collector for the flotation of Zn sulfide, the sulfide ore must be activated with Cu2+ before the flotation process. The reason can also be explained according to the SHAB theory. According to the classification table of soft–hard acid proposed by Pearson, Fe3+ is hard acid. The ion parameters of Fe3+ carboxylic acid and Fe3+ xanthic acid are 73 % and 19 %. Therefore, Fe sulfide (Fe2+) can be floated by xanthate; Fe oxide (Fe3+) can be floated by carboxylic acid. For the interim base type of hydroximic acid, it can be used for the flotation of both Fe and Cu oxides. Meantime, hydroximic acid has a good selectivity because it is hard to react with Ca and Mg gangues. In the course of studying the structural chemistry, An-bang Dai proposed that ionization potential, electron affinity, and interatomic potential could be used for the determination of the acid–base. The expression can be given by the following: SHA ¼ SHB ¼
X X
IPn =n 25Z =ro 1 EAn =n 5:88Z =rc þ 30:39
where RIPn refers to the sum of n-level ionization potentials; Z* refers to the atomic effective charges; rC refers to the covalent radius; and REAn refers to the sum of nlevel electron affinities. When SHA is positive value, the compound is hard acid. When SHA is negative value, the compound is soft acid. When SHB is positive value, the compound is soft base. When SHB is negative value, the compound is hard base.
6.6.7
Application of HMO and Synergism of Back-Donation Bond to Discuss the Bonding and Selectivity of Reagent
Based on ligand field theory and molecular orbital theory, the r bond (M ← r) forms between hybrid electronic orbital of metal ion (such as dsp2, sp3, d2sp3) and r orbital of reagent. When metal ion and reagent do not form p bond, the p bond can
6.6 Molecular Orbital Approach of Reagent Performance
253
Fig. 6.17 Molecular orbital diagram of pyrite
also form if reagent contains p orbital. In the bonding process, the p bond is called as positive ligand bond (M ← p) when the reagent is electron donor; the p bond is referred as negative ligand bond or back-donation bond (M ! p) when metal is electron donor. In general, positive ligand bond only includes pp type. But negative ligand bond includes pp–pp type, dp–pp type, and dp–dp. There had been some studies on the interaction between reagent and mineral by using ligand field theory and molecular orbital theory [50]. For sulfide minerals such as pyrite, it possesses the complex structure of FeS6. Fe atom contains six hybrid r bonds (d2sp3) and three back-donation bonds (dp–dp type). Copper pyrite and blende have a tetrahedral coordination structure of CuS4 and ZnS4, respectively. The molecular orbital pictures of copper pyrite and blende are shown in Figs. 6.17 and 6.18. As shown in Figs. 6.17 and 6.18, their M atoms contain four hybrid r bonds (sp3) and two back-donation bonds. For oxide minerals, Fe3+ and O2– ion is octahedral coordination structure and tetrahedral coordination structure, respectively. Fe atom contains six hybrid r bonds (d2sp3) and non-bonding energy level of half-packed t32g and e*2 g orbital. However, the molecular orbital of hematite is characterized by 2p orbital. In comparison with sulfide mineral, hematite has no back-donation bond. Ligand orbital is the main contributor in the formation of mineral molecular orbital. Therefore, molecular orbital of sulfide mineral and oxide mineral reflects the features of S atom and O atom, respectively. The sulfide collector has a good selectivity for sulfide mineral. The reason lies in the following aspects:
254
6 Theoretical Criteria and Calculation for Collector Performance
Fig. 6.18 Molecular orbital diagrams of chalcopyrite and sphalerite
(a) The 3p electron of S atom can enter into the vacant orbital of sulfide mineral. In addition, the energy of S atom is close to that of sulfide mineral. Therefore, the bonding capability of sulfide collector appears strong. (b) The bonding S atom of reagent has vacant orbital which can accept the nd electron of sulfide mineral to form back-donation bond. In addition, the stability of coordination increases because of synergy. For oxide collectors such as carboxylic acid, it has 2p electron. The orbital energy of carboxylic acid is higher than that of sulfide mineral. In addition, there is no back-donation bond between oxide collector and sulfide mineral. Accuracy calculation of the molecular orbital is hard to achieve. Therefore, various approximate methods are used to deduce the bonding tendency of reagent and mineral, as well as the selectivity of reagent. These approximate methods include frontier electronic density (fr) and electrophilic-nucleophilic reactivity (sr). The values of fr and sr of various common collectors are given in Table 6.50. Comparison of various calculation data of three collectors (xanthate, imidazole mercaptan, and thionocarbamate) is given by the following: Dithiocarbonate qr 1.9601 0.7412 O C ðEÞ
Sr ðNÞ Sr
0.97 O 0.028
0.32 C 0.91
Imidazole mercaptan
1.6493 S 1.6493 S 1.42 S 0.25 1.42 S 0.25
1.2913 0.9445 C N
3.09 0.58
N
0.86 C 0.86
1.8787 S(H) 1.8853 N(H) 3.74 S(H) 0.099 3.42 N(H) 0.093
Thionocarbamate 1.5333 S 1.7915 0.7234 C N(H)
3.51 0.43 N(H) C 0.19 1.17
1.9517 O
1.32 S 0.42 0.97 O 0.04
6.6 Molecular Orbital Approach of Reagent Performance
255
where q refers to the p-electron density; s refers to the superdelocalize capability. (E) According to the data of qS, qN, s(E) S , and sN , imidazole mercaptan is S N type collector. Unlike the S N type xanthate, the orbital energy of S atom is close to that of sulfide mineral; the orbital energy of N atom is close to that of oxide mineral. Therefore, imidazole mercaptan can be used in the flotation of sulfide minerals as well as secondary oxide minerals. The value of s(N) of thionocarbamate is bigger than that of xanthate and imiS dazole mercaptan. It indicates back-donation bond is prone to form in thionocarbamate. Thionocarbamate can be used in the flotation of copper sulfide, but not in the flotation of iron sulfide. In other words, thionocarbamate has a good selectivity toward polymetallic ore. The reason for the formation of back-donation bond, from the reagent structure perspective, involves the following two aspects: (a) When the vicinity of the bonding atom appears in those atoms (including N, O, P, and S) which contain lone-pair electron, those atoms are prone to donate their electron to decrease the effective charges of metal. Then, the d orbital electron of metal ion transfers to reagent to further form back-donation bond. (b) When the group that can weaken the electron density of the bonding atom appears in the polar group, back-donation bond can also form. The reason lies in that the group decreases the repulsion force between the bonding atom and the donated electron of metal. Although one end of thionocarbamate molecule is like xanthate (O–C–S), the other end is like imidazole mercaptan (N–C–S), and the structure of thionocarbamate is different from that of xanthate and imidazole mercaptan. The electron structures of xanthate, imidazole mercaptan, and thionocarbamate are given by the following.
S
.. R
O
C
-
.. R
S
NH
S
-
S
..
C S
R
NH
.. C
O
R`
,
In the xanthate, imidazole mercaptan, and thiocarbamate ions, P64 conjugated system is comprised of three p-electrons donated by C, S, and S atoms, as well as a lone-pair electron and an ion donated by O or N atom. However, P64 conjugated system is comprised of two p-electrons donated by C and S atoms, as well as two lone-pair electrons donated by O and N atoms in thionocarbamate. Therefore, the (N) values of qS, QS, and S(E) S are not very large. But the values of SS are very large. As well known, thiambutosine (also called white drug) can be applied in the flotation of Pb–Zn sulfide mineral. Meantime, it also has a good selectivity in the
256
6 Theoretical Criteria and Calculation for Collector Performance
flotation of pyrite. The explanation is that there are two N atoms with lone-pair electrons in the vicinity of the bonding S atom in thiambutosine. Based on these discussions, providing that xanthate, aerofloat, and thiocarbamate acid are, respectively, linked to an R group:
.. S
S
.. ,R
O
.. C
S
R`
,
.. R
N(H)
R
O
, R
O
.. C
S
S P
R`
.. S
R`
The selectivity of reagent can be improved. According to molecular orbital theory, the interaction between reagent and mineral can be divided by the following: (a) Chemical adsorption of normal r/p-bond and back-donation p-bond It involves in the interaction between sulfide collector and nonferrous metal sulfide mineral. (b) Chemical adsorption of covalent bond (including r- and p-bond) It mainly involves in the interaction between oxide collector and transitional metal oxide mineral. The selectivity of reagent usually is bad. (c) Chemical adsorption of ionic bond It mainly involves in the interaction between oxide collector and oxide mineral. The selectivity of reagent is also bad. (d) Electrostatic force adsorption of electric double layer It mainly involves in the interaction between oxide mineral and collector with low activity. (e) van der Waals force and hydrogen bond adsorption It mainly involves in the interaction between non-polar mineral and non-polar oil, as well as the interaction between polar mineral and polar reagent with low activity.
6.6.8
Application of HMO to Discuss the Structure—Performance of Non-polar Group
(1) Effect of hydrocarbon chain length Hydrocarbon chain length can directly influence the interaction between polar group and mineral. Taking the interaction between non-polar group of xanthate and mineral, non-polar group has an impact on the inductive effect of the adjacent O atom. The explanation can be expounded by the MO calculation of the Coulomb integral of O atom.
6.6 Molecular Orbital Approach of Reagent Performance
257
Compared with p-electron orbital, the locality of r-electron orbital of saturates is stronger. The linear combination of sp3 hybrid orbital in the C–C chain of alkyl can be given as follows: X ui ¼ Cij ui i
When the electron orbital belongs to p-electron, the b-integrals of adjacent orbits are the same. When the electron orbital belongs to r-electron, the b-interorbital integral of the same C atom is relatively larger. Therefore, the b-interorbital integral of two C atoms can be expressed as follows: Z b¼
ucr Huc þ r ds
The b-interorbital integral of one C atom can be expressed as follows: Z mb ¼ ucr Huc þ r ds m2 ¼ 0:12 For r electron orbital, aO ¼ a þ 0:5b; bCO ¼ 0:5b; k ¼ Eiba. For C2H5O–, hence, it can be obtained: k 1 0 0 1 k m 0 ¼0 D4 ¼ 0 0 k 0:5 0 0 0:5 0:5 k Semiexpanded formula: C CH3 O D2 ¼ kð0:5 kÞ 0:25 ¼ 0 C3 H7 O D6 ¼ ðk2 1ÞD4 m2 k2 D2 m4 kð0:5 kÞ ¼ 0 C4 H9 O D8 ¼ ðk2 1ÞD6 m2 k2 D4 þ m4 kD2 þ m6 kð0:5 kÞ ¼ 0 C5 H11 O D10 ¼ ðk2 1ÞD8 m2 k2 D6 þ m4 k2 D4 m6 k2 D2 m8 kð0:5 kÞ ¼ 0 C6 H13 O D12 ¼ ðk2 1ÞD10 m2 k2 D8 þ m4 k2 D6 m6 k2 D4 þ m8 k2 D2 þ m10 kð0:5 kÞ ¼ 0 C7 H15 O D14 ¼ ðk2 1ÞD12 m2 k2 D10 þ m4 k2 D8 m6 k2 D6 þ m8 k2 D4 m10 k2 D2 m12 k2 ð0:5 kÞ ¼ 0 C8 H17 O D16 ¼ ðk2 1ÞD14 ðk2 1ÞD12 þ m2 k2 D10 m6 k2 D8 þ m2 k2 D6 m2 k2 D4 þ m12 k2 D2 þ m4k2 ð0:5 kÞ ¼ 0
258
6 Theoretical Criteria and Calculation for Collector Performance
The roots can be given as follows: k1 ¼ 0:8090; k2 ¼ 0:7575; k3 ¼ 0:7327; k4 ¼ 0:7160; k5 ¼ 0:7049; k6 ¼ 0:6959; k7 ¼ 0:6882; k8 ¼ 0:6826: For alcohol, the value of a and b is –7.3976 and –5.0097 eV, respectively. For random atom or replaced group, the Coulomb integral of p-electron can be expressed as follows: ax ¼ a0 þ dx b0 where a′ and b′ are similar to a and b, respectively; dx refers to the effect parameter of C atoms on the Coulomb integral of O atom. According to the relation between ionization potential (IP) and Coulomb integral of p-electron, then, it can be obtained: dx ¼
Ip 7:2 3:0
Therefore, the Coulomb integrals of p-electron of O atom corresponding to different C atoms in hydrocarbon chain are given by the following: C1 : a0 þ 1:26 b0 ; C2 : a0 þ 1:14 b0 ; C3 : a0 þ 1:08 b0 ; C4 : a0 þ 1:04 b0 ; C5 : a0 þ 1:01 b0 ; C6 : a0 þ 0:99 b0 ; C7 : a0 þ 0:97 b0 ; C8 : a0 þ 0:95 b0 : For the Coulomb integral of O–C, it is in connection with the bond distance of O–C. If the effect parameter (dx) is introduced into the linear combination of p-electron of xanthate, it can be obtained: dx k 0:6 0 0
0:6 k 1:2 1:2
0 1:2 0:9 k 0
0 1:2 ¼0 0 0:9 k
Through the calculation of the equation above, the results indicate qS of the S atom increases with increasing the number of C atoms of non-polar group. Under the condition of reagent concentration, the adsorption amount of xanthate also increases with increasing the number of C atoms of non-polar group. It further confirms the indirect effect of non-polar group on the bonding capability of polar group. In general, the effect is obvious when the number of C atoms is less than six. When the number of C atoms exceeds six, the qS of the S atom keeps unchanged. It indicates inductive effect may dominate the effect of non-polar group.
6.6 Molecular Orbital Approach of Reagent Performance
259
(2) Effect of hydrocarbon chain isomer The effect of hydrocarbon chain isomer can be expounded by studying the relation between ionization potential (IP) and atomic Coulomb integral of polar group. The MO results of various alkyls calculated by Franklin are given as follows: Ip
Ip
Alkyl Ethane Propane N-butane Isobutane
13.04 11.76 11.23 10.97 10.82
n-pentane Isopentane Hexane 2,3-dimethyl butane 2,2-dimethyl butane
10.82 10.67 10.72 10.48 10.40
Those results above indicate that the ionization potential (IP) of isomer is smaller than that of normal alkane when the C atoms of polar groups are the same. That is, non-polar group is able to improve the bonding capability of polar group in certain limits of hydrocarbon chain length. (3) Additivity of homologous reagent performance In classical physical chemistry, additivity of homologous reagent performance can be expressed as follows:
DH ¼ A0 þ Bn þ d0 where A′ is a specific constant of homolog; n refers to the number of C atom; d refers to the linear correlation factor; and DH˚ refers to the enthalpy change. Based on the LCAO MO, the secular determinant of methane is as follows: k þ a l 0 0 0 0 0 0
l k m 0 m 0 m 0
0 m k l m 0 m 0
0 0 l k þ a 0 0 0 0
0
0 k l m 0
0 0 0 0 l k þ a 0 0
0
0 m 0 k l
0 0 0 0 ¼0 0 0 l k þ a
The orbital energy of methane is as follows:
Alkyl Ethane Propane Butane
Orbital energy
Energy difference
4.1644b 7.3316b 10.4995b 13.6760b
>3.1672 >3.1679 >3.1765
It can be seen that the energy difference keeps unchanged.
260
6.6.9
6 Theoretical Criteria and Calculation for Collector Performance
Application of HMO to Discuss and Compare Several Collectors
(1) Comparison of xanthate, aerofloat, and dithiocarbamate According to the data of Table 6.50, aerofloat is S S type collector with small electronegativity. Compared with xanthate, the electronegativity of the two O atoms of aerofloat is large. The electron density of aerofloat is large. But S(N) S of aerofloat is relatively small. In contrast, the back-donation bond is prone to form in xanthate. Compared with xanthate, the bonding capability of dithiocarbamate is large. The reason lies in that the value of qC of dithiocarbamate is larger than that of xanthate. In addition, the value of qS of reagent increases with increasing value of qC. The AP and ABP of these two reagents can be given as follows: Dithiocarbamate: 0.821
H(2)
0.777
6.803
S6
0.986
C(4)
0.436
C(2)
2.891 0.970
H(8) 6.870
H (9)
0.710
3.761
C (5) 0.810
0.582 O 7.048 (3)
0.811
4.410
H(10)
H(11) 0.876
S1
6.832
Xanthate: 0.807
H(7)
H(
8)
0.807
6.821
S(
6)
0.962
0.658
C(2)
0.795
3.230
C(4)
4.073
H(9)
N(3)
0.874
5.738
0.962
S(1)
0.806
0.806
C(5)
H(12) 0.874
4.073
6.821
H(10) 0.874
H(11) 0.874
The data above also confirm that the bonding capability of dithiocarbamate is stronger than that of xanthate. Meantime, the electron density of the S atom of dithiocarbamate is larger than that of xanthate. It indicates that (CH3)2N– is prone to donate the electron. The ABP of C(2)–O is bigger than that of C(2)–N.
6.6 Molecular Orbital Approach of Reagent Performance
261
(2) Comparison of phenol aerofloat and amino aerofloat The structure of diamido phosphorodithioic acid is as follows: S
RNH P RNH
SH
According to the data of Table 6.36, diamido phosphorodithioic acid is also S S type collector. Compared with RO–, however, RNH– is prone to donate the electron. Therefore, qS and qP of amino aerofloat are larger than that of phenol aerofloat, respectively. Thus, the bonding capability of amino aerofloat is larger than that of phenol aerofloat. (3) Comparison of thiazole, imidazole, and oxazole mercaptan The structures of thiazole, imidazole, and oxazole mercaptan are as follows: Thiazole mercaptan
S C
SH
C
SH
C
SH
N
Imidazole mercaptan
NH
N
Oxazole mercaptan
O
N
According to the data of Table 6.50, thiazole, imidazole, and oxazole mercaptan are also S S type collectors. As mentioned above, the orbital energy of N atom is close to that of oxide mineral. Therefore, these reagents are able to be used as sulfide collector, as well as soft metal oxide collector. Among of these three reagents, qN of imidazole mercaptan is largest. Therefore, the collecting capability of imidazole mercaptan is strongest. Among these three reagents, the electronegativity of oxazole mercaptan is smallest. Therefore, the collecting capability of imidazole mercaptan is weakest. According to the actual flotation results, the collecting capability of thiazole mercaptan is good in the flotation of natural cerussite. Imidazole mercaptan performs well in the flotation of copper oxide.
262
6 Theoretical Criteria and Calculation for Collector Performance
(4) Comparison of thionocarbamate derivatives Besides for those thionocarbamate derivatives which had been mentioned above, there are also some more complicated thionocarbamate derivatives. The structures of some thionocarbamate derivatives are as follows: S
S R
NH
O
C
R ' , R1
X
NH
R2
NH
O
R3
S
R3
S
S R
C
S
C
R ' , R1
X
NH
R2
C
Based on the experimental results, the change of R or R΄ that is linked with N atom has an impact on the reagent performance obviously. It confirms that these derivatives are S N type collectors. Under the condition of different pH, the morphology of these derivatives can be given as follows: SH
S R
O
C
NH
R'
R
O
C
NH R'
When the solution pH is low, these derivatives appear in the form of “thionic acid.” When the solution pH is high, these derivatives appear in the form of “thiol acid.” According to the data of Table 6.36, the positive back-donation bond of “thiol acid” is stronger than that of “thionic acid.” Therefore, the selectivity “thiol acid” is more obvious. (5) Comparison of hydroximic acids The structures of the two isomers of hydroximic acid are as follows: R
C
NH
OH
R
N
C
OH
OH
O
(a)
(b)
In comparison with carboxylic acid, hydroximic acids can be used as oxide collector. According to the analysis of qr and Sr, the (b) isomer may be O O or O N type collector; the isomer (a) may be O O type collector. Because of large SN and SO, the isomer (b) performs better collecting capability and selectivity.
6.7 Comprehensive Applications of Various Theoretical Criteria
6.7
263
Comprehensive Applications of Various Theoretical Criteria
Various theoretical criteria had been discussed in the first seven sections. These theoretical criteria are also called as quantitative structure-activity relationships (QSAR) in documents. QSAR of reagent can be divided into three categories: valence bond factor, hydrophilicity–hydrophobicity factor, and steric factor. The calculation of solubility product is the synthesis criterion which includes these three factors. QSAR is based on the relation between structure factor and reagent performance: DFA ¼ f ðDB; DH; DSÞ where DFA refers to the change of reagent activity; DB refers to valence bond factor; DH refers to hydrophilicity-hydrophobicity factor; and DH refers to steric factor. According to these three factors, various theoretical criteria are listed in Table 6.52. Based on Table 6.52, the following three fundamental relations can be obtained: (a) Linear relationship between structure factor and reagent activity The linear relationship between structure factor and reagent activity is the combinational type. For example, the relation between free energy of non-polar group and the number of –CH2– can be expressed as follows:
DGn ¼ /n where n refersPto the number of –CH2–. For n-alkyl, L ¼ 0:475n, the relation between HLB and the number of –CH2– can be expressed as follows: HLB ¼
X
H
X
Lþ7
or HLB ¼
X
H 0:475n þ 7
(b) Exponential function relationship between structure factor and reagent activity The exponential function relationship between structure factor and reagent activity is the structural type. The expression can be given as follows: 1=n 1 FA ¼ a þ b a
Group electronegativity
Valence bond factor
Electron density, reactivity index
Theoretical criteria
Structural factor
X
vc2 ; X c2 Sr ¼ 2 k
qr ¼
xg = 0.31[(n* + 1)/ r] + 0.5 MMO = (Ip + EA1/2); Dv2 ¼ ðvg vM Þ2 P P i = Dx2/ nФ
Calculation method Sulfide mineral: xg = 2.5–3.3; oxide mineral: xg = 3.5–4 nonmetal ore: xg > 4; i = 0.2–0.5
(1) judging the specificity of reagent; (2) judging flotation performance of reagent; (3) analyzing structure–activity relationships; (4) inferring dissociation and solubility of reagent; (1) judging position of the bonding atom; (2) judging flotation performance of reagent; (3) judging selectivity of reagent; (4) analyzing structure–activity relationships; qr indicates the position of the bonding atom; refers to the S(E) r strength of positive coordination bond; refers to the S(N) r strength of negative coordination bond;
Number range Collector
Application
Table 6.52 Quantitative structure–activity relationships (QSAR) of flotation reagent
–
i = 0.38– 1.0
Frother
(continued)
As same as collector
The value of Dx2 is bigger than that of collector; i > 0.2;
Depressant
264 6 Theoretical Criteria and Calculation for Collector Performance
(1) judging the classification of reagent; (2) judging flotation performance of reagent; (3) judging proportion relationships of polar and non-polar groups; (4) inferring reagent dosage; (1) judging the classification of reagent; (2) judging flotation performance of reagent; (3) judging proportion relationships of polar and non-polar groups; (4) inferring application field of reagent;
log CMC ¼ A Bn
AdditivePmethod: P HLB = H − L + 7 ratio method: HLB = K(inorganic group/organic group)
CMC
HLB
Hydrophilicity-hydrophobicity factor
Application
Calculation method
Theoretical criteria
Structural factor
Table 6.52 (continued)
Sulfide ore: additive method: 4– 7; ratio method: 8–15; oxide ore: additive method: 1– 4; ratio method: 3–7
Number range Collector 1 CMC CHC ffi 100 CDC ffi 4CMC
Additive method: 5-7; ratio method: 6-10;
Frother
(continued)
Additive method: > 10; ratio method: >35;
Depressant
6.7 Comprehensive Applications of Various Theoretical Criteria 265
Cross section diameter of molecule Parachor, van der Waals’ volume
Solubility product
Steric factor
Synthesis criterion
Group electronegativity
Theoretical criteria
Structural factor
Table 6.52 (continued)
vg as a abscissa, dg as a vertical coordinate
Ksp ¼ ½M n þ m ½A n
P r=( P npD/M)4 VMW = VAW
dg
Calculation method
(1) judging the specificity of reagent; (2) inferring flotation conditions;
Sulfide ore: 3.7– 10.4 oxide ore: 3.6–5.8 The value of r is moderate;
Judging selectivity of reagent (1) inferring surface tension of reagent; (2) judging reagent structure; (3) analyzing structure–activity relationships; (4) judging selectivity of reagent; Judging flotation performance of reagent The bonding capability of reagent is large when the value of Ksp is relatively small;
Number range Collector
Application
The value of r is relatively small;
Frother
The bonding capability of reagent is large when the value of Ksp is relatively small;
The value of r is relatively big;
As same as collector
Depressant
266 6 Theoretical Criteria and Calculation for Collector Performance
6.7 Comprehensive Applications of Various Theoretical Criteria
267
where FA refers to the reagent activity; a, b, and a refer to the constants, respectively; and n refers to the number of –CH2–. (c) Power function relationship between structure factor and reagent activity The exponential function relationship between structure factor and reagent activity is the agglomerate type. The expression can be given as follows: r¼
X
P
D M
4
where r refers to the surface tension of solution; P refers to the parachor; M refers to the molecular weight of reagent; and D refers to the solution density. Based on those criteria, the main characteristic of reagent is summarized by the following. It can provide some clues for the development and the selection of reagent.
6.7.1
Characteristic of the Sulfide Collector
(a) The electronegativity of polar group is small (5.8). (e) The non-polar group is usually not big. The size of non-polar group is equivalent to that of C2–C6. The isoalkane has a better performance than normal one. And the performance of the unsaturated alkane is bad in general.
6.7.2
Characteristic of the Nonmetal Oxide Collector
(a) The electronegativity of polar group is large (>4.0). And the electron density of the bonding atom is also large comparatively. (b) The bonding atom of polar group is O atom in general. When the electronegativity of adjacent atom is small, or the electronegativity of adjacent atom and interval atom is large, the bonding capability of polar group is relatively strong.
268
6 Theoretical Criteria and Calculation for Collector Performance
(c) The diameter of polar group is relatively small (100,000
As shown in Fig. 9.5, the dispersant effect of polyacrylic acid with low molecular weight is better that those of polyphosphate and sodium silicate.
Fig. 9.5 Dispersant effect of reagent with low molecular weight toward dolomite (1—polymer; 2—polyphosphate; 3—sodium silicate; 4—amylase)
351
Quantity of dispersed solids (mg)
9.3 Structure and Performance of Organic Flocculant
Reagent dosage (mg/L)
(2) Effect of bend capability of hydrocarbon chain The bendability of hydrocarbon chain also influences the performance of flocculant. For example, the flocculability of reagent with flexible aliphatic hydrocarbon is limited because the reagent molecule is in the shape of curl because of the appearing of hydrogen bond between polar groups. Comparatively speaking, the flocculability of reagent with rigid hydrocarbon chain such as cellulose and starch is higher.
9.4 9.4.1
Flotation Application of Various flocculants Demand for Molecular Weight and Dissociation Degree of Flocculant
The bridging effect of organic polymer is beneficial to the flocculation of coarse-grained mineral because the electrostatic force of inorganic electrolyte and the hydrophobic association of surfactant are not enough to cause the flocculation of coarse-grained mineral. Therefore, the interaction between coarse-grained mineral and reagent increases with increasing the molecular weight of reagent. However, inorganic electrolyte is helpful to the flocculation of fine-grained mineral. According to the settlement tests [7], the reagents for different particle sizes of diatomite can be given as follows: Cationic flocculant: (i) phenylamineformaldehyde condensate (ii) Polyhexamethylenethiocarbamide H2 N ðCH2 Þ6 NHCSNH n ðCH2 Þ6 NH2 ; n ¼ 810
352
9 Structure and Performance of Flocculant
Nonionic flocculant:
(iii) carbamide formaldehyde condensate (iv) polyacrylamide-H, molecular weight 178 104 (v) polyacrylamide-M, molecular weight 42.7 104 (vi) polyacrylamide-L, molecular weight 3.9 104 Surfactant: Phenylamine hydrochloride Inorganic electrolyte: BaCl2. The research results about the interaction between these reagents and different particle sizes of diatomite can be concluded by the following: (1) For coarse-grained diatomite Surfactant and inorganic electrolyte cannot flocculate coarse-grained diatomite. The flocculation of nonionic flocculant increases with increasing the molecular weight. It reflects that nonionic flocculant adsorbs on diatomite via bridging effect. The flocculation of nonionic flocculant decreases when the reagent concentration is too large. The reason is that dispersant effect increases with the increase of reagent concentration. (2) For medium-grained diatomite BaCl2 and surfactant phenylamine cannot flocculate medium-grained diatomite. Nonionic flocculants have good flocculabilities because they also adsorb on diatomite via bridging effect. (3) For colloidal-grained diatomite Nonionic flocculants cannot flocculate colloidal-grained diatomite. Ionic flocculants such as reagent (1) and (2) have good flocculabilities toward colloidal-grained diatomite. Surfactant and inorganic electrolyte can also flocculate colloidal-grained diatomite. It indicates that those reagents adsorb on diatomite via electrostatic force. For different particle sizes of minerals, demand for molecular weight and dissociation degree of flocculant is listed in Table 9.7.
9.4.2
Demand for Adsorption Rate of Flocculant and Necessary Agitation
Adsorption rate of flocculant and necessary agitation are required in the flotation. The effects of adsorption rate of flocculant and necessary agitation on the flotation process are mainly discussed by the following.
Nonion or same ion △
△
High molecular weight Low polymerization degree Oppositely Nonion or charged ion same ion
○
○ , △
○
High polymerization degree Oppositely Nonion or charged ion same ion
△ △ ○ ○ ○ ○ ○ ○ refers to that flocculant is noneffective; △ refers to that flocculant is partly effective
Low molecular weight Inorganic salt Surfactant Oppositely Oppositely charged ion charged ion
Coarse particle −1 mm + 74 lm Fine particle −74 lm , △ Colloidal solid ○ where ○ refers to that flocculant is effective;
Mineral granularity
Table 9.7 Demand for molecular weight and dissociation degree of flocculant for different particle sizes of minerals
9.4 Flotation Application of Various flocculants 353
354
9 Structure and Performance of Flocculant
(1) Effect of adsorption rate of flocculant and necessary agitation on electrolyte coagulation According to the adsorption rates of flocculants, polyelectrolyte flocculation can be further divided into the following two kinds: (1) When the f potential of mineral reaches unstable potential (10–20 mV), polyelectrolyte flocculation occurs slowly. Because mineral particle still owns the f potential, this flocculation process depends on the concentration and category of polyelectrolyte. (2) When the f potential of mineral becomes zero, however, polyelectrolyte flocculation occurs quickly. The concentration and category of polyelectrolyte have no impact on flocculation process. The necessary agitation is required in these two kinds of flocculation processes. However, overhigh agitation and overlow agitation are both not propitious for further flocculation process. Under the condition of scheelite grain 1 µm, suspension concentration 0.35 g/L, the scheelite can be flocculated when NaCl concentration and agitation are, respectively, 0.5 mol/L and 200 r/min. When agitation is enhanced to 850–1700 r/min, flocculation becomes bad. Meantime, the size of flocculation particle varies with agitation strength. For example, the size of flocculation particle is 1.3–5 µm under the condition of agitation 200 r/min. The size of flocculation particle becomes 1.25–1.8 µm under the condition of agitation 1700 r/min. (2) Effect of adsorption rate of flocculant and necessary agitation on bridging effect of polymer The settlement test of scheelite with nonionic polyacrylamide shows that the grain diameter of floc is 20 µ under the condition of agitation 200 r/min. But the floc is comprised of 2–4 particles when agitation strength becomes 1700 r/min. The reason is that the overhigh shear force destroys the polymer chain. (3) Effect of adsorption rate of flocculant and necessary agitation on hydrophobic flocculation The settlement test of scheelite with sodium oleate shows that the grain diameter of floc increases with increasing the agitation strength. The result reflects that shear force is helpful to the hydrophobic flocculation of scheelite. When MgCl2 is added into the scheelite suspension simultaneously, the f potential of mineral will be decreased to −40 or −25 mV. And the flocculation of scheelite becomes more obvious. The explanation for the shear flocculation is that shear force is helpful to remove the hydration shell of mineral surface. The related settlement tests are shown in Figs. 9.6 and 9.7.
References
355
Fig. 9.6 Effect of flocculant on the turbidity value of scheelite suspension
Turbidityvalue
Stirringtime 90 min
0.5 M NaCl
Polyacry lamide 10-4M NaCl
Fig. 9.7 Effect of mixing strength on the settlement of scheelite suspension (1—reagent dosage 0.35 g/L, 300 r/min; 2—reagent dosage 0.35 g/L, 850 r/min; 3—reagent dosage 3.5 g/L, 1700 r/min; 4—reagent dosage 0.35 g/L, 1700 r/min; 5—MgCl2, pH 9.3, reagent dosage 0.35 g/L, 1700 r/min)
Absorbence (%)
Stirring speed (r/min)
Stirringtime (min)
References 1. F.F. Aplan, D.W. Fuerstenau, Forth Flotation 50th Anniversary Volume (AIME, INC., New York, 1962), p. 170 2. D.W. Fuerstenau, Flotation foundation (notes): central and south mining and metallurgy college intelligence document (1979) 3. D.Z. Wang, Nonferrous metals. Miner. Process. Extr. Metall. Sec. 2, 12 (1979) 4. D.Z. Wang, Structure and Flotation Properties of Flotation Reagents (Central-South Institute of Mining and Metallurgy. Mine Department) 5. C.R.A. Clauss et al., Intern. J. Min. Proc. 31, 27 (1976) 6. Revue de Soc. Royale Belge des Ing. Et des Ind. 12 (1970) 7. Noda, Jpn. Chem. Mag. 82, 1614 (1961)
Chapter 10
Molecular Design of Reagents for Mineral Processing
10.1
Energy Criterion for Reactivity of Reagents
For the interaction between reagent (R) and mineral (L), the chemisorption or surface chemical reaction can be expressed as follows: R þ L ! Rd þ Ld ! RL
ð10:1Þ
Based on generalized perturbation theory (GPT), the total energy changes (DETRT ) corresponding to the charge migration from reagent and mineral to intermediate product Rd+ Ld− can be given by the following: ðr Þ
DETRT ¼ ¼
ðlÞ
ðrÞ
ðlÞ
QðrÞQðlÞ qocc quocc Db2rl kquocc qocc Db2rl þ R þ L L R Rrl e 2 EHOMO ELUMO 2 EHOMO ELUMO DE1RL
þ DE2RL
ð10:2Þ
þ DE3RL
where Q(r) and Q(l) refers to net charge of the bonding atom in reagent molecule ðrÞ ðrÞ and the bonded atom in mineral, respectively; qocc and quocc refer to electron density of the bonding atom of reagent molecule in HOMO and LUMO, respecðlÞ ðlÞ tively; qocc and quocc refer to electron density of the bonded atom of mineral in R R and ELUMO refer to energy of reagent HOMO and LUMO, respectively; EHOMO molecule in HOMO and LUMO, respectively; k refers to the number of d electron pairs; DE1RL is to the contribution of electrostatic interaction to DETRT ; DE2RL is the contribution of covalency of positive coordination bond to DETRT ; DE3RL is the contribution of covalency of back-donating bonding to DETRT .
© Metallurgical Industry Press, Beijing and Springer Science+Business Media Singapore 2016 D. Wang, Flotation Reagents: Applied Surface Chemistry on Minerals Flotation and Energy Resources Beneficiation, DOI 10.1007/978-981-10-2030-8_10
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Molecular Design of Reagents for Mineral Processing
When reagent molecule contains two or more bonding atoms, the formula above can be expressed as follows: DETRT ¼
N X Qðri ÞQðli Þ
N X
i¼1 2 RL RL DE1 þ DE2 þ DE3RL i¼1
¼
Rri li e
þ
ðr Þ ðl Þ
i qocci quocc Db2ri li
R L EHOMO ELUMO
þ
N X i¼1
ðr Þ
ðl Þ
i i kquocc qocc Db2ri li
L R 2 EHOMO ELUMO
ð10:3Þ where N refers to the number of the bonding atom in reagent molecule; ki refers to the number of d electron pairs in certain metal ion. The formula 10.3 can be used as the expression for the reactivity energy of flotation reagent. It can be concluded that the reactivity of flotation reagent is increased with decreasing the value of DETRT . Because the relationship between ðr Þ
ðr Þ
i R R , EHOMO and EHOMO is described reagent performance and Qðri Þ, qocci and quocc RT quantitatively, it is more suitable that DET is used as the criterion of reactivity of flotation reagent. ðr Þ ðr i Þ , By adopting quantum chemistry calculation, the values of Qðri Þ, qocci and quocc ðli Þ ðli Þ R R L L EHOMO , ELUMO , Qðli Þ, qocc and quocc , EHOMO and ELUMO can be obtained. The values of Rri li and Db2ri li can also be obtained by the following:
Rri li ¼ rri þ rli
ð10:4Þ
1 Db2ri li ¼ KðDb2ri li þ Db2ri li Þ 2
ð10:5Þ
where rri and rli refers to Pauling radius of the bonding atom in reagent molecule and the bonded atom in mineral, respectively; K refers to empirical constant, for ionic reagent (K = 1), for nonionic reagent (K = 0.75). Taking the flotation of pyrite using ethyl xanthogenic acid, for example, the calculation process of DETRT can be given by the following: (1) The basic quantum chemistry parameters of ethyl xanthogenic acid calculated by CNDO/2 method are as follows (Fig. 10.1): Q(2) = −0.3560
Q(3) = −0.0282
ð2Þ
quocc ¼ 0.4232
ð3Þ
quocc ¼ 0.1558 ELUMO = 0:113562 (a.u)
qocc = 1.6938 qocc = 0.0288 EHOMO ¼ 0:368650 (a.u)
ð2Þ ð3Þ
10.1
Energy Criterion for Reactivity of Reagents
359
Fig. 10.1 Steric configuration of ethyl xanthogenic acid
Fig. 10.2 Crystal structure of pyrite (001)
(2) The basic quantum chemistry parameters of pyrite (FeS2) calculated by CNDO/2 method are as follows (Fig. 10.2): Q(Fe1) = −0.784200 ðFe1 Þ qocc ¼ 0:135000 EHOMO ¼ 0:666928 (a.u)
ðFe1 Þ quocc ¼ 0:267000 ELUMO ¼ 0:307154ða:uÞ
(3) Calculation of RS-Fe and bS-Fe: rS = 1.84 Å bS = −18.50 eV RS–Fe = rS + rFe = 2.64 Å
rFe = 0.80 Å bFe = −26.0 eV bS-Fe =
1 2 K(bS
+ bFe) = −22.075 eV
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Molecular Design of Reagents for Mineral Processing
Table 10.1 Energy criterion of common flotation reagents with chalcopyrite and pyrite Collectors
Molecular formula
Energy criterion DETRT (a. u.) Chalcopyrite Pyrite
Ethyl monothiocarbonic acid Ethyl dithiocarbonic acid Ethyl trithiocarbonic acid Ethyl dithiocarbamate acid Dimethyl phosphorodithioic acid Dimethyl dialkyl thiourea Dimethyl sulfur amino formic acid ester Dimethyl xanthate ester Dimethyl thionocarbamate Dimethyl monothiophosphoryl chloride Trimethyl phosphorothioate Ethyl mercaptan
R–OCOSH R–OCSSH R–SCSSH R2–NCSSH (RO)2–PSSH R–NHC(S)NH–R R–NHC(S)O–R′ R–OCSS–R′ R–NHC(S)SR′ (RO)2PSCl (RO)2PS(OR′) R–SH
−1.127289 −1.470099 −2.014373 −1.646643 −1.458589 −1.304419 −1.302794 −0.714019 −1.337452 −0.345485 −0.455963 −0.849807
−0.274461 −0.312768 −0.364154 −0.281152 −0.275973 −0.214137 −0.203567 −0.166062 −0.208867 −0.134686 −0.121147 −0.245661
(4) Calculation of DETRT :
DERT T
22:0750 2 0:3560 ð0:784200Þ 1:6938 0:267000 ð 27:2120 Þ þ ¼ 2:64 80 2ð0:368650 þ 0:307154Þ 22:075000 2 Þ 3 0:4232 0:1350 ð 27:212000 þ 2ð0:666928 0:113562Þ ¼ 0:001325 0:241835 0:072258 ¼ 0:312768ða:uÞ
Energy criterion of common flotation reagents with chalcopyrite and pyrite are listed in Table 10.1. The relationship between energy criterion of common flotation collectors for sulfide minerals and their silver salts are given in Table 10.2. It can be seen from Table 10.2 that the smaller the collector silver salt, the more negative value of energy criterion is. Therefore, energy criterion reflects the bonding capacity of flotation reagent on mineral surface. Relationship between metallic compounds of two typical collectors and their energy criterion corresponding to sulfide minerals is plotted in Fig. 10.3.
10.2
Application of Energy Criterion to Discuss the Relationship …
361
Table 10.2 Energy criterion of common collectors with chalcopyrite Collectors
Molecular formula
Energy criterion DETRT (a. u.)
Ksp
Ethyl monothiocarbonic acid Ethyl dithiocarbonic acid Ethyl trithiocarbonic acid Ethyl dithiocarbamate acid Dimethyl phosphorodithioic acid Phenylmercaptan Dimethyl sulfur amino formic acid ester
C2H5OCOSH C2H5OCSSH C2H5SCSSH C2H5NCSSH (C2H5O)2–PSSH C6H5SH C2H5NHC(S)O–CH3
−1.127289 −1.470099 −2.014373 −1.646643 −1.458589 −1.527681 −1.302794
– 4.4 – 4.4 1.4 2.4 –
10−19 10−21 10−16 10−21
25
20
Me(EX)n /Ethyl xanthate Me(EP)n /Ethyl thiophosphates
Cu(CuFeS2)
Pb(PbS)
pKsp
15 Cu(CuFeS2)
10 Fe(FeS2)
Pb(PbS)
Zn(ZnS)
5 Zn(ZnS)
0 0.0
-0.4
-0.8
-1.2
ΔE
RL T
-1.6
-2.0
(a. u.)
Fig. 10.3 Relationship between metallic compounds of two typical collectors and their energy criterion corresponding to sulfide minerals
10.2
Application of Energy Criterion to Discuss the Relationship of Polar Groups of Reagents and Performance
10.2.1 Relationship of Polar Groups of Flotation Reagents and Performance The basic quantum chemistry parameters of ethyl monothiocarbonic acid, ethyl dithiocarbonic acid, ethyl trithiocarbonic acid, ethyl dithiocarbamic acid, and ethyl phosphorodithioic acid are given as follows:
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Steric configuration
LUMO
HOMO
Fig. 10.4 Steric configuration, HOMO and LUMO surface of ethyl monothiocarbonic acid
(I) Ethyl monothiocarbonic acid (Fig. 10.4)
Qð3Þ ¼ 0:202568 ð3Þ qocc ¼ 1:124922 EHOMO ¼ 0:275572 ða:uÞ
ð3Þ
quocc ¼ 0:239876 ELUMO ¼ 0:015368 ða:uÞ
(II) Ethyl dithiocarbonic acid (Fig. 10.5)
Qð2Þ ¼ 0:223051 ð3Þ qocc ¼ 0:230019 EHOMO ¼ 0:242820 ða:uÞ
ð3Þ
quocc ¼ 0:203723 ELUMO ¼ 0:092230 ða:uÞ
(III) Ethyl trithiocarbonic acid (Fig. 10.6)
Qð3Þ ¼ 0:249915 ð3Þ qocc ¼ 1:167465 EHOMO ¼ 0:238467 ða:uÞ
ð3Þ
quocc ¼ 0:215779 ELUMO ¼ 0:085830 ða:uÞ
10.2
Application of Energy Criterion to Discuss the Relationship …
Steric configuration
LUMO
HOMO
Fig. 10.5 Steric configuration, HOMO and LUMO surface of ethyl dithiocarbonic acid
(IV) Ethyl dithiocarbamic acid (Fig. 10.7)
Qð3Þ ¼ 0:304676 ð3Þ qocc ¼ 0:222194 EHOMO ¼ 0:223369 ða:uÞ
ð3Þ
quocc ¼ 0:201194 ELUMO ¼ 0:045172 ða:uÞ
(V) Ethyl phosphorodithioic acid (Fig. 10.8)
Qð3Þ ¼ 0:275171 ð3Þ qocc ¼ 0:507184 EHOMO ¼ 0:246545 ða:uÞ
ð3Þ
quocc ¼ 4:209559 ELUMO ¼ 0:073143 ða:uÞ
For flotation reagents (I), (II), (III), (IV), and (V), (1) The order of net charge of QðSÞ is as follows: (IV) > (V) > (III) > (II) > (I)
363
364
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Molecular Design of Reagents for Mineral Processing
Steric configuration
HOMO
LUMO
Fig. 10.6 Steric configuration, HOMO and LUMO surface of ethyl trithiocarbonic acid
ð SÞ
(2) The order of qocc is as follows: (I) > (V) > (II) > (IV) > (III) ð SÞ
(3) The order of quocc is as follows: (V) > (I) > (III) > (II) > (IV)
(4) The order of EHOMO is as follows: (IV) > (III) > (II) > (V) > (I)
(5) The order of ELUMO is as follows: (I) > (IV) > (V) > (III) > (II)
10.2
Application of Energy Criterion to Discuss the Relationship …
365
Steric configuration
HOMO
LUMO
Fig. 10.7 Steric configuration, HOMO and LUMO surface of ethyl dithiocarbamic acid
The MO index has an effect on performance of flotation reagents. It can be seen from Table 10.1 that the order of energy criterion DETRT for collectors above is as follows: (III) > (V) > (II) > (IV) > (III) The order relationship reflects the collecting capacity of these collectors.
10.2.2 Relationship of Polar Groups of Humic Substances-Based Binder and Performance For humic substances-based binder in the process of iron ore agglomeration, the basic structural unit of humic substances is HOy–Ar–xCOOH. For example, the molecular structure of humic substances proposed by Schnitzer is displayed in Fig. 10.9. As one of the active fractions in humic substances-based binder, fulvic acid, the molecular structure model is given by the following (Fig. 10.10). The basic quantum chemistry parameters of fulvic acid calculated by DFT B3lYP method are listed in Table 10.3.
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Molecular Design of Reagents for Mineral Processing
Steric configuration
LUMO
HOMO
Fig. 10.8 Steric configuration, HOMO and LUMO surface of ethyl phosphorodithioic acid
OH
O OH OH
OH
C
O C OH
OH
C
O
OH O
OH
O
OH C
C C
OH OH
O
O
OH
O
OH C
C O
O
C
OH
C
OH
C
C OH
O
OH
O
OH
OH C
OH
OH
O O
O
C
C O
OH
OH C
C
O C
OH
OH
OH C
C
O OH
C
O OH
OH
O
OH
OH
O OH
C
O OH
OH
Fig. 10.9 Molecular structure of humic substances proposed by Schnitzer
OH
10.2
Application of Energy Criterion to Discuss the Relationship …
367
Fig. 10.10 Steric configuration of molecular structure of binder
Table 10.3 Quantum chemical calculation results of molecular structure of binder Quantum chemistry parameters
Fulvic acid (C14H12O8)
Molecular total energy ET (a.u) Molecular dipole Energy of frontier molecular orbital (a.u)
−1142.831411 11.105500 EHOMO ¼ 0:246004 ELUMO ¼ 0:080915
Frontier electron density q
qocc ¼ 0:081914
ð2Þ
quocc ¼ 0:732478
ð3Þ
quocc ¼ 0:041276
qocc ¼ 0:127038
ð8Þ
quocc ¼ 0:858469
ð9Þ qocc ¼
0:007502
quocc ¼ 0:007842
qocc ¼ 0:002792
ð10Þ
quocc ¼ 0:023102
qocc ¼ 0:097237
ð12Þ
ð12Þ uocc ¼
ð14Þ qocc ¼
ð14Þ quocc ¼
qocc ¼ 0:110564
Mulliken net charge Q
0:028633 Qð2Þ ¼ 0:240731 Qð3Þ ¼ 0:150667 Qð8Þ ¼ 0:253361 Qð9Þ ¼ 0:252537
ð2Þ ð3Þ ð8Þ ð9Þ
ð10Þ
0:003664
0:024642 Qð10Þ ¼ 0:206011 Qð12Þ ¼ 0:399497 Qð14Þ ¼ 0:462389 –
Jiang et al. calculated the energy criterion of interaction between fulvic acid and three iron minerals. The crystal structures of the target minerals are given as follows (Fig. 10.11). The energy criterions of interaction between fulvic acid and iron mineral surface calculated by DFT B3lYP method are listed in Table 10.4. It can be seen from Table 10.4 that the order of energy criterion DETRT for iron minerals and fulvic acid is as follows:
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(a) Fe3O4
(b) Fe2O3
(c) FeTiO3
Fig. 10.11 Crystal structure of the target minerals
Table 10.4 Energy criterion of interaction between fulvic acid and iron minerals
Fe3O4
Fe2O3
FeTiO3
−2.403 −2.162 −2.470 DETRT ða:u:Þ Note interaction between fulvic acid and all the metal atoms in mineral crystal cell
FeTiO3 [ Fe3 O4 [ Fe2 O3 The order relationship reflects the adsorption and binding capacity of these iron minerals with organic binder.
10.2
Application of Energy Criterion to Discuss the Relationship …
369
Fig. 10.12 Steric configuration of benzoic acid and phenolic hydroxyl
Table 10.5 Quantum chemistry parameters of benzoic acid and phenolic hydroxyl Quantum chemistry parameters
C6H5–COOH
C6H5–OH
Molecular total energy ET (a.u) Molecular dipole Energy of frontier molecular orbital (a.u)
−420.939988 2.940800 EHOMO ¼ 0:274164 ELUMO ¼ 0:072273
−307.549696 1.962000 EHOMO ¼ 0:239023 ELUMO ¼ 0:02330 0
Frontier electron density q
qocc ¼ 0:000107
ð12Þ
qocc ¼ 0:181548
quocc ¼ 0:364046
ð12Þ
quocc ¼ 0:249987
ð13Þ qocc ¼
0:008268
qocc ¼ 0:003450
quocc ¼ 0:212705 ð14Þ
quocc ¼ 0:000081 –
ð14Þ
–
ð13Þ
qocc ¼ 0:001580 Mulliken net charge Q
quocc ¼ 0:086981 Qð12Þ ¼ 0:065217 Qð13Þ ¼ 0:363922 Qð14Þ ¼ 0:335190
ð6Þ ð6Þ
ð12Þ ð12Þ
Qð6Þ ¼ 0:531164 Qð12Þ ¼ 0:460943 –
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Benzoic acid and phenolic hydroxyl is the basic structural unit in the molecule of humic substances. It was found that there is some difference in the quantum chemistry parameters between these two units (Fig. 10.12).
Fig. 10.13 Steric configuration of the binder structure units with varying hydroxyls
10.2
Application of Energy Criterion to Discuss the Relationship …
371
The basic quantum chemistry parameters of fulvic acid calculated by DFT B3LYP method are listed in Table 10.5. Jiang et al. calculated the effect of number of phenolic hydroxyl on basic quantum chemistry parameters of binder structure unit. Taking C6H5–COOH, HO–C6H4–COOH, (HO)2–C6H3–COOH, and (HO)4–C6H1–COOH, for example, the binder structure units are shown in Fig. 10.13.
Table 10.6 Quantum chemical calculation results of C7H6O3 and C7H6O4 Quantum chemistry parameters
HO–C6H4–COOH
(HO)2–C6H3–COOH
Molecular total energy ET (a.u) Molecular dipole Energy of frontier molecular orbital (a.u)
−496.188106 2.673100 EHOMO ¼ 0:252818 ELUMO ¼ 0:065406
−571.419568 6.097000 EHOMO ¼ 0:241857 ELUMO ¼ 0:062612
Frontier electron density q
qocc ¼ 0:078430
ð4Þ
qocc ¼ 0:150664
ð4Þ
quocc ¼ 9:391827
qocc ¼ 0:002587
ð11Þ
qocc ¼ 0:154618
ð11Þ quocc ¼
0:200055
quocc ¼ 5:285463
qocc ¼ 0:030888
ð12Þ
qocc ¼ 0:007822
quocc ¼ 0:108416
ð12Þ
quocc ¼ 0:769192
ð13Þ qocc ¼
0:006914
qocc ¼ 0:000676
quocc ¼ 0:044159
ð13Þ
quocc ¼ 0:159010
qocc ¼ 0:121969
ð15Þ
qocc ¼ 0:001352
ð15Þ quocc ¼
quocc ¼ 0:219020
quocc ¼ 0:167875
Mulliken net charge Q
0:038291
ð2Þ ð2Þ ð6Þ ð6Þ
ð10Þ ð10Þ ð11Þ ð11Þ ð12Þ ð12Þ
–
qocc ¼ 0:148593
–
quocc ¼ 0:073034
–
qocc ¼ 0:147434
–
quocc ¼ 0:045164 Qð2Þ ¼ 1:600134 Qð6Þ ¼ 1:758326 Qð10Þ ¼ 0:238074 Qð11Þ ¼ 0:344326 Qð12Þ ¼ 0:329324 Qð14Þ ¼ 0:354220 Qð15Þ ¼ 0:366073
Qð4Þ ¼ 0:659565 Qð11Þ ¼ 0:034523 Qð12Þ ¼ 0:372809 Qð13Þ ¼ 0:336385 Qð15Þ ¼ 0:431022 – –
ð14Þ ð14Þ ð15Þ ð15Þ
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Table 10.7 Quantum chemical calculation results of C7H6O6 Quantum chemistry parameters
(HO)4–C6H1–COOH
Molecular total energy ET (a.u) Molecular dipole Energy of frontier molecular orbital (a.u)
−721.900586 9.847100 EHOMO ¼ 0:218697 ELUMO ¼ 0:068084
Frontier electron density q
qocc ¼ 0:009260
quocc ¼ 1:415421
ð2Þ qocc ¼
0:179486
quocc ¼ 2:839558
qocc ¼ 0:209930
ð3Þ
quocc ¼ 0:314709
ð5Þ
quocc ¼ 0:472741
qocc ¼ 0:177835
ð6Þ
quocc ¼ 2:784491
ð8Þ qocc ¼
0:004283
quocc ¼ 0:358027
qocc ¼ 0:000127
ð9Þ
quocc ¼ 0:218272
qocc ¼ 0:000194
ð10Þ
quocc ¼ 0:092797
ð12Þ qocc ¼
0:138067
quocc ¼ 0:057631
qocc ¼ 0:232983
ð14Þ
quocc ¼ 0:061810
qocc ¼ 0:104574
ð16Þ
quocc ¼ 0:038776
ð18Þ qocc ¼
quocc ¼ 0:031181 Qð9Þ ¼ 0:352691 Qð10Þ ¼ 0:353866 Qð12Þ ¼ 0:445211 Qð14Þ ¼ 0:401842 Qð16Þ ¼ 0:537989 Qð18Þ ¼ 0:527281
ð1Þ
qocc ¼ 0:228136
Mulliken net charge Q
0:120683 Qð1Þ ¼ 1:697277 Qð2Þ ¼ 1:043734 Qð3Þ ¼ 0:079509 Qð5Þ ¼ 0:049591 Qð6Þ ¼ 1:406902 Qð8Þ ¼ 0:453987
ð1Þ ð2Þ ð3Þ ð5Þ ð6Þ ð8Þ ð9Þ
ð10Þ ð12Þ ð14Þ ð16Þ ð18Þ
The basic quantum chemistry parameters of the binder structure units with varying hydroxyls calculated by DFT B3lYP method are listed in Tables 10.6 and 10.7. The effects of number of phenolic hydroxyl on basic quantum chemistry parameters of binder structure units are shown in Fig. 10.14. The results in Fig. 10.14 show that the molecular total energy and total net charge of bonding atom (O) decrease with increasing the number of phenolic hydroxyls. But the EHOMO of structure units increases with increasing the number of phenolic hydroxyls. The results indicated that the bonding capacity of binder molecule with mineral surface is enhanced when the polar groups increase.
Application of Energy Criterion to Discuss the Relationship …
10.3
373
(a) -300
ET (a.u)
-400 -500 -600 -700 -800 0
1
2
3
4
The number of phenolic hydroxyls
(c) -0.20
0.0
-0.22
-0.6
-0.24
-1.2
Q (Total)
EHOMO (a.u)
(b)
-0.26 -0.28
-1.8 -2.4
-0.30 0
1
2
3
4
The number of phenolic hydroxyls
-3.0 0
1
2
3
4
The number of phenolic hydroxyls
Fig. 10.14 The effects of number of phenolic hydroxyl on basic quantum chemistry parameters of binder structure units
10.3
Application of Energy Criterion to Discuss the Relationship of Nonpolar Groups of Reagents and Performance
10.3.1 Relationship of Nonpolar Groups of Flotation Reagents and Performance Thioureas have been applied in the flotation of sulfide ore. Thiourea is an organosulfur compound with the formula SC(NH2)2. It is similar to urea, except that the oxygen atom in molecule is replaced by a sulfur atom, but the properties and performance of urea and thiourea exist in huge difference. Thiourea is mainly a chemical in organic synthesis. “Thioureas” is a broad class of organosulfur compounds with the general structure (R1R2 N)(R3R4 N)C = S. Thioureas are related to thioamides, e.g., RC(S)NR2, where R is methyl, ethyl, etc. The annual production of thiourea is about 10,000 tons. About 40 % of thiourea is produced in Germany, another 40 % in China, and 20 % in Japan. Thiourea can be produced from ammonium thiocyanate, but more commonly it is produced by
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Molecular Design of Reagents for Mineral Processing
the reaction of hydrogen sulfide with calcium cyanamide in the presence of carbon dioxide. The basic quantum chemistry parameters of thioureas with varying nonpolar alkyls calculated by DFT B3LYP method are given by following: (1) Methyl thiourea (Fig. 10.15) EnergyðRB3LYPÞ ¼ 587:602831 ða:uÞ Qð2Þ ¼ 0:148178 ð2Þ qocc ¼ 1:174179 ð3Þ qocc ¼ 0:303440 ð4Þ qocc ¼ 0:431904 EHOMO ¼ 0:206616 ða:uÞ
Qð3Þ ¼ 0:502378 Qð4Þ ¼ 0:279630 ð2Þ quocc ¼ 1:291091 ð3Þ quocc ¼ 0:099654 ð4Þ quocc ¼ 0:163621 ELUMO ¼ 0:023885 ða:uÞ
(2) Ethyl thiourea (Fig. 10.16) EnergyðRB3LYPÞ ¼ 626:926939 ða:uÞ Qð2Þ ¼ 0:150779 ð2Þ qocc ¼ 1:189117 ð3Þ qocc ¼ 0:299209 ð4Þ qocc ¼ 0:417118 EHOMO ¼ 0:204460 ða:uÞ
Qð3Þ ¼ 0:493374 Qð4Þ ¼ 0:265580 ð2Þ quocc ¼ 1:25356 ð3Þ quocc ¼ 0:337831 ð4Þ quocc ¼ 0:248959 ELUMO ¼ 0:021619 ða:uÞ
(3) Propyl thiourea (Fig. 10.17) EnergyðRB3LYPÞ ¼ 666:248988 ða:uÞ Qð2Þ ¼ 0:145825 ð2Þ qocc ¼ 1:126339 ð3Þ qocc ¼ 0:312428 ð4Þ qocc ¼ 0:343294 EHOMO ¼ 0:206371 ða:uÞ
Qð3Þ ¼ 0:492907 ð2Þ quocc ¼ 1:115520 ð3Þ quocc ¼ 0:899134 ð4Þ quocc ¼ 0:696360 ELUMO ¼ 0:023379 ða:uÞ
Qð4Þ ¼ 0:200037
Qð3Þ ¼ 0:495408 ð2Þ quocc ¼ 1:169610 ð3Þ quocc ¼ 0:050894 ð4Þ quocc ¼ 0:605820 ELUMO ¼ 0:023290 ða:uÞ
Qð4Þ ¼ 0:195438
(4) Butyl thiourea (Fig. 10.18) EnergyðRB3LYPÞ ¼ 705:570783 ða:uÞ Qð2Þ ¼ 0:146419 ð2Þ qocc ¼ 1:124001 ð3Þ qocc ¼ 0:314207 ð4Þ qocc ¼ 0:334405 EHOMO ¼ 0:206164 ða:uÞ
10.3
Application of Energy Criterion to Discuss the Relationship …
Fig. 10.15 Steric configuration, HOMO and LUMO of methyl thiourea
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Molecular Design of Reagents for Mineral Processing
Fig. 10.16 Steric configuration, HOMO and LUMO of ethyl thiourea
10.3
Application of Energy Criterion to Discuss the Relationship …
Fig. 10.17 Steric configuration, HOMO and LUMO of propyl thiourea
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Molecular Design of Reagents for Mineral Processing
Fig. 10.18 Steric configuration, HOMO and LUMO of butyl thiourea
10.3
Application of Energy Criterion to Discuss the Relationship …
379
Table 10.8 Energy criterion of thioureas collectors with chalcopyrite
Reagents
Energy criterion DETRT (a. u.)
Methyl thiourea Ethyl thiourea Propyl thiourea Butyl thiourea
−0.954044 −1.041930 −1.145964 −1.281275
Fig. 10.19 Effect of the number of –CH2 units on energy criterion of thioureas collectors with chalcopyrite
0.3
ln(−ΔΕΤRL)
0.2
0.1
0.0
-0.1 0
1
2
3
4
5
The number of ⎯CH2 units
The energy criterions of thioureas with chalcopyrite are listed in Table 10.8. The effect of the number of –CH2 units on energy criterion of thioureas collectors with chalcopyrite is shown in Fig. 10.19.
10.3.2 Relationship of Nonpolar Groups of Humic Substances-Based Binder and Performance Jiang et al. also calculated the size of nonpolar aromatic hydrocarbon on basic quantum chemistry parameters of binder structure unit. Taking naphthyl carboxylic acid, pyrene carboxylic acid, and korra carboxylic acid, for example, the binder structure units are shown in Fig. 10.20. The basic quantum chemistry parameters of naphthyl carboxylic acid, pyrene carboxylic acid, and korra carboxylic acid calculated by DFT B3LYP method are listed in Table 10.9.
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Molecular Design of Reagents for Mineral Processing
Fig. 10.20 Steric configurations of the carboxylic acids with thick ring aromatics. a C11H8O2, b C17H10O2, c C25H12O2
The calculation results demonstrated that there are obvious differences in the quantum chemistry parameters among these carboxylic acids with thick ring aromatics. The effects of the number of benzene rings on basic quantum chemistry parameters of carboxylic acids with thick ring aromatics are shown in Fig. 10.21.
10.3
Application of Energy Criterion to Discuss the Relationship …
381
Table 10.9 Quantum chemical calculation results of the carboxylic acids with thick ring aromatics Quantum chemistry parameters
Naphthyl carboxylic acid
Pyrene carboxylic acid
Korra carboxylic acid
Molecular total energy ET (a.u) Molecular dipole Energy of frontier molecular orbital (a.u) Frontier electron density q
−574.615548
−804.534898
−1110.716614
3.132900 EHOMO ¼ 0:238363 ELUMO ¼ 0:080415
3.629400 EHOMO ¼ 0:221749 ELUMO ¼ 0:095317
3.886100 EHOMO ¼ 0:221323 ELUMO ¼ 0:0091273
ð18Þ
qocc ¼ 0:008025
ð26Þ
qocc ¼ 0:000062
ð18Þ
quocc ¼ 0:144883
ð26Þ
quocc ¼ 0:165659
qocc ¼ 0:019712
ð19Þ
ð19Þ quocc ¼
qocc ¼ 1:013554
ð27Þ
qocc ¼ 0:000946
ð27Þ quocc ¼
0:096184
quocc ¼ 0:109273
ð20Þ
qocc ¼ 0:009075
ð28Þ
qocc ¼ 0:000152
ð20Þ
quocc ¼ 0:041655 Qð26Þ ¼ 0:598610 Qð27Þ ¼ 0:354633 Qð28Þ ¼ 0:327600
ð28Þ
quocc ¼ 0:040829 Qð36Þ¼ 0:465958 Qð37Þ ¼ 0:342886 Qð38Þ ¼ 0:326136
qocc ¼ 0:001643 quocc ¼ 0:241209 0:141243
qocc ¼ 0:000807 quocc ¼ 0:069736 Qð18Þ ¼ 0:311805 Qð19Þ ¼ 0:361639 Qð20Þ ¼ 0:343131
Mulliken net charge Q
(a)
ð36Þ ð36Þ ð37Þ ð37Þ ð38Þ ð38Þ
-200 -400
ET (a.u)
-600 -800
-1000 -1200 0
2
4
6
8
The number of benzene rings
(b)
(c)
-0.20
-0.66 -0.67
E
-0.68 (Total)
-0.24
Q
HOMO
(a.u)
-0.22
-0.26
-0.69 -0.70
-0.28
-0.71
-0.30
-0.72 0
2
4
6
The number of benzene rings
8
0
2
4
6
8
The number of benzene rings
Fig. 10.21 Effects of the number of benzene rings on basic quantum chemistry parameters of carboxylic acids with thick ring aromatics
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The results in Fig. 10.21 show that the molecular total energy ET decreases with increasing the number of benzene rings. But the EHOMO and total net charge of bonding atom (O) of structure units increase with increasing the number of benzene rings. In the view of chemical adsorption or reaction, the results indicated that the bonding capacity of binder molecule with mineral surface is enhanced when the size of nonpolar groups increases. In terms of the physical adsorption, however, the bonding capacity of binder molecule decreases when the size of nonpolar groups increases.