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Ion Exchange in Environmental Processes

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Ion Exchange in Environmental Processes

Fundamentals, Applications and Sustainable Technology

Arup K. SenGupta

ProfessorLehigh UniversityBethlehem, USA

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This edition first published 2017© 2017 John Wiley & Sons, Inc.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in anyform or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law.Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Arup K. SenGupta to be identified as the author of this work has been asserted in accordance with law.

Registered OfficeJohn Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA

Editorial Office111 River Street, Hoboken, NJ 07030, USA

For details of our global editorial offices, customer services, and more information about Wiley products visit us atwww.wiley.com.

Wiley also publishes its books in a variety of electronic formats and by print-on-demand. Some content that appearsin standard print versions of this book may not be available in other formats.

Limit of Liability/Disclaimer of WarrantyIn view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow ofinformation relating to the use of experimental reagents, equipment, and devices, the reader is urged to review andevaluate the information provided in the package insert or instructions for each chemical, piece of equipment,reagent, or device for, among other things, any changes in the instructions or indication of usage and for addedwarnings and precautions. While the publisher and authors have used their best efforts in preparing this work, theymake no representations or warranties with respect to the accuracy or completeness of the contents of this work andspecifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitnessfor a particular purpose. No warranty may be created or extended by sales representatives, written sales materials orpromotional statements for this work. The fact that an organization, website, or product is referred to in this work asa citation and/or potential source of further information does not mean that the publisher and authors endorse theinformation or services the organization, website, or product may provide or recommendations it may make. Thiswork is sold with the understanding that the publisher is not engaged in rendering professional services. The adviceand strategies contained herein may not be suitable for your situation. You should consult with a specialist whereappropriate. Further, readers should be aware that websites listed in this work may have changed or disappearedbetween when this work was written and when it is read. Neither the publisher nor authors shall be liable for any lossof profit or any other commercial damages, including but not limited to special, incidental, consequential, or otherdamages.

Library of Congress Cataloging-in-Publication Data

Names: SenGupta, Arup K. author.Title: Ion exchange in environmental processes: fundamentals, applications and sustainable technology /

by Arup K. SenGupta, Professor, Lehigh University, Bethlehem, USA.Description: First edition. | Hoboken, NJ, USA : Wiley, [2017] | Includes

bibliographical references and index. |Identifiers: LCCN 2017016090 (print) | LCCN 2017016885 (ebook) | ISBN

9781119421283 (pdf) | ISBN 9781119421290 (epub) | ISBN 9781119157397(cloth)

Subjects: LCSH: Ion exchange–Industrial applications.Classification: LCC TP156.I6 (ebook) | LCC TP156.I6 S45 2017 (print) | DDC

660/.29723–dc23LC record available at https://lccn.loc.gov/2017016090

Cover image: Courtesy of Arup SenGupta and Michael German; Background: © MirageC/GettyImagesCover design by Wiley

Set in 11/13pt WarnockPro by SPi Global, Chennai, India

10 9 8 7 6 5 4 3 2 1

Printed in the United States of America

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ToSusmita, Neal and Soham for their love and supportandMother Nature for Her infinite tolerance

“Thy right is to the work only, but never to the fruits thereof”

Bhagvad Gita: Verse II:47

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vii

Contents

Preface xiiiAcknowledgment xvii

1 Ion Exchange and Ion Exchangers: An Introduction 11.1 Historical Perspective 11.2 Water and Ion Exchange: An Eternal Kinship 61.3 Constituents of an Ion Exchanger 91.4 What is Ion Exchange and What it is Not? 101.5 Genesis of Ion Exchange Capacity 121.5.1 Inorganic 121.5.2 Organic/Polymeric Ion Exchanger 131.5.3 Strong-Base Type I and Type II Anion Exchanger 201.6 Biosorbent, Liquid Ion Exchanger, and Solvent Impregnated Resin 231.6.1 Biosorbent 231.6.2 Liquid Ion Exchange 251.6.3 Solvent-Impregnated Resins 271.7 Amphoteric Inorganic Ion Exchangers 281.8 Ion Exchanger versus Activated Carbon: Commonalities and Contrasts 331.9 Ion Exchanger Morphologies 341.10 Widely Used Ion Exchange Processes 341.10.1 Softening 351.10.2 Deionization or Demineralization 40

Summary 44References 45

2 Ion Exchange Fundamentals 502.1 Physical Realities 502.2 Swelling/Shrinking: Ion Exchange Osmosis 512.3 Ion Exchange Equilibrium 552.3.1 Genesis of Non-Ideality 572.4 Other Equilibrium Constants and Equilibrium Parameters 592.4.1 Corrected Selectivity Coefficient 592.4.2 Selectivity Coefficient, K se

IX 60

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viii Contents

2.4.3 Separation Factor (𝛼AB ) 60

2.4.4 Separation Factor: Homovalent Ion Exchange 612.4.5 Separation Factor: Heterovalent Exchange 622.4.6 Physical Reality of Selectivity Reversal: Role of Le Châtelier’s Principle 652.4.7 Equilibrium Constant: Inconsistencies and Potential Pitfalls 662.5 Electrostatic Interaction: Genesis of Counterion Selectivity 692.5.1 Monovalent–Monovalent Coulombic Interaction 692.6 Ion Exchange Capacity: Isotherms 732.6.1 Batch Technique 752.6.2 Regenerable Mini-Column Method 792.6.3 Step-Feed Frontal Column Run 812.7 The Donnan Membrane Effect in Ion Exchanger 842.7.1 Coion Invasion or Electrolyte Penetration 842.7.2 Role of Cross-linking 902.7.3 Genesis of the Donnan Potential 902.8 Weak-Acid and Weak-Base Ion Exchange Resins 922.8.1 pKa Values of Weak Ion Exchange Resins 942.8.2 Weak-Acid and Weak-Base Functional Groups 962.9 Regeneration 982.9.1 Selectivity Reversal in Heterovalent Ion Exchange 1002.9.2 pH Swings 1012.9.3 Ligand Exchange with Metal Oxides 1052.9.4 Use of Co-Solvent 1062.9.5 Dual-Temperature Regeneration 1082.9.6 Carbon Dioxide Regeneration 1112.9.7 Regeneration with Water 1122.10 Resin Degradation and Trace Toxin Formation 1122.10.1 Formation of Trace Nitrosodimethylamine (NDMA) from Resin

Degradation 1142.11 Ion Exclusion and Ion Retardation 1152.11.1 Ion Exclusion 1152.11.2 Ion Retardation 1162.12 Zwitterion and Amino Acid Sorption 1182.12.1 Interaction with a Cation Exchanger: Role of pH 1192.13 Solution Osmotic Pressure and Ion Exchange 1212.14 Ion Exchanger as a Catalyst 124

Summary 126References 127

3 Trace Ion Exchange 1303.1 Genesis of Selectivity 1303.2 Trace Isotherms 1363.3 Multi-Component Equilibrium 1383.4 Agreement with Henry’s Law 1403.5 Multiple Trace Species: Genesis of Elution Chromatography 143

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Contents ix

3.5.1 Determining Separation Factor from Elution Chromatogram 1433.6 Uphill Transport of Trace Ions: Donnan Membrane Effect 1493.7 Trace Leakage 1513.8 Trace Fouling by Natural Organic Matter 1533.9 Ion Exchange Accompanied by Chemical Reaction 1563.9.1 Precipitation 1563.9.2 Complexation 1573.9.3 Redox Reaction 1573.10 Monovalent–Divalent Selectivity 1583.10.1 Effect of Charge Separation: Mechanistic Explanation 1583.10.2 Nitrate/Sulfate and Chloride/Sulfate Selectivity in Anion Exchange 1603.10.3 Genesis of Nitrate-Selective Resin 1623.10.4 Chromate Ion Selectivity 1643.11 Entropy-Driven Selective Ion Exchange: The Case of Hydrophobic Ionizable

Organic Compound (HIOC) 1663.11.1 Focus of the Study and Related Implications 1673.11.2 Nature of Solute–Sorbent and Solute–Solvent Interactions 1693.11.3 Experimental Observations: Stoichiometry, Affinity Sequence, and Cosolvent

Effect 1733.11.4 Energetics of the Sorption Process 1773.11.5 Unifying Hydrophobic Interaction: From Gas–Liquid to Liquid–Solid

System 1793.11.6 Effect of Polymer Matrix and Solute Hydrophobicity 1823.12 Linear Free Energy Relationship and Relative Selectivity 1833.13 Simultaneous Removal of Target Metal Cations and Anions 1863.14 Deviation from Henry’s Law 1883.14.1 Ions Forming Polynuclear Species 1883.15 Tunable Sorption Behaviors of Amphoteric Metal Oxides 1923.16 Ion Sieving 1953.17 Trace Ion Removal 2013.17.1 Uranium(VI) 2013.17.2 Radium 2033.17.3 Boron 2043.17.4 Perchlorate (ClO−

4 ) 2053.17.5 Emerging Contaminants of Concern and Multi-Contaminant Systems 2083.17.6 Arsenic and Phosphorus: As(V), P(V), and As(III) 2103.17.7 Fluoride (F−) 214

Summary 215References 216

4 Ion Exchange Kinetics: Intraparticle Diffusion 2244.1 Role of Selectivity 2244.2 State of Water Molecules inside Ion Exchange Materials 2324.3 Activation Energy Level in Ion Exchangers: Chemical Kinetics 2354.3.1 Activation Energy Determination from Experimental Results 236

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x Contents

4.4 Physical Anatomy of an Ion Exchanger: Gel, Macroporous and FibrousMorphology 242

4.4.1 Gel-Type Ion Exchanger Beads 2424.4.2 Macroporous Ion Exchanger Beads 2434.4.3 Ion Exchange Fibers 2464.5 Column Interruption Test: Determinant of Diffusion Mechanism 2484.6 Observations Related to Ion Exchange Kinetics 2504.6.1 Effect of Concentration on Half-time (t1∕2) 2514.6.2 Major Differences in Ion Exchange Rate 2524.6.3 Chemically Similar Counterions with Significant Differences in Intraparticle

Diffusivity 2524.6.4 Effect of Competing Ion Concentrations: Gel versus Macroporous 2544.6.5 Intraparticle Diffusion during Regeneration 2554.6.6 Shell Progressive Kinetics versus Slow Diffusing Species 2554.7 Interdiffusion Coefficients for Intraparticle Diffusion 2574.8 Trace Ion Exchange Kinetics 2644.8.1 Chlorophenols as the Target Trace Ions 2644.8.2 Intraparticle Diffusion inside a Macroporous Ion Exchanger 2664.8.3 Effect of Sorption Affinity on Intraparticle Diffusion 2684.8.4 Solute Concentration Effect 2714.9 Rectangular Isotherms and Shell Progressive Kinetics 2724.9.1 Anomalies in Arrival Sequence of Solutes 2744.9.2 Quantitative Interpretation 2754.10 Responses to Observations in Section 4.6 2764.10.1 Effect of Concentration on Half-time (t1∕2) 2764.10.2 Slow Kinetics of Weak-Acid Resin 2774.10.3 Chemically Similar Counterions: Drastic Difference in Intraparticle

Diffusivity 2774.10.4 Gel versus Macroporous 2784.10.5 Intraparticle Diffusion during Regeneration 2784.10.6 Shrinking Core or Shell Progressive Kinetics 2794.11 Rate-Limiting Step: Dimensionless Numbers 2804.11.1 Implications of Biot Number: Trace Ion Exchange 2814.12 Intraparticle Diffusion: FromTheory to Practice 2844.12.1 Reducing Diffusion Path Length: Short-Bed Process and Shell–Core

Resins 2854.12.2 Development of Bifunctional Diphonix® Resin 2884.12.3 Ion Exchanger as a Host for Enhanced Kinetics 289

Summary 292References 293

5 Solid- and Gas-Phase Ion Exchange 2975.1 Solid-Phase Ion Exchange 2975.1.1 Poorly Soluble Solids 2975.1.2 Desalting by Ion Exchange Induced Precipitation 303

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Contents xi

5.1.3 Separation of Competing Solid Phases 3055.1.4 Recovery from Ion Exchange Sites of Soil 3065.1.5 Composite or Cloth-like Ion Exchanger (CIX) 3075.1.6 Heavy Metals (Me2+) with Solids Possessing High Buffer Capacity 3095.1.7 Ligand-Induced Metal Recovery with a Chelating Exchanger 3155.2 Coagulant Recovery fromWater Treatment Sludge 3175.2.1 Development of Donnan IX Membrane Process 3185.2.2 Alum Recovery: Governing Donnan Equilibrium 3185.2.3 Process Validation 3225.3 Gas Phase Ion Exchange 3235.3.1 Sorption of Acidic and Basic Gases 3245.3.2 CO2 and SO2 Capture with Weak-Base Anion (WBA) Exchanger 3255.3.3 Effect of Ion Exchanger Morphology 3275.3.4 Redox Active Gases: Hydrogen Sulfide and Oxygen 3305.4 CO2 Gas as a Regenerant for IX Softening Processes: A Case Study 334

Summary 339References 340

6 Hybrid Ion Exchange Nanotechnology (HIX-Nanotech) 3456.1 Magnetically Active Polymer Particles (MAPPs) 3476.1.1 Characterization of MAPPs 3516.1.2 Factors Affecting Acquired Magnetic Activity 3536.1.3 Retention of Magnetic Activity and Sorption Behavior 3556.2 Hybrid Nanosorbents for Selective Sorption of Ligands (e.g.,

HIX-NanoFe) 3576.2.1 Synthesis of Hybrid Ion Exchange Nanomaterials 3596.2.2 Characterization of Hybrid Nanosorbents 3616.2.3 Parent Anion Exchanger versus Hybrid Anion Exchanger

(HAIX-NanoFe(III)): A Comparison 3636.2.4 Support of Hybrid Ion Exchangers: Cation versus Anion 3656.2.5 Efficiency of Regeneration and Field Application 3696.2.6 Hybrid Ion Exchange Fibers: Simultaneous Perchlorate and Arsenic

Removal 3706.3 HAIX-NanoZr(IV): Simultaneous Defluoridation and Desalination 3766.3.1 Field-Scale Validation 3776.4 Promise of HIX-Nanotechnology 381

Summary 383References 384

7 Heavy Metal Chelation and Polymeric Ligand Exchange 3917.1 Heavy Metals and Chelating Ion Exchangers 3917.1.1 Heavy Metals: What are They? 3917.1.2 Properties of Heavy Metals and Separation Strategies 3937.1.3 Emergence of Chelating Exchangers 3957.1.4 Lewis Acid–Base Interactions in Chelating Ion Exchangers 398

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xii Contents

7.1.5 Regeneration, Kinetics and Metals Affinity 4027.2 Polymeric Ligand Exchange 4057.2.1 Conceptualization and Characterization of the Polymeric Ligand Exchanger

(PLE) 4067.2.2 Sorption of Polymeric Ligand Exchangers 4077.2.3 Validation of Ligand Exchange Mechanism 410

Summary 413References 413

8 Synergy and Sustainability 4178.1 Waste Acid Neutralization: An Introduction 4178.1.1 Underlying Scientific Concept 4188.1.2 Mechanical Work through a Cyclic Engine 4218.2 Improving Stability of Anaerobic Biological Reactors 4238.2.1 Potential Use of Selective Ion Exchanger 4248.2.2 Ion Exchange Fibers: Characterization and Performance 4248.3 Sustainable Aluminum-Cycle Softening for Hardness Removal 4298.3.1 Current Status and Challenges 4298.3.2 Sodium-Free Approaches and Alternatives to Na-Cycle Softening 4298.3.3 Underlying Scientific Approach of Al-cycle Cation Exchange 4308.3.4 Comparison in Performance: Na-Cycle versus Al-Cycle 4328.3.5 Regeneration Efficiency and Calcium Removal Capacity 4368.3.6 Sustainability Issues and New Opportunities 4388.4 Closure 438

Summary 439References 440

A Commercial Ion Exchangers 445

B Different Units of Capacity, Concentration, Mass, and Volume 457B.1 Capacity 457B.2 Concentration (Expressed as CaCO3) 457B.3 Mass 458B.4 Volume 458

C Table of Solubility Product Constants at 25 ∘C 459

D Acid and Base Dissociation Constants at 25 ∘C 461

Periodic Table and Atomic Weights of Elements 463

Index 467

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xiii

Preface

Ion exchange is a fascinating scientific field, as central to natural and biological systems,as to the engineered processes. Historically, application of ion exchange always stayedfar ahead of theory and the design approaches for ion exchange systems were mostlyempirical. The intrinsic complexity of the field was poorly understood and the scienceof ion exchange was accepted as mere exchange of ions. After the Second World War,ion exchange theory took root, progressed gradually on a scientific foundation and newapplications were conceived and implemented. The intrinsic complexity of the field ofion exchange and itsmany seemingly eccentric behaviors were unraveled. Understand-ably, learning the subject requires revealing its scientific core in appropriate sequence,interjected with key scientific inquiries of “why” and “how.”It was during the fall of 1996 when I was in England on a sabbatical leave at the

invitation of long-time friend and colleague, Prof. Michael Streat, that the thought ofwriting a book on Ion Exchange dawned onme and I initiated the process.While there,I was informally giving a series of lectures to a group of senior graduate students andyoung faculty members on topics related to fundamentals and recent developments inion exchange. Some difficulties arose. I struggled to communicate some experimen-tal observations of others that are seemingly counter-intuitive. So I started prepar-ing notes of my own and that was the modest beginning. Needless to say, the effortwent back and forth, the book project proceeded at a snail’s pace and turned dormant.Finally, 3 years ago, I undertook the assignment as amission that needs to be brought toa closure. However, the key questions or motivating factors – Is such a book necessaryand whom is this book for – remained unchanged throughout.No specialty grows in isolation. Ion exchange is not a recent invention, but over the

last five decades, the science of ion exchange has permeated into a myriad of othergrowing fields – from decontamination to deionization, from mining to microelec-tronics, from gas separation to green processes, from novel synthesis to nanotechnol-ogy, from drug delivery to desalination, to name a few. The following figure from theGoogle patent search includes the number of ion exchange-related US patents issuedduring the last three decades, illustrating continued inventions of new products andprocesses.

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xiv Preface

70000

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Very highUSpatent numbers only reinforce the dynamics of the field and its blendingwithmany other seemingly disjointed scientific areas. It is only appropriate tomentionthat the worldwide push for sustainability and stringent environmental regulations hasseen ion exchange technology as a major player in the development of the next gener-ation of environmental processes and efficient materials. Such a move has demandeda need to revisit the fundamentals of ion exchange with a renewed perspective. Asexpected, this book presents the “why” and the “how” of multiple ion exchange phe-nomena with varying degrees of complexity. However, a conscious attempt has beenmade to present physical realities of every ion exchange phenomenon of interest rightup front. Only then, underlying theories and quantitative approaches have been dis-cussed to validate observed physical realities.Presentation of theoretical tools that might help the reader in solving or address-

ing specific problems were given due importance. At the same time, overemphasison mathematical models and abstract theories has been avoided. Even when mathe-matical deductions and related equations have been adequately presented, qualitativeexplanations and interpretations have not been ignored. Thus, a mathematically or athermodynamically disinclined reader, with deep understanding of the subject throughexperience or othermeans,may comfortably navigate through the entire book and gainnew knowledge or identify areas warranting further innovation.Writing or introducing a new book on Ion Exchange will always remain incomplete

unless an honest discussion is made about how it complements or adds to the existingtitle on Ion Exchange written by Fred Helfferich over 50 years ago. Helfferich’s bookis a seminal contribution in the field and will continue to remain so. I take pride instating that I knew Fred Helfferich. He was an esteemed professional colleague andwe interacted in several ways. I personally keep a copy of his book both at home andin the office, consulting it whenever necessary. Nevertheless, it is also my finding thatpeople always refer to Helfferich’s book when confronted with a question or uncer-tainty, but rarely do they read it for learning the subject of ion exchange. Classicalstep-by-step learning through Helfferich’s book and applying the knowledge appro-priately pose some genuine challenges. The book was not really written to serve thatpurpose. Also, during the last few decades, new ion exchangers, namely, macroporous,fibrous, hybrid and biomaterials have emerged with distinctive attributes; novel use of

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Preface xv

the Donnan membrane principle has opened up new opportunities to produce sus-tainable materials and processes. Further, gas- and solid-phase ion exchange may soonprovide new platforms for novel, environmentally benign processes. More and more,ion exchange is being used synergistically with other known processes resulting in keybreakthroughs in processes with enhanced sustainability. This new book will substan-tially complement the existing body of knowledge in the public domain and serve as amajor learning tool for young scientists and engineers.Readers with a moderate knowledge of physical chemistry, chemical/environmental

engineering principles and mathematics, should be able to progress through indi-vidual chapters on their own. For academic teaching, the book is suitable as a textor a reference for an undergraduate senior or first- year graduate level chemicalor environmental engineering course in separation, environmental processes orion exchange. Attempts have been made so that a potential reader, while graduallyassimilating the content, will be prepared to apply the acquired knowledge for real-lifescenarios, improve existing processes and develop an instinct for innovation throughuse of fundamentals. From that perspective, the content of the book will be usefulalso for polymer chemists, consulting engineers and technology companies seekinglong-term holistic solutions. To facilitate the use of this book as a text or a handout ina short course, several numerical exercises have been included.The book has altogether eight chapters that unfold connecting ion exchange

processes and materials with fundamentals:Chapter 1. Ion Exchange and Ion Exchangers: An IntroductionChapter 2. Ion Exchange FundamentalsChapter 3. Trace Ion ExchangeChapter 4. Ion Exchange Kinetics: Intraparticle DiffusionChapter 5. Solid- and Gas-Phase Ion ExchangeChapter 6. Hybrid Ion Exchange Nanotechnology (HIX-Nanotech)Chapter 7. Heavy Metal Chelation and Polymeric Ligand ExchangeChapter 8. Synergy and SustainabilityA reader with prior exposure to the field of ion exchange, does not need to be deterredfrom jumping into any chapter of choice out of sequence and still comprehending thematerials. Over the decades, widely used softening and deionization processes havebeen tailored to be more sustainable from chemical usage point of view and the sub-ject has been discussed in bothChapters 1 and 2. Along the same vein, the ion exchangefundamentals have been appropriately harnessed to produce selective sorbents fornitrate, arsenic, fluoride, phosphate, boron and others. A relatively new field of hybridion exchange nanotechnology or HIX-Nanotech has emerged and the Donnan mem-brane principle plays a crucial role in expanding its application potential. Solid andgas-phase separations show promise for recovery of valuable materials with minimumchemical usage. In every such discussion presented in Chapters 5–8, the role of scien-tific fundamentals has been adequately articulated. Chapter 8 includes a new route toa simple-to-apply softening process without using an excessive amount of brine, oftencausing major disposal problems in arid regions.It is generally agreed that the solutions to challenging problems of our timewill not so

much occur through evolution of new fundamental knowledge, but through synergistic

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xvi Preface

integration of knowledge from seemingly disconnected fields. As the author of thisbook, I am quite optimistic that the science, technology and materials related to ionexchange, as presented here, will help fill some void and create new synergy for thenext generation of innovators and inventors in the field.

Arup K. SenGuptaNovember, 2016Lehigh UniversityBethlehem, USA

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xvii

Acknowledgment

During my first job as a process chemical engineer, my then supervisor in earlyseventies, N. K. Chowdhury, introducedme to the complexity and excitement of waterscience and technology.The excitement is yet to cease and my professional world dur-ing the last four decades has truly revolved around water in so many ways. In the sameperiod, I was also exposed to the field of producing ultra-pure water for electric powergenerating utilities using ion exchange processes. Subsequently, I worked with Profes-sor Dennis Clifford for my PhD; my graduate student life in the University of Houstonwas truly eventful and intellectually stimulating.The concept of gradual breakthroughduring fixed-bed column runs was solidly confirmed through my doctoral workon chromate ion exchange. Dennis and I have remained friends and professionalcolleagues for nearly four decades and I am thankful to him in so many ways.During the eighties and nineties, I had the opportunity and privilege to meet, chat,

befriend and discuss matters of mutual professional interest related to different sep-aration processes including ion exchange with many personalities around the worldduring Gordon Conferences on Reactive Polymers, IEX conferences at Cambridge(UK), and various ACS and AIChE conferences. I have very fond and rewarding mem-ories of meeting and interacting with George Boyd, Robert Kunin, Fred Helfferich,Jacob Marinsky, Mike Streat, Charlie O’Melia, Wolfgang Hoell, David Sherrington,Spiro Alexandratos, Robert Albright, Steve Cramer, Menachem Elimelech, RuslanKhamizov, Zdenek Matezka, Mimo Petruzzelli, Nalan Kabay, Kesava Rao, GaryFoutch and others. I am thankful to Jacob Brodie and Francis Boodoo for theircontinued cooperation with material support pertaining to our research efforts inenvironmental separation. The electron microscopy work of Debra Phillips for HybridIon Exchanger-Nanotechnology is gratefully acknowledged. I sincerely acknowledgethe US Department of State, US Fulbright Program, the Department of Science andTechnology of the Government of India, WIST, Inc., Rite Water Solutions (I) Ltd.and Technology with a Human Face (NGO) for their support and assistance towardfield-level implementation of ion exchange technologies invented in LehighUniversity.However, more than anything, I am most grateful to my graduate students and

post-docs with whom I have worked closely for over three decades. Since I may nothave many more opportunities, I would like to recognize them by name who havemade meaningful contributions to push the frontiers of ion exchange science andtechnology inch by inch through their research: Yuewei Zhu, Sukalyan Sengupta, AnuRamana, Yi-min Gao, Ping Li, Indra Mitra, Dongye Zhao, Esmeralda Millan, Matthew

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xviii Acknowledgment

DeMarco, David Leun, Luis Cumbal, Arthur Kney, John Greenleaf, Parna Mukherje,Sudipta Sarkar, Prakhar Prakash, Lee Blaney, Prasun Chatterjee, Surapol Padungthon,Ryan Smith, Mike German, Yu Tian, Jinze Li, Chelsey Shepsko, Robert Creighton andHang Dong. Most of them started as students, but down the stretch, most of thembecame mature, thoughtful and innovative in their own rights. I sincerely believe thatthe knowledge acquisition has truly been a two way process and the students haveenriched my professional life. It is likely that some names may have been omitted butthat is unintentional and I offer my sincere apology in advance.During the last four years, Beth Yen, the department secretary, unfailingly responded

to my every request – be it copying, typing, scanning, editing or even running anerrand, and often with time constraints due to poor planning on my part. I amimmensely thankful for her cooperation and continued service.For my education, from the second grade in the elementary school in India to my

PhD in the US, I never paid any tuition. It was gratis all the way for my entire studentcareer. Now I know that ordinary people, who pay taxes or are undercompensated,truly funded my education. I consider myself immensely fortunate and blessed.I acknowledge continued cooperation from Wiley, the publisher of the book, and I

am thankful to SaleemHameed, Beryl Mesiadhas andMichael Leventhal for attendingto necessary details and bringing the book project to a successful closure.Last but by no means the least, without the incessant help and involvement of

Michael German, this book could not be brought to a successful completion. Inaddition to carrying out his regular duties as a senior PhD student, Mike relentlesslyresponded to various details about the book project – from completing figuresto collecting copyright permissions and many other associated pieces of work inbetween. Mike helped me overcome the activation energy barrier with his unselfisheffort and I am indeed indebted to him.

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� �

1

1

Ion Exchange and Ion Exchangers: An Introduction

1.1 Historical Perspective

Evolution is traditionally viewed to occur in a slow but continuous manner for livingorganisms and creatures gradually acquiring new traits. To the contrary, many areasof “science” undergo periods of rapid bursts of fast development separated by virtualstandstill with no significant activity.The first historically recorded use of ion exchangephenomenon is from theOld Testament of the Holy Bible in Exodus 15:22–25 describ-ing how Moses rendered the bitter water potable by apparently using the process ofion exchange and/or sorption. Another often quoted ancient reference is to Aristotle’sobservation that the salt content of water is diminished or altered upon percolationthrough certain sand granules. From a scientific viewpoint, however, the credit forrecognition of the phenomenon of ion exchange is attributed to the English agricul-ture and soil chemists, J.T. Way and H.S. Thompson. In 1850, these two soil scientistsformulated a remarkably accurate description of ion exchange processes in regard toremoval of ammonium ions from manure by cation exchanging soil [1,2]. They essen-tially simulated the following naturally occurring cation exchange reactions as follows:

NH+4 (aq) +Na+(soil) ↔ NH+

4 (soil) +Na+(aq) (1.1)2NH+

4 (aq) + Ca2+(soil) ↔ (NH+4 )2(soil) + Ca2+(aq) (1.2)

Some of the fundamental tenets of ion exchange resulted from this work: first, theexchange of ions differed from true physical adsorption; second, the exchange of ionsinvolved the exchange in equivalent amounts; third, the process is reversible andfourth, some ions were exchanged more favorably than others.

As often with many groundbreaking inventions, the findings of Way and Thompsoncast doubts, disbeliefs and discouragement from their peers. In the following years, thesetwo soil scientists discontinued persistent research in this field.As a result, the evolutionof ion exchange process progressed rather slowly due to the difficulties inmodifying ormanipulating naturally occurring inorganic clayey materials with low cation exchangecapacities.Inorganic zeolites (synthetic or naturally occurring aluminosilicates) later found

wide applications in softening hard waters, that is, removal of dissolved calciumand magnesium through cation exchange. However, the anion-exchange processesremained unexplored and practically unobserved. Even at that time, it was not difficultto conceptualize that the availability of both cation exchangers and anion exchangersIon Exchange in Environmental Processes: Fundamentals, Applications and Sustainable Technology,First Edition. Arup K. SenGupta.© 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc.

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� �

2 Ion Exchange in Environmental Processes: Fundamentals, Applications and Sustainable Technology

in the ionic forms of hydrogen and hydroxyl ions, respectively, would create a newnon-thermal way to produce water free of dissolved solids as indicated below:

H+(solid) +OH−(solid) +Na+(aq) + Cl−(aq)↔ H2O(aq) +Na+(solid) + Cl−(solid) (1.3)

The biggest obstacle to realize this concept was to identify and/or synthesize ionexchangers which will be chemically stable and durable under the chemically harshenvironments at very high and low pH. The immense potential of ion exchangetechnology scaled a new height when the first organic-based (polymeric) cationexchanger was synthesized by Adams and Holmes [3]. In less than ten years, D’Alelioprepared the first polymeric, strong/weak cation and anion exchangers [4–6]. Sincethen, synthesis of new ion exchangers never seemed to slow down and applicationof ion exchange technology in industries as diverse as power utilities, biotechnology,agriculture, pharmaceuticals, pure chemicals, microelectronics, etc. are continuallygrowing. No specialty grows in isolation; ion exchange fundamentals, ion exchangeresins and ion exchange membranes continue to find new and innovative applicationsglobally. Figure 1.1 includes the number of ion exchange related US patents issuedduring the last three decades, illustrating continued inventions in new products andprocesses.Ironically, the Second World War and, more specifically, the race for nuclear tech-

nology helped catalyze the growth and maturity of the field of ion exchange at anaccelerated pace. Ion exchange was found to be a viable process for separating someof the transuranium elements and, for understandable reasons, its application arouseda great deal of interest. In fact, some of the most fundamental works on ion exchangeequilibria and kinetics were carried out during the SecondWorldWar period by Boydet al. and reported afterwards in the open literature [9–11]. All along, the scientificunderstanding of ion exchange fundamentals consistently lagged well behind its appli-cations. Table 1.1 attempts to summarize milestones in regard to the development andapplication of ion exchange technology over time.

0

2000

4000

6000

8000

10,000

12,000

14,000

16,000

18,000

20,000

1985 1990 1995 2000 2005 2010

Num

ber

of pate

nts

Figure 1.1 Number of patents per year for “anion exchange” and “cation exchange” per a GooglePatents search. Source: Data taken with permission from Google [7,8].

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� �

Table1.1

His

toric

alm

ilest

ones

inio

nex

chan

ge.

Year

Description

Patent#

Authors

1850

Disc

overyof

ionexchan

geprop

ertie

sofsoil

N/A

Thom

pson

andWay

[1,2]

1876

Zeolite

sora

luminosilicatesrecog

nizedforb

aseexchan

gean

dequivalenceof

exchan

geisproved

N/A

Lemberg

[12,13

]

1906

–191

5Indu

stria

lmanufacture

ofsodium

perm

utitforh

ardn

essrem

oval

914,40

5;94

3,53

5;1,13

1,50

3

Gan

s[14

]

1934

Inventionof

sulfo

natedcond

ensatio

npo

lymersa

scationexchan

gers

2198

378A

Ellis

1935

Firstsyn

theticorganicionexchan

gers

2104

501A

,21

5188

3AAdamsa

ndHolmes

[15]

1938

Mixed

-bed

ionexchan

geprocesso

rdup

lexionexchan

ger

2275

210A

Stem

en,U

rbain,

andLe

wis

1939

Inventionof

sulfo

natedpo

lystyren

epo

lymerizationas

catio

nexchan

gers

Inventionof

aminated

polystyren

epo

lymerizationas

anionexchan

gers

2283

236A

2304

637A

Soday

Vernal

1942

Cationexchan

geresin

beadsm

adefrom

polymerized

acrylic

acids

Cationexchan

geresin

swith

sulfo

nated,po

lymerized

poly-vinylarylparent

resin

Anion

exchan

geresin

swith

aminated

,polym

erized

poly-vinylarylparent

resin

2340

110A

,23

4011

1A23

6600

7A23

6600

8A

D’Alelio

1947

Elem

ent6

1(Promethium

)was

discovered

byionexchan

geof

theby-produ

cts

offissio

nN/A

Marinsky,Glend

enin,and

Coryell[16]

1953

Use

ofzeolite

sasm

olecular

sieves

Magne

ticionexchan

geresin

forN

OM

removal(M

IEXprocess)

Inventionof

weakacid

catio

nexchan

gers

Firstc

ountercurrention

exchan

geusingsuspen

ded/agita

tedbe

dsof

resin

2882

243A

2642

514A

2838

440A

N/A

Milton

Herkenh

offTh

urmon

Swintonan

dWeiss

[17]

1954

Higgins

coun

tercurrent

ionexchan

gecontactorinv

ented

2815

322A

Higgins

[18]

1955

Ligand

exchan

ge28

3924

1AAlbise

tti19

56Pellicularion

exchan

geresin

2933

460A

Richtera

ndMcB

urne

y19

58Agitatedbe

dcontactorfor

semicon

tinuo

usionexchan

geIonexchan

gein

drug

delivery

N/A

2990

332A

Arden

,Davis,and

Herwig[19]

Keating

(Con

tinue

d)

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� �

Table1.1

(Con

tinue

d)

Year

Description

Patent#

Authors

1958

(pub

licly

released

)

Uranium

separatio

n,intrapartic

lediffu

sion(M

anhatta

nProject)

2956

858A

Powell

1959

–196

0Th

ebo

okon

“Ion

Exchan

ge”b

yFriedrichHelffe

richwas

printedan

dlaid

the

theoretic

alfoun

datio

nsforthe

field

ofionexchan

geN/A

Helffe

rich[20]

1962

–197

1Cloete–

Streat

coun

tercurrent

contactorinv

ented

3551

118A

(196

2)37

3881

4A(196

9)39

5763

5A(197

1)

Cloetean

dStreat

[21]

1964

Cellulosic

ionexchan

gefib

erss

ynthesized

3379

719A

Rulison

1965

Sirotherm

process–

thermallyregene

rableionexchan

geresin

s274-029;

59,441

/65

(Australia)

Bolto

,Weiss,and

Willis

Partially

func

tiona

lized

catio

nexchan

ge(sha

llow-shelltechno

logy)

3252921A

Han

senan

dMcM

ahon

1966

Macropo

rous

ionexchan

geresin

3418

262A

Grammon

tand

Werotte

1968

Boronselectiveresin

2011

0108

488A

1Che

mtob

1969

Develop

mento

fpoly(methylm

etha

crylate)

anionexchan

geresin

sor

macroretic

ular

polymersthatred

uced

foulingby

naturalo

rgan

icman

ner

N/A

Kressm

anan

dKu

nin[22,23

]

1971

Con

tinuo

usmovingbe

dionexchan

ge37

5136

2AProb

stein,

Schw

artz,and

Sonin

1972

Phen

olicionexchan

gefib

ers

3835

072A

Econ

omyan

dWoh

rer

1973

Iminod

iacetic

acid

chelatingresin

Metal-selectiv

ebiosorbents

3936

399A

CA10

3671

9A1

Hira

i,Fu

jimara,an

dKa

zigase

Stam

berg,P

rochazka,and

Jilek

1973

Iminod

iacetic

acid

chelatingresin

3936

399A

Hira

i,Fu

jimara,an

dKa

zigase

Metal-selectiv

ebiosorbents

CA1036719A

1Stam

berg,P

rochazka,and

Jilek

1975

“Him

sleycontactor”multistage

fluidized

bedcontinuo

uscoun

ter-currention

exchan

gecontactor

CA980467A1

Him

sley

1976

Solventimpregnatedresin

s4220726A

Warshaw

sky

etal

.[24

,25]

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� �

1980

Mon

osph

ereionexchan

geresin

(Dow

Che

micalCo.)

4444961A

Timm

1979

Ionexchan

geindu

cedsupe

rsaturation(IX

ISS)

N/A

Muraviev[26,27

]1981

Radium

selectiveresin

sEP

0071810A1

Hatch

1983

Nitrateselectiveresin

CARIX(carbo

ndioxideregene

ratedionexchan

ge)p

rocess

forb

rackish

water

desalin

ation

4479

877A

EP00

5685

0B1

Guter

Kiehlin

gan

dWolfgan

g

1985

Shortb

edionexchan

ger

EP02

0164

0B2

Brow

n19

90Selectivean

ionexchan

geforg

oldfrom

cyan

idesolutio

nwith

asim

plean

dstraightforw

ardchem

icalregene

ratio

nN/A

Schw

ellnus

andGreen

[28]

1991

Bifunc

tiona

lion

exchan

geresin

s(Dipho

nix)

EP06

1884

3A1

Alexand

ratos,Chiarizia,and

Gatrone

1997

Polymericlig

andexchan

ge61

3619

9ASenG

upta

andZh

ao20

03Fluo

rideselectiveresin

s:strong

acid

catio

nexchan

geresin

inalum

inum

form

WO20

0506

5265

A2

Jang

barw

alaan

dKr

ulik

2004

Don

nanprinciple-basedhybrid

ionexchan

ger

7291

578B2

SenG

upta

andCu

mbal

(IonEx

chan

ge)M

embran

ecapacitiv

edeionizatio

n(M

CDI)

6709560B2

And

elman

andWalker

2007

Macropo

rous

copo

lymersw

ithlargepo

res(0.5–

200μ

m)

2008

0237

133A

1Dale,So

chilin,

andFrom

ent

2008

Rapidsensingof

toxicmetalsw

ithhybrid

inorganicmaterials

WO20

0815

1208

A1

Chatte

rjeean

dSenG

upta

2009

Removalof

alkyliod

ides

bystrong

acid

catio

nexchan

geresin

loaded

inAg+

-form

7588

690B

1Tsao

2010

Separatio

nof

ionicaque

ousm

ixturesw

ithionexchan

gematerialsin

anim

misc

ibleorganicph

ase

8940175B

2Kh

amizov

2013

Hybrid

ionexchan

ge-reverse

osmosisprocesses

Fluo

ride-selectiveresin

s:hybrid

anionexchan

geresin

with

zircon

ium

oxide

nano

particles

WO20

1419

3955

A1

2013

0274

357A

1SenG

upta

andSm

ithSenG

upta

andPa

dung

thon

Not

e:Pa

tentsa

reiss

uedfrom

theUSA

,unlessm

entio

nedothe

rwise

.

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� �

6 Ion Exchange in Environmental Processes: Fundamentals, Applications and Sustainable Technology

1.2 Water and Ion Exchange: An Eternal Kinship

Ion exchange is a heterogeneous process where water, themost abundant polar solventin our planet, is inevitably present. Even the ion exchange processes involving gases orsolids require the presence of water. It is imperative that we understand the fundamen-tal properties of water in order to follow the science of ion exchange. Oxygen is presentin Group VIA of the periodic table and water (H2O) is essentially a dihydride of oxy-gen. Note that sulfur (S) and selenium (Se) are also in the same group with oxygen buttheir dihydride, namely H2S and H2Se are volatile at room temperature. In contrast,water is liquid and an excellent solvent for salts with ionic bonds. In the electroneg-ativity scale, hydrogen and oxygen are far apart. While hydrogen is electropositive,oxygen is strongly electronegative. Thus, covalent O—H bonds in water molecules arepolar due to unequal sharing of bonding electrons with residual negative and posi-tive charges on oxygen and hydrogen atoms, respectively. Hence, water molecules areessentially dipoles (dipole moment= 1.85D), as shown in Figure 1.2a. The electronicstructure of the water molecule corresponds to the tetrahedral arrangement with theoxygen atom having two lone pairs of electrons as presented in Figure 1.2b.The dipolarwater molecules experience a torque when placed in an electric field and this torque iscalled a dipole moment. When molecules have dipole moments, their intermolecularforces are significantly greater, especially when dipole–dipole interactions or hydrogenbonding is possible. Water molecules are particularly well suited to interact with oneanother because each molecule has two polar O—H bonds and two lone pairs on theoxygen atom. This can lead to the association of four hydrogen atoms with one oxy-gen through a combination of covalent and hydrogen bonding as shown in Figure 1.3.Watermolecules thus exist as trimers (H6O3) and boiling requires a high heat of vapor-ization to break the intermolecular hydrogen bonds among water molecules. Thus,water has the highest boiling point among the entire Group VIA hydrides as shown inFigure 1.4.

2.202.20

The bent structure of a water molecule

(a) (b)

Tetrahedron

Lone

electron

pairs

3.44

Figure 1.2 Shape of water molecules (a) Dipolar O—H bonds with electronegativity values;(b) Electronic structure with tetrahedral arrangement.

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� �

Ion Exchange and Ion Exchangers: An Introduction 7

Figure 1.3 Interaction of water moleculesthrough association of four hydrogen atoms witheach oxygen atom.

8+

8+

8+

8+

8–

8–

8–

8–

–100

–50

0

50

100

0 1 2 3 4

Boili

ng p

oin

t (˚

C)

Period on atomic table

H2S

H2O

H2Se

H2Te

Figure 1.4 Anomalous boiling point behavior of H2O in Group VIA hydrides.

Like dissolves like. Ionic compounds such as sodium chloride (NaCl) are highly sol-uble in water, which is an excellent polar solvent. When sodium chloride is addedto water, the dipolar water molecules separate sodium from chloride ions forming acluster of solvent molecules around them due to the ion–dipole interaction as pre-sented in Figure 1.5. This interaction is known as hydration and the hydrated ionicradius of an ion is always greater than its ionic radius.The degree of hydration dependsprimarily on the charges and the atomic mass of the ions. Ions with higher charges,and similar masses, always are more hydrated, that is, divalent calcium ion (Ca2+) ismore hydrated than monovalent sodium ion (Na+). For monatomic ions with identi-cal charges, hydrated ionic radius increases with a decrease in atomic mass or crystal

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� �

8 Ion Exchange in Environmental Processes: Fundamentals, Applications and Sustainable Technology

O

H

+ –

H

H H

HH

H

O

O

O

Na CIO O

Oδ+

δ+

δ–

δ–

O

H

H

HH H

HH

H

H

δ+δ

+

Figure 1.5 Illustration of ion–dipole interaction: Sodium chloride (ionic compound) solution inwater (polar solvent).

Table 1.2 Hydrated ionic radius and atomic mass of typicalmonatomic ions of interest.

Ions Atomic massCrystal ionicradii (pm)

Hydrated ionicradii (pm)

Li+ 6.94 59 382Na+ 22.99 102 358K+ 39.09 151 331Rb+ 85.46 161 329F− 18.99 133 352Cl− 35.45 181 332Br− 79.9 196 330Be2+ 9.01 27 459Mg2+ 24.3 72 428Ca2+ 40.07 100 412Sr2+ 87.62 126 412Ba2+ 137.33 142 404

Source: Conway 1981 [29]. Reproduced with permission of Elsevier.

ionic radius as illustrated in Table 1.2. Since the process of heterogeneous ion exchangeinevitably involves hydrated ions, the following observations are universally true:

(i) Binding of an ion onto a rigid ion exchanger requires partial shedding of water ofhydration and hence, all other conditions remaining identical, an ion with lowerhydrated ionic radius shows higher affinity. For example, both K+ and Na+ aremonovalent cations, but K+ is preferred over Na+ by cation exchange resins dueto its lower hydrated ionic radius.

(ii) An ion with a larger hydrated ionic radius is less mobile, that is, it has a lowerdiffusion coefficient. The kinetics of ion exchange are often a diffusion-controlledprocess. Thus, binding of an ion with a higher hydrated ionic radius is always akinetically slower process.

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� �

Ion Exchange and Ion Exchangers: An Introduction 9

1.3 Constituents of an Ion Exchanger

An ion exchanger is ideally defined as a framework of fixed coions, which can be per-meated and electrically neutralized by mobile counterions from the aqueous (liquid)phase. The underlined terms in the foregoing definition require further elaboration.FRAMEWORK is much like a skeleton that constitutes a continuous phase, which

is held together by covalent bonds or lattice energy. For polymeric ion exchangers,covalent bonds predominate and the framework is often referred to as the matrix. Ininorganic ion exchangers, the lattice energy helps retain the ion exchange sites in thesolid phase and the framework is constituted by amorphous or crystalline structures.FIXED COIONS are electric surplus charges (positive or negative) on the framework,or the matrix, unable to leave their phase.This surplus charge is due to covalent bond-ing for polymeric ion exchangers and isomorphous substitution for zeolites and clays.MOBILE COUNTERIONS are solutes with charges opposite to the fixed coions.Theycompensate the charges of fixed coions in the exchanger phase and can also be replacedby other ions of the same sign on an equivalent basis. Unlike fixed coions, the counte-rions can permeate in and out of the exchanger phase and by doing so, they maintainelectroneutrality in both the liquid and the solid phase.For synthetic ion exchangers, fixed coions are known as functional groups or

ionogenic groups, while the exchanging ions are known as counterions. To readilygrasp the underlying concept without loss of generality, let us consider a polymeric ionexchanger where the three-dimensional cross-linked polymer constitutes a separateinsoluble phase or matrix. The covalently attached functional group is essentially thefixed coion that is permeated and electrically balanced by an exchangeable counterion.Figure 1.6 shows a simple schematic of a cation exchanger with sulfonic acid functionalgroups loaded with sodium counterions.Thermodynamically, the activity or concentration of an ion exchanger is not a

unique number, but it varies with the type and concentration of the counterion in the

Legend

Counterion

Functional group

Crosslinking:

Divinyl-benzene (DVB)

Polystyrene matrix

Commonly represented as: R-SO3–Na+

Figure 1.6 Schematic illustration of a strong acid cation exchange resin bead wherematrix/framework is represented by R, fixed coions or functional groups by —SO3

− andcounterions/exchanging ions by Na+.

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� �

10 Ion Exchange in Environmental Processes: Fundamentals, Applications and Sustainable Technology

exchanger phase. However, the fixed coions in an ion exchanger are always balancedby permeating counterions, that is, the ion exchanger is always electrically neutral.Ideally, the ion exchange capacity is equal to the concentration of the fixed coions.We will later see that the capacity is not a constant and it depends, to some extent, onthe external liquid phase concentration.To be familiar with the basic premise and terminologies of ion exchange processes,

let us consider the following cation exchange reaction between potassium and sodiumions:

(R − SO−3 )Na+ + K+(aq) + Cl−(aq) ↔ (R − SO−

3 )K+ +Na+(aq) + Cl−(aq) (1.4)

where the overbar denotes the exchanger phase; sulfonic acid functional group(—SO3

−) is the fixed, non-diffusible coion and Na+ and K+ are the permeable orexchanging counterions. The chloride ion does not participate in the cation exchangereaction and is referred to as a mobile coion. Both the exchanger and aqueous-phaseelectroneutrality remain undisturbed at every stage of the cation exchange reaction.Likewise, the anion exchange process is fundamentally the same, but the exchangerphase has positively charged fixed coions (e.g., quaternary ammonium functionalgroups, R4N+) as shown for the nitrate-chloride exchange reaction below:

(R4N+)Cl− +NO−3 (aq) +Na+(aq) ↔ (R4N+)NO−

3 + Cl−(aq) +Na+(aq) (1.5)

While NO−3 and Cl− are the permeating counterions, R4N+ and Na+ are the fixed and

mobile coions, respectively.

1.4 What is Ion Exchange andWhat is it Not?

Prior to getting into the details of the various materials presented in this book, it isimperative that we present a scientifically coherent definition of what we call “ionexchange.” A list of reactions, as shown below, are often mistakenly presented in theopen literature as ion exchange simply because the process appears to involve anexchange of equivalent amounts of cations or anions:

Pseudo-cation exchange:

FeS(s) + Cu2+(aq) ↔ CuS(s) + Fe2+(aq) (1.6)Fe2+(aq) + Zn0(s) ↔ Fe0(s) + Zn2+(aq) (1.7)

Pseudo-anion exchange:

BaCO3(s) + SO2−4 (aq) ↔ BaSO4(s) + CO2−

3 (aq) (1.8)

These are essentially precipitation–dissolution and redox reactions involving a puresolid phase denoted by “(s).” Since the activity of a pure independent solid phase(e.g., crystalline) is unity, the equilibrium constant of Reaction 1.6, consideringideality, is given by

K = [Fe2+][Cu2+]

(1.9)