Copyright Faculty of Science, Banaras Hindu University, Varanasi , India, All rights reserved.

Copyright Faculty of Science, Banaras Hindu University, Varanasi - 221005, India, 2015. All rights reserved. i

Banaras Hindu University Department of Chemistry Faculty of Science Varanasi - 221005 UNDERTAKING FROM THE CANDIDATE I, Manoj Kumar, hereby declare that I have completed the research work for the full time period in the Department of Chemistry, Banaras Hindu University, Varanasi and the research work embodied in this thesis entitled Non-equilibrium Thermodynamic Studies on Transport through Synthetic Membranes is my own work. To compile the thesis, I have taken proper care to ensure that no mistake is committed in the data included therein. I would be extremely sorry if any wrong information or methods tend to occur in my work. I would like to thank my supervisor for his continuous help, co-operation and valuable suggestions. Date: Place: Varanasi (Manoj Kumar) ii

Banaras Hindu University Department of Chemistry Faculty of Science Varanasi - 221005 ANNEXURE-E (See Clause XIII.2 (b) (iii)) CANDIDATE S DECLARATION I, Manoj Kumar, certify that the work embodied in this Ph.D. thesis is my own bonafide work carried out by me under the supervision of Prof. Bali Ram, for a period of from September, 2009 to August, 2015 at Banaras Hindu University, Varanasi, India. The matter embodied in this Ph.D. thesis has not been submitted for the award of any other degree/diploma. I declare that I have faithfully acknowledged, given credit to and referred to the research workers wherever their works have been cited in the text and the body of the thesis. I further certify that I have not will fully lifted up some other s work, Para, text, data, results, etc. reported in the journals, books, magazines, reports, dissertations, theses, etc., or available at web-sites and included them in this Ph.D. thesis and cited as my own work. Date: Place: Varanasi (Manoj Kumar) Certificate from the Supervisor This is to certify that the above statement made by the candidate is correct to the best of my knowledge. (Signature of the HOD with seal) (Supervisor) Prof. Bali Ram iii

Banaras Hindu University Department of Chemistry Faculty of Science Varanasi - 221005 ANNEXURE F (See Clause XIII.1(c) and XIII.2 (b) (iv)) COURSE/COMPREHENSIVE EXAMINATION COMPLETION CERTIFICATE This is to certify that Mr. Manoj Kumar, a bonafide research scholar of this department, has successfully completed the course work which is a part of his Ph. D. programme. Date: Place: Varanasi (Prof. V. B. Singh) Head Department of Chemistry Faculty of Science BHU, Varanasi. iv

Banaras Hindu University Department of Chemistry Faculty of Science Varanasi - 221005 ANNEXURE-F (See Clause XIII.1 (c) and XIII.2 (b) (iv)) PRE-SUBMISSION SEMINAR COMPLETION CERTIFICATE The Pre-Ph.D. seminar of Mr. Manoj Kumar (Reg. No. CRET- Sept.09/Chem./21), working under the supervision of Prof. Bali Ram, was held on 21 May, 2015 at the Department of Chemistry on the topic Non-equilibrium Thermodynamic Studies on Transport through Synthetic Membranes which is a part of his Ph. D. programme. His performance was quite satisfactory. Date: Place: Varanasi (Prof. V. B. Singh) Head Department of Chemistry Faculty of Science BHU, Varanasi. v

Banaras Hindu University Department of Chemistry Faculty of Science Varanasi-221005 ANNEXURE-G (See Clause XIII.2 (b) (v)) COPYRIGHT TRANSFER CERTIFICATE Title of the Thesis: Non-equilibrium Thermodynamic Studies on Transport through Synthetic Membranes Candidate s Name: Mr. Manoj Kumar The undersigned hereby assigns to the Banaras Hindu University all rights under copyright that may exist in for the above thesis submitted for the award of the Ph. D. degree. (Signature of the candidate) Note: However, the author may reproduce or authorize others to reproduce material extracted verbatim from the thesis or derivative of the thesis for author s personal use provided that the source and the University s copyright notice are indicated. vi

ACKNOWLEDGEMENTS At the outset, I express my gratitude and indebtedness to the Almighty for his countless blessings and first of all, submit my thesis at the feet of God. I feel great pleasure in submitting my thesis. The word of research is full of uncertainties and achievements. Few of them are milestone. From the innermost core of my heart I express my profound sense of reverence, obligations, respect and honour to my supervisor Prof. Bali Ram, Department of Chemistry & Chairman of my Advisory Committee for his inspiration, benign cooperation, industrious guidance, impeccable supervision, timely criticism and benevolent help during investigation and preparation of this thesis. I am truly thankful that I had the Opportunity to work with and learn from him. I wish to express my heartiest thanks to former Heads, Prof. T. R. Rao, Prof. B. Singh and Prof. L. Mishra and present Head, Prof. V. B. Singh, Department of Chemistry, Banaras Hindu University, Varanasi for providing me research facilities. It give me immense pleasure to express my deep sense of gratitude to Prof. Lal Bahadur, Prof. R. N. Singh, and Prof. Om Prakash, the member of my research programme committee for their encouragement, insightful comments and suggestions. I am very much thankful to Prof. N. K. Singh, Prof. N. Singh, Dr. Pankaj Srivastava, Dr. Rajesh Kumar, Dr. Prem Prakash Solanki and Dr. M. K. Bharty for their valuable help and encouragement. I am also thankful to all the respected faculty members for their continuous support and encouragement. I am thankful to Prof. R. K. Mondal, Department of Metallurgical Engineering IIT-BHU, for SEM analysis of the membranes and I am also thankful to Dr. S. Srikrishna, Department of Biochemistry BHU, for providing me regulated power supply for measurements of electro-osmotic flux. All non-teaching staff is equally thankful for their help and support. I am specially thanks to Mr. Vinod Vishwakarma for his every time help and support. Special thanks to UGC, New Delhi for providing JRF & SRF (RGNF) fellowship. I thank my Labmates, Mr. Amulyacharya Malviya, Ms. Chandrakanta Mall, Ms. Shatabdi Paul and Mrs. Shachi Tiwari for their help and support during my research period. vii

At this juncture I would like to thank my friends who stood by me when I needed the most. I am thankful to Mr. Virendra Kumar, Dr. R. K. Dani, Mr. B.P.S. Gautam, Mr. B. Kharediya, Dr. Laxman Singh, Dr. A. Hassan, Mr. Deepak Joshi, Mr. Ajit Gupta, Mr. Ramakant Bharti, Mr. S. Krishna, Mr. K. K. Manar, Mr. Bharat Kumar, Mr. A. Nagaraju and Mr. V. K. Sharma for their valuable helps and supports during the course of this work. I would like to thank my collageous friends Mr. Salil Gupta, Mr. Ajeet Kushwaha, Mr. Amit Kumar Yadav, Mr. Sanjay Kumar, Mr. Sandeep Kumar, Mr. Mahesh Kr. Gautam, Mr. Anil, Mr. Sumit and Mr. Arun for their invaluable support. I acknowledge my family. I thank my grandmother Smt. Rani Devi and my Late grandfather Mr. Gayadeen for their blessings and caring. No word would suffice to express my gratitude to my father Mr. Vishwa Nath and my mother Smt. Kala Wati for their cherished devotional, inspiration, care and blessing. The words of thanks are not enough to express my feelings for their unflagging love and support throughout my life; they have provided the best possible environment for me to grow up physically and mentally. I owe my sincere gratitude to my wife Mrs. Anjana and elder sister Mrs. Rewati, younger sisters Arti, Bharti and my younger brothers Ambuj, Shiva for their affection and moral support, without whom the work would not have been completed. I am indebted to my Jiju Mr. Shailesh for his every time support and encouragement. At last, it is imperative to point out that though all may not be mentioned none are forgotten. August, 2015 (Manoj Kumar) viii

CONTENTS CHAPTER 1 INTRODUCTION AND REVIEW OF LITERATURE 1-33 1.1 Introduction 1 1.2 Definition of the Membrane 1 1.3 Classification of Membranes 2 1.3.1 Biological membranes 2 1.3.1.1 Chemical composition of biological membranes 3 1.3.1.2 Roles of some important inorganic and organic 3 constituent of biological membranes 1.3.1.3 Molecular structure of biological membranes 6 1.3.1.4 Functions of biological membranes 7 1.3.2 Synthetic or Artificial membranes 8 1.3.2.1 Dense membranes 9 1.3.2.2 Porous Membranes 10 1.4 Non-equilibrium Thermodynamics in Membrane 13 Processes 1.5 Basic Parameters and Separation Mechanism through Synthetic Membranes 15 1.6 Synthetic Analogue of Living Membranes: 15 Biomembrane Models 1.7 Membranes in Biomedical Applications 15 1.8 Mechanism of Membrane Transport 16 1.8.1 Passive transport 16 1.8.2 Active transport 17 1.8.3 Facilitated and mediated transport 18 1.8.4 Group translocation 18 1.9 Review of Literature 18 1.10 Present Status of the Work 21 1.11 Aim of the Work 23 References 24 CHAPTER 2 NON-EQUILIBRIUM THERMODYNAMIC THEORY 34-65 OF ELECTRO-KINETIC PHENOMENA AND DOUBLE LAYER MODEL 2.1 Introduction 34 2.2 Basic Principles of Non-Equilibrium Thermodynamics 34 2.2.1 Second law of thermodynamics and entropy 34 2.2.2 Local equilibrium concept 35 2.3 Phenomenological Theories of Non-Equilibrium 35 Thermodynamics 2.3.1 Linear laws 36 2.3.2 Onsager reciprocal relationships 37 ix

2.3.3 Entropy production law 37 2.4 Non-Equilibrium Thermodynamics Theory of 38 Membrane Phenomena 2.4.1 Irreversible phenomena in homogeneous (continuous) systems 38 2.4.2 Irreversible phenomena in heterogeneous 39 (discontinuous) systems 2.5 Electrokinetic Phenomena 39 2.6 Non-Equilibrium Thermodynamic Theory of 40 Electrokinetic Phenomena in the Linear Range 2.6.1 Theory of electro-osmotic effects 40 Steady State Phenomena 44 2.7 Non-Equilibrium Thermodynamic Theory of 46 Electrokinetic Phenomena in Non-linear Range Steady State Phenomena 47 2.8 Electrical Double Layer 48 2.9 Theories of electrical double layer 48 2.9.1 Parallel-plate condenser theory: Helmholtz theory 48 2.9.2 The diffuse-layer theory: Gouy and Chapman s theory 49 2.9.3 Adsorption theory of double-layer: Stern theory 50 2.9.4 Triple-layer model 51 2.9.5 Water-dipole model: DBM-model 53 2.10 Electrokinetic Phenomena in Uncharged Membranes 54 2.10.1 Electro-osmosis 54 2.10.2 Streaming current and streaming potential 56 2.10.3 Sedimentation-potential: Dorn effect 59 2.11 Electro-Kinetic Phenomena in Charged Membranes: 60 Schmid Model 2.12 Limitations of the Double-Layer Theory 62 References 63 CHAPTER 3 EXPERIMENTAL 66-74 3.1 Introduction 66 3.2 Materials 66 3.2.1 Membranes 66 3.2.2 Permeants 66 3.3 Permeability Cell 66 3.4 Scanning Electron Microscopic (SEM) Analysis of the 67 Membrane 3.5 Measurement of Membrane Conductance 68 3.6 Measurement of Viscosity Coefficient of the 68 Permeants 3.7 Determination of Cross-Sectional Area of the Capillary 69 Tube 3.8 Measurement of Hydrodynamic Permeability 69 3.9 Measurement of Electro-Osmotic Permeability 70 x

3.10 Measurement of Streaming Current 72 3.11 Reproducibility of Results and Source of Errors 73 References 74 CHAPTER 4 RESULTS AND DISCUSSION 75-156 4.1 Introduction 75 4.2 Hydrodynamic Permeability 112 4.3 Electro-osmotic Permeability 119 4.4 Streaming Current 119 4.5 Electrical Double Layer 134 4.6 Characterization of the Membrane 150 4.6.1 Morphological studies of the membranes 150 4.6.2 Determination of equivalent pore radii 153 4.6.3 Determination of average number of pores 154 4.6.4 Determination of membrane constant 154 4.7 Zeta potential 154 References 156 CHAPTER 5 SUMMARY 157-160 List of publications and conferences attended Reprints of published papers Personal profile xi

LIST OF ABBREVIATION P : Pressure difference ϕ : Electrical Potential difference A e : Effective cross-sectional area of membrane C : Concentration in molar (M) CA : Cellulose acetate G-3 : Porosity I : Electrical current J v : Volume flux K m : Membrane constant l : Length of pore channel L 11 : Phenomenological coefficient representing hydrodynamic permeability L 12 : Phenomenological coefficient representing electro-osmotic permeability L 21 : Phenomenological coefficient representing streaming current L 22 : Phenomenological coefficient representing conductivity of the membrane-permeant system M : Membrane/surface n : Average number of pores O.H.P. : Outer Helmholtz Plane I.H.P. : Inner Helmholtz Plane r : Equivalent pore radii ϵ : Dielectric constant of the medium ζ e.o. : Zeta potential calculated from electro-osmotic flux data η : Viscosity coefficient χ : Specific conductance xii

PREFACE Development of membrane technology has come of over the past 2-3 decades. Membranes have emerged from a subject of laboratory research to provide the basis for large scale processes with numerous applications in medicine and industry. It is a highly fragmented technology, covering such wide ranging applications as reverse-osmosis, gas separation, controlled release, pharmaceutical formulations and artificial kidney. The disciplines involved in membranology are also varied and include physical chemistry, electrochemistry, polymer chemistry and chemical engineering. But the glue that binds all these varied applications and disciplines together is transport across membranes. The phenomena of mass transmission across membranes are irreversible processes. Further, a number of different driving forces such as potential gradient, pressure gradient and temperature gradients can cause mass permeation across membranes. Therefore, in order to discuss the general theory of mass permeation across membranes the best approach would be to start with the phenomenological theories of non-equilibrium thermodynamics as excellently presented in the monographs of de Groot, Prigogine, Katchalsky and Curran etc. The validity of linear laws and Onsager reciprocity relation have been examined experimentally from electro-osmotic and streaming current transport data by studying the permeation of aqueous, nonaqueous and mixed solvents through different types of membranes by various research workers. Studies on electro-osmotic transport of mass permeation across quartz plug membrane, vanadium pentaoxide membrane and cement plug membrane have already been performed by various research workers at Gorakhpur University. Hadermann et al have extended the domain of irreversible thermodynamics in the non-linear region by using γ- alumina 2- propanol system. Mufson and Higuchi have carried out extensive studies on cholesterol because of its relation to many xiii

diseases. Rastogi et al have carried out investigations on the electrical properties of cholesterol interfaces in the presence of electrolyte and non-electrolyte solutions. A detailed study of electrokinetic phenomena across testosterone and progesterone plug membranes was also performed by Srivastava et al. Many works have been published in the literature on membrane phenomena. But, such studies have not been conducted on nylon-66, cellulose acetate (CA) and pyrexsintered (G-3) membranes. In the present thesis we have made a comprehensive study on transport of aqueous solutions of KNO 3, Pb(NO 3 ) 2, Cd(NO 3 ) 2.4H 2 O and Al(NO 3 ) 3.9H 2 O in the concentration range of 10-4 to 10-3 M as permeants through nylon-66 membrane, cellulose acetate (CA) membrane and pyrex-sintered G-3 membrane. The entire work has been divided into five chapters. Chapter 1 (Introduction); in it, a brief introduction of membranes and membrane phenomena have been described. This chapter also includes the review of literature on related work. Chapter 2 presents an account of theories and models used to describe the non-equilibrium thermodynamic transport of matter through membranes. Chapter 3 (Experimental) describes the details of materials used and experimental work done on permeability and streaming current measurements during the transport of electrolyte salt solutions. Chapter 4 (Results and Discussion) is a record of experimental data. The results obtained have been discussed in the light of theory of non-equilibrium thermodynamics. Membranes parameters have been evaluated using transport coefficient. Chapter 5 is the Summary of the experimental findings. Four research papers have already been published in international and national journals and one has been communicated for publication. A copy of each published paper has been attached in the end of the thesis. xiv