Dielectrics in Electric Fields Gorur G. Raju University of Windsor- Windsor, Ontario, Canada MARCEL MARCEL DEKKER, INC. DEKKER NEW YORK BASEL Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 0-8247-0864-4 This book is printed on acid-free paper Headquarters Marcel Dekker, Inc 270 Madison Avenue, New York, NY 10016 tel 212-696-9000, fax 212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse4, Postfach 812, CH-4001 Basel, Switzerland tel 41-61-260-6300, fax 41-61-260-6333 World Wide Web http //www dekker com The publisher offers discounts on this book when ordered in bulk quantities For more information, write to Special Sales/Professional Marketing at the headquarters address above Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher Current printing (last digit) 10 987654321 PRINTED IN THE UNITED STATES OF AMERICA TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. POWER ENGINEERING Series Editor H. Lee Willis ABB Inc. Raleigh, North Carolina 1. Power Distribution Planning Reference Book, H. Lee Willis 2. Transmission Network Protection: Theory and Practice, Y. G. Paithan- kar 3. Electrical Insulation in Power Systems, N. H. Malik, A. A. AI-Arainy, and M. I. Qureshi 4. Electrical Power Equipment Maintenance and Testing, Paul Gill 5. Protective Relaying: Principles and Applications, Second Edition, J. Lewis Blackburn 6. Understanding Electric Utilities and De-Regulation, Lorrin Philipson and H. Lee Willis 7. Electrical Power Cable Engineering, William A. Thue 8. Electric Systems, Dynamics, and Stability with Artificial Intelligence Applications, James A. Momoh and Mohamed E. EI-Hawary 9. Insulation Coordination for Power Systems, Andrew R. Hileman 10. Distributed Power Generation: Planning and Evaluation, H. Lee Willis and Walter G. Scott 11. Electric Power System Applications of Optimization, James A. Momoh 12. Aging Power Delivery Infrastructures, H. Lee Willis, Gregory V. Welch, and Randall R. Schrieber 13. Restructured Electrical Power Systems: Operation, Trading, and Vola- tility, Mohammad Shahidehpour and Muwaffaq Alomoush 14. Electric Power Distribution Reliability, Richard E. Brown 15. Computer-Aided Power System Analysis, Ramasamy Natarajan 16. Power System Analysis: Short-Circuit Load Flow and Harmonics, J. C. Das 17. Power Transformers: Principles and Applications, John J. Winders, Jr. 18. Spatial Electric Load Forecasting: Second Edition, Revised and Ex- panded, H. Lee Willis 19. Dielectrics in Electric Fields, GorurG. Raju 20. Protection Devices and Systems for High-Voltage Applications, Vladimir Gurevich ADDITIONAL VOLUMES IN PREPARATION TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. TO MY PARENTS. MY WIFE, PADMINI, AND OUR SON, ANAND WHO GA VE ME ALL I VALUE. SOME DEBTS ARE NEVER REPAID IN FULL MEASURE. TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. SERIES INTRODUCTION Power engineering is the oldest and most traditional of the various areas within electrical engineering, yet no other facet of modern technology is currently undergoing a more dramatic revolution in both technology and industry structure. This addition to Marcel Dekker's Power Engineering Series addresses a fundamental element of electrical engineering. Dielectric materials are a key element of electric power engineering, one of the most challenging aspects of improving reliability and economy of materials. For an industry pressed hard to increasingly cram more equipment capacity into ever-tighter spaces, to improve reliability, particularly mean time between failures, modern dielectric materials and engineering methods provide a valuable tool to meet these challenges. Dielectrics in Electric Fields is a well-organized and comprehensive view of both the theory behind and application of dielectric materials in power equipment, industrial equipment, and commercial appliances. At both the introductory and advanced levels, it provides both a solid foundation of theory, fact, nomenclature, and formula, and sound insight into the philosophies of dielectric engineering techniques and their use. Its unifying approach, based on both physics and engineering, makes it useful as a day-to- day reference as well as an excellent tutorial: the book begins with a thorough review of the basics of dielectric and polymer science and builds upon it a comprehensive and very broad presentation of all aspects of modern dielectric theory and engineering, including the lastest analysis and modeling techniques. As the editor of the Power Engineering Series, I am proud to include Dielectrics in Electric Fields among this important group of books. Like all the volumes planned for the series, Professor Raju's book puts modern technology in a context of proven, practical application; useful as a reference book as well as for self-study and advanced TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. classroom use. The series includes books covering the entire field of power engineering, in all its specialties and sub-genres, all aimed at providing practicing power engineers with the knowledge and techniques they need to meet the electric industry's challenges in the 21 st century. H. Lee Willis TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. PREFACE Materials that do not normally conduct electricity and have the ability to store electrical charge are known as dielectrics. The behavior of dielectrics in electric fields continues to be an area of study that has fascinated physicists, chemists, material scientists, electrical engineers, and, more recently biologists. Ideas that explain aspects of dielectric behavior in high voltage electrical cables are also applicable to the insulating barrier in metal oxide semiconductors or interlayer insulation of integrated circuits. Microwave drying of milk, dielectric properties of agricultural products such as flour and vegetable oils to determine their moisture content, and the study of curing of cement etc., are some nontraditional applications of dielectric studies that show potential promise. Deeper insight into the interaction between electric fields and molecules has resulted in many new applications. Power engineers are interested in the study of insulating materials to prolong the life of insulation and determine the degree of deterioration in service to plan for future replacements or service maintenance. Polymer scientists are interested in understanding the role of long chain molecules in varied applications ranging from heat resistant dielectrics to selfrepairing plastics. The intensity of research in this area, after a brief respite, has resumed at a furious pace, the published literature expanding at a rate faster than ever. Advances in instrumentation and theoretical models have also contributed to this renewed interest. Organic polymers are considered to be stable materials at high temperatures and have the ability to withstand radiation, chemical attacks, and high electrical and mechanical stresses, making them suitable for extreme operating environments as in a nuclear power plant or in outer space. Polymer materials have the ability to store electrical charges. Like a diamond-studded sword, this property is wholly undesirable in applications such as electrical equipment and the petrochemical industry; yet it is a sought-after property in applications such as photocopying and telephones. TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. This book explains the behavior of dielectrics in electric fields in a fundamentally unifying approach that is based on well-established principles of physics and engineering. Though excellent monographs exist on specialized topics dealing with a relatively narrow area of interest, there is a need for a broader approach to understand dielectrics. It has evolved out of graduate lectures for nearly thirty-five years at the Indian Institute of Science, Bangalore (1966-1980) and the University of Windsor, Windsor, Ontario, Canada (1980-2002). The probing questions of students has helped the author to understand the topics better and to a certain extent dictated the choice of topics. The book begins with an introductory chapter that explains the ideas that are developed subsequently. The calculation of forces in electric fields in combinations of dielectric media is included because it yields analytical results that are used in the study of the dielectric constant (Ch. 2). The band theory of solids is included because it is required to understand the energy levels of a dielectric, as in the conduction and formation of space charge (Ch. 6-11). The energy distribution function is dealt with because it is a fundamental property that determines the swarm parameters in gaseous breakdown and partial discharges (Ch. 8-9). Chapter 2 deals with the mechanisms of electrical polarization and their role in determining the value of the dielectric constant under direct voltages. Expressions for the dielectric constant are given in terms of the permanent dipole moment of the molecule and temperature. Several theories of dielectric constant are explained in detail and practical applications are demonstrated. Methods of calculating the dielectric constant of two different media and mixtures of liquids are also demonstrated. Chapter 3 begins with the definitions of the complex dielectric constant in an alternating electric field. The Debye equations for the complex dielectric constant are explained and the influence of frequency and temperature in determining the relaxation is examined. Functions for representing the complex dielectric constant in the complex plane are given and their interpretation in terms of relaxation is provided. Several examples are taken from the published literature to bring out the salient points. Chapter 4 continues the discussion of dielectric relaxation from chapter 3. The concept of equivalent circuits is introduced and utilized to derive the set of equations for both Debye relaxation and interfacial polarization. The absorption and dispersion phenomena for electronic polarization are considered, both for damped and undamped situations. These ideas have become very relevant due to developments in fiber optics technology. Chapter 5 deals with the application of these ideas to understand the experimental results in the frequency domain and with temperature as the main parameter in selected polymers. A brief introduction to polymer science is included to help the reader understand what follows. The terminology used to designate relaxation peaks is TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. explained and methods for interpreting observed results in terms of physics and morphology are presented. Chapter 6 deals with the measurement of absorption and desorption currents in the time domain in polymers. Though external parameters influence these measurements our concern is to understand the mechanisms of charge generation and drift. Time domain currents may be transformed into the frequency domain complex dielectric constant and the necessary theories are explained. The low frequency, high temperature relaxations observed in several polymers are explained as complementary to the topics in Chapter 5. The magnitude of electric fields that are employed to study the behavior in dielectrics outlined in Chapters 1-6 is low to moderate. However, the response of a polymer to high electric fields is important from the practical point of view. The deleterious effects of high electric fields and/or high temperatures occur in the form of conduction currents and the complex mechanism of conduction is explained in terms of the band picture of the dielectric. Several examples are selected from the published literature to demonstrate the methods of deciphering the often overlapping mechanisms. Factors that influence the conduction currents in experiments are outlined in Chapter 7. Chapters 8 deals with the fundamental processes in gaseous electronics mainly in uniform electric fields and again, due to limitation of space, physical principles are selected for discussion in preference to experimental techniques for measuring the cross sections and swarm properties. A set of formulas for representing the relevant properties of several gases, such as the swarm coefficients are provided, from recent published literature. Chapter 9 is devoted to studies on nonuniform electric field in general and corona phenomenon in particular. These aspects of gaseous breakdown are relevant from practical points of view, for providing better design or to understand the partial discharge phenomena. Both experimental and theoretical aspects are considered utilizing the literature published since 1980, as far as possible. Several computational methods, such as the Boltzmann equation, solutions of continuity equations, and Monte Carlo methods are included. The results obtained from these studies are presented and discussed. Chapter 10 deals with thermally stimulated processes, mainly in polymers. The theory of thermally stimulated discharge currents and techniques employed to identify the source of charge generation are described to assist in carrying out these experiments Chapter 11 deals with measurement of the space charges in solids and the different experimental techniques are explained in detail. These nondestructive techniques have largely replaced the earlier techniques of charging a dielectric and slicing it for charge measurements. The Theory necessary to analyze the results of space charge experiments and results obtained is included with each method presented. The author is not aware of any book that systematically describes the experimental techniques and the associated theories in a comprehensive manner. TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. The book uses the SI units entirely and published literature since 1980 is cited, wherever possible, except while discussing the theoretical aspects. The topics chosen for inclusion has my personal bias, though it includes chapters that interest students and established researchers in a wide range of disciplines, as noted earlier. Partial discharges, breakdown mechanisms, liquid dielectrics, Outdoor insulation and nanodielectrics are not covered mainly due to limitation of space. I am grateful to a number of graduate students who contributed substantially for a clearer understanding of the topics covered in this volume, by their probing questions. Drs. Raja Rao, G. R. Gurumurthy, S. R. Rajapandiyan, A. D. Mokashi, M. S. Dincer, Jane Liu, M. A. Sussi have contributed in different ways. I am also grateful to Dr. Bhoraskar for reading the entire manuscript and making helpful suggestions. It is a pleasure to acknowledge my association with Drs. R. Gorur, S. Jayaram, Ed Churney, S. Boggs, V. Agarwal, V. Lakdawala, T. Sudarshan and S. Bamji over a number of years. Dr. R. Hackam has been an associate since my graduate student years and it is appropriate to recall the many discussions I have held on various aspects of dielectric phenomena considered in this book. The personal encouragement of Professor Neil Gold, University of Windsor has contributed in no small measure to complete the present book. Special thanks are due to Dr. N. Srinivas who provided opportunity to complete chapters 8 and 9 during sabbatical leave. Prof. C. N. R. Rao, President of the Jawaharlal Nehru Center for Advanced Scientific Research provided opportunity to spend sabbatical leave during which time I could work on the manuscript. Mr. N. Nagaraja Rao extended generous hospitality on campus making it possible to use the library facilities in Bangalore. This book would not have been completed without the help of Mr. S. Chowdhury who showed me how to make software applications cooperate with each other. Extraordinary help was provided by Alan Johns in keeping the computer system in working condition throughout. Ms. S. Marchand assisted in checking the manuscript and Ms. Ramneek Garewal assisted in the compilation of figures and tables. While acknowledging the help received, I affirm that errors and omissions are entirely my own responsibility. I have made sincere attempts to secure copyright permission for reproducing every figure and table from the published literature, and acknowledge the prompt response from institutions and individuals. If there are unintentional failures to secure permission from any source, I render apology for the oversight. Personal thanks are due to Brian Black and B. J. Clark who have patiently suffered my seemingly disconnected communications and, provided great assistance in improving the style and format. Finally the inexhaustible patience of my wife Padmini has been a source of continuous strength all these years. Gorur G. Raju TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. [...]...CONTENTS Series Introduction Preface Chapter 1 Introductory Concepts 1.1 A dipole 1.2 The potential due to a dipole 1.3 Dipole moment of a spherical charge 1.4 Laplace's equation 1.4.1 A dielectric sphere immersed in a different medium 1.4.2 A rigid dipole in a cavity within a dielectric 1.4.3 Field in a dielectric due to a conducting inclusion 1.5 The tunneling phenomenon 1.6 Band theory... Dekker, Inc All Rights Reserved 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 Motion of charge carriers in dielectrics Ionic conduction Charge injection into dielectrics 7.4.1 The tunneling phenomenon 7.4.2 Schottky emission 7.4.3 Hopping mechanism 7.4.4 Poole-Frenkel Mechanism 7.4.5 Space charge limited current (trap free) 7.4.6 Space charge limited current (with traps) Space charge phenomenon in non-uniform fields. .. corona charging TM Copyright n 2003 by Marcel Dekker, Inc All Rights Reserved 10.8 10.9 10.10 10.11 Compensation temperature Methods and analyses TSD and AC dielectric properties References Chapter 11 Space Charge in Solids Dielectrics 11.1 The meaning of space charge 11.2 Polarons and traps 11.3 A conceptual approach 11.4 The thermal pulse method of Collins 11.5 DeReggi's analysis 11.6 Laser intensity... 11.8 Experimental Results 11.9 Closing Remarks 11.10 References Appendix Appendix Appendix Appendix Appendix TM 1: Trade Names of Polymers 2: General Classification of Polymer Dielectrics 3: Selected Properties of Insulating Materials 4: Relative Ranking of Thermoplastic Polymers 5: Selected Propertiers of Polymer Insulating Materials Copyright n 2003 by Marcel Dekker, Inc All Rights Reserved ... Negative corona 9.5 Basic Mechanisms: Positive corona 9.6 Modeling of corona discharge: Continuity equations 9.7 Non-equilibrium considerations 9.8 Monte Carlo simulation: Negative corona in SF6 9.9 Monte Carlo Simulation: Positive corona in SF6 9.10 Concluding Remarks 9.11 References Chapter 10 Thermally Stimulated Processes 10.1 Traps in insulators 10.2 Current due to thermally stimulated depolarization... 8.1.14 Recombination 8.1.15 Secondary ionization coefficient 8.1.16 Photo-ionization 8.1.17 Electron swarm coefficients 8.2 Electron Growth in an Avalanche TM Copyright n 2003 by Marcel Dekker, Inc All Rights Reserved 8.3 8.4 8.5 Criteria for Breakdown Paschen's Law Breakdown time lags 8.5.1 The statistical time lag 8.5.2 Formative time lags in uniform fields 8.5.3 Formative time lags in cylindrical geometry... of uniform field gaps in SF6 8.9 Sparkover characteristics of long gaps 8.10 Breakdown voltages in air with alternating voltages 8.11 Concluding remarks 8.12 References Chapter 9 Fundamental Aspects of Electrical Breakdown-ll 9.1 Electron energy distribution functions (EEDF) 9.1.1 EEDF: The Boltzmann equation 9.1.2 EEDF: The Monte Carlo method 9.2 Streamer formation in uniform fields 9.3 The corona... Copyright n 2003 by Marcel Dekker, Inc All Rights Reserved 5.5 5.6 5.7 5.4.1 Polypropylene 5.4.2 Poly(vinyl chloride) 5.4.3 Polychlorotrifluoroethylene 5.4.4 Polycarbonate 5.4.5 Poly(methyl methacrylate) 5.4.6 Poly(vinyl acetate) 5.4.7 Polystyrene 5.4.8 Polyethylene terephthalate) 5.4.9 Polyisoprene 5.4.10 Epoxy Resins 5.4.11 Polyamides 5.4.12 Polyimides Scaling methods Concluding Remarks References Chapter... Absorption current in a dielectric 6.2 Ramon's approximation 6.3 Distribution of relaxation time and dielectric function 6.3.1 Cole-Cole function 6.3.2 Davidson-Cole function 6.3.3 Fuoss-Kirkwood function 6.3.4 Havriliak-Negami function 6.4 The Williams-Watts function 6.5 The G(i) function for William-Watt curent decay 6.6 Experimental measurements 6.6.1 Poly(vinyl acetate) 6.7 Commercial dielectrics 6.7.1... non-uniform fields Conduction in selected polymers 7.6.1 Conduction in polyethylene 7.6.2 Conduction in fluoropolymers 7.6.3 Aromatic polyimide 7.6.4 Aromatic polyamide Numerical computation Closing remarks References Chapter 8 Fundamental Aspects of Gaseous Breakdown-l 8.1 Collision phenomena 8.1.1 Elastic collision 8.1.2 Collision cross section 8.1.3 Probability of collision 8.1.4 Inelastic collisions 8.1.5 . engineering, including the lastest analysis and modeling techniques. As the editor of the Power Engineering Series, I am proud to include Dielectrics . of electrical engineering. Dielectric materials are a key element of electric power engineering, one of the most challenging aspects of improving