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Energy Storage A New Approach
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Ralph Zito
Scrivener
©WILEY
Copyright © 2010 by Scrivener Publishing LLC. All rights reserved. Co-published by John Wiley & Sons, Inc. Hoboken, New Jersey, and Scrivener Publishing LLC, Salem, Massachusetts. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., Ill River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. http://bbs5.techyou.org/?fromuser=sergio147 For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. For more information about Scrivener products please visit www.scrivenerpublishing.com. Cover design by Kris Hackerott. Library of Congress Cataloging-in-Publication ISBN 978-0-470-62591-0
Printed in the United States of America 10
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Contents Preface Dedications and Acknowledgements
xi x v
1
Introduction
2
Comments on Classical Mechanics 2.1 Force 2.2 Energy Sources
3
Conversion and Storage 3.1 Availability of Solar Energy 3.2 Conversion Processes 3.2.1 Photovoltaic Conversion Process 3.2.2 Thermoelectric Effects: Seebeck and Peltier 3.2.3 Multiple P-N Cell Structure Shown with Heat 3.2.4 Early Examples of Thermoelectric Generators 3.2.5 Thermionic Converter 3.2.6 Thermogalvanic Conversion 3.3 Storage Processes 3.3.1 Redox Full-Flow Electrolyte Systems 3.3.2 Full Flow and Static Electrolyte System Comparisons
21 25 27 27 28 30 30 32 32 34 34
Practical Purposes of Energy Storage 4.1 The Need for Storage 4.2 The Need for Secondary Energy Systems 4.2.1 Comparisons and Background Information
41 41 44 45
4
1
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v
7 1 12 8
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CONTENTS
4.3
Sizing Power Requirements of Familiar Activities 4.3.1 Examples of Directly Available Human Manual Power Mechanically Unaided 4.3.1.1 Arm Throwing 4.3.1.2 Vehicle Propulsion by Human Powered Leg Muscles 4.3.1.3 Mechanical Storage: Archer's Bow and Arrow 4.4 On-the-road Vehicles 4.4.1 Land Vehicle Propulsion Requirements Summary Rocket Propulsion Energy Needs Comparison 4.5
47 49 49 49 51 52 53 54
Competing Storage Methods 5.1 Problems with Batteries 5.2 Hydrocarbon Fuel: Energy Density Data 5.3 Electrochemical Cells 5.4 Metal-Halogen and Half-Redox Couples http://bbs5.techyou.org/?fromuser=sergio147 Couples 5.5 Full Redox 5.6 Possible Applications
55 56 59 62 63 68 71
The Concentration Cell 6.1 Colligative Properties of Matter 6.2 Electrochemical Application of Colligative Properties 6.2.1 Compressed Gas 6.2.2 Osmosis 6.2.3 Electrostatic Capacitor 6.2.4 Concentration Cells: CIR (Common Ion Redox) 6.3 Further Discussions on Fundamental Issues 6.4 Adsorption and Diffusion Rate Balance 6.5 Storage by Adsorption and Solids Precipitation 6.6 Some Interesting Aspects of Concentration Cells 6.7 Concentration Cell Storage Mechanisms that Employ Sulfur 6.8 Species Balance 6.9 Electrode Surface Potentials
75 76 77 79 81 82 83 89 94 97 100 104 106 107
CONTENTS
6.10 6.11 6.12 6.13 6.14 6.15 6.16 6.17 6.18 6.19 6.20 6.21 6.22 6.23 6.24 6.25 6.26 6.27 6.28
6.29
Further Examination of Concentration Ratios Empirical Results with Small Laboratory Cells Iron/Iron Concentration Cell Properties The Mechanisms of Energy Storage Cells Operational Models of Sulfide Based Cells Storage Solely in Bulk Electrolyte More on Storage of Reagents in Adsorbed State Energy Density Observations Regarding Electrical Behavior Concluding Comments Typical Performance Characteristics Sulfide/Sulfur Half Cell Balance General Cell Attributes Electrolyte Information Concentration Cell Mechanism and Associated Mathematics Calculated Performance Data Another http://bbs5.techyou.org/?fromuser=sergio147 S/S"2 Cell Balance Analysis Method A Different Example of a Concentration Cell, Fe +2 /Fe +3 Performance Calculations Based on Nernst Potentials 6.28.1 Constant Current Discharge 6.28.2 Constant Power Discharge Empirical Data
108 111 114 115 121 123 126 130 130 133 133 134 135 136 138 140 143 145 146 147 148 150
Thermodynamics of Concentration Cells 7.1 Thermodynamic Background 7.2 The CIR Cell
153 153 156
Polysulfide - Diffusion Analysis 8.1 Polarization Voltages and Thermodynamics 8.2 Diffusion and Transport Processes at the (-) Electrode Surface 8.3 Electrode Surface Properties, Holes, and Pores 8.4 Electric (Ionic) Current Density Estimates 8.5 Diffusion and Supply of Reagents
165 166 168 169 174 176
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CONTENTS
8.6
Cell Dynamics 8.6.1 Electrode Processes Analyses 8.6.2 Polymeric Number Change 8.7 Further Analysis of Electrode Behavior 8.7.1 Flat Electrode with Some Storage Properties 8.8 Assessing the Values of Reagent Concentrations 8.9 Solving the Differential Equations 8.10 Cell and Negative Electrode Performance Analysis 8.11 General Comments
177 177 178 190 190 198 199 211 218
Design Considerations 9.1 Examination of Diffusion and Reaction Rates and Cell Design 9.2 Electrodes 9.3 Physical Spacing in Cell Designs 9.3.1 Electrode Structures 9.4 Carbon-Polymer Composite Electrodes 9.4.1 Particle Shapes and Sizes 9.4.2 Metal to Carbon Resistance http://bbs5.techyou.org/?fromuser=sergio147 9.4.3 Cell Spacing 9.5 Resistance Measurements in Test Cells 9.6 Electrolytes and Membranes 9.7 Energy and Power Density Compromises 9.8 Overcharging Effects on Cells 9.9 Imbalance Considerations
219 219 220 221 221 225 228 229 229 231 233 234 237 238
10 Calculated Cell Performance Data 10.1 Electrical Performance Modeling
239 239
11 Single Cell Empirical Data 11.1 Design and Construction of Cells and the Materials Employed 11.2 Experimental Data
253 253 257
12 Conclusion: Problems and Solutions 12.1 Pros and Cons of Concentration Cells 12.2 Future Performance and Limitations
261 262 263
CONTENTS
ix
Appendix 1: A History of Batteries Al. 1 A History of the Battery A1.2 The Electric Car and the Power Source Search A1.3 The Initial Survey A1.4 Review of a Research Path for a Long-life, High ED Battery
265 266
Appendix 2: Aids and Supplemental Material A2.1 Properties of Homogeneous Membranes A2.1.1 Diffusion Tests A2.2 The van der Waals Equation and its Relevance to Concentration Cells A2.3 Derivation of Electrolyte Interconnectivity Losses A2.4 Efficiency Calculations A2.5 Specific Resistivity and Specific Gravity of Some Reagents
283 283 284
268 270 271
285 286 290 294
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Bibliography Index
297 301
Preface The main purpose of this book is to present a different phenomenological approach to practical energy storage. Throughout the book, a main thread of the problems associated with the generation, transmission, conversion, and storage of energy is proposed, and various technologies are addressed primarily from a phenomenological viewpoint. The exploration of new processes is a major part of the continual search for improved means of the generation and storage of energy. Although some mathematical developments are presented, this http://bbs5.techyou.org/?fromuser=sergio147 book is not intended as a text on thermodynamics or electrochemistry. Certainly, thermodynamics is employed and generous use is made of mathematical tools, but this is not a text directed toward the development or teaching of such principles. It is assumed that the reader possesses some knowledge of elementary classical physics and mathematics and differential calculus in order to easily understand some of the details of thermodynamics and diffusion processes upon which the mechanisms of concentration cell operations are based. This book presents a broad review of energy technology only in summary fashion in order to provide a background so that the concentration cell approach will be viewed in context with other available means of energy storage. It is necessary to cover a reasonable portion of these subjects in order to make this narrative understandable as an alternative presentation. The rationale behind the concentration cell approach should become apparent as the reader moves through the arguments and reviews. The primary aim is to suggest and describe an alternative approach to energy storage other than the ones that have been pursued in the past, especially so vigorously within the past thirty to forty years. xi
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PREFACE
The recognized need for improved and practical ways to store large quantities of energy for later use, such as in load leveling for the electric power utilities, has resulted in innumerable programs sponsored by the Atomic Energy Commission, the Energy Research and Development Administration, and the present Department of Energy. However, many of the concepts regarding the processes at electrode surfaces evolved during the prolonged writing of this book, and the mathematics was developed subsequent to the experiments with laboratory cells described here. The work is hardly complete, and much still needs to be explained. Our astonishment was significant when we first observed the large voltages produced in symmetrical cells with electrodes of large micro-areas. Hopefully, this book will engender interest in acquiring a basic understanding and stimulate further explorations into other, alternative methods of storing energy that may have been largely overlooked, such as the class of phenomena generally referred to in electrochemistry as "concentration cells." There is much opportunity to store energy in an efficient and easily reversible fashion. Since this type of cell makes use of the colligative properties of subhttp://bbs5.techyou.org/?fromuser=sergio147 stances, many different combinations of materials can be employed in such cells. The first five parts are devoted to a general discussion of energy issues and the presentation of tutorial information. The author gathered most of the data and operation and construction details during the various development projects undertaken in redox and concentration types of cell and battery development. Much of the technical information, performance data, and design parameters were obtained while the author was with the Westinghouse Electric Co. Research Center in Pittsburgh, the General Electric Co., the Research and Development Center in Schenectady, NY, and the Technology Research Laboratories, Inc. in Durham, NC. The practical application aspects of a category of phenomena in physics and electrochemistry have been largely overlooked. That category is the source of electric potentials that can be produced from concentration differences of the same chemical ionic species opposite electrode surfaces. The only practical answer to all-around energy storage needs may lie in the application of the class of phenomena referred to as electrochemical concentration cells. The electrical potential results from structured cells with intense differences in concentration of the
PREFACE
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same elemental (chemical) specie at two different oxidation states. Storage continues to be a main concern in the whole spectrum of energy related issues. There is no question regarding the efficacy or scientific soundness of the principles employed for storing energy in this fashion. The approach is well beyond such serious concerns. The questions that remain are those regarding the ultimate practicality and competitiveness with respect to other methods of reversible energy storage in such matters as its ultimately achievable efficiency cost, and energy density. The information presented in this book is the result of forty years of search and experimental researching for a method of storing energy in a reversible, dependable, and life-long manner. Research has largely been centered on the electrochemistry of what has in recent years become known as redox systems. Both static and full flow electrolyte systems have been explored. The resultant system that satisfied most, if not all, of the imposed practical requirements and appeared to offer the least limited performance with future development was the concentration cell - a significant departure from the normal path of such studies. http://bbs5.techyou.org/?fromuser=sergio147 This mechanism for storage is based upon Nernst's equation for the chemical potential that can be derived from the ratio of concentrations of the same ionic substance at opposing electrodes in an electrochemical cell. There are two further volumes planned in this series on energy storage, the first of which, tentatively titled, Concentration Cells: Fabrication Methods and Materials, is due to be published by Wiley-Scrivener in September 2011. The aim of this second volume will be to provide the engineer and scientist with the most comprehensive coverage of the concentration cell yet written, with a view toward employing the concentration cell in the storage of energy on a large scale.
Dedications and Acknowledgements I am taking advantage of this written opportunity to express my deep appreciation and thanks to some of the many people who have made writing this book possible. With their participation and contributions over the years in research and development programs at TRL, Inc. and GEL, Inc., they have made many contributions to accumulating more experience with these energy technologies. It is not practical to even attempt to list all those individuals who, over many years, have designed and constructed experimental hardware, from which we have learned how to cope with a multitude of related problems,http://bbs5.techyou.org/?fromuser=sergio147 and who have made writing this book possible. In particular, I would like to acknowledge the following for their direct influences on the developments. Special thanks go to Prof. Richard S. Morse and Prof. David Ragone at MIT, who both launched this whole area of redox systems in Cambridge, MA in 1968. Also, I would like to thank Keith Poulin for his administrative and managerial skills, Graham Wilson, whose fertile imagination, combined with his engineering capabilities, resulted in most of our very early hardware display devices, Joseph O. Dixon for his engineering skills, faith, and confidence, D. Morris for his problem solving, tenacity, and positive attitude, and Prof. Charles Harman from Duke University for his technical and personal support and patience. There are so many people, including my dedicated secretaries over the years, Phoebe Rasmussen, Sarah Tortora, and Patricia Pearson, who need to be commended for staying with us through difficult situations. Others include the many shop and laboratory people who coped with rather messy conditions in handling such materials as graphite and carbon black and unfriendly electrolytes in large quantities. xv
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DEDICATIONS AND ACKNOWLEDGEMENTS
I would like to thank one individual in particular, Sir John Samuel, who has steadfastly maintained a confidence in our technical accomplishments and has been responsible for obtaining much needed support for our programs. This book reflects only a tiny portion of all the work from so many others who preceded its writing and made writing it possible.
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Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
1 Introduction
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All the discussions and dire announcements in technical literature during recent years have certainly made everyone aware of the "energy problem." There is not much doubt that we are confronted with this problem and that it is an issue of domestic and international importance. The critical issues concerning the availability of energy sources and their efficient use are rapidly becoming vitally important. Increasing population, in conjunction with the greaterthan-ever energy and materials demands that people are making in order to increase their comfort, travel, etc., is indeed causing greater stress. All of these require not only an increased availability of energy but also more effective ways of utilizing what is available. The main efforts of research and development have been directed towards the development of new alternatives or finding more primary sources of energy. For the present, and until the discovery of a new class of phenomena, we have a fairly good idea of what can be accomplished. We know what alternative sources are possible alternative presumably to petroleum products. Yet, none of them are nearly as attractive for portable or motive power unless we significantly lower our criteria. 1
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ENERGY STORAGE
It would appear that sources of energy are plentiful on planet Earth. However, they are often locally unavailable, too bulky, too unpredictable (solar and wind), a n d / o r too dangerous to be portable. An effective method for storing energy would greatly reduce the problem and would provide low-cost energy for everyone. It seems that not nearly as much attention or support has been directed toward the problem of storage as that which has been directed toward generation. Perhaps this difference is due to the absence of many promising approaches to accomplishing the latter. This book presents a different approach and aims to stimulate additional efforts toward the search and development of better storage. There are not many attractive choices for storage, and most are not portable or cheap. We cannot carry windmills around - they are huge and dangerous. A waterfall, due to topographical considerations, is not available everywhere, and its size is immense for the intermittent power and energy produced. Batteries are the least obtrusive and the most predictable limited secondary sources, but they are not practical as large-scale primary or secondary sources. Windmills and photovoltaic cells are almost useless without either storage or the assistance of an electric utility http://bbs5.techyou.org/?fromuser=sergio147 power grid, which operates on nuclear power or coal fuel. It would appear that the energy source trap has merely changed shape. Ideally, high energy and power density "batteries" of some sort that are charged by nuclear or fossil fuel would be a good solution to smoothing the irregularities in the distribution and availability for the planet's population. The term "batteries" used here only refers to some mechanism for practical storage. So far, the most promising is probably an electrochemical method. Compressed air, metal springs, flywheels, etc., all have very serious drawbacks. Most generating facilities are not portable, nor would most people wish to live with them in their midst. Storing energy in its many forms in nature is a vital part of all processes as well as life itself on Earth. As one explores these processes and their importance to us, we can gradually make observations that lead to some revealing conclusions. One of our purposes is to examine the general area of energy storage and to identify the key mechanisms that have significant roles in nature and civilization. Then we will develop a description and a reasonably detailed understanding of why we need to store energy and how the various mechanisms we employ work to satisfy these needs. Most of this book is devoted to electrochemical processes
INTRODUCTION
3
and, in particular, full flow electrolyte cells that are frequently referred to as redox batteries. In a very general sense, there are only three purposes for the storage of energy: to make an energy supply portable from essentially non-portable sources, to store from an ongoing source for use at a later time, and to change the ratio of power-to-energy, as accomplished by flywheels, capacitors, etc. All applications of energy storage can be put into one or more of these categories. Certainly, if we wish to power a portable power tool or an electric automobile, a hydroelectric plant is hardly practicable. However, if we use the energy produced by the hydroelectric station and store part of what is not immediately needed in an electric battery, it becomes a practical situation for the electric vehicle. Nuclear energy sources are hardly portable on a small scale. But in similar fashion, as for non-portable hydroelectric stations, storing portions of the generated energy in some sort of device such as a battery could become useful in mobile electric vehicles. In the second instance, we might have the need to store solar energy during the daylight hours for use after sunset to power lights, etc. There are many cases where the convenience factor is http://bbs5.techyou.org/?fromuser=sergio147 not met - where the generation or the source of energy is occurring at a time that does not coincide with the need or application time. It must be noted here that when we refer to energy we are essentially referring to the "capacity to do work" in the classic sense of Force χ Distance. This capacity is being transferred from one source to a device that is capable of storing that capacity for work to be used at a later time. The storage of energy in one form or another for later use has been extremely important not only to mankind but also to virtually every form of life. Storing energy in the form of chemical structures, such as carbohydrates, enables life forms to survive for periods of time between food intake activities. Obviously, all activity and motion are manifestations of exchanges of energy from one level to another. The exchange of potential energy for kinetic energy of motion for falling objects is a simple example. Few energy-expending actions make use of prompt sources. It can be argued that even the processes that produce solar radiation make use of energy that was stored at some earlier stages of cosmic evolution. An energy bank deposit must be made at an earlier time for energy to be in an available and usable form at the time of demand.
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This stored, but temporarily unavailable energy is usually not in a form that is needed for the specific operations at the demand time. Hence, there is usually a conversion mechanism accompanying the stored energy device in order for the energy reserve to be useful. There are many examples that can illustrate this simple, but basic, premise. They are presented in a later section of this book. In biochemical processes, the stored carbohydrates, perhaps in the form of sugars, are oxidized in order to produce the heat necessary to sustain life. Chapter 3 lists other, simpler forms of energy storage that are familiar to all of us. At the outset, I would like to make clear the major purpose of this book. Its purpose is to emphasize the importance of this general approach to energy storage as a rather new technical viewpoint wherein the physical principles employed are basic to all matter. Perhaps the best example of this is the mechanical and thermal behavior of gas compression. This book focuses on a single and particular class of artificial means of energy storage, a general class of energy conversion known as electrochemical processes. More specifically, this book concentrates on aqueoushttp://bbs5.techyou.org/?fromuser=sergio147 systems that are largely compatible with ambient conditions of temperature, pressure, and a chemical environment. Some mention will be made to these other systems and devices, but only in passing, so that we may retain a better perspective regarding in placing the electrochemical systems of prime interest here. The reasons for this selection will become clear as the argument develops and as some background information associated with major application criteria is provided. In the chapters to follow, I outline the requirements of our energy needs and establish a background of information upon which we can more clearly assess the various storage options available to us. However, the primary purpose is the description of a new approach. The science is not new, but it has received scant attention as a possibility for reducing our energy problems. The first three sections describe the background and rationale of electrochemical storage and, more specifically, redox types of systems, based on first-hand knowledge in developing earlier attempts at large-scale energy storage for load leveling and standby power. Justifications for redox systems for large-scale, bulk energy, stationary storage applications will also be identified. The first six chapters present not only a general background of energy requirements, competitive methods for storage, and
INTRODUCTION
5
a description of the basics of concentration cell operations, but they also provide sufficient information to comprehend this different approach to storage along with some justifications for taking that technical direction. However, in order to fully appreciate the important details of cell operational mechanisms, it is necessary to delve a bit into the various key processes of diffusion and transport processes. This entails rather lengthy and tedious mathematical analyses. I have collected and placed the major portion of such activities in Chapters 8 and 9. A significant amount of space is devoted to explaining the thermodynamics of the concentration cell, and the explanations of the operating principles are numerous. Moreover, keeping track of the materials transport mechanisms and the source of electric potential can be confusing. However, in order to contend with the many aspects of present day energy technology, it is important to have a working knowledge and comprehension of the basic underlying physics. This book is directed to those readers who would like to have an appreciation of the wide vistas of energy technology and wish to acquire enough understanding to make independent evaluations of modern trends in such matters as conservation, fossil fuels http://bbs5.techyou.org/?fromuser=sergio147 versus solar energy, and so on. The purpose of this book is to stimulate interest in the subject of energy and the dynamics of the physical world around us. Some mathematics are employed where it is necessary in order to establish quantitative energy relationships in solving problems or in the design of devices. The purpose of the mathematics is to provide those who have the interest and skills with a more in-depth understanding of the factors and limitations of the physical world as we now know it. There are also many excellent texts written on energy, theoretical mechanics, and the mathematics of theoretical physics. Some of these are listed in the accompanying bibliography.
Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
2 Comments on Classical Mechanics http://bbs5.techyou.org/?fromuser=sergio147
The concept of energy is elusive and more than a bit mysterious. It is constantly being re-examined for greater understanding. It's an idea or concept of which nearly everyone thinks they have some understanding. It is interesting to note how we refer to the idea by such phrases as "burning excess energy," "using a lot of energy/' or "someone has a lot of energy," as if it were a fuel of some sort. The repetition of the word, as with most concepts, conveys a vague feeling of comfort with the notion, and that we indeed have a grasp of it. Frequently, in ordinary conversation or in more popular literature, the term energy is confused with or substituted for force. This confusion dates back many centuries beginning with man's attempts to comprehend physical phenomena and the world around him. Even after the beginning of what is known as the scientific method, attributed to Galileo, much about the subject has confounded our comprehension. In the next pages I will address the issue of what energy is. We are never actually able to observe the quantity named "energy," but its effects are certainly, and easily observable. Perhaps this also adds to the mystery of energy. Lindsay and Margenau presented 7
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a timeless review of the history of physical concepts in their book Foundations of Physics, 1936. Though dated, this text presents a very comprehensive treatment of basic concepts both in classical and quantum mechanics. Since I have seen little to compare with this and I don't wish to compete with their treatment of mechanics, I quote their pointed and well-said statements. All the problems of classical mechanics can be solved without reference to it (energy). The question at once arises: why then should it have been introduced at all? This is what we wish to discuss. We must first remark, however, that the idea if energy is historically much older than the name. Without doubt it goes back at least to Galileo on his observation with respect to machines that "what is gained in power is lost in speed," referring to the fact that the force required to lift a weight (by means of a pulley system) multiplied by the distance through which the force has to be applied remains constant, though either factor in itself may vary. The concept of work is involved here. Its importance was, however, overshadowed by Galileo's epoch-making discoveries of the laws of motion, and it was not until the time of Huyghens that it again became prominent in http://bbs5.techyou.org/?fromuser=sergio147 the concept of "vis viva" or "living force", i.e., a quantity varying as the mass multiplied by the square of the velocity. The attribution of the term energy to the concept of "vis viva" did not come until the nineteenth century. (121) The origin of the word energy is Greek, and it means active, or the capacity to do work. In more recent times, the idea has taken hold that energy is some ethereal form of substance. In quantum and relativistic mechanics, energy is interchangeable with mass (matter) as indicated, for example, in the celebrated equation from Einstein's Relativity Theory, E = mc2. Kinetic energy remains kinetic energy when, for example, a moving mass slows down by frictional losses. The collective kinetic energy of the mass is disbursed as kinetic energy (motion) of many more, smaller particles (molecules) and measured as a temperature rise. However, kinetic energy can be converted or swapped for potential energy when, for example, a mass loses velocity while slowing down as it moves against an attractive field of force such as gravity. In more recent times, the idea has taken hold that energy is a substance. For those who wish to acquire a detailed knowledge of the
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history of the concept of energy and force, including the evolution of these concepts over the centuries, the books Concepts of Mass and Concepts of Force by Max Jammer would be helpful. As far as we know, and consistent with observations, energy cannot be created or destroyed. We will ignore, in this book, the processes wherein energy and matter are equivalent, i.e., that matter can be transformed into energy and vice versa because all the phenomena associated with our lives do not occur at the atomic nuclear level. The availability of energy to do work can and does change. We can only transform energy from one of its two forms into the other, when possible, to suit our practical purposes, such as from kinetic energy to potential energy and back to kinetic. Ultimately, all these transformations resolve in an increase of entropy (order) in the universe and, therefore, an increase in world temperature. When all things are finally at the same temperature, there is no more useful energy. Another penetrating and early analysis of the subjects of energy (kinetic and potential), mass, and force was put forth by James Clerk Maxwell, author of the electromagnetic theory of radiation, among other profound and basic contributions to physics. In his preface to http://bbs5.techyou.org/?fromuser=sergio147 Matter and Motion, he states; Physical science, which up to the end of the eighteenth century had been fully occupied in forming a conception of natural phenomena as the result of forces acting between one body and another, has now fairly entered on the next stage of progress that in which the energy of a material system is conceived as determined by the configuration and motion of that system, and in which the ideas of configuration, motion, and force are generalized to the utmost extent warranted by their physical definitions. (1877) What is energy? It is not observable in the classical sense. Theoretical physicists have debated its ability to be observed interminably and have variously defined the concept over many years. First, it is necessary to identify or define what we mean by an "observable quantity." Interestingly, there are few direct observable. The rest of these concepts, such as energy, momentum, temperature, etc., are inferred by various experiments and indirect observations. What we call momentum is calculated and seen as the force necessary to change the momentum of a body.
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We are using the word "observable" in a rather sophisticated sense. It is necessary to divorce our ideas of what we directly experience from those of theories intended to explain the process or sensation. Force, a push or pull, is a directly observable magnitude, as are the velocity of a body in motion, pressure, volume, length, temperature, and even quantity of heat. In reality, the subject of what is legitimately observable is highly debatable. Not only are the semantics of the subject in question, but we must also identify the level of primitiveness or experience of the individual making the observation. However, such quantities as entropy and enthalpy in thermodynamics are not directly observable. Implicitly, we think of energy as being some sort of substance or quality that enables one to overcome an opposing force and move an object to a different position spatially in opposing this force. Examples of certain non-observables are electric and magnetic fields. We can observe their effects, but we are not able to see or observe the field directly. In the case of a magnetic field, the attraction force of a magnet for iron particles can be seen or experienced directly, but not the field itself. In fact, the magnetic field is an http://bbs5.techyou.org/?fromuser=sergio147 invention by physicists to structure a logical and working explanation of that observation. Similarly, we cannot experience an electric field directly, but surely the consequence of such a field is seen or felt when a statically electrified insulator, such as a rod of glass or plastic, gathers bits of fur or paper. The dilemma we tend to fall into is the result of familiarity with the concepts and objects that we think we understand but unfortunately do not. The idea of energy in any form is very complex and sophisticated. Sometimes energy is described as having many different forms - chemical and mechanical energy and perhaps thermal energy as temperature. In actuality these are superficial manifestations of the same thing. We need to distinguish basic ideas and concepts from those involving superficial property assessments. In deference to undo involvement in philosophic issues, let us take a deeper look into the matter of observables, dimensions, and measurable quantities in the physical sciences. As always, along with the benefits reaped from greater numbers of tools and concept evolution in physics, the more likely we become separated from basic contact with the outside, physical world. The tendency is to become too involved with word pictures and symbols, and
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then it becomes increasingly difficult to separate the reality that we "directly" perceive from the physical models generated in our minds and placed there by myriad conversations and teachings in physical science. Returning to the subject of energy, for example, when we see a large mass such as an automobile moving at speed of say 60mph, we might remark upon the large amount of kinetic energy the automobile has, especially if it collides with a rigid object and suffers severe damage. In this case, as in all others, we do not really make a direct observation of its "energy." In fact, it is not possible to see or experience energy as such, only the consequences of its transference. In order to make sense out of our observations, we simply invent concepts and weave a fabric of theories, hypotheses, and other explanatory structures. In this manner, we are attempting to not only acquire a better "understanding" of the world around us but also to be able to predict the results of our actions, and perhaps even control their outcome by making use of these concepts. Now, let's takehttp://bbs5.techyou.org/?fromuser=sergio147 a critical (analytical) look at the main subject of this book - energy. We cannot make direct measurements of this rather elusive substance. Only the effects or results of energy can be observed and measured. We cannot hold energy in our hands as we can grasp material substances such as a stone or stick of wood, nor can we see it as directly as we see wood, that same stone, or a source of colored light. Energy makes no sound that we can perceive. In fact, energy is more of a concept in classical physics than a "substance," as in a material object. The idea of energy existing is mostly to explain motions and activities in life. If someone is very active and has great strength, we tend to say that the individual has a lot of energy, implying that he or she is in possession of a larger quantity of some substance that enables him to perform tasks greater or faster than normal. When an explosion takes place we think that a great amount of energy is released. Exactly what do we mean? Large forces are manifest when an explosion takes place, and we see solid objects torn apart and many particles of matter thrown away from the center of the explosion with great velocities. Knowing that large forces operating over very short periods of time are required to do this, the conclusion is that this large amount of stored (potential) energy is released in the form of much action and motion.
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The quantity we call kinetic energy implies motion (kinetic from the Greek signifying movement). It is the energy associated with physical bodies in motion. Potential energy is the latent ability to do work. Work and energy are essentially synonymous as employed in mechanics. However, doing work implies action. Let us get a bit more involved in the details, units, and ways of measuring energy, always keeping in mind that we quantify on the basis of the results of transformations of what we refer to as energy.
2.1
Force
Pushing on a body to move it against frictional resistance forces and the force of gravity are too familiar to all of us in our everyday experiences. The force we must exert through our leg muscles to climb a flight of stairs is frequently experienced and readily comprehensible. The term work may have originated in times past because of the idea that effort had to be exerted to do the common tasks nechttp://bbs5.techyou.org/?fromuser=sergio147 essary to life. The amount of energy involved in lifting weights to certain heights is also defined as work. One can appreciate how we probably acquired the terminology and the idea that energy, or work, is defined as force times distance. In other words, the amount of energy required or produced is the product of the distance through which a force is acting times the force. This is simply expressed as Force x distance = F x d = Energy (work).
(2.1)
The above equation assumes that the force is constant throughout the distance it is acting. Before getting into the more quantitative aspects of energy, we should examine the basic units of measurement that are employed. That subject is usually referred to as dimension theory or dimensional analysis. Despite the seemingly abundant, and perhaps unlimited, number of phenomena and effects in nature ranging from electric, mechanical, thermal, magnetic to hydraulic, gravitational, and more, there is only a limited number of basic units that we must use in analyzing, measuring, and calculating these different processes.
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Most processes can be described mathematically in terms of four basic parameters. Along with the most commonly used units, they include the following: Dimension Units 1. 2. 3. 4.
Mass (M) - grams, slugs Length (L) - meters, feet Time (t) - seconds Electric charge (q) - coulombs
Let's quickly explore the meaning of what has just been stated. Later in this book, we will return to the subject of dimensions when we pursue the subjects of energy conversion and use. All physical (mechanical) processes and properties can be described in terms of mass, length, and time. If we include the electric field, magnetic field, properties of conductance, permeability, electric current, etc., in our catalog of phenomena, then we need to add the fourth dimension, electric charge, to the list. http://bbs5.techyou.org/?fromuser=sergio147 Units of measurement are necessary to quantify these parameters. There are many forms of the units in which energy is measured. Depending on whether the English or metric system is employed, the most common units are as follows. In equation (2.1) above we defined energy or work as the product of force multiplied by distance. The units of force are found, from its definition, as the product of mass times acceleration, or F = M x a,
(2.2)
where a is acceleration. Acceleration is the rate of change in velocity of a body (mass). Since velocity, v, is expressed as the rate of change in distance versus time, its units are v = L/t. The rate of change in velocity with time, similarly, is v / t = L/t 2 . We experience numerous types of forces. Among them are the forces due to gravitational attraction, attraction and repulsion of electric charges in an electric field, and magnetic attraction and repulsion forces. Somewhere in the development of these observations and concepts, the decision was made that all these forces are dimensionally the same. In order to remain consistent in the
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Figure 2.1 Acceleration of a mass by a constant force.
logic of mathematical representation, all types of forces have the dimensions of ML/t 2 . How did this occur? Mechanical force as mass times acceleration was probably first proposed by Newton in his Principia Mathematica as part of his Laws of Motion. Maintaining that a body in motion will remain in motion and that a body at rest will remain at rest unless acted upon by an external force seemed a reasonable and almost intuitive proposition after its statement. Unfortunately, the statement itself provides no method for measuring this force, and its utility is limited. In order for any postulate regarding physical interactions to be useful, there http://bbs5.techyou.org/?fromuser=sergio147 must be some way to quantify the results and to accurately predict future results given enough facts or data. It seems that Newton may have felt that the idea of force was intuitively known and did not need further explanation. Even though most of us proceed through life without being bothered by much thought of the concept of force, that sentiment does not pervade all of theoretical physics. The ideas of force and energy are still subjects of great conjecture and debate. The history of the development of physical concepts is not the prime concern here, but some knowledge of their evolution does serve to bring more closely to our attention and scrutiny a better appreciation of terms that we employ daily. Sometimes it is necessary to begin understanding or developing a body of knowledge in order to make certain basic assumptions on an entirely intuitive basis. As scientifically unsatisfying as that may be, it is unavoidable at times. One could draw a weak comparison to plane geometry (Euclid) with regard to its various axioms and the declaration that parallel lines never meet. Even the concept of straight lines is rather intuitive in nature. Perhaps the best definition is that a force is required to change the motion of a body.
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Many problems arise in finding acceptable definitions for the basic parameters of physical science, namely, the abstract concepts of mass, time, force, and energy. However, we must learn to be satisfied with definitions that leave something to be desired in order to move on toward generating a working body of mechanics that enables us to design and build practical devices that serve our purposes. An interesting definition of energy comes from the Grolier Encyclopedia, which states: Energy can be measured in terms of mechanical work, but because not all forms of energy can be converted into useful work, it is more precise to say that the energy of a system changes by an amount equal to the net work done on the system... In classical physics, energy, like work, is considered a scalar quantity; the units of energy are the same as those of work. These units may be ergs, joules, watt-hours, foot-pounds, or foot-poundals, depending on the system of units being used. In modern science, energy and the three components of linear momentum are thought of as different aspects of a single fourdimensional vector quantity, much as time is considered to be http://bbs5.techyou.org/?fromuser=sergio147 one aspect of the four-dimensional space-time continuum... Energy exists in many different forms. The form that bodies in motion possess is called kinetic energy. Energy may be stored in the form of potential energy, as it is in a compressed spring. Chemical systems possess internal energy, which can be converted by various devices into useful work; for example, a fuel such as gasoline can be burned in an engine to propel a vehicle. Heat energy may be absorbed or released when the internal energy of a system changes while work is done on or by the system. (1993) The force of gravity on ponderable bodies that have the quality or property of mass is given as Mass x gravitational acceleration constant = M x g.
(2.3)
From experience we learned that the larger (more massive) the body the greater the force needed to accelerate that body to the same velocity on a smooth, low friction surface. The rationale of defining the mass and force is rather circuitous because we employ the same phenomena to assess each parameter. In determining
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Figure 2.2 Weight of a mass due to gravitational attraction.
the mass of an object, its weight is used. Hence, the more a body weighs the proportionately greater is its mass. The property of a body's mass to resist being moved or accelerated is known as inertia. Thus, a mass that is acted upon by a gravitational force has a weight directly proportional to its mass. Since all bodies fall in a constanthttp://bbs5.techyou.org/?fromuser=sergio147 gravitational field with the same acceleration (Galileo), the gravitational and inertial masses are declared to be one and the same. This principle of equivalence explains why all bodies, when acted upon by gravity and permitted to fall freely with no opposing forces, will experience the same acceleration. Hence, the velocities they attain over the same vertical distance will be equal. The force acting upon a mass with a gravitational mass, M is Fg = M g g .
(2.4)
The inertial mass, M., which is accelerated by some force, F, described in equation 2.2 is expressed as F = M.a.
(2.5)
More properly, force is defined as directly proportional to the rate of change in momentum of a body, or d(mv)
dt
(2.6)
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With this assumption of equivalence, or M. = M , we arrive at a means of measuring force in a quantitative manner. A mass of 1 kg is thought to have a force of 1kg times 9.80m/sec 2 , or 1 Newton. In the "c-g-s" system (centimeter-gram-sec), 1 gram of mass has a force of 1 dyne exerted upon it by gravity at the earth's surface. The acceleration constant of gravity in the metric system of measurements is 980cm/sec 2 . In the English system of units, the acceleration, g, is 32 ft/sec 2 , and in the metric system g = 980 cm/sec 2 . By inspection we see that the unit of force, as defined above, is F = MLt" 2 .
(2.7)
Now, is that true for all types of forces, including electrical and magnetic? The answer apparently is yes. As the need arises in the development of our discussion of energy, we will explore each of these types of forces. Returning again to the main topic, we will see how the idea of energy is explored and how a useable and quantitative definition is generated. The formulation of relationships in physics involves http://bbs5.techyou.org/?fromuser=sergio147 a lot of mathematical trickery. Some of these manipulations might even appear at times to employ the practice of self-deception in order to arrive at the desired answers to posed questions. For instance, the derivation of the very familiar expression for kinetic energy, l/2mv 2 , is interesting. How is it that the energy of a moving body with mass, m, is the product of its momentum, mv? Plus, where does the factor Vi come from? Look again at how we have defined the idea of energy, or work, in equation (2.1) as the sealer product of force times distance. Without questioning further at this point how we have justified this leap of confidence, the next step is to quantify the idea. If force can be defined as the product of the mass of a body times the acceleration produced by that force acting upon the body, as in equation (2.2), then an increment, dE, in energy, E, in moving a small distance, dx, can be represented as d2x dE = F - d x = m a - x = m — ^ - - d x , dt
(2.8)
where acceleration, a, is represented as the second derivative of distance with respect to time.
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So far so good, if we accept the force times distance premise. It is now necessary to integrate distance in order to obtain an expression for a finite amount of energy produced by a force, constant or otherwise, moving through a distance, x. Thus,
E=fF-dx = mf^-4-dx. J
J
dt
2
(2.9)
Since acceleration is the first derivative of velocity, v, we substitute d v / d t for acceleration in equation (2.8) and obtain E = m f — dx. J dt
(2.10)
If we make the dt term the denominator under dx, we obtain another velocity term under the integral sign and have the following upon integration: E = m[dv
= m f v - d v = —mv 2 , dt 2
J J http://bbs5.techyou.org/?fromuser=sergio147
(2.11)
the well accepted formula for the instantaneous kinetic energy of a moving body. The problem of defining energy has been attacked in a rather pragmatic fashion. We know that lifting weights requires doing what we generally call work, and that weight lifting can be converted into other useful forms of work, such as turning a paddle wheel, grinding grain, and powering wood working tools.
2.2 Energy Sources There are essentially only four "primary" energy sources of which we are presently aware. There is only one source that we know of from which all others have derived, and that source is nuclear. This can be a philosophical issue, bordering on the question of primal causes. That question is perhaps unanswerable, and it has no relevance to our subject matter in this book, except to dispel some of the vague popular literature and general conversations on the problem of finding or developing alternative energy in order to meet the increasing demands worldwide.
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In actuality we know little of the causes and the effects, such as whether electromagnetic radiation is the result of nuclear (subatomic) phenomena or the reverse. Regardless, the overall macroscopic benefits to us on Earth are sunlight and all its attendant benefits and nuclear reactor systems. However, despite all the delightful speculations, the subject of available energy sources on Earth reduces to the following list: • Nuclear (in the form of radiation from the Sun) • Nuclear (in the form of terrestrial based reactors to produce steam power) • Gravitational (tides due to the motion of our Moon about the Earth) Various other substances and processes are referred to as power sources or energy, such as coal, petroleum, wood, wind, hydroelectric, etc. Yet, if we simply trace their sources back to the origin, then it becomes obvious that they are all different manifestations, perhaps in delayed fashion of the three sources identified above. For example, hydroelectric power and wind power http://bbs5.techyou.org/?fromuser=sergio147 are, in essence, different manifestations of solar energy. Water evaporating from bodies of water at lower elevations, as a result of solar heating, and transporting the vapor to areas of higher elevation to become rainwater for reservoirs can provide electric power. Similarly, solar heating of various ground regions causes air turbulence, which can be quickly transformed into horizontally moving air masses as wind and can be utilized for windmill operations. Burning coal or petroleum to run heat engines of various sorts merely makes use of the solar energy that was incident on the Earth's surface long ago and over a long period of time. These resources will eventually become extinct, especially at the increasing rate with which people everywhere are depleting them. The advertised searches for new or alternative energy sources need to be identified in clearer terms. If what is meant by "finding and developing alternative energy" is to actually find some source other than solar in one form or another, or nuclear, then that declaration is misleading, if not actually false. All we (science) know is clearly evident. Looking for an unidentified supply of usable energy is almost like looking for a new color that no one has yet seen - a rather impossible task.
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To look for this new, unidentified source implies discovering a new phenomenon in nature. Such discoveries do happen, but rarely by design or systematic searching. The development of new technologies comes only after a discovery has been made. At the turn of the last century, Henri Becquerel accidentally discovered radioactivity when his photographic plates placed close to uranium ore showed signs of exposure. In a series of steps over a rather short period of time other investigators such as Madame Curie, with her separation of radium from masses of pitch blend, and almost concurrently with Roentgen, who discovered what he called X-rays that emitted from a cathode ray tube whose anode was bombarded by high speed electronsery of X-rays, all suggested a far more complex structure of matter. Then, others such as Bohr and Rutherford began developing hypotheses and models to explain these new events in the laboratory. Without these discoveries we probably would not have any knowledge of nuclear processes or how to make practical use of the immense energy available from within the atom. Until there is one has empirical evidence of some new phenomenon, or at least a workable theory, there is little purpose to searching aimlessly http://bbs5.techyou.org/?fromuser=sergio147 for something that may not exist, and if it does exist, we have no idea what to look for. The idea of developing new energy sources is pointless, unless the intention is to engineer and make those sources, of which we are already aware, more readily available for application. Meanwhile, perhaps something will come along before the earth runs out of suitable radioisotopes and fossil fuels. It appears that until, and only if a truly new source appears, we will have to utilize the innumerable variations of presently known energy source systems.
Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
3 Conversion and Storage
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Energy storage is a growing issue in our society. Fossil fuel resources such as petroleum are becoming not only more scarce in some areas but also increasingly inaccessible and costly. Most nations are now addressing the possibilities of providing energy in as many forms possible from sources other than fossil fuel. Petroleum products have largely been responsible for the immense progress made in Western society. Since the beginning of the 20th century, petroleum products have enabled the development of railroads, aircraft propulsion, large ocean-traversing vessels, as well as the automobile. As far as we know now, there is no other equivalent source of energy in the form of combustible fuel, except perhaps for alcohol (ethanol). However, we are rapidly realizing that alcohol is not a practical solution to the greatly increasing demands for portable world energy. Here, we will briefly review the role and merits of many competitive mechanisms available for secondary energy sources, ranging from compressed air and fly-wheels to electrochemical cells. Electrochemical cells still appear to be the most promising method of storing energy, which is probably the principal reason for its attractiveness. There are many practical considerations 21
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involved in selecting one means for another to store energy for use overtime. Among these factors, perhaps cost is the most critical. Considerations such as safety, availability, life, dependability, cost, etc., would follow next. Unfortunately, nature doesn't provide unlimited choices to achieve an inexpensive reliable, safe, and readily available means of storing useful energy. To focus our attentions, we should establish two general categories of energy sources and identify them as primary or secondary. In reality, there is only one source in the strictest sense of the origin of energy. Secondary sources are actually intermediary places or devices where energy, from one of the few primary sources, is stored until needed at a later time. The next pages describe and compare the various mechanisms offered by nature and made practical by present-day technology to store energy, followed by a section on electrochemical systems that concentrates on the redox type of devices that now seem to offer the most promise for solving long-term storage problems. Subsequently, details of performance, electrochemistry, and methods of constructing and testing these systems are presented. http://bbs5.techyou.org/?fromuser=sergio147 First, in order to establish a firmer base, I have presented a physics background along with the development of an argument for redox cells as practical devices. This book describes a particular class of approaches to largescale energy storage. Large scale is defined here as amounts of energy exceeding 1 kWh that is stored in a single unit or group of energy storing units. The class of main interest here is that of reversible electrochemical cells. Since most cells or batteries with which we are familiar in our daily lives, such as the dry cell, alkaline cells, lithium ion batteries, and the ubiquitous lead acid battery, are not likely candidates, they will not be covered here. Only the approaches that have a chance to succeed as secondary batteries for solar, wind, load leveling, and emergency power applications will be discussed. Storing energy in its many forms in nature is a vital part of all processes and life itself on earth. As we explore these processes and their importance to us, we can gradually make some observations that lead to revealing and important conclusions. Unfortunately, nature is not very cooperative when it comes to providing a multitude of materials with the totality of desirable and needed properties, such as low-cost, safety, availability,
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electrochemically well-behaved in aqueous solutions, and a large enough energy and power density potential to make simple, practical storage systems. All applications or manifestations of energy storage can be put into one or more of these categories. Certainly, if we wish to power a portable power tool or an electric automobile, a hydroelectric plant is hardly useable. However, if we use the energy produced by the station for storage in an electric battery, it becomes a practical situation. That's an example of the portability or mobility reason for storage. In the second instance we might have the need to store solar energy during the daylight hours for use after sunset to power light, etc. There are many cases where the convenience factor is not met - where the generation of energy is occurring at a time that coincides with the need or application time. Must be pointed out here that when we refer to energy we are essentially referring to the "capacity to do work" in the classic sense of Force x Distance. It is this capacity that is being transferred from one source to another device that is capable of storing this capacity for work. http://bbs5.techyou.org/?fromuser=sergio147
Table 3.1 Energy sources accumulated by "natural" processes over recent and remote past. Energy Source
Process of Formation
Wind
Form of delayed solar, non-uniform heating of earth
Hydropower
Form of delayed solar evaporation and condensation, rain
Incident solar
Promptly available energy when converted to thermal or Photovoltaic
Tides
Gravity of moon and relative motion of earth & moon
Geo-thermal
Residual thermal energy (compression) of earth formation
Nuclear
Remnants of initial matter formation processes
Fossil fuels
Accumulated conversion of organic matter deposits (solar)
Organic fuels
Wood, hydrocarbon gasses, (delayed solar)
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Table 3.2 Man-made energy storing mechanisms (other than thermal). Metal stressing
Steel springs
Elastic deformation
Rubber bands
Elevated weights
Impact devices, clocks
Compressed gasses
C 0 2 or compressed air powered devices
Chemical reactions
Gun powder and explosive mixtures
Masses in motion
Fly wheels, rotating masses and linear, high-speed impact
Electrochemical
Batteries and fuel cells
Storage of energy in one form or another to be used at a later time has been extremely important not only to mankind, but also to every form of life. Storage of energy in the form of chemical structures such as carbohydrates enables life forms to survive for periods of time between food intake activities. http://bbs5.techyou.org/?fromuser=sergio147 Other, simpler forms of energy storage that are familiar to all of us are listed below. These forms of energy are categorized for the purpose of distinguishing between basic differences in the origin and the physical processes involved. Since all of the above are commonly known and familiar to the reader, there is little need to give many examples of each of these processes or mechanisms. It is interesting to note here that energy sources that are derived from "natural" sources provide, by far, the largest amount of the energy consumed by industry and commerce. Especially in the case of fossil fuels, the available energy density is much greater than any other competing made-made source for most common applications - nuclear power not included. Returning to a less esoteric domain, the outline of the presentation is a follows, listing the primary topics that will be covered: 1. Primary energy sources - On a grand cosmic scale, primary sources are limited to nuclear and gravitational. All subsequent forms of energy are consequences, as far as we know at present, of these two principal sources. These are sources over which man has no control.
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2. Secondary sources of energy - It is necessary to define what we mean by "secondary." Usually the definition involves some process of storing, and is associated with those resultant processes over which we do have control. 3. Conversion processes - Those devices that enable us to transform one form of energy into another more.
3.1 Availability of Solar Energy Indicative to this explanation is a comparison between the solar energy that is available from photovoltaic conversion mechanisms and the solar energy that is available via plants' conversion into combustible fuels, such as methanol. The total available energy via combustion from 1 gallon of gasoline in an internal combustion engine is about 36 kWh. The conversion efficiency of an automobile engine to mechanical output is at most about 20%. Thus, if we had very efficient electric motors instead, we would need to have at least 1/5 of the 36 kWh x 500 http://bbs5.techyou.org/?fromuser=sergio147 million gallons per day. That number is 3500 million kilowatt-hours of energy from sunlight per day. Again, if the conversion efficiency were 100%, dividing the numbers would reveal that we need about 5,000 square miles of area to provide the equivalent of gasoline. Unfortunately, we must multiply that figure by 10 to account for conversion losses, giving us a total of about 50,000 square miles. However, the following problem remains: How does one use solar energy to operate cars without storage? The practicality and cost of solar energy for consumer use. to power industry and residential homes has become a widespread concern that stems from questioning energy sources and their limits. A simple estimate of available solar energy per unit land area, especially if it is to be collected and transformed directly into electric power, reveals that immense land areas are required to provide even modest amounts of energy for commercial use as illustrated below. The following calculations present a rather dismal prospect for wide spread use of solar energy as a substitute for the more "conventional" sources presently in use. Regardless, the problem of providing energy to meet the increasing demands of the future is very serious. Other than oil and coal, there are no realistic answers. Nuclear, along with cheap and reliable energy
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storage (such as batteries), could be an answer to well designed, plug-in hybrid vehicles, giving a range of 200 or more miles on a single charge. As an example, consider a middle region of the North American Continent and use simple approximations. At high noon (normal incidence) on a cloudless day at the Equator, incident solar power surface density is in the range of 0.12 watts per square cm. Since sunlight is available only half the day (about 10 hours of useful daylight), the energy density is reduced to approximately 1.2 watt-hours per square cm per day. And, due to Earth's rotation on its axis, the sun's radiation makes a changing angle to the earth's surface perpendicular. Therefore, we can simply approximate that by another 50% factor. Hence, the energy density over a 24-hour period is further reduced to 0.6 watt-hours per square cm. The above energy per unit area per day becomes 0.6Wh/cm 2 = 3.6 Wh/in 2 , or 3.6 Wh/in 2 = 500 Wh/ft 2 . Since there are about 5,300 square feet per square mile, there are 5300x5300x500 = 28 million x 500 WH from 1 square mile, or 15,000 megawatt hours per square mile in any one clear day at the http://bbs5.techyou.org/?fromuser=sergio147 equator. At latitudes of the mid-USA region, we might need to divide that number by two, making the total sunlight energy equal to about 7,000 megawatt-hours per day per square mile of area. Now let's take a brief look at what the order of magnitude of the needs are for domestic energy per day or per year in the USA. According to the Web site called Globilis, the amount of energy produced and consumed per year in 2002 was 4 million kilowatt-hours. That number reduces to 10,000 million kWh per day consumption. So, if we want to produce (assuming 100% conversion efficiency of electromagnetic energy from the Sun) that amount of energy, we would need an area of about 1400 square miles. Present day efficiencies of solar photovoltaic cells are in the order of 10% to 20%. Using these lower efficiency figures, we need 7,000 to 14,000 square miles of accessible area to generate the electrical energy presently being used by the United States. Imagine the maintenance and access roads required for such a solar collector field. Simply the problem of keeping the surfaces of semi-conductors and collectors clean and repaired would be monumental. Now, consider the gasoline situation. The United States uses between 21 million barrels of oil per day (as of 2007). The yield at
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the refineries is about 20 gallons of gasoline per barrel of oil, which means we actually use over 400 millions of gallons of gasoline per day - an astronomical figure. The problem remains unsolved. In addition, we must also have available storage to make the energy portable and useable whatever peak-demands arise. Now, consider corn as a source of methanol. The data from the US Department of Agriculture shows that the average yield of corn per growing period of at least six months is about 150 bushels per acre. A bushel of corn will yield 2.5 to 3 gallons of ethanol. Ethanol has less than half the energy content per gallon than gasoline. Thus, we would obtain about 200 gallons of gasoline equivalent per acre of cornfield. Returning to the gasoline consumption rate above, if the United States consumes about 400 million gallons per day multiplied by 300 days per year, then the country consumes about 12,000 million gallons per year. After dividing the numbers for corn yield, close to 100 million acres of farmland would be required. A square mile is equal to 700 acres. After dividing again, it appears that about 150,000 square miles of farmland is needed under ideal http://bbs5.techyou.org/?fromuser=sergio147 circumstances - no provision is made here for roads, buildings, fertilizer, machinery, etc., which is not very encouraging.
3.2 Conversion Processes The following are non-mechanical methods for converting from one form of energy to another. A simple mechanical example would be the generation of electric energy by mechanically moving an electric conductor through a magnetic field as is done in a dynamo. This is intended only as a brief review of a few well-known means employed to convert energy from one form directly into an electrical output.
3.2.1 Photovoltaic Conversion Process The photovoltaic process converts direct conversion from light energy (photons) to electricity (volts and amps) via p-n solidstate devices. Electrons are raised to the necessary high levels of kinetic energy and cross over the junctions with a corresponding voltage.
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Figure 3.1 Photo-voltaic semi-conductor cross section.
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Efficiencies are 20+%, costs approximate $10K/kw, and thin film costs are less, but at lower efficiencies.
3.2.2
Thermoelectric Effects: Seebeck and Peltier
The search continues for materials with lower thermal conductivity, higher electrical conductivity, and higher Seebeck coefficients. Some materials that are used as a thermoelectric heat pump (cooling device), such as bismuth telluride, would give higher conversion efficiencies if they could be operated at higher sustained temperatures. Unfortunately, electrical contact deterioration, materials diffusion within the structure, and melting points exclude them from such application. The amount of heat loss due to heat conduction along the paths from the hot to the cooler junctions significantly contributes to conversion efficiency degradation. Joule heating, due to ohmic resistance of these paths, adds to the inefficiencies. The attractiveness of no mechanically moving parts does not quite make these devices practical, except in special applications where inertness and long life are important. In addition, these types of devices are subject to the ever-present Carnot efficiency limitations
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Thermoelectric couple
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Figure 3.2 Semiconductor thermoelectric couple.
encountered by all heat engines. Heat to electrical efficiency is 12 to 18%. Thermal energy, Q, pumped into or out of a thermoelectric junction per unit time is simply expressed as ΐπ =
dt
= current x Peltier voltage. ö
(3.1)
The Seebeck effect is utilized in many ways, but it is most commonly used in the well-known thermocouple used to measure temperature. The materials (usually metal alloys) are selected for this purpose on the basis of their thermoelectric coefficients and stability at high temperatures. The alumel-chromel, or ironconstantan materials couples, is very common. The Seebeck coefficient is very dependent on both operating temperature ranges and materials choice.
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3.2.3
M u l t i p l e P - N C e l l Structure S h o w n w i t h H e a t
It is necessary to conduct heat to and from the hot and cold junctions, respectively, in parallel for an array of junctions while still providing electrical conduction in series. At times this can be a somewhat formidable engineering and materials application problem. In general, semiconductor materials with large Peltier potentials, low thermal conductivity, and high electronic conductivity are desirable. Unfortunately, these properties can become mutually exclusive because of the physics of the processes. For example, at 300°C temperature differential, output is about 0.05 volts per junction.
3.2.4 Early Examples of Thermoelectric Generators Thermoelectric energy conversion systems were devised in the midnineteenth century and employed for limited practical purposes to
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Thermal conductor Electrical insulator
Thermal conductor Electrical conductor
Figure 3.3 Multiple themo-electric junctions - thermopile. From: Introduction to energy technology, Ann Arbor Science, 1976.
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Materials are usually: BiTe, PbTe, Sb-Sn (n & p-types) Figure 3.4 Russian power supply for radios combined with an oil lamp also providing in remote areas. From: Semiconductor thermoelements, and cooling, by A.I. Joffe, USSR, 1956.
operate communications equipment. There are records of Edison experimenting with very large arrays of metal alloy wire junctions wrapped around Franklin stoves to generate sensible electric power. In more recent times, numerous similar devices were constructed in Russia and utilized to broadcast news and propaganda to remote
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ENERGY STORAGE
Figure 3.5 Illustration of an operating thermionic converter.
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areas in that country that had no other sources of electrical power to operate radios. 3.2.5
Thermionic Converter
For a thermionic converter, theoretical efficiency is about 75%, practical efficiency is about 15%, and the hot electrode comes to about 1600-2000°C. These devices, with a perhaps misleading name, convert heat energy into electrical output primarily by "boiling" conduction band electrons from metallic surfaces placed in a vacuum. The drawbacks to this approach seem to be largely associated with their operating life, particularly with the emitter. 3.2.6
Thermogalvanic Conversion
Thermogalvanic conversion is a process going directly from a temperature differential to an electrochemical potential. An example of a symmetrical cell employing the phenomenon described by
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the Gibbs-Helmholz relationship is shown in Figure 3.6. For thermogalvanic conversion, d E / d T ~ 0.01 volts per deg C, efficiency is about 15%, and temperature range is from 140° on the cold side to 350° on the hot side. There is another mechanism for transforming heat energy directly into electrical form without the necessity of mechanically moving parts or any other such complexities. As in the case of thermoelectric effects, there is an analogous one in chemistry. It is known as the thermogalvanic effect, as expressed by the Gibbs-Helmholtz equation. At first glance, this could be mistaken as another colligate property of matter. However, upon closer examination we see that the electric potential /temperature behavior of substances is quantitatively dependent upon the material property itself, namely, the free energy of formation as a function of temperature. The equation relating the enthalpy, H, and the free energy change ΔΡ, to the rate of change of free energy with temperature is AF = AH + T
9(AF) 9T
(3.2)
Jp http://bbs5.techyou.org/?fromuser=sergio147
where pressure is assumed to be constant. The equivalent of free energy can be put into terms of voltages and the quantity of electric charge, e.g., AF = -nF f E watt-seconds,
(3.3)
where E is in volts, Ff is Faraday's number of 96,500 coulombs per equivalent, and n is the electric charge on the ion. Thus, we then have the following equation as a net expression for the change in electrochemical voltage as a function of temperature: r)E n F f T — = AH + nF f E, dT
(3.4)
dE/dT = AH/nF f T + Ε/Γ.
(3.5)
or
By applying this last relationship to a symmetrical "thermo-galvanic cell" that employs the silver/silver chloride electrodes, as shown in
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ENERGY STORAGE
Limitations: Low efficiencies, about 15 to 20% Limited operating life before polarity reversal is necessary Irregular accumulation of silver causes short cycle life Advantage over semiconductor thermoelectrics is much higher couple voltage dE/dT - http://bbs5.techyou.org/?fromuser=sergio147 1CT 2 volts/deg-C Figure 3.6 Thermogalvanic cell depiction employing silver iodide electrolyte.
the drawing below, the value of dE/dT at an average temperature of 300°C can be estimated from enthalpy data that is readily obtained from sources such as the Handbook of Chemistry and Physics, published by The Chemical Rubber Publishing Co. Solid silver iodide, or Agl, was explored some years ago as a possible electrolyte for a galvanic version of thermoelectricity. This compound has properties that lend themselves to such application because its electrical ionic resistivity as an electrolyte is a usable range, and the gradient of voltage versus temperature has unusually high values. Some of this data is presented in Figure 3.6.
3.3
Storage Processes
3.3.1 Redox Full-Flow Electrolyte Systems The storage of electrical energy in chemical form by reversible electrochemical processes is in widespread use. The main
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limitations to all present electrochemical couples (batteries) are their shelf and cycle (operational) life as well as their energy density and power delivery capabilities. For stationary applications, energy and power densities are not of primary importance. Their energy turnaround efficiencies, cost, and operational life are more significant. This technical exhibit describes an electrochemical cell, which stores energy on the basis of concentration differences at opposite electrodes and between the same chemical species. The low electric potentials at which these cells operate eliminate the possibilities of water electrolysis and the formation of hydrogen or oxygen gas at the electrodes during charging. Thus, a sealed system can be constructed that requires no maintenance. Since the cell is chemically symmetrical, its cycle life is indefinitely great. One of the few basic electrochemical processes that can be employed in an energy cell and also has little deleterious effects upon either electrode or cell structure materials is S + 2e<=>S = .
(3.6)
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This energy storage system is described and compared with other methods as candidates for numerous space applications. This technical exhibit is about simple energy storage for applications where reliability and life are among the primary considerations. In those cases where the primary energy is generated from solar, wind, tides, and even I.C. engines, there is a need for storage for some period of time. This energy is then used at a later time when the demand requires it. The electrochemical system that is proposed here and identified for reference convenience as a symmetric cell appears to be an attractive process. A brief review of a number of more likely competitive systems in terms of performance is also presented. Cell electrochemistry, transport processes, and cell performance are also presented here.
3.3.2 Full Flow and Static Electrolyte System Comparisons Redox cells with two electrolytes and all liquid reagents can be designed and operated as either static electrolyte systems or full flow electrolytes. In the first case the electrolytes remain in their
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ENERGY STORAGE
respective compartments (negative and positive sides of a cell with a barrier or membrane separating the two compartments) as in conventional batteries. The drawing in Figure 3.7 below shows such a basic design. The static electrolyte version of the redox cell offers the advantages of simplicity in design, no mechanically moving parts, and it is easily sealed. However, the energy and power densities of any particular cell design are a compromise because inter electrode cell spacing will affect both coulombic capacity as well as internal cell resistance and reagent availability for discharge. Also, charge retention time is significantly smaller because of ionic and molecular diffusion across the membrane separator. In the full flow configuration, the two electrolytes are circulated from reservoirs into and out of their respective cell compartments through appropriate manifolds and pumps as shown in the Figures 3.8 and 3.9. The following are the advantages of this design approach: • Indefinitely long charge retention times • No cell imbalance problems with large cell arrays http://bbs5.techyou.org/?fromuser=sergio147 • System can be electrically shut off by electrolyte draining • Separation of energy capacity from power delivery parameters in system designs • Ability to be recharged chemically by replacing electrolytes • Electrolytes may be electrically recharged in an external device In some applications the advantages or salient characteristics of full flow redox may outweigh the necessary additional complexity and mechanisms. In striving for the realization of a very long-life, secondary battery, one of the developmental paths that can be followed is the use of reagents that remain in solution at all times. In other words, there is no deposition, removal, or change of composition or change in structure of solid reagents at electrode surfaces in the energy storing process. There are very few choices of chemical components that have all the properties necessary to make it a practical electrochemical process. Those that are candidates are listed in Chapter 5 of this book. Virtually all of the materials combinations have the
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Static redox cell in discharge mode
Figure 3.7 Fixed electrolyte redox cell. http://bbs5.techyou.org/?fromuser=sergio147
Figure 3.8 Full flow electrolyte redox battery system.
singular drawback of having dissimilar materials on opposite electrolytes. Furthermore, since these reagents are in solution, there is the inexorable transport of catholyte materials into the anolyte region and vice versa. In most cases, there is no direct method of
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ENERGY STORAGE
Separation of power output from energy storage system parts Example shown below of internal combustion engine and the fuel storage
Horse power hours Gasolene tank
i-iorse power Fuel Mechanical pov http://bbs5.techyou.org/?fromuser=sergio147 I.C. Engine
'
Oxidizer, Air
Figure 3.9 Comparison of power/energy separation to I.C. engine system.
returning these unwanted components from one. electrolyte to their origin. An example of such a red ox cell is the chromium/iron couple where chromium and iron chlorides are in the negative and positive sides of a two-compartment cell. Since the energy process participants all have positive charges, once any chromium diffuses to the iron side of such a cell it is lost permanently. This type of transfer of ions results in a gradual deterioration of the electrolyte, and the cell will cease functioning until a new electrolyte is introduced from an external source. Another example of a redox system employs the sulfur/bromine couple and was first developed by TRL, Inc. for National Power, PLC. This is also a materials asymmetric couple whose
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cycle life is limited by unwanted diffusion of sulfide ions from the negative cell side into the positive, bromine side. Cation membranes are employed (usually NAFION) to maintain effective electrolyte separation, and cycle life can be large, but the electrolytes must be chemically processed periodically in order to sustain performance. The only redox system that employs the same chemical species for energy storage currently in development (University of New South Wales, Australia) is the vanadium redox. In order to recognize an operating cell that meets the conditions of all liquid electrolytes and has the same chemical reagents on both sides, it is necessary to have at least three oxidation states of an anion or cation that are soluble in a polar solvent such as water. Vanadium is the only element with those properties that is reasonably well behaved. The circulating electrolyte design being pursued for load leveling application is illustrated in the drawing of Figure 3.10.
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Electrolyte storage tanks for positive and negative electrolytes, energy conversion cell, pump for circulating electrolytes and pipes. (This battery delivers or stores electric power by changing the oxidation states V(2), V(3), V(4), V(5) of vanadium ions.)
Figure 3.10 Schematic of a vanadium redox cell.
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ENERGY STORAGE
In principle the electrolytes should have an indefinitely long life because vanadium ions are on both sides of the cell, and any unwanted diffusion can be corrected electrically by the transport during the recharging mode. Some limitations, however, are (1) high cost, (2) electrolyte maintenance, (3) hydrogen evolution and an ineffective seal, and (4) energy density limited by materials solubility in water.
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Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
4 Practical Purposes of Energy Storage http://bbs5.techyou.org/?fromuser=sergio147
4.1 The Need for Storage Despite the continuing disappointment with using electrochemical batteries for long-term, bulk, or even vehicular propulsion power, they are still favored in many applications, ranging from small vehicles to computer power, because of their inherent simplicity in configuration and because they provide direct output power directly in electrical form. However, virtually none of these various electrochemical systems (other than the familiar lead-acid battery) have found its way into extensive and practical use. In most instances, they are in the stage of engineering prototypes or demonstration projects and publicly funded programs. Immense attention and support has been expended on energy matters in recent decades, mostly with regard to its sources or production, i.e. wind, solar, methanol fuels, etc. Relatively little resources have been devoted to the storage of energy. In fact, a significant number of the problems with which we are faced could be resolved with more effective storage. Energy is frequently available to the user, but often not at the needed time or location. 41
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Usually, until a technology shows immanent promise as practical, industrial a n d / o r commercial products, they are not supported by commercial enterprises, which must realize a return on investment in the predictable future. A recent exception to this is the lithium-ion or polymer-based technology, which has found widespread use in portable devices such as computers, navigation equipment, cameras, etc., and use as auxiliary power for electric hybrid cars. Despite its limited life and rather high cost, it presents an opportunity for making some progress in areas in which other batteries cannot be applied. Let us take a brief look at the overall energy situation about which there is so much scientific discussion. The broad view certainly encompasses not only the issue of storage but also the matter of primary energy sources. In actuality, we have very few options. From a very practical standpoint there are only two primary sources, and they are either solar or nuclear energy. (More will be discussed in later chapters.) The position that seems to predominate any discussion these days about the environment and energy favors alternative energy sources. What arehttp://bbs5.techyou.org/?fromuser=sergio147 these alternatives? Unfortunately, there are precious few alternatives that we are, at present, aware of to "solve the world's energy problems." In Chapter 5 we will examine these options more closely. For the present, the options can be summed up as being either fossil fuel (petroleum products) processes or nuclear processes. All others, such as wind, solar photo-voltaic, geothermal, lunar, etc., are at best only supplementary sources when one considers the immense amount of energy that we use and will increasingly continue to use on a global scale. We are no longer at the level of one manpower to one horsepower per person that was predominant well before 1900 in Western civilizations. Now we are at the tens to hundreds of horsepower machinery at the disposal of each person. To sustain the level of accommodations in travel, living comforts, and convenience that Western countries enjoy will require increasing amounts of readily available energy. Meanwhile, our oil reserves are surely dwindling because they are finite (no new oil deposits are being created on earth at this rate of usage), and the demand is increasing. At present, wind and solar, other than solar thermal, provide small amounts of intermittent and usually unpredictable power to the user. There are no large-scale, practical, and economic means available as yet to store vast quantities of energy to make their extensive
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use practical. In most instances, windmills and solar collector field outputs are connected to a nearby electric power utility to "level" the power in a continuous fashion. We certainly don't want to be in a situation where our electrical appliances work well only when the sun is shining brightly or only when there is enough wind. Hence, we must either store this energy when the source is producing more than we need at that moment, or we sell our excess wind-generated power at windy times to a power grid, and then buy some back when the local moving air mass (wind) is insufficient to power our home, office, or factory. That situation ties everything inexorably to available power lines. That restriction reduces the places where alternative sources such as these can be employed effectively. Hence, no remote, stand-alone wind or solar power is practical without storage. All of the above are fine as auxiliary power for perhaps reducing the use of and our dependence upon fossil fuels. However, unless we drastically change our way of life in the more civilized and prosperous parts of the world, these measures will not solve our overall energy needs for the future. So far, the only two sources with http://bbs5.techyou.org/?fromuser=sergio147 universal applicability are fossil fuels and nuclear. Nuclear along with hydro can run virtually all of our stationary power needs. However, portable nuclear power is very limited to large vehicles such as ocean-going ships. There has been much speculation about developing nuclear powered aircraft and large land-going vehicles. Unfortunately, the issues of fissionable mass criticality, controls, safety, radiation, and shielding greatly limit its applicability to moving conveyances. Certainly, we cannot look forward to street buses and private cars being powered this way. That leaves us with the situation of how to power all the various vehicles and industrial equipment even if we have universal nuclear power for power generating plants. Should we use gasoline, diesel fuel, or propane? Perhaps, but there may be a time in the not so distant future when science will have found either a new source of portable energy or an entirely new approach (mechanism) for the creation of available energy, in much the same fashion that, prior to 1900, nuclear energy was inconceivable. Knowledge of the atomic nucleus, with all of its associated subatomic particle physics, gamma radiation, relativity theory, and quantum mechanics, didn't exist. Thus, there was no way to even think constructively about such matters before that time.
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Similarly, there may indeed be a whole way of attacking the energy question if we were armed with new knowledge of the nature of things in the Universe. Then again, there may not be any other alternatives beyond what we now know about matter, energy, space, time, etc. If there is some qualitatively new approach that utilizes new principles of physics in generating usable energy to satisfy our needs, and if we find it in time, the limited availability of fossil fuels may just buy us that needed time without having to change our life styles too drastically. However, storing energy effectively would make all primary energy sources available for many applications, including load leveling. It would also enable us to physically transport available energy from one place to another without wires. In addition, electric vehicle propulsion could become practical. Storing energy in a directly useable, electrical form, as distinguished from compressed gas, would be ideal. Batteries and some forms of regenerable fuel cells offer that opportunity. They are able to store energy provided electrically from a source (e.g., generators, solar photo-voltaic) by changing oxidation states of ionic materials. http://bbs5.techyou.org/?fromuser=sergio147 Then they are able to deliver the major portion of that energy at a later time directly in the form of electrical output. Virtually all of the complexities and inefficiencies of converting from one form of energy to another is avoided. Converting, for example, from mechanically moving components, such as expanding gas or rotating flywheels, requires a generator and regulation. An electrochemical device requires little ancillary equipment. The basic simplicity of such systems make them quite attractive, even though in most instances there is the necessity for electronic circuitry to manage the power and probably convert from ac to dc and back again.
4.2
The Need for Secondary Energy Systems
The ability to store energy from a primary source for later use is important in many situations, especially when that primary source of energy is from an uncontrollable and variable source, such as solar radiation through the atmosphere at the earth's surface. Even in those instances where the primary source is controllable, such as in petroleum-fueled gas turbines, there may be a
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45
need for peak bursts of power at random or scheduled times. Also, the ability to store energy would provide uninterrupted power delivery to the electrical load in those instances where a temporary breakdown or malfunction is encountered at the primary source. The diagram of Figure 4.1 illustrates the idea of the multiple functions that storage might provide in a total energy system. The storage stage shown can serve the following purposes: • Provide uninterrupted power • Briefly provide peak power exceeding that of the primary source • Smoothing function in those instances where the power from the source is not constant • Standby, emergency source.
4.2.1 Comparisons and Background Information There are a number of mechanisms that have been employed, and currently still are, for storing energy to either make it porhttp://bbs5.techyou.org/?fromuser=sergio147 table from one place to another or use it for peaking and standby purposes. Among the more common methods are the following, listed along with their respective energy densities and general areas of application. Where the primary energy source is electrical, such as in photovoltaic collectors, the secondary electrochemical cell has proven most applicable and practical. There are those instances where the primary source is in the form of mechanical energy.
Primary energy source
Storage, buffer stage secondary battery
Electronic control system
Figure 4.1 Function of storage in a total energy system.
Electric load
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Table 4.1 Secondary sources, energy storage methods. Process
ED, wh/lb
Use or Application
Springs
0.02
Suspensions, triggers
Ultracapacitors
1
Peak power
Compressed gas
lto4
Propulsion and starting
Flywheels
4 to 7
Peak and interim power
Batteries
10 to 40
General purpose
and the flywheel is the practical solution to smoother operating characteristics, but its energy density is quite low. Electrical capacitors also have low energy densities, and their problems with use are compounded by the steep discharge curve and the necessity to operate at very high voltages in order to obtain even modest capacities. There are a few more options for storage such as superhttp://bbs5.techyou.org/?fromuser=sergio147 conducting magnets and full flow redox, but they all seem to be complex in construction as well as in operation. To date, these options seem to not offer significant improvements in storage capabilities over more conventional systems. Even though electrochemical cells offer the simplest form of storage, batteries have their own limitations and problems. Their relatively short life in conjunction with high costs and very limited energy and power densities creates a rather discouraging picture for widespread applications where large amounts of energy must be stored. To date, it appears that the lithium-ion cell and the vanadium redox system are in the forefront for application, respectively for motive power, and for load leveling applications. If we are to develop alternative energy sources such as solar and wind power, it is mandatory that some form of practical storage be available. These alternative (non-fossil fuel) sources are mostly unpredictable and very dependent upon climatic conditions and the time of day necessitating either storage or connection into a very large power grid where loads and sources can be shared and programmed. Without some form of storage, stand-alone solar and wind systems would not be practical.
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Fossil fuels have been providing us with a primary source, and it represents the basis upon which most of our society functions. Petroleum derivatives provide more than an order of magnitude greater energy and power densities than any other source of portable power. In the case of hydrogen/oxygen fuel cells, energy is stored by generating hydrogen from some primary energy source as fuel for use at a later time in an electrochemical cell. Hydrogen gas is generated by employing one primary energy source or the other, e.g., hydro-electric, nuclear, solar, etc., and it represents a portable means of storing energy for use at a later time by being oxidized in a heat engine or an electrochemical fuel cell. It is important to emphasize that redox types of electrochemical systems offer the greatest promise to date for a solution to storing large quantities of energy in a stationary situation. The promise of success is largely due to the higher degree of control available in full flow cells compared to fixed electrolyte and reagent cells. Redox offers independence from cell imbalance problems and the possibility of very long life since reagents are fluids and there are no solid deposits on electrodes. The only possible competition at http://bbs5.techyou.org/?fromuser=sergio147 present seems to be the possibility of the "liquefaction" of coal as a fuel for the internal combustion engine. Speculating further, there is always the possibility that combustible fuels, resembling the organic hydrocarbons, can be artificially produced by some process at large centers of primary energy sources such as the nuclear reactor. However, all of these appear to be a ways off in the future, if ever, in a practical sense.
4.3
Sizing Power Requirements of Familiar Activities
Examining the energy needed to perform a number of familiar activities may prove informative. Some of these activities are common, everyday actions. The illustrations that follow emphasize the familiar in order to gain some perspective on the range of energy and power required to perform various common tasks. One of the most common activities with which many can identify is the act of throwing a ball. A hardball baseball weighs
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approximately Vilb, and when thrown by an adult with some practice, it achieves velocities in excess of 50 to 60 miles per hour. Speeds of over 80mph have been reported. Consider the case of a 60mph ball speed. That corresponds to 88 feet per second. To calculate the energy of motion, we use the formula 1 /2mv 2 , with m being in units of slugs in the English system. The exercise in estimating the energy and power associated with throwing the ball is as follows: 1 , Kinetic Energy = — m v 0.51bs 32ft/sec 2
(88ft/sec) 2 ft - lb = 60ft - lb. (4.1)
Remember, the mass units have been converted to slugs by dividing the weight by the acceleration of gravity. That amount of energy would be equal to, for instance, the impact energy of dropping a 1 lb weight from ahttp://bbs5.techyou.org/?fromuser=sergio147 height of 60 feet. Now consider the power involved. If you recall, power is the rate of doing work, or expending or transferring energy. A simple estimate of the power that a human arm can develop for a brief period of time is found by taking the above information and making a few realistic assumptions. The swing or arc of the pitcher's arm from the beginning of the throw to the moment the ball is released will be approximated as 180°, or half of a full circle. The radius of the pitcher's arm is about 2.5 feet. Hence, the total distance through which the ball is accelerated· to its release velocity is Arc D i s t a n c e = - ( 2 R J C ) = 2.5π« 8ft.
(4.2)
Next, if we assume that the ball is linearly accelerated through the throw, an average speed of the ball through the arc while still in the hand of the pitcher is about 44 ft/sec. The time then spent in accelerating the ball is 8ft/44ft/sec = 0.2sec. During this short time, about 60 ft-lb of energy was imparted on the ball, corresponding to 300 ft-lb per second as the average rate of
PRACTICAL PURPOSES OF ENERGY STORAGE
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doing work, or power output of the pitcher's arm. Converting this number to other, more familiar units, we get 300 ft-lb/sec = 300 ft-lb/sec/550 ft-lb/sec-hp = 0.54 hp, (4.3) or 0.54 hp = 0.54 hp x 746 w a t t s / h p = 400 watts.
(4.4)
So, it seems that a human can generate significant amounts of power, but only for very brief periods of time. 4.3.1
Examples of Directly Available Human Manual Power Mechanically Unaided
4.3.1.1
Arm Throwing
An experienced baseball player can easily pitch a ball at 60 mph. Taking the data available for a typical ball pitching, the following http://bbs5.techyou.org/?fromuser=sergio147 information is generated: • • • • 4.3.2.2
Ball weight ~ 8 oz Propelled velocity ~ 88 ft/sec Kinetic energy ~ 60 ft-lbs Power Out for 0.2 sec ~ 1 /2hp ~ 400 watts. Vehicle Propulsion by Human Powered Leg Muscles
As an addendum to the above, consider the amount of energy a human can generate on a sustained, but limited, basis with leg muscles only. This is illustrated below in the form of bicycling uphill. Employing the same mathematics as before in ball pitching, we can see how much power is required to pedal at different speeds up hills with different inclinations. A 1801b man with a 201b bicycle, pedaling at the speed of 3 mph, moves vertically at the rate of grade fraction x speed. In the steepest case shown in Table 4.2, a speed of 5 mph is 88x5/60 = 7 ft/sec. At a 5% grade, that would be 0.05 x 7 = 0.35 ft/sec in the vertical direction. Lifting 200 lbs at a rate of 0.35 ft/sec requires about 70 ft-lb/sec of power. Assuming a 100% efficiency of the bicycle
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Table 4.2 Hill climbing: 1801b person + 201b bicycle. 3% grade at 3 mph
- 5 0 watts
5% grade at 3mph
-100 watts
10% grade at 5 mph
-200 watts
mechanisms and no friction loss to the road surface, converting to hp and watts results in almost 100 watts. Using similar arithmetic, the numbers for a bicyclist climbing different hills at different rates are shown below. As we know from experience, it is possible to sustain such effort for only brief times, perhaps limited to minutes rather than hours of such power outputs. Before leaving the realm of human muscle power capabilities in transforming one form of energy into another, we will make an estimate of the sort of performance that can be achieved with the use of mechanical aids that enable us to store some energy over a short http://bbs5.techyou.org/?fromuser=sergio147 time to be released in an even more brief interval of time. The use of spring-like materials, such as resilient wood and steel, have enabled us to hurl objects much further and with greater speeds than are possible by efforts of directly throwing. A classic example of this is afforded by the bow-and-arrow of antiquity and modern times. The limit to the storable energy is, of course, the arm and shoulder strength of the archer. As a sample calculation, let us assume that the archer is capable of exerting a 100 lb pull on a bow string, and that the string is pulled back a full 2 feet from its rest position. In addition, if we assume the arrow weighs about 4 oz (while these figures may not be completely accurate, they are sufficient for illustrative purposes), then the computations below follow. There is a constant force term, k, that one can assume for the bow that expresses the force as a function of the tension or stretch of the bowstring. That distance, x, at the center of the bow is the difference from the zero point of the string when there is no pulling force to the position of the string center at maximum extension, or pull. The incremental force, dF, is then
dF = kdx
(4.5)
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4.3.1.3 Mechanical Storage: Archer's Bow and Arrow The energy, E, stored in the bow string upon extending it a distance, x, from the relaxed position and normal to the string is
E = J"kxdx
(4.6)
where k is the "spring constant" of the bow. If we assume that k is constant over the string extension, then E = l/2kx 2 . For a bow and arrow with the properties given below, we obtain the results shown for energy and speed of the projectile: • • • • • •
Full Bow Pull-1001b Total string displacement ~ 2 feet Arrow weight ~ 4 oz Energy imparted to arrow ~ 100ft-lb Exit velocity ~ 112 ft /sec ~ 76 mph Power out for 0.018 sec ~ 1 hp.
The energy with which the arrow leaves the archer's bow is quite http://bbs5.techyou.org/?fromuser=sergio147 high, and the speed exceeds that which throwing can attain. This was a formidable distance weapon in its time, and it still is employed for silent or stealth operations. The exit energies of other projectiles, such as bullets propelled by gunpowder, is mentioned elsewhere in this book. Among the more commonly found forms of portable energy sources for general use are the myriad electrochemical cells and batteries that are available everywhere and are used for almost every imaginable purpose. These applications range from the flashlight to large batteries that are used to start internal combustion engines and to power electric vehicles. These are all secondary devices in the sense that the capacity for releasing or making energy available to the user has been provided by some primary source at an earlier time. In the case of a primary battery, its energy deposit is made at the time of manufacture. In the case of a rechargeable battery, its ability to repeatedly store energy upon electrical recharging has also been provided at the time of its manufacture. At the other extreme is the hydroelectric generating station or dam. Here also, the system is secondary because the water at a useable elevation in the reservoir was provided by the sun as accumulated rainfall.
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These two secondary sources have the energy characteristics given below: • Flash light with 2 D-cells ~ 0.5 to 1 watt over 5 to 10 hours intermittent • Hydro-electric Generation (water fall) at 40 gallons per minute from 100 foot elevation ~ 1 hp (746 watts). There is a huge difference in the economics, the life, and the practicality of all the various means of storing and making available energy for practical purposes. A quick look at the costs of the energy from these two sources is pertinent in our overall views on the subject. The purchase price of a D-cell alkaline battery with a useable capacity of around 6 watt-hours is approximately $1. That would make the cost of energy on a larger scale about $160/kwh. Compare that to the figure of about $0.10 per kWh for energy from an electric power utility. This should help explain why we don't use primary batteries to power electric cars or our homes. However, the convenience factor of having a small amount of http://bbs5.techyou.org/?fromuser=sergio147 portable energy and power when needed for lights, computers, and other electronic apparatus makes it well worth the cost - as long as we are not using large amounts of energy at that cost rate. The single shortcoming of an electrochemical battery is its inability to deliver high, short-term bursts of power that one can obtain from chemical reactions like explosions or mechanical contraptions like catapults and large springs.
4.4 On-the-road Vehicles Now, we will turn our attentions from human powered efforts to devices that are capable of doing greater amounts of work, devices such as the internal combustion engine in passenger cars. Consider the amount of energy and power required to propel an automobile in its different modes of operation. The least amount of energy per unit time is needed to maintain cruise speeds, but much more power is required in accelerating and hill climbing. And, of course, passing on an upgrade hill is the most demanding on power from the engine. Most modern cars
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are designed with engines that will deliver the type of performance that the motorists demand under the worst conditions. That means that the purchaser is buying a vehicle with a power plant significantly larger than what is needed to more slowly climb hills and that perhaps doesn't accelerate from 0 to 60 mph in less than 10 seconds.
4.4.1 Land Vehicle Propulsion Requirements Summary A typical or test vehicle that weighs about 3,0001b when loaded with passengers is used here for illustrative purposes. The table below lists a few of the energies and power levels required to accomplish the cited performances. At 60 mph the kinetic energy of the vehicle is - m v 2 = -(30001bs/32 ft/sec 2 ) x (88 ft/sec) 2 2 2 http://bbs5.techyou.org/?fromuser=sergio147 = 363,000 ft-lb.
(4.7)
If the vehicle were to accelerate from full stop to 60 mph in 10 seconds, the power requirement of the engine would be H p = (3.6 x 105 ft-lb/10sec)/550 f l - l b / s e c / h p = 65 h p (4.8) In order to maintain a speed of 25 to 35 mph, about 25 to 35 hp is required to overcome road friction, drive train losses, and wind resistance. These calculations indicate that almost twice the engine power is required to climb hills and accelerate at the rates shown than what is needed to propel the car along a level road to overcome the frictional forces, etc., encountered in machinery and wind and road contact. It should be noted here that cruise power must be added to the hill climbing power because those cruise losses still pertain.
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4.5
ENERGY STORAGE
Rocket Propulsion Energy Needs Comparison
For rocket propulsion, the equation for thrust force versus mass and energy of the propellant is Force =
d(Mv)=AM|2^ dt At 1 M
where φ = fuel energy density m = mass of fuel M = total mass of expelled material. Gasoline as fuel, with liquid oxygen, gives 12,000 pounds of thrust per gallon burned per second. All the above applications of portable power sources have both power and energy density requirements far outside the current or future battery capabilities. http://bbs5.techyou.org/?fromuser=sergio147
Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
5 Competing Storage Methods
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Electrochemical secondary batteries are still the predominant means of energy storage in everyday situations. They take the form of either the ubiquitous dry cells (button cells included) or the familiar lead storage battery. Uses have a very wide range, from small electronic devices to power systems for diesel railway locomotives and emergency standby power sources. Despite their undeniable utility and the fact that they have made possible a vast variety of consumer and industrial products, they each suffer from some debilitating problems. Unfortunately, the life of most batteries is very limited either in terms of the number of charge/discharge cycles or simply their age. The aging and deterioration of batteries, as compared to mechanical or electronic devices, are caused by many inherent factors over which we have little control. These inherent factors have mostly to do with the very nature of chemical changes and their limited reversibility. Frequently, this irreversibility and cumulative deterioration are not only due to chemical changes but also the physical changes brought about by the chemical processes, such as lowering the mechanical strength of materials resulting from chemical changes. 55
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ENERGY STORAGE
Why and how do batteries fail? What have we done to circumvent or improve upon the limitations? It is not our intention here to analyze in any detail the many mechanisms that contribute to battery failure. However, a brief review of some of the more familiar electrochemical cells might contribute to our understanding of why the search continues for improved electrochemical processes that might be applied to the purpose of energy storage. Some typical, common secondary cell reactions include the following: • NiCad Cd + 2Ni(OH) 3 = CdO + H 2 0 + Ni(OH) 2 (from Junger) • Zinc/Iron cell Zn + Fe 2 0 3 = 2FeO + ZnO • Lead-Acid Pb + PbO z + H 2 S0 4 = 2PbS0 4 + 2H 2 0 (from Plante) • Nickel-Iron Fe + 2Ni(OH) 3 = FeO + 2Ni(OH) 2 + H 2 0 (from Edison) • Ni-MH Charge to the right, discharge to the left: • Ni(OH) 2 + M = NiOOH + MH, where the metal MH is usually ahttp://bbs5.techyou.org/?fromuser=sergio147 charged hydrogen absorbing alloy such as LaNi 47 Al 03 (H 6 ) • Lithium Ion (-) anode: C + Li+ + xe" = Li C X
• N(+) cathode: LiMO, = Li, MO, + xLi+ + xe" '
2
1-x
2
An anode is where oxidation takes place, and cathodes are reduction sites. There are other lithium cells that employ solid a n d / o r polymer electrolytes such as the Li-ion SPE cells that use LiCo0 2 cathodes and graphite anodes. The Li/SOCl 2 , lithium thionyl chloride, cell has energy producing reactions at the electrodes during discharge - anode is Li = Li+ + e~, and cathode is 2SOCl2 + 4e" = 4CF + S0 2 + S.
5.1
Problems with Batteries
Despite their convenience, batteries have a number of limitations and serious disadvantages. The cost per unit of stored energy is hardly important when the application calls for very small amounts of energy such as in watches, cell phones, and other small electronic communication devices. However, it becomes a major consideration in motive power or bulk energy storage cases.
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When one considers large-sized energy facilities, other matters in addition to initial capital equipment (battery) costs become important. Safety, cycle, standing life, and dependability become issues to address. In virtually all electrochemical batteries, solid materials that are part of the electrode structures participate in the energy storing processes. Electrochemical reactions in which solid materials undergo changes in structure or composition are not completely reversible. Hence, there are inexorable and unwanted changes that occur with each cycle that eventually result in the demise of the battery. The lead-acid cell is an example of this situation. The principle energy storing reaction is essentially P b 0 2 + Pb + 2 H 2 S 0 4 = 2 P b S 0 4 + 2 H 2 0 . The inherent following:
failure
mechanisms
of batteries
(5.1) include
the
• Shrinkage of the negative plate sponge lead • Sulfation of plates, exposed plates, or long discharged http://bbs5.techyou.org/?fromuser=sergio147 times • Changes in crystalline structure • Spallation of active materials • Grid corrosion by long overcharging. These are all consequences of chemical reactions involving solids at or part of the electrode structures. Other batteries, such as the Edison cell, nickel-cadmium, lithium-ion, etc., involve changing the chemical composition of solid materials. All of the energy cells listed above are fairly common and presently available. They all have solid reagents at both electrodes. The continual cycling of cells directly involves or necessitates the restructuring of these solids as the cell is charged and discharged. Unfortunately, such physical (chemical) processes are not entirely reversible. Each time the electrode materials chemically change, a certain degree of irreversibility is encountered. Materials are re-deposited with the same uniformity, some of the solids become physically detached from the electrode, and some loss of continuity or capacity results. The operating life of the electrochemical cells is limited by these mechanisms. In addition to the limitations cited above, there
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ENERGY STORAGE
are also concerns with the passivation of electrode materials, or memory effects in which cell capacity or electrical performance is adversely changed as a result of continued partial charge cycling. Because of these factors and the need to develop energy systems with longer lives and more useable operational characteristics, a search has been continuing for electrochemical cells with energy storing (producing) reagents in either a liquid or gas phase. Such systems are usually referred to as either fuel cells or redox batteries. In the former gas phase, reagents such as oxygen and hydrogen are introduced into the reaction chamber, or electrode compartment, and oxidation of the fuel (hydrogen) and reduction of the oxidizing agent (oxygen) takes place with the release of energy in the form of electric current to an external load. In redox batteries, essentially the same process takes place but with different reagents and the singular difference that the reaction products can be regenerated externally to be reused in the cell an unlimited number of times. In actuality, the water produced in a fuel cell can also be "reused" by dissociation into H 2 and 0 2 . However, in the redox system the intent is to reuse the reagents rather than discard them. http://bbs5.techyou.org/?fromuser=sergio147 Energy density of an electrochemical couple is obviously one of the many important properties to be considered when evaluating it as a potentially viable means of storing energy. Because of the large difference in available energy per unit weight of electrochemical processes as compared to other currently employed sources of energy, a different level of standards must be adopted in their assessment. A comparison between batteries and fossil fuels shows a vast difference in energy levels. This situation is illustrated in Table 5.1 which shows the performance numbers for fossil fuels. The remarkable aspects of these sources of energy are that they are in convenient liquid form, easy to handle, and they make use of the surrounding oxygen in the atmosphere as oxidant. Because of these features, petroleum products have risen rapidly to their prominent position as universal fuels for most mobile and remotely powered machines ranging from electric power generators to automobiles and aircraft. In applications where power, energy capacities, safety, and "portability" are critical, there is no rival. Only in very specialized situations such as in naval vessels, where the ability to remain at sea for great distances and for long periods of time without refueling,
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has nuclear power competed. Also, in many instances where air pollution is a concern, or where fossil fuels and hydropower are not options, nuclear power is competitive. A quick comparison of some of the better-known energy sources for doing our work is presented below. Relevant details about gasoline as our universal fuel are also illustrated below.
5.2
Hydrocarbon Fuel: Energy Density Data
The following is an outline of the energy densities of various common hydrocarbon fuels that have been employed for the propulsion of vehicles via internal combustion engines. The most common among these fuels are the petroleum derivative polymers, heptane and octane. Table 5.1 shows the total energy of combustion for some of these fuels when combustion is complete and when it takes place Table 5.1 Heats of http://bbs5.techyou.org/?fromuser=sergio147 combustion for some hydrocarbons. kWh/Kg
Private Name (Phase)
Formula
Ethane (G)
C2H6
14.9
6.78
n-Pentane (L)
C 5 H 12
13.45
6.11
n-Hexane (L)
C 6 H 14
13.35
6.06
n-Heptane (L)
C 7 H 16
13.34
6.06
C
13.26
6.02
n-Octane (L)
8H18
kWh/lb
Methanol (U
CH 3 OH
6.2
2.8
Ethanol (L)
CH.OH
8.27
3.76
2
D
kWh/Gal
kWh/Liter
35.7
9.8
24.7
6.78
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ENERGY STORAGE
at 20°C. These hydrocarbons may be represented as having the general molecular form of C x H O r When complete combustion takes place, assuming no formation of nitrogen compounds, the general form of the reaction is n 0 2 + C x H y O z => x C 0 2 + y H 2 0
(5.2)
where
Such complete combustion is an idealized situation since some of the products are CO and the process is invariably not isothermal. However, these data do give representative maximum values for their useful available energy. Octane rating of gasoline is usually the percentage of octane to heptane in the fuel mixture. A 100-octane fuel might then be all octane. Ethanol fuel's energy density of over 8kWh/Kg is a very high value, especially http://bbs5.techyou.org/?fromuser=sergio147 when compared to most other processes for storing energy in a controllable and usable form. However, when one examines the other factors associated with its actual application to the conditions necessary to its use and the characteristics of engines, we see this number significantly diminished. A look at the amount of energy available from a gallon of octane for the mechanical energy necessary to propel a vehicle gives the following figures. Maximum energy conversion efficiency of a tuned, constant speed I.C. engine is in the order of 20%. Hence, at a specific gravity of about 6 pounds per gallon, only 1 / 5 of the 35.7kWh per gallon is actually available, or about a 7 kWh/gallon maximum. Burning 1 gallon, 6 pounds, of octane completely requires 24 pounds of oxygen for the reactions. That amount of 0 2 has a volume at STP of 260 ft3. Since only 20% of the composition of air is oxygen, a minimum volume of air of 5 x 260 = 1300 ft3 is required to "burn" 1 gallon of octane. Under ideal conditions, a vehicle with a mileage performance of 30 mpg traveling along a roadway at 60 mph would be consuming 2 gallons of octane per hour. That vehicle engine would be taking in a minimum of 2,600 ft3 of 20°C air per hour for complete combustion to occur. The air cleaner and fuel system must be able
COMPETING STORAGE METHODS
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to handle airflow rates at least in the range of 3,000 ft 3 /hour, or 50ft 3 /minute. After over a century of development, we have learned how to accomplish these feats with what have become extremely reliable machines. However, two very important facts should be borne in mind: 1. Only a small fraction of the stored energy is utilized in the current internal combustion engines. 2. A much larger amount of oxygen in both weight and volume must be available from the surrounding atmosphere for the fossil-fueled I.C. engine to function. An interesting fact should be noted here about energy densities. The extremely attractive energy density of petroleum products is made possible only because it is not necessary to carry the oxidizer on board the vehicle. The oxygen is supplied by the immediately surrounding environment and is available when needed at any demand rate. If ithttp://bbs5.techyou.org/?fromuser=sergio147 were necessary to carry the oxygen on board the vehicle, the number would be quite different. An amount of oxygen about four times the weight of fuel is needed. Thus, if the practical 20% efficiency of conversion is taken into account, 1.2 kWh / l b of fuel would be realized, and if we add the four times weight of oxygen, the figure becomes 240 Wh/lb. If now we also include the weight of nitrogen in the air, we obtain the low value of 40 W h / l b for the energy density of a power source system that not only had to carry the fuel but also its own air comprised of only 20% O r All of the proceeding may seem a bit unfair in assessing the "true" energy density of a hydrocarbon fuel, but in actuality this is the situation with which any contending energy system must compete. The "unfairness" lies mainly in the fact that these fossil fuel systems breathe air and do not have to carry the weight of the oxidant along. By virtue of the same fact, the combustion products are exhausted into the atmosphere, thus increasing pollution problems in some instances. To eliminate air pollution entirely, it is necessary to devise energy producing systems that do not involve combustion products of any sort, other than perhaps water vapor, into the surrounding environment. This essentially means that a non-combustion method of
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ENERGY STORAGE
producing heat or power must be substituted for the burning of fossil fuels. In fact, the only combustible materials are either carbon or compounds of carbon, all of which yield C 0 2 as the ultimate product of the process. The necessity of carrying not only the fuel or reducing agent on board the system but the oxidizers as well does present a severe handicap when attempting to develop a competing high energy density system.
5.3 Electrochemical Cells Electrochemical cells suffer not only from the lower energy densities associated with such processes but also from the necessity of carrying all of the chemical reagents necessary to the available energy reactions. This situation does enable the cell to remain independent of the external surroundings during its operation. These factors contribute to energy densities of electrochemical reactions, which are at least an order of magnitude lower than those of hydrocarbons.http://bbs5.techyou.org/?fromuser=sergio147 Among the most energetic of electrochemical reactions are those between metals and halogens. The highest specific energy capacity is that between lithium and fluorine because of their low atomic weights and high reactivity, or free energy of combination. The reaction of the formation of solid salt, Li + F —> LiF, occurs with a free energy of 140kcal/gm mol. wt. and at a potential of over 6volts. This corresponds to an energy density of 3,100Wh/Kg for the direct or electrochemical reaction of the elements. This value is quite attractive and even competitive with fossil fuels. However, there are no practical ways of handling the highly reactive components. Both the metal lithium and the element fluorine react energetically with water and most other substances associated with the construction of electrochemical cells. Hence, in order to make an operable cell employing this couple, it is necessary to find some non-aqueous, probably polar solvent in which the salt LiF is soluble and that will not react with either of the two reagents. Fused salt electrolytes are possibilities, but they involve high temperatures, difficult operating conditions, and increased hazards. There is also the problem of storing free fluorine as an available reagent for a charged cell. These problems are formidable, and no short term, practical solutions are in sight.
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5.4 Metal-Halogen and Half-Redox Couples The term redox has been used in recent times in a manner that is not entirely clear when applied to electrochemical cells. All such processes involve oxidation and reduction. The fuel (reducing agent) is oxidized, and the oxidizing agent is reduced in the process, thus producing energy in a hopefully usable fashion. The term redox, as applied to electrochemical systems, refers to a system that employs reducing reactants and oxidizers that are passed through the cell, or reaction chamber, for the production of electric power. The reactants are subsequently regenerated at some location external to the reactor cell. In primary cells where only the discharge process takes place, the oxidation process occurs at the negative electrode, and the reduction of a chemical occurs at the positive electrode. In the case of the LeClanche (dry) cell, zinc is oxidized to zinc-oxygen compounds, and manganese dioxide is reduced. Secondary, or electrically rechargeable cells, have dual process electrodes. During http://bbs5.techyou.org/?fromuser=sergio147
Figure 5.1 Enhanced concentration cell operation.
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ENERGY STORAGE
charging from an external electrical source, the reduction occurs at the negative electrode and oxidation at the positive. Half-redox implies that the processes at one of the two electrodes in a cell involve reagents that remain mobile as liquids or gasses so that they may be introduced and removed from the respective electrode region. The general form of such reactions is M+n + nX"1 -> MX . n
Metal-halogen cells are in the half-redox category. Halogens are liquid or gas at room temperature and can be caused to flow over the surface of an electrode as needed to sustain the reaction processes or to remove reaction products. If the product of oxidation, such as the salt, ZnBr2, in the case of the zinc/bromine couple, is soluble in the electrolyte, there are no solid products formed onto or removed from the surface of the (+) electrode during charging or discharging. Since the reactant and reaction products can, in principle, be supplied during discharge to the electrode surface and removed for regeneration at some external location, the bromine electrode qualifies as a redox type reagent. The importancehttp://bbs5.techyou.org/?fromuser=sergio147 of this aspect of redox behavior in this case is not primarily because of its ability to be removed from the cell for storage or re-conversion elsewhere but because it reacts directly with the reducing agent, zinc, to produce the salt. Furthermore, its storage at the electrode or in a reservoir is mobile and can be made uniform. Cells with reagents that will recombine by direct union offer the possibility of an extremely long life. Another couple that has received little attention and has the attributes of half redox cells and homogeneous cation is the Fe/Fe +3 couple. Oxidation/reduction reaction is Fe° + 2Fe+3 —> 3Fe+2. The diagram in Figure 5.2 shows the rather interesting and unique characteristics whereby one can make use of the two oxidation states of the single element iron. The disadvantages of this system are the facts that iron is an electronically conductive solid with poor plating properties, and that hydrogen gas evolves not only upon charging but at times due to the necessarily low pH of the electrolyte. However, with further development in such matters as the use of non-aqueous electrolytes and improvements in plating quality, the iron-redox system could become practical for some applications where cost is important and size is relatively unimportant.
COMPETING STORAGE METHODS
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Solid iron plating Fe° Negative electrode
-0.44 volts H
Fe+2 + 2e -> Fe°
Positive electrode
Fe+2 -> Fe+3 + e
Charging
Charging
Figure 5.2 Energy level diagram for the iron redox cell. http://bbs5.techyou.org/?fromuser=sergio147
Of the four halogens (fluorine, chlorine, bromine, and iodine), bromine has been selected for serious evaluation as an oxidant because of its more favorable physical and chemical properties. For example, it is much more reactive than iodine and has lower costs, but it is not nearly as volatile and ill behaved as a storable component in a cell as either chlorine or fluorine. Chlorine will hydrolyze much more rapidly in water than bromine will, and it does not form reversible complexes as well as bromine does. Fluorine is an extremely difficult and costly material to work with in elemental form. A number of companies in recent years have produced some reversible cells and batteries on a laboratory prototype basis, in which the chlorine was stored as a clathrate (frozen hydrate) in a zinc/chlorine battery. Because of life and hazard considerations, among others, the battery has not emerged as a practical secondary source for widespread use to date. These factors contribute to the difficulties of achieving practical battery designs using higher energy density reagents such as those above. Figure 5.3 is a chart that compares the free energy of reaction per kilogram of reactants for a range of metal-bromine
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ENERGY STORAGE
AI
Cd
Ca
Na
Fe
Pb Li Mg Metal cation
Ni
K
Sn
Zn
Cu
See bibliography reference 5; Latimer, Oxidation potentials
Figure 5.3 Energy densities of metal-bromine couples.
http://bbs5.techyou.org/?fromuser=sergio147 couples. These values were calculated from the free energies of the reaction and sum of the half-cell potentials available from the literature. The most attractive couple, strictly from an energy standpoint, is that of Li/Br. Unfortunately, there is currently no technology that allows us to either electro-deposit lithium metal out of aqueous solution or even-exist in an air/water environment. Nonaqueous solvents present problems not only of hermetic sealing but limited life, simultaneous chemical compatibility with free bromine, and low electrolytic conductivity. Fused salt electrolytes must be operated at high temperatures, and cells experience many other types of problems ranging from chemical durability, thermal expansion/contraction, mechanical strength, and sealability. A high temperature metal/halogen system seems quite impractical for any application at any time in the foreseeable future. High temperature fused salt cells, such as the N a / S system, have been constructed with some degree of success, but they do not employ free halogen as the oxidizer. All of the couples that employ aluminum and alkali metals have higher energy densities because of their high reactivity as chemical
COMPETING STORAGE METHODS
67
agents. This greater reactivity also results in greater problems of cell containment and reaction rate control. As we descend lower in specific energy density, the couples become increasingly easier to manage as an operating cell. However, their attractiveness as sources of energy also diminishes. One must then look for a compromise, hoping that a delightful selection can be found that is easy to mange, well behaved, and has useful energy and power densities. To increase the likelihood of applicability of a couple, it is important to stay as much within ambient conditions as possible. A cell that is operable at near room temperature ranges is compatible with an aqueous environment and is also compatible with materials of desirable construction. Also, electrodes and separators that are chemically resistant and have reasonable costs are required. Why explore and attempt to select a metal-halogen couple in the first place? The following two reasons can explain why: 1. This category of reagents as electrochemical cells offers high energy density and perhaps higher power http://bbs5.techyou.org/?fromuser=sergio147 density. 2. There is the possibility of long cycle life because of the totally reversible nature of the cell, in principle. Of all of the couples compatible with aqueous electrolyte systems and ambient conditions, the zinc-bromine has appeared most attractive. Zinc is the metal furthest from hydrogen in the electromotive series as a reducing agent that can be plated out of solution in water. Bromine is similarly compatible in water and has a relatively low vapor pressure at 25°C. In the absence of catalysts, bromine hydrolyzes at a low rate, and equilibrium is attained at very low concentrations of HBrO in acidic solutions. The reactions at the negative and positive electrodes during discharge are Zn -> Zn+2 + 2e at 0.76 volts and Br2 + 2e -> 2ΒΓ"1 at 1.07 volts. The whole net reaction is simply Zn+2 + 2Br_1 —> ZnBr2 at 1.82 volts. The high reaction potential that is actually realized is slightly over 1.8 volts per cell. Almost 200 watt-hours per pound of reactants are available for the reaction if it goes to completion and
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no other electrical losses are incurred. These figures are quite attractive for many application possibilities. Lead-acid cells have a theoretical energy density for the energy storing reagents alone of 70 to 80Wh/lb, or about 200Wh/kg, as compared to the upper limit offered by the Zn/Br2 couple of 440 W h / k g . The zinc/bromine system has some very fundamental problems, such as zinc plating being spongy and dendritic, zinc reacting in an acidic solution evolving hydrogen, and bromine being extremely oxidizing, difficult, and expensive to store. The second of the attributes of metal-halogen couples is their ability to return to the initial conditions of the discharged state as secondary cells. When the couples are discharged completely, the chemistry has returned to the initial conditions the cell possessed when first fabricated, and any remaining reagents will react directly if given the opportunity in cell design. Assuming no deterioration of electrodes, etc., and no loss of components from the system, the cell has no permanent memory, in principle. Obviously, if it is possible to "tame" the reaction in a manner rendering it reasonably safe, low cost, and long-life, applications such as load leveling, peaking, and even the electric vehicle are http://bbs5.techyou.org/?fromuser=sergio147 possibilities. An interesting comparison of the performances of a variety of common energy systems is provided in the Ragone type diagram in Figure 5.4. We see that the performance on both an energy and power basis is far superior for heat engines such as the turbines and internal combustion engines. Fuel cells are significantly better performers on an energy basis than other batteries or electrochemical devices, but are not yet competitive on power density.
5.5 Full Redox Couples There are couples, other than metal/halogen, that are compatible with aqueous solutions and are entirely redox in character. However, the selection is not very attractive when one imposes the usual conditions of low cost, environmentally benign, wellbehaved, long life, usable energy, and power densities. Table 5.2 is a partial list of the better-known reducing and oxidizing agents that could be utilized in an electrochemical cell as a source of electrical energy.
COMPETING STORAGE METHODS
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Figure 5.4
Table 5.2 Redox cell reactants at room temperature. Oxidizer
Potential
Potential
so-*
0.93
-1.36
Cr+2
0.41
-1.07
S
0.50
o2
-1.23
F2
-2.87
ci2 Br2
-0.54
i2
s2o8Fe+
Reducer
2
3
-2.01 -0.77
MnO; 1
-1.51
y+yy+5
-0.25
Fe +2
v + 2 /v + 3
-0.77
1.1
69
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ENERGY STORAGE
Oxidizers and reducing agents (fuels) are listed as either chemical elements or ions (radicals) depending on their form in a cell at the beginning of "discharge," or at the start of the energy-producing mode. The potentials are given in volts above or below hydrogen. Following convention, positive volts are above hydrogen, and negative volts are below hydrogen in the electromotive series. As is evident, there are relatively few choices for chemical reagents that satisfy the pre-requisites of acceptable voltage, chemical stability, and being liquid in both states of oxidation, relatively safe, low-cost, and compatible with ambient conditions. Of all of the above, and more that are not listed here, the oxidizers that show most promise are still ferric ions, bromine, and vanadium in acid solutions. Of the even fewer choices available for reducing agents, it seems that sulfur (complexed) and vanadium are most likely to yield some practical systems. We have elected to pursue sulfur as the most attractive element for the reducing agent in a room temperature aqueous electrolyte. The properties that are most attractive, and quite remarkable when considered in light of its use as the reagent in the negative side of a cell, include the following: http://bbs5.techyou.org/?fromuser=sergio147
• Plentiful supply • Low cost • High solubility as a polysulfide complex in water solutions • Low equivalent weight • Reasonable potential • Well-behaved electrochemically • Low volatility. Many oxidizing agents have been tested in conjunction with sulfur as the negative electrode material. Bromine has been of most interest because of the potential for a completely reversible cell. Looking back into past decades, we see that other redox couples have been explored intensively in the past, such as that of Cr +2 /Fe +3 . The NASA Lewis laboratory has probably contributed most toward its research. One of the problems associated with its cycle life and coulombic efficiency is that of maintaining separation between the chromium and iron ionically in solutions. Imperfect separation is achieved by employing ion-exchange membranes between cell compartments, but cross diffusion inexorably results
COMPETING STORAGE METHODS
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in deterioration of the electrolytes. Since both ions have positive electric charges, they cannot be separated during charging as in a metal-halogen couple with oppositely charged cations and anions. Anion membranes with low resistance, low cost, and very high transport number ratios for the transport of chloride ions in the NASA cell are difficult to fabricate. At present, the vanadium redox couple is receiving a fair amount of attention because of a number of interesting features. The fact that it is homogeneous, regarding the active reagent vanadium, and the reasonable solubility in water of the vanadium salts make the system attractive as a long life energy storage mechanism. However, the negative aspects are the high cost of vanadium and its compounds, high molecular weights of the reagents, the necessity for operating electrolytes at very low pH, and the complexities of operating a system that requires full flow electrolytes. The potential market for such a system appears to be mainly as load leveling or standby emergency power sources. http://bbs5.techyou.org/?fromuser=sergio147
5.6 Possible Applications
In selecting electrochemical couples to investigate and perhaps develop into operable systems and products, it is vitally important to keep the intended application criteria constantly in mind. The application potentials impose their own needs for cost, life, reliability, and energy and power density. Some application possibilities for full flow redox systems include the following: • • • •
Utility load leveling at generating and customer sides Peaking at user or customer side of power lines Emergency energy source in cases of power failure Portable power for convenience, or for remote locations • Perhaps for electric vehicles and small boats. With each area of application, there are certain requirements for a secondary battery power source that determine its usefulness. For example, in the case of load leveling, battery weight or energy density and power density are not directly significant factors because
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ENERGY STORAGE
they are in stationary locations. These parameters are meaningful only when converted into cost. Usually, larger physical equipment (batteries) has larger costs because of the required ground area and support structures, such as buildings. Hence, higher energy density batteries tend to be more attractive because of their associated costs. More materials of construction and a larger amount of floor space (footprint) and building needed to house the energy storage battery system increases the initial cost. However, longer cycle life systems will tend to amortize initial costs. Cost would naturally be greater as a consequence for lower energy density (ED) batteries. Storing energy output from generating equipment during low demand times to use for later peak demand periods can save in the cost of hydrocarbon fuels and generating capital equipment, but only if the economics of the battery are favorable. Storing for peak power demand periods at the user end of the power line can also save in the capital cost of transmission lines and transformers to the energy user. Cell imbalance in arrays of large numbers of battery cells can become a severe http://bbs5.techyou.org/?fromuser=sergio147 problem, especially for deep discharge cycling. Deep cycling is desirable because it reduces the amount of battery needed to store the usable energy. However, because battery cells are not identical in structure and performance, deep cycling can result not only in a decreasing usable output of stored energy but also in permanent damage to cells that have been reversed. Leadacid batteries are particularly prone to damage by reverse charging. To compensate for this cycle life limitation, lead-acid batteries are usually not subjected to deep cycling, thus resulting in the necessity to build and purchase more energy storage capacity than will be in actual use. Safety, though always a serious consideration in the design and use of energy systems, is not as important in bulk energy storage applications because proper provisions can be made to cope with potentially hazardous situations by proper containment and trained personnel. In the case of consumer product areas such as the electric vehicle or portable power for tools and recreational purposes, safety is one of the prime concerns. In order to appreciate the directions in which battery development efforts are, or should be, headed some of the principle features or aspects of battery sources are identified below.
COMPETING STORAGE METHODS
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For Bulk Storage • • • •
High energy turn-around efficiency Flat discharge voltage versus current curve Minimum or absence of cell imbalance Competitive costs of capital equipment amortized over cycle life • Low maintenance because of cost considerations For Portable or Electric Vehicle Use • • • • • • •
Low capital cost Safe operation Highest energy density possible Highest power density possible Compactness in size as well as small weight Minimum maintenance Chemical recharge ability desirable
Except for the higher sensitivity to energy efficiency in bulk http://bbs5.techyou.org/?fromuser=sergio147 energy applications, consumer applications and particularly the electric vehicle have even more difficult application requirements to meet. The latter has especially difficult criteria of safety and compactness imposed upon the battery design that exceed those for bulk energy uses. The lead-acid battery has been in use extensively for over a century, and it still retains its position of prominence in industrial and consumer applications. Even though its energy density is lower than what is desired in many instances, its familiarity, dependence over a wide range of operating conditions, and acceptable cycle life give rise to its universal character. Other contenders as large storage batteries include the Edison (nickel-iron) cell and the Junger cell (nickel cadmium). Because of either cost or performance factors, their application is much more limited than the lead-acid. With a maximum specific energy density ranging between 12 and 18Wh/lb, or 26 to 40Wh/kg, the lead-acid battery leaves much to be desired in electric vehicle applications. The usual range of such Pb-Ac power vehicles is 50 to 70 miles maximum. Doubling the energy density of a battery would certainly be a welcome improvement, but it would still limit a vehicle to a 100 to 150 mile range between lengthy charging times.
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ENERGY STORAGE
The redox battery systems do offer the possibility of chemical "re-fueling," thus extending the usable range of an electric vehicle indefinitely as long as sources or fueling stations of the chemical reagents are available en-route. Numerous electrochemical couples making use of oxygen in the atmosphere as an oxidant have been experimented with and prototyped over recent decades. Perhaps the most common of these are the alkaline versions of metal-air cells. The more common versions include, Mg-air, Al-air, and Zn-air. Most suffer from problems of available power density and the deterioration of air electrode catalysts due to poisoning contaminants. And when these devices are considered for use as chemically rechargeable cells, the complexities and inconveniences of removing and replacing many depleted metallic electrodes and handling caustic electrolytes containing the spent products are severe. Consequently, they also have not gained a position in any of the large-scale consumer /industrial application areas. To summarize, the three areas of metal-halogen, half-redox, and redox, and more specifically, the zinc/bromine, iron-redox, and sulfur/bromine have been selected for investigation over past years http://bbs5.techyou.org/?fromuser=sergio147 at TRL, and they are presented here because of certain inherent characteristics. These include the following: • Zinc/bromine couple - high energy density, well behaved, completely reversible • Iron/ferric couple - low cost, long life, completely reversible, great safety • Sulfur/bromine couple - low cost, long life potential, no cell imbalance, chemically rechargeable. In all the cases above, reverse charging has little or no permanent, negative consequences on the cells. There are, however, some serious negative factors that have precluded their extensive use. These include such issues as safety encountered with the use of strong oxidizing agents such as bromine, difficulty with managing metal plating, the generation of hydrogen gas and the decomposition of water, rising acidity of electrolytes causing the evolution of gasses, and the compatibility of materials of construction in the presence of halogens.
Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
6 The Concentration Cell
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Perhaps one of the more captivating and promising approaches to the practical storage of energy is in making use of the simple particles or billiard ball properties of matter. This view of the problem is enticing perhaps because of its direct simplicity. In other words, we might be able to make use of the straightforward "mechanical" properties of matter as described in classical molecular theory. In doing so, it appears we might be able to avoid many of the pitfalls of other energy systems that depend on specific properties of dissimilar materials (molecules), in which there are inherent mechanisms of degradation due to such issues as irreversible chemical changes, molecular diffusion from one region of the system to another, resulting in process contamination, or even just changes in molecular and physical structure that produce operational incompatibilities. This approach does seem to offer ways around such life-limiting circumstances. In general, there is only one chemical species that participates in the energy storing process, and the processes all appear to be completely reversible by means of electrical input of appropriate polarity. If one is willing to design around or endure the peculiar electrical characteristics of such devices, perhaps a series of practical, low-cost systems can be produced in order 75
76
ENERGY STORAGE
to solve some of the more pressing energy problems we face in daily life. We will proceed to outline some of the background physics and review the general behavior of concentration cells as electrochemical elements.
6.1 Colligative Properties of Matter The various properties of a large aggregate of material particles that seem to behave as though they possessed properties that can be described as due only to their common "physical" or "mechanical" attributes are frequently referred to as colligative properties. Webster's Unabridged Dictionary defines colligative as "depending on the number of molecules or atoms rather than on their nature." This more than implies that this class of attributes is independent of any chemical differences and is only concerned with the net effect of characterless particles regarding bulk behavior. Examples of such properties and their effects include the following: http://bbs5.techyou.org/?fromuser=sergio147
• • • • •
Lowering of vapor pressure of a liquid Lowering of the freezing temperature of a mixture Boiling point elevation Osmotic pressure of solutions Electric potential difference between same ionic solutions with different concentrations.
At low concentrations of solutes in any of the above instances, the properties of the solutions are changed in a manner directly proportional to the amount of solute particles. This is especially true when their concentrations are so low that the properties of the solvent are unaltered and the interactions between solute particles are minimum. The vapor pressure depression, p o - p, of a solution where p o is the vapor pressure of the pure solvent, and p is the vapor pressure of the solution is expressible as £
^
2
- = l-X.
Xa is the mole fraction of the solute, a, in question.
(6.D
THE CONCENTRATION CELL
77
Note that nowhere in these types of expressions does any property specific to the materials appear other than the vapor pressure of the solvent. However, we are concerned in these discussions only with the differences, p o - p, that result from the introduction of any solute. The idea of basing an energy system on a set of colligative properties is attractive because it might become possible to make a device that is independent of specific materials and, thus, symmetrical in construction, other than such factors as pressure, concentration, and temperature differentials between the same components of the device. Hence, we might be able to avoid any degradation in performance or life of that device due to the transfer of materials that differ in composition.
6.2 Electrochemical Application of Colligative Properties The following is an initial technical description of the principles of operation of such a concentration cell. We will also refer here http://bbs5.techyou.org/?fromuser=sergio147 to the concentration cell as a Common Ion Redox cell (CIR), as a convenient abbreviation for this class of energy storage systems. These cells are, at times, also referred to as symmetrical cells since the cells are constructed the same at each electrode side. Electrodes are physically identical, electronically conductive, and chemically inert. It makes use of the colligative properties of matter, or in this case, the large collections of iron atoms and ions in solution. In essence, the CIR cell employs the non-substance, specific properties of components and their physical behavior in an operating system. The raising and lowering of a solvent boiling point or freezing point as a consequence of the concentration of dissolved solute are colligative properties because they are virtually independent of materials composition. They are mostly strictly a result of the amount of solute molecules present in the liquid. Another example of colligative properties is the interdependence of temperature and pressure of a gas (in the ideal gas range). These parameters are independent of the specific gas that is present and only dependent on the number of molecules present. The search for a process, other than mechanical devices or electrochemical couples, that would enable the storage of energy in
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ENERGY STORAGE
an inexpensive and reliable manner and that has a minimum of inherent failure mechanisms has resulted in the exploration of the characteristics of concentration cells as potentially practical devices for these applications. For the sake of brevity, we will refer to such cells as CIR devices (Common Ion Redox). These devices are all redox in nature because, as is necessarily the case in chemical transformations, reduction and oxidation of chemical species occur within the device for the transference of energy. However, the label should not imply that these devices or cells are full flow designs with provision for removing or replacing electrolytes. They may be operated as either stationary, or static, electrolyte systems. The particulars of design and physical configuration depend on the intended applications. For example, it may be desirable to employ external liquid reservoirs, pumps, etc., in a full flow system if exceedingly long charge retention times are required. In such cases, the additional system's complexity and costs may be justified. This approach very closely resembles the process of the isothermal compression of a gas to store energy for later use. However, the energy input and http://bbs5.techyou.org/?fromuser=sergio147 output in gas compression is mechanical. A pump is employed to compress the gas, such as air within a confined volume, while dissipating the heat generated to the outside world. The input is usually a mechanical piston pump. To regain the stored energy in the form of a gas at higher than ambient pressure, the gas is permitted to expand back to the outside usually via a piston or centrifugal pump, thus returning some of that energy in useful mechanical form. It is also necessary to provide a heat exchange system to not only dissipate the thermal energy to the outside during compression but to also return thermal energy to the expanding and cooling gas. In the CIR system, we are interested in a device that will operate with energy input and output directly in electrical form. In order to accomplish this end, it is obviously necessary to have electrical potential difference present, rather than a mechanical pressure, and charge transfers taking place within the device so that an electric current can flow in an associated external circuit. That circuit would provide the energy output as a current flow through an external electric load. The energy potential difference between electrodes in a concentration cell is a consequence of the electrodes being immersed in electrolytes with different concentrations of the same chemical
THE CONCENTRATION CELL
79
species. If the chemical species at these electrodes exist at different oxidation states, this energy difference is manifested as a net electric voltage between the electrodes. The electric field is proportional to a function of species concentration ratios. This approach to storing energy is interesting because it appears that it is not only possible but also practical to obtain any level of electric potential in a CIR cell quite independently of the nature of the chemical agent(s), other than their solubility, electrical conductivity, and other general physical properties. Plus, the charge density is limited only by the amount of the chemical species that one can contain or compress in the locality of the electrodes. The CIR cell is not limited to the electrochemical potential difference between two chemical agents. Instead, the voltage range is a continuum limited only by the ratio of concentrations that can be achieved by physical and mechanical methods. Some cell design possibilities are suggested. Probably the most expeditious method of introducing and explaining the basic attributes and design parameters of concentration cells is to present this additional tutorial on the subject. http://bbs5.techyou.org/?fromuser=sergio147
6.2.1 Compressed Gas There are just a few steps in the explanation that will briefly describe some of the important, underlying fundamental principles of physics. Let us take a look at the ideal gas law, PV = nRT
(6.2)
where P = gas pressure, V = volume occupied by the gas, n = number of moles (number of molecules in that volume), R = universal gas constant, and T = temperature in absolute degrees. Figure 6.1 shows a container with two compartments (equal volumes). These separate compartments can be connected by a gas p u m p to extract gas from one side to the other and by a valve permitting the compressed gas to flow (expand) from the highpressure side to the other. The number of molecules initially in each side is n. If all the molecules were to be compressed into one side of the container, the compressed gas side would be at a pressure P' = 2P. The amount of energy stored (isothermally) is then
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ENERGY STORAGE Liquid pump
Pressure vessel
Relief air valve
Figure 6.1 Closed system gas compression.
simply PV. Mechanical energy can be expressed as force times http://bbs5.techyou.org/?fromuser=sergio147 distance, or Energy, E = F · L and,F = P-A, or,E = P - A L
(6.3)
Such a method for storing energy in this configuration is quite ineffective in terms of volume of space. Hence, the gas (air in this case) is usually compressed from the outside infinite supply source into a confined space such as the volume, V, of one compartment. Then the limitation of how much energy can be stored in that volume, V, is limited only by the strength of the container to withstand high pressure differentials between the outside (one atmosphere pressure) and its interior. Not shown or discussed here is the considerable amount of temperature control and heat exchangers needed to maintain a near isothermal process. During the compression portion of a cycle heat, energy must be dissipated to the outside of the system, and during the expansion phase, heat must be supplied to the expanding gas.
THE CONCENTRATION CELL
81
6.2.2 Osmosis Now let us turn our attention to another complementary process, or mechanism, known as osmosis. We can now move to a different environment, from that of a free gas to that of matter in the liquid state (much closer molecular proximity). Figure 6.2 shows a simple diagram of a container with two compartments. A semi-permeable membrane separating the two compartments will more readily permit solvent (water) than the solute (salt, or other dissolved materials) to migrate through. This results in the "cell" developing an osmotic pressure differential, it, across that membrane. The value of π is analogous to the gas pressure in the previous relationship and found as π ν = nRT.
(6.4)
In this case, v is the volume of the solution. In operation the solutes remain essentially in place, and the solvent, pressured by osmosis, moves through the barrier from the dilute side to the concentrated side until the hydrostatic pressure (or some externally http://bbs5.techyou.org/?fromuser=sergio147 supplied pressure) is equalized.
Pressure vessel
Relief air valve Figure 6.2 Open-air osmosis compression system.
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ENERGY STORAGE
This is a reversible process. An externally applied pressure will move solvent through the semi-permeable separator, creating an increasingly dilute situation on the low-pressure side. The energy that went into creating a concentration differential can be reclaimed in part by permitting the osmotic pressure to reverse the situation. Unfortunately, this process is not as practical for energy storage as the compression of a gas. In both instances, the process is mechanical and would require additional processes for the transformation into useful forms of energy.
6.2.3 Electrostatic Capacitor An example of energy transfer and storage is that which is associated with the accumulation of electrical charge in a capacitor (condenser) as the result of an externally impressed electrical potential. Figure 6.3 shows such a simple arrangement in the form of a parallel plate condenser. This is a practical and widely used method for storing energy for brief periods of time in electrical circuitry, for load smoothing, and for providing large amounts of power for brief http://bbs5.techyou.org/?fromuser=sergio147 periods.
Resistive load
Voltage supply
Figure 6.3 Electrostatic capacitor.
THE CONCENTRATION CELL
83
The relationship between charge and voltage is CV = Q,
(6.5)
where Q = electric charge in coulombs, V = electric potential in volts, and C = capacitance in farads. A simple parallel plate capacitor has a capacitance, C, that can be represented as
where A = plate area, D = separation distance of plates, and ε = permittivity of the dielectric medium between the plates. When the plates are connected to an electric potential source, charges flow from that source to the plates until the voltage across the plates, as dictated by the above relationship, just equals the source potential. The energy stored is http://bbs5.techyou.org/?fromuser=sergio147 2
Energy = - C V .
(6.7)
There is no "real" current flowing internally between the plates. However, a displacement current concept is employed to maintain continuity in the sense of a complete electric circuit. This is, again, an example of a concentration process to store energy. In this instance, the energy storing material in motion is not molecular but electric charges. Capacitors provide a very useful and convenient method of storing for later use in large power applications.
6.2.4 Concentration Cells: CIR (Common Ion Redox) Another approach to storing energy in direct electrical form, much as is accomplished in electrochemical cells that employ couplepotentials between dissimilar materials, is the electric potential obtained via concentration differentials with the same materials. Voltages can be produced within an electrochemical cell at the surfaces of electrodes if the concentrations of the same ionic
84
ENERGY STORAGE
species are different. This is expressed by the well-known Nernst equation: nRT a: V= —^log^, zF a.
(6.8)
where z = electric charge of the specific ions, F = faraday number, ai = activities at electrode (1), and a2 = activities at electrode (2). A more convenient and a more easily calculated value for the concentration voltage is the substitution of reagent concentrations for their activities. This practice results in calculated values of electric potentials that are not as accurate as would be obtained if activities were employed but are reasonably valid if the concentrations are low. However, the ratios of the activity coefficients at different concentrations of specific ionic species do not differ much over a wide range on concentrations. For our purposes here, the agreement is close enough to provide a working basis for preliminary estimates of cell potentials. The table below shows fairly constant values for activity coefficients over a wide concentration range. This is true for weak as well as strong electrolytes. The activity, a,http://bbs5.techyou.org/?fromuser=sergio147 of an ion or ionic compound is related to the activity coefficient, γ, by the simple equation (6.9)
γ =. where c is the concentration in molarity. Table 6.1 Activity coefficients, γ, at 25°C. Molarity
HC1
NaCl
NaOH
0.005
0.930
0.928
0.01
0.906
0.903
0.89
0.732
0.05
0.833
0.821
0.80
0.584
0.10
0.798
0.778
0.75
0.524
0.50
0.769
0.68
0.68
0.510
1.00
0.811
0.656
0.66
0.725
2.00
1.011
0.670
0.68
1.554
CaCl2 0.789
From: Physical chemistry by Alberty & Daniels, 1955, John Wiley & Sons.
THE CONCENTRATION CELL
85
The activities for HC1 at 0.005 molarity and at 2.00 molarity multiplied by their respective concentrations are M a = 0.930 x 0.005 = 0.0047 at c = 0.005 and M a = 1.74 x 4.0 = 6.96 at c = 4, which are vast differences for a. Figure 6.4 is a simple representation of such a cell where the two electrode compartments are separated by a microporous or ion transfer membrane. The specific species is relatively unimportant, except for its solubility mobility, and concentration as seen by each electrode. If the chemical species were merely a compound such as NaCl that ionizes in the solvent (water in this example), there would be no electric current flow possible even if the concentrations at the two depicted electrodes were vastly different. Only an osmotic pressure difference would be realized and no electrical potential. In order to have ionic substances migrate from one electrode to another within the cell, it would necessitate an accumulation of opposite electric charge at the electrodes (as occurs in a capacitor), and there must be a closed circuit through a means external the cell to provide an external electric current flow. The former condition is not possible because the electrolyte between the electrodes http://bbs5.techyou.org/?fromuser=sergio147 is conductive. Hence, no static electric charge can be sustained, and the latter can occur only if there is an electric potential across the cell. In order for an external current flow to be developed, there must be some mechanism at the electrodes to take on and give up electric charges (electrons). A process that can be used to complete the charge exchange cycle at electrodes is that of moving up or down the scale of state of oxidation or reduction for an element or compound. Then, a continuous path for electric charge flow within the
C, Electrolyte
Figure 6.4 Simple electrochemical cell.
Electrodes
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ENERGY STORAGE
electrolytic cell as well as electron migration through the external circuit can be provided. It can readily be seen that we now have a compression procedure (concentration differential of the same molecular species) that lends itself to a reversible process for the storage of energy in electrical form. The general exchange process below illustrates this for a species that we will identify as A, with two oxidation states, A+n and A^- 1 '. Then, A +n + e" <=> Α +(η " υ . As a very simple situation to illustrate the principle, let us assume that the element or species exists in solution as a compound, ΑχΒ , with another species, B, that does not change oxidation state. Then, the process, as shown in Figure 6.5, would be the transport A ions across a separator from one side to the other. Furthermore, electrons would flow in the external circuit to maintain total electrical neutrality. Examining the situation quantitatively, we see that, in a cell as described in Figure 6.4, the maximum concentration of solute is limited by the solubility of that compound. In most cases, the solubility of such ionic materials is in the range of 3 to 6 molar. If A carries a single transfer charge per ion, then the maximum charge http://bbs5.techyou.org/?fromuser=sergio147 density for a given volume of 4 molar solution would be 2 x 25 AH per mole, or about 100 AH per liter per side. That figure reduces to 50 AH per liter of total volume of cell. Even with the 4 molar limitation and only one charge carrier per ion, the charge density is still quite attractive. l-^WV-i
|A"|
Figure 6.5 Charges stored by surface adsorption.
THE CONCENTRATION CELL
87
However, one must look at the voltage at which the charges are delivered to an external load. For a simple cell in Figure 6.4, the voltage rises as the cell is "charged," meaning that the concentration of ion A increases and proportionately decreases on the respective cell side. Total cell volume is 1 liter, as shown in Table 6.2 below. As one can see, the energy stored and the available voltage both rapidly diminish as the cell bulk concentration difference progressively diminishes. The storage of reagents at the electrode sites in extremely concentrated form is one of the numerous contributions or innovations. Figure 6.5 diagrammatically illustrates this effect. The reagents are stored as uncharged molecular structures within sites by "ion injection" and van der Waals-type forces. These molecular species are slowly released as ions in solution in the immediate vicinity of the electrode surfaces in accordance with the demand during discharge. The important issue in assessing or computing the performance of cells and their operating voltages is to realize that the cell potentials are the result of the electrolyte environment in the immediate region of the electrode surfaces (frequently referred to as the http://bbs5.techyou.org/?fromuser=sergio147 Helmholtz layer). Conditions in the bulk electrolyte region are mostly irrelevant with regard to electrode potentials. Only what the electrodes "see" to some limited distance away is important. To use the example above of active species A, the potential of a concentration cell is expressed essentially as r\ nx ΓΐΑΐη lAln_1 V = ^ l o g |A|2 A|2
z
S
L|A|r |A|" J
.
(6.10)
Cells at TRL have been operated with as much as 1.2 to 1.4 volts open circuit. Such high voltages would entail concentration ratios Table 6.2 Calculated voltages vs amp-hour input.
c,
c2
AH Input
End Voltage
Energy Stored
3.9 M
0.1 M
50
0.05
-1/2(2.5) Wh
3.99
0.01
5
0.10
-1/2(0.5)
3.999
0.001
0.5
0.15
-1/2(0.075)
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ENERGY STORAGE
of between 1020 and 1024 for the logarithm to the base ten to be high enough to achieve these potentials. It may seem that somehow the cell operation violates some fundamental law involving conservation of energy or a related issue. Even though the cells depicted in Figures 6.4 and 6.5 are almost identical, because their volumes are the same and the reagents are the same due to the electrode structure and mechanism of storage, one gives immensely greater voltages. Note that the charging takes place at much higher voltages. Hence, the energy input, or work done on the charged ions in "compressing" them into storage at high molecular densities, is also great. As in compressing a metallic spring, the force needed to further compress the metal coil will increase as compression progresses, but that energy is available upon "discharge," minus some irreversible frictional heat losses. This CIR process may be regarded as analogous to a molecular (ionic) spring. The important issues regarding the CIR approach are its very low cost, extremely long life, and abuse resistance. These are the prime factors that motivated exploring the concentration cell approach. In addition, it is an approach that departs in principle from all other batteries. This system depends solely on concentrahttp://bbs5.techyou.org/?fromuser=sergio147 tion differentials of the same materials. Hence, the problems of cell materials and structure corruption due to irreversible diffusion and non-uniform deposition of active reagents are absent. This approach to energy storage enables us to avoid irreversible materials transfer problems and presents an opportunity for exploring many different materials combinations as well as the relatively unlimited possibility of making cells with very high voltages. A brief comparison between the full flow and a static electrolyte does point out the obviously greater complexity of the former. Problems with full flow include the following: • Maintaining reasonably uniform flow through many parallel cell channels • Additional hardware of tanks and plumbing, pumps, and manifolds • Increased complexity of battery module with feeder tubes, etc. • Additional power required for pumps • Self discharge losses when sitting idle with flow • Necessity to build hardware as pressure vessels • The static cell method avoids all of these problems.
THE CONCENTRATION CELL
89
6.3 Further Discussions on Fundamental Issues The following is intended as a quick review of the origin of concentration potentials in an electrochemical cell. Sometimes these potentials are referred to as polarization voltages resulting from starvation at electrode surfaces of reactant containing electrolyte. Concentration cell behavior will be developed here in terms of familiar chemical principles. First, we must define the meaning of half-cell potential to understand the development of the concepts of concentration dependent voltages. The kinetics, diffusion equilibrium, sorption rates, and electric field penetration depths are not discussed at this time because they don't contribute to the basic understanding. There are trade-offs between storage capacity and discharging ability. However, none of these issues are necessary in order to comprehend the technical approach and its configuration. The main purpose is the identification of the important issues in a step-by-step fashion so as to grasp the physical essentials of a concentration cell.http://bbs5.techyou.org/?fromuser=sergio147 Let us examine the potential between a metallic electrode and its ions in solution in its immediate vicinity. Consider the familiar configuration of a copper plate immersed in a copper sulfate solution. One may reasonably ask what the electric potential is between the copper and the solution of its own ions, as shown in Figure 6.6. Unfortunately, there is no physical way of making Pos +
Neg -
Probe electrode
\ - - ^ ' ~ ' Cu ++
_
CuS0 4 solution
Figure 6.6 Standard reference electrode potentials.
H+
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ENERGY STORAGE
such a measurement without the presence of a second electrode. Such measurements have long ago been standardized by the use of either a silver/silver chloride, a calomel electrode, or a hydrogen reference electrode. In general, whenever electric potentials of the various elements are given, they refer to a hydrogen electrode, and that hydrogen reference is arbitrarily set at zero. In this case, the cupric potential is +0.337 volts with respect to hydrogen: Cu+++2e->Cu
+0.337 v
H2^2H++2e
0.00 v
(6.11)
Since the potential of any electrode in an electrolyte is dependent on the concentration of the specific ion involved in the attendant reaction, we know that the voltage for copper is determined at a standardized electrolyte (copper ion) concentration. In most cases, this has been standardized as a concentration in which the "activity" is unity. Usually, the condition for activity = 1 at STP is in a 1 molar solution. The standard hydrogen potential is established at 1 atmosphere pressure of H 2 gas phase and surrounded by http://bbs5.techyou.org/?fromuser=sergio147 hydrogen ions at unit activity. The above is important because one must establish a series of reference or standardized conditions in order to explore any of the cell properties. In the classic Daniel Cell, we have the two metals Zn and Cu in solutions of their respective salts. In Figure 6.7, a porous barrier separates the solutions. The potential between the two electrodes is as follows: Zn^Zn+++2e Cu
++
+2e^Cu
N e t potential
+0.763 v +0.337v 1.10 v
(6.12)
Now, let us look more closely at the situation encountered by an electrode when it is immersed in electrolyte at a "bulk concentration" of any specific solute or ions. The diagram shown below in Figure 6.8 is a standard representation of an interpretation of ion concentration and electrode potential in view of distance from an electrode. The above tells us clearly that there must be "intimate" contact between the electronic conducting electrodes and the molecular
THE CONCENTRATION CELL Positive
Negative
Copper
—
Zinc
Porous barrier
Figure 6.7 The Daniel cell. Helmholtz layer Gouy diffuse layer http://bbs5.techyou.org/?fromuser=sergio147
\
Θ
®e Θ °
2>
©
©
© © ©
© © ©
Distance
Figure 6.8 Electrolyte regions at electrode surfaces.
Solution
91
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ENERGY STORAGE
species undergoing electron exchange. This all happens within a very short distance. The usual porous electrodes are simply not useable here. Their site distances are too great. If we are not able to maintain the intimacy then the cell will be very severely limited in performance by diffusion to the outer reaches of the bulk electrolyte. An electrode immersed in a static electrolyte (non-flowing) sees only a small distance into the surroundings. This distance is not much more than into the beginning of the Gouy diffuse layer. The layer, referred to as the Helmholtz layer, is essentially an electric double layer. The voltage, Δφ, between the electrode and the remainder, or bulk electrolyte, is given as
Δφ = φιη-φ5=ΔφΗ+ψ.
(6.13)
The distances involved are quite small. In most instances where electrolyte concentrations are appreciable, the diffuse layer is in the order of 10~7 cm, or a few ionic (molecular) diameters thick. Obviously, if electric current is produced at the electrode surface, or if there is significant flow in the surface region, the potential http://bbs5.techyou.org/?fromuser=sergio147 diagram above would be distorted accordingly. We can now return to the matter of electric potentials and concentration conditions. In fact, we will use one of the specific couples we have explored as a quick example. Consider the cell (see Figure 6.9) between hydrogen and an inert electrode such as Pt or carbon. One side of the cell is a hydrogen
3 Carbon electrode
Fe+
Hydrogen reference electrode, Pt
i yt
Fe +++ #
H+
Porous barrier Figure 6.9 Hydrogen reference electrode cell.
THE CONCENTRATION CELL
93
probe in an acid solution (H+ ions), and the other is a carbon electrode immersed in a solution of a mixture of ferric and ferrous ions (perhaps ferric and ferrous chloride). The anion, chloride, has little to do with the whole process. The cell reaction is -H,+Fe+++->Fe+++H+. 2 2
(6.14)
Applying the Nernst equation, which says that the potential is proportional to the logarithm of the ratio of the activities, to determine voltage, E=E°-^ln n F
*£**" , Η2 V ~
&
(6.15)
but since aH+= 1 and aH = 1, http://bbs5.techyou.org/?fromuser=sergio147 0
E=E -—ln-^-. nF aFe+++
(6.16)
E° is the electromotive force of an inert electrode surrounded by equal activities of ferrous and ferric ions when measured against the standard hydrogen electrode. When afe++ and ap +++ are equal, the last term becomes zero. These activities have direct relationships to concentrations, and in some instances (dilute solutions) it is possible to substitute concentrations for activities as a very first approximation of cell voltages. Now imagine a cell wherein both electrodes are chemically inert (carbon) and are immersed in a mixed solution of ferrous and ferric salts. The net potential between them would obviously be zero, if for no other reason than the symmetry or sameness of both sides of a cell. An oxidation/reduction process does take place but strictly to provide a mechanism for electric charge transport. In no way does this redox contribute to either the cell voltage or the energy level. As you can see from the basic thermodynamic equations resulting in the Nernst relationship, nowhere do the properties of the specific reactants appear other than their concentration.
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ENERGY STORAGE
Figure 6.10 illustrates a simple concentration cell for non-porous electrodes. Both sides are the same except for the differences in concentrations of ferrous and ferric salts (not ions by themselves). Not shown is the fact that the solution is acidified and conduction is mainly by H + ions. Cation membranes are employed, and iron is notoriously sluggish as a charge carrier. All reagents, whether they are ferrous, ferric, or sulfide salts in polysulfide cells, are assumed to be in uniform solution in the bulk electrolyte volume on their respective sides of a cell. Cells with more practical characteristics do not have as simple a configuration as those shown above. In order to design them for more practical uses, they store reagents in a very concentrated (or very diluted) format within the electrode structures themselves. Such configurations are shown and described in considerable detail in the pages to follow.
6.4 Adsorption and Diffusion Rate Balance http://bbs5.techyou.org/?fromuser=sergio147
The following is a description of the principal aspects of a concentration cell as configured in this development and is in the form of a device where the internal charges are ions in "solution." There are few chemical elements and compounds that lend themselves well to such processes. The active material chosen as
Right side
-
Carbon electrodes
•"■*-
Fe++
f -Γ s(.·:
%
$^
-
Fe++ +
Microporous barrier or ion exchange membranex Figure 6.10 The iron concentration cell.
— —
Fe++
Left side
THE CONCENTRATION CELL
95
representative of this class of device employs sulfur as both oxidizer and reducer. In addition to treating the diffusion rates through a separator into and out of the bulk storage regions, the rates of adsorption/ desorption must be taken into account. As a first approximation, let us use the expression by Langmuir regarding adsorption isotherms. This approximation does not account for changes in adsorptivity as the surface sites become more occupied, nor does it account for any changes in the ratio of the coefficients oca and ccd, the adsorption and desorption, in the constant relationships below. Rate of adsorption = cca (1 - Q)C Rate of desorption = ccd0
(6.17)
C is the concentration of the species in solution being adsorbed, or the adsorbent, and Θ is the fraction of the total available sites that are occupied by adsorbent at point in time. The introduction of this new term changes not only the mathematical balance equations but also the very nature of the mechanisms of storage.http://bbs5.techyou.org/?fromuser=sergio147 Now the electrode is no longer just seeing the concentration of specific ions in the surrounding bulk electrolyte, but it primarily sees the concentration of the adsorbed ions readily available at the electrode surface. Therefore, it becomes necessary to modify the model and our way of thinking about what may be happening within the cell. The rates are as follows: • Rg = generation rate of S= ions, always at the (-) electrode = K I g
• Rs = adsorption rate = 0^(1-6)0 • Rd = desorption rate = ocd6 • R = net diffusion rate across the membrane = m
K m /V ( 2 Q r Q o ) . In more general terms, this may be expressed as a sum of differentials as follows. Figure 6.11 is a diagram of the "compartmentalized" nature of the cell, with the "Helmholtz" region being essentially what the electrode sees, and is the concentrated electrolyte in dynamic equilibrium with its solid forms on the surface of the porous electrodes.
96
ENERGY STORAGE Inner electrolyte region, CH
Bulk electrolyte region, CB
Conductive substrate
KS Hi 5
I
its! Porous carbon
S
Separator-membrane http://bbs5.techyou.org/?fromuser=sergio147 Figure 6.11 Half-cell representation.
This region of electrolyte is also in dynamic equilibrium with the bulk electrolyte occupying the volume between the electrodes and the separator membrane. The bulk concentration differentials across the separator determine the diffusion rate of soluble components, e.g., sulfur complexed with sulfides and sulfide ions from one side of a cell to the opposite side. Low solubility versus high salt solubility is an interesting issue. Also, we want salts to go into solution fast to sustain higher cell currents but to also precipitate out of solution for higher retention purposes.
dQ Ϊ f d Q W d Q ^ J*Q) J*Q) (6.18) dt A* U t A UtAiff UtAa UtApt In equation (6.18) the terms are defined as follows: (dQ/dt) n e t is the net rate of increase of the specific ion. (dQ /dt); is the rate of ion production by charging electric current.
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(dQ/dt) diff is the loss rate by diffusion away from the electrode. (dQ /dt) ad is the loss rate from solution by adsorption. (dQ/dt) p p t is the loss rate by precipitation of their compounds. Thus, there are the balances between the rates of desorption as well as the solubilization of the precipitated reagent, in this case, Na2S. The rates of sorption and diffusion are placed in the loss category since they represent losses from the (-) electrolyte. Furthermore, desorption and the electrical generation rates are to be considered gains, or sources of S= ions to the (-) electrolyte. In this fashion, we can handle the ensuing balance equations. Thus, the net rate, R, into the (-) electrolyte can also be represented by equation (6.19): R = Rg+Rd-Rs-Rm,
(6.19)
where R is the production rate by electric current, Rm is diffusion rate, Rs is the sorption rate, and Rd is the desorption rate. More specifically, the above becomes http://bbs5.techyou.org/?fromuser=sergio147 R = K a I - oca (1 - e ) Q + a d 0 - ^
(2Q 1 - Q 0 )
(6.20)
6.5 Storage by Adsorption and Solids Precipitation The most important parameters for optimum cell operation are (1) to maximize energy capacity by increasing the amount of charge density per unit area of electrode and (2) to establish high and sustainable concentration ratios of ionic components, i.e., large concentration at the (-) electrode and small concentration at the (+) electrode. One way to enhance charge capacity while reducing diffusion losses is to make use of solid precipitates. If the solubility of the sulfide compounds is exceeded, then they will precipitate out of solution and, by design, onto the surfaces of the electrodes. This provides for the additional supply of reagents and in a form that will remain within the (-) and (+) cell compartments for longer periods of time.
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ENERGY STORAGE
If we stipulate a simple linear relationship between the solution and dissolution (re-solubilizing) rates for the solid sulfur and polysulfides that fall in and out of solution, we can express this additional factor as follows. Let the rates R x and R 2, the rates with which the compounds are precipitated and dissolved, be represented as R^ß^Q-C.) Rp2=Pß2,
(6.21)
where ß : and ß2 are constants at any given temperature, C^ is the concentration of the S= ions in solution, and P is a constant associated with the amount of solid Na 2 S in solid precipitate form. The term Cs is the maximum concentration that the electrolyte will tolerate prior to "salting out." This last term is not a constant and tends to be very dependent on conditions such as temperature, presence of suspended solids, etc. The concentration tendencies of Cv being somewhat above Cs, will drive the precipitation of material out of solution. We can assume, for the sake of simplicity, that http://bbs5.techyou.org/?fromuser=sergio147 the relationships are linear. Thus, the complete rate equation takes the form Κ = Κ.Ι-α,(1-θ)^ +ad9-(C1-C.)ß1+Pß2
^(20,-Q0) (6.22)
The net quantity of interest to us at the end of charging is the amount of S= ions available for discharge. That is found by equating the input rates and loss rates at dynamic balance for any charging current, I, as the maximum achievable charge, which occurs when R = 0, or when K.I + a d 6 + Pß 2 = a a (1 - 9)C 1 + ^
(2Q, - Q 0 ) + ( Q - C s )ß, (6.23)
Our main interest in the above derivations is the evaluation of the amount of species, Q a , adsorbed within the electrode. In this case, it's the sulfide ion in the form of the electrically neutral compound,
THE CONCENTRATION CELL
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sodium sulfide. (Ions cannot be adsorbed as such without the accumulation of an inordinately high electrical charge). It is necessary then to put Θ into terms of quantity of material rather than the ratio of occupied sites to total available sites. This is easily accomplished. If we let A = the total number of available sites (per unit electrode volume), then the factor (l-θ) can be replaced in terms of A: =1
K = QK.
= 1 - Θ, then the adsorption rate is "A-Qa A
(6.24)
The only explanation for the magnitude of voltages obtained from our experimental cells is that the mechanism of "electroadsorption" or its equivalent takes place. That would necessitate a small layer of "stagnant" electrolyte at the electrode porous surfaces. This layer might be thought of as a very dense cloud layer, δ, of concentrated species (S= ions) that are about to be adsorbed. The balanced http://bbs5.techyou.org/?fromuser=sergio147 rate equation is thus modified to reflect this micro-layer assumption as K a I + a d 9 + Pß 2 = a a ( 1 - 8 ) ^ + ^ ( 2 0 , - Q 0 ) + ( C B - C . ) f c , (6.25) where Cg is the concentration of S= in the immediate neighborhood of the electrode and precipitate surfaces. Substituting the expression for Θ in terms of Q a , the amount adsorbed, we get
K.I + a d ^+Pß 2 = a . ( l - ^ ] c 8 +^(2Q]-Q0)+(C8-Cs)ß1.
(6.26)
The time delay between adsorption and generation by electric current and charge transfer largely gives rise to this δ layer of not much more than a number of molecular diameters, or mean free paths in thickness.
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ENERGY STORAGE
It is very important to the successful operation of such concentration cells, regarding their practical application, that the capacity and charge retention are not entirely, or even largely, dependant on membrane characteristics. Otherwise, we would be engaged in the continuing compromises between electrical conductivity and diffusion coefficients of such materials. Virtually everything that is done to reduce separator electrical resistance also promotes molecular diffusion in membranes. Hence, we seek mechanisms wherein molecular species can be collected to very high concentrations by some sort of bonding or retardation process, while not significantly detracting from either the cell potential or ionic mobility. The membrane serves the purpose mainly of keeping the two bulk electrolytes apart. A high effective concentration of the ionic species of interest (the S= ion in this instance) must be established and maintained throughout the charging process in order to "force" the diffusion of that ion into the carbon surfaces to be adsorbed. A gel electrolyte might very well serve that purpose. Some of our experimental results have shown that excellent operation can be obtained with only a gel electrolyte to immobilize http://bbs5.techyou.org/?fromuser=sergio147 the substances. However, it is necessary to pay attention to the mechanism of electrode starvation when employing gels because the S= ion can be depleted in the δ layer, resulting in high resistance and little charge transfer. The risk with gel electrolytes is that a large amount of the total reagents in the needed oxidation state can be trapped too far from the reaction sites for prolonged periods of time, becoming essentially unavailable for electron exchange.
6.6 Some Interesting Aspects of Concentration Cells 1. All active materials employed have some solubility, enabling all solids that are formed during the cycling processes to be returned to new and uniform positions within the cell. 2. The cell is symmetric in the materials sense, i.e., the active materials are the same throughout the cell. However, they are not symmetric with regard to oxidation state population densities.
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3. There are only two oxidation states available with materials selected, hence the symmetry at discharged condition. 4. Ionic, energy-storing components are stored within electronically conductive, high surface area pores of electrodes, thus enabling high coulombic capacity. 5. To further increase coulombic capacity, active materials are stored in quantities that exceed their solubility in the electrolytes. These precipitated components are deposited and stored also within the pore structure of electrodes so that they may be readily available for re-solubilization and subsequent participation in the electrolytic, energy producing reactions. 6. To obtain and maintain high electric potentials, the concentrations of reducing and oxidizing agents are replenished by the respective precipitation of components. An example of this is during the discharge mode of a cell at the positive electrode. As the sodium ions arrive, the sulfur stored in that electrode solubilizes and generates sulfur ions in association with the newly http://bbs5.techyou.org/?fromuser=sergio147 arrived sodium ions, thus maintaining a high sulfide ion concentration within the close (Helmholtz) region to contribute to cell voltage. A similar, but opposite, process takes place at the negative electrode where solid sodium sulfide salt is precipitated out of solution. 7. All active components are electronically nonconductive to prevent internal short circuit situations that are encountered with metal plating, dendrite growth, etc. For the sake of simplicity, let us replace activities with concentrations R and L for the right and left sides, respectively. Now the expression for net cell potential, E, can be represented as
RT K ++U +++ E = — In Fe Fe .
(6.27)
Examining this cell more closely will reveal some serious limitations regarding maximum attainable voltages and energy densities. Even if we had a perfect barrier (separator with zero resistance and
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ENERGY STORAGE
zero unwanted diffusion or transport), the first limitation would be due to the maximum solubility of the iron salts. They are limited to about 3 molar at room temperature. That means that the limitation would be 1.5 molar solution on each side at the start (assuming equal volumes on either side). Looking now at the voltages that might be expected, we see that, if upon charging we went from 1.4M to 2.9 M of ferrous on the left side, ferrous concentration would be down on the right side to 0.1 M, and, correspondingly, the ferric ion concentrations would be up on the left to 2.9 M and down to 0.1 M on the right. A total charge transfer could be calculated on the basis of cell volumes. Substituting these values into the Nernst equation above, we get E = -0.06log6
'
X
'
0.10x0.10
0.06 logö 840 = 0.15volts. (6.28)
Even if we were able to achieve concentrations of 0.01 M and 3 M on the respective sides, the maximum voltage realizable would be about 0.25volts. Let's now look at the total electric charge http://bbs5.techyou.org/?fromuser=sergio147 available. Taking the maximum molarity change of 1.5 and a volume of 1 cm2 per cell side, the maximum charge transfer would be 0.035 amp-hours at an average voltage of 0.15 volts. Obviously, this needs to be improved. The greatest limitations to attaining higher voltages and energy densities are due to two principal factors: 1. Limitations of solubility of reagents 2. Subsequent limitations to concentration differentials Hence, we cannot be limited by the solubility of reagents if we want high ED. We must, therefore, synthesize another means of keeping the reagents around and available. Reagents are, in this example of an iron cell, ferrous and ferric compounds. If we try to increase bulk electrolyte concentration, the reagents will merely precipitate out and fall to the bottom. However, an actual concentration cell would not have a bottom as such because very porous, conductive materials would occupy most of the intervening space in a cell. In order to overcome these factors, we may resort to storing reagents in an adsorbed or "pseudo-solid" form within electrode structures themselves. This single feature enables us to go well beyond solubility limitations as well as developing and maintaining
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concentration ratios for higher voltages. It is especially possible to achieve these ends because reagents in solid form are not metallic and do not conduct electronically. Figure 6.12 shows, in principle, this approach method. The entire intervening space between electrodes and the separator is occupied by extremely high surface area and electronically conductive carbon. These micro or nano-porous particles are selected for their conductivity range, pore size, and pore distribution. The carbon employed has an available surface area measured as between 1,500 to 2,500 m 2 per gram. This corresponds to a structure whose walls are in the range of 2 to 6 atomic diameters thick. Much of the reagents are stored in an interstitial state on the carbon structure. Estimates based on these kinds of data and experimental findings indicate it might be possible to attain performances equivalent to 10 to 15 molar solutions. Also, by the self-constricted, controlled ionization constants within these structures, it appears that we are able to attain effective concentration ratios of 1010 to 1014 from each oxidation species. In looking at the basic equation for the voltage, it can be seen that, in order to achieve a cell potential of even 1.2 volts, the logarithm http://bbs5.techyou.org/?fromuser=sergio147 term in the expression for voltage must be as high as 20. Neg
Pos
Figure 6.12 Simple non-mobile electrolyte concentration cell.
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ENERGY STORAGE
An additional benefit is the reduction of diffusion losses (increased charge retention) because much of the reagents are stored in an interstitial solid state. Such cells and their electrodes must be fabricated and prepared before assembly to utilize such compactness. There is a balance between undissociated and ionized molecular ferrous and ferric compounds as part of the storage and transport release processes. Our understanding of this and various other processes and energy level change mechanisms is not yet clear, but progress is being made. The attractiveness of these cells is their simplicity and their reversibility for an indefinite number of times.
6.7 Concentration Cell Storage Mechanisms that Employ Sulfur In the CIR system it is necessary to store reagents in very concentrated form at the electrode surfaces themselves. The reagents can be stored as ions in the form of soluble compounds or as their solids ready to go into solution as needed during charging/discharging http://bbs5.techyou.org/?fromuser=sergio147 modes. Bulk storage of reactants, oxidized and reduced state ions, in the electrolyte as dissolved compounds provides very low voltages and specific energy storage density. Most compounds of useable materials, such as those of iron, sulfur, bromine, copper, etc., are limited to about 4 molar at standard temperatures and pressures. Such limitations in solubility give rise to small energy densities. The cells with which we are concerned here are classified as cells with liquid junctions and in which transference takes place. The sulfur system will be our first analytic model for determining the balance of materials at the beginning and end of a charge cycle. If we were to regard only the soluble forms of the sulfur salts, e.g., sodium, potassium, or lithium compounds, the maximum ED attainable is calculated as follows. Let us assume as a first approximation that no polysulfides are formed and that the process is strictly between sodium monosulfide and elemental sulfur. Also, we need to start any charge cycle with the same materials with their concentrations equal on both sides of a cell. The minimum concentrations for balance would be 2 Na 2 / / 2S (fully charged), where / / indicates a divider or ionically conducting
THE CONCENTRATION CELL
105
separator between cell compartments. Also, we will assume for simplicity that the two cell compartments are equal in volume and that only sodium ions are transported across the separator. Let us take this step to discharge. The discharged situation would be Na 2 S + 2S / / Na 2 S + S, which is a symmetrical balance with no difference in concentration on either side of Na 2 S or S. The net transfer of charge per liter per side would be 50 AH. The next workable concentration for balance is an even number of moles, or 4Na2S / / 4S fully charged, 2S + 2Na2S / / 2Na2S + 2S discharged state. The net transfer per liter per side here would be 100 AH. The next, of course, would be 6Na2S / / 6S charged, 3Na2S + 3S / / 3Na2S + 3S discharged. Net charge transfer per 2 liters total of volume is 150 AH. In generalized form, if n is any integer, then the process proceeds as above as 2nNa 2 S + 2nS / / 2nNa 2 S + 2nS charged, and the net charge transfer per total liter volume is simply n x 50 AH. Let us examine briefly the structure of the final reactants. If the highest possible polymers were formed upon discharge, they would be the dimers, or http://bbs5.techyou.org/?fromuser=sergio147 Na2S2. If the cell electrodes were unable to effectively (reversibly) store elemental sulfur, then we would need to resort to the maximum polysulfide at the charged state. That seems to be the pentasulfide, Na2S_. Then the cell at total charge might be xNa2S / / yNa2S5, and thus limited in reactant weight by the necessity for higher ratio of sodium ions per sulfur atoms present. Let us start with a one molar solution of the pentasulfide on one side of the cell and the appropriate molar monosulfide on the opposite side so that we conclude at the end of discharge with the same materials at the same concentrations on each side. The steps toward total discharge are as follows: 1. 2. 3. 4. 5.
XNa2S//Na2S. ( X - l ) N a 2 S / / N a 2 S 4 + Na 2 S (X-2)Na 2 S//Na 2 S 3 + 2Na2S (X-3)Na 2 S / / Na 2 S 2 + 3Na2S (X-4)Na 2 S//5Na 2 S
Hence, the value of X = 9 makes the balance exact at the discharge end. The total charge from this 9 molar mono-sulfide solution would be 200 AH, and the total weight exclusive of water would be 862 grams. The ED for the dry salts at 1 volt is then 105 WH/lb.
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ENERGY STORAGE
Now we shall examine the possible mechanisms for storing the materials in their two states of oxidation. The goal is to structure a system such that a maximum of concentration difference can be achieved between S"2 and S on the two opposite electrodes. It is important to sustain that high voltage over the longest portion of the discharge, or charge delivery.
6.8 Species Balance There are three explanations possible that, at this point, could describe the situation of affairs within the cell at any state of charge. First, let us assume that all species remain solution at all times, that the only charge carrier within the cell is Na + ions, and that there is no net migration of sulfur from one cell side into the other. Vertical bars, I I, enclose concentrations. The two sides of a cell (opposite the separator) are indicated by subscripts a and b: IS°I + I S°l = constant, and
(6.29)
http://bbs5.techyou.org/?fromuser=sergio147
IS;21 + ISb2l = constant.
(6.30)
The above also assumes that the sodium sulfide exits within the pores of the carbon electrodes as ionized molecules. This assumption seems not to satisfy the very high cell potentials experimentally measured in the laboratory with solute concentrations in the range of 2 to 3 molar. We will later examine the diffusion rates and possible high concentration differentials in such a configuration. Secondly, it seems more likely, however, that the species sulfur, polysulfide or monosulfide, would partially be in either a solid state or in an adsorbed state on the pore surfaces. If so, the balance of materials may be expressed as [ ^ l + t ^ l + t ^ l + t S b ] , constant,
(6.31)
where the subscripts relate to the cell sides a and b, and i and s indicate ionic or solid state, respectively. The brackets contain the absolute quantities of the respective ions, or atoms, in either the a or b side of the cell.
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There is also the possibility that these materials may exist not as solids but in the form of an "interfacial state." See "Physical Chemistry" by E. A. Moelwyn-Hughes, Pergamon Press, 1957, pages 894 - 950.
6.9
Electrode Surface Potentials
It is important to consider whether the cell configuration is one with or without transport in order to account for any liquid junction potentials supplementing the electrode voltages. Nernst's relationship does not account for the very high electric potentials attained in laboratory test cells solely on the basis of measured bulk electrolyte concentration differences on either side of cell separators. Since there are no other significant reactions taking place the electrodes must be experiencing ionic concentrations ratios orders of magnitude greater than the bulk electrolyte ratios. The search then begins for a plausible explanation of how a cell with no other energy related processes taking place, other than the difference in http://bbs5.techyou.org/?fromuser=sergio147 concentration of the two oxidation states of the same chemical element, can produce such high potentials and sustain high electrical charge densities. If there are no other processes involved, then we must look toward some mechanism whereby the chemical species in question are able to be accumulated at the electrode surfaces and give rise to such high voltages. At the present time, it is speculated that the specific ionic species, in this case the ferric and ferrous ions, are injected by the process of electro-sorption directly into the pore regions of the microporous carbon at very high effective concentrations. In the case of a concentration cell based on iron chemistry even though the maxim u m concentrations of the compounds of ferric and ferrous chlorides are limited to not much over 3 molar at room temperature, the population densities of the adsorbed and stored ferrous and ferric ions become equivalent to extremely high activities seen by the electrodes. In order to accomplish this, more energy than what is normally needed would be required to separate the oxidation states during the "charging" process. This condition, for the maintenance of conservation principles, has been observed during cell cycling in terms of the volt-amp inputs and outputs. There are undoubtedly many processes and mechanisms that take place at the electrode surfaces that call for greater understanding
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and quantifying. Let us first list and then examine the physical and chemical activity possibilities. Omitting the chances that there are any net or permanent chemical changes occurring in the electrical cycling of the cell, the following are possible, reversible processes: • Exceeding salt solubility at electrodes during charging, resulting in solid compounds at the surfaces with attendant free energy changes (energy of ionization and dissolution) • The creation of immense concentration ratios of S= in the sulfur based cell and of Fe++ and Fe+++ ions in solution at electrode surfaces in iron cells, which are far greater than could exist in the bulk electrolyte perhaps in an interstitial state • Adsorption of iron ions, and perhaps the salt compounds themselves, within the carbon porous structure, which may be Langmuir or van der Waals processes, depending on whether they are attached as electrically charged components or as neutral molecules with dipole moments. http://bbs5.techyou.org/?fromuser=sergio147
6.10
Further Examination of Concentration Ratios
In examining the cell from a practical viewpoint, it is obvious that most inorganic salt compounds are soluble in water only to the extent of 2 to 4 molar concentrations. If we evaluate the performance that can be expected from simple, two compartment concentration cells, depending on bulk concentration differences, the performance as practical storage cells is quite low. For a concentration ratio of 10:1 of a divalent active species, such as sulfide, the cell potential is -0.03 volts. A concentration ratio of 100:1 results in a potential of 0.06 volts. These are exceedingly low values for a device to be practical, and the major portion of the stored electrical charge would be delivered at substantially lower voltages than the above. The maximum charge transfer per liter of 3 molar solution to 0.03 molarity is only slightly more than the transfer from 3 molar to 0.30 molar. In the experiments conducted that relate to this invention, potentials of 1.0 volt and higher are regularly attained and sustained.
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This development provides a mechanism for increasing the voltages and charge densities of a concentration cell by over an order of magnitude above that which are realized simply from differences in bulk electrolyte concentration differences of chemical species on opposite sides of a cell membrane separator. The voltages obtained are associated with concentration ratios of well over 1000:1. An extremely important aspect of this development concerns the method of collecting and storing the differentials in concentrations at the electrodes. In the method employed here, the substances that produce the electric potentials are electrolytically produced ions injected into the micro-pores of both cathode and anode. Activated carbon, especially micro-pore coconut charcoal, is the most effective means for storing most molecular species in an available and reversible fashion. The cell reagents are stored by means of adsorption of the van der Waals type. The carbon structure appears unaltered even after 10,000 cycles of charge/discharge events. Activated carbon has a surface area of approximately 1,000 to 2,000 square meters per gram of accessible surface, depending on electrolyte conditions and physical properties of the solute to be http://bbs5.techyou.org/?fromuser=sergio147 adsorbed. Assuming about 103 m2, or 107 cm2 area per gm, and an average molecular area for sulfur or sodium polysulfide of 3 x 10~8 cm2, the number of molecules that could occupy the surface area of one gram of carbon as a mono-molecular layer is in the order of 1022 molecules, or about 2 x 10~2 moles. That number corresponds to about 0.1 ampere-hours of electric charge for a divalent species, such as sulfur. The bulk density of the active carbon used is in the range of 0.60 gm/cm 3 , and its void space is about 60%. Hence, about 60% of the space occupied by 1 cm3 of charcoal would be filled by electrolyte in a concentration cell that employs such a material as the major electrode structure. From the preceding estimates, about 0.006 ampere-hours of charge can be stored per cm3 of electrode volume. The potential at the electrode surface is dictated by the concentration of the specific ion that is in the immediate vicinity (Helmholtz layer) rather than the bulk concentration that is some significant distance away. Returning to the above estimate of the number of moles adsorbed per gram of carbon, we find that the quantity of material in one cm3 of carbon is ~2 x 10"2 moles. That quantity of molecules, if dissolved in the 0.6 cm3 volume, would correspond to a 40 molar solution. In actuality, the electrodes encounter a much
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ENERGY STORAGE
higher effective concentration because of the manner in which the species exists at the interface. The necessity for introducing the specific reagents into the active carbon pores by direct ion migration by means of an electric field gradient in the charging process can be explained as follows. The rate of molecular diffusion, J, due to a concentration gradient is simply dc J = - D — g r a m s - cm" 2 sec" 1 , dx
(6.32)
where D is the diffusion coefficient, and c is the concentration of a particular molecular species in solution. Generally, D has a value of about 2 x 10"5 cm2 sec -1 for most salts in water solution. The thermal diffusion of solute into the pores of activated carbon would have to take place only as a result of the concentration gradient generated by the adsorption rate out of solution of the specific chemical species. That rate is quite slow. In effect, it would give rise to only a very small value of d c / d x in the above expression. The rate of adsorption of molecules from solution is directly prohttp://bbs5.techyou.org/?fromuser=sergio147 portional to the number of adsorption sites that remain available and the concentration of the chemical species in the immediate vicinity of the carbon surface. This is expressed by the familiar equation Rate of a d s o r p t i o n , R a = (1 - G)k a ,
(6.33)
where Θ is the fraction of the total number of available sites that are occupied by the adsorbents on the carbon surface, and ka is an experimental constant of the tests. If the storage of a substance by adsorption depends solely on thermal diffusion as the driving force, the process is very slow and is severely counteracted by diffusion in the opposite direction as sites are increasingly occupied. However, if an electric current is applied to the ionized salt solution with a current density of 0.01 amps/cm 2 , then the migration rate of the species will be in the range of 1016 ions per second, or about 3 x 10~7 gm s e c 1 cm2. That is a much greater rate than can be expected from the thermal diffusion rate estimated above.
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6.11 Empirical Results with Small Laboratory Cells The voltages experimentally obtained in single cells do not conform to the simple expression (RT/nF) x l n ^ / c ^ . The values are much greater than predicted. The main question is why Since the cell is symmetrical, voltages are kept low, and since there are no sources of energy other than concentration differences on opposite sides of the separator, the operation would appear to be a simple concentration cell. Let us examine some of the cells' performances. Doing so requires the following data: • Cell electrolyte capacity ~ 12 cc per side • Electrolyte composition and AH capacity to same composition on either side • Some test data, i.e., AH input and voltages obtained • Empirical potentials agree with the concentration relationship even when assuming no loss due to diffusion, http://bbs5.techyou.org/?fromuser=sergio147 etc. Solutions have been 2.5 molar in Na 2 S with added sulfur of 100 gm per 100 cc of 2.5 molar monosulfide solution. This would make the solution at full charge Na 2 S//Na 2 S 4 . However, this does not result in 0.05 AH capacity per 1 cc of total solution (both sides of cell). The empirical shapes of the charge/ discharge curves for the single cell-porous secondary cells do not conform to concentration cell mathematical predictions. A 10 cell module with no significant storage on porous electrodes did give the performance predicted by concentration cell math. A significant question is whether the van der Waals "forces" provide additional energy for discharge in the porous electrodes, or whether it simply provides for a higher apparent concentration differential. Also, there is the issue of the thermodynamics (energetics) associated with adsorption. Heat is usually liberated when molecules drop into the adsorbed state. If so, how does that affect the storage of energy? Usually, heat must be applied to free adsorbed state molecules. Hence, that cannot contribute to the cell potential. Perhaps it contributes indirectly by making the apparent concentration
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ENERGY STORAGE
greater by holding onto species in greater surface densities. Is it possible that simply the huge increase in concentration as charging proceeds would account for this? Let's assume that the electrolyte is the large "storage volume" of a cell for the reagents to reside in as a reservoir. Upon charging, these species are concentrated in very small volumes on the porous electrode surfaces and appear considerably more concentrated than the simple equations that employ the reservoir electrolyte volumes in the log relationship. Generally, the energy (evolved) of adsorption is low, about 10 kcal/mole adsorbed, which is about the same given off when gas condenses to liquid. Thus, the energy of adsorption is to be subtracted from the potentials realized via concentration differences. To explore single layer and multilayer adsorption, reviewing the Freundlich and Langmuir equations would be helpful. Langmuir relations apply best to saturated situations. Equilibrium is reached when desorption rates are equal to adsorption rates. One of the adsorbents can also be the solvent, taking up space in the adsorbent surfaces. Now we will discuss what the electrode experiences in terms of electrochemical potentials within these layers. Is it strictly a http://bbs5.techyou.org/?fromuser=sergio147 concentration voltage, or are there other processes involved? For treatments of energies of interfacial states, etc., see Moelwyn and Hughes, pages 922 et. seq. Some factors that influence the shapes of curves of cell behavior are listed below: 1. Electrical current, upon charging, "forces" the ions or molecules to become more concentrated than can be accomplished otherwise. The greater the current density, the greater the concentration of ion densities. 2. As proximity of these ions increase, the greater are the van der Waal "forces" that tend to further concentrate them. 3. As the population density of the species increases, the rate of adsorption increases at the electrode porous surfaces. 4. At least the "apparent" concentration differences between cell electrodes are enhanced. 5. We should address the reagent ion concentration seen by the electrode as the number of ions per unit volume in the immediate vicinity of the electrode rather than
THE CONCENTRATION CELL
113
the calculations based on the "bulk" concentration of the cell on either side. 6. The voltages observed across a cell are well beyond what the simple macroscopic calculations predict. They might then be due simply to a temporarily high build-up caused by slow reagent diffusion away from the electrodes during charging. Then, the dwell time of these voltages would be very much shorter than observed in laboratory cells. If the above is true, then we must determine the specific volume for the electrode so that the concentration of reagents can be computed. So, let us see if we can approximate the performance of a cell as if it had small volume but molarity in the ranges of 10,20, to 100. A good number to use for effective molecular diameters in these types of calculations, as obtained from diffusion and viscosity measurements, is about 5 x 10"8cm. Then, examine the adsorption process on the basis of sorption rates due to thermal motion of molecules impinging on the outer porous electrode surfaces. Consider how movement under a voltage gradient impressed across the cell http://bbs5.techyou.org/?fromuser=sergio147 would change anything in terms of capture probability or desorption rates. For additional information about mean free paths and activation energies see pages 443, 448, and 348-350 of Daniels and Alberty. For some straightforward mathematical treatment of adsorption and capture probability see page 523 et. seq. Similarly, the Langmuir isotherms should lead the way for energy and electric potential relations in adsorption processes. Koreyta, in his book on electrochemistry, provides some inputs on pages 226, 227, (Helmholtz layer and Gibbs free energy of adsorption) and 246 on electrode processes and adsorption. He also discusses the solvent as being a structure less dielectric in which ions move about and interact. Now consider the diffusion rate of a molecule or ionic species at room temperature within a solvent such as water. We can estimate this strictly from the classical kinetic theory. Then, see how many will diffuse across a unit area per unit time and compare this with the flow rate of an ion if a voltage gradient were imposed across that same area. The diffusion coefficient D is defined in the relationship d q / d t = D (dc/dx), where the linear concentration gradient is in the direction normal to some unit area. The problem here in determining
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ENERGY STORAGE
the amount of net flow, or number of molecules diffusing into the porous charcoal sites, is that there is no thickness layer to assign. Hence, we might just look at the desorption rate for the solid surface (and make a guess as to its surface volume) and solve for a diffusion layer thickness that would match adsorption rate data and diffusion. For example, if we plot the rate d c / d t for a given solution and molecular species and then look for where the curves of adsorption rates and diffusion rates intersect, it should tell us what the initial conditions are. As adsorption progresses, the rate of adsorption will decrease because sites are being filled and desorption becomes a significant factor in the ultimate equilibrium. Moving boundary layer data with ionic solutions provides some useful insight into ion mobility as well as ionic velocities. The migration or diffusion of ions under the influence of a voltage gradient follows the same mathematical format as Fick's law for molecular diffusion. One simple configuration of a concentration cell employs the two soluble oxidation states of iron. In the case of metallic materials, we are much lesshttp://bbs5.techyou.org/?fromuser=sergio147 interested in using their elemental state because of the consequent possibilities of short-circuiting a cell via metallic dendrites and gas evolution, especially of free metals on electrode surfaces in an acidic electrolyte. The reaction of ferrous/ferric solutions discussed previously does operate very well as a concentration dependent cell, but care must be exercised during "charging" to maintain voltages below the hydrogen evolution level, usually in the vicinity of 1.2 volts in the acidic electrolyte. However, this problem can be avoided by resorting to non-aqueous solvents as electrolytes. Such cells employing organic solvents generally have higher electrical resistance, and the salts will usually be less soluble. Limited solubility is not necessarily a serious problem if the cells are designed to operate beyond that point with solids in the electrolyte.
6.12 Iron/Iron Concentration Cell Properties Balancing the concentrations of components in a ferric/ferrous cell for the basic reactions that take place at either electrode is simply Fe+3+e"^^Fe+2.
(6.34)
THE CONCENTRATION CELL
115
The components on either side of a functioning concentration cell can be represented as shown below. The composition of the reagents must be the same on both sides of a cell separator at the end of discharge. At the beginning of discharge (charged state), the conditions are 2FeCl2 111 FeCl3. The cell could be represented at the end of discharge as FeCl3 + FeCL, / / FeCl2 + FeCl3 symmetrical. We can now calculate the maximum available energy density for this process, assuming a maximum of 1 volt potential difference in aqueous solutions to keep below the hydrogen evolution voltage in an acidic environment. The total molecular weight, ignoring that of water, is 2 x (56 + 2 x 35) + 2 x (56 + 3 x 35) = 574. Since there is a single charge carrier, there is 26.6 AH per 454/574 = 0.79 lb of reagents. This works out to about 1 volt x 26.6 x 0.79 = 21 W h / l b divided by 2 as an average load voltage, or about 11 W h / l b or dry reagents. The actual number is quite a bit lower when accounting for weight of water, or other solvent, and the dead weights of electrodes and enclosure. Despite the low ED, the system may be useful because of its low cost, high safety, and reliability of performance in stationary http://bbs5.techyou.org/?fromuser=sergio147 applications. The above estimates presume that the electrical charge carrier is the chloride ion, Cl". A second version of this concentration cell could depend on positive ions as charge carriers. Perhaps the best would be the hydrogen ion, H + , because of its high mobility and consequent higher conductance in solution. A cation, or positive ion transfer membrane, could be employed in the cell for best separation and lowest diffusion losses. However, a microporous membrane could serve well also. The cell composition at full charge might look like 2FeCl2 + HC1 / / 2FeCl3. At the end of discharge, the components on either side of the separator would be the same with the exception that HC1 has been transposed, or FeCl2 + FeCl3 / / FeCl2 + FeCl3 + HC1. The ED of this process is even less than that of the preceding because we must account for the additional weights of HC1 in the reaction.
6.13 The Mechanisms of Energy Storage Cells There are a few chemical elements and their compounds that lend themselves well to such processes. Preference at this time is
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ENERGY STORAGE
for sulfur, and it is the material about which we have the most empirical data. The reactions occurring at each electrode during both charge and discharge are S + 2e ^± S"2. The element and its alkali-metal compounds are cheap, plentiful, safe, well behaved at room temperature, and have very useful properties such as the ability to readily form "polymers." These polymers are merely sulfur atoms attached to the sulfide components such as the following: Na2S + S
Na 2 S 2
Na 2 S 2 + S :
Na2S3
Na2S3 + S :
Na 2 S 4 a n d so forth
(6.35)
All of the above are very soluble in water and other polar solvents. Please note, however, that the sodium ion has nothing to do with the potential producing mechanisms. It is merely the cation http://bbs5.techyou.org/?fromuser=sergio147 part of the compound that could just as easily be served by K, or NH 4 . In order to have conduction within a cell and not have an accumulation of electrical charge on either electrode, the transport mechanisms must be accompanied by suitable oxidation/ reduction processes for the exchange of electrons in an external circuit. Figure 6.13 below shows a very simple cell of two electrodes, an ion transfer separator, and two equal volumes, V, of electrolytes.
Ci
Figure 6.13 Cell diagram.
THE
CONCENTRATION CELL
117
The cell voltage is proportional to the logarithm of the concentration ratios in the immediate vicinity of the electrode surfaces. However, for the sake of mathematical simplicity, let us assume that the cell potential, E, can be expressed as
E=K
Lc2J
Q f = K /vl = K
LQ 2 J
(6.36)
where
Q^Q^Jidt, Q2 = Q 0 -Jidt
(6.37)
The simplified descriptive approach above avoids mathematical complexities http://bbs5.techyou.org/?fromuser=sergio147 that contribute virtually nothing to the main arguments of cell operation. A plot of the voltage versus charge before substitution of the last expressions is a straight line. As the cell is charged from its totally discharged state, in which all concentrations are equal to Q o , more Sulfides accumulate on one side (-), and the sulfide ions are depleted on the other (+) side. However, if we substitute idt for the variable Q, the dependency of E upon Q is transformed from a linear dependency to a different
Q
—►
Figure 6.14 Simple linear dependence of voltage on concentration.
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ENERGY STORAGE
shape. Making the substitutions, the subsequent approximations lead to the following equation for E: E=
Qo+Jidt
Qo + iAt
Q0-}idt
Qo-iAt
(6.38)
To simplify further, we may just let iAt = x to see how the parameters are interdependent. So, we obtain E=
a+x
(6.39)
a-x
where a also represents Qo. Differentiating the above with respect to x, — = d|(a + x)(a-x) L dx
J
\ =--f f. (a-x) (a-x)
http://bbs5.techyou.org/?fromuser=sergio147
(6.40)
A plot of E versus x looks like the illustration below, in which the voltage changes increasingly rapidly as x increases and approaches the value a. This is hardly a linear relationship. It is obvious that, as x increases, the voltage is large for smaller intervals of x as x approaches a. But, at these higher potentials, the ion carrier population density grows quite small, meaning that less charge is available at higher voltages until x = a, when no further conduction is possible. In practice, we would want to modify this behavior in a cell because only a small portion of the total charge would be delivered
dx Figure 6.15 Shape of the functional relationship in equation 6.39.
THE CONCENTRATION CELL
119
at the higher electric potentials. Herein lies the rather important, if not critical, part of this approach. First, we want to have as high a concentration of our reagents, in this case S"2 and S, as possible from the very start. This is partly accomplished by having some of the reagents Na 2 S and S initially in solid form within microporous carbon electrodes. Remembering that only the sulfide ion S~2 counts in the math for determining potential, we want high concentrations of such ions along with the necessary sulfur molecules to be available at both electrodes. Normally, this availability is limited at any time because of the solubility of the salt, Na 2 S. Therefore, we store a fair amount of it in "solid form" at the electrodes. Initially the cell has equal amounts of both sulfur and sulfides at each electrode. As charging progresses, sulfides are created at one electrode and sulfur at the other. A maximum value of sulfides at one electrode is reached, and continued charging results in solids coming out on that electrode stored for later discharge. Similarly, at the opposite electrode sulfur is deposited for later discharge. When discharge begins, the cell voltage is quite high because http://bbs5.techyou.org/?fromuser=sergio147 of the concentration differential that develops. As the cell is discharged, some of the sulfides become solubilized, replacing the loss of sulfides on the concentrated side and, thus, keeping the potential up. On the opposite side during discharge, the transferred sodium ions that are produced result in continued diminishment of sulfide ions and the release of sulfur. Thus, we have a reservoir of ions beyond solubility that is available to the electrolyte/electrode interface at some rate determined by diffusion constants and dynamics of electron transfer and solubilization rates. The discharge currents must be kept low enough so that the supply mechanism can keep up with the demands and maintain high potentials. This is the case because inordinately high voltages have been obtained with cells that have been provided with such structures at the electrode surfaces. Cells with no porous carbon provisions generate potentials in the range of at most 0.03 to 0.08 volts even after prolonged charging. Smooth electrodes give the expected performance shown by the Nernst equation. The thermodynamics are certainly correct, but practical performance is immensely altered with storage, probably by virtue of interfacial forces of the van der Waals type.
120
ENERGY STORAGE
The exact mechanisms of how the reagents are stored are not entirely understood, that is whether they are stored as solids adjacent to the electrode surfaces or actually adsorbed as ionic materials, etc. It makes a difference when one wishes to perform analyses or optimize parameters. Let us assume for the moment that, after solution saturation of the sulfides and polysulfides have been attained, further charging results in solids accumulation. Then we must consider the rates at which solution and dissolution takes place. Let us assume further that the rates with which the species are removed as solids and returned as solutes are simply proportional to the concentrations Ca and C b of the respective species, sulfide and sulfur. Then the rates R at which the sulfides and sulfur solidify can be expressed as the following functions:
R. = 4 ( ^ 0 . 4 ) Rb=fb(C2,Cb,i)
(6.41)
Obviously, the rate of removal of sulfide will be directly proporhttp://bbs5.techyou.org/?fromuser=sergio147 tional to its concentration in solution, inversely proportional to the amount already in solid form at the electrodes, and to some extent due to the electrical current density. The exact form of the above functions can be better estimated with more modeling of the rate mechanisms. The very reproducible and consistent experimental evidence that we have obtained to date with hundreds of cycles and many lab cells would indicate, according to the Nernst equation, that the electrodes are seeing concentration ratios as high as 1020 or more for us to be able to obtain 1.5 to 2.0 volts: The N e r n s t Voltage, E = 0.059 L o g i Q / C 2 )
(6.42)
A fascinating aspect of this system is that it does not depend on the voltages of any couple such as Zn/Br (1.8 volts), Z n / C u (0.8 volts), etc. The materials are the same on both sides of the cell only at different concentrations. Diffusion of unwanted materials from one side to another does not result in irreversible run down of the cell. Aging mechanisms are scant, no gasses evolve, and pH stays constant. The carnival prize seems to be worth the effort to squeeze maximum ED out of it.
THE CONCENTRATION CELL
121
The oxidation and reduction at the two electrodes necessary to get an electrical output is simply S + 2e = S=. Iron will do the same thing between ferrous and ferric. The ionic species, sulfide ion, is stored within the porous electrode structure at effective concentrations that are much greater than what can be achieved in solution. The sulfide ion storage is at electrode surfaces. Some of that storage is probably in the form of solid sodium sulfide immediately adjacent to electrode surfaces and available to those surfaces as they return into solution. Some storage probably takes place in ionic form as adsorbed materials. Charge retention is a function primarily of the solubilization rates of reactants and diffusion across a membrane barrier. Dependence on the latter should be minimized because of the unavoidably encountered trade off between molecular diffusion and electrical conduction.
6.14 Operational Models of Sulfide Based Cells It is now necessary to develop some simple working models of http://bbs5.techyou.org/?fromuser=sergio147 the processes within a cell during both charging and discharging modes at each electrode. It will also be necessary to make some simplifying assumptions in our first attempt to explain what is happening at interfaces and at boundaries between phases. There are only three forms in which the reagents can exist in the immediate vicinity of the electrodes: (1) as solids of composition Na.S and s, (2) in solution with water as Na + and S= ions or dis2 x
'
solved as polysulfides (unionized sulfur attached to the Na 2 S molecule), and (3) in the adsorbed state on the porous carbon electrodes as ionic species or as polysulfides. This situation is illustrated in Figure 6.16 with some assigned designations for the concentrations β
Electrode
_
Solids
Adsorbed layers (Interstitial)
' // //
Figure 6.16 Sulfur species at electrode vicinities.
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ENERGY STORAGE
of these various quantities. The diagram is strictly a schematic form and does not necessarily display the actual physical structure and relative locations of the components. Certain additional presumptions must be made at this point in order to move forward with an analysis. These presumptions can and will be modified as we learn about what takes place inside the cell. When possible, we will take the path of greatest simplicity, Occam's Razor approach. As a first model for analytical purposes, let us assume only two non-porous electrodes and a membrane that separates the two compartments. This is shown in Figure 6.17 below. The storage of reactants and reagents takes place in this first model solely in the electrolyte as dissolved components. The initial concentration, Co, of the active reagent, Na2S in this case, is simply
c=v
(6.43)
where V is the volume for electrolytes on each side of the cell. If we designate I as thehttp://bbs5.techyou.org/?fromuser=sergio147 electric current (ionic) passing through the cell upon charging, then the rate, d Q / d t , with which sulfide ions are produced from dissolved sulfur (polysulfides) in the (+) side of the cell is as follows: dt — - k — dt ~ ' V
(6.44)
Solution
Na,S [Na+, S=]
Figure 6.17 Storage and flow model - first balance analysis.
THE CONCENTRATION CELL
123
There are four principal mechanisms that we know are involved in the operation of a cell. At the negative electrode during charging, they are the following: • The generation of sulfide ions by migration of positive sodium ions toward the negative electrode • The diffusion of ions across the barrier from one side of the cell to the other by virtue of concentration differentials of those specific species • The adsorption and desorption of molecules onto and out of the surfaces of porous carbon electrodes • As solute concentrations rise within an electrolyte, some portion will come out of solution (precipitate) as solids. There are some other secondary issues associated with cell operation, such as concentration gradients within cell compartments, the number of water molecules adsorbed onto electrode surfaces with the solutes, and whether the adsorbents are still "in solution" as ionichttp://bbs5.techyou.org/?fromuser=sergio147 species or as undissociated molecules. However, for the present we will ignore these matters to keep the operational explanations and descriptions as simple as possible.
6.15
Storage Solely in Bulk Electrolyte
To further shorten and make more specific the ensuing descriptions, let us treat the sulfur/sulfide system as the one in question, and let us be concerned, at the beginning, solely with the processes within the negative side of the cell. That then defines the species with which we are concerned - the S= ion and the S molecule. During charging, sulfur is reduced to sulfide with the acquisition of two electrons at the negative electrode. At the positive electrode, Sulfides are oxidized to sulfur by giving up two electrons, a remarkably simple and symmetrical cell. Looking strictly at the flow balance of S= ions generated at the electrode and diffusing across the barrier per unit area of working electrode and barrier, Ra = generation rate of S= ions = K I, and Rb = loss rate by diffusion (Fick's first law) = IC^Cj - C2), where CT and C2 are respectively the S= concentrations in the negative and the positive sides.
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ENERGY STORAGE
Net rate, R, of accumulation of S~ in the negative side is R = R - Rv
(6.45)
Putting the above in terms of electric current and ion quantities, we get the following: at any time, t, the amount of S= ions present in the negative and positive sides are Qj and Q2, respectively, and the sum of these amounts is always Qo. Thus, R-
^ L = Kb(C1-C2) = ^ ( Q 1 - Q 2 ) = ^ ( 2 Q 1 - Q 0 ) . (6.46)
Initially in a discharged cell Qj = Q2, and as the cell is charged by the electric current Q^ becomes larger until it reaches a value great enough such that the rate of charging equals the loss of S= ions via diffusion across the barrier. This value is attained when R = R,, or a
K ahttp://bbs5.techyou.org/?fromuser=sergio147 I = Kb(C1-C2) = ^ ( 2 Q 1 - Q 0 ) .
b'
(6.47)
The concentration differential attainable in such a simple cell is severely limited by diffusion losses, and the cell potential is limited by the maximum concentrations that can be provided for the electrodes. The total electric charge available at higher cell potentials would be quite small, as is evidenced by the algebraic comparisons below of charge density at different voltages. Since the sum of the sulfide ions present within the cell is a constant, we shall designate it Qo. Then, it follows that Qj + Q 2 = Qo. As Qj approaches Qo, Q 2 approaches zero. If we continue, for the purposes of mathematical simplicity, in letting the cell potential, E , be directly proportional to the cell concentration ratios rather than its more representative form given by Nernst, (the relationships will be corrected later after the present arguments for dynamic cell balance are established) then we can state the following: E =K
|"c21 = K [Qil = K \ Q, 1 Q2
Qo-Qi
(6.48)
THE CONCENTRATION CELL
125
Upon charging or discharging the energy, Ψ, we can evaluate the integral between two different sets of limits and compare the numerical results for energy input or output over the respective voltage ranges. The energy over any interval of time or voltage may simply be represented as Ψ=Ε, xQ.
(6.49)
Expressed in a more useful manner, the incremental change in energy because Ec dQ = Q dEc is Qi
ά Ψ = EdC^ = k
Qo-Qi
dQr
(6.50)
The integral of this equation is
Jc«' = -k[Q1 + Q0ln(Q0-Q1)].
(6.51)
http://bbs5.techyou.org/?fromuser=sergio147 Putting the above expression in terms of voltage, we obtain the more convenient form
E Q 0 = Q 1 ( k + E) Wl
(k + E)·
(6.52)
And the differential of energy assumes the form d ¥ = Q0
-dE. (k + E)
(6.53)
Integrating this last expression in terms of E, we get Ψ = ίJΕ α Ε = < 2 J0 ί — Ε — dE = E - k l n ( E + k ) (k + E)
(6.54)
Now, to illustrate that there is less energy available over any voltage interval upon discharge at the higher voltages, we need to merely look at the derivative of Ψ to see that as E becomes very large
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ENERGY STORAGE
the slope of the curve of Ψ decreases and approaches a constant value of Q . At a later time, the more representative Nernst expression can be substituted for cell potential, E, i.e., E= kRTln^. C2
(6.55)
At present, the exact form of the voltage dependence on concentrations is not important to establishing the argument for dynamic stability of the cell.
6.16 More on Storage of Reagents in Adsorbed State In our previous approach to describing a dynamic balance of ion flow we considered only the rate of species generation via electric current counterbalanced by the loss of those species across to the http://bbs5.techyou.org/?fromuser=sergio147 opposite side of a cell by diffusion through a membrane. Membrane impedance to diffusion loss is limited mainly by a compromise with electrical conductivity through the same separator. Let's introduce an additional and primary method of materials storage - adsorption. This is accomplished by employing microporous carbon attached to the surface of both electrodes. In the negative electrode, S= ions are stored in the form of the Na 2 S compound, and in the positive electrode the S is stored as either Na2S unionized, Na 2 S x , or as the element S. Actually, S is stored at both electrodes during the entire process as a reservoir of reagents during charging at the negative electrode and for discharging at the positive electrode. However, the presence of S at either electrode does not enter into the thermodynamic relationship for electric potential. With such a modification of cell design we are able to develop much higher effective ionic concentrations. Let me use a fictitious configuration below to illustrate the essence of such improvement. If it were possible to establish a very small compartment with volume, δ, per unit area immediately adjacent to each electrode by means of an idealized barrier, as shown in Figure 6.18, we would be able to build electrolytically gigantic concentrations of species supplied by the much larger reservoirs of volume V.
THE CONCENTRATION CELL
127
,δ
Immediate region to electrode surfaces
Separator Figure 6.18 Hypothetical compartments at electrode surfaces.
From our earlier relationship regarding potentials and concentration ratios (we will stay for a short while longer with the linear model rather than the more representative logarithmic one), the cell potential as a function of charge now becomes associated only with the concentrations in the region δ. Before we can proceed further with modeling the cell it is necessary to more closely examine the processes at the electrodes within the δ region. (See Figure 6.19). In the previous simple situation of flat electrodes and a single membrane, we assumed perfect and instantaneous mixing of electrolyte solutes. If we make that assumption again in this new model, http://bbs5.techyou.org/?fromuser=sergio147 we encounter some difficulties. Let us look at what happens at the negative electrode (realizing that a similar situation takes place at the positive side). In order for the reduction of sulfur to sulfide ions to occur, it is necessary to have a continuous supply of sulfur immediately available at the negative electrode. This supply can exist as Neg o
1
A
t
<
Na+
t 2Na + + S + 2e"-4 Na2S ] N a 2 S o 2 N a * + S= f
Charging process
Figure 6.19 Representation of processes at electrode surface regions.
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ENERGY STORAGE
solid sulfur in the electrode or as polysulfide ions in solution. In order to be able to charge the (-) electrode, sulfur must have either been previously stored within the δ compartment, or it must be made available as a stream from the large V reservoir. A mechanism is needed to keep the S= ions in the immediate neighborhood of the (-) electrode in order to retard their drifting away into the bulk solution. The latter explanation is based on the small compartment having free access via molecular diffusion to the entire electrolyte. That would make the situation identical to "storage in bulk electrolyte," as described in the first case. In addition, high concentrations cannot be accumulated because of mixing. Then, other than the storage of sulfur prior to charging, there is no method we can visualize in which the δ region can sustain the high concentrations necessary for high electrode potentials. However, it is possible to accumulate extremely high sulfide concentrations by adsorption within the electrodes during the charging process. An example of high surface area carbon shows that as much as 2,000 square meters of area is available per gram of activated carbon. Looking at what that might mean in terms of http://bbs5.techyou.org/?fromuser=sergio147 molecules of storage capability, we perform the following quick approximations. Since the average, effective molecular diameters are in the order of 2 - 5 x 10~8 cm, the average area of small molecules is in the order of 10"15 cm2. The available area of activated carbon surfaces is 2 x 103 m 2 = 2 x 107 cm2. Dividing the two numbers gives us about 2 x 1022 molecules or atoms stored per gram of active (micro-porous) carbon. An interesting note here concerns the wall thickness of the porous carbon. One gram of carbon is 1/12 of a molecular weight. Since there are about 6 χ 1023 molecules per gram equivalent weight of substance (Avogadro's number), about 5 x 1022 molecules of carbon are present to do the adsorbing, or about 3 molecules of carbon per molecule of adsorbent. If we further assume an agreement with the Langmuir model of molecular surface bonding via a Van der Waals type of force, then the adsorbent is a monomolecular layer, and the carbon wall structure is on average not much more than 2 to 3 carbon atoms thick. The average specific gravity of such activated carbon is in the range of 1 gram per cm2. Then we see that about 2 x 1022 molecules, or ionic species, are stored per cm3 volume of porous electrode. To find the storage capabilities of this electrode in terms of
THE CONCENTRATION CELL
129
electrical charge (amp-hours), we look at the relationship provided by Faraday. The Faraday equivalent is 96,500 coulombs per equivalent, or about 105 coulombs per single valence molecule. Since sulfur has two charges, that number becomes 2 x 105 coulombs. Since there are about 2 x 10 22 /6 x 1023 = 0.03 Avogadro numbers of S atoms stored, it requires in the order of 0.03 x 2 x 105 = 6 x 103 coulombs to electrolytically transport that number of dual charged ionic species across the cell. That number is 6 x 103 ampere seconds, or about 1.7 ampere-hours of charge (per cm3 of electrode). That is a fairly high charge density for an adsorbent electrode. There is significant evidence that adsorption of molecular species in solution will occur in more than one molecular layer, better described by Freunlich's equation below. Now we can return to the consideration of rate processes. Superposed on the previous situation of bulk storage, the rates of adsorption/desorption must be taken into account. Again, as a first approximation, let us use the Langmuir expression regarding adsorption isotherms. As discussed earlier, this approximation does not account for changes in adsorptivity as the surface sites become more occupied, and the ratio of the coefficients oca and http://bbs5.techyou.org/?fromuser=sergio147 a d , the adsoption and desorption, in the relationships of previous equations is not constant. Rate of adsorption = oca (1 - G)C Rate of desorption = a d 0
(6.56)
If we re-examine equations (6.25) and (6.26), perhaps we can put all the variable quantities of S= ions in terms of the amount adsorbed, Q a . We know that at time zero the following conditions exist: • Qa = 0 • P=0 • • 1 o
c =c
•
=c = Q„ = cQ, =c 1
Also, at t = 0, the rate of change, or increase of Qa is
dt
= aa.
(6.57)
130
ENERGY STORAGE
We can next proceed to conclude that the electric potential of the cell can be approximated as a function of the ratio of adsorbed species on each of the two electrodes, or E = 0.0591n [Q,l-
[Q.L
(6.58)
6.17 Energy Density An interesting estimate is the energy density available from a cubic centimeter of elemental sulfur in the charge transfer of one volt. The specific gravity of the sulfur atoms is about 2 grams per cm3, and its atomic weight is 32. With two electrons per atom transfer upon oxidation/reduction, about 100,000 coulombs x 1/32 x 2 would be the charge exchange per gram of sulfur to S=. However, since 2 grams are present per cm3, the math works out to about 1.2 x 104 coulombs per cm3 Since 1 coulombhttp://bbs5.techyou.org/?fromuser=sergio147 is an ampere-second, the charge transfer is about 3 amp-hours, which corresponds with 3 watt-hours of energy. Since the cells are symmetrical and there is an equal amount of material on either side, these numbers need to be divided by 2. Accounting for both sides of the cells, this works out to a maximum energy density, assuming an average potential of only 1 volt of about 24 Wh per in3, or over 41 kWh per cubic foot of cells. That is a very respectable number, even neglecting weights of water, electrodes, case, etc. Also, these cells might be able to operate at levels of many volts, thus increasing the energy proportionately.
6.18 Observations Regarding Electrical Behavior To provide a general idea of the shape of some typical chargedischarge curves, the following graphs qualitatively show how these cells behave. Actual data with current and voltage values are supplied later in the book. For the present, these do show the nature of the cells and clearly show that they do not behave in any linear fashion. The discharge curve for constant current, constant load, or any other control is not "flat" with time. Efficiency of charge and discharge can be very high if the difference between open circuit
THE CONCENTRATION CELL
131
and charging/discharging potentials are maintained small and, perhaps, constant as diagrammed in the last drawing. The power supply and load should be designed to follow these curves for best efficiency.
Constant charge voltage, Ec
Time, t Voltage limited charging
Figure 6.20 Voltage limited charging.
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Time, t Figure 6.21 Constant current charging.
Time, t Figure 6.22 Fixed load discharge from "overcharge"
132
ENERGY STORAGE
Time, t Figure 6.23 Constant current discharge.
http://bbs5.techyou.org/?fromuser=sergio147
Time, t Figure 6.24 Maintaining a constant charge to open circuit differential.
Lab cell of 0.50 cubic inch active volume
0.7
3
0.6
2.5
0.5 ω
-2
^xVolts
0.4
- 1
0.2
0
0.2
3 CO O
Amps
0.1 0
|
- 1.5 Έ
o
= 0.3
oΦ
<
0.5 - 1 0.4
0.6
0.8 Hours
Figure 6.25 Discharge at constant power output.
1.2
1.4
THE CONCENTRATION CELL
6.19
133
Concluding Comments
The following is only a general outline of the basic rationale behind the development of concentration cells. These types of cells do offer a new and different class of phenomenon that can be engineered into practical devices for the storage of energy. Even though the above discussion is centered on the element sulfur, there are many other compounds that could serve the same purpose. Sulfur has ebb, chosen here primarily because it has been experimentally studied most extensively and because its physical and chemical properties lend themselves to experiment easily. There are no problems with high oxidation rates, toxicity, solubility, etc., with which to cope. Iron will serve the same purpose as sulfur. The ferric, Fe3, and the ferrous, Fe+2, states are analogous to the S= and S states of the elements. Iron poses one problem of inconvenience in the laboratory, which is its tendency to oxidize in the presence of air. However, that is certainly not a problem in the development of practical hardware. In order to achieve high working potentials of over 2 volts, a non-aqueous electrolyte must be employed to avoid the decomposition of water during cell charging. Again, that is not a problem in http://bbs5.techyou.org/?fromuser=sergio147 a reasonably well-equipped laboratory. There are numerous stable and compatible non-aqueous solvents that can be employed with good conductivities. One concern is the necessity for the occlusion of air and, particularly, water vapor because most of such solvents tend to be quite hygroscopic. The diagram shows both cations, M+, as well as anions, X", migrating from the respective electrodes with opposite electrical polarity as charge carriers during the charge mode. Upon arrival at the (-) electrode, the Ma ions are reduced to M b form and acquire electron(s) from the power supply in the external circuit. In the positive electrode side of the cell X", ions associate with the Ma ions, whose charge is greater formed at that surface. During the discharge mode, exactly the opposite of these processes occurs, and stored electrical energy as complex concentration differences in X' and M+ are restored.
6.20 Typical Performance Characteristics The plot below shows typical test bench results of small engineering cells with an electrode area of 10 square inches. The curve is
134
ENERGY STORAGE
0.7
Discharge at constant power output Lab cell of 0.50 cubic inch active volume
3
0.6
2.5
0.5
I 0.4
-2
\Volts
- 1.5 §
8 °-3
-
0.2 0.1 0
I <
0.5
Amps 0.2
0.4
1 I
0.6 0.8 Hours
1.2
1.4
Figure 6.26 Volt-amp data.
for the discharge mode of operation at constant power delivery to a load. Total charge capacity of the cell in this instance is about http://bbs5.techyou.org/?fromuser=sergio147 0.40 amp-hour. Voltage and current are continuously changing to maintain constant power at 0.10 watt. External power management circuits are employed to achieve this type of performance.
6.21
Sulfide/Sulfur Half Cell Balance
The information contained in the following text, graphs, and mathematical development concerns the properties of a symmetrical electrochemical cell employing the basic and reversible reaction at both electrodes. The electrolyte is an aqueous or other suitable solvent such as alcohol or a solution of an alkali sulfide salt such as (NH4)2S, Na 2 S, or K2S. Since such sulfide salts solubilize sulfur, there are no solids present during normal operation of the cell. A microporous membrane with ionic selectivity is employed as the separator between (-) and (+) electrolytes. In this instance, both Na + as well as S~2 ions migrate in opposite directions as dictated by the electrical polarity of the electrodes. The rate of such transport for these ions is determined by their respective mobility through the solutions.
THE CONCENTRATION CELL
135
The polysulfide Na 2 S x is the state common to both sides of the cell at the totally discharged stage. There are m-moles of each compound in solution on each side. When charging begins, higher polysulfides are generated at the (+) electrode, and lower Sulfides are produced at the (-) electrode. If posilytes and negalytes have equal volumes, then at full charge the (-) side will have a saturated solution of the maximum solubilized sulfur, or Na,S-, as electrolyte, and the (+) side will be a maximum concentration of Na 2 S electrolyte. If the concentration a n d / o r volume of the (+) side is greater than that of the (-) side, then some free, solid sulfur may be deposited onto the (-) electrode surfaces at full charge. Such a configuration results in an increase in energy storage capacity of the cell since there would be less sodium and, perhaps, water needed for cell operation.
6.22
General Cell Attributes
The primary reason for pursuing a cell of this type is its potentially http://bbs5.techyou.org/?fromuser=sergio147 long life and maintenance-free operation. Since both sides of the cell contain the same chemical species, there is no possibility of degradation of performance or structure with time or cycling. The electrical potential in the cell is derived from the difference in concentration of one chemical species. In this instance, it is the sulfur/ sulfide couple. Initially (cell in the "discharged state"), the concentrations of sulfur and sulfide ions are the same on either side of the cell. Each side is separated from the other by a microporous or ion selective membrane. Attributes of the cell include the following: • • • • • •
Benign chemical environment No maintenance Unlimited shelf life Unlimited cycle life No gas production Versatile system for either sealed unit or circulating electrolyte designs • Very inexpensive and abundantly available chemical reagents • Simple and inexpensive cell construction
136
ENERGY STORAGE
It would seem that the advantages of indefinitely long life, abuse withstanding, and low cost would more than compensate for the above limitations. The high dependence of cell voltage on the state of charge is not different from that of employing compressed gas, rotating mass (flywheel), or capacitive storage since their working potential is similarly dependent on the amount of stored energy at any moment in time.
6.23
Electrolyte Information
The three salts cited earlier have high solubility in water and in alcohol. Some data is provided below: Voltage produced within the cell is due to the concentration ratio of chemical species at the electrodes and does not depend on the absolute concentrations of solutes. It is important to operate cells at high salt concentrations in order to minimize water, electrode, and cell structure weights, and to maximize energy density. Consider a cell http://bbs5.techyou.org/?fromuser=sergio147 that employs a near optimized electrolyte composition such that all materials balance in the ion transfer processes. If we wish to keep all components in solution, then the electrolytes are as follows at the beginning of discharge: (-) side Na2S_ / / 5 Na 2 S (+) side. As discharge proceeds (assuming only Na + ions are transported), compositions of each cell side come, as indicated in the following steps, all the way u p to reverse total charge. The table below shows how the cell potential decreases as discharge progresses and how the electrical polarity reverses if carried further by an external power supply. The flow of electrons during "discharge," in such a symmetrical cell, is from the negative electrode Table 6.3 Salt data. Salt
Molecular Wt.
Na2S
78
K2S (NH4)2S
Solubility
Resistivity
200to500g/L
4 to 8 ohm-cm
110
>800g/L
3 to 6
68
>1000g/L
6 to 10
From: Handbook of chemistry & physics, 1981, CRC Co.
THE CONCENTRATION CELL
137
Table 6.4 Cell potential decreases. Cell Potential
(-) Side
(+) Side
0.02 volts
Na,S-
5Na2S
0.09
Na2S4 + Na2S
3Na2S + Na 2 S 2
Na 2 S 3 + 2Na2S
Na 2 S 3 + 2Na2S
-0.09
Na 2 S 2 + 3Na2S
Na2S4 + Na2S
-0.02
5Na2S
Na 2 S 5
2
D
Discharged 0.00 Charging
to the external load. When zero potential is reached at the same concentrations of S and S=, the flow of electrons goes to the negative electrode from the power supply during the "reverse charge" shown below. http://bbs5.techyou.org/?fromuser=sergio147 There are 26 AH of charge per liter per gram equivalent weight. Thus, there are 156 AH transferred for the 6 moles of sodium ions. This corresponds to 0.156 AH/cc of total electrolyte, or about 9.36 AM per cc. For a cell with 1 in2 electrode area and a total spacing of 0.020 in, its electrolyte volume would be 0.020 in3 = 0.328 cc. This cell would then have a charge capacity of 9.36 AM/cc x 0.328 cc = 3.07 AM. Higher capacities can be achieved if the polymerization of sulfur can proceed further or if free sulfur is allowed to accumulate. Also, there are additional small voltage contributions from the formation energy of the polysulfides. For example, the following are some measured values from Oxidation Potentials by W. M. Latimer: 2S~2 = S2"2 + 2e E = 0.48 v
(6.59)
S"2 + S2"2 = S3~2 + 2e E = 0.49 v,
(6.60)
and
which gives differences of 0.01 volts per "polymerization" stage.
138
ENERGY STORAGE
If we were to postulate that sulfur would polymerize to the S7 state, we would have a series of concentration and corresponding oxidation exchanges such as the following: N a 2 S 7 / / 7 N a 2 S ~ +0.25 volts Na 2 S 6 + N a 2 S / / 5 N a 2 S + Na 2 S 2 ~ +0.14 N a 2 S 5 + 2Na 2 S / / 3 N a 2 S + 2 N a 2 S 2 ~ +0.065 Discharge N a 2 S 4 + 3 N a 2 S / / N a 2 S + 3 N a 2 S 2 0.00 C h a r g e N a 2 S 3 + 4 N a 2 S / / 2 Na 2 S 2 + N a 2 S 3 ~ - 0 . 0 6 5 Na 2 S 2 + 5 N a 2 S / / N a 2 S 3 + N a 2 S 4 ~ - 0 . 1 4 7Na2S//Na2S7
0.00
(6.61)
However, it is not necessary to rely on polymerization greater than 4 or 5 for sulfur since any sulfur on the (-) side would eventually be solubilized as the cell discharges. The first chemical equation of the above group could be written as 2S+Na2S5 / / 7 N a 2 S , http://bbs5.techyou.org/?fromuser=sergio147
(6.62)
with the same performance results. As a matter of convenience, and to reduce the number of characters in these chemical balance equations, the sulfur is all expressed as polymer attachments. The manner of implementing this increase in AH capacity is via plating out free sulfur if necessary and increasing concentration or quantity (volume) of the polysulfide side at the beginning of discharge. As one can see, if there is an excess (stoichiometrically) of polysulfides on the (-) side, then free sulfur can be generated on the (+) side during charge, thus giving rise to a very small concentration of Na + and S 2 ions in that electrolyte. The resultant concentration ratio of ions across the separator would be very large. However, such a large ratio would be dissipated quickly upon discharge, as will be seen in the ensuing equations.
6.24
Concentration Cell Mechanism and Associated Mathematics
For any chemical reaction of the common form aA + bB = gG + h H ,
(6.63)
THE CONCENTRATION CELL
139
the lower case letters are the numerical ratios of the upper case reactants. The free energy change for the reaction is expressed as the following: AF = - R T l n
G«
Hh
^V
+ RTln
G8
a
Hh
AaaBb
(6.64)
Or, it can be represented as AF = - R T l n K + R T l n Q ,
(6.65)
in which K represents the equilibrium constant for activities in the equilibrium state, and Q represents the activity quotient or ratio of activities of the products to those of the reactants. Since, and if reactants and products are at unit activity, ln(Q) = 0 and E = E°. Thus, E = E° - RT/nFln(Q). For most situations of interest here, the expression becomes http://bbs5.techyou.org/?fromuser=sergio147
nF
(6.66)
LaB
where aA and aB are the activity coefficients for ions A and B. For those conditions encountered in these electrochemical cells, the ratio of activity coefficients is equal to their concentration ratio, or in this instance of a sulfide/polysulfide concentration cell,
Ε = Ε Ά KS- ) c nF C
.
2
(6.67)
2(S"2).
In addition, we have the potential due to the sodium ion concentration differences, or
E = E°-H l n Cl ( N a ) +
nF
c2(Na )
(6.68)
+
where C : and C2 are the concentrations of the same ionic species on each side, respectively, of a cell.
140
ENERGY STORAGE
Now, let us examine a specific cell configuration for analysis and study. We will choose a unit cell with an active frontal area of 1 in2 and an electrolyte thickness of 0.010 inch on each side of the separator. This cell has a total electrolyte volume of 0.020 in3 x 16.4 cc/in 3 = 0.328 cc. An initial solution of concentration of 9 molar has Na 2 S in the (-) side and the equivalent of Na2S9 polysulfide in the (+) side. These may be in the form of undissolved monosulfide and undissolved sulfur on the (+) electrode. See the diagram below for such a cell with cation membrane separator.
6.25 Calculated Performance Data Returning to the expression for concentration potential, we must relate the concentrations to the specifics of the cell volume and the dynamics of electric current flow. In general, the concentrations C : and C, may be written as C : = Qj/V and C2 = Q 2 /V, where V is the volume on each side of the membrane. http://bbs5.techyou.org/?fromuser=sergio147 During discharge at any time, t, after full charge, the quantities of reagents in each side are as follows: Ql0=Ql0-|idt, Q2=Q2o+Jidt.
(6.69)
The reason for normalizing the performance model is to relate the discharge rate to capacity, cell resistance, voltage polarization rates, and eventually diffusion limiting considerations. Thus, our model is a one square inch area configuration with electrolyte spacing of 0.010 inches. Its volume is 0.328 cc. Concentration of initially charged solution in the (-) side is 9 molar Na 2 S. The transfer of 18 normals of Na + ions would give a total of 28.1 ampminutes per cc of total solution. The (+) side has a concentration of 1 molar 2Na + ions corresponding to 28.1/9 = 3.12 AM/cc. If this is indeed the initial condition of the cell at the start of discharge, then we can set up a mathematical relationship to evaluate voltages as discharge progresses. Now, it is necessary to set the initial concentrations and then calculate potentials versus discharge time.
THE CONCENTRATION CELL
141
Then the ampere-minute quantities in the 0.328 cc volume cell become
Q!=9.2-Jidt, Q2=1.02 + Jidt
(6.70)
The complete expression for the cell potential at various stages of discharge is determined by RT E= —In nF
9.2-Jidt
8.314 x 298.1
1.02 + Jidt
96,500
In
9.2-0.02At 1.02 + 0.02At (6.71)
where we have employed 0.02 amp as constant discharge current, n = 1 for sodium ions, and operation is at standard temperatures. This expression has been programmed into a Lotus spreadsheet and a sequential method was employed to estimate voltages, energies, and power output during discharge. Since there is some uncerhttp://bbs5.techyou.org/?fromuser=sergio147 tainty as to the sources of voltages between concentration ratios of Na + , S"2, and the formation of polysulfides during concentration changes, we will look at the type of performance obtainable for different assumptions. Empirical data is available for single cell in shallow cycling operation. The rather high potentials realized at early stages of charging suggest that there are numerous mechanisms present as well as some significantly steep concentration gradients established at the surfaces of electrodes, even at low current densities. Table 6.5 Charge equivalents. Charged State
AH/L
AM/cc
(A) Na 2 S.//5Na 2 S
260
15.6
5.12
(B)NaS//7NaS
364
21.8
7.15
(C)Na 2 S 9 //9Na 2 S
468
28.1
9.2
(D) N a 2 S n / / l l N a 2 S
572
34.3
11.3
AM/0.328 cc
142
ENERGY STORAGE
In attempting to estimate performance via mathematical modeling, we have choices to make regarding the range of molarity change of ionic species, the initial concentration ratio (depth of dilution of sodium ions), and whether a multiplier is appropriate to the voltage equation in order to account for the observed shape and magnitude of empirical voltage discharge curves. Three different cases (A, B, and C) will be selected for graphing. Case (A) is a situation of least energy capacity, where the multiplier = 1, 5 molarity of Na 2 S, and initial ratio of concentration is 5:1. The equation describing the voltage versus discharge time is E = 0.0257 In
9.2-0.02At 1.02 + 0.02At
volts,
(6.72)
depending on the extent to which the cell is charged beyond its above stipulated stoichiometric ratios Case (B) involves a mid-range energy density cell, where multiplier = 5, and m = 7 molarity of Na 2 S, and initial concentration ratio = 70:1. http://bbs5.techyou.org/?fromuser=sergio147 Based on experimental evidence, it seems that a multiplier of value 5 for the entire concentration potential equation is reasonable and consistent with experimental results. In addition to the energy of formation of the polysulfides, concentration differentials are generated within the cell for sulfur, sulfide, and sodium ions. The figures to follow are graphical representations of a cross section of numerical cell value combinations of the factors discussed above. The more general equation for voltage may be given as E = m^ 0.0257 In
(1.02M + d ) - 0 . 0 2 A t (1.02-d)+0.02At
(6.73)
We arrive at the initial concentrations of the (-) and (+) reagents as follows. If the ratio desired is R, and the increment, d, is added to the (+) side, at the decrement of the (-) side is R=
1 0 2 M + d
1.02-d
.
(6.74)
THE CONCENTRATION CELL
143
Hence, if we wish a ratio of 70:1, about 10 times as that obtained, and if the concentrations were 5 molar and 1 molar, respectively, then solving the above for d gives 70(1.02 + d) = 1.02(7) - d, and d = 0.905, and the new equation for voltage is E = 5 x 0.0257 In
8.05-0.02At 0.115 + 0.02At
volts.
(6.75)
Case (C) involves a high capacity cell configuration, with multiplier = 5, an 11 molarity (+) solution, and an initial concentration ratio = 1100:1. The values calculate as follows: 1100(1.02 + d) = 1.02(11) - d, and d = 0.99, and the voltage, E, becomes E = 5 x 0.02571n
12.21-0.02At 0.03 + 0.02At
volts.
(6.76)
6.26 Another S/S 2 Cell Balance http://bbs5.techyou.org/?fromuser=sergio147 Analysis Method Perhaps another more direct and simple method of showing the materials balance and estimating the energy density of a concentration cell is that shown below for the sulfur/sulfide cell. We can assume that the process will no longer be limited to the maximum amount of sulfur that the polysulfide can solubilize. As an idealized example, the initial condition for a fully charged cell is Na 2 S / / S, or more generally aNa 2 S / / bS, where a and b are whole numbers of moles. In order for the process to balance at zero charge (complete discharged) state, a = b, and a > 1. We can now compute the maximum charge stored per unit weight of reactants in this concentration cell. The simplest example would be 2Na2S / / 2S at full charge, and Na 2 S + S / / Na 2 S + S at total discharge, with a transfer of 50 AH per total molecular weight of reactants. This amounts to 2(78) + 2(32) = 220 gm with a charge transfer of 50 AH giving as energy density 50 AH/220 gm χ 454 g m / l b = 103 A H / l b of dry materials. It is possible to further generalize the analysis for the cell processes wherein the sulfur is always attached to the sodium
144
ENERGY STORAGE
polysulfide molecules. Since the details of interim stages of complexing can be readily known, we will assume the following steps in the charge transfer and discharge of a cell that begin with the polysulfide on one side and the monosulfide on the opposite side. Let us take the pentasulfide as the largest size complex available. The cell configuration and reactions become those shown below. Starting with the fully charged state as before, but with the bisulfide on one side and the monosulfide on the other, aNa2S / / bNa 2 S 2 . The smallest value for a is 3 since it is necessary to remove two 2Na atoms from the monosulfide in order to meet the conditions of no free sulfur on either side of the cell. Without going through the approximation sequences, the numerical ratio that results functions to make both sides of the cell identical after discharge is a = 3, b = 2, 3Na2S / / 2Na2S2 Charged, and Na 2 S + Na 2 S 2 / / 2Na2S + Na2S2 Discharged. The total gram molecular weight of both sides is 234 + 220 = 454, and the charge transferred by 2Na + ions is 50 AH. The charge density of dry salt is simply 50 AH x 454 g m / l b /454 gm = 50 A H / l b . http://bbs5.techyou.org/?fromuser=sergio147 If we start out with the trisulfide, the reaction balance, etc. are aNa 2 S / / bNa 2 S 3 Charged, a = 3, b = 1,3Na2S / / Na 2 S y and Na2S + N a 2 S 2 / / N a 2 S + Na2S2. Total weight = 3 x 78 + 142 = 376, and the charge density = 50 AH x 454/376 = 60 AH/lb. The cell reaction making use of the next higher initial polymer of sulfur and sulfide is as follows: aNa2S / / bNa 2 S 4 , a = 5, b = 1, 5Na2S / / Na 2 S 4 ,3Na 2 S + Na2S2 / / Na 2 S + Na2S3, and Na 2 S + 2Na2S2 / / 2Na2S + Na2S2. Total weight is 390 + 174 = 564. Since there are four Na + ions transferred from fully charged to symmetrical distribution of ions at discharge, the charge density is 100 χ 454/564 = 80 AH/lb. Taking the pentasulfide as the last or highest complex, the cell parameters become aNa2S / / bNa2S_, a = 7, b = 1, 7Na2S / / Na2S-, 5Na2S + Na2S2 / / Na 2 S + Na2S4, 3Na2S + 2Na2S2 / / 2Na2S + Na 2 S^ Na 2 S + 3Na2S2 / / 3Na2S + Na2S2. Total weight is now 546 + 206 = 752. There are three transfers of 2Na+ ions, hence the charge density is now 150 AH x 454/752 = 90 AH/lb. If it were possible in a practical cell to utilize higher complexes, the charge density would merely approach the maximum value of
THE CONCENTRATION CELL
145
103 AH /lb. In order to compute the energy density of such cells, it is necessary to multiply the charge density by an appropriate voltage. Since the cell potential is so dependent on the state of charge, a reasonable value of working cell voltage over the entire range of charge storage would be half of the full open circuit voltage of 1.0 to 1.2 volts, or about 0.5 to 0.6 volts. Hence, the maximum energy density of the cell, assuming no water (solvent) weight or other contributions to inefficiencies, would be about 52 to 62 W H / l b of reactants. The operating open circuit potential is purposely limited to between 1.0 and 1.2 volts to prevent the evolution of hydrogen gas at electrode surfaces. H, evolution would necessitate the periodic readjustment of electrolyte composition and the venting of cells and would eventually result in mechanical erosion of electrodes. Another approach to preventing gas generation at electrodes is the employment of non-aqueous solvents such as absolute alcohol, pyridine, DMSO, and nitriles.
6.27 A Different Example of a Concentration http://bbs5.techyou.org/?fromuser=sergio147 Cell, Fe+7Fe+3 The principles employed in concentration cell design are not restricted to the use of sulfur and numerous polysulfides such as those of potassium, ammonium, lithium, etc. In fact, the above concentration cell approach to energy storage can make use of numerous other materials that have properties suitable to practical methods of implementation and different characteristics that may make them more applicable to certain uses. These materials include the use of the elements iron, bromine, iodine, and chromium. Their behavior as electrochemical species is well known and readily available. The balance relations for the iron concentration cell are as follows. We will make use of the two oxidation states of iron, Fe2 and Fe+3 ions. Their solubility is such that high concentrations (two to four molar, respectively) of these are easily attained in water. Potentials during charge must be kept below that for the formation of free iron, Fe°. That potential in water solutions is about 1.2 volts. The reaction of interest to us here is of the form aFeCl2 + bHCl / / cFeCl3 + dHCl fully charged state.
146
ENERGY STORAGE
The charge carrier is the hydrogen, H + , in this cell. A cation exchange membrane, or a microporous separator, is employed in this cell. In order for the reaction to proceed and have a symmetrical situation on both sides of the separator, i.e., no further oxidation/ reduction energetics remain, the minimum values for the coefficients a, b, c, and d are 2, 1, 2, and 1. Thus, the initial and final states are 2FeCl2 + HC1 / / 2FeCl3, and FeCl2 + FeCl3 / / FeCl2 + FeCl3 + HC1. There is only one charge carrier (exchange) per such step. Hence, the total weight of reagents is 252 + 36 + 322 = 910 gm. The charge density is then 25 AH x 454/910 = 13 AH/lb. Even though the energy density is not as attractive as that of the sulfide system, there are some outstanding features such as extremely low cost of materials, low hazard, and no chance of solids deposition if potentials are kept below that for Fe+2 + 2e_ —> Fe°.
6.28
Performance Calculations Based on Nernst Potentials http://bbs5.techyou.org/?fromuser=sergio147
A series of graphs and calculated data plots has been generated based on a simplified model of the volt-amp behavior of a basic cell. This was done in order to acquire a preliminary appreciation of the type of behavior that can be expected from actual cells, which were simultaneously fabricated and laboratory tested. Such calculations, along with graphs of the voltage versus current-time or state of charge of a cell, enable us to determine whether our actual test cells are operating in an expected fashion, or whether there are some discrepancies between actual behavior and our simplified understanding of the mechanisms involved. Even if the data might be quantitatively different from that calculated, the main importance in these types of investigations is whether the qualitative aspects are as predicted, or in other words, are the shapes and general behavior of the two groups of data, i.e., the calculated versus the empirical curves. Despite the absence of many factors in the modeling such as diffusion and coulombic inefficiencies, it was found that the agreement between the two is quite close. To best illustrate these initial attempts to analytically represent cell performance, a few simplified models follow.
THE CONCENTRATION CELL
6.28.1
147
C o n s t a n t Current D i s c h a r g e
We will now look at the behavior of a cell when confined to discharging at a constant current by providing a suitably varying electrical load at its terminals. The mathematical formula for the value of cell voltage as it varies with the state of charge, on which the plot is based, is given as En=lni^-j,
(6.77)
where the terms a and b are the concentrations of the active reagent in the opposite sides of the cell. In this case, that reagent is the sulfur ion, S=. The subscripts n and n - 1 are employed to designate the sequence in time of the terms. For example, the voltage at any time, t, indicated by subscript n is found from the value of an, which occurs at that same time, and the value of a ,, which occurred at the previous time interval. This arithmetical approximation enables us to make the evaluations in a spreadsheet program such as Lotus http://bbs5.techyou.org/?fromuser=sergio147 or Excel. The evaluations can thus be made piecewise, and plots can be generated from the calculated data. It is also assumed here that the volumes on either side of the cell are the same and normalized to give a one-to-one correlation between AH and change in concentrations. To complete the mathematical description, the relationships for the a and b terms are as follows: an=a-0.05(tn-tn_0 bn=bn_1+0.05(tn-tn_0
(6.78)
A constant current of 0.05 amps is almost arbitrarily assumed here per square inch of electrode surface area, and the time interval in obtaining readings of voltage is expressed as tn - tn-1 in the expressions (6.78). The amount of electrical charge, Q n , removed from a cell over a time interval t - 1 ^ is given as Qn=Qn_1-0.05(tn-tn.O·
(6.79)
148
ENERGY STORAGE
Figure 6.27 is such a graph where the cell potential, E, is plotted against the percentage of remaining electrical charge within the cell. A distinct disadvantage of concentration cells is the high dependence of voltage on SOC. However, this characteristic can be largely overcome, as discussed earlier in this chapter and later in Chapter 8, by having most of the reagents (sulfide ions) in the solid state at the electrodes with controlled dissolution as charging or discharging progresses, depending on which electrode polarity is involved.
6.28.2
Constant Power Discharge
Another informative graph that shows the behavior of cells, when operated to deliver constant power during discharge, is obtained from the simple assumptions and relationships shown below. In these analyses, the predominant shape of the curves is logarithmic because of the fundamental equation for voltage as set forth in Nernst's equation. As before, the voltage is proportional to the log of the ratio of concentrations of specific ions on each cell side, orhttp://bbs5.techyou.org/?fromuser=sergio147
E = ln
(6.80)
Calculatec — voltage versus remain ng charge
2.5 2 w "δ
1
Φ
1.5
ϋ
1 κ
20
30
40
50 60 70 80 Percentage of remaining charge
Figure 6.27 Calculated - voltage versus remaining charge.
90
100
110
THE CONCENTRATION CELL
149
Similar to equations (6.78) and (6.79), the expressions for a, b, and Q now are as follows: an=an-i-p(tn-tn_i)/EI1_1 bn = bn_1+P(tn-!„_,)/£„_, Qn=Qn-1-P(tn-tn_1)/En-!
(6.81)
The total electrical charge that has passed through the load at constant power of course is
-total
ZQi-
(6.82)
where N is the total number of samples taken over the time interval of interest. A chart of such a discharge is shown in Figure 6.28. The major portion of the electrical energy, or charge, is delivered at the lower levels of voltage because of the very rapid http://bbs5.techyou.org/?fromuser=sergio147 decline of the ratios a / b from fully charged. The only method we know of to reduce this rapid decline is the introduction of a stabilizing feature. This would maintain high a / b values by storing the major portion of charge in the form of unionized (solid) reagents at the electrode sites and then gradually replenish the Calculated - voltage versus discharge time
2 3 4 Discharge time - hours — Cell volts _ % of charge remaining Figure 6.28 Voltage versus discharge time @ constant power.
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ENERGY STORAGE
ionic reagents by controlling their precipitation and dissolution at the respective electrodes.
6.29 Empirical Data Countless laboratory cells and arrays based on concentration differentials have been constructed and tested over the past 10 years. Most of these test cells were either sulfide or ferric/ferrous based chemistry systems. Numerous other systems such as bromine/bromide, iodine/iodide, and cupric/cuprous cells have been explored as well. The electrical results, as one would expect, obtained are very similar to those with the sulfide devices. However, other problems were encountered with these and other alternative cells associated with chemical stability (attack of surrounding materials of construction), volatility, costs, and incompatibility with surroundings. A graph of the empirical results, or electrical behavior of such cells, is shown in Figure 6.29. It is typical of simple cells with no provisions made in their design for diffusion limitations, solidification of reagents, or any other performance controls. These early http://bbs5.techyou.org/?fromuser=sergio147 cells illustrate the very basic characteristics one can expect from this class of concentration cells. These curves were generated by discharging cells across a constant resistive load - not the optimum arrangement for either high Single cell cycling data Sodium sulfide cell with 5 sq. in. area
o
>
400
600 800 Elapsed minutes
— Volts UU porous carbon & sybron separator
· Amps
Figure 6.29 UU carbon, sybron separator, spec. Grav. soln, +1.2.
THE CONCENTRATION CELL
151
efficiency or good performance. However, they do demonstrate the general characteristics of voltage rise and decay during charging and discharging, respectively. One of the main purposes of such extended cell testing is to learn a bit more about life and cycling limitations. Over 5,000 cycles have been accumulated on single cell laboratory devices with no discernable deterioration in performance or chemical composition of the electrolyte or erosion of electrodes, thus making predictions of cycle life rather difficult with no degradation data from which to extrapolate.
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Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
7 Thermodynamics of Concentration Cells http://bbs5.techyou.org/?fromuser=sergio147
Concentration cells are all "redox" in nature because, as is necessarily the case, the reduction and oxidation of chemical species occur within the device for the transference of energy. However, in this instance the redox label does not imply that these devices or cells are full flow electrolyte design with provisions for removing or replacing electrolytes. They are best operated as stationary (static) electrolyte systems. The particulars of design and physical configuration depend upon the intended applications. For example, it may be desirable to use close spacing between electrodes for higher power density application requirement devices, thus proportionately reducing their energy density.
7.1 Thermodynamic Background The fundamental principles upon which the CIR system is based are probably best identified from the following thermodynamic considerations. Here, we quickly review some of the important and relevant thermodynamic functions upon which the analysis of cell behavior is based. 153
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ENERGY STORAGE
In order to arrive at the intended expression for the electrical potential of a CIR cell, we will begin with the familiar equation of state for an ideal gas: PV = nRT,
(7.1)
where P and V are pressure and volume, respectively, of a quantity of gas consisting of n moles. T is temperature in degrees, absolute Kelvin, and R is the universal gas constant with a value, in the MKS system of units, of 8.31 joules/mole-degree. To prepare for the relationship for cell potentials, we return to some fundamental concepts. The Gibbs function, G, for any chemical system is given as G = H-TS,
(7.2)
where H is the enthalpy, and S is the entropy of the system. Taking the total derivative of G, we obtain dG = d H - S d T - T d S .
(7.3)
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Also, the enthalpy, H, is defined as H = U + PV, where U is the internal energy of a system. To place the above in more useable terms, we now proceed through the next manipulations aimed at obtaining a final, more useable expression for the free energy (Gibbs function) and the chemical potential. The total derivative of H is d H = d U + PdV + VdP.
(7.4)
For neighboring reversible processes, dU = TdS-PdV
(7.5)
Substituting for dU in the equation for dH, we get d H = T d S - P d V + P d V = VdP,
or
d H = TdS + VdP.
(7.6) (77)
Substituting the following into the equation for dG, d G = V d P - SdT,
(7.8)
THERMODYNAMICS OF CONCENTRATION CELLS
155
since T is constant for isothermal processes, the differential free energy becomes d G = VdP.
(7.9)
Integrating, we obtain the more familiar expression G = nRT[J
— = nRTln^. R p
r. pP Jp,
(7.10)
The idea of chemical potential, u, is crucial to the study and analysis of electrochemical cells. Here we simply introduce the chemical potential, u, in the following fashion. For a specific constituent, k, of a phase state, u k , is the potential as described by u
k
=|^, 8n k
(7.11)
for a multi-component system. If we have but one component, in solution, then http://bbs5.techyou.org/?fromuser=sergio147
U = dG/dn,
(7.12)
and the chemical potential is the molal Gibbs function and is a function of T and P, or u = G / n , where n = moles. Now, addressing the electrochemical cell subject, let us convert pressure, P, for an ideal gas into the equivalent parameters for an ionic solution. Additional intermediate terms must be introduced in order to bridge any gap in the continuity of reasoning of thermodynamic equilibrium. The concepts of fugacity f, and activity, a, have proven to have a significant benefit. If Fm is the partial molal energy and a measure of the escaping tendency, for example, of a vapor from its liquid phase, then the fugacity has been defined by the relationship below: F m = R T l n ( f / f 0 ) + B(T),
(7.13)
where B is a constant serving as reference point. If f refers to some standard state, then
Fm=JpPVdP = RTlni
f ΌJ
(7.14)
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A more commonly employed parameter in electrolytic solutions is the "activity" of the solution in the immediate vicinity of an electrode. This is usually represented as a = f/f , and it is usually directly proportional to the molality of dilute solutions because the solute behaves closely to that of a free gas. Hence, we may finally obtain as the free energy, or Gibbs function, of the solution G = RTln(a).
(7.15)
In determining the voltage, E, associated with chemical potential in electrochemical cells, the free energy may be simply divided by the number of electrical charges that are being transferred in a particular process. In the case of the transference of n moles of singly charged ions at an electrode, the relationship assumes the following form: RT E = —ln(activities), (7.16) zF http://bbs5.techyou.org/?fromuser=sergio147 where F is Faraday's number of 96,500 coulombs per equivalent. In general, the equation may be put into the format RT oxidized form E = E0 - — I n r e d u c e d form ° zF
(7.17)
where z is the difference in electric charge of the ions in question.
7.2 The CIR Cell Configurations of the CIR cells may employ two or three of the available oxidation states of an element or compound. A cell is diagrammatically represented in equation 7.18 that makes use of two oxidation states of a metallic element, M. It will be assumed here for illustrative purposes that the oxidation states are M+i and M+i. Then, we may represent a "materially symmetrical" cell employing these agents as Pt;M+i,M+j I I M+j,M+i;Pt.
(7.18)
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157
Platinum electrodes are shown in the diagramed cell. They merely represent electrode properties with non-reactivity properties (no chemical participation in the cell processes) and high electronic conduction. In actuality, carbon structures are employed in practical cell designs because of their much lower cost and because the carbon physical properties are better suited to the optimum operation of these cells. This cell has two chemically inert electrodes, each in its own electrolyte with electrolytes separated by a porous plate. In this case, the separator might be either a microporous membrane that simply retards the diffusion and consequent mixing of the electrolytes, or it might be perm-selective (ion selective membrane). In this instance, the separator could be a cation membrane that permits (+) charged ions such as H + to pass. The electrolyte is a solution consisting mainly of salts of the metal, M, and usually a simple acid. Charge transfer within such a cation type cell is principally via hydrogen ions. Very high cell conductivity can be achieved. The activities associated with each of the ionic species as shown in equations 7.18 http://bbs5.techyou.org/?fromuser=sergio147 and 7.22 are as follows: O n the left side the activity forM+I=
ai,andforM
+i
= a2
(7.19)
O n the right side the activity for M +i = a 3 , and for M +I = a 4
(7.20)
When substituting the activities in the Nernst equation, care must be taken with their order of appearance and algebraic sign of the terms. Perhaps the simplest way to calculate the voltages for a cell is to follow the above format of oxidized form/reduced form. First, we will convert to the log at base 10 for convenience of arithmetic. Then, the expression for voltage will become T7
C
0
·
0 5 9 2
V I
oxidized
try ^ 1 \
reduced _\[
Consider the cell described above, in which both sides have identical inert electrodes and iron ions present. In this symmetrical instance E is zero. o
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ENERGY STORAGE
The voltage for this symmetrical cell is evaluated from the activities of the pertinent ions on either side of the separator for the two electrolytes. The voltage due to the differences in activities for the identified ionic components is found by calculating E - 0.0257
(7.22)
In
Charge, z, is 1 for the ion transport number. As a result of our cell development the above expression is modified to take into account the preferential storage processes as part of cell design. Electrode processes have been modified to provide for a very selective storage and large activity coefficient enhancement. The design and operational techniques have produced charge storage at cell potentials well over an order of magnitude greater than ascribable to the unmodified Nernst equation. These may be effectively represented in the Nernst type expression as
- In ßa
http://bbs5.techyou.org/?fromuser=sergio147 3
E = 0.0257
v a4 y j
(7.23)
where a and ß are multipliers of the activities due to a dipolemultilayer storage specific to the molecule associated with that ion. During the development of the iron/redox system we have learned how to control the activities of each specific ion in the processes, and there is no metallic iron in its elemental state present in the concentration cell. Hence, it is possible to attain very high electric potential differences in these cells, which makes them practical as energy storage devices. There are no electronically conductive solids at any time present within the cells, other than the inert carbon electrodes. Any solids that might result from cell operating conditions are reversibly soluble and do not result in possible short-circuiting or other deleterious effects. This approach, with appropriate modifications in design geometry and inactive materials of construction, can be applied to a number of active materials that will dissociate in polar solvents and with two or more soluble oxidation states. A full flow electrolyte system has some distinct advantages despite its greater complexity and costs. These advantages include
THERMODYNAMICS OF CONCENTRATION CELLS
159
(1) the separation of energy density factors from those of power density, (2) an infinitely long charge retention, and (3) total reversibility, in principle. However, our tests in a limited development program have shown little adaptability of the CIR system to full flow electrolyte configurations. It appears that, in order to benefit from high concentration differences, the reactants are best electro-deposited into porous electrodes that occupy the entire space between the separator and the conductive electrodes. If a cell is designed to permit full flow past the electrode surfaces, then sulfide ions and polysulfides must molecularly diffuse into the depths of the carbon pores. That diffusion process is slow and gives rise to undesirably high concentrations in the bulk electrolyte with consequent diffusion losses through the cell separator. It may be possible with some clever composite designs of electrodes to overcome this deficiency and benefit both from concentration cell performance and the advantages of a full flow system. The mechanical complexities, costs, and size may well be worth it in some applications that have peculiar power and energy density demands or in which long charge retention times are required. http://bbs5.techyou.org/?fromuser=sergio147
Nature offers few selections from its list of elements and compounds that have all the properties desirable in such redox systems. Among these desirable qualities for practicality are an ambient temperature operation, a low hazard, a plentiful supply of materials, benign behavior, and minimum side reactions that can result in operational failure. TRL has investigated and developed a number of redox-type of systems with varying success in the past. These include the zinc/bromine, iron/redox, and the polysulfide/ bromine secondary batteries. Other than the last system, they were all "half redox" cells because only one of the two components of the electrochemical couples are in solution at all times. Both the zinc/bromine and the iron/redox cells suffer from all of the problems associated with the deposition and dissolution of solid metal onto the surface of an electrode. These virtually unsolvable problems include dendrite shorting, non-uniform plating, metal particle fall-off, passivation, and gas generation in acid solutions. These are very severe problems that have been scrutinized for many years. Unfortunately, these characteristic problems will always be present regardless of how successful some of the cures and improvements in performance become. The polysulfide/bromine system does offer the situation where all reagents are soluble
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ENERGY STORAGE
at all times. However, the electrolyte is acidic on one side of the separator and basic on the other. Without some additional subsidiary processes, the pH differences are difficult to maintain. Also, there is the problem of gradual and irreversible diffusion of bromine and sulfide diffusion to opposite sides of a cell as cycling proceeds. TRL has contended with these problems with some degree of success. Unfortunately, these deleterious effects are present and lead to inexorable and ultimate cell failure. Then, it becomes necessary to resort to some complex external method to restore operation. The most attractive of the above cells, in terms of low cost, safety, and simplicity, is the iron/redox cell, wherein we make use of the three oxidation states, Fe°, Fe++, and Fe+++. The energy storing reaction for the couple Fe°/Fe+++ is Fe° + 2Fe + + + = 3Fe ++ 1.2 volts.
(7.24)
After considerable effort, this couple has essentially been set aside as a practical means of energy storage, not because of its rather limited energy density (maximum of -75 W H / l b for the dry reagents), but because of its unmanageability with regard to http://bbs5.techyou.org/?fromuser=sergio147 iron plating qualities and hydrogen evolution (hydrolysis and iron attack) in the necessarily low pH electrolyte. It is possible that a non-aqueous solvent can be employed, in which the iron salts are soluble and have a sufficiently low resistivity so that practical levels of power can be realized from such cells. However, as of this date no significant effort has been expended to search for likely solutions to the problems associated with iron in acidic, aqueous environments. We have all been searching for a means of electrochemically storing energy that avoids all of the above problems completely and with energy density sufficiently high to make it attractive for largescale, stationary applications, such as load leveling and solar and wind power. On the basis of our collective past experiences with redox types of systems, we turned our attentions to the possibilities of concentration cells. This type of cell has the very attractive property of symmetry. The materials of either side of the cell are the same but at different oxidation states. An example of a "materially symmetrical" cell is the vanadium redox battery. The vanadium redox cell is not a concentration cell as such. Rather, it is a cell that makes use of an electrochemical couple between three or four of the soluble oxidation states that are available for vanadium. There are problems of reversibility
THERMODYNAMICS OF CONCENTRATION CELLS
161
and high costs associated with the materials that tend to limit its application potentials. The CIR cells rely on only two soluble oxidation states of the same material, or compound, as in iron+2 and iron+3. The potential is easily calculated from the above relationships if we know the activity of the specific ions at the electrode surfaces. Returning to equation 7.23, the Nernst equation, we can calculate voltages from concentrations in dilute solutions where the activities are nearly the same as the concentrations. In order to measure the potential due to concentration differences, one would normally employ a cell with a reference electrode, such as H + /H 2 , that would provide a known potential at one end of the cell. However, for the sake of illustration, we can simply postulate a cell with the following conditions. In an operating concentration cell, we are primarily dependent upon the concentrations of the two primary reactants (oxidation states of iron) at their respective electrodes - in this case, the concentration of Fe++ and Fe+++ at the negative and positive electrodes, respectively. Due to the fact that the sum of all Fe++ and Fe+++ ions on both sides is constant at all times because, for example, as Fe++ ions are generated at one electrode the same number is removed at the http://bbs5.techyou.org/?fromuser=sergio147 opposite electrode, the expression for the voltage in this instance becomes ~
In
(
\ 3
lai)
(
= 0.0592φ In c -
\
l J_
where φ reflects the interdependence of Fe++ and Fe+++ concentrations in this cell. It is significant to examine the accuracy of using concentrations in place of activities. Certainly, in very dilute solutions the numerical equivalence of activity with concentration is very close. In fact, for most dissolved materials the values of activity do not change very drastically with low concentrations of the particular chemical species. The terms c2 and c4 have cancelled, and the concentrations were substituted for activities. Let us look at a magnitude of the voltage one might expect from such a concentration cell. If the concentrations c3 and Cj are 1.0 and 0.01 molar, then the potential, E, would have an impractical, low maximum value of 0.0592(log 100) = 0.118 volts.
(7.26)
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ENERGY STORAGE
Proceeding further, it is obvious that a concentration ratio of reactants of 106:1 or more at their respective electrodes would be required to achieve an open circuit potential of 1.0 volts. This is a rather discouraging prediction of the practicality of concentration cells. Our preliminary lab experiments with two or three chemical systems did verify these data. However, when a charging cycle was performed with a cell with thick porous structure, potentials of over 1.2 volts were obtained. Furthermore, the cells were capable of delivering on a sustained basis a significant electric charge to the external circuit at these levels of voltages. Quite obviously, something else was taking place besides the bulk concentration differences in the electrolytes of a two-compartment cell. The micro- or nano-porous carbon particles are in intimate, physical, and electrical contact with the electrodes. This type of simple cell with inexpensive components and reagent materials prompted us to explore the mechanisms involved in the storage of charge at such unexpected high values. The same sort of behavior was attained with very similar structures employing compounds of sulfur. The electrical performances of the cells were consistent and http://bbs5.techyou.org/?fromuser=sergio147 repeatable. The sulfur-based cells employ alkali salts of sulfur such as sodium, potassium, and ammonium mono and polysulfides. The search begins for a plausible explanation of how a cell, with no other energy related processes taking place other than the difference in concentration of the two oxidation states of the same chemical element, can produce such high potentials and sustain high electrical charge densities. If there are no other processes involved, then we must look toward some mechanism whereby the chemical species in question are able to accumulate at the electrode surfaces and give rise to such high voltages. At present we speculate that the specific ionic species, in this case the ferric and ferrous ions, are injected directly into the pores regions of the microporous carbon at high effective concentrations by the process of electro-sorption. Even though the maximum concentration of the compounds of ferric and ferrous chlorides is limited to not much over 3 molar at room temperature, the population densities of the adsorbed and stored ferrous and ferric substances become equivalent to extremely high activities seen by the electrodes. In order to accomplish this, more energy is required than would normally be to separate the oxidation states during the
THERMODYNAMICS OF CONCENTRATION CELLS
163
"charging" process. This condition, for the maintenance of conservation principles, has been observed during cell cycling in terms of the volt/amp inputs and outputs. There are undoubtedly many processes and mechanisms taking place at the electrode surfaces that call for greater understanding and quantifying. Let us first list and then examine the physical and chemical activity possibilities. Omitting the chances that there are any net or permanent chemical changes occurring in the electrical cycling of the cell, the following are possible, reversible processes: • Exceeding salt solubility at electrodes during charging, resulting in solid compounds at the surfaces with attendant free energy changes (energy of ionization and dissolution) • The creation of immense concentration ratios of Fe++ and Fe+++ ions in solution at electrode surfaces • The adsorption of iron ions and, perhaps, of the salt compounds themselves within the carbon porous structure, http://bbs5.techyou.org/?fromuser=sergio147 which may be Langmuir type processes or Van der Waal's, depending on whether they are attached as electrically charged components or as neutral molecules with dipole moments. Meanwhile, the following is an encapsulated glance at the energies of solution, or the dissolution for the ferrous and ferric chloride salts present in the cell being discussed. A perhaps overly simplified, but nevertheless indicative, view is suggested here. Consider the free energies (integral heat of dilution) to infinite dilution as given by La timer's "Oxydation Potentials": • Fe++ in aqueous solution — 2 0 kcal/mole • Fe + + + ~-2.53 • Cl-~-31.35 • FeCl2 in solid, crystal form —72.2 • FeCl 3 ~-80.4 If, in the reduction of ferric to ferrous ions at the negative electrode during the charging process, the generation of ferrous salts occurs too rapidly for it to remain in solution, then the process
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ENERGY STORAGE
of Fe+++ + e = Fe++ is accompanied by the precipitation of ferrous chloride into the pores of the electrode, i.e., FeCl 2 = Fe + + + 2 C T .
(7.27)
Then, there is another exchange of energy involving the heat of solution. Its net value is AF = -72 + 20.3 + 2(31.35) = + 7.8 kcal/mole at the positive electrode when charging. Similarly, one can estimate the free energy at the negative electrode. The net reaction would appear to be FeCl 3 = Fe + + + + 3C1".
(7.28)
Here, AF = - 80.4 + 2.53 + 3(31.35) = - 16.8 kcal/mole. This result can be related to an electric potential by the relationship below: AF(net) = - nE x 23,060,
(7.29)
where E is in volts, and n is the number of charge changes on the ion. http://bbs5.techyou.org/?fromuser=sergio147 Upon adding the free energy changes, we see that the voltages associated with this dissolution are in the vicinity of 0.3+ volts, a not insignificant amount. Or, we may represent the processes at the two opposite electrodes during charging as Fe + + + + 3 C r + e = FeCl 2 + Cl".
(7.30)
Free energy for this reduction and dissolution is AF = - 2.53 - 3(31.35) + 72.2 + 31.35 ~ + 7 kcal, (7.31) and, Fe + + + 3C1" = FeCl 3 + e,
(7.32)
where AF = - 2 0 - 3(31.35) + 80.4 + 31.35 ~ - 2.3kcal. (7.33) Also, it is important to examine the dynamics and kinetics of the transport and molecular diffusion.
Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
8 Polysulfide - Diffusion Analysis http://bbs5.techyou.org/?fromuser=sergio147
The ensuing analysis was prompted by problems encountered with the sulfur (-) electrode while developing a bromine/sulfide secondary cell for load leveling application possibilities. The lives of our composite carbon/plastic, negative electrodes were severely limited upon extensive cycling. After much research and experimentation, the puzzle of limited electrode cycle life was solved. The problem was caused by the erosion of carbon particles from the composite structure by the formation of hydrogen gas just under the surface of the somewhat porous plate. The polymer (plastic) component adheres very well to the total electrode structure and has a physical continuity that does not characterize the very frangible carbon components. After extended operation of this sort with gasses ejecting carbon, the electrode acquires a very high interface resistance and ceases operating as a functioning electrode, producing mono-sulfides due to starvation in the depths of the holes left by the separated carbon. It is most important that we try to take into consideration any and all possible processes and mechanisms in our analysis of the experimental observations. It must also be understood that much of what is offered as explanations for cell behavior is in the realm 165
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ENERGY STORAGE
of speculation - to be verified as we continue with these empirical studies. The dynamics of molecular diffusion, ionic conduction, and the oxidation-reduction processes that occur at the electrode/electrolyte interfaces are considered here with a view toward simplifying and qualifying. In concentration cells, these are considerations of prime importance in the study of the balance of materials transport. Certain operational models must be assumed for such an analysis to be initiated and progress. As we learn more and attempt to match the theoretical modeling to empirical data, some of these assumptions may be abandoned or changed in order to provide a better picture of what actually occurs within a cell. In concentration cells, in which the situation usually involves the movement of uncharged molecules as well as ionic species toward and away from electrodes necessary to its operation, a great amount of attention must be devoted to these transport mechanisms. In the pages to follow, a straightforward examination of the ionic and molecular transport processes that occur within an electrochemical cell are examined. The subject cell makes use of sulfur/polysulfide reactions at electrode surfaces. It is the intention that this simple http://bbs5.techyou.org/?fromuser=sergio147 exploration of the diffusion balances will enable us to better assess cell performance and charge capacity for not only the sulfide cell but for other concentration cell systems based on different chemistry. The sections to follow discuss the various mechanisms that take place within electrochemical cells of this type. Various mechanisms take place within electrochemical cells of this type and present a preliminary analysis of current density distribution and reagent diffusion at the surface of porous electrodes. This initial review is intended primarily to provide a basis for some further attempts at characterizing the kinetics that occur at the surface of the negative electrode.
8.1
Polarization Voltages and Thermodynamics
Voltage losses within a cell, other than those encountered by the electrolyte ionic resistance and electrode electronic resistance, can be classified into three categories: 1. Interface resistance, or ohmic over-potential is due to the resistance of "contact" between electrolyte and electrode.
POLYSULFIDE - DIFFUSION ANALYSIS
167
2. Activation energy, or the rate with which a reaction proceeds, is associated with an energy barrier or activation over-voltage. 3. Concentration over-potential is a polarization voltage that is a function of the concentrations of reactants and reaction products. These factors may be derived and represented as follows. The Nernst equation for an electrode reaction of the form aA
+ bB = cC + d D ,
(8.1)
is given in general terms as E= E°-—InW, nF
(8.2)
where R is the universal gas constant, F is the Faraday number, and n is the charge on the ion. W is defined as http://bbs5.techyou.org/?fromuser=sergio147 c
v(a cc ) (a DD)
d
w = (a; );a;(a; ) fcb , A
R
(8.3)
where the a-terms are the activities for the reactants and the reaction products. For the reaction of interest at the (-) electrode during the charge mode, (see equation (8.5)), equation (8.3) becomes ,2x-2
W ^
S
;
^
(8.4)
Since the activities depend on concentration, or population density of the reactants, high over-voltages can be generated under severe starvation conditions at electrode surfaces. This possibility is especially real if cells are charged by constant current sources. Some cell operating conditions can lead to the evolution of hydrogen, thus tending to further complicate conditions and contribute to additional starvation of electrode sites.
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ENERGY STORAGE
Our primary interest at this time is in the mechanisms associated with the negative (sulfur/sulfide) electrode and, more specifically, the processes involved in the charging mode. Since precisely the opposite occurs at the positive electrode during "charging" in a symmetrical concentration cell, the reverse processes can be analyzed to provide complete cell analysis.
8.2 Diffusion and Transport Processes at the (-) Electrode Surface The processes and reactions that occur at the (-) electrode during charge are more complex and "limiting" than those during the discharge mode. The solubilized sulfur attached to S= ions are supplied only by mechanical means or thermal diffusion against the (-) electrode repulsion. Sodium ions, on the other hand, migrate toward the (-) electrode via electric field attraction. Figure 8.1 shows the transport processes of interest as defined by us for further examination. For the primary energy storing reaction, shown below, to take http://bbs5.techyou.org/?fromuser=sergio147 place at the (-) electrode, N a 2 S x + 2(x - l)Na + + 2(x - l)e" - » 2 ( x - l)Na 2 S.
Figure 8.1 Negative electrode in charging mode.
(8.5)
POLYSULFIDE - DIFFUSION ANALYSIS
169
There must be adequate supply of not only Na + ions to the surface, as demanded by the charging current density, but also a corresponding quantity of polysulfide. If these conditions are not met, then starvation at the electrode surface will occur, and if the voltages are high enough, water will be broken down and hydrogen will evolve in accordance with Na++H20 + e-^NaOH +-H2.
(8.6)
As shown in Figure 8.1, if some hydrogen is produced, then it further complicates the situation since it too must be removed from the reaction site to enable the reduction of sulfur to take place. To summarize, the transport of various species may be put into the following categories. There is the obvious necessity to provide high accessibility to the (-) electrode, especially during the charging mode since only the sodium and mono-sulfide ions are assisted by the electric field gradients and the polysulfide must be provided at the sites by forced flow for higher current densities. http://bbs5.techyou.org/?fromuser=sergio147
8.3 Electrode Surface Properties, Holes, and Pores In order to enhance the electric current density of the frontal area of the electrode, it is quite reasonable to think in terms of increasing the total available working area by making the electrode surface porous or in terms of providing a high degree of irregularities on the surface, instead of a smooth, dense, non-porous electrode. As this direction is taken, the electrode area is increased, and the Table 8.1 The transport of various species. Transport Mechanism
Toward Electrode
Away from Electrode
Electric field assist
Na+
S=
Neutral diffusion
H20
H2
Electric field retard
x
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ENERGY STORAGE
effective, or working, electric current density for any given frontal area current density is decreased. This would seem to be better since the demand rate for reagents to and from the electrode (micro-surfaces) is reduced, thus lessening the chances for starvation and high polarization potentials to appear. However, one must consider the fact that this increased surface area is not as readily available to the reagents as the smooth frontal area was, and the electric field strength within valleys and pores will be diminished. The following is a simple exercise as a very preliminary attempt to explore the interrelations between increased electrode "porosity" and its effect on performance. As a first step in the investigation, the shapes and intensities of electric fields and field gradients were examined as functions of geometry. Figure 8.2 shows some of the more direct and early approaches toward increasing electrode area per unit frontal (normal projection) of a flat plate electrode. As can be seen in both cases above, the working surface area has been increased by either putting a portion of the electrode at an angle or by making an indentation in the electrode surface. http://bbs5.techyou.org/?fromuser=sergio147 Looking at the electric field, one sees that the field gradient is also changed, and the electric current will be modified accordingly as well. The question here is whether there is a net gain in performance and how much.
Figure 8.2 Shaped electrode fields.
POLYSULFIDE - DIFFUSION ANALYSIS
171
Much has been done in the past regarding electric field configurations for various geometrical shapes of conductors. One excellent source is W. R. Smythe's Static and Dynamic Electricity published in 1950 by McGraw-Hill Co. Unfortunately, even the simplest of geometry leads quickly to very lengthy and complex computations for field shapes. Consequently, we have taken a much more simplified approach merely in order to see trends in the results of providing pores and holes on the surface of electrodes. Smythe (see Bibliography reference 26, particularly Chapters I and V) and others have explored the solution of Laplace's equation for plane conductors with infinite extension, or slotted planes. For example, the application of the Schwarz transformation to the computation of charge distribution, σ, in the x-direction on a plane conductor with a slot of width 2a gives the following expression:
εΕ σ = — 1±I http://bbs5.techyou.org/?fromuser=sergio147 2 2 2 2 (*
-
)
(8.7)
J
The conductive plane extends infinitely in the x and y directions, and the slot of width 2a extends indefinitely in the y-direction. In this case, an electric field exists in the z-direction, imposed by parallel plate conductors extending in the x and y-directions. An approach we have taken here to approximate the field strength within a hole or slot, as compared to the electric field intensity at the plate surface, is as follows. Figures 8.3a and 8.3b show configurations of parallel plate conductors as a means of establishing extreme conditions of geometry. The first drawing is for a conductor that has a very large area (slot width). In this case, the electric field is quite uniform within the slot, and the voltage linearly varies with the distance in the y-direction. In other words, the field strength, or voltage gradient, φ, is ,
φ =
3Ε
E
' 3Γ(ΕΤλ)
(8 8)
'
within the slot and E/L at the plate surface, whereas the field strength is close to zero in the very small slot shown in the second
172
ENERGY STORAGE (A)
Lt\--?.s;-\-z.^-.-r?.<-.-\
ΔΕ^ΔΕ,
Figure 8.3 (A) Electrodes with large area depressions. (B) Electrodes with narrow slots.
drawing. The electric field does not bend very much into the narrow hole. The field for this case is approximated by http://bbs5.techyou.org/?fromuser=sergio147
Φν=^
(8.9)
both within the hole as well as at the surface of the plate. In essence, for deep and very narrow slots or holes there is no electric field within the depression. Now consider the situation where the size of the slot is in between the two above extremes, as shown in Figure 8.4. In this case, which more closely represents actuality, the electric potential drop, ΔΕ, from the top of the hole to the bottom can be expressed in numerous approximate ways. One very simple view is to let the portion, ΔΕ, which appears in the pore of the total field, E, between conductors, be further modified by a parameter, β, as follows: ΔΕ = Ε
λ L + λ ß,
(8.10)
where ß is a multiplier or an adjustment factor dependent on the ratio of depth to width of the slot or hole. Perhaps, a workable
POLYSULFIDE - DIFFUSION ANALYSIS
173
3E
/ ■ ' '
>kf
/ - s 'ήν f r s ' / / / / / • /
i
ΔΕ
V. ( / /
k
r s ' >
*
w
Figure 8.4 Dimensioned hole or slot.
representation of the manner in which the field strength varies within a pore in accordance with the ratio of w to λ is
ß == l - e
λ
.
(8.11)
http://bbs5.techyou.org/?fromuser=sergio147 An equally useable expression could be
wα
τ
ß =\ 1 + — w ' a
(8.12)
λ
where a is a constant of proportionality. In both cases, equations (8.11) or (8.12), β goes to zero as w / λ , and β goes to unity as w / λ becomes large. For small pores, equation (8.12) can be approximated by β = ( w A ) a , and then the complete expression, equation (8.10), for small pores becomes ΔΕ = Ε
w
L+λ
α.
(8.13)
Assuming a linear field, the voltage gradient within the hole is ΔΕ
Δλ
=E
w
λ ( ί + λ)
α = Φλ·
(8.14)
174
ENERGY STORAGE
The approximation is not valid in those cases where the pores, or electrode surface depressions, are shallow and have large areas. Since these are not the conditions of interest to us, and the mathematics are unnecessarily more complex to cover the entire range, this approach has been taken for the present. If the above is a reasonable first approximation for the ion attractive force producing fields within electrode pores or depressions, then the next step is to examine the magnitude of electric current densities that result from such surface irregularities.
8.4
Electric (Ionic) Current Density Estimates
Ionic mobility, μ, in the y-direction is given as μ = (y/t) (l/φ), where t is time an φ is the electric field gradient, or φ = 3E/3y, and the ionic speed is - = —.
t at http://bbs5.techyou.org/?fromuser=sergio147
(8.15)
More useful to this analysis is the specific resistivity, p, of the electrolyte, expressed as
Φ = ΐ-?-' A
(8-16)
i = - ^ = current, dt
(8.17)
where
and A= area normal to the current flow. By applying equation (8.13) and solving for the current, i, in the pore entrance where the electric field gradient, φλ, is as described in equation (8.12), we obtain A w A i =
(8.18)
POLYSULFIDE - DIFFUSION ANALYSIS
175
Since the expressions are all normalized for a unit thickness of electrode into the plane of the page (the z-direction), area, A, is equal to w, and equation (8.14) becomes
ί=
< = Ε λο5φ α
(819)
This can be compared to the current of Ew/Lp at the top surface of the plane conductor. It is seen that, as the width of the slot is made smaller and the depth, λ, is made larger, the current into the pore decreases, and the current densities, i/w, also change in accordance with W - =E a w A (L + λ ) ρ
(8.20)
into the pore, and
1_
= http://bbs5.techyou.org/?fromuser=sergio147
Lp
(8.21)
at the top surface. As the electrode becomes more porous, i.e., more internal surface area per unit frontal area of the plane face, the current density will reduce proportionately. However, if we further assume, as another first approximation, that the current density within the hole is uniformly distributed along the entire available surface area of walls and bottom, then the expression for the current density, σρ, within the pore becomes σ
i _ Ew2a ρ = :ΤΤ— = , , „ , . Λ/ . , χ , 2X + w ~ λ ( 2 λ + ν ν ) ( Τί + λ ) ρ
(8-22)
It should be also remembered that the specific resistivity, p, of the electrolyte within the pores will not be constant as the depletion of charge carriers continues with charging. When one integrates the total current across the face on the porous plate electrode, it also becomes apparent that the largest portion of the current flow is to the outermost surface of the electrode and not within the pores.
176
ENERGY STORAGE
8.5
Diffusion and Supply of Reagents
The supply of free sulfur to the (-) electrode takes place only by molecular or thermal diffusion or forced convection. Since attachments to negatively charged sulfide ions solubilize the free sulfur, the difficulty of supply is compounded by the electric repulsion of the (-) electrode. Perhaps, the greatest problem associated with over potentials arises from the difficulty of sulfur supply during charge. If we assume a uniform field gradient into a pore, then, in order to maintain a steady rate of supply, (dQ/dt) s , of SxS= during charge into the pore, the rate must be equal to the charging current into the pore with entrance area w, or dQ dt
= 1.
(8.23)
Figure 8.5 represents a pore with concentrations Ca and Cb outside and inside, respectively, of the pore. In accordance with Fick's First Law, the rate of diffusion is directly proportional to the concentration gradient or difference across a http://bbs5.techyou.org/?fromuser=sergio147 boundary: dQ dt
-KAÄC = - K A
dC
(8.24)
dx
Applying the relationship above, ( ^ ) = - K . ( C . - C > = -K.(C.-C.R) where R = C, / C . Neg charged
w i
'I t / f I / /(. svs=
w
ft Electrolyte region
Ί
t / S / / rt '
Figure 8.5 Carbon conductor electrode pore.
Carbon electrode
(8.25)
POLYSULFIDE - DIFFUSION ANALYSIS
177
In reality, the diffusion situation for the supply of SxS= is worse than described above. Since there is in fact concentration gradient all along the pore length, λ, the availability of sulfur diminishes at greater pore depth. The question that arises now is whether the value of R must be so small that, to maintain the balance of sulfur flow into the pore to match the conversion rate of sulfur into sulfide ions, severe polarization will be encountered and hydrogen gas will be produced. Under the best of conditions, and from equations (8.16) and (8.21), the rate match is ~ =E W T ! ^
=K.(C.-C,R) = K.C>(1-R)/
(8-26)
and that does not account for the electric repulsion forces of the (-) electrode. Solving for R in equation (8.26), we obtain —Ew , ™ „ +1. K e C . ( L + X)Ap
http://bbs5.techyou.org/?fromuser=sergio147
R=
(8.27)
Since no materials are lost (plated on) or generated (plated off) within the pores, only conversion takes place, and spent products must be removed and active reagents must be provided. Mono-sulfide is removed from the pore by diffusion processes but assisted by electric fields, whereas the same fields retard the supply of polysulfide. Composite expressions can be devised in order to describe the total migration rates of the various species by introducing some additional factors associated with coulombic forces.
8.6
Cell Dynamics
8.6.1 Electrode Processes Analyses The general expression describing the half-cell potential at the (-) electrode for the charging reaction, S + 2e~ —> S=, as given by the Debeye-Huckel theory and the Nernst equation, is shown in equations (8.1) through (8.4).
178
ENERGY STORAGE
We will proceed to outline an initial approach to solving the problem or answering the questions that surround the shapes of the charging voltage curves for an LS-2 cell.
8.6.2
Polymeric Number Change
It should be noted that the sulfur/sulfide concentration cell has an alkaline electrolyte due, in part, to the hydrolysis of the Na 2 S salt in accordance with the following reaction: N a 2 S + H 2 0 ^ ^ 2 N a O H + H 2 S.
(8.28)
If a salt, AB, is dissolved in water, it will undergo some degree of hydrolysis. This can be expressed simply as AB + H 2 0 < = > H A + BOH.
(8.29)
The extent to which this occurs is usually measured as the degree of hydrolysis. In the case of a salt of a weak acid and strong base, as in this instance,http://bbs5.techyou.org/?fromuser=sergio147 the equilibrium constant, Kh, for hydrolysis may be expressed as κ
"
[ΟΗΊΙΗΔ1. [A-][H20]
(8.30)
The ionization equilibrium constant, K, is generally expressed as KJA^n.
[AB]
(8.31)
The ionization constant for NaOH is orders of magnitude greater than that of H2S, hence the resultant solution is quite basic. In the sulfide/polysulfide alkaline concentration cell, the important issues of the behavior of sulfide ion and sulfur atoms in the immediate vicinity of the electrodes become quite important. These concerns exist during the charging and discharging processes, as well. The situation is different than what is normally encountered in electrochemical cells because of the fact that both the oxidizing agent, S, and the reducing agent, S~2, are the same chemical specie. Furthermore, the output potential is not derived from a difference
POLYSULFIDE - DIFFUSION ANALYSIS
179
in chemical potential between two different species, but instead is a consequence of differences in concentrations of the same chemical element. To review, again, the elemental sulfur, S, is the oxidizer when being reduced by the addition of two electrons from an external voltage supply circuit at the negative electrode during charging. The exact opposite takes place at the electrode during the discharging mode when electrons are given up to the negative electrode and then subsequently conducted to an outside electric circuit load. We will now take a deeper look into the current density distribution and reagent diffusion at the surface of porous electrodes. This initial review is intended primarily to provide a basis for some further attempts at characterizing the kinetic actions that take place at the surface of the negative electrode in a sulfide electrolyte. This analysis is independent of the processes that occur at the opposite, positive electrode because the electrolytes are assumed to be independent. The only transfer between electrolytes across a cation membrane in this analysis is presumed to be Na + , sodium ions. The initial form of the electrolyte when the cell is in the dishttp://bbs5.techyou.org/?fromuser=sergio147 charged state is presumed to be Na2S_, or the penta-sulfide form, which can be represented as Na 2 S-S 4 . There are then four sulfur atoms available as essentially free sulfur attached to the sodium mono-sulfide in solution. If we now consider the various sequences in which the sulfur becomes detached from the salt during the charging processes, the following seem to be the available choices. 1. Random generation of various polysulfides, Na 2 S-S x , where x can have values from 0 to 4 - In this case, we would assume some statistical distribution function to describe the molecules in solution at any point in time. 2. To assume that the SxS= decreases in size by one sulfur atom at a time during charge and then promptly leaves the immediate electrode surface region to make way for the next SxS= ion until all SxS= species have been converted to S x l S = - The next stage in the reduction of size would take place until, via such systematic procedures, the electrolyte is converted to Na 2 S at full charge.
180
ENERGY STORAGE
3. To assume that each SxS= goes all the way to S= in a series of consecutive steps and then leaves the electrode surface area - This assumption would state that there is always only a ratio of S= to S4S= with which to contend. In any event, if we let the availability of sulfur for reduction to sulfide be the same independent of the multiple attachment factor to sulfide, there should be little practical or analytical concern here as to the exact distribution of sulfur at any time during the charging process. Figure 8.6 shows the diffusion rates in which we are interested for this present analysis. The drawing diagrams the simple but essential aspects of a half-cell. The volume, V, indicated in the figure includes the entire negative electrolyte volume for a unit area of (-) electrode, including that which is stored in the reservoirs external to the cell. Hence, the distance between the membrane and the electrode is not representative of the true geometry. We will use method #3 above to represent a species in the analysis regarding the availability of S (or concentration of S) as independent http://bbs5.techyou.org/?fromuser=sergio147 of x, or the total concentration of S in the form of S S= taken as I SI. Now we have only two kinds of anionic species in solution in the negative electrolyte of volume V, (other than O H - and any Br~ ions that have migrated through from the (+) side), and they are S= and S4S=. Then, the diffusion processes to and from the electrode surface can be represented as shown in Figure 8.7. It should be noted that there is no storage (build up or depletion of reagents at the electrode surface) of reagents within some region of immediate proximity to the electrode surface. Volume, V
Negative electrode
\ \ \
S*S=
electrolyte
Figure 8.6 Diffusion representation.
Membrane
POLYSULFIDE - DIFFUSION ANALYSIS
181
Volume, V
Negative electrode
\ \ \ \
SVS=
Electrolyte
\ \ Figure 8.7 Diffusion to and from electrodes.
There are, in fact, six analytical approaches that we will try to take toward describing the kinetics at the electrode surface. These http://bbs5.techyou.org/?fromuser=sergio147 will be taken in succeeding steps and are listed below. • Case 1 - Flat surface electrode, no surface storage region, instantaneous and perfect mixing of reagents throughout the volume, V, no hydrogen generation • Case 2 - Flat surface electrode, some reagent storage at the surface, instantaneous mixing of reagents within each of the two volumes, volume v is designated as the surface region storage, volume V is designated as the bulk (-) electrolyte, no hydrogen generation • Case 3 - Porous Surface electrode, some storage region, instantaneous mixing in both volumes, no hydrogen generation, smaller diffusion coefficient • Case 4 - Flat surface, some storage, some hydrogen generation, instantaneous mixing • Case 5 - Porous surface, some storage, some hydrogen generation, instantaneous mixing • Case 6 - Porous surface, some storage, some hydrogen generation, reagent concentration gradient at electrode surface volume, instantaneous mixing within volume V.
182
ENERGY STORAGE
For perfect, instantaneous mixing there are no diffusion equations. Only the concentration changes as the various species are generated electrochemically. Referring to Figure 8.7, we see that the expression describing the half cell potential, E, is RT Y,|S-| E = E0 - — I n nZ Y.|S|
(8.32)
and it is the final expression for this particular, somewhat unrealistic case of full access to the electrode surface, with no stagnant electrolyte region at the electrode surface. Activity coefficients for sulfide and sulfur are being researched in the chemical literature. Meanwhile, since we are primarily concerned here with functional relationships, we can proceed with a general analysis of the electrode processes. At present, our main interest is in the functional dependency of, and trends in, the voltages during cell operation. Figure 8.8 gives a few values of generally available activity coefficients for various compounds in aqueous solution (Latimer 1952) http://bbs5.techyou.org/?fromuser=sergio147
1.5
0.5
^3
I —I—·
2
3
Concentration - molarity ■HBr
H 2 S0 4
- ^ N a O H -n-CuS04
■NaBr
-ZnCI,
Figure 8.8 Activity coefficients for strong electrolytes from Latimer's oxidation potentials.
POLYSULFIDE - DIFFUSION ANALYSIS
183
where yi = activity coefficient for the sulfide ions = as_/ I S= I, and ys = activity coefficient for the "free sulfur" = aSx/ I SI. The concentrations of the species are further defined in this particular case as, |S = | = ^ l I v
(8.33)
|S| = - ^ .
(8.34)
and
There is also a useable relationship between Q. and Qs. The total of the numbers of sulfide ions and sulfur atoms remains constant since one sulfide ion is produced for each sulfur atom lost during charging. Q■ + Q = Q equals the sum of both species present initially, and http://bbs5.techyou.org/?fromuser=sergio147 At any time, t, later the expression assumes the form
q = Q0 = qi+qs·
(8.35)
If we normalize the analysis for a unit of electrode area, then the volume in the main negative solution per unit area is V. Now it is necessary to address the rate, R , of sulfide ion generation during charge. This can be expressed as Rg = α σ η ,
(8.36)
where a = constant of proportionality, σ = current density, a m p s / unit area, and η = coulombic efficiency. Thus, we may represent the rate of generation, dq./dt, of S= ions as R = - ^ = αση, 8 dt which is also the exact rate of reduction of available sulfur.
(8.37)
184
ENERGY STORAGE
Since Q o + 4Q. = Q. by substitution between equations (8.37) and (8.32), we obtain (8.38)
Q.=^. ' 5 Solving for q. by integrating equation (8.33),
(8.39)
qi = α σ η ί + k. From the limits of the problem when t = 0,
(8.40) and the final expression becomes (8.41) http://bbs5.techyou.org/?fromuser=sergio147 It is now possible to place the values for q. and qs into equation (8.26) to solve for E as a function of time. Using the relationships in equations (8.27), (8.28) and (8.29), and substituting into equation (8.26),
RT E = E0+—In ° nZ
Yi
ys
V Qo-q.
(8.42)
v
Substituting the value of q. from equation (8.33) into equation (8.34), γ ασηί + ^ RT E= E+—In Ys 4 Q 0 / ° nZ ασηί
(8.43)
is the final expression for this case of full access to the electrode surface and no stagnant region at the electrode surface. We have not yet found the activity coefficients for sulfide and sulfur in the literature. However, since we are primarily concerned here with functional relationships, the details of specific values for
POLYSULFIDE - DIFFUSION ANALYSIS
185
the activities can be left for a later time when we become interested in more dependable, quantitative evaluations of these expressions to compare with experimental results obtained in the laboratory. At present, our main interest is in the functional dependency of, and trends in, the voltages during cell operation. It appears that the chemical potentials of neutral and S= ions and neutral S are independent of whether they are "polymerized" or not, and that the effective reaction is S + 2e" —> S=. While this is an approximation, it is quite reasonable given that the half-cell potentials for the reactions given below are so close together. 2S = -»S= + 2e _1 S=+S; ^ S ; + 2 e ~ =
S +S;->S=+2e"
0.48 volts 0.49 0.52
Since pH is usually very high, reactions of the form HS" —> H + + S and the presence of HS" ions are ignored for the present. Figure 8.8 is a plot of a few values of generally available activity coefficients for various compounds in aqueous solution http://bbs5.techyou.org/?fromuser=sergio147 (Latimer 1952). An interesting graph is the plot of half-cell voltage versus time as expressed in equation (8.37). In order to generate such a plot, the values of a few constants are needed. The values are listed below. Some assumptions or simplifications have been made in a few coefficients outside of the values of the physical constants. =
• R = universal gas constant = 1.99 cal deg"1 mole -1 = 8.3 joules deg"1 mole"1 • a = conversion constant = mole/52 amp-hours = 0.0019 mole amp"1 hour 1 = 5.34 x 10"6 moles amp"1 sec"1 • η = coulombic efficiency = 1.0 • Y; = Ys = as an interim assumption • V = storage volume in liters per unit area of electrode • n = number of electrons transferred per event • E = 0.50 volts half cell voltage at standard conditions • Z = Faradays number = 96,500 coulombs/equiv = 26 AH/equiv. Now we need to assess the values of σ, Q., and Q s on the basis of a particular current density. Since most of the experiments performed
186
ENERGY STORAGE
at TRL with single cells of a 25 in2 area were performed between 4 and 6 amps, we will take 0.03 amps per cm2 as the current density. A total charging time of 5 hours is also commensurate with most of the data accumulated to date. Thus, a total charge of 0.15AH/cm 2 corresponds to the capacity of the electrolyte of volume, V. Now, there are Q s = 0.15AH/(52AH/mole) = 2.9 x 10"3 moles of available S, and Q. = Q s /4 = 7.2 x 10"4 moles of S=. Substituting the above values into equation (8.37), the following is obtained: E = E +0.013· In
7.2xl0" 4 + 1.6xl0" 7 t 2.9xl0"3-1.6xl0"7t
volts.
(8.44)
Figure 8.9 is a plot of equation (8.38) of half-cell voltage versus time in hours. Equation (8.38) then has the form 7.2 x l 0 " 4 + 5.76 x l O ' V
E = E +0.013-In
2.9 x l O " 3 - 5.76 x ! 0 " 4 t http://bbs5.techyou.org/?fromuser=sergio147
0.58
3 Anal-2.doc
4 Time - hours
Figure 8.9 Half-cell potential versus time.
5
(8.45)
POLYSULFIDE - DIFFUSION ANALYSIS
187
Ohmic resistance of the electrolyte and any interface resistance have not been included in the plot. As can be seen, the voltage is below 0.5 volts at the beginning of charge when there are relatively few sulfides present, as compared to the available sulfur. As charging progresses, the potential rises fairly linearly until the concentration of sulfides becomes great and that of available sulfur has diminished significantly. In theory, the cell potential would rise to extremely high values if the charging were continued in the constant current mode. In reality, as the charging potential rises high enough the decomposition of water would take place, and hydrogen would evolve. The factors influencing the shape of the plot include the following: • relative values of γ. and ys • the manner in which γ. and γ. change with or depend on the concentration of the electrolyte • electric current density http://bbs5.techyou.org/?fromuser=sergio147 If, for example, the ratio γ./γ 5 were to be greater or less than unity, as was assumed in the exercise above, the general shape of the voltage versus time curve does not change. Rather, it is displaced on the vertical axis accordingly, as shown in Figure 8.10. The data calculated and plotted above assumes that the activity coefficient ratios are constant throughout the range of solution concentrations. In reality, they probably do vary between the two extremes of very dilute to very concentrated. Figure 8.11a graphs two sample functions of the ratio of r = γ ; / γ . For the low-mid values, the ratio r : = γ./γ. starts at 1.5 and goes down to 0.5 midway, and then it returns to 1.5 at the end of charge. In the second instance, r2 = γ./γ starts at 0.5 and goes up through values of 1.5 and returns to 0.5 at the end of charge. The purpose is to observe the effect of widely varying ratios, r, upon the charging curve for the half-cell. Figure 8.11b gives plots of the cell voltage for the two r-functions above. The shapes change noticeably with such a spread of values, one with a peak in the mid-concentration range and the other with a saddle in mid-range.
188
ENERGY STORAGE Two different values or activity coefficient ratios
0.6 0.58
A
0.56
y
0.52 « x
0.5 0.48
.
I
■
^
< * * " " *
0.46 0.44
0
Anal-2.doc
1
3
4 Time - hours
- * - Ratio = 2
5
- · - Ratio = 0.5
Figure 8.10 Half-cell potential versus time.
http://bbs5.techyou.org/?fromuser=sergio147
The preceding analysis was performed for the very simplified situation, Case 1, where there is not a boundary layer on the electrode and the idealized perfect mixing of electrolyte components. The analysis continues with the circumstances described in Case 2. This next stage in the development of descriptive modeling more closely approximates actual conditions within a cell. It is expected that these exercises will significantly improve our investigations for electrode structures with lower polarization losses and will explain the seemingly peculiar voltage versus time curves and their changing behavior with cycling. A graph would plot the half-cell voltage versus time, as expressed in equation (8.35). In order to do so, the values of a few constants are needed. They are set as the following: • R = universal gas constant = 1.99 cal deg. -1 mole -1 • 8.3 joules deg. -1 mole -1 • a - conversion constant = mole/52 amp-hours = 0.0019 mole amp - 1 hr_1= 5.34 x 10-6 moles amp - 1 sec -1 • η = coulombic efficiency = 1.0 • Y; = Ys = as an interim assumption
POLYSULFIDE - DIFFUSION ANALYSIS (A)
189
Plots for non-constant activity coefficient ratios
0
20
40
60
80
100
120
State charge in percentage - ■ - r1 low mid values Anal-2.doc
- » - r2 high mid values
http://bbs5.techyou.org/?fromuser=sergio147
(B)
Plots for non-constant activity coefficient ratios 0.59 0.58 0.57
y /l SJ
0.56 0.55 0.54
! *
1
0.53 0.52 0.51 0.5
■*■■■■■■■ H
0.49
^—"""
-*-"
0.48 /■* 0.47 0.46
0
Anal-2.doc
1
2
3 Time - hours
- ■ - r1 high mid values
4
5
6
- ♦ - r2 low mid values
Figure 8.11 (A) Activity coefficient ratios versus charge state. (B) Half potential versus time.
190
ENERGY STORAGE
• V = storage volume in liters per unit area of electrode • n = electrical charge per ion = 2 equiv/mole • Z = Faradays number = 96,500 coulombs/equiv. = 26 AH/equiv. By substituting the above values into equation (8.35), the voltage values of half-cell potentials can be obtained.
8.7
Further Analysis of Electrode Behavior
8.7.1 Flat Electrode with Some Storage Properties The earlier analysis assumed simplified conditions, in which no delayed boundary region existed at the electrode surface for reagent storage and instantaneous solvent mixing. The purpose of this analysis and report is to present a sequence of studies aimed at understanding the fundamental processes associated with cell behavior at the negative electrode, in particular. The bromine electrode is comparatively well behaved and presents no inexplicable or unwanted electrical characteristics. http://bbs5.techyou.org/?fromuser=sergio147 The conditions under which this next stage in the analysis has been done are described fully in the text. The results are realistic and provide valuable assistance in understanding the rate process balances. A constant current mode of charging was assumed, and the coulombic efficiency is set at 100% all the way through. In reality, the current efficiency very much depends on current density and reagent concentrations. In the next sequence, we will explore cell behavior when current efficiency is treated as a function of both current density and polysulfide concentration in the immediate vicinity of the (-) electrode. The conditions we will examine are as follows: • Case 2 - Flat surface electrode, some reagent storage at the surface, instantaneous mixing of reagents within each of the two volumes, volume, v, is designated as the surface region storage, volume, V, is the bulk (-) electrolyte, no hydrogen generation. Figure 8.12 illustrates the regions in question and the distribution of reagents at any time within these two regions.
POLYSULFIDE - DIFFUSION ANALYSIS
H
Electrode
191
Stagnant Electrolyte reservoir V Region V Region Boundary
Concentration of S = ions
k
During charge Initial concentration
Distance http://bbs5.techyou.org/?fromuser=sergio147 Figure 8.12 Flat electrode with two associated storage regions.
The concentrations of sulfur and sulfide are considered uniform at all times throughout the respective regions. In other words, the concentration of SxS= for each value of x is assumed to be uniform in volume, v, and volume, V, separately. The chart in Figure 8.12 illustrates this idea that the concentration of each species is constant at all times in the cell regions. Figure 8.13 depicts the rate processes for the gain and loss of sulfide ions and available sulfur for each of the two cell regions. Sulfide ions and available sulfur are entering and leaving the regions across the boundary (artificial separation of the two regions) by diffusion. Also, sulfide ions are generated at the rate R (-) into the boundary layer at the electrode surface by electrolysis (reduction). Available sulfur is lost at the rate Rg(S) to the region by the very same electrolysis process. Hence, R „ ( - ) = -R B (S) = R is the generation rate.
(8.46)
192
ENERGY STORAGE Boundary region vol. = v
Reservoir region vol. = v
R(s)
Na2S
R(l)
Na2S5
km q ir
k p q sr
Na,S
Mit
k■pMsb Pq,
Figure 8.13 The rates of gain and loss of sulfide ions.
Figure 8.14 identifies the various species within the solutions. In order to minimizehttp://bbs5.techyou.org/?fromuser=sergio147 the complexity of the symbols, the ionic species in each of the two regions have been given the following designations for the amount of reagents present at any instant of time during the charging process: • qib = quantity of S= ions in the boundary layer at the electrode surface • qsb = quantity of free sulfur within the electrode surface boundary layer • q.r = quantity of sulfide ions present in the reservoir region • qsr = quantity of free sulfur in the reservoir region. The rate, R (-), with which sulfide ions are being generated by the charging process is R
( g B
-)
=
= aOT
^
i'
(8.47)
dt and the rate with which free sulfur is reduced is R K ( S ) = % * - = CKJTV s
dt
(8.48)
POLYSULFIDE - DIFFUSION ANALYSIS
193
q,r
H
qSb
Psr
Membrane
Figure 8.14 Identification of ionic specie regions.
The net rate, dq i r /dt, of increase in sulfide ions in the reservoir region (volume, V) due to sulfide ions leaving and entering the boundary region via diffusion of both monosulfides and polysulfides into and from the reservoir is represented as d
qir _ qib K qir k m , qsb k P q s http://bbs5.techyou.org/?fromuser=sergio147 dt v l V λ. v λ, V λΓ
(8.49)
The rate, dq s r /dt, of increase in free sulfur in the reservoir region due to diffusion into and from the boundary is dq s r
dt
=
q5b
k
P
v λ„
q sr k P
(8.50)
V λ '
where λ is a diffusion path length. In volume, v, or the boundary region, the rate balance equations are
dt
—
Υλ.
~
ρ
γ λ
km-^+kp-^ p νλ, νλν,
(8.51)
and
dqsb
dt
-R +
ΥλΓ
ρ
qsb νλ,
ρ
(8.52)
The diffusion constants represented by k for the sodium mono-sulfide and the sodium penta-sulfide molecules should be
194
ENERGY STORAGE
self-explanatory. There are four diffusion terms in the expression for dq i b /dt above because available sulfide ions are transported via both the polysulfides and the mono-sulfides. Since immediate mixing in each of the regions is assumed to take place, no provision has been made here to account for any repulsive electrical forces of the (-) electrode acting upon the different ionized components. Hence, in this treatment any deficiency or surplus of ionic species at the immediate surface of the electrode is accounted for in the layer referred to as the boundary region. Since we are concerned at this time only with the neutral molecular diffusion of the reagents, and not ionized charge layers, the diffusion constant, km, and k , for Na 2 S, and Na 2 S. respectively, are considered the same whether they are in the boundary region diffusing away from or toward the (-) electrode or in the reservoir region drifting in either direction. Now it is possible to solve for a set of simultaneous differential equations that describe the concentration balances at any time during charging. There are four variables and four equations: http://bbs5.techyou.org/?fromuser=sergio147
qib+qir+q S b+q S r = Qo·
(8.53)
Since volume, v, is so much smaller than V, q1b+qSb«q1r+qsr·
(8.54)
The variables that are available in this analysis are v and k. Proceeding with the mathematical operations, the following ensues. For purposes of convenience of representation, let a =-, v
a n d b = —. V
(8.55)
To simplify the use of symbols for representing the various constants and multiplier factors in the equations, this interim shorthand notation is employed: —s!- - ak m b cm 2 sec" 1 cm^crrT 1
(8.56)
POLYSULFIDE - DIFFUSION ANALYSIS
k
k νλ Γ k
P
νλ1) k
P
νλ
195
= bk mr
(8.57)
= bk mr
(8.58)
= a
kpb
(8.59)
= bk pr
(8.60)
Representing the differential operator with the symbol D in equations (8.49) through (8.52), we have a series of relationships that assumes the following forms: (VIII.49a)
http://bbs5.techyou.org/?fromuser=sergio147 Dq ir = ak mb q ib - bk mr q ir + ak pb q sb - bk pr q sr
(VIII.50a)
Dq sr = ak pb q sb - bk pr q sr
(VIII.51a)
Dq ib = R + bk mr q ir - ak mb q ib + bk pr q sr - ak pb q sb
(VIII.52a)
Dq sb = - R + bk pr q sr - ak pb q sb
We are particularly interested in solving for the terms qib and qsb the quantities, respectively, of sulfide ions and free sulfur within the boundary layer at the (-) electrode. Equations (8.49a) and (8.51a) contain too many q terms for easy solution. Hence, in order to solve for the variable, qib, the quantity of sulfide ions and free sulfur in the stagnant, or boundary, layer region we must first solve for qir, and qsr by equations (8.50a) and (8.52a). Using these as selected simultaneous differential relationships to be solved, the following are the manipulations. Taking equations (8.50a) and (8.52a) we have, (Vm.50a)
(D + bk pr )q sr = ak pb q sb
(VIII.52a)
(D + ak pb )q sb = bk pr q sr - R
196
ENERGY STORAGE
Since the model assumes perfect mixing in the reservoir region, and since the distance to be traveled by any diffusing specie can be from the outer edge of the boundary region or from within the region, the average distance to be traveled by that specie is half the thickness of the boundary region. Thus, we may set the terms λ and Xm as equal distances. Then the equations become somewhat simplified because k = k = k , and k = k , =kD. pr
pb
F
Equation (8.52) is multiplied by (D+b), and equation (8.53) is multiplied by bkp, and both equations are added together. The resultant equation gives a solution for qsb:
bk p (D + bk p )q sr =abkJq sb
(8.61)
(D + bk p )(D + ak p )qsb = bk p q sr - (D + bk p )R
(8.62)
As a further shorthand notation for simplifying the equation symbols, we set http://bbs5.techyou.org/?fromuser=sergio147 k p = K, and
km = β
(8.63)
By adding (8.55) to (8.56), we obtain [D + aK][D + bK]q sb = K 2 abq sb - [ D + bK]R,
(8.64)
[D 2 + aKD + bKD] qsb = - [D + bK]R,
(8.65)
[D 2 + aKD + bKD] qsb = -bKR.
(8.66)
or
or
Employing the method for the general solutions to the linear differential equation, we have u = c : +c 2 e- K ( a + b \ v = c3t,
and (8.67)
POLYSULFIDE - DIFFUSION ANALYSIS
197
where u = complimentary function, and v = the particular integral. Substituting v into equation (8.55), 0 + (a + b)c 3 = -Rb, and Rb c3= -, a+b
(8.68)
Thus, qsb=Cl-^-t a+b
+
c2e-K^.
(8.69)
There are two boundary or limiting conditions from which we may evaluate the constants Cj, and c2. They are when t = 0, qsb(t = 0) = Qs = Cj + c2, and the rate processes at the beginning of charge are such that when t = 0, ^ = -R-K[bqsro-aqsb0], http://bbs5.techyou.org/?fromuser=sergio147
(8.70)
where the initial conditions within the cell are q sro +q sbo = Qo/
and
qSbo = Q s -
(8·71)
Thus, the net rate of production or removal of polysulfides at the beginning of charge, as a function not only of the electrolysis rate but also due to the initial differences in concentrations of reagents within the two regions when t = 0, is dq;sb (t = 0 ) = - K [ ( Q o - Q . ) b - a Q , ] - R . dt
(8.72)
Differentiating equation (8.69) and setting it equal to equation (8.71), we find ^
bR = - K (va + b)c 2 e- K ( a + b ) t dt a+ b = -K[b(Q0-Q.)-aQ.]-R/
(8.73)
198
ENERGY STORAGE
or c2 =
bR -K(Qs(a + b)+bQ0)-R a+b
-K(a + b)
,
(8.74)
and c2=Qs +
bR R 2-+K(a + b) ' K(a + b ) '
bQ 0 a+b
(8.75)
Since c: = Q. - c2, the final expression for qsb becomes bR q sb = K(a + b) 2 bQ
bQ 0 a+b
R K(a + b) bR
R
0 + Q s + a + b K(a + b)' - +K(a - + b)
-K(a+b)t
bR -t. a+b (8.76)
Equation (8.75)http://bbs5.techyou.org/?fromuser=sergio147 is the first of the two needed expressions for concentrations to be used in the Nernst equation.
8.8
Assessing the Values of Reagent Concentrations
The initial quantity, Qsb, of sulfur in the boundary region is merely that fraction of the total in both volumes, or isb
—
v: Qs st v + V-v.
(8.77)
Capital Q indicates initial values of solutes. Similarly, for the other initial quantities as they will appear in the ensuing equations, ^sr
v+V v+V
'
(8.78) (8.79)
POLYSULFIDE - DIFFUSION ANALYSIS
199
and, Qir=-%rV. v+V
(8.80)
The initial quantities in the (-) compartment (negative electrolyte) are related as Q 0 = Q st + Q I t ,
(8.81)
where the quantity of ions, Q., includes the quantity of sulfide ions contained in the polysulfides as well as those in the mono-sulfides. Since there is a one-to-one trade off between ions formed during charging and sulfurs lost, the quantity, Qo, is constant throughout cell operation. If the molarity of the pentasulfide solution at the start of charge is M p and the total volume of electrolyte in the negative chamber is v+V, then the number of moles of initial sulfide is (v+V)M and 4(v+V)M for the available sulfur. Thus, Q
(v + V ) M ,
and
I = p http://bbs5.techyou.org/?fromuser=sergio147
Q s = 4 ( v + V)Mp.
8.9
(8.82)
Solving the Differential Equations
Now, we must also solve for qsr so that these may be substituted into equations (8.49) and (8.51) to obtain expressions for the required terms qib, and qsb. Just as we know at any point in time what the relationship is between qsr, qsb and Q o , (see equation (8.71)), we know also that q.+q^-^+Rt
(8.83)
for the constant rate of electrolysis and concentrated pentasulfide initial solution. Referring to equation (8.51), the above is substituted for the polysulfide terms so that we may find a solution for q.b: ^ - = ß[bq i r - a q i b ] + K [ b q s r - a q s b ] + R.
(8.84)
200
ENERGY STORAGE
Substitution of terms gives us dt
P
bl^+Rt-qfrHb
+ K [ b ( Q 0 - q s b - R t ) - a q s b ] + R.
(8.85)
Converting to operator format gives us (D + ßa + ßb)q lb = ^ L + ß b R t + KbQ 0 - K b R t - q s b ( a + b)K.
(8.86)
From the previous calculations, qsb has the form qsb=c1e-K^t+c2
+
c3t,
(8.87)
and the two solutions to equation (8.86) are a -ß(a+b)t u = c4e http://bbs5.techyou.org/?fromuser=sergio147
v = c 5 +c 6 t + c7e-
-K(a+b)t
(8.88)
Substituting v into equation (8.86), the constants may be found separately as follows: [D + ß(a + b)] x [c 5 + c6t + c7e-K(a+b)t ] = c6 - c7K (a + b) e - K(a+b)t + ß(a + b)c 5 + ß(a + b)c 6 t + c 7 ß(a + b)e" K(a+b)t
(8.89)
Taking each equation term separately as it relates to constants, multipliers of t, or exponential terms, we find the following for the constants: c7 [K (a + b)+ ß (a + b)]e"K(a+b)t = -K C l c 7 (a + b)e" K(a+b)t , or c7 [K + ß](a + b) = - K (a + b)c 1 c7 =
K-ß
(8.90)
POLYSULFIDE - DIFFUSION ANALYSIS
201
ß(a + b)c 6 t =ßbRt + K R b t - K ( a + b)c 3 t ß b R - K R b - K ( a + b)c 3 c6-ß(a + b) c6 + ß(a + b)c 5
C
5
_ßbQ0 + KQ 0 b 4
(8.91)
K(a + b ) c 2 + R
ßbQ 0 - + KQ0b-K(a + b)c2+R-c6 4
ß(a + b)
(8.92)
The final form of the solution is ß(a+ b ) t + c 5 + c 6 t + c7e-K(a+b)t. qib = c4e"
(8.93)
The coefficient c4 is found from the limiting condition of when t = 0, and qib has some initial value of Q s , so we have c4=Qs-c5-c7.
(8.94)
http://bbs5.techyou.org/?fromuser=sergio147
These expressions can now be placed into a mathematical spreadsheet program, and qsb and qib can be quantitatively evaluated as a function of charging time or state of charge. It is now appropriate to arrive at values for the constants K, ß, v, V, α, σ, η, Q s , Q o , v, and V. Diffusion coefficients, D, for various inorganic compounds in aqueous solution at a concentration of 1 molar are given below. Table 8.2 Diffusion coefficients for various inorganic compounds. Molecule
Diffusion Coefficient, D, cm2 sec"1
HC1
3.44 x 10"5
HBr
3.87
NaCl
1.48
KC1
1.89
CaCl2
1.20
KI
2.06
Nal
1.66
202
ENERGY STORAGE
The diffusion coefficient for mono-sulfide and polysulfide molecules in relatively concentrated aqueous solutions can be estimated by employing a spherical model for molecular shapes, Fick's law, and Stokes's law. The resultant formula for calculating the diffusion coefficient is k =
RT
Γ4πΝ^
N67CTiV3Mvy
(8.95)
where the constants, and units are as follows: k = diffusion coefficient, cm2 sec -1 N = Avogadro number, 6 x 1023 R = universal gas constant, 8.3 x 10"7 erg deg"1 mole -1 T = absolute Kelvin, deg M = molecular weight, gm v = partial specific volume, cm 3 gm _1 η = 0.00894 poise = 0.00894 dyne - sec - cm"2 http://bbs5.techyou.org/?fromuser=sergio147
The molecular weight of Na 2 S is 78, and that of Na 2 S. is 206. Specific gravity data of sodium sulfide solutions taken by laboratory measurement at TRL gives the following values: • 1 molar Na 2 S solution sp.gr. = 1.054 (sp.gr. means specific gravity) • 2 molar Na 2 S. solution sp.gr. = 1.233 Molecular weights of the anhydrous salts are as follows: • Na 2 S = 78.04 gm/mole • Na 2 S. = 206 gm/mole In 1 liter of 1 Na 2 S molar solution there are 1054 - 78.04 = 976 grams of H 2 0. Since the specific gravity of water is 0.997 at 298 deg, there is then 1000 - 979 = 21 ml of 78.04 gm of Na 2 S present in the solution. Dividing through that gives for the partial specific volume, v , of the mono-sulfide v = 0.269 cm'grrT 1 .
(8.96)
POLYSULFIDE - DIFFUSION ANALYSIS
203
Similar computations for the polysulfide gives v = 0.422 cm 3 gm _ 1 .
(8.97)
Returning now to equation (8.92) and substituting for the constants found, we can compute values of km and k as follows: 4π(6.02χ1023)
8.3xl07(298) ρ
~6.02χ1023(6π)(0.00894) 2.47x10
10
3(78)(0.269)
75.6x10 23
1.014x10 23 3 (78) (0.269) = 2.44x10 ■13
3 2 x 1 0 21
\
0.269
k m = 2 . 4 4 x 1 0 " " (4.92xlO 7 ) = 1 2 x l 0 - 6 c m 2 s e c - :
(8.98)
http://bbs5.techyou.org/?fromuser=sergio147 By the same formula, the diffusion coefficient for the pentasulfide is found:
_ 2.47xlO 1 0 p
75.6x10 23
~ 1.014xl0 2 3 3(206)(0.422) = 2.44x10 •13
/
75.6χ1023Λ 260.8
k p = 2.44 x 10"13 (3.07 x 10 7 ) = 7.49 x 10"6 cm 2 sec
(8.99)
Even though the molecular weights and partial volumes differ considerably, they appear under the cube root, and their effect on the diffusion coefficient is not great. On the basis of Fick's law, d q / d t = k(dC/dx) cm sec -1 , where d C / d x is the concentration gradient normal to the electrode of that specific solution component in the cell. The value of Q o is determined by the initial molarity of the pentasulfide at the discharged state and the designed charge capacity per unit area of electrode.
204
ENERGY STORAGE
We are now able to calculate half-cell potentials. The two expressions for qsb, and q.b, as represented respectively in equations (8.77) and (8.87), are evaluated for graphing potential versus time (or state of charge) for different boundary thickness and current densities at the negative electrode: R = αησ, where a = 1.92x10 = 5.3xl0~
6
2
moles/AH, moles/A-sec
or (8.100)
In order to estimate the volume of the electrolyte needed per square centimeter, it is necessary to fix the initial molarity, current density, and time of charging to 100%. A period of five hours has been a reasonable time to charge a storage system at constant current, and current densities in the range of 0.04 amps/cm 2 and an initial concentration of 0.75 molar Na 2 S. have been employed during cell testing on this project. These would result in a total electrolyte volume of 1.28 cm3 (ml) per square centimeter of electrode area, a total charge capacity of 0.20 AH, and a total of 9.6 χ 10~4 moles of http://bbs5.techyou.org/?fromuser=sergio147 sodium pentasulfide in both regions. Now, the two volumes, v and V, can be set to different values to observe how they affect the shape of the charge curves. A new parameter, Γ, is established for the sake of convenience: Γ =—— v+V
(8.101)
At the onset of charge the total number of moles of available sulfur in the 1.28 ml volume of the unit area cell is 4 x 0.00096 moles, and there are initially 0.00096 moles of sulfide ions present. The number of moles of reagents in the boundary region at the beginning of charge is as follows: Qsb = 3 . 8 5 x l 0 " 3 r
moles
Q i b = 0 . 9 6 x l 0 ~ 3 r moles
(8.102)
We must also estimate the terms a, b, and c from the diffusion coefficients, region volumes, and diffusion path lengths. Since this model is based in part on a stagnant boundary region and perfect mixing in the flowing reservoir region, a reasonable first approximation of the diffusion path ascribable to the reagents is as follows.
POLYSULFIDE - DIFFUSION ANALYSIS
205
The average distance that must be traversed by reagents within the boundary region is ^=1.28 Γ/2, and the average distance (assuming perfectly uniform distribution within the flowing reservoir region) that a reagent molecule must travel from the outer edge of the boundary region to the middle is also λ Γ =1.28Γ/2. The diffusion path lengths are arguable, depending on electrode design and how far into the boundary region electrolysis takes place. Consider the following, Since, 1 1 0.78 a = —= = , v 1.28Γ Γ b=
-U V
)
1.28 ( 1 - Γ )
and
™
(1-Γ)
(8.103)
and since we also have established that λ is the same for all species, „ kP „ 7.5 xlO" 6 11.7 xlO" 6 K = —=2 = , and http://bbs5.techyou.org/?fromuser=sergio147 λ 1.28 Γ Γ km „ 12ΧΚΓ 6 18.75 x l ( T 6 Q
ß=
T=2'T^F=^^-
(8 104)
·
The binomial term (a + b) appears frequently in the expressions, and its value is (a + b ) = \ - = °/78 ,. v ' 1.28Γ(1-Γ) Γ(1-Γ)
(8.105)
These multipliers are then inserted into the relationships for qsb, and qib in order to obtain the final expressions that can be quantitatively evaluated and employed to provide graphs for cell half voltage as the state of charge progresses for different coulombic efficiencies, boundary layer thickness, current densities, and even diffusion coefficients. To develop graphs for volts versus time at different settings of Γ and σ, the two expressions for q must be inserted into equation (8.26). The parametric analysis that has been programmed into a Lotus spreadsheet and database provides a convenient means for examining the shapes of charging voltage profiles as different values of
206
ENERGY STORAGE
gamma sigma are inserted. Some of these typical results are shown in the accompanying graphs. As a first step in the review and presentation, consider how the shape of the volt/time curve depends on the thickness of the boundary region (porosity or accessibility of the electrode surfaces). Extensive experimental data has clearly shown that the smooth, nonporous surfaced electrode gives a flatter shape than a porous electrode with, for example, imbedded active carbon. It should be noted that, since the mathematics in its present form does not distinguish between positive and negative matter, and especially since the coulombic efficiency is constant, at higher current densities the concentrations could become "negative." There is obviously no validity to any projected data beyond zero concentrations, and the analysis ceases being useful beyond these limits. The graphs do clearly indicate that at the higher current densities the limitations imposed upon cell performance, in terms of achieving full charge capacity of the electrolyte, is increasingly limited by thicker boundary layers. The series of nine graphs that follow shows how the logarithm of the concentration http://bbs5.techyou.org/?fromuser=sergio147 ratio, q ib /q sb / is dependent upon Γ and σ. Diffusion path is assumed the same for both directions
. 2.5 CO ■a
c
^Ν^
O
.Q
: I
.f· 1-5 jo o E
Γ' 5 *M*
0
'·*· ♦♦«»1»
20
40
80
60 Percent SOC
- » - v / v + V = 0.02 Current density = 0.04 amps/cm
-»-0.10
2
Figure 8.15 qsb pentasulfide concentration versus SOC.
-0.15
100
POLYSULFIDE - DIFFUSION ANALYSIS
0
20
40
60 Percent SOC - ■ - v / v + V = 0.02 - » - 0 . 1 0 -A-0.15 Current density = 0.04 amps/cm2
207
80
100
80
100
Figure 8.16 qib monosulfide concentration versus SOC. http://bbs5.techyou.org/?fromuser=sergio147
20
15
-3
10
in
σ
Very poro
f£0
i
j
„+·*******-** 3latively smooth
20
60 Percent SOC - " - v / v + V = 0.02 -»-0.1 Current density = 0.04 amp/cm2
Figure 8.17 ln(q ib /q sb ).
40
0.15
208
ENERGY STORAGE
f 2.5
K.
Diffusion path is assumed the same for both directions
*
to
Io 2 .Q
.•|~ 1-5 a o E 1
°l oi
ft*
« |
0.5
^^^T"l 0
==dF==5ap-w-
20
40
60 Percent SOC v/v + V = 0.05 o 0.20 - * - 0.50
80
100
Current density = 0.01 amps/cm2 Figure 8.18 qsb pentasulfide concentration versus SOC. http://bbs5.techyou.org/?fromuser=sergio147 Diffusion path is assumed the same for both directions
6 o 'σι 5 ω ■a
c 3
o
4 3 2 1
s!
0
20
40 60 Percent SOC — v/v + V = 0.05 o 0.20 -> ■0.50 2 Current density = 0.01 amps/cm Figure 8.19 qib monosulfide concentration versus SOC.
80
100
POLYSULFIDE - DIFFUSION ANALYSIS
209
Diffusion path is assumed the same for both directions 20
15
_
10
Ä
5
I
o
0
20
40
60
Percent SOC v/v + V = 0.05 o 0.20
80
100
•0.50
Current density = 0.01 amp/cm2 Figure 8.20 ln(q ib /q sb ). http://bbs5.techyou.org/?fromuser=sergio147
I
Diffusion path is assumed the same for both directions
2.5
I
\
Γ\
Γ 0)
1
| Έ if
0.5
~
V ""> n
°°°°°o0 20
°°°°0O
40
60
80
Percent SOC — v/v + V = 0.01 Current density = 0.10 amps/cm
o 0.03
2
Figure 8.21 qsb pentasulfide concentration versus SOC.
-0.06
100
210
ENERGY STORAGE Diffusion path is assumed the same for both directions o CD
(0
§ 4
J3
■I"
3
a P o o o o oc o ° ° o oo oo ε 2
-uuooooooooooo<
Φ
T3
0
0
20
40 60 Percent SOC v/v + V = 0.01 o 0.03 Current density = 0.10 amps/cm2
80
100
-» 0.06
Figure 8.22 qsb monosulfide concentration versus SOC.
http://bbs5.techyou.org/?fromuser=sergio147
Diffusion path is assumed the same for both directions
20
15 - s 10
■£
—-κ*^
5
¥
U o o o o c
-5
0
oooooooo
20
Ο θ
ο°
40 60 Percent SOC v/v + V = 0.01 o 0.03
Current density = 0.10 amp/cm
2
Figure 8.23 ln(q ib /q sb ) versus SOC.
80 0.06
100
POLYSULFIDE - D I F F U S I O N A N A L Y S I S
211
Diffusion path is assumed the same for both directions 20 I
1
1
1
1
1
15
~ 10 W
£
.
_ _ _
^ / -
5
0 /
0
"~
20
40 60 Percent SOC v/v + V = 0.05
80
100
Current density = 0.10 amp/cm2
Figure 8.24 ln(q ib /q sb ). http://bbs5.techyou.org/?fromuser=sergio147
8.10
Cell and Negative Electrode Performance Analysis
These studies are directed at acquiring a better understanding of the mechanisms associated with rate processes at the (-) electrode. Earlier in this book we presented the beginnings of a parametric study of the diffusion rates and reaction kinetics for the (-) electrode (sulfur/sulfide reaction). This study was prompted by the need for reducing polarization losses and by the desire to explain observed cell performance degradation. During the past three years of single cell development and testing, we have consistently observed a diminishment in cell performance in terms of voltage efficiency and shape of the charging potential with the accumulation of cycles at high voltage (well over 1.6 volts). These tests were conducted with two half-cells - one, of course, was the sulfur/sulfide reaction, which is of primary interest to us here, and the other was a predictable and reversible half-cell process such as bromine/bromide reaction. The latter reactions are very well behaved and fairly constant in value.
212
ENERGY STORAGE
The sketch, Figure 8.25, describes the essence of our observations. The first cycle of any newly assembled cell has the flat charge shape and slowly sloping discharge shown by curve-A. Initial coulombic efficiency is close to 100%. As cycle numbers increase, the shape assumes that of curve-B. There is a marked rise in charging potential, the discharge curve droops downward, and the coulombic efficiency becomes lower. Significant attention has been paid to the matter of cell performance degradation in the past. Many tests were done in our attempts to isolate the cause of these observations. Quite obviously, and assuming that the opposite half-cell reaction remains constant over the cycling, there are only three possibilities, which center around the three main factors in cell behavior: 1. Electrolytes 2. Electrodes 3. Membrane It was determined, via isolation experiments, that changes in neither of the two electrolytes caused the deterioration of performance. http://bbs5.techyou.org/?fromuser=sergio147 After a cell was cycled numerous times and the changes were observed, electrolytes were drained and replaced by fresh solutions. Some return toward initial performance was seen, but even that was only temporary. Cells were taken apart after cycling and membranes were replaced with very little change in performance. The tests left little doubt that the cumulative changes in cell characteristics were due to electrode changes. If this is the case, the next
Cell area ~ 30 in2, Current ~ 4 amperes Charging mode
Percentage, SOC
100%
Figure 8.25 Deterioration of negative electrode due to H2 evolution.
POLYSULFIDE - DIFFUSION ANALYSIS
213
question naturally concerns the mechanism of electrode property change. There are, once again, only a limited number of speculations possible regarding the source or cause of such changes, which includes the following: • Sulfur accumulation within the electrode • Some form of electrode contamination or passivity • Structural change leading to greater polarization effects. Of the three possibilities, the third seemed most probable to us based upon much past experience with composite electrodes in salt solution electrolysis. It has been noted in previous experimental work with electrodes of similar construction that a gradual and inexorable deterioration of its properties occurs when gas is generated at the electrode surface. Based on these experiences, a study (analysis) was conducted to ascertain whether or not a simple mathematical approach to electrode behavior and half-cell potential dependency on diffusion layers bears out our speculations of electrode causes of cell http://bbs5.techyou.org/?fromuser=sergio147 changes. In the analyses, a dependency of cell potential upon diffusion boundary regions was demonstrated. Since then, the analytical approach has been somewhat simplified, and changes in coulombic efficiency as a function of sulfur concentration have been taken into account. There are many analytical approaches that can be taken to describe the probable behavior of the ionic and molecular species in the immediate vicinity of the (-) electrode. Some of these are being explored and are discussed in attached separate appendices that will be part of ensuing reports. However, for the sake of expediency, and in order to mostly point out the mechanism possibility as an offered explanation for electrode behavior, the following is presented. In the analysis given for the concentrations of available sulfur and sulfide at the (-) electrode, we assumed a constant coulombic efficiency. In fact, the current efficiency for the reduction of sulfur to sulfide depends at least upon the concentration of available sulfur at the electrode. A simplified method of initially examining such a dependency was taken, wherein the coulombic efficiency dependency at any
214
ENERGY STORAGE
point in time during charging is accounted for as a correction factor. In effect, we selected an exponential dependency as follows. The rate, R, with which sulfur is removed and sulfide is generated is R = ησα,
(8.106)
a = 5.3xl0" 6 m o l e s / a m p - s e c ,
(8.107)
where
and η = coulombic efficiency, a n d σ = current density, a m p s / c m 2
(8.108)
A function that satisfies the condition of 100% coulombic efficiency from very high values of sulfur concentration, qsb, (molar range) in the boundary region to very low (0.01 molar levels) is http://bbs5.techyou.org/?fromuser=sergio147
__c_ n = eqs\
(8.109)
where C = a constant. C is evaluated for this exercise by setting η = 0.99 when qsb = 0.01 molar. Then C = 0.001 molar units. Figure 8.26 shows the manner in which the concentration ratio of, q ib /q sb changes with state-of-charge, SOC. In all of the calculations and plots, a current density of 0.040 amps/cm 2 is assumed since it represents typical values in lab cell tests. The boundary thicknesses of four different values were selected to illustrate the manner in which the slope of the curves depends upon the diffusion layer. As the boundary becomes thicker, qsb approaches small values earlier along the SOC axis. Figure 8.27 shows the manner in which q.b changes with SOC. Again, qib arrives at its highest values earlier in the charge mode with increasing boundary value thickness, Γ = v / ( v + V) = r. Naturally, the quotient of qib divided by qsb achieves higher values earlier in the SOC as Γ is made larger. This is shown in Figure 8.28 below.
POLYSULFIDE - DIFFUSION ANALYSIS
Ratio v/v + V = r Figure 8.26 Sulfide to sulfur concentration versus SOC. http://bbs5.techyou.org/?fromuser=sergio147
1.7 o
Π) tl)
Diffusion path is assumed the same for both directions
1 β
i» 1.5 ffl 1.4 r3Ü 1.3
■o
c
&
1.2
m o 1.1
b
o
>
1 0.9 OR 0.7
50
150
100 Percent SOC
v/v + V = r
- * - r = 0.01
— 0.05
-*- 0.10
Figure 8.27 q.b monosulfide concentration versus SOC.
0.20
215
216
ENERGY STORAGE
500
Current density = constant 0.040 amps/cm2
400
300 200
100
/J J J 50
100
150
Percent SOC r=0.01
— 0.05
-+- 0.10
0.20
Ratio v/v + V = r Figure 8.28 Sulfide to sulfur concentration. http://bbs5.techyou.org/?fromuser=sergio147
When the logarithm of the ratio q ib /q sb is evaluated and plotted as shown in Figure 8.29, it can be seen that the cell voltage will increase higher and earlier in the charge mode as Γ becomes larger. According to the Nernst equation, the half-cell potential can be expressed by RT E00 +—In ysq sb nF Yiq.i
(8.110)
Assuming that the activity coefficients remain constant over the entire range of interest, cell potential will increase with the log of the concentration ratios. It should be noted here that little attempt has been made so far to establish accurate or even reliable approximations to absolute values of constants such as diffusion coefficients, activity coefficients, etc. At this point our main concern is the identification of basic mechanisms for the empirical observations obtained from cell testing. It is our contention at this point that the major cause of cell charging voltage changes with increasing cycles is due to changes
POLYSULFIDE - DIFFUSION ANALYSIS
217
Current density = constant 0.040 amps/cm2 10 i
1
0
20 - - - r= 0.01
1
1
r
40 60 Percent SOC —0.05
—0.10
80
100
-e- 0.20
Ratio v/v + V = r
Figure 8.29 ln(q ib /q sb ). http://bbs5.techyou.org/?fromuser=sergio147
in electrode surface properties. Experience with carbon composite electrodes, where gasses such as hydrogen or oxygen are generated, has consistently shown that deterioration in coulombic efficiency takes place for the generation of other species. Carbon particles, whether they have the form of activated porous structures, graphite crystals, or very short range "amorphous" carbon, black will be mechanically chipped and eroded away by the formation of occluded gasses. As these particles leave the eroding surface of the electrodes plastic (Kynar), polyvinylidene fluoride binder is left behind, thus presenting a less conductive outer electrode surface. Ionic species such as polysulfides must diffuse greater distances into the electrode surfaces for electrolytic reduction to take place. The increasing boundary thickness, Γ, tha is synthesized mathematically via the simple modeling above corresponds to this increasing distance for diffusion in an eroding electrode. Also, as such electrode deterioration takes place, electrical contact (continuity) is gradually lost to any layer of porous carbon bonded to the electrode substrate surface. This loss of contact further reduces the effectiveness of the electrode and even increases the diffusion path beyond that of an eroding substrate.
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ENERGY STORAGE
As the processes continue, the hydrogen will be produced even earlier in the charge mode and in greater percentage, thus further accelerating electrode deterioration. Some speculations have been made regarding the effects of free sulfur (solid) accumulating within the pores or surfaces of the (-) electrode during the discharge mode. It has been offered that changes in electrode behavior during subsequent charging modes might be due to such factors.
8.11 General Comments The validity of some of the preceding speculations can be verified or abandoned by further laboratory investigations. It is suggested that these steps be taken to further the study of these mechanisms: 1. Test above theory by purposefully placing diffusion barriers immediately adjacent to the (-) electrode to create the conditions predicted by the modeling. 2. Examine http://bbs5.techyou.org/?fromuser=sergio147 electrode surface structure after subjecting to severe, repeated cycling. 3. Explore solutions to the design of non-eroding electrodes.
Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
9 Design Considerations
http://bbs5.techyou.org/?fromuser=sergio147
9.1
Examination of Diffusion and Reaction Rates and Cell Design
When embarking on the design of a new electrochemical cell, there are numerous factors to consider at the initial stages. After deciding on the chemistry and electrolyte to be employed, perhaps the most important factor to be reviewed is that of electrodes. What electrode materials will be used as the basic structure upon which the energy storing reactions will occur? In most electrochemical cells, the electrode participates directly in the processes. Examples of this are the lead-acid, nickel-cadmium, lithium-ion, and metal hydride cells. In the case of redox-type cells, whether they are of the full flow chemical couple devices or the static electrolyte concentration cells, the electrodes are designed to be electronically conductive but chemically inert. This property is chosen so that the system will have a relatively long life with chemically reversible reactions such that there are essentially no inherent chemical changes with a cell even after a very large number of cycles. There are very few systems that truly offer this distinctly desirable advantage. In almost all energy processes that employ 219
220
ENERGY STORAGE
chemical reactions, there are some irreversible processes that take an eventual toll on the device life. The concentration cells offer the opportunity of circumventing most problems that beset conventional "batteries." Electrodes are of great concern in these new types of cells because they are the "weakest link" in the operating cell life. All other processes are reversible in a practical sense. A material must be chosen that will not only be chemically inert but also inexpensive and have sufficient electronic conductivity to enable efficient performance at higher currents.
9.2
Electrodes
Electrodes are possibly the single most demanding factor in cell design and performance. The only practical material that can meet these stringent requirements is carbon. There are many forms of carbon. The most conductive is what is generally known as graphite, a crystalline consisting usually of flake-like components staked in a somewhat orderly manner, dependhttp://bbs5.techyou.org/?fromuser=sergio147 ing on its method of production. Usually, commercial graphite is produced from a carbon granular material or hydrocarbon (organic) substance that is adhered together by another carbon compound bonding agent such as a phenol resin. The raw brick thus formed is placed in an oven in which the atmosphere can be controlled, and it is baked at elevated temperatures such that the hydrogen and oxygen are mostly driven away by decomposing the brick in an inert atmosphere to prevent the combustion of the carbon materials. The result is a substance that is mostly elemental carbon in composition (about 90-99%). If the appropriate temperature controls permit, the carbon brick can become mostly graphitic in form with a relatively high specific electrical conductivity. Depending on how the brick was initially formed in its compression, the graphite particles may be largely aligned in a specific direction, thus making the final product anisotropic in both thermal as well as electrical resistivity. Subsequently, these bricks are cut into sheets or plates anywhere upward from 1/16 inch. Even though these plates are relatively fragile (brittle) and cannot easily be managed as a sheet of metal such as copper or zinc, they are chemically inert.
DESIGN CONSIDERATIONS
221
Other substitutes are available, such as exfoliated graphite sheets known commercially as Grafoil. They are expensive, have little mechanical strength, and will eventually separate in liquids. Pyrolytic carbons are far too expensive and have poor electrical and mechanical properties for this application. The only other materials with desirable properties are the noble metals such as platinum and ruthenium, but they are incredibly costly for any industrial or commercial use here. Titanium and tantalum have very high chemical resistance except, in certain cases, when used as a positive electrode where oxidation is taking place. Unfortunately, their resistance to chemical attack in active devices such as batteries is low, and they also tend to be quite expensive. Electroplating or vapor depositing Pt or Ru onto the surface of titanium as electrodes is not only fairly costly, but it also provides a failure mechanism for cells when the thin plating wears off. So, for large-scale, inexpensive systems carbon in one form or another is about the only choice. There is another method for forming electrodes from graphite or other elemental carbon materials - compression molding or graphite electrodes bonded by suitable polymeric materials such as high http://bbs5.techyou.org/?fromuser=sergio147 molecular weight polyethylene, PVC or PVR The resultant product of this process is a thinner, less costly, and mechanically much stronger plate. The electronic resistivity is not much less than that of an all graphite plate, usually in the range of 10~2 to 10~3ohm-cm. Metal conductors such as copper and zinc have specific resistivity in the range of 10~6 to 10~5 ohm-cm, at least 100 to a thousand times smaller. This difference has quite an influence over the physical design of a concentration cell that employs carbon electrodes.
9.3
Physical Spacing in Cell Designs
In view of the electrical limitations of a carbon electrode, more attention than normal must be given to metallic electrodes and their size and shape.
9.3.1 Electrode Structures Electrode properties are very critical to effective and long-life performance of any electrochemical cell. It is the component wherein the electronic conduction into and from within the cell electrons
222
ENERGY STORAGE
are able to pass through an external load. Thus, it is desirable to have electrodes with minimum electronic resistance and the ability to make intimate contact with the electrolyte. Most electrochemical cells employ metallic electrodes. An example of this is the lead-acid battery, in which lead is used to conduct the current and also participate in the electrochemical processes. Fortunately, lead is not chemically attacked by the sulfuric acid solution electrolyte and, consequently, has a reasonably long life. In the redox type of systems described here, metallic electrodes are not useable because of chemical oxidation and eventual destruction, if not upon exposure to the electrolyte, then certainly with charging/ discharging cycling. As described earlier, one of the greatest goals of redox types of secondary cells is a long cycle life. It was realized that the electrodes must not directly participate in the electrochemical process, in the sense that the solid materials of which it is constructed undergo any chemical or physical change necessary to the mechanism of the storage of energy. In the cases of the zinc/bromine, vanadium, zinc/chlorine, and iron redox systems, carbon is the only practical material to use for electrodes. Carbon is electrically conductive http://bbs5.techyou.org/?fromuser=sergio147 (though not nearly as much as most metals), readily available, inexpensive, and quite inert to chemical attack by most other substances at ambient and near ambient conditions. However, there are many other problems with which one is confronted when attempting to fabricate practical electrodes. Carbon in its elemental form is a hard, electronically conductive substance in various crystalline forms, and it is most readily seen as coal or sublimed materials resulting from the combustion of organic compounds. There are virtually innumerable solid forms of carbon, thus making it difficult to generalize the material's physical forms and properties. For example, graphite tends to have high electronic conductivity and a structure comprised of fairly long or large crystals. "Carbonizing" organic substances with high porosity such as peach pits and coconut shells can produce another form of carbon that has an extremely large surface area. If the carbonization of such materials is properly controlled, then the product can be almost 100% carbon with extremely high porosity. These latter products usually have lower electrical conductivity than the more graphite, larger crystal structures. Since carbon is chemically inert to attack at ordinary temperatures, it is a very attractive material for electrodes in electrochemical cells,
DESIGN CONSIDERATIONS
223
especially in redox type of devices. It is available in great quantities, and the element is consequently very inexpensive. However, the problem of fabricating carbon into the required geometric shapes (usually flat plates) must be dealt with. Industrial or commercial carbon used in the construction of various devices is usually available in familiar bricks, plates, rods, and cylinders. Carbon can also be made into cloths and sheets by carbonizing any organic material in controlled ovens with an inert atmosphere such as nitrogen or argon so that most of the hydrogen, oxygen, and other components of the original material are driven off without oxidizing the carbon component, thus leaving behind the original skeletal carbon structure. Carbon electrodes that are mostly used in electrolytic cells are produced from graphite granules mixed with a suitable binder. Then they are fired in an oven, thus driving off or oxidizing the binder and leaving the initial carbon particles bound together as a plate or block. Costs of such components are essentially due to the labor, energy, and capital equipment required to perform these manufacture operations. Unfortunately carbon components that are fabricated as thin plates in this fashion are very fragile and easily fractured. http://bbs5.techyou.org/?fromuser=sergio147 Also, such carbon plate electrodes are rather porous, ranging from a minimum of 5% to 20% interconnected pores. These holes are the result of the manufacturing process. The plastic (frequently a resin of some sort) binder that is used as the glue is decomposed and largely converted to carbon during the oven baking process. The gas components of the decomposed resins escape through holes in the plaques, leaving behind a somewhat porous end product. Another limitation of such plate electrodes is their relatively low conductivity. Most graphite plates fashioned in this manner have a specific volume resistivity in the order of 0.01 to 0.001 ohm cm or a conductivity in the range of 102 to 103 mhos-cm, which is not much different, at best, than the values for graphite itself. If a plate electrode is to be made of this material for an electrode of 10 cm by 20 cm and 0.11 cm thick, then its resistance, R, along its length from top to bottom is found as R=p^,
(9.1)
where p = specific resistivity, and L and A are the length and the area, respectively, of the plate. If p is 10 -3 ohm-cm, then the plate
224
ENERGY STORAGE
resistance from end to end would be approximately (10~3) x 20 x 10 x 0.11 ohms, or 0.02ohms. To evaluate this in terms of usefulness in a cell, we must know the electrolyte resistivity and then the cell resistance. Strong electrolytes such as HC1 and NaCl have a volume resistivity of 0.5 to 10 ohm-cm, respectively, at about 1 molar concentration. Employing these figures for a typical cell with the above dimensions for the electrodes and a space between electrodes in the range of 0.10 inch, or about 0.2 cm, the electrolyte resistance of the cell (if we use an average value of 5 ohm-cm for the solution) is about 5 x 0.2 x (10 x 20)"1 = 0.005 ohms. Such a cell would have most of its resistance contributed by its electrodes. If we were to reduce the contribution of each electrode by an averaging factor of two because the current is continuous along its length, then the ratio of electrode to electrolyte resistance would be 2:1. The above situation strongly suggests that bipolar electrodes be employed in cell design. However, that type of design presents its own set of problems. Certainly, if conduction through the electrodes is perpendicular to the surface (assuming for the present that these electrode structures are isotropic), then their contribution to http://bbs5.techyou.org/?fromuser=sergio147 cell resistance is much less. The four principal concerns in such cell arrays of bipolar electrodes are the following: 1. 2. 3. 4.
Electrode porosity Mechanical strength Cost Making contacts at the end electrodes to the outside circuitry.
Carbon plate pores can be significantly reduced by vacuum impregnation with various wax or low viscosity polymers. However, the porosity cannot be brought down to zero. Hence, we must still contend with some degree of porosity. This problem manifests mostly as a chemical attack from the electrolyte on any metallic contact made along the electrode length to reduce resistance. This situation is illustrated in the half-cell of Figure 9.1 below. Establishing effective electrical contact with the graphite plate electrode is another serious problem. It is necessary to use a conductive adhesive such as graphite-loaded epoxy or silver loaded resins and epoxies. Silver provides the best (lowest resistance) bond, but
DESIGN CONSIDERATIONS
225
Figure 9.1 Metallic contact to electrode substrates.
it is very susceptible to corrosion upon exposure to the electrolyte via diffusion through the plate pores. Unfortunately, as was mentioned earlier, other than platinum, http://bbs5.techyou.org/?fromuser=sergio147 ruthenium, rhodium, and perhaps gold, there are no metals that can be employed as electrodes. These are all obviously too costly, and all other metals will be chemically attacked in a short time when exposed to the cell environment and especially when used as the positive terminal of the cell where oxidation takes place during charging. The very high electronic conductivity of most metals, their ability to be formed into any shape desired, their resiliency, and usually their ease of making a good electrical connection to external circuitry make them attractive to use in cells. Returning to the matter of carbon in its many forms, there are methods that can be employed to make use of carbon as the electronic material interfacing the electrolyte while still avoiding high costs and physical limitations of fragility and handling. That approach is the use of carbon-plastic composites. Structures of this sort have been fabricated with great success.
9.4 Carbon-Polymer Composite Electrodes Carbon particles such as graphite flakes can be molded with a suitable binder to any shape desired. In electrochemical cell applications,
226
ENERGY STORAGE
flat plates are most the most common geometry. Compression molding the carbon particles with thermoplastic polymers as the binders has been employed with significant success. An example of this is an electrode with usable conductance, mechanical strength, and acceptable porosity. Graphite particles are almost always in flat, flake-like shapes primarily because of the crystalline nature of the materials. These graphite particles are mixed with dry particles of a plastic binder in a ratio that will yield a product molded, a flat plate product that can be employed to conduct electrical current within a cell. Since the particles have flake profiles, the final product of compression molding will be a plate with anisotropy properties regarding electrical and thermal conduction and also mechanical strength. For the present, let us examine more closely the conduction mechanism through an electrode. The mathematics of dealing with real electrodes that are anisotropy and have a distribution of particle sizes and shapes is quite difficult to handle. The mathematics that describes conduction through somewhat irregular (non-uniform) distribution of particles throughout the structure becomes even more complex to http://bbs5.techyou.org/?fromuser=sergio147 deal with. Hence, we will assume a rather simplified approach in analyzing conduction through plates by making the following assumptions: 1. All graphite particles are spherical in shape, and all are of the same size. 2. The binder is assumed to be amorphous and totally compliant in shape. 3. The distribution of carbon is random-orderly. We will explore only one hypothetical configuration here. It assumes that all carbon spheres are aligned vertically such that all the spheres form a series of vertical columns perpendicular to the plane of the plate after compression into a plate. To simplify the drawing and visualization of this configuration, we will also let the polymer binder assume the shape of spheres in order to show the uniform spacing, as depicted in Figure 9.2. In reality, the polymer assumes a range of irregular shapes. The simple illustration is meant to show a 50% carbon to a 50% polymer ratio with all particles uniformly distributed in space. It is important to note here that the thermoplastic polymer is not caused to flow around the carbon particles during compression molding.
DESIGN CONSIDERATIONS
rc^^wwwwwv
w
Λ-ΝΛ^ΛΛΛνί
227
Copper screen
;N Carbon & plastic particles >.\\\N\\N\NN\N\\NNNNNN\SNNNSN\N\N\\SNSNS\\\NN\SN\\\N\\NVNS\W AVlWiSWV \\\N\\\\\\\\\\S\S\\.\> NXVOVWIXW Electrolyte COA\\\\\\N\\\\\\\\V
a = 0.50 σ=0 Figure 9.2 Electrode cross section.
In fact, polymer binder materials (rigid plastics) that do not easily flow as a liquid at higher temperatures are selected. This selectivity is to prevent it from encapsulating, or surrounding, the conductive particles. The compression molding is more similar to a sintering process than to a casting process. Returning to Figure 9.2, assuming that contact is made only between carbon particles in vertical direct contact, an idealized http://bbs5.techyou.org/?fromuser=sergio147 situation would exist in which no carbon particles are in contact with each other that can provide a continuous path from the first, top layer to the bottom layer. There then can be no electrical conduction through the plate. However, the introduction of a single carbon particle (shown as a particle with an "x" in its center) in this depicted three layer configuration would enable some electrical continuity because that symmetry has been disrupted. If there are four vertical layers, then it takes at least two additional, well placed carbon particles for electrical continuity in a vertical direction. This model permits contact conduction between adjacent particles as well as vertically adjacent or contiguous carbons. A plot of conductivity versus composition ratio of carbon to plastic has the idealized curve as shown in Figure 9.3. According to this simplified model, the conductivity would be zero until a 50% ratio was achieved, and then the conductivity would slowly and linearly rise as the ratio of carbon to plastic increased. We can approximate the shape of this curve via the following analysis. The configuration shown in Figure 9.2 is an exceedingly simple representation of an idealized situation in which all particles are assumed to have a spherical shape and there are no physical, hence
228
ENERGY STORAGE
Conductivity
0%
y^ a£l
100%
Carbon/plastic percentage
^
Figure 9.3 Conduction of composites on carbon/binder ratios.
no electrical, contacts between carbon spheres in any one column and those in another adjacent column. Even though it is hardly a realistic model, it does provide a first configuration that can be subjected to simple analysis. Then, if practical, we might move on to the more complex configurations and conditions that more closely approximate actuality. Isotropy was http://bbs5.techyou.org/?fromuser=sergio147 assumed initially for the sake of simplicity. Spherical particles should exhibit some anisotropy because of the direction or compression. And, if particles are flakes or some other shape, then the longitudinal conduction might be greater than the transverse.
9.4.1
Particle Shapes and Sizes
The binder is treated as amorphous in shape even though we know that is not so. We also may assume that the resistance of contact between carbon particles is the dominant factor, or the volume resistivity of the carbon is the larger factor. We will assume for the present that all the carbon particles are spherically shaped and are all the same size. It is further assumed, for the sake of simplicity of analysis, that they are all stacked vertically, and the spheres are maximally compressed together. Even though this is hardly an entirely realistic representation, the model can serve as a starting point for developing more representative structures for analysis. It does appear that the porosity of the carbon particles is far greater than that of the binders, especially when using high molecular weight Saran (polyvinilidene chloride), Kynar (polyvinilidene fluoride), or CTFE (monochloro-trifuoro-ethylene).
DESIGN CONSIDERATIONS
229
These latter polymers are generally known to have low porosity and higher viscosity.
9.4.2 Metal to Carbon Resistance In order to permit acceptable conductivity along the length of a carbon electrode for use as end electrodes in cells in bipolar arrays or in all cells in a unipolar array, it is necessary to have a metal conductor, such as copper, bonded to those electrodes along their length. Low interface, or contact resistance, between metal and carbon requires that all surfaces be clean and flattened and that the metal be in a perforated or screen form in order to maximize adherence and bonding to carbon particles. It is interesting to note here that there are few materials that will "form a bond" with carbon in the sense that it will weld or adhere in some fashion. The only approach to holding onto a carbon plate is by mechanical means. In fabricating a solid plate from carbon particles and binder, the carbon is held together by being physically trapped by the binder materials in such a fashion that they are no longer free to move about as a powder. However, they are not bound so http://bbs5.techyou.org/?fromuser=sergio147 well that the carbon particles are isolated from each other. Hence, a binder is chosen that will have poor flow characteristics under high pressure and temperature. In this manner, care is taken to prevent the polymer binder from becoming a low viscosity liquid and encapsulating a large fraction of the carbon. When attempting to bond a metal screen to such an electrode, the intention is that the binder polymer will adhere and become entrapped in the metal perforations while still providing good contact to the carbon particles that form a large part of the total electrode. In general, this technique works quite well.
9.4.3 Cell Spacing Let us now return to the design issue of component spacing within a cell and how that contributes to the total cell resistance. The principal contributors to total cell resistance, Rj., are the following: • Electrode bulk (volume) resistance, Rb • Interface resistance between electrode and electrolyte, R • Electrolyte resistivity, Re
230
ENERGY STORAGE
• Membrane or separator resistance, Rm • Contact resistance between metallic leads and carbon electrodes, R . These five factors are the principal contributions, but there are a few others, such as polarization effects due to electrolyte starvation and potentials resulting from the interfaces between different electrolytes, that ultimately cannot be ignored. The total cell resistance can now be simply expressed as R = R + R + R + R T
b
i
e
m
+R. c
(9.2)
x
'
Now, we can attempt to assign some realistic values to these factors. First, consider the electrode bulk resistance contribution. The electrical conduction in the electrode is considered to take place by electrons flowing down the length of the plate electrode. As described above, the plate resistance from end to end is p(L/A). If an electrode were 10 cm long, 5 cm wide, and 0.30 cm (1/8 inch) thick, and if the specific resistivity of the carbon plate were set at a realistic minimum value of 0.005 ohm-cm, then its total http://bbs5.techyou.org/?fromuser=sergio147 resistance would be approximately 0.03 ohms. Now let us look at some empirical values for the other resistance terms. The interface resistance of electrodes' surfaces treated with wettable materials of high surface area such as microporous carbon particles can be as low as 0.005 ohms for a 50 cm2 area electrode. Adhering conductive materials to the surface of the bonded carbon plates markedly improves their ability to make more intimate contact with the water-based electrolyte. Electrolyte resistivity from Table 9.1 indicates that the resistivities are in the broad range of 1 to 10 ohm-cm, depending on the materials in solution. If we take 5 ohm-cm as a low average for the types of salt solutions such as the alkali metal sulfides and iron halides, then a cell with such salt solutions as electrolyte and spacing on each side of 0.3 inches would have a value of Re is 0.06 ohms for total electrolyte contribution to its resistance. That leaves the contact and membrane resistance contributions to be determined. Membrane resistance varies greatly depending on whether the type of structure is merely mechanically porous or ion exchange materials. In essence, the electrical resistance of separators is a tradeoff between its effectiveness as a diffusion barrier and its ability to permit transport of ions under the influence of an electric field.
DESIGN CONSIDERATIONS
231
Table 9.1 Resistivity of some common solutes dissolved in water*. Solute
Concentration, Molarity
NH4C1
5.6
1.9
3.0
3.8
Resistivity, Ohm-cm
Cu 2 S0 4
0.63
HC1
2.7
1.6
10.8
1.9
0.6
14.7
2.4
3.2
Na 2 C0 3
3.1
3.2
NaOH
3.1
3.1
6.2
3.0
1.0
2.55
KI
H 2 S0 4
http://bbs5.techyou.org/?fromuser=sergio147 4.0
ZnCl 2
KOH
Na2S
31
1.7
0.74
13.8
1.48
11
2.5
2.7
10.0
1.9
4
7
*A11 measurements were made at 18°C.
9.5 Resistance Measurements in Test Cells A very simple and direct method for measuring the contributions of the various components of total cell resistance is described below. A test cell is constructed in which the distance of separation between the electrodes can be varied in a controlled manner. In order to determine quantitatively the resistance of the electrolyte in such a cell, a number of measurements are taken at various separations, and a plot, Figure 9.4, is made of these values. If care is
232
ENERGY STORAGE
Figure 9.4 Cell resistance versus electrode separation.
taken to keep all other factors constant, the plot should be a straight line whose intersection with the ordinate, as shown in Figure 9.4, is the value of the sum of all other resistances in that cell, including interface, contact with electrical connections, and electronic contributions of the electrodes themselves. The electrolytehttp://bbs5.techyou.org/?fromuser=sergio147 resistance from equation (9.1) is evaluated by taking two or more measurements at different distances: In this instance, we normalize the values of p by multiplying the resistance readings by the area, A, and the expression for p becomes R P =
L'
(9.3)
or, at two different intervals, L^ and L2: R/Li+IVLz
(9.4)
The next task is to separate these other factors. The interface resistance of electrode-to-electrolyte is readily obtained by inserting a typical electrode surfaced on both sides between the two cell electrodes. Assuming that the contribution of electrode volumetric, electronic resistance is negligible, the measured increase in cell resistance would be due to the interface factor. Similarly, contact resistance can be determined by employing an electrode with a metallic conductor encapsulated between two
DESIGN CONSIDERATIONS
233
carbon plates, and of course, surfaced in the same manner. Any difference between that resistance and the previously measured interface resistance should be due to contact between the metal and carbon plate. There are other methods for determining this latter resistance factor involving test electrodes bonded together with and without metal screens to isolate their contributions.
9.6 Electrolytes and Membranes Figure 9.5 is a bar chart that compares the resistance at room temperature of various, relatively common diffusion barrier materials. Except for the phenolic membrane (a microporous structure with no ion selective properties), all the others are made with ion exchange materials and are largely cation transfer membranes. Along with their resistance values, electrolyte and electrode resistances are given for a measurement cell using a 2 molar NaCl solution as a special standard. The resistance of most membranes contributes less resistance than both electrodes and electrolyte. The lighter shaded regions http://bbs5.techyou.org/?fromuser=sergio147 show the total or sum of cell resistance for each membrane. Table 9.1 is a partial listing of some of the more common electrolytes employed in similar devices. As one would expect, acids have
Figure 9.5 Resistance contribution of cell components.
234
ENERGY STORAGE
the lowest resistance due principally due to the very low specific ionic resistivity of hydrogen. Furthermore, the resistivities of the compounds of the heavy elements tend towards the higher end. The concentrations of the solutes are given in molality rather than in terms of the more common molarity units. The conductivity of our example concentration cell that makes use of Na 2 S is in the range of the better conducting solutes.
9.7 Energy and Power Density Compromises Certainly, the most important properties, other than operating life and cost, of any energy system are its abilities to store energy and deliver power efficiently to a useful load. A cell design with static electrolyte is limited in its ability to deliver either of these two important characteristics because it is invariably a compromising situation to offer acceptable performance for a particular set of applications. Other than some materials variations and selection of components, the major design latitudes involve cell geometry. In particular, cell spacing has the greatest influence simultaneously on http://bbs5.techyou.org/?fromuser=sergio147 energy density, ED, and power density, PD. As the spacing between electrodes in a concentration cell increases, the capacity of that cell with the same area of electrodes increases. In fact, the increase is linear with respect to spacing. However, the internal resistance of the cell also increases with spacing. If the cell is optimized in terms of minimum contributions to resistance by all other factors other than electrolyte, then the increase in cell resistance also increases linearly with electrode separation distance. A quick glance at the tradeoff shows a square relationship between power density and spacing. Even though most of us are familiar with the relationships between source resistance and the efficiency of power output, it is worthwhile to briefly review the salient aspects of the subject with regard to an electrochemical cell. In the simplified circuit shown in Figure 9.6, the power, PL, delivered to the load is PL = i 2 R L = E ( Q ) / ( R r + R L ) ,
(9.5)
where E(Q) is the cell voltage at any time, but more appropriately, when the charge remaining in the cell is Q. RL is load resistance, and Rj. is total cell internal resistance.
DESIGN CONSIDERATIONS
-
235
^
RT
i
RL
E
Figure 9.6 Electric current flow in a single cell circuit.
Continuing with the mathematics,
f pL =
E(Q)
y
RT + R J
RL,
(9.6)
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and if we solve for the load voltage giving the maximum power delivered to the load by differentiating PL with respect to RL, then we obtain dP,L dR L
RL = E(Q) 2 d ~ dRL(RT+RLy
= (R T + R L ) " 2 - 2 R L ( R T + R L ) -
(9.7)
By setting this to zero and dividing both sides by (Rj.+R ) -2 , we obtain 2R L (RT + R L )
0, R L = ΚΊ
(9.8)
Of course, operating a cell in such a fashion would result in half of the energy being dissipated uselessly within the cell in the form of heat. Thus, it is important to again reach a compromise between efficiency and the size of the device and PD versus ED. The tradeoff is between power delivery capabilities and
236
ENERGY STORAGE
energy density. Unfortunately, all devices have some amount of internal mechanism that results in energy dissipation. In this case, it is the sum of all resistances within a cell. As the spacing between electrodes increases, the ED increases, and the internal resistance due to the increased path length through the electrolyte increases also. Let us assign a ratio, ß = Ry/R^ to those parameters. In all cases it is desirable to have ß as small as possible. As cell spacing increases, ß increases. As spacing increases in the design of a cell, its ED increases as well because its charge capacity is directly proportional to the thickness of the storage region of porous carbon layers. If we neglect the contribution of the electrodes and use separators with near zero resistance, then the cell resistance can be equated to its thickness per unit area, or R, = Kw,
(9.9)
where K is a constant of proportionality and w is the cell width. Now, since the unit volume of cell per unit area is simply w, and the volumetric energy density is ED = Q/w, the power density can http://bbs5.techyou.org/?fromuser=sergio147 similarly be equated to the cell thickness as follows. Referring to equation (9.2) and substituting RL= R[./ß, we have P D = E(Q) 2
. = E(Q) 2 //β ., (RT+RT/ß) R T (1 + Vß)
/
Κτ/β
(9.10)
which shows that as R,. becomes smaller and as ß becomes larger, the PD and ED increases. It becomes obvious also that as w is made larger PD diminishes and ED increases accordingly. That is demonstrated by substituting equation (9.10) into the value for RT, or P D = E(Q) 2
-^—-5-.
Kw(l + l/ß)
(9.11)
As we explore the various parameters and their influence on cell performance, it becomes more obvious why other approaches to cell array designs have been adopted. Since carbon is the only material that is chemically inert, electronically conductive, and reasonably inexpensive when compared to any other metal with suitable
DESIGN CONSIDERATIONS
237
properties, the attractiveness of its use is obvious for any electrochemical cell where the material of the electrodes are not intended for participation in the energy storing processes. Conduction down the length of a carbon electrode has high resistance. Hence, the alternative immediately apparent is to insert (encapsulate) a highly conductive metal such as copper within the electrodes to conduct longitudinally, which permits the conduction through the carbon plate to take place in a low resistance manner perpendicular to its surface direction. This tactic involves making more complex electrodes more susceptible to failure. However, it is a solution to the problem. Another approach is the full flow electrolyte cell (and arrays of cells in a module). Such a design is more complex and requires additional components, but it can solve the problems of cell imbalance while also providing a means of separating the power delivery and energy capacity characteristics of the system. The energy would be stored not within the cells but in the liquid electrolyte storage reservoirs. By such designs, the PD and ED of a cell are made independent of each other, especially if the module arrays used electrodes in stacks of cells using bipolar electrodes. As always, however, new http://bbs5.techyou.org/?fromuser=sergio147 difficulties arise, such as maintaining uniform flow through all cells and preventing electrolyte starvation in any one cell due to very different hydraulic impedance between cells in series electrically and in parallel hydraulically. If designs with static electrolytes were to employ intermediate series cells as bipolar so that conduction would be normal to the electrode surfaces, then the need for conduction down the electrode length would be only for the end electrodes. These end plates can be quite thick or can embody a metallic backing to reduce impedance. In either case, their increased cost and weight can be amortized over a fairly large number of bipolar electrodes in an array.
9.8 Overcharging Effects on Cells Concentration cells are essentially self-regulating. Overcharging should not result in damage to the cells, nor should any gas be evolved. Once again, let us take the case of the sulfide system. When full charge is reached in these cells, and if further charging is attempted, the cell will reduce the charging current because its
238
ENERGY STORAGE
internal resistance will be greatly increased by the augmented formation of free sulfur at the positive electrode surfaces. There is always the risk of the evolution of hydrogen in the decomposition of water that would eliminate the possibility of a truly hermetic seal. One solution is to employ non-aqueous solvents that would not generate hydrogen ions. The other solution is to carefully control the charging voltage so that it does not exceed the decomposition of water potentials.
9.9 Imbalance Considerations When more than one cell is in a series array, a serious risk of cell imbalance is encountered. Since quality control does not permit an absolute match of cell characteristics in actuality, some cells will reach full charge before others. In that event, if charging continues, some cells will tend to become overcharged. In most batteries such as the lead acid, this situation is largely self-regulating because hydrogen evolves at the negative electrodes when full charge is achieved. Some deleterious effects will result, but the situation is http://bbs5.techyou.org/?fromuser=sergio147 not severe if imbalance can be minimized. A solution to this problem is either to employ non-aqueous solvents or to charge cells in parallel and discharge in series, which requires some complex and, perhaps, impractical circuitry.
Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
10 Calculated Cell Performance Data http://bbs5.techyou.org/?fromuser=sergio147
10.1 Electrical Performance Modeling Prior to laboratory construction and testing single cell concentration devices, a general modeling of such cells was undertaken as a means of attempting a prediction of test results as well as providing a basis for evaluating the electrical characteristics of these cells. Based upon the Nernst equations for cell potentials, a simple mathematical model was devised. Since open circuit potentials of these types of concentration cells have no theoretical upper limit, they can cause a certain amount of performance speculation. Even though the energy storing and producing reactions at the electrodes are simple and can be readily identified, the various other dynamic processes, such as ionic and molecular diffusion, concentration gradients, degree of ionic dissociation, etc., associated with the main reactions tend to rapidly become complex and difficult to quantify. The limitations to cell voltages are a result of practical considerations such as polarization effects and the possible generation of gases (hydrogen and oxygen) in the decomposition of water if an aqueous electrolyte is employed. 239
240
ENERGY STORAGE
As an example of this, we will attempt a simple analytical approach to a parametric representation of a cell discharge curve under different imposed conditions. The ampere-hour (coulombic) charge, Q, stored, without losses, in any cell can generally be represented as
Q = Jidt.
(10.1)
For purposes of illustrating the general behavior and shapes of voltage versus time and the state-of-charge (SOC) of electrochemical concentration cells, we will make some simplifying assumptions that will not significantly change the basic principles and expected experimental results obtainable with actual cells. Even though the cell potentials are logarithmic functions of the activities of electrolytes in close proximity to the electrodes, cell voltages will be considered as functions of the concentration of the relevant ionic constituents as a means of simplifying the mathematics while still conveying the essence of cell behavior. In fact, that is a fairly accurate representation of electrolytes of low concentrahttp://bbs5.techyou.org/?fromuser=sergio147 tion (dilute solutions). Hence, a first approximation for potential difference, ΔΕ, between electrodes will have the following form: AE = K k Ä C2
(10.2)
The concentration, CJ7 is on one side of a cell, and the concentration designated as C2 is on the opposite side. In an initially and totally discharged cell, q = C2.
(10.3)
Concentrations can be expressed as the quantity, Q, of solute reactant (common ion) per unit volume of a cell. Thus, C^ = Q,/V 1 and C2 = Q 2 /V 2 . In a symmetrical cell, Vl = V2. At any time, t, the quantity of the ionic reagents present in compartment, 1, the cell side that is experiencing an increase during charging, could be expressed as
Q1(t) = Q 0 +Ji c dt, 0
(10.4)
CALCULATED CELL PERFORMANCE DATA
241
where C0 is the initial concentration (the same on both sides). And, the charge at the opposite cell side, 2, where the ionic concentration is being diminished by the charging current, or the quantity, Q 2 (t), at any time, t, after the beginning of charge is expressed as
Q2(t) = Q 0 -Ji c dt.
(10.5)
and ic is the charging current. Since the voltage, E(t), at any time, t, during charging is represented by
C,(t) E(t) = kln = kln L C 2 (t)
Qo + JVt 0 t
(10.6)
Qo-Jicdt
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if we wish to make a graphic plot of E(t), this continuous equation would be most difficult to handle. Hence, we might simply resort to a piece-wise approximation, in which the values of Q under the integral signs are established as follows: n-l
E(tn) = kln
Q o + Σ in-lAt 0
Qo-XVlAt
(10.7)
If the intervals are small, then the approximation is quite good, and programs such as Excel and Lotus can be effectively employed to produce graphical representations and enable one to easily change parameters such as the values of Q0, i , and power levels or energy efficiencies. As an example of the techniques that can be employed in a spreadsheet program, which is somewhat limited for these types of computations, the following information is offered as a model that was used in many evaluations to see how some of our simple modeling results compare with actual empirical data.
242
ENERGY STORAGE
The relationships that can be employed in a LOTUS 123 spreadsheet format to model and, perhaps, predict the performance of a simple concentration cell whose discharge performance is tailored to give a discharge at constant power output to an electrical load are as follows. Since the software program is not capable of solving simultaneous equations, linear or otherwise, the equations for voltage and current versus time must be put in a different format in which the values desired are solved in a sequential manner in discrete bits. Hence, the overall relationship that is developed is
kin
c2
= k[ln((an_1-in_]dt)/bn_1+in_1dt)] (10.8)
En_, The above terms are defined as follows:
http://bbs5.techyou.org/?fromuser=sergio147 • k = constant of conversion • a = ampere-hour stored in as S= in negative cell side at beginning of discharge (concentrated) • b = ampere-hour stored as S= ions in positive side at beginning of discharge (dilute) • Q 0 = initial S= ion concentration on both sides before charging begins • i = electric current (varies with P) • Ci and C2 are concentration at any time on opposite sides of a cell.
The additional equations defining the quantities are the following:
a„=a n _ 1 -P(t n -t n _ 1 )/£„_! Q»=Q»-i-P(t„-tn_1)/En_1 All the columns in the spreadsheet contain these parameters, the first one being the appropriate constants, such as for a0 and for b 0 . The unique aspect of this set of numbers is that the power
CALCULATED CELL PERFORMANCE DATA
243
output, P, has been set as a constant, or an invariant. After the other fixed terms, such as Q 0 ,and the ratio of a / b at the beginning of the charge are set, all the other parameters must then follow accordingly. The same type of routine can be established in a spreadsheet format by letting any other parameter be an invariant such as the current, i, or the load resistance, RL. In the case above, the power output, P, was fixed, and the current and all other parameters left as variables had to fit that condition. The electric current values are inserted in accordance with some parameter we wish to maintain constant, such as power level, efficiency, etc. An example of the type of constraint that might be imposed is that of charging and discharging at constant power, or constant current. It should again be noted here that merely having a concentration difference between two chemical substances such as salt dissolved in water (NaCl and H 2 0) will not produce or even provide a practical mechanism for storing energy in a useable fashion. Without an electric charge transfer accompanying processes of oxidation and reduction at electrodes, only an osmotic pressure http://bbs5.techyou.org/?fromuser=sergio147 difference would be realized across a porous separator employed in a cell to keep the two liquids from physically mixing together. There are no electronic exchange processes present unless it is a "redox" situation in which a chemical species at one electrode gains a negative or positive charge and a species at the positive electrode respectively gains a positive or negative charge. The electric circuit for this associated charge flow is, of course, completed through an external circuit. There are not many choices available from the roster of chemical substances that will provide properties suitable for application in a concentration cell. We have chosen chemical systems to explore based on iron and sulfur primarily because they appear to offer possibilities for low cost, well-behaved, reasonably high energy density systems. It is possible to model cell performance in a very simplified manner based on the equations above. By fixing cell volume and electrolyte concentrations and specifying electrical resistance and power levels, a graph of cell voltage versus time or state-of-charge, SOC, can be plotted from calculated data. Let us assume values listed below for a parallel plate electrode cell design. In order to perform some illustrative calculations, the
244
ENERGY STORAGE
following physical parameters are assumed for predicting cell performance: • Spacing on each side between electrodes and separator = 0.25 cm • Cell volume = 50 cm3 • Electrode area = 100 cm2 • Electrolyte resistivity = 10 ohm-cm • Cell resistance = 0.10 ohms total for both sides • Maximum solubility of reagents = 5 molar • Carbon plate electrodes with microporous surfaces filling inter-electrode space. The vertical axis is the cell voltage, and the horizontal axis is the time of charging. The cell behavior is for discharging at constant power output to an external electrical load. As can be seen, the voltage decreases as discharging progresses due to the diminishing difference in concentration of the ionic species. In order to maintain constant power (in this case, the imposed condition), the electric current increases to compensate for the diminishing cell voltage in http://bbs5.techyou.org/?fromuser=sergio147 order to maintain a constant power delivery to a load. Upon examining Figure 10.1 closely, it becomes obvious that the slope of voltage versus either time or SOC is quite steep.
Cell volume = 50 cu. cm.
0.6 0.5
100 -I - 90 80
0.4
-
70 60
-
bu 40
0.3 Φ
ü
0.2
\Volts
30
0.1
-
Amps 0.2
0.4
Total interelectrode spacing = 0.5 cm Area= 100 sq. cm.
0.6 Hours
Figure 10.1 Discharge at constant power output.
0.8
1.2
20 10
ω 1_L F
<
cCD ■σ
CO
o
CALCULATED CELL PERFORMANCE DATA
245
Voltage drops very rapidly from a high value of 0.60 volts to a low of almost 0.2 volts within 0.20 hours. It continues its descent to 0.05 volts over the next 0.60hours. Most of the stored energy is delivered at much lower voltages in order to maintain, in this case, a constant power level at the external load. The current increases rapidly to maintain constant values of the product of volts times amps. Unfortunately, this characteristic is typical and unavoidable for any device whose driving potential is dependent upon the remaining energy within the device. Metal springs, electrical capacitors, and compressed air systems, for example, have this general shape for charging and discharging. There are many methods employed to "flatten" these potential versus time curves, but they all exact an operational penalty. In the case of concentration cells, the method that appears to best reduce the decline in voltage with time as well as increase specific energy capacity would be to store much of the reagents in solid form within the cell and, perhaps, within the porous electrodes themselves. Since the solid phase of any substance has the greatest specific gravity, it presents the maximum energy density for storage of active materials in terms of watt-hours per http://bbs5.techyou.org/?fromuser=sergio147 pound. And since the electrode potentials are independent of chemicals present in the (non-ionic) solid form, this approach is theoretically viable. Let us take a closer look at the situation in a cell in terms of not only energy density but also the way in which this energy is available at an external load if we were to incorporate a method of compensating for the depletion of a reagent at one end of a cell and the accumulation of the ionic constituent at the opposite electrode. This proposed control method is internal to the cell. In order to maintain relatively high cell potentials without resorting to external control circuitry, it is necessary to keep the cell electrode where the specific ions are being depleted during discharge, for example, supplied with new components, and it is necessary to remove those very same ions at the opposite electrode where new ones are generated during that same discharge mode. We will stay with the sulfur/sulfide system to describe the process of solid reagent storage within a cell. During the charging mode, as shown in Figures 10.2 and 10.3, sulfide ions are generated at the negative electrode, and sulfur is produced at the positive, while sodium or potassium or lithium ions are transported from the (+) to the (-) electrode.
246
ENERGY STORAGE
Let us assume, as shown in both drawings, that there are reservoirs of insoluble sulfur in the (-) side and reservoirs of solid S as Na 2 S x and Na 2 S, both exceeding their solubility in the electrolyte. If the rates of dissolution and precipitation are matched reasonably
Na+ Solid reservoir
S + 2e~ - > S " Reaction at electrode http://bbs5.techyou.org/?fromuser=sergio147 2Na+ + S -* (Na2S)S0|id
within the reservoir
Figure 10.2 Charge mode.
Pos.
-►Na + Solid reservoir
S" -> 2e -> S
Reaction at electrode
S + Na2S -> Na2Sx Figure 10.3 Discharge mode.
within the reservoir
CALCULATED CELL PERFORMANCE DATA
247
well to the rates of generating and removing S= ions, then a stable situation might occur, in which the concentrations of ions will change from the early stages of charging or discharging until their respective solid reservoirs are depleted. After their solid materials backup is removed, the voltage versus time curves will assume the shapes shown earlier. Let us examine the cycling characteristics via an expansion of our earlier mathematical model by introducing a term that shows this additional process of reagent storage in solid form. Many investigators pursued the subject of solution rates during the nineteenth and twentieth centuries. A basis has been established, which is well summarized in Molwyn and Hughes' text (1957,1174-1176) on physical chemistry, in order for us to make an assumed mathematical model for such a balance of processes. (See also A. A. Noyes and Z. Whitby, Physikal Chem., 1897, and Z. Nernst, Physikal Chem., 1904). It is necessary to represent the additional term in the form developed below in order to account for the dissolution and precipitation of sulfur and sulfides. If we identify and label the important parameters such as Cs = maximum concentration a particular solute can assume in a solvent http://bbs5.techyou.org/?fromuser=sergio147 under typical conditions, it becomes possible to set up simple expressions that describe the dynamic equilibrium of solution and dissolution. To attain a higher energy density cell with flatter charge/discharge curves, it is necessary to devise methods of maintaining a fairly constant concentration level throughout most of the charge/discharge cycle. The rate, d N / d t , of solution (dissolution) of materials from their solid form with a surface area, A, when immersed in a solvent is — = n0Av-KsnA. dt
(10.9)
The terms in the above expression are as follows: • A = surface area • no = number of solid molecules per unit area of the submerged solid • v = probability of escape into solution • KsnA = rate of deposition (precipitation) of molecules out of solution onto that surface • N = concentration in solution of the molecules • n = solute concentration in the liquid solvent.
248
ENERGY STORAGE
At saturation, maximum solubility, d N / d t = 0, and nsat = novKs. From the preceding, the rate of solution is simply a constant, K, times the surface area times a difference in concentrations, or ^
= KA(nsat-n).
(10.10)
As can be observed, the rates of precipitation and dissolution depend on the available or exposed area of the solid. The precipitation rate is a function of the concentration of solute and not the difference between saturation and concentration. Returning now to the equations developed earlier to describe the charging and discharging dynamics of a cell, let us briefly explore how the mathematics of storing reagents in solid form might appear in the charge/discharge relationships. New terms can be introduced that carry out the effects of solid storage. During discharge, sulfide ions are generated in the (-) side while sodium ions are transported from the (+) side while the stored Na 2 S x and free sulfur are depleted. Simultaneously, at the (+) side of the cell the stored solid mono-sulfide diminishes as it becomes dissolved in order to http://bbs5.techyou.org/?fromuser=sergio147 provide a source of more sodium ions. Hence, at all times there is a reservoir of sulfur and polysulfides close to the (-) electrode and a reservoir of mono- sulfides close to the (+) electrode. A brief look at the processes of precipitation and solubilization on either cell side should facilitate visualization of what occurs, as depicted in the figures above. As these reservoirs are either enlarged during charge or diminished during discharge, the surface area of the solids and the concentration of the ions will change. These will be represented as A and A+ on the respective sides of the cell. Also, concentrations of the sulfide ions will be represented as [S]. In equation (10.11), the concentration, C, of the sulfide ions is represented at any point in time as
V
Q0±Jitdt
(10.11)
where V is the volume of electrolyte on either side of the cell, Q 0 is the initial amount of S= ions in either side of the cell at complete discharge, and Q = Q(t) is the amount at any time, t, during either charging or discharging. Since the volumes are the same, V cancels out in equation (10.12):
CALCULATED CELL PERFORMANCE DATA
249
L
E(t) = k l n
QCt) C,(t)
Qo+Jicdt kin
0
t
(10.12)
Qo-Jicdt
To take our model further, consider the process at the negative electrode during the charging mode in which sulfide ions are generated. The equation for the amount of S= ions, Q, at any time becomes
a V
v
- j i d t - ( a m o u n t of S precipitated).
(10.13)
The quantity, Q p , of S= ions taken out of solution and returned to the reservoir as solids over time, t, and to be re-dissolved during the discharge mode again as sulfide ions, is expressed as follows: http://bbs5.techyou.org/?fromuser=sergio147
Q P = !
K A
V
dt,
(10.14)
in which Q is divided by V to make it a concentration factor. Substituting into the equation for the value of total sulfide ions present in the (-) electrolyte at time, t, we obtain the following as the composite expression for the amount of sulfide ions in solution on the (-) side of the cell:
Q_ = Q0+]idt-JKsA_^dt.
(10.15)
We may look at the positive side of the cell and perform a similar analysis by evaluating the third term in the equation for quantity, Q + , of the sulfide ions in the (+) cell side. Now the relationship takes the form L
Q + = Q + - j i d t + ( a m o u n t of sulfur solubilized).
(10.16)
250
ENERGY STORAGE
The amount of sulfur, Q_, brought back as S~ ions from the (+) side reservoir of sulfur and polysulfides is Qs=KA+-(Qsat-Q+).
(10.17)
Inserting this term into the total expression for Q + , we get the following:
Q + =Q + -}idt + Q s =Q + -Jidt + JKA + (Q sat -Q + )ldt. 0
V
0
(10.18) The same mathematical methods may be employed to evaluate these quantities during discharge. In actuality, during discharge mode the preceding processes described are reversed at the electrodes and the equations that describe the rates in the (-) and (+) sides are exchanged. The slopes of voltage versus time will be far less steep due to the http://bbs5.techyou.org/?fromuser=sergio147 compensation of the reservoirs of ions and solids in the cell. The improvements in charge/discharge shapes will depend on how
35 30
^ \
25 I 03
■a
\
20 15
v /
10
Enen y density I
1
'
Power density
5 0
1
/
/ 0
50
100 150 Elapsed time - Minutes
200
Multiplier = 5, concent = 7 molar, max initial ratio = 70:1 Figure 10.4 Polysulfide concentration cell: 0.01 Spacing & 0.02 A / s q . in.
250
CALCULATED CELL PERFORMANCE DATA
0
10
20
30
Load resistance ~ 0.50 ohms
40 50 60 Time in seconds
70
80
90
251
100
Area < 3 sq in, UU surfaced electrode Figure 10.5 High drain rate experiment. http://bbs5.techyou.org/?fromuser=sergio147
well the behavior of the reservoirs can be controlled to provide and remove ions to and from solution as cycling progresses. Figure 10.4 was produced by an extrapolation of empirical data obtained from single cells in order to predict the relationship between the available energy and power density at any point as a cell is discharged. It is apparent that, as a cell is left with less charge, both the ED and PD diminish accordingly. This characteristic is common to all electrochemical and most capacitor and pneumatic devices. Figure 10.5 shows the results of a cell operated in a high drain manner. The maximum power delivery possible was the criterion, and the internal voltage drop was essentially ignored. The initial power level was about half of the total, i.e., the internal dissipation is about equal to the external power over a brief length of time delivery. The cell is small, less than 0.50 cubic inches volume, and has an initial output of over 0.7watts.
Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
11 Single Cell Empirical Data
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11.1 Design and Construction of Cells and the Materials Employed Concentration cells offer opportunities of many design forms. The materials employed can be fashioned in many shapes and sizes. There are no basic problems in producing devices with very special characteristics. Materials are most easily taken as flat sheets for electrodes because that configuration lends itself to a host of design application requirements. The simple parallel plate electrode design approach is probably the easiest to describe and represent in drawings. For that reason alone, the configuration descriptions employed here will be confined to such designs. Other cell and battery shapes are certainly possible if required for particular applications where, for example, cylindrical forms would offer advantages over rectangular structures. The following are the principal components and materials for construction: • Carbon for electrodes • Porous plastic sheets as separators 253
254
ENERGY STORAGE
• • • •
Cation exchange membranes Plastic containers for cell or battery assemblies Electrical contacts for external connections Microporous carbon with large surface areas.
The electrodes are basically graphite plates with a "surfacing" of microporous carbon frequently referred to as activated charcoal. This layer of active carbon provides very large surface areas for storing reactants as well as electrochemical reaction sites. This general design is shown as an edge view of a cell in Figure 11.1. The simple sandwich structure has the entire intervening space between electrodes, other than the presence of a separator, occupied by porous carbon. The prime function of the separator, as mentioned earlier, is to keep the carbon particles from electronically short circuiting the cell and prevent, or at least retard, the bulk mixing of electrolytes in the two cell compartments. A very porous, non-conductive material such as porous polyethylene or PVC can serve that purpose. Unfortunately, mechanically porous materials will not prevent the diffusion of electrolytes sufficiently to give cells high charge http://bbs5.techyou.org/?fromuser=sergio147 retention. Hence, in most instances sheets of ion exchange materials are employed rather effectively. Electrical resistance is increased, but the benefits appear to warrant that increase. As the development of concentration cells progresses, it may be possible to eliminate relying mainly upon separators or membranes to retard diffusion (primarily of S= ions) from migrating to lower concentration sides. This may be accomplished by making greater use of the reactant storage within the cell in the adsorbed state and,
Epoxy seals
Figure 11.1 Edge of an assembled cell.
1 Separator '
\ porous carbon
SINGLE CELL EMPIRICAL DATA
255
perhaps, as solids waiting to become solubilized when needed for charging and discharging. An exploded view of this cell is provided in Figure 11.2, and typical dimensions for laboratory test cells are shown in Figure 11.3. Cells of the above dimensions are the easiest to construct and are the most practical as experimental vehicles for studying their basic characteristics. Inter-electrode spacing is amenable to the insertion of porous carbon granules even after cell assembly if an open top is provided. In most laboratory test cells, the carbon is contained within a plastic frame. The cells are assembled in a series of steps with the array being in a horizontal position. The first step is to adhere a frame to the graphite plate electrode using either an epoxy resin or RTV sealant, depending on whether the cell is to be used as a permanent structure or as a structure that can be disassembled at a later time to either change components or materials, such as the type of porous carbon or membrane. There are advantages to both designs. For example, a cell that is capable of being disassembled also provides the opportunity to examine its internals after cycling. These differences are http://bbs5.techyou.org/?fromuser=sergio147 shown in Figures 11.4 and 11.5.
Figure 11.2 Exploded view of cell components.
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ENERGY STORAGE Separator Electrodes
1 0.04" 1
Plastic frames
http://bbs5.techyou.org/?fromuser=sergio147
Figure 11.3 Internal dimensions typical of present cells.
Figure 11.4 Open top disassemblable test cell.
SINGLE CELL EMPIRICAL DATA
257
Figure 11.5 Encapsulated laboratory cells.
The next step is to fill the space in the frame with the particles of carbon. Then, thehttp://bbs5.techyou.org/?fromuser=sergio147 membrane or separator is adhered to the frame. The second frame is then glued to the membrane, and the void provided by the second membrane is filled with carbon particles. The final step is to adhere the second electrode to the frame. If needed, the entire assembly can be clamped together in order to maintain integrity, and the cell can be stood upright for normal operation. At some point during the fabrication of the cell, wires are attached to the carbon plates by metal screws and wire lugs through holes drilled in the plates. Two holes are provided in the tops of the frames (the top when in the upright position) for filling with electrolyte prior to electrical cycling. In some cases, especially where the initial electrolyte contains solids such as sodium sulfide and free sulfur, the electrolyte composition is physically mixed with the porous carbon and placed into the frame voids prior to assembly.
11.2
Experimental Data
Over fifty cells have been fabricated and tested over a five-year period. Some of these cells employed graphite plates as described above, and others used electrodes fabricated by compression
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molding of graphite and rigid plastic binders such as high density polyethylene, PVC, polypropylene, and ABS. This electrical performance data is presented here in order to give the reader a better idea of the behavior of such concentration cell systems. A typical, small laboratory cell performance is shown in Figure 11.6. The total volume of the cell is about 5 in3 and the working electrode area is 10 in2. Charge and discharge curves of cell volts and cell voltage versus time are reproduced. In this instance, the discharge is into a constant resistive load while the charging takes place at near-constant voltage. As can be observed, the voltage drops off rather rapidly, and the amperage climbs proportionately. These curves are not as sharp as those obtained by maintaining a constant power level at discharge because the demands on the current are considerably less. The very rapid decline in cell potential during the beginning of discharge is evident. This is due to the rapid dissipation of sulfide ions (and the consequent drop in concentration) on the concentrated side while the diluted side quickly experiences an influx of sulfide by diffusion across the separator as well as by the creation of sulfides due tohttp://bbs5.techyou.org/?fromuser=sergio147 the discharge electric current. Not much change is required in these concentrations at the peak of full charge to make a great change in the ratio of ion concentration. Hopefully, these conditions will be significantly improved as we begin to rely more upon the storage of reagents in reservoirs in the solid state, as discussed in Chapter 10. Sodium sulphide cell Cell # S-4 1.8 AH
2 AH
.83 AH
\
/
Z^CJ^
/AH
\
/
\
^Χ^ L
Ϊ
/
Total X-axis time span = 24 hours Cell area= 10 sq. in.
Volts
—
AmpsAmps
Figure 11.6 Sodium sulfide cell of 10 sq. in. electrode area.
;
SINGLE CELL EMPIRICAL DATA Cell #S-11 continuous cycling Cycle # 76 I .tJ
259
0.15 0.1 0.05
o
u5 Q.
>
0.5
0
E <
-0.05 Total time segment 17 hours Cell area = 2.5 sq. in.
-0.1
Volts —*- Amps
Figure 11.7 Cycle number 76 of test cell #S-11.
Figure 11.7 shows that open circuit voltages were automatically recorded at different intervals during cycling. The mode of charge/ discharge should be obvious upon inspection. This data was taken http://bbs5.techyou.org/?fromuser=sergio147 at constant load, and the peaks of the brief open circuit blips indicate little polarization effects. Until the techniques for reagent storage are developed to a practical stage, the electrical characteristics will be about the same. Merely charging the cells to greater concentration differentials by producing very high concentrations at one electrode and very low concentrations at the other with all reagents in the liquid phase (dissolved state) will not result in significant improvements. There is very little equivalent storage capacity at the low concentration electrode, and molecular diffusion will quickly raise its concentration level. In order to achieve higher energy storage capacities, it is necessary to develop highly dependable, solid-state storage, as discussed in previous chapters.
Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
12 Conclusion: Problems and Solutions http://bbs5.techyou.org/?fromuser=sergio147
As noted earlier in Chapter 5 of this book, electrochemistry still offers the most attractive method for storing energy because it is in the most useful and convenient form. Another benefit is its high thermodynamic efficiency. Since electrochemical processes are not heat engines, the Carnot efficiency limitation is avoided. The efficiency, η, of a heat engine, a device for the conversion of thermal energy to mechanical or electrical work output, is expressed as follows: T -T η=-^—^, T
(12.1)
where Th and Tc are the low temperatures and high temperatures of the thermal reservoirs between which the engine is operating. However, as in the case of all proffered solutions to any problem, there are negative aspects. Probably the single largest drawback to electrochemical cells is their relatively low energy densities. The second limitation is their relatively short, useful life and consequent high cost. 261
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ENERGY STORAGE
Perhaps the most intriguing aspect of the concentration cell approach is its utter simplicity at least in terms of its basic operation. The fact that it is possible to store usable amounts of energy with only a single element or compound in merely a rarified or compressed state in the immediate presence of an electrode is remarkable. That a potential can be obtained in such a fashion between the same materials simply at different concentrations holds a certain fascination fact. Furthermore, that it requires no sensible difference in pressure to maintain these concentration differentials is also quite attractive. The easiest way to understand this notion is to relate it to the compression of a gas as an analogous means of storing energy in mechanical form.
12.1 Pros and Cons of Concentration Cells The search for hardware simplicity long operating life, and low cost has lead the author to explore the concentration cell as a means of storing energy in electrical form and returning it in the same form. Probably the single greatest attraction of this class of device is the http://bbs5.techyou.org/?fromuser=sergio147 possibility of an extremely long operating life and very high energy densities. Since such cells are entirely symmetrical physically as well as in materials, it offers promise of a sustained and easily regenerated format. The concentration cell is symmetrical around an axis at the center. In other words, the two electrodes are identical in materials of construction as well as physical size and shape. An electrolyte is also the same at the time of construction. Cycling the cell merely changes the concentrations of the same materials. A completely discharged cell has electrolytes identical at each electrode. These concentrations change during charging but will return to the initial value when discharged. The main motivation for pursuing this approach is its independence of specific materials properties. In principle, there is no limitation to energy density as there is in electrochemical couples where voltages are direct functions of the materials. Since energy is stored as "compressing and rarefying" a single substance, the capacity limitation, though real, is due only to physical material storage capacity. The second attraction is the low cost and easily managed electrolytes and electrodes. The electrolytes, usually a compound of iron or sulfur, are chemically well behaved. Carbon in various forms is employed as the electrode material, and it is exceedingly inert at the
CONCLUSION: PROBLEMS AND SOLUTIONS
263
temperatures at which cells are operated. Depending on cell design and the materials employed, it is possible to construct well functioning cells without the necessity of expensive or special property ion transfer membranes. On the negative side, there are a number of cell characteristics around which one must design in order to obtain a power source and practical device. Perhaps the most serious of these inconvenient characteristics are the self-discharge rates and the non-constant load voltage. Cell potential is directly proportional to its state of charge. Hence, these types of concentration dependent devices will have "sloping voltages," or voltages that change with time. Such undesirable characteristics necessitate the use of external circuitry to "flatten out" the voltage versus time, or voltage versus stateof-charge" curves, in order to make them more compatible with practical load and power supply situations. If there is improvement in employing the reagents in such cells in the solid form, as was described in some detail in Chapter 10 and earlier in Chapter 8, then the concentration cell might very well be the leading contender for energy storage on a large scale and for electric vehicles of various kinds. An energy density of 100 W H / l b http://bbs5.techyou.org/?fromuser=sergio147 at the very least or 200+ W H / K g is needed for any electric car to become practical even on a limited basis.
12.2
Future Performance and Limitations
The energy density of just the reagents can be estimated by assuming a nominal operating cell voltage. It is necessary to make such assumptions because a concentration cell has no specific voltage in the same sense that a "conventional cell" has due to its different, specific electrode materials. Again, let us continue with the sulfur/ sulfide cell employing sodium as cations as a means for making such projections. Looking again at the simplest version of this concentration cell based upon sulfur chemistry, we see that at full discharge the composition of electrolytes in both chambers must be the same. When such a cell is in the discharged state, symmetry dictates that the concentration of ionic components must be identical. Thus, when discharged the chemical compositions on either side of the cell are
Na 2 S +S 11 Na2S + S,
(12.2)
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and when totally charged its electrolyte form is
2Na2S 11 2S.
(12.3)
Considering this as the normalized minimal electrolyte condition, the charge available for each mole is 52 ampere-hours. A one mole-per-constituent cell would have a total weight of reactants equal to about 220 grams. About 52 ampere-hours are minimally required to charge such a cell with one mole of reactants on each side of the separator. If we assume an average working voltage of 1.0 volt, then the energy density of the cell exclusive of weight contributions of water, case, or electrodes becomes 215 watt-hours per pound of reagents - a respectable number, but hardly impressive. Replacing sodium with lithium can contribute to an increase in ED. The atomic weight of lithium is about 7, as compared to 23 for sodium. In order to significantly raise the energy density of these cells, it is necessary to resort to non-aqueous solvents, thus enabling cell voltages that are much higher than the maximum 1.2 volts. If this is done, then the http://bbs5.techyou.org/?fromuser=sergio147 upper limits of energy density can be many times higher. Regardless of how high the ED can be raised, concentration cells' advantages of low cost, dependability, and long life make such an approach to energy storage attractive enough to be pursued further and with some intensity in the future.
Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
Appendix 1: A History of Batteries http://bbs5.techyou.org/?fromuser=sergio147
More frequently than not, looking back in time to see where we have been can be very beneficial in assessing whether we are repeating the same old mistakes, or determining a new, future direction. At times we forget the additional problems presented by a particular problem solving approach, and we become so immersed in the current difficulties that we revert to old methods that were abandoned for very sound reasons. When actively involved in the present, there can be a tendency to ignore past difficulties. Our individual and collective memories are short and quite selective, resulting in repeating the failures as well as the successes of the past. This applies not only to social and political issues but also to the rather short recollections or lack of study from researchers in the physical sciences and engineering. Events, experiences, or facts are too frequently treated without perspective, simply as disconnected bits of data rather than as parts of a larger picture. The information presented in this book is largely concerned with the concentration cell approach to energy storage, and a limited background has been given concerning the supporting science. It is also helpful to know the history that pertains specifically to the 265
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identification and pursuit of the concentration cell as a practical means of storing energy.
Al.l
A History of the Battery
Just a short time ago, the world of convenience, comfort, communications, and immense power, available and controlled by the individual, was nonexistent. That was hardly more than 100 years ago. The self-propelled automobile, aircraft, electronics, and all the other vitally important and generally accepted amenities of life, such as air-conditioning and nuclear energy as well as nuclear instrumentation for medical purposes, weren't even imagined as probable engineering accomplishments. The storage of energy at that time was hardly an important concern since primary sources of electrical energy were scarce. Before the 1870s, no practical, rotating machinery generators used coal or any other hydrocarbon for fuel. Hence, there was no need for a secondary system, such as a secondary battery, to store electrical energy. Charging such a battery would present some rather difhttp://bbs5.techyou.org/?fromuser=sergio147 ficult problems. Plante invented the lead-acid cell, or battery, in about 1860. It was at that time, and still is, an excellent electrochemical cell for storing energy for prolonged periods of time at fairly inexpensive costs. Unfortunately, at that time there was little use for such a device. The principal interest was in primary sources, if not electromagnetic systems, then certainly for primary batteries to power telegraph lines and other special purpose systems in the middle nineteenth century. In fact, if it was not for the development of the internal combustion engine and, to some lesser extent, the electric car, then Plante's invention might have lain dormant for an even longer time. The advent of the electric starter (first put into a Cadillac by Charles Kettering in about 1912 for test purposes) was the main force that put the lead-acid battery into high volume production. It was, and still is, the only relatively inexpensive battery that had the power density to start a large internal combustion engine for a long enough time to get ignition. Anyone who tries to develop an alternative storage system to the lead battery would soon develop a respect and appreciation to the lead system. Much has been written on this subject in the form of papers, magazine articles, and books. One of the best descriptions of
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the early forms of electrochemical systems is in Volume I of George Heise and N. Corey Cahoon's book The Primary Battery. The mid- and late nineteenth century was indeed exciting and eventful with regard to many aspects of engineering and applied electricity (pre-electronic era of vacuum tubes and semiconductors). Perhaps the most familiar form of the primary battery is the LeClanche cell invented in about 1860. The early forms were wet cells with zinc as the reducing agent and manganese dioxide as the oxidizer (initially called depolarizer). The modern versions (alkaline cells) are dry cells and have remarkably high energy densities and long charge retention times, making them suitable for many applications ranging from the familiar flash lights to modern day electronic gadgetry. With the advent of greater technological demands, especially in warfare, and the increase in power needs of societies, increased efforts were made to provide power sources for the evolving machinery that required immense electrical power for short periods of time, such as the naval torpedo, in rapid development. Powerful and expensive batteries such as the silver/zinc cell and the zinc/dichromate cells were developed for these purposes. http://bbs5.techyou.org/?fromuser=sergio147 They were able to deliver large amounts of power for many seconds to minutes in order to propel, for example, a torpedo on its way to an enemy ship. These batteries not only required careful handling and trained personnel for proper and safe use, but they were also very costly. In special applications for military or space vehicle use, cost is at best a secondary consideration since the importance of the mission, and the costs of the rest of the associated equipment, are so great. In these instances, reliability is just as important as energy and power density. The lead-acid battery simply cannot perform for these applications, so other systems had to be developed. Unfortunately, few of these batteries are valuable in the commercial or consumer market. Despite the fact that requirements in the consumer market place were increasing, little was new or in way of significant improvements to the existing batteries. Only recently have such new developments as the lithium cell moved forward in the industry. It's major application lies with small portable electronic products that require small amounts of stored energy. The large system applications, such as the all-electric car, still await a practical battery.
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A1.2 The Electric Car and the Power Source Search Most of our early development efforts were directed towards finding new methods or perfecting existing methods of transforming energy from one form to another, mostly for transducer, communication, and instrumentation purposes. The detection of missile paths and the conversion of sonic to electrical signals were predominant. As events progressed and nuclear energy became tamed sufficiently for commercial and military use, our work became more directed towards control methods in reactor systems. As time moved on, it became more obvious to many that the generation and supply of primary sources of power for industrial and commercial use were not the lagging technologies. Instead, means of storing energy for later use or for portability purposes was the greater problem, and we will be increasingly confronting it. At that time, in the 1960s, the only commercially viable storage device for directly storing energy in electric form was still the lead-acid battery. It certainly seemed incongruous that such an ancient technology would predominate in our daily lives http://bbs5.techyou.org/?fromuser=sergio147 while all the other advances were taking place at a ferocious pace. With the goal in mind of finding an electrochemical couple that would permit high energy storage density and long life, many of us embarked upon a long journey, only to realize how difficult it is to surpass the venerable lead-acid battery on all fronts. The two largest applications are automotive power and bulk storage for emergency and standby use. The lead battery really does not offer a solution due to its high cost and short cycle life. Especially in the case of the auto market, the ED is much too small. To power a typical family car at 50+mph, energy requirements range minimally between 250 and 400 watt-hours per mile of travel. If it is required that the vehicle be capable of traveling a minimum of 300 miles on one charge, we see that a total of 75,000 to 120,000 Wh of energy must be available from the battery. An upper limit for a passenger vehicle would seem to be in the vicinity of 1,000 lbs. That means that the battery must possess an energy density of 75 to 120 watt-hours per pound - a very high figure for any short-term foreseeable technology. The lead battery has an ED between 10 and 16 W h / l b depending upon how it is discharged - a far cry from the required numbers shown above.
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An interesting bit of information is the little known fact that the electric automobile began its short journey back in the nineteenth century along with many other competitive projects ranging from steam powered cars to compressed air propulsion systems. Ferdnand Porsche of VW first began his career with very advanced electric car designs. In fact he had four-wheel drive powered by separate motors in each wheel and regenerative braking in the 1890s. The photo shown below is an electric car of 1900. The performance figures of these ancient vehicles are comparable to those presently attained by modern electric cars, ranging anywhere between 25 and 40 miles on fairly level ground at moderate city speeds. It appears that, despite all the updated electronic wizardry, there has been little, real progress in developing an electric all-purpose car. This is undoubtedly because of the lack of significant improvements in electric propulsion power, despite the sleek, lightweight body designs. To add to the dilemma of the lead battery, its cost is too great, and its life is too short. Depending on the depth and rates of discharge, the lead battery will give useful service for between 500 http://bbs5.techyou.org/?fromuser=sergio147 and 1,000 cycles. These numbers are debatable, but the point is
Figure Al.l Early version of an electric automobile. From: Porsche archive photos.
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ENERGY STORAGE
that its life and cost are outside the useful range. For example, a series of six, traction, lead batteries for a golf cart cost about $400+ for perhaps a total of 3,000 to 5,000 watt-hours of useful storage. For interesting reading on the subject of transportation, and particularly the history of the electric car, M. Schiffer's book entitled "Taking Charge" is highly recommended, see bibliography reference 38.
A1.3
The Initial Survey
When attempting to find an alternative electrochemical process that might offer higher ED and longer life, the tendency is to search the known possible couples. If one wishes to produce a long-life system, then simplicity as well as reversibility are suggested. One approach to longevity of operation is to identify reactions that will not only proceed to completion but will also have reagents that will react directly if mixed together physically. In other words, the reagents in an electrochemical couple, if left alone, will eventually interact, leaving the state of the cell http://bbs5.techyou.org/?fromuser=sergio147 in its original condition before charging. This suggests that metal oxidizer couples such as the metal-halogens, e.g., metal reducers and halogen oxidizers, will not only react electrochemically in the appropriate circumstances but will also react by direct contact. Of the five halogens, fluorine, chlorine, iodine, and bromine, the most attractive is bromine because of many factors. It is relatively inexpensive and plentiful, it is a liquid at room temperature with a tolerable vapor pressure, and it is electrochemically active with most metals. Bromine also has the ability to be stored easily because of its high solubility of bromide salts (and most of its salts) in water solutions, and active, porous materials readily adsorb it. Chlorine has many of these features, but it is not readily adsorbed, does no form complexes as easily, has a high vapor pressure, and hydrolyzes quickly in aqueous environments, thus creating HC1. Iodine (derived mostly from sea weed) would be a good competitor were it not for its high cost and high molecular weight. Fluorine, on the other hand, is totally unmanageable in aqueous solutions, and it is so reactive that few materials can withstand its very strong oxidizing nature. That leaves little choice but bromine for a workable halogen. Examination again of
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Figure 5.3 in Chapter 5 will show the relative ED for the various metal-halides. In an attempt early on to keep the cell simple and most compatible with ambient conditions (air and moisture environment, freezing to boiling points of water), only those metals that can exist in the free state in our environment were selected for further study. Despite the obvious attractiveness of lithium at over 1,200 watt-hours per lb, dry salt (lithium bromide), and other alkali metals, they were set aside for immediate study until methods of handling them should be developed in the future. Such possible methods include non-aqueous solvents (organics), high temperature, or fused salt operations.
A1.4 Review of a Research Path for a Long-life, High ED Battery The aqueous zinc/bromine system, at about 200 watt-hours per pound for dry salt and delivering 1.8 volts open circuit, offers most of the attractive features we would like. Zinc is an inexpensive and readily available http://bbs5.techyou.org/?fromuser=sergio147 metal, and its bromide salt is extremely soluble in water with a reasonably high electrical conductivity. Many configurations of this system were designed and extensively tested by many researchers, including the author. The problems associated with this system are (1) the hydrolysis of bromine, (2) zinc dendrite growth when plating with subsequent shorting a n d / o r fall off of metal from the negative electrode, (3) the formation of hydrogen gas as zinc is attacked by the HBr formed by hydrolysis, and (4) the loss of bromine in storage by hydrolysis and molecular diffusion. Among the many attractions of the Zn/Br cell are its remarkably well-behaved performance, its high efficiency, its quite flat discharge characteristics, and its ability to return to its original discharged state of just ZnBr2 solution when left for prolonged periods of time or when discharged completely. The above listed problems are formidable and become more evident as development efforts progress. The storage of bromine has been accomplished rather poorly by mechanical means such as compartment or cup-like structures on the positive electrode and then later by merely storing the bromine in solution as the complex ion, Br~, but diffusion is so severe in a static electrolyte cell that self-discharge occurs at a prohibitively high rate. This
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method does work if circulating electrolyte systems are employed and the positive electrolyte is largely stored in a reservoir external to the cell. Membranes of some sort must obviously be employed as well. Some other techniques have also been developed by the author, such as complexing the bromine with an agent that physically immobilizes the reagent without affecting its chemical activity. There are numerous such agents, such as the alkyl-ammonium halides, that will accomplish the task. The agents we selected for extensive study were various weights of polyethyleneglycol. Depending on the molecular weight of the complexes the association with bromine structures ranges from a liquid to a solid. The diffusion rate of these types of complexes is much lower than free bromine, but it is still too fast for good charge retention. The method that has proven more successful is the adsorption onto activated carbon as part of the electrode. Between 20 and 30Wh/lb was realized in large multi-cell modules. This electrochemical couple has been well investigated, and many fair sized systems have been constructed and operated. At about this time there was an increasing interest in full flow http://bbs5.techyou.org/?fromuser=sergio147 electrolyte configurations. There are many reasons to seriously explore these types of battery systems because of the advantages offered by resorting to such increased complexities. Some of these advantages include the following: • The separation of energy density from power density • The possibility of "refueling" a battery rather than the slow electrical recharging process • The increased charge retention times because of the separation of reagents during idle periods • The greater control of operation in general, especially thermal control • The increased design latitude for different applications, in principle • The charge imbalance problems can be better handled than with static cells. However, there are a few negative factors that must also be considered, such as the necessity for better leak proof designs to withstand the increased pressures internal to the battery, the electric current losses due to electrolyte interconnectivity through a
APPENDIX I : A HISTORY OF BATTERIES
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http://bbs5.techyou.org/?fromuser=sergio147
Figure A1.2
common reservoir, the pump power losses, and the increased cost and complexity for such systems. Examples of the Zn/Br battery systems are shown in Figures A1.2 through A1.5. The first is an installation that was made in about 1978 for the Duke Power Company in Charlotte, NC. Its capacity was about 150 KWh, and it has a discharge/charge cycle period of 16 hours. It delivered about 20 kW for almost 8 hours and was operated as an early test setup for about two years. Small high drain units were also designed and constructed with very closely spaced electrodes. The unit shown in Figure A1.3 had a maximum discharge period of five minutes and delivered 5 to 15KW depending on the length of time. The system experienced a
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Figure A1.3 http://bbs5.techyou.org/?fromuser=sergio147
Figure A1.4
APPENDIX I : A HISTORY OF BATTERIES
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Figure A1.5 http://bbs5.techyou.org/?fromuser=sergio147
fair degree of deterioration in capacity over the time it was tested. Postmortem inspections revealed a serious attack by bromine on almost all non-fluorocarbon materials as well as on many of the plastic components such as membranes. Using materials that are more resistant to oxidation by bromine could solve all these problems. Figure A1.6 shows a battery fabricated for the Delco Division of General Motors in late the 1970s as one of a series of multiple cell modules to be tested for possible use in electric vehicles. Interest in electric vehicle projects diminished greatly, and the industry began looking long term at the possibilities of lithium-ion batteries that were being developed in Japan at the time. Many versions and applications were explored for the zinc/bromine battery, both in static as well as full flow electrolyte designs. Figure A1.4 is a photo of a golf cart provided by the Cushman Company to TRL in 1970 as a test bed for some early batteries. A set of six Zn/Br batteries powered the cart almost 40% further and with even more acceleration power than the equivalent lead-acid batteries. However, the cost of manufacturing these units in the limited quantities was far too great to be practical. The low lead cost of lead batteries is primarily due to the automotive industry where the demands are in the tens of millions of units merely for
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http://bbs5.techyou.org/?fromuser=sergio147
Figure A1.6
new car production and many times larger for the replacement market. And, since the lead battery performs so well as the SLI system (starting, lighting, and ignition), there is little need for a new replacement technology. It becomes sort of the "chicken or the egg" situation; the costs remain high until a large market is established, and a large market requires low cost to get started. All of these systems were full flow electrolyte developments, but the bromine was stored within the porous positive electrode. The purpose of the Circulation of electrolyte was to maintain a uniform temperature throughout the cells and prevent internal shorting by zinc dendrite. As interesting as these systems were, they were beset by many technical problems associated with the ones identified above. Also, there is serious and understandable reluctance on the part of consumers as well as the industry to place products containing free bromine. That leaves the market potentials for such systems for special industrial and perhaps military uses, where proper training and precautions would be available.
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In the 1960s there was an awakening of full flow batteries in the form of the NASA, Lewis-sponsored program to develop an iron/ chromium redox cell. The chemistry is, as in other redox systems, quite simple. The reaction is Fe +3 + Cr +2 -> Fe +2 + Cr +3
Discharging,
(Al .1)
where the ferric ions are the oxidizing agents. This system is resplendent with problems as well. The effective operation of such a cell depends on a functioning anion exchange membrane. These types of membranes are not nearly as efficient as cations, and, consequently, the chloride ion usually transfers the electric charge in the cell. Eventually, the iron is transported over to the chromium die and vice versa with the result that it ceases to function. Costs and operational problems of this type have made the Fe/Cr cell impractical. Because of the hazard and chemical attack problems encountered with bromine, we searched for alternative systems that posed less danger but still had the attractive properties of small failure modes. In 1971, some early engineering work was started at TRL, Inc. with http://bbs5.techyou.org/?fromuser=sergio147 what is known as the iron-redox cell. The attractive features of this cell include (1) low cost of materials, (2) safe chemicals, (3) a completely reversible operation, (4) a reasonable energy density of ~ 80 watt-hours per pound of dry salts, and (5) an acceptable potential of 1.2 volts open circuit. Some of the problems encountered with the systems are (1) the low conductivity of the electrolyte, (2) the necessity for low pH to maintain salts in solution, (3) the poor quality of iron plating, and (4) an inexorable rise in electrolyte pH due to hydrogen evolution at low pH. Again, we embarked on an exploratory and development journey to see what practical problems existed and how we might produce practical devices. From about 1971 intermittently to 1993, extensive work was performed to develop and fabricate carbon-polymer bonded and compression molded electrodes with high conductivity and low porosity. Static electrolyte cells yielded poor results. Diffusion of ferrous and ferric chloride across almost any type of diffusion barrier is too great to provide cells with reasonable capacity and charge retention. Cation exchange membranes proved to be too costly and had much too high electrical resistance to enable cells to deliver useable power. If the pH of cells were kept very low,
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ENERGY STORAGE
ion exchange membranes would function quite well, but the iron plating is consumed by the high acidity, and hydrogen gas evolution becomes a serious problem along with high self-discharge. If pH is permitted to raise the salts of iron, then chloride and oxygen begin precipitating in great quantities, thus rendering the cell inoperative. Nevertheless, we proceeded to develop many ways of handling the problem, including ancillary automatic pH control units, which functioned quite well but needed some attention and consumed some of the charge stored in the cell. Numerous single cells and multiple cell arrays were built, and many of them were installed in various apparatus for test and demonstration purposes. Figure A1.6 is an early eight cell module employing a method of encapsulation of electrodes, membranes, and support structure, which essentially eliminates any possibility of electrolyte leaks within, from cell to cell, as well as to the outside. Prior to this form of construction, modules or arrays of cells were fabricated as plate-and-frame construction typical of most fuel cells, electrodialysis systems, and batteries, and they were fraught with leakage problems that rendered them impractical http://bbs5.techyou.org/?fromuser=sergio147 if not unsafe for general use. The principal energy storing reaction for the iron redox cell is shown in Figure 5.2 of Chapter 5 in this book. It is a unique situation where the iron ion is moved both upwards and downwards during charging and during the discharge mode. There are few elements that offer similar properties for practical exploitation, vanadium being one other. The cost of the iron system is markedly lower, but it does have its own collection of problems. Among the early working hardware that was constructed to demonstrate the potential practicality of iron/redox, a small power source was constructed and put in place of the gasoline-fueled engine in a go-cart. The version shown in Figure A1.7 was assembled in 1973 and operated as a fun vehicle for three years. It was a dual full flow electrolyte system in which the ferric (ferric chloride) solution was stored in the larger tank, and the ferrous solution flowed past the plated iron on the negative electrode. A microporous plastic separator (Daramic, produced by the W.R. Grace Co. for the lead-acid battery) was employed to keep the two solutions from mixing too quickly and internally discharging the cells. A twelve-volt auto starter motor was used to propel the cart. Later in about 1974, a program was initiated with the sponsorship of EPRI and the Mississippi County Community College in
APPENDIX I : A HISTORY OF BATTERIES
279
Figure A1.7 Early motive power demonstration for a full flow electrolyte iron redox battery - Golf Cart circa 1974. http://bbs5.techyou.org/?fromuser=sergio147
Arkansas to develop and design a storage system for a solar collector field to provide uninterrupted power to parts of the college. The total energy capacity was about 20 KWH. Figures A1.8 and A1.9 show portions of the system that was built and tested in Durham, North Carolina prior to installation. The larger tank held the ferric chloride solution, and the smaller one held the ferrous solution. The electrical load was a series of electrical heaters immersed in a cooled tank of water. As discussed earlier, the iron system was plagued with a couple of serious problems regarding pH drifting upward and iron plating falloff from the electrode surfaces. It is possible that resorting to non-aqueous solutions can solve these problems, but not nearly enough data has been obtained to justify expenditures of large sums until more real evidence is acquired. In order to avoid all the problems associated with plating solids onto electrode surfaces, the sulfide/bromine couple was identified and pursued as a possible solution to large-scale, stationary electrical energy storage. TRL proceeded to investigate this
280
ENERGY STORAGE
MC3 project, power conditioning circuitry & module arrays. Figure A1.8 http://bbs5.techyou.org/?fromuser=sergio147
MC3 project electrolyte tanks 900 gal posilyte & 400 gal negalyte 1976-77 @ peace St. Figure A1.9
APPENDIX i: A HISTORY OF BATTERIES
281
possibility in 1989 and accumulated enough understanding and empirical data of the couple S = /Br 2 to fabricate and test numerous laboratory single cells. Later, in 1991 National Power, PLC in the UK developed enough interest to support research at TRL and within National Power. The experimental results continued to be promising, and over three years of intensive R & D was invested in the couple. As always, there are sets of attributes and problems associated with any approach to solving practical energy storage. In this case, the main issues that presented the greatest concern are as follows: • Electrodes with long life at high current densities, i.e., greater than 1 ampere per square inch of active area • Cation membranes that will stand up in high concentrations of free bromine, other than NAFION, a DuPont material that functions reasonably well in such cells but is much too costly at low current densities • The loss of bromine to the entire system when Sulfides diffuse into the positive electrolyte with high http://bbs5.techyou.org/?fromuser=sergio147 bromine concentrations (In rich bromine solutions, sulfur and sulfides will be oxidized all the way to the sulfates. When that occurs there is no electrical means of restoring or returning the sulfur component to the negative side in a usable form. That then provides one mechanism that will inexorably bring about the malfunctioning of a cell, and it can be corrected only by treating the electrolyte externally and with chemical means). Again, it is possible to overcome these shortcomings, but only with the investment of sizable funding and testing. Non-aqueous electrolytes may indeed hold an answer to some of the problems. Finally, we arrived at the concentration cell approach. This mechanism is entirely different than an electrochemical couple and appears to offer an answer to virtually all of the seemingly insurmountable issues encountered repeatedly with other electrochemical means. The concentration cell, which has been described in thorough detail throughout this book, was explored by the author and associates beginning in 2002, and it is still being pursued.
282
ENERGY STORAGE
The following are the main reasons for the optimism: 1. There are no electrically conductive solids deposited on electrodes to cause shorting or loss problems. 2. pH stays very steady in the case of the sulfide system, at relatively high values. 3. The reactions are completely reversible. 4. Reagents are inexpensive and quite safe in normal usage. 5. Voltages and energy densities are reasonably high. 6. Reactions are well behaved with very few side reactions. 7. It operates very well in simple configurations with no necessity for the complexities of circulating electrolytes or compensating networks. The hope now is that others will perform additional work to determine the ultimate possibilities of such an approach to practical energy storage for industrial and commercial applications. http://bbs5.techyou.org/?fromuser=sergio147
Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
Appendix 2: Aids and Supplemental Material http://bbs5.techyou.org/?fromuser=sergio147
This appendix contains a collection of material that is relevant to the subject matter of this book. It is intended as a working aid and supplement to the information in the body of the book. The usual lists of the chemical elements, periodic table, electromotive series, etc., that are found in many scientific texts have not been provided because they are readily available in many sources.
A2.1
Properties of Homogeneous Membranes
A series of experiments were performed with five samples of ion transport membranes. Ion exchange membranes have proven to be the best means of reducing diffusion between two compartments of a dual liquid electrolyte cell. These tests were directed at determining the diffusion rate of molecular bromine in a NaBr solution. The relative electrical (ionic) conductance of these membranes was also measured.
283
284
ENERGY STORAGE
A2.1.1 Diffusion Tests Two 250 ml glass flasks with side tubes were employed per test setup. A membrane sample was placed over the flat ground mouths of the flasks with an RTV sealant. Two flasks were brought together, mouth-to-mouth, with the side tubes facing upwards. Both flasks were then filled with 250 ml of 2 molar NaBr solution. Free bromine was introduced into one of the flasks to make a 1/8 molar solution of Br2. Five such setups were made, one for each of the membranes. The start times of the tests were recorded. A titration solution of 0.001 N sodium thiosulfate was prepared to measure the bromine in the dilute side periodically. A 1 ml sample was extracted from the dilute side flask and diluted with a 0.01 N solution of H,SO. 2
4
starch and iodine indicator solutions were employed to provide good end-point indications. The following membranes were tested: 1. NAFION N324, untreated, not pre-wetted 2. NAFION N324, pre-treated in hot water, cathode side away fromhttp://bbs5.techyou.org/?fromuser=sergio147 bromine 3. NAFION N324, pre-treated in hot water, cathode side facing bromine 4. RAI R-4010-5, special 6 mils thick experimental membrane 5. RAI 4010, standard 3 mil thick membrane. Data presented are in terms of ml of 0.001 N of titrant needed per ml of sample, after normalizing for the background factors. Table A2.1 Diffusion rates of bromine across various membranes. Elapsed Time, Hrs
Membrane Membrane Membrane Membrane Membrane #5 #2 #1 #3 #4
5
0
0
0
0
0
24
0
0
0
0
?
49
0
1.3
1.3
0.7
2.6
93
0.4
5.1
4.8
2.1
7.1
APPENDIX 2: A I D S AND SUPPLEMENTAL MATERIAL
285
The above data shows that the diffusion rate of bromine through unpre-treated NAFION 324 is 1 / 5 of that of the R-4010-5 RAI, which is the membrane provided by TRL in the cells delivered to NP. Now, consider the significance of these numbers if they, indeed, represent the diffusion process accurately. Taking the data from membrane #4, the RAI membrane, about 2.1 x 10"3N of bromine had diffused across a membrane with an area of about 0.8 in2 after 93 hours. This corresponds to about 1 / 4 x 2.1 x 10~3 gram equivalent weight of bromine since the solution volume is 250 ml, or 1/4 liter. At 26AH per equivalent weight, we get 26 x 1/4 x 2.1 x 10"3AH over 93 hours. Or, we have as the current equivalent of the diffusion a figure of 0.014AH over 93hours. This is roughly equal to O.lOma per square inch of membrane area if the concentration difference is 1/8 molar Br r That is a fairly small number. This means that a fully charged cell with 2 molar bromine in solution would be discharging at 16 times this rate per in2 of membrane area, or about 1.6 ma/in 2 of area. If the cell normally discharges at 200 ma per in2, then the self discharge rate would be less than 1% of the current flow. http://bbs5.techyou.org/?fromuser=sergio147
A2.2 The van der Waals Equation and its Relevance to Concentration Cells These types of forces are frequently important to the processes that transpire in any electrochemical system. Where interfaces appear in an electrochemical cell, such as that between the electrolyte and an electrode, we are apt to encounter some form of a van der Waals type of effect and probably mechanisms of adsorption as well. These physical effects are particularly important in the operation of a concentration cell where the storage of a component within an electrode is designed to take place to a very high degree. It is important to explore the subjects of forces other than the classical, macroscopic ones that are so familiar in physical mechanics because we are seeking an explanation for observed conditions that arise in the experimental concentration cells regarding capacity, electrical, and population densities of species. An interesting phenomenon was observed in the mid-nineteenth century when various gases were compressed at different constant temperature conditions. Attempts were made to come up with a modified version of the simple gas equation (Boyle's Law) that
286
ENERGY STORAGE
would conform to the new experimental data. A gas was seen to depart from the standard relationship for an ideal gas, viz, PV = nRT.
(A2.1)
At the low-pressure ranges and lower temperatures, it appeared that within certain ranges, at constant temperature, the pressure remained quite constant while the volume changed significantly. In 1879, van der Waals proposed a relationship of the form
P=ip< + » n ( V - n b ) , V
2
(A2.2)
J
which seemed to fit the empirical data quite well. If the process involves the adsorption of a gas, then the mathematics and assumptions for a model to describe the process can be structured in a more simple fashion. Hence, much of the early work focused on the circumstances of a gas being adhered to a solid absorbent. It is much easier to treat this sort of situation than that of solids or ions being captured http://bbs5.techyou.org/?fromuser=sergio147 by solid adsorbents. The pressure or force term is replaced in this case by F in order to differentiate from that of a pure gas. Obviously, a new term appears for the force to condense the gas or compress the gas to a very small volume or, perhaps, the liquid state.
A2.3 Derivation of Electrolyte Interconnectivity Losses The efficiency of operation of a multi-cell, full-flow electrolyte array is affected by the dissipative losses through the electrolyte common to all cells that are connected electrically in series. Unless appropriate design compensations are incorporated, these coulombic losses can be significant. Multiple cell arrays considered here are arranged as a series of bipolar electrodes connected together by electrolyte electrically in parallel via manifolding and associated hydraulic (fluid) circuits. A single electrolyte is supplied from a hydraulic circuit in parallel connection as shown in Figure A2.1. The equivalent electric circuit represents half of what one would observe for a two-electrolyte array. A simple circuit is illustrated in Figure A2.2.
APPENDIX 2: A I D S AND SUPPLEMENTAL MATERIAL
287
3-*— Manifold
Flow
i
I
N -*- Electrodes
Flow
Channeling.
JL
JL
3
Membranes
Figure A2.1 Hydraulic circuit in parallel.
Figure A2.2 Equivalent circuit.
R equals the resistance of the feeder channels from the manifold http://bbs5.techyou.org/?fromuser=sergio147 into the cell compartment. The manifold cross sectional area is so large that it contributes very little resistance to the above circuit. An analysis proceeds as follows. Referring to the circuit in Figure A2.2, for a single loop, or single cell N = 1, where N is the number of series cells, the electric current, ilX in this loop is found by Kirchoffs law. For a circuit where N = 2, we have h1 = h2 = — / R /
(A2.3)
as is shown in Figure A2.3 below. The currents i : and i2 are those in the first and second loops, and they are equal in magnitude. For a three-loop circuit, the solution of the first loop current is found in similar fashion and is 3E 2R Next, as is illustrated in Figure A2.4, i^ = i3.
(A2.4)
288
ENERGY STORAGE For N = 2
O
R
E = 2i,R-i2R
\ i2~)
E
E = 2i2R-i1 R
E
i, = 2i
In this case, i-, = i2 = E/R
E
R
Figure A2.3 A two loop circuit.
For N = 3 E = 2i1R-i2R
E = 2i 3 R-i 2 R = 2i 1 R-i 2 R 2[2L - | ]R - 2i, R = E/R and 2i, = 3 1 or i, = f | http://bbs5.techyou.org/?fromuser=sergio147
Figure A2.4 A three loop circuit.
A four-loop configuration (not shown) gives the following as a first loop current, 2E
h=Y>
(A2.5)
where i : = i4, and i2 = i3. A five-loop current is represented by
ii=f§,
(A2.6)
where i} = L, and i2 = i4, and so the progression proceeds. It is obvious that a symmetrical pattern is developing here. A six-loop current is as follows: 3E
ί = γ, where L = i,, L = L, and i, = L. 1
6' 2
6'
3
D
(Α2.7)
APPENDIX 2: A I D S AND SUPPLEMENTAL MATERIAL
289
The general expression for the first and last loop of a circuit in an array with N loops is ii = i
N
= ^ ·
(A2.8)
It is apparent that the electric current in any one of the series' coupled loops is not necessarily equal and that its value depends on the number of cells in series. A rapid examination of the relationship to find a repetitive symmetry is shown here. We will now derive the expression for the current in the nth loop (cell) of an N cell array in terms of E, R, and i r As was learned previously, for n = 2, i2 = 2ix - E / R , and for n = 3, i3 = 3 i 1 - 3 E / R . By carrying out these steps in a manner similar to the preceding, we can see a pattern developing. The series of steps that must be performed in order to see the format develop are not shown here. However, these are the results of the process. The general form of the relationship for the nth loop current, I , is http://bbs5.techyou.org/?fromuser=sergio147
F F i = m \1 - a — + b R R
F
R
for n > 4 .
(A2.9)
For those circuits with four or more loops, the above relationship is valid. Examination of the iterative pattern shows that the coefficients a and b are a = (n-l)(n-2) b=£(y-3).
(A2.10)
y=4
The resultant expression is then .
E 1
R
(n-l)(n-2)l(y-3) + l y=4
(A2.ll)
The dissipative currents through interior cells in an array are greater than those through the end cells, necessitating periodic
290
ENERGY STORAGE
equilibrating or rebalancing of such batteries if they depend on electro-deposition and the removal of materials such as metal plating during charging and discharging. By substituting the expression for i , or the first loop current, which is also the last loop current in an array (see equation (A2.8)), into the above equation and solving for n = N / 2 , the innermost and highest self-discharging rate cells gives
iN = 2
NE
E
4R
R
(HHV
1
(A2.12)
In the design of modules, the above dissipation factors should be taken into account, and electrolyte channels or feeder tubes should be configured to give the maximum electrical isolation without either unduly increasing hydraulic impedance to the electrolyte flow or increasing risks of passage blocking. http://bbs5.techyou.org/?fromuser=sergio147
A2.4 Efficiency Calculations
The total energy efficiency of a secondary battery system is exceedingly pertinent when evaluating its importance to applications such as wind, solar, and load leveling uses. In these applications, increasing the efficiency and effectiveness is among the main considerations for selecting a storage mechanism. Costs associated with the capital equipment and its operation are greatly affected by the overall, or energy turnaround, efficiency. Losses are incurred during charging as well as during the discharge mode. The following can summarize energy loss mechanisms for the battery: Voltage Losses • Ohmic potential drops through the electrolyte • Polarization voltage loss at electrode interfaces • Electrolyte concentration potentials in the immediate vicinity of the electrodes • Electrical connections and electrode ohmic resistance.
APPENDIX 2: A I D S AND SUPPLEMENTAL MATERIAL
291
Coulombic Losses • Dissipation through electrolyte interconnections via manifolding • Diffusion of reactant species away from electrodes or into opposite membrane sides • Plating fall off from electrodes such as metallic zinc or iron • Gas evolution • Hydrolysis and irreversible formation of acid or base • Electrolyte pump power. All of the above and additional, perhaps somewhat more subtle, losses such as circulating parasitic currents contribute to the turnaround efficiency of redox systems. As an example of the many sources of energy loss, consider the case of a zinc/bromine system. Some of the more predominant loss mechanisms, with some estimate of the magnitude of their contributions to the total, are listed in the table below. These values are based on many designs and operating data http://bbs5.techyou.org/?fromuser=sergio147 with numerous large-scale zinc/bromine systems. In all of these instances, the bromine was stored in the adsorbed state in microporous carbon positive electrodes. Such methods do promote the formation of HBr and consequent coulombic losses due to hydrogen evolution and zinc consumption. Certainly, the energy efficiency of a battery system is of paramount importance when estimating operating power costs. It is Table A2.2 Energy loss mechanisms in metal/halogen batteries. Coulombic Losses
Voltaic Factor
Br2 diffusion 2 - 3%
Polarization 0.05 - 0.10 volts
H 2 evolution - 1 - 5 %
Internal resistance 0.05 - 0.10 volts
Zinc dendrites ~ 1% HBr formation 2 - 3 % Manifolds < 1% Pump power ~ 1 %
292
ENERGY STORAGE
also reflected in the net energy storing capacity of the power source as well as in determining the capital equipment costs. Total turn-around energy efficiency, η, is defined as the ratio of output energy to the electrical load from the battery divided by the total energy expended elsewhere and required to charge the battery. Let us now define coulombic efficiency, r\c, and the voltage efficiency, η ν . If we let ic be the charging current and Id the discharging current, then the coulombic inputs to outputs from the cell are the following:
Q c = j i c dt = the c o u l o m b i n p u t o
(A2.13)
and Td
Q d = J i d dt = C o u l o m b o u t p u t . o
(A2.14)
http://bbs5.techyou.org/?fromuser=sergio147
The coulombic efficiency then is simply Q d /Q c The voltage efficiency factor is another matter. There actually is no direct way to measure that parameter, but we may find it interesting to invent such a function and define it in a manner similar to that for T|c. It can be considered the ratio of the driving potential over the charging potential over the entire range of the two modes. Unless one were to average the voltages and call their quotient the voltage efficiency, or unless the voltages were constant, then we could ascribe a physical significance to the term without too much difficulty. However, in real situations both current and voltage will vary during the charge mode as well as during discharge. We can define the voltage efficiency term, which is usually referred to as T
η
ν
Η
jvddt Jvcdt o
.
(A2.15)
This brings us to the main issue at hand - the total efficiency of battery operation.
APPENDIX 2: A I D S AND SUPPLEMENTAL MATERIAL
293
Power at any instant in time is P = iv.
(A2.16)
The energy, dE, over a period in time, dt, is dE = ivdt.
(A2.17)
The total energy efficiency then becomes the quotient of input energy divided into output energy over the entire span of time for charge and discharge, or T
/ idvddt
(A2.18)
η =— E, = TτI i v dt c c
Depending on the module design, the number of cells in a series array, the type of electrolytes employed, rates of charging and discharging, and many other factors, efficiencies ranging between 60% and 75% for total http://bbs5.techyou.org/?fromuser=sergio147 turn-around can be expected. In certain applications where convenience, emergency availability, etc., are the main application values, efficiency may not be as important. However, in load leveling and solar and wind power applications, energy efficiency is very important and second perhaps only to cost considerations. Specific resistivity of NaOH solutions 18 degrees centigrade
5.5 « 5 ω | 4.5
1o
4
\
/ \
E 3.5 .c
°
3 2.5
;i
:3
Froni chemica rubber b()ok
\
!5
<■
Molarity
Figure A2.5 Resistivity of NaOH solutions.
(
?
t
294
ENERGY STORAGE
A2.5 Specific Resistivity and Specific Gravity of Some Reagents The graphs below are plots of Na 2 S electrolyte resistance and specific gravity as it depends on its concentration in water. Figure A2.5 shows the change of resistivity of NaOH, depending on its concentration in water. The importance of such information is realized when it is employed to control the pH of the electrolyte in a sodium sulfide concentration cell. The pH is important because
Specific gravity of FeCI3 solutions @ 20 degrees centigrade
1.7 1.6
^^
1.5 1.4 1.3 0) Q. CO
1.2
^-"" n Q
0
http://bbs5.techyou.org/?fromuser=sergio147
1
2
Data from rubber handbook
3 Molarity
4
Figure A2.6 Specific gravity of FeCl3 solutions.
1.3
Sodium monosulfide solution specific gravity @ 18 degrees centigrade
1.25
_^_
1.2 1.15 u O Φ
o.
CO
1.1 1.05 1 0.95 0.9 0 0.5 From rubber handbook
1.5 Molarity
Figure A2.7 Sodium monosulfide solution specific gravity.
2.5
APPENDIX 2: A I D S AND SUPPLEMENTAL MATERIAL
295
it minimizes the formation of hydrogen gas during charging at the negative electrode, especially when the availability of sodium ions is at a minimum. Also, adding NaOH to the solution will increase electrolyte conductivity. In cells that make use of the ferric/ferrous system, salt solution weights of these heavy salts are important in determining cell power and cell energy to weight delivery capabilities, i.e., PD and ED. Figure A2.6 shows specific gravity versus concentration. Similarly, we are interested in the specific gravity versus water concentration of the salt Na 2 S as shown in Figure A2.7.
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Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
Bibliography 1. Gileadi, Electrosorption, New York, Plenum Press, 1967. 2. Champion and Davy, Properties of Matter, Blackie and Son, pp. 210-221, 1959. 3. Daniels and Alberty, Physical Chemistry, New York, John Wiley & Sons, 1959. 4. Millard, Physical Chemistry for Colleges, New York, McGraw-Hill Book Co., 1946. 5. Latimer, Oxidation Potentials, New Jersey, Prentice-Hall, 1959. 6. Moelwyn-Hughes, Physical Chemistry, New York, Pergamon Press, 1957. http://bbs5.techyou.org/?fromuser=sergio147 7. Slater and Frank, Introduction to Theoretical Physics, New York, McGrawHill Book Co., 1933. 8. Koryta, Dvorak, and Bohackova, Electrochemistry, London, Methuen & Co. Ltd, 1970. 9. Conway, Electrochemical Data, Amsterdam, Elsevier Publishing Co., London, 1952. 10. Slater, Introduction to Chemical Physics, New York, McGraw-Hill Book Co., 1939. 11. Klotz, Chemical Thermodynamics, Englewood Cliffs, Prentice-Hall, Inc., 1960. 12. Shepard, Cocks, Chaddock, and Harman, Introduction to Energy Technology, Ann Arbor, Ann Arbor Science, 1977. 13. A. F. IOFFE, Semiconductor Thermoelements and Thermoelectric Cooling, London, Infosearch Limited, 1957. 14. Francis Weston Sears, Mechanics Heat and Sound, Addison-Wesley Press, Inc., 1944. 15. R. B. Lindsay and H. Margenau, Foundations of Physics, John Wiley & Sons, 1936. 16. Max Jammer, Concepts of Mass, Dover Publications, 1997. 17. Max Jammer, Concepts of Force, Dover Publications, 1999. 18. R. N. Adams, Electrochemistry at Solid Surfaces, Marcel Dekker, Inc., 1969. 297
298
BIBLIOGRAPHY
19. J. S. Mattson and H. B. Mark Jr., Activated Carbon, Surface Chemistry and Desorption from Solution, Marcel Dekker, Inc., 1971. 20. W. S. Brey, Jr., Principles of Physical Chemistry, Appleton-CenturyCrofts, Inc., 1958. 21. A. W. Adamson, Physical Chemistry of Surfaces, John Wiley & Sons, 1982. 22. M. Dole, Experimental and Theoretical Electrochemistry, New York, McGraw-Hill Book Co., 1935. 23. F. Walsh, Electrochemical Engineering, Portsmouth, The Electrochemical Consultancy, 1993. 24. W. J. Weber, Jr., Advances In Chemistry Series, Washington, D.C., American Chemical Society, 1968. 25. William D. Smythe, Static and Dynamic Electricity, New York, McGrawHill Book Co., 1950. 26. Duncan A. Maclnnes, The Principles of Electrochemistry, New York, Reinhold Publishing Corporation, 1939. 27. George W. Heise and N. Corey Cahoon, The Primary Battery, Vol. 1, New York, John Wiley & Sons, 1971. 28. W. C. Gardiner, Jr., Rates and Mechanisms of Chemical Reactions, Menlo Park, W A . Benjamin, Inc., 1969. 29. J. A. G. Drake, ed., Electrochemistry and Clean Energy, Cambridge, Royal http://bbs5.techyou.org/?fromuser=sergio147 Society of Chemistry, 1994. 30. George Wood Vinal, Storage Batteries, John Wiley & Sons, 1955. 31. H. A. Frank & E. T. Seo, eds., "The Twelfth Annual Battery Conference on Applications and Advances," proceedings of the conference at California State University, Long Beach, Institute of Electrical and Electronics Engineers, 1997. 32. V. Barsukov and F Beck, eds., New Promising Electrochemical Systems for Rechargeable Batteries, Boston, Kluwer Academic Publishers, 1996. 33. Daniel H. Doughty, ed., "Materials for Electrochemical Energy Storage and Conversion: Batteries, Capacitors, and Fuel Cells," San Francisco, Materials Research Society, symposium held April 1995. 34. S. Srinivasan, D. D. Macdonald, and A. C. Khandkar, "Proceedings of the Symposium on Electrode Materials and Processes for Energy and Conversion," Pennington, Electrochemical Society, 1994. 35. David Linden, Handbook of Batteries, New York, McGraw-Hill Book Co., 1995. 36. A. R. Landgrebe and Zen-ichiro Takehara, "Proceedings of the Symposium on Batteries and Fuel Cells for Stationary and Electric Vehicle Applications," Electrochemical Society, 1993. 37. J. Giner, "Screening of Redox Couples and Electrode Materials," NASA-Lewis Research Center, Sept. 1976.
BIBLIOGRAPHY
299
38. M. B. Schiffer, "Taking Charge, The Electric Automobile in America," Smithsonian Institution Press, Washington & London, 1991. 39. R. Zito and C. M. Harman, "The Iron-Redox Battery in Large SolarPhotovoltaic Application," Second Annual Battery Development and Electrochemical Technology Conference, 1978. 40. R. Zito, "Energy Storage (Redox Systems) and Photovoltaic Generation," paper delivered as guest speaker at Princeton University, 1978. 41. R. Zito, "The Iron-Redox Battery," DOE Battery Conference, 1979. 42. Joseph Lee, R. Zito, and Vincent D'Agostino, "Ion Exchange Membranes as the Separator for Iron-Redox Battery," Proceedings at the Symposium on Ion Exchange, Transport and Interfacial Properties, The Electrochemical Society, Inc., Vol. 81-2,1980. 43. R. Zito, "Thermo-galvanic Energy Conversion," AIAA Journal, Vol. 1, No. 2,1963.
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Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
Index activated carbon & surface area, 63,109,128, 272,298 activity coefficients, 84,107,139, adsorption rate, 111, 115,126,130 auxiliary power sources, 42,43 Avogadro number, 128,129,202
constant power graph, 132,134,149 Coulomb, 129,130, coulombic efficiency, 183,185,190, 206 cycle life, 35,39, 67, 70,165, 222
Daniel cell, 90,91 Delco, GM, 259 desorption rate, 95,112,129,298 diffusion rate balance, 94 http://bbs5.techyou.org/?fromuser=sergio147 Capacitors, 03, 46, 83 dimensional analysis, 12 capacity, 261,101 discharging process, 178 Carnot, 28, 261 Duke Power Co., 273 cell construction, 67, 74,162,213, 253 et. seq. Edison cell, 73 cell design, 36,157,219 et seq Einstein, 8 charge retention, 37, 78,238 electric car, 52, 263,267 charging process, 100,107,147, electro-sorption, 297 163,179,272 energy, 88 CIR, common ion redox, 77, 79, 83, energy, 11, 78,153 energy conversion, 4,13 156 energy sources, 18, 24, 59 classical mechanics, 7,19 ethane, 59 colligative properties, 76 experimental data, 241 combustion, 25, 59 comparison of storage methods, 59, 69, 88 Faraday equivalent, 129 Compressed air, 24, 245 Ferdinand Porsche, 253 Fick's law, 114,202 concentration, 110,113,176,239 concentration cell, 55, 75 et. seq. field, 170,174,176 conservation, 5,104,107,163 flat surface electrodes, 122, 94,169 constant current graph, 131,132, Flywheels, 46 Force, 10,12, 54, 93,177,194,285 147,190, 240,147, baseball, 47, 49 bipolar, 286
301
302
INDEX
fossil fuels, 5, 20, 59, 62 Franklin, 31 Freundlich, 112 full flow electrolytes, 34 Galileo, 7,16 gel electrolyte, 100 Gibbs-Helmholtz, 33 Globilis, 26 Gouy diffuse layer, 91 gradient half redox, 63, 64, 74,159 halogens, 62, 64, 74, 270 Helmholz, 33, 87, 95,101,109,113 human muscle power, 33 hybrid car, 42 hydrocarbon fuel data, 59, 61 hydrogen reference electrode, 89,92
NASA, 70, 71, 277, 298 National Power, PLC, 38, 281 need for storage, 29, 25 Nernst, 84, 93,102,110,146,157, 167,226, 247 Newton, 14,17 nickel cadmium cell, 58, 71, 73 nickel iron cell, 56, 73 nickel metal hydride cell, 203 nuclear energy, 3, 43 observables, 10 Occam's Razor, 122 octane, 59, 60 operating life, 32,234,262 Operational models, 121,166 osmotic pressure, 76, 81, 85 overcharging effects, 237 oxidation, 56,166, 63, 66,93,101 oxygen, 47, 54, 58, 63, 74
peak power, 45, 72 I.C. engines http://bbs5.techyou.org/?fromuser=sergio147 Peltier, 39 ideal gas laws, 77,154,286 ion injection, 87 pentane, 59 ions, 104, photo-voltaic, 28, 42, 44 iron chromium battery, 277 polysulfide diffusion, 167 iron redox battery, 64, 65, 74,158, porous surface electrodes, 92,112, 277-279 113,121 Potential energy, 3, 8,9,11,12,15 practical uses of energy, 78 Kettering, C.F., 266 precipitation rate, 248 Kinetic energy, 8,18, 49, 53 primary sources, 1, 22,24, 42, 266 Principia Mathematica, 14 Langmuir, 95,112,128,163 LeClanche, 68, 267 principles, 107,163 lithium ion cell, 42, 56,267 problems with batteries, 56 load leveling, 39, 44, 68, 71,165 loss, 286, 291 quantum mechanics, 8, 43 Maxwell, 9 metal air batteries, 74 metal bromine couple, 65, 66 metal-halogen couples, 66,291 Methanol fuel, 25,27, 59 molecules, 156
Ragone diagram, 68 Reagent storage, 181,190, 247,259 redox, 34 reference electrode potential, 89, 90, 92,161 rocket propulsion, 54
INDEX
safety, 22, 72,160,174 secondary sources, 2, 22, 25, 44 separator, 101, 36, 67,100,103, V 140,150 sodium sulfide cell, 150 solar energy, 25 solubility, 102,104,136,163, 248 solution rate, 231 springs, 24, 46, 229 symmetrical balance, 105 thermionic conversion, 32 thermoelectricity, 34 thermogalvanic, 11, 78,104, transference TRL, 38, 74, 87 U.S. Dept. of Agriculture, 27
van der Waals force, 87, 111, 85, 286 vanadium redox battery, 39, 71, 160,278 vis viva, 8 voltage Peltier, 29, 34,171,173 Thermogalvanic, 33 flat discharge, 73 polarization, 89 photovoltaic, 27 weight, 8,12,16 wind power, 19, 48,161,293 zinc bromine battery, 67, 74,222, 271, 275, 291
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Energy Storage: A New Approach by Ralph Zito Copyright © 2010 Scrivener Publishing LLC.
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