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BATTERY SEPARATOR MECHANISMS--LITERATURE SURVEY REPORT

M1Ot FSFDERAL SCIEN AND

TECFHNICAL INFO'..

D DC26SEPTEMBER 19jDC 4

NOL A

UNITED STATES NAVAL ORDNANCE LABORATORY, WHITE OAK, MARYLAND

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Z Distribution of this document isunlimited.

NOLTR 64-136

BATTERY SEPARATOR MECHANISMS-- LITERATURE SURVEY REPORT

Prepared by:Charles F. McClure

ABSTRACT: In order to improve the characteristics of batteries,it has become necessary to gain a greater understanding of bat-tery separators and how they can inhibit the motion of ions andmolecules. This report, based upon a three-month literaturesurvey, reviews some of the theories invented to explain thetransport of material through solutions and barriers. Included,for example, are the major fields of diffusion, electrodiffu-sion, irreversible thermodynamics and reaction rate theory, withspecific reference to the work of Fuoss, Laity, Lamm, de Groot,Laidler and Eyzing, and others. This report is intended toserve as a guide for future research.

APPROVED BY: A. G. HELLFRITZSCH, ChiefElectrochemistry Division

CHEMISTRY RESEARCH DEPARTMENTU. S. NAVAL ORDNANCE LABORATORY

White Oak, Silver Spring, Maryland

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NOLTR 64-136 26 September 1966

This literatuve survey on the theories of mechanismsapplicable to the functions of battery separators has been con-ducted as a part of a Battery Evaluation and SupportingResearch project funded by Task RUTO 3E000/212. This projectis directed toward understanding and improving the performanceof the silver-zinc battery. A study of the ionic speciesinvolved in the battery reactions has been under way for sometime. It is apparent that the ionic barrier (separitor) usedin this system is extremely critical to the successful con-struction of a battery. In preparation for a program expan-sion into a separator study, the readily available literaturehas been reviewed. This bibliography of pertinent literatureconcerning theories of separator performance is submitted asreference material for planning a separator study program.

A. A. BARTHESCaptain, USNActing Commander

ALBERT LIGHTBODYBy direction

1a

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CONTENTS

OBSTRUCTIONS TO THEORETICAL PROGRESS..................... 1

FACTORS IN TRANSPORT..........,........................ 2

- FORCES. •ee • • g•e....... ....... e.... •......... •• ••....... 4

REVIEW OF THEORIES...,........ ,,,,..........,.,.•.,. 5

A. Hydrodynamic ..,.*,.... ...................... 5B. Membrane Potential... 6C. Reaction Rae..,........,....•. 7D. Diffusion..••.•.. ........ ,... 9E. Non-Electxodiffusion of Ions ........... 12F. Electrodiffusion................ ....... 13

G. Statistical Mechanics .... , .. ..... •........ 15H. Irreversible Thermodynamics ....... . . .... ..... 16

RESTRICTED PROBLEMS .......... ,..,...... .......... 17

I. Selective Permeability•.......... 17J. Boundary Barriers.......... ...... ....... . . . 18K. Transpot Number. .... ..... ....... 19L. Membrane Mechanism.. ... . .. .i. .. .. 20M. Charge Transfer..... . . . . 21N. Biological Problems. . . . 210. Measurements........ . . . . 23

CONCLUDING REMARKS. ... ,.....,...•... ................. 24

BIBLIOGRAPHY..•..,.,..,....,•,•..,.,............,.....,.• 26

Books..,.,,•,.....•..,......,......,....,,..... 26Journals.,. . .. ... .. . . .. . .,.. ... .. . .. ...,,,... 26

Miscellaneous Repots....... .. ,. ........ 38Additional Bibliography.....,,... .......... 38

APPENDIX I. List of Symbols............... ...... ,, 39

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INTRODUCTION

With the exception of some fairly recent technical reportsfrom industry, the volume of literature pertaining directly toseparators is quite small. And unfortunately, very few of thetechnical reports are concerned with the fundamental problemswhich must be solved. However, since the passage of ions andmolecules through a separator is basically a diffusion problem,the literatuze has been searched for information concerningdiffusion, especially diffusion through barriers, and relatedtopics such as ionic size, hydration effects, and viscosity.During this study, some references devoted to battery separa-

* tors were naturally discovered; these, and a few of the bettertechnical reports, axe also included in the bibliography.

* This report may be roughly divided into two main sections,the first dealing primarily with the general aspects of diffu-sion and membrane transport, the theoretical explanations, andthe influencing factors. The second part is devoted to itemsof a more specific nature, such as permselective membranes,monolayers, and specific papers of interest. This division

V emphasizes the two main approaches which may be followed infuture research: the general versus the specific. Theoreticalexplanation of electzodiffusion is needed in addition to thedetailed knowledge of individual systems used fox commercialapplications.

OBSTRUCTIONS TO THEORETICAL PROGRESS

Self-diffusion and the binary-diffusion of "ideal" liquidsand gases are well known phenomena which can be analyzed bystandard methods, although the careless selection of boundary

I : and initial conditions can make this very difficult mathemat-ically. Literature on these problems is plentiful, both inbooks such as Crank's Mathematics of Diffusion, Barfer's Diffu-sion in and through Solids and Jost's Diffusion in Solids,

l Liquids and Gases; and in the periodicals.'O Consequently,only a few articles pertinent to these topics are mentionedhere or included in the bibliography. The situation is quitedifferent with respect to the diffusion of real liquids or theelectrodiffusion of ions in solution. Knowledge about thesesystems (equations of state, etc.) is slight compared to theunderstanding of gases or liquids that approximate idealbehavior. This deficiency is a serious impediment to progressin these fields.

Ki

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j . Probably the greatest obstruction is the dependence ofdiffusion processes upon environment. Any -hange in the physi-cal or chemical nature of a diffusion system can, and fze-quently does, alter the results significantly. For example,this dependence automatically precludes the simple extension ofdilute solution theories to more realistic concentrations, andit prohibits the study of complex systems by decomposition intosimple units. Linearity does not apply except in crude appzox-imations. Honest attempts to study real problems without sim-plification are few, and many existing studies applicable todilute solutions, such as membrane potential theory, are uselessat higher concentrations. Binary diffusion, the diffusion ofone substance through another medium, is fairly easy to treatusing Fick's law on the assumption that the diffusion constantis independent of concentration. However, the addition of athird diffusing substance seriously complicates the problem byrzequiring k ~hu9i4tion of two coupled partial differentialequations' ,."~'~' subject to proper initial and boundary

-. conditions.

FACTORS IN TRANSPORT

Before continuing with a more detailed discussion of thetheories, it will be best to have some conception of the manyfactors and mechanisms involved in diffusion and membrane prob-lems. Incipient theories must either account for specifically,be independent (tacit inclusion) of, or neglect these factors.Unfortunately, since it appears impossible to include specifi-cally most of these factors, the practice is often to neglectthem, giving theories which at best axe only applicable for veryspecial cases. Although extensive, the following list of trans-port factors cannot be called complete.

1. Physical size and shape of the membrane pores and theparticles, effective surface area and thickness of the m lrane,etc. Many of these topics are discussed in Scheidegger;ionic 1 ize is discussed in a review article by Stern andAmis.

2. Relative rate of adsorption on the membrane surfaces.Most surface chemistry books devote considerable.space toadsorption phenomena and both Crank7B and Barterl" discussadsorption. The latter is the better reference for the physi-cal picture (Chapter IX), particularly for cellulose membranes.

3. Relative rate of reaction of diffusate with electrodematerials, with other species in the solution, or with the mem-brane itself. Crank discusses the mathematical aspnts of theproblem (Chapter 8) and Bird, Stewart and Lightfoot include

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it in their general equations and present a number of problems

involving diffusion with chemical reaction.

4. Concentration diffezences--a few effects of:

a. Osmotic pressures.

b. Changes in the diffusion constants,84 mobilities(especially when ions of different valence are present), adsorp-tion rates, etc.

5. Formation of complex ions.

6. Hydration:

a. Decrease in mobility n the solution and in themembrane as hydration increases.L 31,149

b. If a hydrated ion cannot physically pass throughthe membrane, en g ytu be supplied to remove the (ordered)water molecules.

7. Electronic charge of 7he ion, especially if a field ispresent. Jackson and Coriell"' indicate its importance even inthe absence of an imposed electric field; it is, of course,fundamental in electrodiffusion.

8. Magnitude of the electric current.83

9. True ion-exchange processes (generally an increase inpermeability as the exchange sites are exhausted).

10. Electric field effects.

a. Electro-osmosis.42 9183A

b. Ionic current--magnitude and direction of ionicvelocities.

11. Chemical transport by complexing with a carrier mole-cule or by coTRg jng * jh the membrane and subsequentlyredissolving. ,3 p.2A3

12. Proton-transfer processes 15B(p.57) and similar typeprocesses for hydroxyl ion.

13. Convection due to mechanical forces.

14. Temperature effects:

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a. As a first approximation, we may suppose thetemperature dependence of the diffusion constant to be of theform Agl-A~E/kT as suggested by Glasstone, Laidlex andEyng OBp.522, Experimental evidence for simple systems isS ven by Bowers and Wilson28 and Zowleski, Eyring and Reese. 75

b. Convection currents from heat due to chemicalreactions and resistance to current flow.

15. Time dependence of membrane parameters:

a. Physical clogging or chemical destruction.

b. Swelling tind degree to which it has been "wet.'120

16. Liquid Junction and phase boundary effects--barriersto flow.

17. Electrical double layers.183A

18. Mass flow of solvent:

a. Effect increases with size of solvent particles24

and is an aid to diffusion if both are in the same direction.

b. Viscosity of the fluid. 31

FORCES

In a free solution we may expect three general types offorces to contribute to the movement of ions. These are thefrictional forces resulting from contact between particles ofdifferent velocity and the chemical and electrical forcesresulting from gradients in the concentration (or chemicalpotential) and the electric potential. One of the best quali-tative discussions of the int4iplay of these forces is pre-sented in an article by Laity~z in addition to his mathematicaltreatment of the same problems. A simple example of his quali-tative reasoning which is simply a balancing of forces is givenin the following paragraph.

Consider the steady state movement of positive ions in abath of neutral solvent molecules through a thin "stagnant dif-fusion layer" to a negative (planar) electrode. At the surfaceof this electrode the ion concentration is zero as a result ofchemical removal. There are few negative ions compared to thenumber of solvent molecules, and they do not contribute to thecurrent. Consequently, they may be neglected completely. Inthe steady state there is no net movement of solvent molecules

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and since the molecules are neutral, the forces due to frictionand the concentration gradients must be equal in magnitude andopposite in direction. The force due to friction results fromthe movement of the positive ions through the solution and con-sequently this force on the molecules must be directed towardthe electrode. The balancing force due to concentration grad-ients is in the opposite direction, implying the solute is moreconcentrated near the electrode surface, and the positive ionsless concentrated. This yields immediately the Cirection offorce on the ion due to its concentration gradient. It must betoward the electzode surface, and since this is also the direc-tion of the electrical force, the frictional force must be inthe opposite direction (which is known already from Newton'sthird law) and equal in magnitude to the sum of the other twoforces.

Laity, with the aid of diagrams, applies this type ofreasoning to more complex systems to obtain similar qualitativeresults. It is an easy and valuable way of viewing problemswhich should also be applicable to phenomena such as electro-osmosis and the transport of ions ana molecules through mem-branes.

REVIEW OF THEORIES

In the following paragraphs some of the more importanttheories related to the transport of matter through membraneswill be discussed. Their order of appearance reflects a desireto index them according to both popularity and vintage, andconsequently should not serve as a basis for judgment.

A. Hydrodynamic

The extension of hydrodynamic laws--the most popularvictim appears to be Poiseuille's law--to membranes is a proce-dure which occurs far too frequently in separator studies, ascan be seen from the industrial technical reports. This exten-sion begins with a simplified model for the membrane and thepermeating substances, and the generally false hope that nothingessential has been omitted. The most common yet most unrealis-tic model assumes the membrane can be represented as a bundleof thin, cyclindrical, chemically unreactive capillary tubesand that the permeating substance may be represented as a liq-uid composed of spheroidal particles. A simple application ofPoiseuille's law to data on the rate of water flow through themembrane (with a known pressure gradient) determines the "poreradius." The pore radius value obtained in this fashion prob-ably represents the actual average physical dimensions of thepores (if they exist) to within an order of magnitude and

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perhaps much closer. The simplicity of both the mathematicsand the experimental work makes this a valuable method for ob-taining such estimates of the physical dimensions. However,the assumption, even in the most elementary cases, that onesubstance will pass through the membrane easier than another,based upon comparison of the pore size with the particle radius,is nonsense (even when the particle radius is larger than themeasured pore radius). Some surprise is justified in elemen-tary situations if the larger particles axe transferred morerapidly than the smallex, but not in the complex cases. When-ever this phenomenon occurs, it is an indication that mechan-isms other than mere physical screening are important. Foxthis reason, size measurements may be very useful. Realizationof the shortcomings of this membrane model as led to theintroduction of parameters like tortuosity9b and effectivesurface area which probably improve the accuracy of the resultssomewhat, although they cannot cover the basic faults of thisapproach.

Anothex model frequently employed assumes that themembrane can be represented as a bed of packed spheres. Foxdiscussion of the water flow through sand beds, glass beadcolumns and porous rocks resulting from "pressure gradients"this is a fairly realistic model, but its extension to othertypes of barriers and other types of driving forces (electxo-chemical gradients) is unjustified and can only lead to failure.

Fox fuxther information on membrane models and the hydro-dynamic method of analysis the best reference is The Physics ofFlow through Porous Media by Scheidegger. 14 B An example of amore detailed analysis of a specific problem is given byGoodknight, Ki koff and Fatt.5 5 More on the positive side,Solomon's work 1 4 indicates Poiseuille's law may be applied tomicroscopic capillaries, thus supporting its use in certaintypes of pxoblems. Additional xefezences are available in theAmexican Institute of Chemical Enqineers Journal.

B. Membrane Potential

Much of the literature on membranes is devoted to membxanepotentials and related topics such as Donnan equilibrium theory.The membrane potential is the voltage actoss the membtane whichoccuxs when it separates solutions of electrolytes having anyconcentration differences. The origin of the membrane potentialis attributed to differences in the rate of diffusion of ionsacross the membrane which upsets the electrical neutrality ofthe solution.

The analysis of this potential is generally based on theNernst equation (or very similar equations) with occasional use

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of the Donnan theory. Most of the work follows closely theeaxly efforts of Michaelis, Teorell, and Meyer and Sievexs,based on the theory of liquid junction potentifiR. The discus-sion of liquid juncf£n l tentials by MacInnis±20 and thearticles by Wxllie,",',' 4so containing a review of the workof MarshallI1 and Sollnez, 14 2-152 are good examples of thisapproach. Provided the membrane potentials and chemical acti-vities axe known, the determination of mobility ratios for ionsin simple systems such as NaCl solutions becomes possible.Unfortunately, in systems of more than three diffusing ions,especially if there are several (diffexent) valence magnitudes,the equations become too complex to allow any simple determina-tion of these ratios. There are also questions about thevalidity of this appxoach, especially in very strong solutions,and the drawback that mobilities are not determined underconditions of constant current.

The Meyer-Teorell-Sievers (M.T.S.) theory is the mostpopular explanation of membrane potentials, but there are

other, more sophisticated methods. Kobatak.,81 982 fox example,derives expressions for the voltage and permeation rates ofions fxom the entropy production in the membrane. A morerecent discussion of membrane potentials is given by Hills eta168 969 who reformulate, in terms of present concepts, the oldtheories of Scatchaxd and M.T.S. Additional references givenin the bibliggaphy are the articles by 1 IfIa and Staverman,

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He6h,6 Meyex,108 Nagasawa et al, 1z 'xz Sollnex etalf,±fu and Spieglex et al. 15 6

C. Reaction Rates

There axe two basic theoxies to be discussed in thissection, both developed pxincipally by Laidler and Eyxing.These are "reaction rate" theories for the diffusion of mole-cules in solution and through membranes.

Laidlex and Eyring's theory of liquid diffusion is basedon a lattice-like stxucture for the liquid, with some latticesoccupied by molecules and others vacant. Each molecule isassumed to occupy a Amall space and to interact only with itsimmediate neighboxs.A1 Diffusion then occurs by the jumpingof a molecule to a vacant site. These siteslOB p.518) axeconsidered as potential wells separated from each other by adistance x (considering here only one dixection). Then, ifthe concentration at the first site is C, at the next site inthe dixection of diffusion it is C + X(dC/dX). The number ofmolecules moving in the direction of diffusion per sq. cm. persec. is v+ = NoCkk, where No is Avogadro's number and k isthe specific rate constant for diffusion. Similaxly, fox thereverse motion we have vb = No[C + k(dC/dX)]Xk. Consequently,

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the net flow is v =-N X2k(dC/dX) which requires only a fewchanges of units to be te familiar expression of Fick's lawwith D = )'k. Further refinements of this axe discussed in

DChapter IX of The Theory of Rate Pxoceses.lOB This techniqueis developed further by Zowlanski, Eyzing and Reese,1'5 who useit to discuss membrane permeability.

In three articles, Laidler and Schulex86 -88 discuss mem-brane permeability and related problems. They start by assum-ing the solutions on each side of the membrane axe highlystirred, so that the rate determining steps are adsozption anddesorption at the membrane-solution interface and diffusionthrough the membrane. If N = the mole fraction of solute inthe solution and N' the mole fraction of the soluteadsorbed on the membrane face, then the rate of adsorption isgiven by vi0 kIN(1-N). That is, vi is propor~tional to theconcentration of solute in the solution and to the number ofsites available for molecules to be adsorbed on the membraneface. The rate of desorption is simply v_1 k_iN'. Usingsolutions to the diffusion equation by other authors, Eyringand Schuler justify the assumption that the rate of diffusioninto the sclid membrane is V k N' ,where k2 is a functionof the diffusion constant. N the rate o entry into thesolid is much greater than the rate of change of concentrationof molecules on the interface, a steady state process occurs.Hence,

klN(l - N') - k 1 N' - k2N' = 0

Solving this equation for N', the rate of entry into themembrane is found to be

v = klk2 /(k N + k1 + k2)

With this equation as a starting place, Laidler and his co-workers discuss a number of important membrane pxoblems.

Glasstone, Laidler and EyringlOB(pp "522-27) extend the"rate process" method to electrolytes, giving the followingexpressions for the conductance and the diffusion constant(for a single univalent electrolyte).

DiZiF2

Ai RT

D 2RT A+A_

F A++A._

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Some supporting experimental evidence for these equations ismentioned by these authors. These results are only applicableto "simple" electrolytes.

D. Diffusion

Use of the diffusion equation in either of its two forms,the first known widely as Pick's law, is the most commonapproach to analysis of the movement of material through mem-branes. Fick's law assumes that the rate of transfer of thediffusing substance (diffusate) through a surface of unit areais proportional to the concentration gradient; that is,

where D is the diffusion constant. A simple application of the"conservation of matter" to an infinitesimal rectangular volumeelement then gives the standard form of the diffusion equationfor isotropic media:

a-= div (D grad C)

which becomes DV2Ca t

if D is independent of concentration.7B(pp.1 -5) This form ofthe diffusion equation is stxictly applicable only to self- andbinary-diffusion situations and these must be free from theadded complication of chemical reaction and electric fieldeffects. If a diffusion system consists of (n + 1) substances,there must be a diffusion equation fox each species, and itmust contain terms to account for the pres pce of the other ncomponents. This is frequently neglecte, o The resultingsystem of equations can be summarized as 94 ,12,141

ac. m-- D '7% for i = 1,2, . . . (n+l)j=l

One of these equations, say the (n+l)st can be eliminated byconservation principles directly or by use of the equation ofcontinuity, giving a system of n coupled equations. Fox binarydiffusion, with the solute and the supporting solvent, thisreduces to the familiar diffusion equation.19 Some authorsprefer to express the interdependence by addition of extraterms representing the friction between molecules of differentspecies. These terms give the equations a strong resemblanceto the phenomenological relations of Ixreversible Thermodynamics

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(from which they probably originated). A typical exa sethis type of alteration is given by Meares and UssingT6U,8 o as:

Ja AUaCa dx A Aia (JiVigia))]aai= a

Additional modification is required if chem* al reaction occursin the system. Bird, Stewart and Lightfootig give an excellentderivation of a general diffusion equation which provides forchemical reaction and other complicating factors in Chapter 18of their text. The-moze typical treatment, discussed fully inChapter 8 of Crank " involves the simple addition of a rateterm characteristic of the chemical reaction to the xight sideof the diffusion equation. FoR. f § order immobilizingreaction, the equation become$yP • 1

ac DV72C - WC.

This type of reaction may be resRnsible for the concentrationdependence of D in some systems. 3 If chemical reaction occursonly at electrode surfaces, it may be treated as a boundarycondition fox the ordinary diffusion equation by assuming thediffusate concentration is zero at the surface.I34 The addi-tional changes required by electrical potential gradients exist-ing in electrolytic solutions will be discussed under "electro-diffusion" (section F).

It must be zemembered that diffusion constants are func-tions of concentration, temperature and physical and chemicalenvironment in general. Consequently, when the diffusionequation is applied to a system in which a membrane separatestwo "distinguishable" solutions, a separate equation must beapplied to each of the three individual xegions. The finalsolution is then obtained by matching the solutions fox eachregion to the bounday onditions such as continuity of flowand concentration.17X,14

In connection with the diffusion equation, there axe twosubjects which sometimes cause confusion. The first is purelya physical problem: that of deciding whether the transfe; ofmaterial is the result of diffusion or bulk permeation.163Unless there is a hydrostatic pressure gradient, it is fairlysafe to assume the transport is by diffusion. The second con-cerns the basic formulation of the diffusion equation. SomeauthorslB,7B,18 assume the driving forces are concentrationgradients, whie others use the gradient of the chemicalpotential.44,105,138 Even assuming that the standard relationbetween chemical potential and activity (concentration) is valid,

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D becomes a function of 67(p.138)

d loQ ad log C

Propez understanding of this problem is necessary for the studyof real systems.

One of the useful features of the diffusion equation isthe presence of the arbitrary parameter D, which is used to fitthe same equation to very different situations. This gives thediffusion equation a certain freedom (like thermodynamics) fromthe many contributing factors. The diffusion constant is gen-erally determined experimentally, and it, together with thedifferential equations and the boundary and initial conditions,characterize the (non-electrical) system entirely. Thereremains, of course, the minor problem of solving the system ofequations. Ideally, however, one would like to make the diffu-sion equation completely detexminate by evaluation of theconstant from theory. Unfortunately, even partial success inthis area has been limited to the diffusion of gases and simpleliquid systems. The best known expression of this type resultsfrom an7application of Stoke's law made by Einstein andothers, which gives:

D = RT/6TmrN

Another familiar expression for the diffusioo constant is givenby Glasstone, Laidler and EyxinglOB(pp.522-5) as

D = 2k

where

k = f(T)e€eo/kT

A basic problem in this case is knowledge of the parameter X.These expressions and seven 1 others are discussed in thereview by Johnson and Bab.'° They axe primarily useful onlyfox work with simple fluids or mixtures of such fluids. Otherexpressions axe available for moxe complex solu jons but theyaxe often unreliable and difficult to evaluate. In Chapter Xof their book, Glasstone, Laidler and EyxinglOB discuss diffu-sion in electrochemical systems and derive the diffusion con-stant fox simple electrolytes in the presence of electricfields. Another good discussion of the djffusion of chargedparticles is given by Jost.llBtpp.139-143)

There are four basic references on diffusionlB,2B,7BllBwhich--because they axe invaluable to workexs in the field--deserve discussion in this paper. The Mathematics of Diffusion

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by Crank ., as the title implies, basically a mathematics book.Crank sel.cts systems possessing initial and boundary condi-tions tha.t can be easily expressed in rectangular, cylindricalox spheqical coordinants and shows the detailed mathematicalsolution. The antithesis of this in approach is Diffusion inand through Solids, by Baxxex, which uses mathematics only toexplain physical problems. The last of the three "classic"texts is Diffusion in Solids. Liquids and Gases, by Jost. Itcovers a wider range of physical topics than either of theothers and makes greater use of mathematics than.Bax ffs text.Transpoxt Phenomena, by Bird, Stewart and Lightfoot,IL is anentirely different type of book. It is a chemical engineeringtext and as such it is oriented towards problems. However, itgives probably the finest dexivations of the general transportequations that are available in print. Mass and energy flow,diffusion, and the interplay of these three transport mechanismsaxe discussed theoretically and in the solutions to hundreds ofexample problems, making this an extremely valuable reference.

E. Non-Electrodiffusion of Ions

The diffusion of ions in the absence of an electric fieldis a problem intermediate between that of diffusion of simplefluids and that of electrodiffusion. The requirements of elec-tzoneutrality and conservation of charge often allow electxo-lytes to be treated as non-electrolytes, although with somespecial pxivileges. Many solutions, fox example, such asKCI-NaCl in water can be viewed as texnaxy diffusion systems,wherea .a IK+ move through a medium of water and chloxide

ions.9,47,±±2 However4 as the papers by Lifson and Jackson95

and Jackson and Coriell 4 illustrate, the electrical forces ofattraction and repulsion between ions or between ions and mole-cules (hydration) cannot be forgotten. These authors assume alattice-like structure for the solution with an electric poten-tial that is a periodic function of the space coordinants as aconsequence of the structure. This solution model, which isbasically a pextuxbation of the cxystal type structure (s.,...ilaxto Laidlex's model) implies too strong an influence fox theelectrical forces. The results, however, are intexesting andshould be useful qualitatively. As a consequence of the stxuc-ture, diffusing ions are subjected to a periodic potentialwhich strongly affects the observed diffusion constant. Lifsonand Jackson, using the method of Pontyagin et al, conclude, foxone dimensional problems, that the diffusion constant is alwaysless than it would be if the potential did not exist. Using adifferent, but very interesting, technique, Jackson and Coriellarrive at the same conclusion for the three dimensional case.They also find, among other conclusions of intexest, that thediffusion constant is greater for particles moving throughpotential maxima than thxough potential minima; this is

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explained qualitatively by saying the particle is less likelyto be trapped.

F. Electrodiffusion

The problem of electrodiffusion--the diffusion of ions inan electric field--has been approached in many different ways,some of which are reviewed here. The selection has been madeon the basis of usage and possible merit.

One of the earlf§t papers of note in this field was writ-ten by H. J. S. Sand and published in 1901. In this paperelectrodiffusion is treated as "ordinary diffusion" under theassumption that the changes of concentration are neutralized bythe diffusion that takes place according to Fick's law, whichis not affected by the passage of current through the liquid.The electric field effects are then included as boundary condi-tions.

A frequent assumption in many types of diffusion problemsis that the molecules or ions reach a steady velocity (as in thederivation of Stoke-Einstein relation for D) due to a balancebetween the driving forces and a resistive force which is gen-erally assumed to be proportional to the velocity. Consequently,with the neglect of the dv/dt term, the equation of motion maybe easily solved, giving the velocity proportional to thedriving force. From here it is only a short step to anexpression like J = Et±/zFR, where J is the rate of diffu-sion through a membrane.8u

The Nernst equation, either directly or in one of itsmodified forms (Henderson equation, Nernst-Planck equation,etc.), is frequently applied to electrodiffusion problems. Oneexample of this (mentioned earlier) is its use in determiningionic mobilities in membranes from the membrane potential.Another example, which is worth mention on its own merits, isfrom a paper by Davies. 39 He found experimentally that therate at which a salt passes through a phase boundary betweenliquids is proportional to (klCl - k2C2), where kl and k2 areconstants and Cl and C2 are the concentrations on the two sidesof the boundary. The basic equation used is a highly modifiedNernst equation having the form:

dE u RT dC u 0dv _U7

where v is the velocity and u the mobility of the ion in ques-tion. An interesting result is that an interface 10 Xthickcan decrease the ionic mobility by a factor of (say) I00.

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Many authors use, instead of the concentration gradients,the gradient of the chemical potential. This may be carried afurther step with the use of the electrochemical potential,44 ,105

which includes both the usual chemical potential term and a termrepresenting the electric potential. That is,44

dtie = (dlie)d =O + ZifFd cp

where the first term on the right is the non-electrical partand cp is the electric potential. It might appear in the diffu-sion equation as

J. = -DVi"

This is quite similar, when expanded, to the Nernst equationshown above, and when put in the foxm of the second diffusionequation, to the expressions used by Bak and Kauman18 in theirtreatment of electrodiffusion. A continuation of the work ofBak and Kauman, beginning with a correction of an error in theintegrated equations, is given by Scholten and Mysels.137

The field of electroanalytic chemistry contains someliterature which is applicable to electrodiffusion problems ofinterest. The articles included here for reference are byBowers et al,28,29 Delahay et al,25 ,40 ,4 1 and by Markowitz andElving.I01 Of particular interest is a paper by Bowers andWilson28 and a paper covering similar material by Delahay andMamantow.41 Bowers and Wilson discuss a situation in whichthe electrode being studied is wrapped tightly with cellophane.They make the fundamental assumption that the rate controllingstep is diffusion through the membrane. Then, the coricentra-tion of the electrolyte between the electrode and the cello-phane is zero as a result of rapid chemical removal, and isequal to "C" at all other parts of the solution exterior tothe membrane. Since

J 6C

in the membrane and i = JnFA, when a steady state isachieved, the expression (used as a boundary condition)

i nFDA( ,c=0x =O

is valid. In this case, the approximation (bC/aX)x=0 = C/lis probably quite accurate. If the factor A/1 is known, theprocedure gives a fairly easy method for evaluation of D forthe current carryiny ions in the membrane. This same type of

14

I l

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procedure should be applicable to stirred solutions (althoughl35

stirring may aiter results) separated by a membrane, the onlychange being the replacement of C by AC. Additionally, Bowersand Wilson discuss the effect of area on current, the evalua-tion of diffusion constants by the rate of approach to steadystate, and by a small-time approximation (not requiring knowl-edge of A/1), the determination of the amount of cadmiumadsorbed by the cellophane from differences between predictedand experimental results, and the temperature dependence of thediffusion constant.

Most of the present fundamental research in the field ofelect-rodiffusion is divided between three different types ofapproaches. These three axe well represented by the work of:

I Fuoss: a hydrodynamic attack based on the Navier-Stokesl83A equation, ionic size and shape, etc.

50

2. Laity: whose wcrk89 ,90 ,9l is an application of theirreversible thermodynamics of Onsager, de Groot and others(about which more will be said), and

3. Lamm: who develops the concept of friction coeffi-cients and uses them to modify the diffusion equation. Thereis also some appeal to irxevexsible thermodynamics.92 ,93 ,94

The omission of a detailed review of these theories inthis paper is not an indication that they ate insignificant;the reverse is actually true. Any individual doing researchon electtodiffusion problems should at least be familiar withthem. Unluckily, the subject of membranes is rarely introducedin this work, although Duncan's paper is an exception;electrodiffusion has enough difficulties of its own. Someother reseatchets utilizing. he approaches ate Meares andUssing,105,106 Hills et al, °,u Dunlop, Dunlop and Gosting,46

and Millet.112

G. Statistical Mechanics

,s with the current theories of electrodiffusion, littlecan be said here on the application of Statistical iechanicsapplied to diffusion and membrane transport problems. Thetheory, as might be suspected, is far better developed forgases than for even the simplest liquids. The literature onthis subject is somewhat meager, although activity is, appar-ently, increasing. Some references in the field which providehelpful bibliographies in addition to useful information arethe books by Cox6B and Prigoginel3B and the paper by Bearrman. 22

The first of these, Statistical Mechanics of irreversible Changeby R. T- ox, is an excellent little book which devotes several

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chapters to the discussion of Brownian motion and transportphenomena. The second, a recent monograph entitled "Non-Equilibrium Statistical Mechanics" by Pxigogine, takes the moremodern approach of irreversible thermodynamics. The paper byR. J. Beazman examines, from the standpoint of statisticalmechanics, the equation of Eyring, Hartly and Crank, and/orGordon, with respect to the concentration dependence of thediffusion constant in lipid solution. It gives a good pictureof the state of development of this mode of analysis. Althoughstatistical mechanics is a comparatively unpopular approach asa result of the training necessary and the mathematical barriersto rapid progress, it will probably be much more important inthe future as a result of the desire to link macroscopicphenomena with microscopic behavior.

H. Irreversible Thermodynamics

Irreversible thermodynamics in the form usually applied todiffusion ang electrodiffusion is discussed in the famous bookby de oot and in the more recent work by de Groot andMazur. Another recent and very sophisticated discussionwhich is slanted toward statistical mechanics is available inthe monograph by Prigogine.13B Applications of this subject topractical diffusion problems axe given in references mentionedin the last paragraph of the discussion of electrodiffusion(section F).

The expression

n

j=l 1 i 3

where the flows Jj ate lineatlily related to the forces Xj andthe sum is over all the species, is representative of theequations found in this formulation of flow problems. The"phenomenological coefficients" L- are symmetric; that is,Lij = n sJj i These are known aste Onsaget recipzocity rela-tions.ll In addition to being linear (and integral), equationsof this form place no unwarranted emphasis on a limited numberof flows (an advantage of Lagrange Multipliers) and 4hey atereadily susceptible to tteatment by matrix methods.A

The linear equations ate not restricted to flow ratesalone. For example, Laity uses the following expression foxthe gradient of the electrochemical potential:

-Vji = Z xik Xk(vi - vk)

k

where the r ik(= r ki) ate friction coefficients and the vi ate

16

-. - _ _ _ __ _

NOLTR 64-136

velocities. The rate of entropy production inside systems

undergoing dissipative processes is given by Millerll2 andsimilarly by de Groot88 as

AS = JiXi•

The existence of these linear relations seems to imply thatirreversible thermodynamics is applicable only to steady stateprocesses. This contention is supported by the absence of atime factor in the equations and also the proportionalitybetween velocities and forces which is reminescent of resultsof other steady state approximations. Consequently, thistheory cannot be applied to analyze the transient behavior ofsystems. This should not, however, seriously restrict its usein the study of battery type problems in which currents oftenexist for relatively long periods of time.

RESTRICTED PROBLEMS

This completes the discussion of the theoretical approachesto membrane behavior and transport problems; it certainly doesnot include all the methods of analysis, but it does cover themain categories. The remainder of the paper is devoted to morespecific topics, some theoretical and others experimental.

I. Selective Permeability

One such problem which certainly deserves study (theoret-ical and experimental) is the determination of the mechanismswhich allow a membrane to pass some ions or molecules, -vhile itpartially or completely restricts the motion of others. It isa problem which must be studied for each individual membraneand each solution (even if only the concentrations are differ-ent). Evidence for this last statement is plentiful. Forinstance, Sollner 5 -152 describes membranes which are perma-selective--they inhibit completely either the mot An of allcations or all anions. However, Kressman and Tye discussmembranes of this type but state they are completely selectiveonly in certain concentration regions. Size restrictions occurin the classic osmotic pressure and Donnan equilibrium experi-ments, but it is one of the least important factors in functionof the separator for the silver oxide-zinc battery. Thiscellophane separator apparently restricts the motion of silverions by reducing them to silver metal.1 78Rl18 1 Evidently, tihequestion of mechanism is not an easy one, and it is not surpris-ing that such studies are difficult to find in the literature.Only in a few areas are the mechanisms understood or elsereceiving proper study. These areas include the sieve type

17

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membrane which functions only by size exclusion; the perma-selective membranes whose basic mechanism is well known, andthe biological membranes which are receiving intensive study.Fox the large remainder, comparatively little is known. Onepoint seems clear, however; an adequate study of the inhibiting

2" mechanisms of a particular membrane cannot be made withoutknowledge of the exact chemical identity of the diffusingparticles. Judging from discussions with other people engagedin battery research, there seems to be considerable confusion,at least with respect to the silver-zinc battery, as to whichcomponents actually move, or can move through the cellophaneseparators. There is additional confusion about the chemicalidentity of these components in solution. Some of these ob-scure points could be removed by simple experiments. Forexample, without knowing the exact chemical identity, anestimate of the potassium mobility should be possible by radio-active labeling of one portion of the solution. This is inde-pendent of the fraction of current carried by potassium becauseordinary diffusion will occur. Whatever the choice of theisotope, it must emit gamma rays, since a and 0 particles arestopped by the solution and are consequently undetecta~le. Forpotassium, a usable isotope might be K '+ which emits 0 and p-particles and a gamma ray, with a hfJ6 life o 1.4 x I0 years.Other studies of ifs.ype using Ag and Zn~5 have been per-formed by Palagyi±Lz -Azu apparently without deleterious sideeffects, so that the technique can probably be applied to theother components.

J. Boundary Barriers

There exist, in addition to the conventional membranes andseparators, many other barriers to the flow of material such asliquid junctions, lipoid membranes, and in general any region(or boundary) in which there is a rapid change in physical orchemical properties. Lipoid, or lipid membranes, are of inter-est to biologists and will be discussed in another place.

Many older references such as MacInnis 12B discuss liquidjunctions and liquid junction potentials, although they containno satisfactory treatment of diffusion through these Jyiitions.However, a recent article by Rosano, Duby and Schulman-studies the flux of salt and water through non-aqueous liquidmembranes in a simple yet interesting way based upon the use ofpartition coefficients and the conservation of matter duringsteady state flows. Here as in many other studies the ratecontrolling step is assumed to be diffusion through the inter-face. In addition, activation energies for diffusion throughthe interface are computed, and the effects of hydration arediscussed. A far more rigorous mathematical treatment of dif-fusion through (oxacjss) interfaces is given by Scott et a1

140

and Puex and Murbach.1"

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The subject of monolayers and natuyl membranes is treatednicely in a recent article by M. Blank; it deserves to bereviewed here in some detail.

The use of Fick's law in monolayer studies is severelyquestioned by Blank on the grounds that unavoidable fluctuationsin the thickness cause variations in the diffusion constant D.These same fluctuations in the thickness or density explain whya monolayer is more permeable than a solid, even though thestate of aggregation of the molecules is much the same. Thepermeability is governed by the instantaneous arrangement, notby the average. Molecular jumps in the permeation process seemto be an all or none affair, so that fox small thicknesses suchas monolayexs a strong dependence on thickness should be ex-pected. However, with ordinary membranes the number of jumpsis large enough so that the thickness variations are not import-ant, making D constant over the surface and Fick's lawapplicable.

Blank mentions that the effect of hydration may be viewedin two ways. One viewpoint is that the rate of migrationacross the interface or boundary is retarded by the pxesence ofthe extra step involved in dehydration. The other is that therate is decreased by the presence of the potential barrier pre-sented in the dehydration process. Blank also recommends theuse of paxtition coefficients in the analysis of monolayexs andliquid membranes (see Rosanano et all3l).

The permeation of lipid monolayexs is either by dissolvingor by passage through channels (poxes), depending upon the sol-ubility of the permeate in the lipid material. The assumptionthat membrane characteristics can be approximated by monolayexproperties has led to a model of a homogeneous (lipid) membranehaving functional, or transient, poxes. This eliminates theneed for a complicated mosaic model having both lipid and poreregions for some membranes. Finally, Blank mentions that thepresence of inert substances such as water can affect thepexmeability of monolayers to gases (causing a net decrease).

K. Transport Number

Kxessman and Tye84 studied the concentration dependence ofthe transport number fox current carrying ions passing througha permaselective membrane. The startling nature of their con-clusions makes them worthy of fuxther discussion. Kressman andTye assume that under perfect conditions there is only one cur-rent caxrying ion which can pass through the membrane and thatits true transport number t is a monotonic decreasing functionf(C) = f'(C) of concentration. The symbols C and Z refer tothe concentiations of the electrolyte in the solution and in

19

NOLTh 64-136

the membrane respectively. The subscript D refers to theportion of the system donating the ion to the membrane, and thesubscript R refers to the part of the system receiving the ionfrom the membrane and the D side. As an illustration of theirreasoning, consider the case where CD < CR . This impliesCD < UR and f'(ZD) > f'(ZR). With a current passing throughthe membrane, the change in concentration of electrolyte in onesq. cm. of the membrane per sec is given by

iif (CD) f f(R)]/F

with i > 0. The inequalities imply the change must be anincrease; and furthermore, this increase only ceases when CDhas become equal to CR, at which point steady state prevails.

* Hence, in the steady state the transport number of the ion candepend only upon the concentration of the receiving side. Thisis a marked contradiction to the common assumption that thecurrent density is proportional to the concentration gradientacross the membrane.2 8 Further variations of the problem areexamined by Kzessman and Tye with similar conclusions; thetransport number depends either upon CD or CR alone or in someinstances upon the concentration value CM, fox which t is aminimum (in this case the addition of the term K'C to f'(U)allows t to have a minimum without contradiction). Experimentalevidence is included in their paper, but more work should cer-tainly be conducted along these lines.

L. Membrane Mechanism

The subject of pezmaselective or ion-selective (cation oranion) membranes has been broached in several places, butwithout explanation of exactly what they are or how they func-tion. The identifying feature of this class of membranes istheir ability to restrict the flow of cations (or anions)without causing excessive decrease in the mobility of the otherspecies. This action is accomplished by the presence of fixedcharges within the pores of the membrane. Positive (or nega-tive) charges firmly anchored within the membrane will repelthe positive (or negative) ions in the solution, thus blockingtheir movement through the pores. On the other hand, thenegative (or positive) ions in the solution are attracted bythe fixed positive (or negative) charges, and despite a tend-ency for them to blqrmljxapped, they axe able to travelthrough the poxes.± z - z

There are several possible ways to account for the fixedcharges in the membrane. Sollner, for example, assumes themembranes contain molecules which can become oriented so thatstrong polar ends are projecting into a channel. Anotherpossible mechanism is the preferential adsorption of ions on

20

... . . .. _ _ __ _ _ __ _ _ _ __ _--- ----- --- -- - - /

NOLTR 64-136

the membrane--and hence on the pore--surfaces. Of note hereis the tendency for ions in solution to attach themselves toradicals in the membrane with which they would react stronglyif the radicals were themselves free.

Industrial uses in fields like elect-rodialysisl5B,7O wereeasily found for ion-selective membranes, which may accountfor the abundance of literature material devoted to them. Somep e m " such as the work of Sollnex and Gregor142 - 52,

-,,lll±1 ,- 2 isincluded in the bibliography for thisreport; however, this represents only a small portion of theavailable reports. Further information is available in jour-nals such as J. Phys. Chem., or may be located through use ofthe Chem. Abstracts. Pexmaselective membranes are oftenlisted in these references under the name of "ion-exchangemembranes" so that some confusion may occur. The literatureon true "ion-exchange membranes," which function by the actualexchange of ions between the solution and the membrane, isalso very plentiful and easy to locate if information on themis required.

M. Charge Transfer

"Diffusion and Membrane Technology" by Tuwinezl5B presentsa fair survey of the various fields of activity, both scienti-fic and industrial, in problems jetatin to diffusion. One ofthe topics discussed by TuwinerlS BPe57 aid to a faz gzeaterextent by Glasstone, Laidler and EyringlOB pp.559-575) is theabnormal mobility of the hydronium ion (and others) inhydroxylic solvents. These ions have extremely high mobilitieswhich are attributed to transfer reaction. between the ion andthe solvent in the direction of the diffusion. Typical of thistype of process is the reaction between water and the hydroniumion which is represented as:

H H H H

, + + L1 1-4 + ++direction of diffusion -

Similar mechanisms will certainly enhance the movement ofsome ions through the pores of membranes and perhaps 3n a fewcases where the transport does not occur through physical holes.

N. Biological Problems

Throughout the body of an animal, from the surface skin tothe cell walls, the phenomenon of membrane transport is intim-ately connected with respiration, reproduction, metabolism, and

21

NOLTR 64-136

the other life processes. There is ample justification forthe deep interest biologists have in membranes, and it is notsurprising to learn that they have contributed, and are stillcontributing, much of the important research in this field.Advance in biological research is hindezed by the complexity ofand insufficient knowledge about living organisms, and often bythe necessity for experimental conditions closely approximatingthe zeal environment. However, some simplifications may resultfrom the absence of large electric potentials and by the pres-ence of large particles (cells, molecules ox ions) which axeexcluded from many membranes by physical size alone. There axe,of course, some problems studied by scientists in the biologi-cal fields that ate not seriously examined by other investiga-tors; an important example of this is Donnan equilibrium. Asthe name implies, this is an equilibrium situation; it occursin the simplest form when a membrane separates two solutionshaving a common ion free and one of which contains an ion toolarge for passage through the membrane pores. The Donnan Theoxygives a final expression fox the equilibrium concentration. Anelementa y dis ussicn of this is available in the text byClazk.4B p 15 1 Fax more advanced treatments and references toadditional literature are given in the axticles by Hill.65 ,6 6

Many biological membranes, cell walls, fox example, arecomposed of lipid materials. These fat-like substances maywell pass particles by a mechanism generally not considered foxthe mote solid, inanimate membranes. Early studies, fox example,showed that the permeability of lipid membranes to many chemi-cals increased with their solubility in the lipid substance.Further studies, however, have indicated the existence of poresin these membxanes.24 Another possibility is the combinationof the diffusate with a "carrier" in the membrane. Biologistshave, however, been forced beyond consideration of these elem-entaxy (basically physical) mechanisms. Moxe imaginativechemical schemes such as the sodium, ox xedox pump, have beenadvanced to help explain the occurrence of "active transport."This term, which will presumably disappear as understandingincreases, is used to designate situations in which the fluxpredicted by consideration of chemical and electrical gradientsis vastly different in magnitude and often direction in expex-imental situations. For instance, expeximents24 on frog skinsindicate they axe able to take in Na+ from the environmentagainst concentration gradients as great as 1000:1. Further-more, the txansfer is completely specific with xespect tosodium; there is no potassium ox calcium txansfer even thoughthe electrochemical gradients favor such motion. Experimentsalso indicate that the chloride ion transport is "passive," andthat the membrane potential developed is a direct function ofthe sodium flux. Othm instances of similar phenomena axementioned by Hartley.OV

22

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Only a few biologically oriented articles have beenreviewed fox this repoxt, and most of these come from the 1956"Discussions of the Faraday Society," Vol. 21. Much more mater-ial is available in the biological literature, especially inthe physiology journals, and if a new literature survey isdesized in the near future, this is where it should begin.

0. Measurements

The subject of measurements and measurement techniques isimportant in any field of science. This is particularly truein the study of diffusion due to the difficulties in obtainingrespectable, if not vexy accurate, results, and the confusionresulting from improper conceptions about the measured quanti-ties. The misconceptions concerning diffusion constants andthe effects of changing from one frame of reference to anothercan bI removed by consulting the xefexence books on diffusion.Crank devotes an entire chapter to "The Definition and Meas-urement of Diffusion Coefficients," while Bird, Stewart andLightfoot2B emphasize throughout their work the differencesbetween various types of diffusion constants. The formulationof the diffusion equatirn determines the type of diffusionconstant; proper measurements must then be made for D to be ameaningful quantity. The pxopex definition of the diffusionconstant is not the only source of confusion and error.Duncan44 discusses the thexmodynamic definitions of membraneelectromotive foxs and of flows of electrolytic solutes.Irani and Adanson"° study the thermodynamic complications inthe testing of existing diffusion theoxies.

General discussions of measurement techniques axe avail-able in the review ar jle by Johnson and Bab 76 and also inChapter 3 of Tuwinex. -- These references, if combined, willgive a fair picture of the methods available, but they areshort on details. Experimental determination of factors suchas porosity, poxe size, and other quantities important to thepressure flow of fluids thxough porous media is discussed byScheidegger. Fox measurements on diffusion there axe sevexaloptical techniques based on the refractive index gradients,and interference patterns resulting from concentration dif-fexences. These methods axe extrmely valuable because theypermit non-destructive measurements to be made on diffusionsystems. More detailed information on these optical techniquesis availabl in articles by Dunlop and Gostin g, 5 Kim, Pateland Kegles 9 0'Brien and Rosenfield,121 Bryngdahl andLjunggren,2 Cxeeth and Gosting,36 and Creeth.37

Additional references on measurement techniques used inspecific experiments axe, of course, available in many of thearticles listed in the bibliography. The accompanying titles

23

NOLTR 64-136

should provide some guidance in the selection of articles forthe purpose.

CONCLUDING REMARKS

The last section on measurement techniques concludes thediscussion of the literature that was reviewed for the separa-tor study. All of the articles studied for this report areincluded in the accompanying bibliography, but not all of themhave been mentioned here in previous discussions. Additionally,by aiming for a broad coverage with concentration in the moreimportant areas of research, a large amount of literature hasbeen neglected. A fair number of these articles can be foundfairly quickly, if necessary, because they belong to specificareas that for one reason or another were purposely ignored.For these topics, hopefully all included in the following list,there are many unlisted articles available in the major chemi-cal and physical chemical journals.

1. Permaselective membranes (best source, probablyJournal of Physical Chemistry.

2. Gaseous diffusion (Journal of Physical ChemistryJournal of Chemical Physics, and standard diffusion texts5 .

3. Electroanalytic chemistry (including topics such aspotentiometzy, voltametzy, etc.), Journal of ElectroanalyticalChemistry.

4. Chemical engineering articles concerning diffusionsuch as those which are generously included in the AmericanInstitute of Chemical Engineers Journal.

5. Diffusion time lag studies (Journal of PhysicalChemistry).

6. Diffusion of non-electrolytes (Journal of PhysicalChemistry, Transactions of the Faraday Society). Furthermore,neither the biological journals nor the foreign language publi-cations have been reviewed. There is ample material for acontinuation of the literature survey.

Before concluding the report, I should like to presenttwo personal ideas which might be worthy of further considera-tion; both directly concern the silver oxide-zinc battery andits cellophane separator.

One of the goals of separator research is to decrease theinternal impedance of batteries, especially those designed for

24

- - - - --- -~ ____ _----- /

NOLTR 64-136

high current operations. Cellophane, which is the most success-ful known separator material for AgO-Zn batteries, apparentlyowes its effectiveness to chemical reactiq--its ability toreduce silver ions to neutral molecules. i8R,.81R Hence, apossible means for increasing the permeability of the cello-phane to the current carriers without destroying its effective-ness as a separator is by increasing the size of the pores.Craig and Konigsbuxg34 found that cellophane would not returnto its original size after being stretched; and by their esti-mation a 20% increase in pore size could be produced. Theirexperiments showed the time required for 50% of one diffusate(ribonuclease) to pass through the membrane could be reducedfrom 6.6 hours to 0.9 hour. Unfortunately, only high molecularweight organic substances were used in the experiments. Sincethe physical stretching decreases both the thickness and thedensity per unit area, it may be necessary to use an additionallayer of cellophane to provide the same effectiveness as aseparator. This addition will decrease the permeability ofthe separator, but Poiseuille's law--although not applicable toflux of material through cellophane--indicates that there shouldstill be a net gain in permeability. The actual dependence ofthe flow rate upon thickness and pore size should be (at least)somewhat similar to the (pore xadius)4/length dependence pre-dicted by Poiseuille's law. That is, the size of the physicalopenings should be fax more important than the thickness foxchanging the permeability.

Blocking the movement of silver ions is ostensibly themajor function of the separator in the Ago-Zn battery. Althoughthis is accomplished effectively by cellophane, it is desirableto have a separator that degrades less rapidly in concentratedKOH solutions. Many of the attempts to develop new membranesresistant to chemical attack are centered around modifyingcellophane to reduce the degradation, or trying other materialswhich axe chemically similar to cellophane. As an alternateprocedure, it might be possible to introduce, either into theKOH solution or between the separators, a chemical substancewhich will either combine with the silver ion complex to changethe sign (and probably magnitude) of its valence, or to tie upthe silver ion complex so that it is unable to pass through theseparator.

25

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BIBLIOGRAPHY

Books

(iB) BARRER: Diffusion in an Through Solids (1941).

* (2B) BIRD, STEWART & LIGHTFOOT: Transport Phenomena (1960).

(3B) BOCKRIS: Modern Aspects of Electrochemistry (1954).

(4B) CLARK: Topics in Physical Chemistry (1948).

(5B) CLARKE, (ed): Ion Transport Across Membranes (1954).

(6B) COX: Statistical Mechanics of Irreversible Change (1955).

(7B) CRANK: Mathematics of Diffusion (1956).

(8B) de GROOT: Thermodynamics of Irzever-sible Processes (1951).

(9B) de GROOT & MAZUR: Non-Equilibrium Thermodynamics (1962).

(lOB) GLASSTONE, LAIDLER & EYRING: Theory of Rate Processes(1941).

(1IB) JOST: Diffusion in Solids, Liquids and Gases (1952).

(12B) MacINNES: The Principles of Physical Chemistry (1939).

(13B) PRIGOGINE: Non-Equilibrium Statistical Mechanics (1962).

(14B) SCHEIDEGGER: The Physics of Flow Through Porous Media(1960).

(15B) TlWINER: Diffusion and Membrane Technology (1962).

Journals

(16) ADAMSON: "The Diffusion and Self-Diffusion of Electro-lytes and Hydration Effects," j. Phys. Chem. 58, 514 (1954).

(17) AUER & MURBACH: "Diffusion Across an Interface," J. Chem.Phys. 22, 1054 (1954).

(18) BAK & KAJMAN: "Theory of Electzodiffusion," Trans.Faraday Soc. 55, 1109 (1959).

(19) BALDWIN, DUNLOP & GOSTING: "Interacting Flows in LiquidDiffusion: Equations for Evaluation of the Diffusion Coef-ficients from Moments of the Refractive Index," J. Am.Chem. Soc. 77, 5235 (1955).

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(20) BABRER: "Some Properties of Diffusion Coefficients inPolymers," J. Phys. Chem. 61, 178 (1957).

(21) BARRER, BARIE & SLATER: "Comparison of Ethyl Celluloseand Rubber as Diffusion and Sorption Media," Txans.Faraday Soc. 53, 1145 (1957).

(22) BEARMAN: "On the Molecular Basis of Some Current Theoriesof Diffusion," J. Phys. Chem. 65, 1961 (1961).

(23) BERGSMA & STAVERA .N: "Bi-lonic Potentials," DiscussionsFaraday Soc. 21, 61 (1956).

(24) BERLINER: "Membrane Transpozt," Rev. Mod. Phys. 31, 342(1959).

(25) BERZINS & DELAHAY: "Theory of Electrolysis at ConstantCuxrent in Unstizred Solution. II. Consecutive Electro-chemical Reactions," J. Am. Chem. Soc. 75, 4205 (1954).

(26) BIEBER, BRUINS & GREGOR: "Silver Peroxide-Zinc AlkalineCells: Polymeric Membrane Separators," Id. Eng. Chem.50, 1273 (1958).

(27) BLANK: "Monolayer Permeability and Properties of NaturalMembranes," J. Phys. Chem. 66, 1911 (1962).

(28) BOWERS & WILSON: "Voltametric Membrane Electrodes I:Basic Theory and Characteristics of Thallous and CadmiumReduction," J. Am. Chem. Soc. 80, 2968 (1958).

(29) BOWERS et al: "Voltametric Membrane Electrodes III: Con-trolled Current Voitammetry," J. Phys. Chem. 65, 672 (1961).

(30) BOWYER & WIDDAS: "The Facilitated Transfer of Glucose andRelated Compounds Across the Erythrocyte Membrane," Dis-cussions Faraday Soc. 21, 251 (1956).

(31) BRUSH: "Theories of Liquid Viscosity," Chem. Rev. 62, 513(1962).

(32) BRYNGDAHL & LJUNGGREN: "A New Refractive Index GradientRecording Intezferometer Suitable foz Studying Diffusion,Electrophozesis and Sedimentation," J. Phys. Chem. 64,1264 (1960).

(33) CLARKE et al: "Electrochemical Properties of a PezmionicAnion Membrane," J. Phys. Chem. 56, 100 (1952).

(34) CRAIG & KONIGSBURG: "Dialysis Studies III: Modificationof Pore Size and Shape in Cellophane Membranes," J. Phys.Chem. 65, 166 (1961).

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(35) CRANK: "Diffusion with Immobilizing Reaction," Trans.Faraday Soc. 53, 1147 (1957).

(36) CREETH & GOSTING: "Studies of Free Diffusion in Liquidswith the Rayleigh Method. II. An Analysis for SystemsContaining Two Solutes," J. Phys. Chem. 62, 58 (1958).

(37) CREETH: "Studies of Free Diffusion on Liquids with theRayleigh Method. III. The Analysis of Known Mixtures andSome Preliminary Investigations with Proteins," J. Phys.Chem. 62, 66 (1958).

(38) DALTON, McCLANAHAN & MAATMAN: "Partial Exclusion ofElectrolytes from Pores of Silica Gel," J. Colloid. Sci17t 207 (1962).

(39) DAVIES: "The Mechanism of Diffusion of Ions Across aPhase Boundary and Through Cell Walls," J. Phys. Colloid.Chem. 54, 185 (1950).

(40) DELAHAY, BEREINS et al: "Theory of Electrolysis atConstant Current with Partial or Total Control by Diffusion--Application to the Study of Complex Ions," J. Am. Chem.Soc. 75, 2486 (1954).

(41) DELAHAY & MAMANTOV: "Voltametry at Constant CurrentReview of Theoretical Principles)," Anal. Chem. 27, 4781955).

(42) DESPIC & HILLS: "Electro-osmosis in Charged Membranes:The Determination of Pzimary Solvation Numbers," Discus-

* sions Faraday Soc. 21, 150 (1956).

(43) DIBENEDETTO & LIGHTFOOT: "The Separation of Ions withPermselective Membranes," A.I.Ch.E.J. 8, 79 (1962).

(44) DUNCAN: "Ion Transport Across Membranes I: Definition ofMembrane Electromotive Forces and of Flows of ElectrolyticSolutes," J. Res. Natl. Bur. Std. (U.S.) 66A, 83 (1962).

(45) DUNLOP & GOSTING: "Interacting Flows in Liquid Diffu-sion: Expressions for the Solute Concentration Curves inFree Diffusion and Their Use in Interpreting Gouy Diffu-someter Data fox Aqueous Three-Component Systems," J. Am.Chem. Soc. 77, 5238 (1955).

(46) DUNLOP & GOSTING: "Use of Diffusion and ThermodynamicData to Test the Onsager Reciprocal Relations for Iso-thermal Diffusion in the System NaCl-KC1-H20 at 250C,"J. Phys. Chem. 63, 86 (1959).

28

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(47) DUNLOP: "'Data for Diffusion in a Concentrated Solution ofthe System NaC1-KCl-H20 at 250 C. A Test of the OnsagezReciprocal Relation for this Composition," J. Phys. Chem.63, 612 (1959).

(48) ELEY & HEDGE: "The Structure of Films of Proteins Adsorbedon Lipids," Discussions Faraday Soc. 21, 221 (1956).

(49) FRILLETTE; "Electro-gzavitational Transport at SyntheticIon Exchange Membrane Surfaces," J. Phys. Chem. 61, 168(1957).

(50) FUOSS: "The Velocity Field in Electrolytic Solutions,"J. Phys. Chem. 63, 633 (1959),

(51) GOODKNIGHT, KILKOFF & FATT: "The Diffusion Time-Lay inPorous Media with Dead-End Pore Volume," J. Phys. Chem. 65,1709 (1961).

(52) GOTTLIEB, NEIHOF & SOLINER: "Pzeparation and Propertiesof Strong Base Type Collodion Matrix Membranes," J. Phys.Chem. 61, 154 (1957).

(53) GRAYDON & STEWART: "Ion-Exchange Membranes. I. MembranePotentials," J. Phys. Chem. 59, 86 (1950).

(54) GREGOK & SOLINEh" "Improved Methods of Preparation ofPezmselective Collodion Membranes Combining Extreme IonicSelectivity with High Permeability," J. Phys. Chem. 50,53 (1946).

(55) GREGOR & SOLINER: "Improved Methods for Preparation ofElectropositive 'Pexmaselective' Protamine Membranes," J.Phys. Chem. 50, 88 (1946).

(56) GREGOR & WETSTONE: "Specific Transport Across Sulphonicand Carboxylic Intexpolymer Cation-Selective Membranes,"Discussions Faraday Soc. 21, 162 (1956).

(57) GREGOR & WETSTONE: "Interpolymer ion-Selective Membranes.II. Preparation and Characterization of PolycarboxylicAcid-Dynel Membranes," J. Phys. Chem. 61, 147 (1957).

(58) GRUN & HAEFELFINGER:, "Diffusion in Rubber: Investigationson Diffusion of Substances of Medium Molecular Weight,"Trans. Faraday Soc. 53, 1145 (1957).

(59) HARNED: "Some Recent Experimental Studies of Diffusion inLiquid System," Discussions Faraday Soc. 24, 7 (1956).

29

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(60) HARTLEY: "Theoretical Considexation of UnsymmetricalSystems," Trans. Faraday Soc. 53, 1148 (1957).

(61) HELFFERICH: "Bi-lonic Potentials," Discussions FaradaySoc. 21, 83 (1956).

(62) HELFFERICH & PLESSET: "Ion Exchange Kinetics. A NonlinearDiffusion Problem," J. Chem. Phys. 28, 418 (1958).

(63) HELFFERICH & FRPAKLIN: "Ion Exchange Kinetics. A Nonlin-ear Diffusion Problem II. Particle Diffusion ControlledExchange of Univalent and Bivalent Ions," J. Chem. Phys.2, 1064 (1958).

(64) HILL: "Surface Diffusion and Thermal Transpiration inFine Tubes and Pores." J. Chem. Phys. 25, 730 (1956).

(65) HILL: "Electrolyte Theory and the Donnan Membrane Equili-bzium," J. Phys. Chem. 61, 548 (1957).

(66) HILL: "On the Theory of Donnan Membrane Equilibrium,"Discussions Faraday Soc. 21, 31 (1956).

(67) HILL et al: (No title)--Genexal Discussion on LecturePapers. Discussions Faraday Soc. 21, 117 (1956).

(68) HILLS et al: "Membrane Potentials: I. The Theory of thee.m.f. of Cells Containing Ion-Exchange Membranes," Proc.Royal Soc. 262, 246 (1961).

(69) HILLS et al: "Membrane Potentials II: The Measurement ofthe e.m.f. of Cells Containing the Cation-Exchange Mem-brane, Cross-linked Polymethacrylic Acid," Proc. Royal Soc.262A, 257 (1961).

(70) HOCH & WILLIAMS: "Dialysis as an Analytical Tool," Anal.Chem. 30, 1258 (1958).

(71) HOCH & TURNER: "Method for Obtaining a CharacteristicPermeation Function fox Membranes," Anal. Chem. 33, 1450(1961).

(72) HUTCHINGS & WILLIAMS: "Some Uses of Ion-Exchange MembraneElectrodes," Discussions Faraday Soc. 21, 192 (1956).

(73) IRANI & ADAMSON: "Transport Processes in Liquid SystemsIII. Thermodynamic Complications in the Testing of Exist-ing Diffusional Theories," J. Phys. Chem. 64, 199 (1960).

(74) JACKSON & CORIELL: "Effective Diffusion Constant in aPolyelectzolyte Solution," J. Chem. Phys. 38, 959 (1963).

30

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(75) JACOBS et al: (No title) General discussion of lectures.Discussions Faraday Soc. 21, 198 (1956).

(76) JOHNSON & BAB: "Liquid Diffusion of Non-Electrolytes,"Chem. Rev. 56, 387 ?1958).

(77) JOST & OEL: "Diffusion in a System Consisting of Morethan One Phase," Trans. Faraday Soc. 53, 1147 (1957).

(78) KEYNES & ADRIAN: "The Ionic Selectivity of Nerve andMuscle Membranes," Discussions Faraday Soc. 21, 265 (1956).

(79) KIM, PATEL & KEGELES: "Interference Optical Studies ofRestricted Diffusion," J. Phys. Chem. 66, 1960 (1962).

(80) KITTELBERGER: "Diffusion of Electrolytes through OrganicMembranes," J. Phys. Colloid. Chem. 53, 393 (1949).

(81) KOBATAKE: "Irzeversible Electrochemical Processes ofMembranes I," J. Chem. Phys. 28, 146 (1958).

(82) KOBATAKE: "Irreversible Electrochemical Processes inMembranes II. Effects of Solvent Flow," J. Chem. Phys.28, 442 (1958).

(83) KRESSMAN & TYE: "The Effect of Current Density on theTransport of Ions Through Ion-Selective Membranes,"Discussions Faraday Soc. 21, 185 (1956).

(84) KRESSMAN4 & TYE: "The Effect of Concentration on theTransport of Ions through Ion-Selective Membranes," Trans.Faraday Soc. 55, 1441 (1959).

(85) LAGOS & KITCHENER: "Diffusion in PolystyzenesulphonicAcid Ion-Exchange Resins," Trans. Faraday Soc. 56, 1245(1960).

(86) LAIDLER & SCHULER: "The Kinetics of Membrane Processes.I. The Mechanism and Kinetic Laws for Diffusion throughMembranes," J. Chem. Phys. 17, 851 (1949).

(87) LAIDLER & SCHULER: "The Kinetics of Membrane Processes II.Theoretical Pressure-Time Relationships for PermeableMembranes," J. Chem. Phys. 17, 857 (1949).

(88) LAIDLER & SCHULER: "The Kinetics of Membrane ProcessesIII. The Diffusion of Vaxious Non-Electrolytes throughColloiden Membranes," J. Chem. Phys. 17, 860 (1949).

(89) LAITY: "An Application of Irreversible Thermodynamics

to the Study of Diffusion," J. Phys. Chem. 63, 80 (1959).

31

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(90) LAITY: "General Approach to the Study of ElectricalConductance and its Relation to Mass Transport Phenomena,"J. Chem. Phys. 30, 682 (1959).

(91) LAITY: "Diffusion of Ions in an Electric Field," J. Phys.Chem. 67, 671 (1963).

(92) LAMM: "On a Generalization in the Diffusion Theory," J.Phys. Colloid. Chem. 51, 1063 (1947).

(93) LAMM: "The Diffusion of an Electrolyte Solution in aSuperimposed Electric Field," Acta Chemica Scand. 10, 1132(1956).

(94) LAMM: "An Analysis of the Dynamical Equations of ThreeComponent Diffusion for the Determination of FrictionCoefficients I," J. Phys. Chem. 61, 948 (1957).

(95) LIFSON & JACKSON: "On the Self-Diffusion of Ions in aPolyelectxolyte Solution," J. Chem. Phys. 36, 2410 (1962).

(96) LONGSWOTH: "Diffusion in the Watez-Methanol System andthe Walden Product," J. Phys. Chem. 67, 689 (1963).

(97) LORIMER, BOTERENBROOD & HERMANS: "Transport Processes inIon-Selective Membranes (Conductivities, Transport Numbc.sand Electromotive Fozces)," Discussions Faraday Soc. _i,141 (1956).

(98) MACKAY: "The Tortuosity Factor of a Watez-Swollen Mem-brane," J. Phys. Chem. 64, 1718 (1960).

(99) MACKIE & MEARES: "The Soxption and Diffusion of Ethanolin a Cation Exchange Resin Membrane," Discussions FaradaySoc. 21, 111 (1956).

(100) MANECKE & HELLER: "Simultaneous Diffusion of Electrolytesand Non-Electrolytes through Ion-Exchange Membxanes,"Discussions Faraday Soc. 21, 101 (1956).

(101) MARKOWITZ & ELVING: "The Polaxographic Diffusion Current,"Chem. Rev. 58, 1047 (1958).

(102) MARSHALL: "The Electrochemical Properties of MineralMembranes VIII. Theory of Selective Membxane Behaviox,"J. Phys. Chem. 52, 1284 (1948).

(103) McGREGOR & MAHAJAN: "Permeation of Dyes through PolymerFilms," Trans. Faraday Soc. 58, 2484 (1962).

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(104) McKELVEY, SPIEGLER & WYLLIE: "Measurement of Ion andWater Transport Across Membranes," J. Electxochem. Soc.104, 387 (1957).

(105) MEARES & USSING: "The Fluxes of Sodium and Chloride ionsAcross a Cation-Exchange Resin Membrane," Trans. FaradaySoc. 55, 142 (1959).

(106) MEARES & USSING: "The Fluxes of Sodium and Chloride IonsAcross a Cation-Exchange Membrane," Trans. Faraday Soc.55, 244 (1959).

(107) MEARES: "The Permeation of Allyl Chloride Vapor throughPolyvinyl Acetate Membranes," Trans. Faraday Soc. 53, 1148(1957).

(108) MEYER: "The Origin of Bioelectric Phenomena," Trans.Faraday Soc. 33, 1049 (1937).

(109) MEYER: "Artificial Membranes: Their Structure andPermeability," Trans. Faraday Soc. 33, 1073 (1937).

(110) MICHAELI & KEDEM: "Description of the Transport ofSolvent and Ions through Membranes in Terms of DifferentialCoefficients," Trans. Faraday Soc. 57, 1185 (1961).

(111) MILLINGTON & QUIRK: "Permeability of Porous Solids,"Trans. Faraday Soc. 57, 1200 (1961).

(112) MILLER: "Ternary Diffusion and the Validity of theOnsager Reciprocity Relations," J. Phys. Chem. 63, 570(1959).

(113) MITCHELL & MOYLE: "Permeation Mechanisms in BacterialMembranes," Discussions Faraday Soc. 21, 258 (1956).

(114) MUKHERJEE & MARSHALL: "The Electrochemical Properties ofMineral Membranes IX," J. Phys. Colloid. Chem. 55, 61 (1950).

(115) NAGASAWA & KABATAKE: "The Theory of Membrane Potential,"J. Phys. Chem. 56, 1017 (1952).

(116) NAGASAWA & KAGAWA: "Membrane Potentials of an Ion-ExchangeMembzane," Discussions Faraday Soc. 21, 52 (1956).

(117) NEIHOF & SOLLNER: "A Quantitative Electrochemical Theoryof the Electrolyte Permeability of Mosaic Membranes Com-posed of Selectively Anion-Permeable and SelectivelyCation-Permeable Parts and its Experimental Verification,"J. Phys. Colloid. Chem. 54, 157 (1950).

33

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(118) NEIHOF & SOLLNER: "The Physical Chemistry of the Differ-ential Rates of Permeation of Ions across Porous Membranes,"Discussions Faraday Soc. 21, 94 (1956).

(119) NEIHOF & SOLLNER: "The Transitory Overshooting of FinalEquilibrium Concentrations in Membrane Systems which Drifttoward the Gibbs-Donnan Membrane Equilibrium," j. Phys.Chem. §1, 159 (1957).

(120) NEWNS: "The Sorption and Desorption Kinetics of Water ina Regenerated Cellulose," Trans. Faraday Soc. 53, 1150(1957).

(121) O'BRIEN & ROSENFIELD: "An Interfezometric Determinationof Diffusion Constants of Copper (II) Ions in Copper (II)Sulfate Solution," J. Phys. Chem. 67, 643 (1963).

(122) PALAGYI: "Investigations on the Silvez-Zinc AlkalineStorage Battery by the Aid of Radioactive Isotopes," J.Electzochem. Soc. 106, 846 (1958).

(123) PALAGYI: "Investigations on the Silver-Zinc StorageBattery with Radioactive Zn65 Isotope," J. Electrcchem.Soc. 108, 201 (1961).

(124) PALAGYI: "Investigations on the Silvez-Zinc StorageBattery with Radioactive AgII Isotope," J. Electrochem.Soc. 108, 904 (1961).

(125) PALAGYI: "Experiences Obtained While Stoxing Silver-ZincStorage Cells using Zn65 and Agll," Acta Chim, Acad. Sci.Hung. 1, 473 (1962).

(126) PARK: "A Radioactive Study of Two Stage Diffusion in theAcetone and Cellulose Acetate System," Trans. Faraday Soc.53, 1149 (1957).

(127) PEARSON & MUNSON: "The Determination of Ionic MobilitiesDirectly from Resistance Measurements," J. Phys. Chem. 65,897 (1961).

(128) PETERSON & GREGOR: "Diffusion-Exchange of Exchange Ionsand Nonexchange Electrolyte on Ion-Exchan ge MembraneSystems," J. Electrochem. Soc. 106, 1051 (1959).

(129) RENKEN: "Filtration, Diffusion, and Molecular Sievingthrough Porous Cellophane Membranes," J. Gen. Physiology38, 225 (1954-55).

(130) RIDEAL: "Factors in Membrane Permeability," Trans.Faraday Soc. 33, 1081 (1937).

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(131) ROSANO, DUBY & SCHULMAN: "Mechanism of the SelectiveFlux of Salts and H20 Migration through Non-Aqueous LiquidMembranes," J. Phys. Chem. 65, 1704 (1961).

(132) ROTHSTEIN: "Compaxtmentization of the Cell Surface ofYeast in Relation to Metabolic Activities," DiscussionsFaraday Soc. 21, 229 (1956).

(133) ROUGHTEN: "Diffusion through Membranes Followed byDiffusion with Rapid Irreversible Immobilization inanother Medium," Trans. Faraday Soc. 56, 1085 (1960).

(134) SAND: "On the Concentration at the Electrodes in Solu-tion with Specific Reference to the Liberation of Hydrogenby Electrolysis of a Mixture of Copper Sulphate andSulphuric Acid," Phil. Mag. 1, 45 (1901).

(135) SCATCHARD & HELFFERICH, "The Effect of Stirring on Cellswith Cation Exchange Membranes," Discussions Faraday Soc.21, 70 (1956).

(136) SCHOLTEN & MYSELS: "Random Walk Theory of Electrodiffu-sion," Trans. Faraday Soc. 56, 994 (1960).

(137) SCHOLTEN & MYSELS: "Macroscopic Theory of Electrodiffu-sion," Trans. Faraday Soc. 57, 764 (1961).

(138) SCHLOGEL: "The Significance of Convection in TransportProcesses across Porous Membranes," Discussion FaradaySoc. 21, 46 (1956).

(139) SCHULMAN et al: (No title. General discussion of lec-tures), Discussions Faraday Soc. 21, 272 (1956).

(140) SCOTT, TING & DRICKHAMMER: "Diffusion through an Inter-face," J. Chem. Phys. 19, 1075 (1951).

(141) SCHUCK & TOOR: "Diffusion in a Three Component LiquidSystem," J. Phys. Chem. 67, 540 (1963).

(142) SOLLNER: "A New Potentiometric Method to Determine Cationsand Anions with Colloiden and Protamine-Collodion 'Membrane'Electrodes," J. Am. Chem. Soc. 65, 2260 (1943).

(143) SOLLNER & GREGOR: "Membrane Equilibria which Involve onlythe Ions of Strong Inorganic Electrolytes," J. Am. Chem.Soc. 67, 346 (1945).

(144) SOLLNER: "The Physical Chemistry of Membranes withParticular Reference to the Electrical Behavior of Mer-banes of Porous Characte~r I," J. Phys. Chem. 49, 47 1945).

35

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(145) SOLLNER: "The Physical Chemistry of Membranes withParticular Reference to the Electrical Behavior ofMembranes of Porous Character II," J. Phys. Chem. 499 171(1945).

(146) SOLLNER: "The Physical Chemistry of Membranes withParticular Reference to the Electrical Behavior ofMembranes of Porous Character III," J. Phys. Chem. 49, 265(1945).

(147) SOLLNER & GREGOR: "The Electrochemistry of PermaselectiveCollodion Membranes I," J. Phys. Chem. 50, 470 (1946).

(148) SOLLNER & GREGOR: "The Electrochemistry of PermaselectiveCollodion Membranes II," J. Phys. Chem. 51, 299 (1947).

(149) SOLLNER: "The Origin of Bi-lonic Potentials across PorousMembranes of High Ionic Selectivity I," J. Phys. Colloid.Chem. 53, 1211 (1949).

(150) SOLLNER: "The Origin of Bi-lonic Potentials across PorousMembranes of High Ionic Selectivity II," J. Phys. Colloid.Chem. 53, 1226 (1949).

(151) SOLLNER & GREGOR: "The Electrochemistry of PermaselectiveProtamine Collodion Membranes. I," J. Phys. Colloid. Chem.54, 825 (1950).

(152) SOLLNER & GREGOR: "The Electrochemistry of PermaselectiveProtamine Collodion Membranes II," J. Phys. Colloid. Chem.54, 330 (1950).

(153) SOLOMON & GOLD: "Potassium Transport in the Human Eryth-rocytes: Evidence for a Three-Compartment System," J. Gen.Physiology .8, 371 (1954-55).

(154) SOLOMON: "Pores in the Cell Membrane," Sci. American 203#6 (1960).

(155) SPIEGLER: "On the Electrochemistry of Ion-ExchangeResins--A Review of Recent Work," J. Electrochem. Soc. 100,303C (1953).

(156) SPIEGLER, YOEST & WYLLIE: "Electrical Potentials acrossPorous Plugs and Membranes," Discussions Faraday Soc. 21,,174 (1956).

(157) SPIRO: "The Interpretation of the E.M.F.'s of Cells withTransference," Trans. Faraday Soc. 55, 1207 (1959).

36

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(158) STEIN & DANIELLI: "Structure and Function in Red CellPermeability," Discussions Faraday Soc. 21, 238 (1956).

(159) STERN & AMIS: "Ionic Size," Chem. Rev. 59- 1 (1959).

(160) STEWARD & GRAYDON: "Ion-Exchange Membranes. III. WatezTransfer," J. Phys. Chem. 61, 164 (1957).

(161) STIGTER & HILL: "Theory of the Donnan Membrane EquilibriumII: Calculation of the Osmotic Pressure and of the SaltDistribution in a Donnan System with Highly Charged ColloidParticles," J. Phys. Chem. 63, 551 (1959).

(162) TEORELL: "Transport Phenomena in Membranes," (EighthSpiers Memorial Lecture), Discussions Faraday Soc. 21, 9(1956).

(163) TICKNOR: "On the Permeation of Cellophane Membranes byDiffusion," J. Phys. Chem. 62, 1483 (1958).

(164) TOOR: "Diffusion Measurement with a Diaphragm Cell,"J. Phys. Chem. 64, 1580 (1960).

(165) WANG: "Effect of Ions on the Self-Diffusion and Structureof Water in Aqueous Electrolytic Solutions," J. Phys. Chem.58, 686 (1954).

(166) WETSTONE & GREGOR: "InterpolymeX Ion-Selective MembranesIII. Preparation and Characterization of QuaternaryAmmonium-Dynel Anion-Selective Membranes," J. Phys. Chem.6k19 151 (1957).

(167) WILKINS & LONG: "A Free Volume Model for Diffusion ofSmall Molecules in Polymers," Txans. Faraday Soc. 53, 1146(1957).

(168) WILLS & LIGHTFOOT: "Membrane Selectivity," A.I.Ch.E.J. 7,273 (1961).

(169) WRIGHT: "Membrane Potentials fox Keratin and Cellophaneand the Meyer-Teorell Theory," J. Phys. Chem. 58, 50 (1954).

(170) WYATT: "A Possible Conductance Contribution in Dissociat-ing Systems," Trans. Faraday Soc. 57, 773 (1961).

(171) WYLLIE & PATNODE: "The Development of Membranes Preparedfrom Artificial Cation-Exchange Materials with ParticularReference to the Determination of Sodium-Ion Activities,"J. Phys. Colloid. Chem. 54, 204 (1950).

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(172) WYLLIE: "Ion-Exchange Membranes I--Equations for theMulti-Ionic Potential," J. Phys. Chem. 58, 67 (1954).

(173) WYLLIE & KANAAN: "Ion-Exchange Membranes. II. MembraneProperties in Relation to Bi-Ionic Potentials in MonovalentIon Systems," J. Phys. Chem. 58, 73 (1954).

(174) YANG & SIMJAD: "Diffusion of Ions in a Molten Electrolyteunder the Influence of an Electric Field," J. Chem. Phys.23, 1295 (1955).

(175) ZOWLESKI, EYRING & REESE: "Diffusion and Membrane Per-

meability," J. Phys. Colloid. Chem. 53, 1426 (1949).

Miscellaneous Reports

(176R) DIRKSE & LUGT: "Silver Migration and Transport MechanismStudies in Silver Oxide-Zinc Batteries," Contract AF 33(657)-8689; Fourth Report from Calvin College (1963).

(177R) GARVIN et al: "Alkaline Battery Separator Study,"Second Quarterly Report from the Carl F. Norbexg ResearchCentex (1963).

(178R) GREGOR et al: "A Study of the Application of IonExchange to Electric Batteries," Contract NObs-62383;Index #N.S.-677-095. Final Report from the PolytechnicInstitute of Brooklyn (1954).

(179R) MELTZER: "Alkaline Battery Separator Study," ContractNAS-5-2860. First Quarterly Report from the Carl F.Noxberg Research Centex (1962).

(180R) MENDELSOHN: "Separator for Alkaline Batteries," U. S.Patent #2,858,353 (1958).

(181R) MENDELSOHN: "Separator fox Electric Battery," U. S.Patent #2,915,579 (1959).

(182R) OBERHOLZER: "Alkaline Battery Separator Study," ContractNAS-5-2860. Third and Fourth Quarterly Reports from theCarl F. Notberg Research Centex. (1963)

Additional Bibliography

(183A) DRESNER: "Electrokinetic Phenomena in Charged Microcap-illaries," J. Phys. Chem. 67, 1635 (1963).

38

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APPENDIX I

List of Symbols

I. A surface area

2. a activity coefficient

3. C concentration

4. D diffusion coefficient (constant)

5. Dij diffusion coefficient in an n-component system

6. E electric field

7. F Faraday's constant

8. f(C) concentration dependence of the transport number infree solution

9. f'(Z) concentration dependence of the transport number inthe membrane

10. gi frictional force between the ith and the ath com-a ponent

11. i electric current

12. J flux of diffusate per unit area per second

13. K' proportionality constant

14. k rate constant or specific rate constant

15. Lij phenomenological coefficient

16. 1 membrane thickness

17. No Avogadro's number

18. N mole fraction

19. N' mole fraction on the membrane surface

20. n number of moles

21. R gas constant

39

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22. z particle radius

23. rij friction coefficient

24. LS rate of production of entropy per second

25. T temperature

26. t time

27. ti transport number

28. u mobility

29. V, molar volume

30. vi velocity of the particles of the ith species

31. X jth force

32. X distance coordinant

33. Z valence (number of electron charges)

34. n viscosity

35. A conductance

36. x distance between potential minima

37. 4i chemical potential

38. p electric potential

39. V2 the Laplacian

40

'1 /"

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DOCUMENT CONTROL DATA - R&D(Security classification of title, body of abstract and tridexm annotatton must be entered when the overall report is classified)

I OqIGINATIN G ACTIV!'Y (Corporal* uthot) 2s RCPORT SECURITY C LASSIICAOTION

U. S. Naval Ordnance Laboratory UNCLASSIFIEDWhite Oak, Silver Spring, Maryland 2b GROUP

3 REPORT TITLE

Battery Separator Mechanisms - Literature Survey Report

4 DESCRIPTIVE NOTES (Type of report and inclusive dates)

S AUTHOR(S) (Last name. first name. initial)

McClure, Charles F.

6 REPORT DATE70TOANOO AE 7bOOFRS

26 September 1966 40 18328 CONTRACT OR GRANT NO 9. ORIGINATOR'S REPORT NU.*BER(S)

RUTO 3E000/212b PROJECT NO. NOLTR 64-136

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13 ABSTRACT

In order to improve the characteristics of batteries,an understanding of battery separators and how they caninhibit the motion of ions and molecules is desired. Thisreport reviews some of the theories invented to explairthe transport of material through solutions and barriers.

DD FOR* 47D D. IJAN6 1473 UNCLASSIFIEDsecurity Classification

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Separator IMembraneSilver-zinc Battery

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summary of the document indicative of the report, even though7a. TOTAL NUM13ER OF PAGES. The total page count it may also appear elsewhere in the body of the technical re-should follow normal pagination procedures, i.e., enter the port If additional space is required, a continuation sheet shallnumber of pages containing information, be attached

7b. NUMBER OF REFERENCES. Enter the total number of It is highly desirable that the sbstract of classified reportsreferences cited in the report. be unclassified. Each paragraph of the abstract shall end with8a CONTRACT OR GRANT NUMBER. If appropriate, enter an indication of the military security classification of the in-the 4pplicale number of the cc.tract or grant under which formation in the paragriph, represented as (T5) (S), (C), or (U)the report was written. There is no limitation on the length of thc abstract How-8b, 8c, & 8d. PROJECT NUMBER: Enter the appropriate ever, the suggested length is from 150 to 225 wordsmilitary department identification, such as project number,subproject number, system numbers, task number, etc. 14 KEY WORDS y words are techn-cally mesnlngful terms

or short phrases that characterize a report and may be used as9a. ORIGINATOR'S REPORT NUMBER(S): Enter the offi- index entries for cataloging the report. Key words must becial report number by which the document will be identified selected so that no secur!ty classification is required. Identi-and controlleJ by the originating activity. This number must fiers, such as equipment model designation, trade name, militarybe unique to this report. project code name. geograpnic location. may be used as key9b OTHER REPORT NUMBER(S). If the report has been words but will be followed by an indication of technical con-assigned any other report numbers (e ther by the or,,gnator text The assignment of links, roles, and weights is optional.or by the sponsor), also enter 'his number(s).

10. AVAILABILITY/LIMITATION NOTICES- Enter any It-:ts',on on furthe.r disse,,ination of the report, other than hose[ I

UNCLASSIFIED

Security Classification