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DISCUSSIONS OF THE FARADAY SOCIETY No. 21, 1956 MEMBRANE PHENOMENA THE FARADAY SOCIETY Agents f o r the Society’s Publications : The Aberdeen University Press Ltd. 6 Upper Kirkgate AberdeenThe Faraday Society reserves the copyright of all Communications published in the '' Discussions '' PUBLISHED . . . 1956 PRINTED IN GREAT BRITAIN AT THE UNIVERSITY PRESS A B E R D E E NA GENERAL DISCUSSION ON MEMBRANE PHENOMENA 10-12th APRIL, 1956 A GENERAL DISCUSSION on Membrane Phenomena was held in the Great Hall, University of Nottingham (by kind permission of the Vice-Chancellor) on the loth, 11th and 12th April, 1956. The President, Mr. R. P. Bell, F.R.S., was in the Chair and about 250 members and visitors were present. Among the distinguished overseas members and guests welcomed by the President were the following :- Dr.W. McD. Armstrong (Eire), Dr. F. Bergsma (Netherlands), Prof. Dr. K. F. Bonhoeffer (Germany), Miss E. L. Boterenbrood (Netherlands), Prof. C. J. F. Bottcher (Netherlands), Dr. E. J. Casey (Canada), Dr. D. G. Dervichian (France), Dr. A. Despid (Jugoslavia), Dr. A. R. Gilby (Australia), Dr. D. E. Goldman (U.S.A.), Prof. H. P. Gregor (U.S.A.), Dr. F. Griin (Switzerland), Dr. F. Helfferich (Germany), Dr. T. L. Hill (U.S.A.), Mr. A. B. Hope (Australia), Dr. N. Krishnaswamy (India), Dr. A. Kepes, (France), Dr. and Mrs. J. W. Lorimer (Netherlands), Mr. J. J. McDonnell (Eire), Dr. D. MacGillavry (Netherlands), Dr. G. Manecke (Germany), Mr. J. Molliere (France), Mr. R. Murphy (Eire), Dr. and Mrs. R. Neihof (Sweden), Dr. R.N. Robertson (Australia), Dr. Aser Rothstein (U.S.A.), Prof. Dr. Runge (Germany), Prof. G. Scatchard (U.S.A.), Dr. R. Schlogl (Germany), Prof. Dr. Gerhard Schmid (Germany), Dr. Karl Sollner (U.S.A.), Mr. B. R. Stein (Germany), Dr. R. Stephan (Germany), Mr. G. F. v. d. Stoep (Nether- lands), Ing. J. Straub (Netherlands), Dr. C. C. Templeton (Netherlands), Prof. E. T. Teorell (Sweden), Prof. Dr. Heinrich Thiele (Germany), Dr. S. A. Troelstra (Netherlands), Dr. P. W. 0. Wijga (Netherlands), Dr. F. Wolf (Germany), Mr. H. Zierfuss (Netherlands). A particular welcome was recorded to Prof. E. Torsten Teorell of the Fysiolo- giska Institutionen, Universiteit, Uppsala, Sweden, on the occasion of the Eighth Spiers Memorial Lecture which is printed in full in the present volume. 3A GENERAL DISCUSSION ON MEMBRANE PHENOMENA 10-12th APRIL, 1956 A GENERAL DISCUSSION on Membrane Phenomena was held in the Great Hall, University of Nottingham (by kind permission of the Vice-Chancellor) on the loth, 11th and 12th April, 1956.The President, Mr. R. P. Bell, F.R.S., was in the Chair and about 250 members and visitors were present. Among the distinguished overseas members and guests welcomed by the President were the following :- Dr. W. McD. Armstrong (Eire), Dr. F. Bergsma (Netherlands), Prof. Dr. K. F. Bonhoeffer (Germany), Miss E. L. Boterenbrood (Netherlands), Prof. C. J. F. Bottcher (Netherlands), Dr. E. J. Casey (Canada), Dr. D. G. Dervichian (France), Dr. A. Despid (Jugoslavia), Dr. A. R. Gilby (Australia), Dr. D. E. Goldman (U.S.A.), Prof. H.P. Gregor (U.S.A.), Dr. F. Griin (Switzerland), Dr. F. Helfferich (Germany), Dr. T. L. Hill (U.S.A.), Mr. A. B. Hope (Australia), Dr. N. Krishnaswamy (India), Dr. A. Kepes, (France), Dr. and Mrs. J. W. Lorimer (Netherlands), Mr. J. J. McDonnell (Eire), Dr. D. MacGillavry (Netherlands), Dr. G. Manecke (Germany), Mr. J. Molliere (France), Mr. R. Murphy (Eire), Dr. and Mrs. R. Neihof (Sweden), Dr. R. N. Robertson (Australia), Dr. Aser Rothstein (U.S.A.), Prof. Dr. Runge (Germany), Prof. G. Scatchard (U.S.A.), Dr. R. Schlogl (Germany), Prof. Dr. Gerhard Schmid (Germany), Dr. Karl Sollner (U.S.A.), Mr. B. R. Stein (Germany), Dr. R. Stephan (Germany), Mr. G. F. v. d. Stoep (Nether- lands), Ing. J. Straub (Netherlands), Dr. C. C. Templeton (Netherlands), Prof.E. T. Teorell (Sweden), Prof. Dr. Heinrich Thiele (Germany), Dr. S. A. Troelstra (Netherlands), Dr. P. W. 0. Wijga (Netherlands), Dr. F. Wolf (Germany), Mr. H. Zierfuss (Netherlands). A particular welcome was recorded to Prof. E. Torsten Teorell of the Fysiolo- giska Institutionen, Universiteit, Uppsala, Sweden, on the occasion of the Eighth Spiers Memorial Lecture which is printed in full in the present volume. 3CONTENTS PAGE EIGHTH SPIERS MEMORIAL LECTURE- Transport Phenomena in Membranes. By T. Teorell . . 9 GENERAL INTRODUCTION. By G. Scatchard . . 27 A. FUNDAMENTAL STUDIES- On the Theory of the Donnan Membrane Equilibrium. By T. L. Hill 31 The Significance of Convection in Transport Processes across Porous Membranes. By R. Schlogl . . 46 Membrane Potentials of an Ion Exchange Membrane.By M. Nagasawa and I. Kagawa. . . 52 Bi-Ionic Potentials, By F. Bergsma and A. J. Staverman . . 61 The Effect of Stirring on Cells with Cation Exchanger Membranes. By G. Scatchard and F. Helfferich . . 70 Bi-Tonic Potentials, By F. Helfferich . . 83 The Physical Chemistry of the Differential Rates of Permeation of Ions across Porous Membranes. By R. Neihof and K. Sollner . . 94 Simultaneous Diffusion of Electrolytes and Non-Electrolytes through Ion-Exchange Membranes. By G. Manecke and H. Heller . . 101 The Sorption and Diffusion of Ethanol in a Cation Exchange Resin Membrane. By J. S. Mackie and P. Meares . . 111 GENERAL DIscussIoN.-Dr. T. L. Hill, Prof. G. Scatchard, Dr. B. A. Pethica, Ing. J. Straub, Prof. R. Schlogl, Dr.G. Manecke, Dr. M. Nagasawa, Dr. I. Kagawa, Dr. P. Meares, Prof. K. Sollner, Dr. F. L. Tye, Dr. A. Despic, Dr. G. J. Hills, Dr. F. Helfferich, Dr. J. E. Salmon, Dr. R. J. P. Williams, Dr. A. M. Peers, Dr. F. Bergsma, Dr. A. J. Staverman, Dr. N. Krishnaswamy, Prof. F. Runge, Dr. F. Wolf, Dr. E. Glueckauf, Mr. D. Reichenberg, Dr. R. Neihof, Dr. R. D. Keynes, Prof. A. R. Ubbelohde, Prof. R. M. Barrer, Dr. B. A. Pethica. . . 117 B. PROPERTIES OF PARTICULAR MEMBRANES- Transport Processes in Ion-Selective Membranes, Conductivities, Transport Numbers and Electromotive Forces. By J. W. Lorimer, (Miss) E. I. Boterenbrood, and J. J. Hermans . . 141 5CONTENTS PAGE 6 Electro-Osmosis in Charged Membranes. The Determination of Primary Solvation Numbers. By A.Despib and G. J. Hills. . 150 Specific Transport across Sulphonic and Carboxylic Interpolymer Cation- Selective Membranes. By H. P. Gregor and D. M. Wetstone . 162 Electrical Potentials across Porous Plugs and Membranes. Ion- Exchange Resin-Solution Systems. By K. s. Spiegler, R. L. Yoest and M. R. J. Wyllie . . 174 The Effect of Current Density on the Transport of Ions through Ion- Selective Membranes. By T. R. E. Kressman and F. L. Tye . 185 Some Uses of Ion-Exchange Membrane Electrodes. By D. Hutchings and R. J. P. Williams . . 192 GENERAL DIscussroN.-Dr. P. W. M. Jacobs, Dr. J. W. Lorimer, Dr. K. S. Spiegler, Dr. F. L. Tye, Prof. G. Schmid, Prof. G. Scatchard, Dr. P. Meares, Dr. A. Despic, Dr. G. J. Hills, Dr. G. A. H. Elton, Dr. D. I. Stock, Dr. J. A. Kitchener, Mr.D. K. Hale, Mr. D. J. McCauley, Dr. J. E. Salmon, Dr. R. Schlogl, Mr. W. D. Stein, Ing. J. Straub, Dr. F. Helfferich, Prof. K. Sollner, Dr. T. R. E. Kressman, Dr. N. Krishnaswamy, Dr. R. J. P. Williams, Prof. Dr. K. F. Bonhoeffer, Prof. H. Thiele . . 198 C . PROPERTIES OF BIOLOGICAL MEMBRANES- The Structure of Films of Proteins Adsorbed on Lipids. By D. D. Eley and D. G. Hedge . . 221 Compartmentalization of the Cell Surface of Yeast in Relation to Metabolic Activities. By A. Rothstein . . 229 Structure and Function in Red Cell Permeability. By W. D. Stein and J. F. Danielli . . 238 The Facilitated Transfer of Glucose and Related Compounds across the Erythrocyte Membrane. By F. Bowyer and W. F. Widdas . 251 Permeation Mechanisms in Bacterial Membranes. By P. Mitchell and J. Moyle . . 258 The Ionic Selectivity of Nerve and Muscle Membranes. By R. D. Keynes and R. €3. Adrian. . . 265 GENERAL DIscussIoN.-Dr. J. H. Schulman, Dr. F. Bowyer, Dr. B. A. Pethica, Prof. D. D. Eley, Mr. Hedge, Dr. R. J. Goldacre, Dr. R. D. Keynes, Prof. A. Rothstein, Dr. R. N. Robertson, Prof. H. J. C. Tendeloo, Prof. D. MacGillavry, Dr. G. J. Vervelde,CONTENTS 7 PA08 Dr. A. J. Zwart Voorspuy, Dr. W. B. Hugo, Dr. G. Manecke, Dr. P. Mitchell, Prof. J. F. Danielli, Dr. J. B. Finean, Mr. W. D. Stein, Dr. R. J. P. Williams, Dr. W. F. Widdas, Dr. J. H. Schulman, Dr. E. Glueckauf, Dr. G. S. Adair, Dr. D. Reichenberg . . 272 Author Index . . 288

ISSN:0366-9033    

DOI:10.1039/DF9562100001

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

TRANSPORT PHENOMENA IN MEMBRANES EIGHTH SPIERS MEMORIAL LECTURE BY TORSTEN TEORELL Uppsala, Sweden First I want to express my sincerest gratitude for the great honour bestowed on me in inviting me to give this lecture in commemoration of the first secretary to the Faraday Society, Mr. Spiers, of whose biography I do not know very much. I do know, however, that the Faraday Society has ever since his days been a highly active and important body. My first contact with the Faraday Society can be dated back to 1937, almost twenty years ago, when a General Discussion was held on almost the same topic. It was concerned with “The Properties and Functions of Membranes, Natural and Artificial ”.I My own interest and the starting point of my work on membranes and their behaviour was a very definite one.I think it was rather typical of many biologists or medical research people like myself. As a research student I wanted to work on the problem of stomach ulcer formation and did some experiments on the cat’s stomach, on how its hydrochloric acid was produced and how its acidity was “ regulated ”. Soon it was possible to demonstrate that the gastric mucosal membrane, in some formal aspects at least, behaved exactly like a parchment membrane. It could exchange ions by dialysis across it and in that way it was possible for us to propose a hy- pothesis for the so-called “ acidity regulation ” of the stomach, which has since been tested in various medical quarters. The finding, that electrolyte transport processes in the stomach could be handled by something similar to Fick‘s diffusion law and that Nernst-Planck’s formulae for electrical potentials were applicable, encouraged me to proceed further.Like so many other youngsters in the thirties, we had a strong belief in the applicability of physical chemistry to biology and to medicine. Encouraged by great men like Hober and Michaelis, who incidentally were medical people, physico-chemical attacks were made on several biological problems, which were well described, but badly explained. Surface chemistry, solution theory, colloid chemistry, electrochemistry were employed, together with our enthusiasm, in our bold attempts to solve biological problems. For my own part, I must confess that the problem I started with, the riddle of the mechanism of the formation of the gastric acid, is as yet an unsolved problem, although there exist at least half-a-dozen unproven theories.GENERAL ASPECTS OF TRANSPORT IN MEMBRANES 1. IONIC ACCUMULATION-ACTIVE TRANSPORT The gastric acid secretion implied a problem of “ ionic accumulation ”, a term which was popular in the thirties. One spoke of accumulation phenomena in most living cells. It is well known that cells, for instance the red blood cells, do contain much more potassium than the environment, the blood plasma. Plant cells also contain much more potassium than the surrounding sea water or fresh water. In the red cells, which can be regarded as typical for the mam- malian organism, there is about sixteen times more potassium inside the cell than outside. The same is the case with nerves (fig. 1).Incidentally, the sodium which is the other main cation in the living body, is rich in the environment, but 910 TRANSPORT PHENOMENA I N MEMBRANES is depleted in amount inside the cells. Although one was fully aware that these phenomena of ionic accumulation were something peculiar to living things and were linked with metabolism, one attempted in various quarters to explain this peculiar potassium accumulation by the aid of ingenious physico-chemical models, worked out in theory or in practice. On this occasion I want to recall the pioneer work made by Osterhout, the great plant physiologist at the Rockfeller Institute in New York, who was wise enough to understand that collaboration with expert physical chemists (MacInnes, Shedlowsky, Longsworth) was a necessity for an analytical biologist.The ionic accumulation problem is not solved as yet, although I must admit that a great deal more is known about the phenomenological side A X O P L A S M 49 410 40 440 22 5 6 0 ecooo O l A L Y S A T t FIG. 1.-Diagram of giant axon of squid partly cut away in order to show the electric charge across the surface membrane. The approximate internal composition of a fresh fibre is shown for sodium, potassium, and chloride in mM, i.e. millimole per kg of water. The composition of the external fluid is also shown in mM (from Eccles 38). of it now than twenty years ago. One characteristic difference is that the problem has a new label. What was called “ionic accumulation” in the thirties is nowadays frequently named “ active transport ”, a term coined by the Dane, August Krogh.In order to create active transport Dean2 later suggested the existence of a “pump” and gave it the name sodium pump. In other words, the main attention which previously was focused on the potassium, accumulated inside the cell, was now instead turned to the sodium, which is supposed to be forced out of the cell. It is often said nowadays that one ion is transported across the membrane “ actively ” (i.e. the sodium ion), the other ions “ passively ”. A great deal of characterization of the so-called active transport in living material like the red cells, the frog skin and particularly in nerve, has been done in recent years. I want to recall that excellent work has been done in particular by Ussing in Copenhagen on frog skin, and on nerve by Hodgkin, Keynes and their col- laborators in Cambridge and several others. I feel that it is somewhat outside the programme of my lecture to enter into the phenomenology of active transport, although for the biologist it is a most interesting field, to which we cordially invite physical chemists to join us.2. SOME FEATURES OF LIVING MEMBRANES After this presentation of my angle of approach, it might be of some interest for those, who are not directly engaged in biological work, to get some ideas of the nature of a biological membrane, the fundamental unit of transport in our human body. It is the membranes which regulate the transport in the body, e.g. the passage of foodstuffs of various kinds from the stomach and intestines to the blood, from the blood to extracellular fluids and the tissue cells.In the reverse direction, transport takes care of the metabolites, which have to be removed as waste pro- ducts or poisonous products from the body. The cell membranes are the systems in which the physico-chemically-minded biologist places the transport forces. These are invisible, unseen forces, which cannot be dissected by forceps or knives, but which nevertheless are as real as any dissection preparation on the anatomy table. Some recent electron microscope pictures, which have been taken at the Karolinska Institutet, Stockholm,3~ 42 of nerve sheets, etc., are given in fig. 2. This shows a tangential section (a). The membrane is far fromFIG. 2a.-Pile of 8 myelin lamellae isolated from the myelin sheath of osmium-fixed cat motor root fibres.Dow Latex calibration particles (2600A) have been added to determine the thickness of the shadowed lamellae (after Fernandez-Moran 42). FIG. 2b.-Ultrathin section through the myelin sheath of osmium-fixed nerve fibre of the mouse sciatic nerve. The dark lines represent the' principal period. Between these lines a faint line with dark dots is visible. The mean distance between the principal lines is in this specimen 113 A, the space between these lines therefore being 85-90 8, wide. (Electron micrograph kindly provided by Dr. F. S . Sjostrand 3). The thickness of the dark lines is 25A. [Toface page 10.T. TEORELL 11 homogeneous and it is more or less a " sandwiched " membrane, like an American seven-layer cake.In another projection (b) structures, submicroscopical structures, almost down to the molecular level can be seen. The black parallel lines are, for instance, roughly of the order of a few fatty acid molecules in length, about 25w. I think it is appropriate at this occasion to remind you that the surface chemists here in England, I may mention the schools headed by Sir Eric Rideal and by Prof. Neil Adam, anticipated layers of this type already in the thirties. FIG. 3.-Schematic diagram of medullated nerve fibre structure based on polarization optical analysis. (A) N = axon positively uniaxial as referred to axial direction. M = myelin sheath positively unixial as referred to radial direction. (B) Submicroscopic structure of the myelin sheath (after Schmidt) (after Frey-Wyssling 39).In particular, it was Danielli4 who offered the first pictures (in 1935) of layered membranes in which proteins and lipoids were interlaced. And people who worked with the polarization microscope observed phenomena, which could only be explained as due to well-orientated structures of proteins and lipoids (fig. 3). It is amazing to see now on photographs like Dr. Sjostrand's, what could only indirectly be inferred to exist ten years ago. Here the theoretical mind was in front of the experimentalists. The electrical activity in the nerve-the nerve signal-is, as is well known, an electrical event with frequency-modulated signals, called " spikes ", with a frequency of from say ten signals a second up to about 1000 c/sec. The spikes have constant amplitudes roughly of the order of 100mV.The secret of the electrical nerve communication signal is in fact a permeability process and thus a membrane problem. It is a question of ionic transport processes. These phenomena have been most ingeniously characterized, analysed and even partly synthesized by Hodgkin, Katz, Keynes and Huxley here in England. I want to point out that the electrical forces, which operate in the nerves or in many other cell membranes, have a gradient of the order of at least 100 V/cm. This is far more. than in any conventional electrophoresis machine, and the current density is far from a modest one; it is roughly 1 mA/cm2. In other words, appreciable amounts of material would be expected to be electrically transported and that is also the case.Here we have an important feature of the living body : a great deal of the transport forces are surely electrical in character, affecting not only ions but also other substances which are electrically charged like colloids. Even large suspended particles, like the leucocytes, are believed to be subject to elec- trical forces. I think the nerve signal is the most complex membrane process : it shows a rhythmical, self-sustaining process of a special character, far different from what we are used to in the model diffusion set up with a parch- ment or ionic exchange membrane clamped between Perspex gadgets, etc. But12 TRANSPORT PHENOMENA I N MEMBRANES nevertheless, I believe that the elementary parts, at the molecular level of these biological events, complicated as they are, do contain just the same fundamental elements as we can reveal by the model studies on simpler, well-defined systems. 3.SURVEY OF MEMBRANE “ PERMEABILITY PHENOMENA ” I should like to emphasize that the interest of a biologist in membrane pro- cesses or, as it is commonly called in physiology, “ permeability phenomena ”, is usually placed upon several aspects, but in particular on two, namely, the kinetics of transport (the rate of transport across the membrane), and the ionic distribution figures. The first kind of studies was not easy to perform earlier, but nowadays with the advent of radioactive tracers and refined analytical methods, etc., one has been able to study rate processes. It was much easier to determine equilibria of ion concentrations such as distribution studies of K to Na of the type noted above; this is probably the reason why the literature contains more data of this type.In table 1 I have listed these and some other permeability phenomena under five different headings. Any complete membrane theory ought to cover all these five aspects and explain them. Here I will restrict myself to commenting on only a few points concerning the aspects listed. TABLE 1 .-VARIOUS IONIC PROCESSES IN MEMBRANE SYSTEMS, “ PERMEABILITY PHENOMENA ” 1. Ionic transport, “flux ”. Net flux, partial fluxes of different ion species. “ Influx ” and “ outflux ” of one ion species. Flux ratios. 2. Membrane potential. Potential components, “ mixed ” or total transmembrane potential.The diffusion potential. Conductances in steady state systems. Membrane rectification. Reactance properties, apparent capacitance and inductance. ‘‘ Flux equilibria ”, “ diffusion effects ”. 3. Electrical conductivity. 4. Ionic distribution equilibria. 5. Spatial distribution of the ions and the potential within the membrane. A type of membrane transport studies or permeability studies, which has become feasible in recent years, is the ‘‘ influx ” and “ outflux ” studies across membranes. One has to remember that what one usually measures is the net flux. This net flux in turn is composed of two independent streams, an influx and an ourflux across the membrane, which may be of an order of magnitude different from the net flux. One realizes nowadays that the higher potassium content inside many living cells may be due to the fact that the driving forces for the influx are different from those of the outflux.It is not any type of im- permeability. In many biological quarters even as late as ten years ago, one thought that the potassium somehow was “ trapped ” or “ sealed ” inside the red blood cells in the place where it was produced (in the bone marrow), and could not escape. Nowadays, however, it has been shown that we have a form of what I have called “ apparent impermeability ”, which is just a result of a steady state, an interplay of forces. It is also wise to stress the importance of the simple fundamental law valid here : the flux = (total driving force) x (concentration) x (the mobility),T. TEORELL 13 and that the driving force can be built up in superposition from chemical, electrical and hydrostatic components.It cannot be too strongly emphasized that steady states, i.e. zero net flux, sometimes do consist of a very rapid inflow and very rapid outflow of the same magnitude. Partial fluxes can also almost cancel one another and give a small resulting net effect. Fig. 4 represents a so-called charged mem- brane, to which I have devoted some studies (fig. 9a, b). According to the usual terminology this charged membrane would be described as poorly permeable under the conditions prevailing in the experiment. It is, however, very permeable, if one considers the partial processes, the influx and the outflux. (Membrunc cone) wk FIG. 4.-The influence of membrane charge w x upon the net flux, outflux and influx of the ions of a single electrolyte.The ionic mobilities are assumed to be identical (KCl). Note the small net flux at high wXvaIues (where, however, the influx and outflux may be very large or vanishing), thus a negative membrane becomes virtually anion impermeable and a positive membrane becomes cation impermeable (from Teorell7). After having considered the biological background, I now want to outline the present status of membrane research, mainly from the biologists’ point of view, and thereby describe the various types of system that have been investigated in the past and are being investigated now. In fig. 5 I have attempted to show the connections between different cases, which appear in different mathematical forms.The scheme is very incomplete and far from logical. It will only serve to demonstrate how I look upon the “ genealogy ” in membrane research and how the various systems are linked with each other. Furthermore this genea- logical tree is neither a chronological nor a historical one, although it would be very interesting to draw the sequence of how one research worker has depended on another-very few discoveries in this field have been of the type of mutations ! I have chosen the most difficult artificial diffusion transport systems at the bottom and then depicted various special cases upwards in the figure. It is not my intention to describe all the membrane transport “ families”, nor to describe in detail any particular “member ”. Some interesting cases I want, however, to pick out, in what follows in order to demonstrate that many peculiar phenomena which occur show similarity with what can be observed in14 TRANSPORT PHENOMENA I N MEMBRANES biological systems. The various " membrane transports " will now be presented in the following order : (a) uncharged membrane, (b) " fixed charge " membrane (= ionic membranes), (c) convection diffusion.I I _I -_ __ - - - ~ ~ - - - FIG. 5.--S;heme of3fferent type, of membrane transport phenomena.-Z = electric current ; 'u = rate of bulk flow; cox= sign (u) and charge (x> of the membrane ; S = different cation and anion species ; c1 and c2 = outside and inside solution con- centrations ; TMS refers to Teorell16 and Meyer and Sievers.17 SOME FEATURES OF UNRESTRICTED DIFFUSION ACROSS UNCHARGED MEMBRANES 1.THE KINETICS A typical system is a porous glass membrane or porcelain membrane or even a filter paper of a pore size of much larger radius than that of any of the solutes present, but small enough to secure a convection-proof diffusion layer. With a 1 : 1-valent electrolyte it can be shown, as was done by Behn in 1897,s that the flux of an ion, i.e. the amount transported in unit time across the unit area on membrane, follows an equation which in a compact form can be written as (Teorell, 1951,6s 19 1953 7) flux = $ = - Ku(c~~$ - ~ 1 ) .T. TEORELL 15 4 is an exponential function introduced already by Planck and signified as exp (+F/RT). Here + is the electrical potential, F, R, and T are, respectively, the faraday, the gas constant and the absolute temperature.The constant K is a complicated function of the prevailing concentrations and 5; u is the mobility, c1 and cq the concentration " inside " and " outside ". Incidentally, this general flux equation can be used to express possible equilibria between influx and outflux being respectively -KucZ[ and + Kucl. In the steady state one has zero net flux, and one obtains c y /cT as 4' or 58 loglo (cF/cy) in mV. This is a type of steady- state distribution, which I think was shown for the first time by myself9 in 1935 and I will return to it again later (the " diffusion effect "). Nowadays, it is frequently employed in biology to describe ionic equilibria in terms of the transmembrane potential (Hodgkin, Keynes, Ussing, etc.). In passing, it can be remarked that the diffusion across a homogeneous mem- brane consisting of a non-aqueous solvent, can be written in the same mathe- matical form as the general flux equation for electrolytes.In this case the 4 is identical with the partition coefficient instead of an electrical potential function ! 2. ELECTRICAL MEMBRANE POTENTIALS AT UNCHARGED POROUS MEMBRANES These can be described in a general way with Nernst-Planck's well-known equation or the Henderson equation, which is in a few special cases identical with the Planck one. The problem of potentials in homogeneous membranes (c' oil membranes") is a difficult one; it has recently been attacked in Gottingen by the Bonhoeffer school, which has contributed so much to modern membrane theory. 3. " CONCENTRATION PROFILES " Even in this, the simplest of all membrane systems with no membrane charge, accumulation phenomena inside the membrane can take place as was pointed (according to Teorell, J.Biof. Chem., 1936, 113, 735). The results conform reasonably well to the theoretically calculated curves (according to Planck-Plettig 8 or Teorell,6 eqn. (271, (28)). 0- out by Planck and Plettig 8 long ago. Fig. 6 shows what they anticipated theor- etically and which we have confirmed experimentally. This peculiar " concentra- tion profile " can be regarded as a " rudimentary " approach of the system towards a dynamic equilibrium of a type, which is presented in fig. 7 and which we have called the difusion @ect on ionic distribution9 Related effects have been called " harmony " by Staub.4116 TRANSPORT PHENOMENA I N MEMBRANES 4.DIFFUSION EFFECT The diffusion effect is something related to the Donnan effect where one ion, the ‘‘ active ” one, dictates the behaviour of all the other ions, the ‘‘ passive ” ones. In the genuine Donnan case the active ion is completely impermeable. In the diffusion effect all ions are permeable although to different degrees. It is interesting to note that one nevertheless gets the same type of ionic distribution (cp. fig. 7) as is generally regarded as characteristic of the genuine Donnan dis- tribution (which actually appears as a limiting case of the “diffusion effect ”). Intermediate Stea@ sfufe Membrane (0) FIG. 7.-Scheme illustrating the development of a “ diffusion effect ” upon the ionic distribution (uncharged membrane).(Top, left) : the experimental set up : the HC1 (the “ diffusing agent) ” is steadily supplied into ‘‘ inside ” (small volume) and diffuses across the membrane to ‘‘ outside ” (large volume). An electrical potential across the membrane results. (Top, right) : a hypothetical biological counterpart to the experiment (Below): the different stages in the development of the “diffusion effect” upon the distribution of the ‘‘ passive ” ions (K and Br). Black arrow6 indicate electrical flux, white arrows indicate the ‘‘ osmotic ” flux. In the final steady state these fluxes balance each other and the K and Br ions attain a ‘‘ flu, equilibrium ” (from Teorell7~ 9). It is especially worth pointing out that the diffusion effect system shows a transport of passive ions against their concentration gradients, i.e.ionic accumulation. This ionic accumulation model may have biological analogy, but I wish to emphasize that it exhibits no selectivity; potassium and sodium, for instance, are equally influenced in contrast to the behaviour of these ions in biological systems. 5. MEMBRANE RECTIFICATION, ETC. Returning again to the simple porous type of membranes one finds that they can exhibit electrical “ rectification effects ”, i.e. a difference in electrical con- duction according to the direction of the applied electrical current. This is due to re-arrangements of the ion gradients inside the membrane. This type of rectificationT. TEORELL 17 effect seems to appear in most biological tissues, and is probably complicated with fixed charges attached to the membranes ; they were described by Labes and Zain (1922),13 Blinks (1930),14 Cole (1939),14 Teorell (1948),15 see also fig, 8. Related phenomena are " anomalous " capacitance and inductance effects which often appear.lonic events in uncharged porous membranes must show peculiar transition phenomena, when the pores become increasingly smaller and the membrane turns into a micro-porous and finally into a homogeneous layer. Wilbrandt 10 in the early thirties had emphasized the necessity of reconciling the pore and homogeneous membrane effects. Danielli 11 (1936), in particular, appears to have been the (CO f h ode) I :\i FIG. 8.-Distribution of ions and potential within a (multi-)-membrane (cellophane surrounded by large, stirred volumes of 0.1 N HC1 and 0.1 N NaCl).Initial state (middle), steady state values after current flow (left and right). Points and crosses in the middle section are calculated values, the curves are all based on experimental values. The mV values were measured during a short interruption of the current flow (after Teorell 15). first one to attempt a quasi-thermodynamic treatment of thin and more or less thick homogeneous membranes in terms of activation energies, etc. In this respect Danielli pioneered the later general physico-chemical work by Eyring and others,l2 who with some success, have formally introduced their L' transition state theory " into the membrane realm. The kinetic approach, which I have chosen, and the more thermodynamical treatment are, of course, only different languages to describe the same phenomenon.For biologists, the kinetic approach is the preferable one as it is easier to transform into a rational experimentation. Thermodynamics is, on the other hand, less restricted. The formalism in the two different approaches can, of course, be shown to be closely related. THE BEHAVIOUR OF CHARGED MEMBRANES 1. THE GENERAL CONCEPTS OF THE FIXED CHARGE THEoRY.-If we now turn from the uncharged to the charged membranes, i.e. membranes carrying a hxed ionic group in the matrix CL ionic membranes " according to Dean 2) we find that they show more complicated conditions which, however, lead to more inter- esting effects which may come still closer to the biological events (fig. 9).The fixed charged membranes seem to have become a rather popular research object18 TRANSPORT PHENOMENA I N MEMBRANES t t .ni @3-P,l f a2 \ f/anc& ) Donnun (Henderson) Donnon ?bid potenfW FIG. 9cr.-Diagram illustrating the basic concepts of the fixed charge theory (from Teorell 6 , 7). FIG. 9b.-The fixed charge theory applied to a single electrolyte. (A calculated case of HCI diffusing across a positive membrane, OX = 20, mobility ratio NH~VCI = 5.3). The diagram shows the course of the ion concentrations and of the electric potential. Note here that the total P.D. has the opposite sign to the interior membrane potential (42 - 41)~. Observe also the non-linear course of the total concentration, (Cl-), within the membrane. (In this particular case the variation of the potential ($2 - $ 1 ) ~ is approximately linear, which, however, is rather an exception) (from Teorell 6.7).T. TEORELL 19 since the advance of the synthetic ion exchange resins with cross-linked structures. It may be appropriate to recall that a chemical electrolyte character of these membranes was recognized clearly by Michaelis in the twenties. His work on " positive " and '' negative " membranes had a great influence on biological thinking. Michaelis regarded the effects produced by his dry collodion mem- branes as due to electrostatic repulsion and attraction of the diffusing ions. Michaelis' collaborator in 1935, Wilbrandt,lo suggested that the ionic distribution vis ci uis the membrane would be related to the Donnan distribution law. 70 s 8 e 5 0 4 FIG.10.-The variation of the ion concentrations at a charged membrane where the interior membrane potential is zero (cp. fig. 96). An actual counterpart would be a system as depicted with the arrangement : (1) 4 mN KCI + 2 mN NH4Cl ]I membrane w x = - 10 mN 11 2 mN KNO3. (2) The ionic mobilities of K+, N&+, C1- and N03- were assumed identical. In this case the respective concentration gradients inside the membrane signify direction and magnitude of the ion fluxes. Note that the K+ ions flow in the direction (2) -+ (l), i.e. from a lower to a higher Concentration. A simiiar situation would arise with any electrolyte mixture when the " membrane concentration " is high, relative to the bulk total concentration (from Teorell20). At about the same time I was working with the apparent transference numbers of Cellophane 40 and found that the so-called " concentration effect " shown by this membrane, a phenomenon observed and discussed in the early days of our century, especially by Beutner, could be linked with the somewhat high transfer- ence numbers I had obtained.This led to a provisional theory 16 in 1935 which aimed primarily at an explanation of the concentration effect on the membrane potential in terms of what at that time I called a " mixed potential ". This con- sisted of two membrane phase-boundary potentials of Donnan character and a Henderson potential between. A specific feature was the jumps of the spatial20 TRANSPORT PHENOMENA I N MEMBRANES distribution of concentration and the potential (cf. fig.9). Some time later Meyer and Severs 17 independently and at some length formulated an identical theory and also extended it to include oil membranes. Meyer and Severs like myself were at that time mainly interested in the electrical membrane potential and not until much later was a more extended theory formulated for the ion transport. Goldman 18 in 1943 integrated the Nernst-Planck differential equations for a charged membrane. His solution was, however, confined to the conditions inside the membrane and not its overall behaviour with the surrounding solutions. In 1951 6 and 1953 7 we therefore presented a somewhat fuller treatment of the problem, which led to a number of equations for the ionic fluxes, the electrical conductance and rectification, the membrane potential, and also for the “ profiles ” of concentrations and the electric potential. Certain simplifications had to be ’ introduced ; for instance, the activity corrections were disregarded and some very general approximations were made as to the influence of the bulk (water) movement.Extensions were later made by Schogl.20 On the whole it can be said that the same general formalism is valid for charged membranes as for uncharged ones in spite of the introduction of the “ double Donnan ” conception. We have previously shown that the condensed flux formula (for a cation), where u denotes the mobility and (1225 - CI), is equal to the difference in electro- chemical potential. This expression is also valid for a charged membrane; the only change lies in the significance of the constant K, which now will be still more complicated as it also takes care of the Donnan distributions (cf.Teorell,6 eqn. (4), ref. 7, p. 320, eqn. (5)). I am fully aware of the shortcomings of the fixed charge theory as regards the assumptions made, the mathematical procedures employed and the significance of the results. I am convinced that it will soon be superseded by more rigid and realistic treatments, but until that time the fixed charge conception may have fulfilled at least one useful purpose-to challenge other workers and thus stimulate new experiments and new theories. 2. I want now, however, to mention a few features of the consequences of the fixed charge theory which might have biological analogies. First it has been found that the peculiar uphill diffusion so characteristic for many biological membrane systems, i.e.diffusion or transport against the con- centration gradient, can be easily achieved in a fixed charge membrane as is demon- strated in fig. 11. We assume here a negative membrane (fixed charge density, w x = -lo), surrounded by KCl, NH4C1, and KNO3. Due to the Donnan dis- tributions at the membrane boundaries and the interaction of the driving forces in the interior, we obtain the unusual situation that the concentration gradient of the K ions (the full black curve) within the membrane is directed from the low concentration side towards the high concentration side. In other words, there exists an uphill transport of the K ions. Accordingly there need not be anything peculiar about movement against a concentration gradient.There is no “ active transport ” here ; it is an effect of the superposition of a few, well-defined driving forces. Another phenomenon at charged membranes related to the so-called “ diffusion effect ” of uncharged membranes mentioned earlier, is the development of similar steady state distributions of the ions present. Due to the effect of the fixed charges the mobility or transference numbers may be enhanced or decreased as com- pared with the free water situation in uncharged pores. This restriction upon one or several ions leads also to a distribution picture similar to the Donnan distribution. I think Netter21 in 1928 was the first to demonstrate that very pronounced Donnan-like ion equilibria ” could be obtained with Michaelis’ dried collodion membrane.The matter has been well investigated by Sollner 22 + = -Kdc24‘ - Cl),T. TEORELL 21 and collaborators working on the so-called permselective membranes developed in his laboratory. As an example of such distributions I refer to the following table from one of my own experiments (table 2). All ions present retain a dis- tribution ratio across the membrane of a similar order and conform to what can be calculated from the total trans-membrane potential. It is obvious that this ‘‘ equilibrium ” is not a genuine thermodynamic one ; it is ‘‘ gliding ” with time ! I should like to call this type ‘‘ time-variable or time-dependent equilibria.” The “ diffusion effect ” of uncharged membranes and these last mentioned distribution effects may perhaps be called ‘‘ flux equilibria ” (i.e.the influx of one ion con- stituent = the outflux, etc.) in order to distinguish them from the thermodynamical Donnan distribution. I want again to emphasize that these types of distribution equilibria do not show any selectivity, between, for instance, potassium and sodium. It might, however, be possible to get at least a temporary selectivity, if somebody could synthesize a suitable membrane matrix with selective ad- sorption properties (Skogseid 23 claimed some years ago that he had a resin with a pronounced K affinity). In this connection I should like to point out that there is no absolute necessity that the Donnan distribution at the membrane boundaries should be strictly obeyed. When in 1935 16 I first employed concentration jumps at the membrane- solution boundaries I chose for convenience the well-defined Donnan concentration jump.However, as far as I can see it is possible to introduce any ratio, specific for the individual solute species, provided it can be defined in some way or ex- perimentally justified. These ratios may not necessarily be the same or follow “ cellophane ” (1) initial state: 10 mM KCl 1 oXw-ZOmM (2) 1 mM HN4Cl (12 ml) * Note that CI- = K+ + NH4+. the same relationship at the “entrance” and “exit” sides of the membrane surface. I think we have here problems which need further amplification. A related case to be solved is where the fixed charge distribution within the membrane is ‘‘ skew ”, and not uniform as is usually postulated.TRANSPORT PHENOMENA INVOLVING BULK FLOW 1. INFLUENCE OF THE BULK FLOW (CONVECTION-DIFFUSION) We have now to deal with a still more complicated problem, where there is also a bulk movement within the membrane. Thereby we proceed to the field of electro-endosmotic phenomena. (Note that in fig. 5 in order to appreciate that the cases already treated, although common enough, were only ‘‘ branches ”, i.e. special cases, from a quantitative point of view, where the water transport was equal to zero (v = 0)).22 TRANSPORT PHENOMENA IN MEMBRANES A limitation in many of the kinetic formulas for transport in charged mem- branes or ionic membranes has been the neglect of the bulk movenient of the solu- tion which certainly occurs frequently, especially in biological structures.In most model experiments hitherto the water movement, for example in collodion or cellophane membranes, or even in the modern ion exchange resins, is fairly small and can as a first approximation be disregarded. Semi-permanent Porous Semi-permanent membrane membrane membrane 1 - 1 ‘- Thickness 6 V 8 e-- Cleo - -- Steady state . (Flux equilibrium) ’ C p RT-D FIG. 11 .-A hypothetical case of a steady state arising from counter current (convection- diffusion). A single solute is confined between two membranes, permeable to the solvent but not permeable to the solute. A porous membrane, permeable to both solvent and solute, acts as a partition between two, stirred chambers. A constant flow of solvent is imposed on the system (open arrous), black arrow shows direction of diffusion.A perfectly satisfactory treatment of the important problem where electro- chemical potentials arising from concentration gradients and bulk movement co-operate has not yet been given. Promising approaches have, however, been attempted by several workers. Two different modes of approach have been employed, one the kinetic, e.g. by Schlogl209 24 a few years ago, and the other thermo- dynamic founded on the recently formulated laws for irreversible thermodynamics. I think it is appropriate to mention here a few important contributions such as those by Mazur and Overbeek,25 and by Schmid,26 who has also carried out experimental tests, those by Scatchard,27 Staverrnan,28 Lorenz 29 and most recently by Kirkwood,30 who have all derived interesting and biologically important results.It is striking to a biologist to be faced with the situation that such a highly theoretical and abstract treatment as Onsager’s so-called “ reciprocal relation ” can turn out to be of a fundamental importance for the explanation of the mechanisms of biological transport and communication problems. A special feature in these new theories on electrosmosis by Schmid, Schlogl, Staverman and others is that the old zeta potential, so often used to characterize the charge of particles or membranes, can be substituted by the fixed charge symbol, O J ~ , expressed in units of concentration,T. TEORELL 23 The essential new feature in the quantitative treatment of this convection transport in membranes is the appropriate introduction of a third driving force in the fundamental transport equations, besides gradients of chemical and electrical potentials.This is the effect arising from a gradient due to solvent (water) pressure. It may appear unconventional to speak of a pressure (hydrostatic) potential or in a more loose way of a “ water potential ”. But it nevertheless exists It is perhaps more evident if we make use of Hertz principles for convection- diffusion.31 Fig. 11 gives a simple example of a hypothetical case, where only a chemical potential and a hydrostatic potential co-operate. Here the creation of a characteristic unequal concentration distribution could be postulated, somewhat similar to what has been earlier demonstrated in the form of Donnan equilibria or “ diffusion effects ”, i.e.a kind of “ flux equilibrium ”. If by applying some force, the existence of which must be taken for granted, a constant bulk flow rate across this system could be produced, it can easily be shown that eventually a steady state would be attained (i.e. a flux equilibrium) where the concentration distribution could be equal to A similar relationship was valid for the result of the competitive behaviour between the chemical potential of ions and the electric potential. This was then written in the form : The difference is that instead of ($F), v, the linear bulk velocity, 6 the thick- ness of the membrane and D the diffusion coefficient are introduced. If the two equations are expressed logarithmically, it is easy to see from the dimensions that, in the first case ($F) expresses the electrical work ; in the second case (vS)/D sig- nifies the mechanical work.Each in turn is equal to the “ chemical ” work arising from the difference in concentrations, i.e. RT In (cy /@). In other words, the work terms balance one another in the ultimate steady state. For the present general case, where three driving forces are superimposed one therefore can write 7 c? US RTln- - mVF+ - = 0. c2” D Demonstrations of this type of steady-state distribution or flux equilibria seem to be rare. (L. Garby 32 working in our laboratory has carried out somewhat related experiments with heavy water, and Ussing33 has advanced a related theoretical reasoning for the behaviour of the frog skin.) Before finishing this section I should like to comment on a somewhat different case, i.e.when convection forces and electrochemical potentials appear simul- taneously in the charged membrane without a flowing electrical current. In such cases one can sometimes observe the phenomenon of anomalous osmosis, which has received much attention, since it was discovered long ago. In particular, I wish to recall the great biologist Jaques Loeb’s work some forty years ago. In modern days Sollner 34 and his collaborators have investigated this phenomenon thoroughly and they introduced the fixed charge conception in their explanations of this phenomenon. Quite recently a fine achievement was made by Schlogl24 from the Bonhoeffer group in Gottingen. He employed a principle rather similar to the one employed in the building-up of the quantitative fixed-charge membrane model and worked out the “ pressure profile ” at the membrane boundaries and within the membrane.I think he has been able to explain positive and negative anomalous osmosis very satisfactorily in that way.24 TRANSPORT PHENOMENA I N MEMBRANES 2. ELECTRO-ENDOSMOSIS AND RHYTHMICAL TRANSPORT PHENOMENA In the previous section we have touched upon some theoretical approaches to transport problems where three driving forces were simultaneously present. From an experimental point of view there exists a great literature under the label " electro-endosmosis ", describing all sorts of systems where these forces are -- ..... mE 6 -.- kQ 3 5 - 8 3.0- f0 2,s. 2.0. 0 8- L I I 1 ..... .... 0 30 GO 90 t20 MinnvlPs FIG.12.-Oscillatory phenomena during flow of constant electrical current. Experi- ments on a system 0.1 N NaCl I ( porous glass membrane 11 0.01 N NaCl; mA figures refer to different current densities in:mA-cm-2 (from Teorell 37). operating. I believe that the subject of electro-endosmosis deserves still more attention by the theoreticians and by the biologists. There is no doubt that living membranes are more or less " charged " (due to carboxyl-, amino- and other fixed groupings in the membrane matrix) and much evidence shows that flowing electrical currents can be produced, for instance, at the nerve action. One is therefore necessarily obliged to postulate the existence of electro-endosmotic phenomena in living tissues. Such a postulate implies that electrical events in these membranes have to be accompanied by simultaneous bulk (water) streaming.Only a very few biologists have so far paid attention to this possible effect (cf. Tobias,35 Hill36). This is to be regretted, but it can be explained by the great technical difficulties involved in measurements of small volume changes of the living structures. I believe that such studies would be interesting, however, because our recent studies on electro-endosmotic " cell " models have revealed some possibilities of obtaining rhythmicaI or oscillating membrane phenomena (Teorell37). I must confine myself to describing only a few experimental facts. The model was roughly built up according to the scheme AgCl electrode ] 0.1 N NaCl I porous glass membrane 1 0.01 N NaCl ] AgCl electrode.T.TEORELL 25 Constant currents were applied across the electrodes and the whole set-up per- mitted simultaneous recording of the membrane potential, the electrical mem- brane resistance and the water-pressure difference across the membrane. A typical result obtained is demonstrated in fig. 12. The striking feature of these experiments is the appearance of rhythmical variations of the variables mentioned. Perhaps the alternation of the inward and outward movements of the water is the most conspicuous event, Damped oscillations and, under certain conditions, even undamped trains of oscillations could be achieved over rather extended periods. This system behaves in a somewhat similar way to an electronic “ relaxation ” oscillation and it is possible to formulate a theory relating to the “membrane oscillation ” on an analogous basis (to be published).Another remarkable feature can also be mentioned, namely, that this type of system applied to mixtures of alkali ions could exhibit a preferential or selective ion transport as can be seen in table 3. TABLE 3 Initial set up : 50 KCl - 5 KCI (l) 50 NaCl - 5 NaCl (2) (2000 ml) I (12ml) Conc. in mM. ; 25 mA cm-2 time [Klz “alz [KIzhNah 0 5.2 6.4 0.8 1 80’ 1.1 5.3 0.2 1 time tK21 [Lilz tKlz/ILi12 0 4.7 5.8 0.81 80’ 0.7 5.0 0.14 230” 0.2 4-0 0.05 It is, of course, tempting to think that these phenomena of rhythmicity and ion selection could be somehow related to actual living systems like the nerve, which displays just these features. I think however, that this should be attempted with the greatest caution.Much more work is required from the physico-chemical as well as from the biological side before one dares draw significant analogies. I am now at the close of my survey of membrane transport processes. We know a great deal more now than we did nineteen years ago when the Faraday Society last discussed these subjects. I hope that the tradition founded during Mr. Spiers’ secretaryship in the Faraday Society to assemble people of different view-points for a General Discussion on a subject of a common interest will persist and that we can meet again in a co-operative spirit. Co-operation with physical and chemical experts is what we in the biological fields need and appreciate. A meeting of this type to form a general discussion is indeed one of the boldest attacks against the secrecies of the Living Nature.Problems like “ facilitated diffusion ” and “ active transport ” and many other phenomena still await conquest. The descriptive terms of the biologist must be exchanged and translated into the well-defined and unambiguous language of the physicists and chemists. It may, however, be wise to remember that whatever the number of conditions we include in our research and formulas, we shall always be dealing with approximations, if we take the Living Nature as a standard. I believe that Michael Faraday, who was a humble man, felt that limitation of the human mind quite often! 1 The Properties and Functions of Membranes, Natural and Artificial, Trans. Faraday 2 Dean, Chem. Rev., 1947,41, 503. 3 Sjostrand, personal communication.4Danielli, J . Gen. Physiol., 1935, 19, 19; J. Cell. Comp. Physiol., 1936, 7, 393. SOC., 1937, 33, 91 1.26 TRANSPORT PHENOMENA IN MEMBRANE 5 Behn, Ann. Phys. Chem., 1897, 62, 54. 6 TeorelI, 2. Elektrochem., 1951, 55, 460. 7 Teorell, Progress of Biophysics (London, 1953), 3, 305. SPlettig, Ann. Phys. (ser. 5), 1930, 5, 735 (cf. Planck, Sitzungsber. Preuss. Akad. 9 Teorell, Proc. Nut. Acad. Sci., 1935, 21, 152 ; J. Gen. Physiol., 1937, 21, 107. 10 Wilbrandt, J. Gen. Physiol., 1935, 18, 933. 11 Danielli, in The Permeability of Natural Membranes, by Davson and Danielli 12 Zwolinski, Eyring and Reese, J. Physic. Chem., 1949, 53, 1426. 13 Labes and Zain, Arch. Expt. Path. Pharmakol., 1926,125,1,53 ; 1927,126,284,352; 14 Cole and Curtis, J. Gen. Physiol., 1941, 24, 551 ; (cf. Guttman and Cole, J. Gem 15 Teorell, Nature, 1948, 162, 961 ; Arch. Sci. Physiol., 1949,3, 205. 16 Teorell, Proc. Soc. Expt. Biol. Med., 1935, 33; 282. 17 Meyer and Sievers, Helv. chim. Acta, 1936, 19, 649, 665, 987; 1937,20, 634. 18 Goldman, J. Gen. Physiol., 1943, 27, 37. 19 Teorell, Abstr. Comm. XVIZI Znt. Physiol. Congress (Copenhagen, 1950), p. 481. 20 Schlogl, 2. physik. Chem., 1954, 1, 305 ; Schlogl and Schodel, ibid., 1955,5, 372, 21 Netter, Pjziigers Arch., 1928, 220, 107. 22 Sollner, J. Electrochem. Soc., 1950, 97, 139 ; J. Plz-vsic. Chem., 1945, 49, 43 ; Ann. 23 Skogseid, Noen derivater av polystyrol og deres anvendelse ved studirim av ioneut- 24 Schlogl, Z. physik. Chem., 1955, 3, 73. 25 Mazur and Overbeek, Rec. trav. chim., 1951, 70, 83. 26Schmid, Z. Elektrochem., 1950, 54, 424; 1951, 55, 229. Schmid and Schwarz. 27 Scatchard, J. Amer. Chem. SOC., 1953, 75, 2883. 28 Staverman, Trans. Faraday Soc., 1952, 48, 176. 29 Lorenz, J. Physic. Chem., 1952, 56, 775 ; 1953, 57, 341. 30 Kirkwood, Ion Transport Across Membranes (Acad. Press, N.Y., 1954), p. 119. 31 Hertz, Physik. Z., 1922, 23, 443 ; 2. Physik, 1923, 19, 35. 32 Garby, Nature, 1954, 173, 444. 33 Ussing, Advances in Enzymology, 1952, 13, 21. 34 Sollner, Dray, Grim and Neihof, Ion Transport across Membranes (Acad. Press, N.Y., 1954), p. 144. 35 Tobias, Modern Trends in Physiology and Biochemistry (ed. Barron, Acad. Press, N.Y., 1952), p. 310; cf. articles by the same author on related subjects in J. Cell. Comp. Physiol., 195 1-55. Wiss. P1iysik.-Math. KI. X X , 1930). (Cambridge, 1943), chap. XXI and Appendix A. (cf. Blinks, J. Gen. Physiol., 1930, 14, 127). Physiol., 1944, 28, 43). N. Y. Acad. Sci., 1954, 57, 177. vekslingsreaksjoner (Oslo, 1948). 2. Elektrochem., 1951, 55, 295, 684 ; 1952, 56, 35. 36 Hill, J. Physiol., 1950, 111, 284, 304. 37 Teorell, Expt. Cell Res., 1955, suppl. 3, 339. 38 Eccles. The Neurophysiological Basis of Mind (Oxford, 1953). 39 Frey-Wyssling, Submicroscopic Morphology of Protoplasm and its Derivatives 40 Teorell, J. Gen. Physiol., 1936, 19, 917. 41 Straub, Chem. Weekblad, 1949, p. 361. 42 Fernandez-Morh, Expt. Cell. Res., 1952, 3, (fig. 8). (Elsevier, N.Y., 1948), p. 214.

ISSN:0366-9033    

DOI:10.1039/DF9562100009

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

GENERAL INTRODUCTION BY G. SCATCHARD Received 24th January, 1956 For many years I was troubled by a statement attributed to Faraday, which I have not verified, that he held his theories by his finger-tips so that the least breeze of fact might blow them away. I was troubled because it seemed to me that some theories are more trustworthy and tenable than many facts. When I realized that a fact to Faraday meant something different from what it did to me, that for him a fact was not something he read in a book or journal, but was something he had observed in the laboratory, and that Faraday was an exceptionally able observer, my troubles stopped until I began to study membranes. Now I need two handfuls of finger-tips : one for alleged theories and one for alleged facts. It is for this reason that I believe that the most important advance in the study of membrane phenomena is the application of the thermodynamics of irreversible processes, particularly in its phenomenological aspects.Although I have as high an opinion as anyone of the contributions of Willard Gibbs to classical thermodynamics, I think a much more important contribution of thermodynamics to science is the time of imaginative investigators which has been saved for useful work by the denial of the possibility of perpetual motion. I do not expect the complete devastation of a criticism such as, “ If that were so I could devise a perpetual motion machine ”, but perhaps the statement “This does not prove your special theory, but only proves the Onsager relations ” may become nearly as effective as “ This only proves the second law ”.Classical thermodynamics is rigorous about equilibrium. It accepts no substitutes and no approximations. Quasi-thermodynamics and the thermo- dynamics of irreversible processes differ from classical thermodynamics in admitting that temperature, pressure, and chemical potentials exist at a given time and point in a system which is not in equilibrium. Although this is probably an approxima- tion which is never strictly true but is better the closer the system is to equilibrium, it is difficult to imagine science which is not based on it. The most important difference between quasi-thermodynamics and the thermo- dynamics of irreversible processes is that the latter can deal with flows which are not isothermal, while classical thermodynamics and quasi-thermodynamics cannot.Even at constant temperature, however, there is a marked difference in points of view. Quasi-thermodynamics deals with instantaneous states, not too far from equili- brium, and in the relations between various concentrations. The thermodynamics of irreversible processes considers also the relations of these quantities to fluxes of matter, electricity, and heat and is applied to steady states. In the isothermal cases without heat flux the method is not new. It is the method used by Nernst and Planck in the study of liquid-junction potentials, which can be used also for membrane potentials. The difference between the two approaches is well illustrated by the contrast between Planck‘s equation 1 and Henderson’s.2 Both are concerned with dilute perfect solutions.Planck sets up boundary conditions, and from the diffusion constants determines the fluxes, the point-to-point concentrations and potentials. Henderson sets up a simple relation between the point-to-point concentrations and determines the relations of these to the electrical potential. 2728 GENERAL INTRODUCTION He was seeking for a simple approximation of the Planck equation, and the fact that his model corresponds to more junctions than Planck’s is incidental because it does not apply so well to membranes except when the two agree. Three recent papers on the application of the thermodynamics of irreversible processes to membranes show an interesting contrast in their approach. Lorenz 3 merely adds a veneer of the Onsager relations to a phenomenological treatment which without them would show how many proofs prove nothing at all.Staverman 4 gives more detail with a style similar to that of current discussion of the thermo- dynamics of solutions. Kirkwood 5 gives a rigorous and rather abstract treatment which leaves to the reader the detailed applications and the simplifying assumptions which they need. As a specific example we may take the beautiful measurements by Bull 6 of the electrophoresis, electrical endosmosis and electrical streaming potential of glass coated with protein of which Alexander and Johnson7 say “Thus Bull (1935) in showing, for electrodialized gelatin and recrystallized egg albumin adsorbed upon Pyrex, that the 5 potentials from the three types of measurement were, within the limits of experimental error, identical, provides strong evidence for the basic electrokinetic theory ”.The agreement of the electrophoresis and the endos- mosis shows only that the two surfaces were alike in some important respects. The agreement of endosmosis and streaming potential shows even less-that Bull was measuring what he thought he was. From the first days of the Helmholtz double layer and the electrokinetic potential, the study of membranes, like much of colloid science, has been confused by the misuse of theories. It would be so much better if we called most of them models rather than theories. Then we would not have to defend their truth, but only their usefulness. Most of us do need models in order to think.Almost everyone who thinks about membranes first thinks of small holes in a plate which is very thin even compared to the size of the holes. Some biological membranes may be such diaphragms, but synthetic membranes, and many natural ones, have holes which are much smaller than the thickness of the membrane. Almost everyone takes as second choice right-circular cylindrical pores, and as a third model lets the pores curve and change in cross-section. I believe that a much more useful model resembles a pile of sand, or brush, or tangled fish-nets in that as many channels run in one direction as any other, and the channels are continually branching and coming together again. There are few if any dead-end pockets or neighbouring points connected only through long loops.The model need hardly be more specific than this. The pore model has been used effectively by Schlogl4 to show that anomalous osmosis, either positive or negative, may occur in a single pore and therefore may occur in any membrane model. Beyond the fact that there must be electrical neutrality, the most important things to know are the number and sign of the fixed ions and the distribution ratios of various counter- ion pairs between water and the membrane. Ever since Miss Unmack 9 showed that the geo-electrical effect may be explained by convection in the earth’s gravitational field and may be eliminated by vigorous stirring, it has been apparent that events at the interfaces between membrane and solutions must be very important. But we usually use the simplest model for this interface, a mathematical plane with homogeneous membrane on one side and homo- geneous solution on the other.When this model fails, the addition of a “ diffusion layer ” entirely within the aqueous solution seems sufficient. Obviously events which occur at the surface do not require a detailed model of the interior. A chief importance of these surface phenomena is the difficulty which they make for the determination of membrane properties from measured quantities, especially from electromotive force or electrical transference. For desalting it is desirable that a membrane has a high concentration of fixed ions, high electrical conductivity and low electrical transference of water. I am The electrical part of the model may be even less detailed.G .SCATCHARD 29 particularly interested in the use of membranes to replace electrodes in the measure- ment of electromotive force. Here high electrical conductivity is a convenience but not a necessity and low transference of water becomes less important as the solution becomes more dilute, but high concentration of fixed ions is important. I also use membranes for the measurement of osmotic pressure, and there I want as small a concentration of fixed ions as possible, because they slow up the approach to equilibrium. The equilibrium osmotic pressure is independent of the nature of the membrane, but a small relative deviation of the concentration of small ions would give a much larger pressure. The rate of dialysis, or of electrodialysis with only one type of membrane is also greatly reduced by fixed ions in the membrane.We can learn some things by studying membrane phenomena without mem- branes, for example those properties of ion exchangers which are independent of the form. We know now that heterogeneity, both as to chemical identity of the groups and as to distribution of link lengths, is much greater than in the earlier na'ive models. We may soon want a membrane model good enough to use this advance. The concentration of fixed charges, the water content, the distribution of a single small-ion electrolyte between water and exchanger, the distribution ratio of two different counter-ions, the rate of exchange by diffusion and particularly the rate of isotopic exchange by self-diffusion can be measured for the exchanger in any form.Properties which depend upon continuous membrane, bulk, or ribbon form are the permeability to water, the electrical transference of water and of ions, the effect on the electromotive force when the exchanger is placed between two different solutions in an electrical cell, and the usual electrical measurements in a varying field. For those phenomena which can be measured without a membrane, we can determine the effect of small variations in the exchanger, such as changing the amount of cross-linking, and systematic studies have been carried out for some of them. I do not know any such systematization for membranes. If we cannot isolate enough of the membrane to analyse, most of the properties which can be determined without a membrane are no longer measurable.If we must keep the membrane under approximately physiological conditions, the limitations are even greater. Many of us are studying synthetic membranes with the hope that they may serve as models for natural membranes. Sometimes I am hopeful that these model studies will give a positive contribution to our knowledge of physiological membrane phenomena. Often I can only admire the methods of the physiologists, but perhaps remind them of Faraday's finger-tips and of the fact that since their phenomena are more complicated than those of the physical chemists, their thinking must be less naive. I hope that even those of you who have not specialized in the study of membranes appreciate the modesty of Prof. Teorell. I will not attempt to dis- tinguish his contributions from those of his predecessors, but the comparison with those of us who have followed reminds me of the high-flying contest of the birds when the sparrow rode on the eagle's back to the top of his flight, and then flew just a few feet higher.I trust also that you have all appreciated the vast amount of work covered in Prof. Teorell's lecture. The rest of the Discussion will cover lightly a few sections of his " tree " of membrane phenomena. Dr. Hill requires little of his membrane. It must be able to support pressure and must be permeable to the solvent and to at least two species of ions but im- permeable to at least one ion species. Dr. Schlogl requires only that there be some fixed charges in the membrane. The other papers deal with specific membranes.The synthetic membranes have a thickness of the order of a millimetre and a pore size, that is a ratio of available volume to twice the internal surface, of the order of a millimicron. The physiological membranes probably have the same pore size but a thickness of the order of a tenth of a micron.30 GENERAL INTRODUCTION The phenomena which will be discussed are mainly membrane potentials, conductivities, transport of ions, neutral solutes and solvent, diffusion, and dis- tribution between membrane and solution. In treating a transport phenomenon it is possible to consider any one species as stationary. In liquid solutions it is customary since the time of Hittorf to consider the solvent as the stationary species, but " true transference numbers " are measured with some non-electrolyte solute considered stationary. With a membrane present, it is usual to consider the membrane as stationary, but I, at least, reserve the right to consider the solvent stationary, and I recommend that each of you take this point of view sometimes. The relative motion of membrane and solvent which is called endosmosis in the first case is minus the fixed charge concentration times the transference number of the fixed charges in the second, and the mobility of the fixed charges so deter- mined is not greatly different from that of the univalent monomers which con- stitute the membrane. 1 Planck, Ann. Physik., 1890, 39, 161, 561. 2 Henderson, 2. physik. Chem., 1907,59, 118 ; 1908,63, 325. 3 Lorenz, J. Physic. Chem., 1952, 56, 775. 4 Staverman, Chem. Weekblad, 1952,48,334 ; Trans. Faraday SOC., 1952,48,176. 5 Kirkwood, Ion Transport Across Membranes (Acad. Press, N.Y., 1954), p. 119. 6 Bull, J. Physic. Chem., 1935, 39, 577. 7 Alexander and Johnson, Colloid Science (Clarendon Press, Oxford, 1949), p. 299. 8 Schlogl, 2. physik. Chem., 1955,3, 73. 9 Unmack, &I. Danske Vid. Selsk., 1937, 15, no. 5.

ISSN:0366-9033    

DOI:10.1039/DF9562100027

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

A. FUNDAMENTAL STUDIES ON THE THEORY OF THE DONNAN MEMBRANE EQUlLIBRIUM BY TERRELL L. HILL Naval Medical Research Institute, Bethesda, Maryland, U.S.A. Received 27th June, 1955 The Donnan membrane equilibrium is discussed using (i) the classical Donnan method (but introducing Debye-Huckel activity coefficients) and (ii) the McMillan-Mayer method. In most of the paper all ions are treated as point charges. If the potential of average force between ions in the outside solution (containing d8usibIe ions only) of the osmotic system is assumed to be of the Debye-Huckel limiting form, the second, third and fourth osmotic pressure virial coefficients are easy to calculate from the McMillan-Mayer equa- tions. The McMillan-Mayer method leads directly to the osmotic pressure, by-passing the membrane potential and other details.However, in a special case, these can be calculated by combining the Donnan and McMillan-Mayer procedures. Both the Donnan and McMillan-Mayer methods have certain limitations, which are pointed out. 1. INTRODUCTION The McMillan-Mayer solution theory 1 is particularly suited to osmotic systems, that is, systems with a semipermeable membrane. The theory has been used to calculate the osmotic pressure of dilute solutions of large molecules by, for example, Zimm 2 and Onsager.3 Zimm considered uncharged polymer mole- cules while Onsager discussed, for the most part, “ hard ”, charged, colloidal particles of various geometrical shapes with electrostatic repulsion between the charged particles entering implicitly through the effective “ size ” of the “ hard ” particles.In the present paper we apply the McMillan-Mayer theory to the Donnan membrane equilibrium. The charge on and electrostatic repulsion between the nondiffusible ions enters explicitly in this treatment. The McMillan-Mayer method is an alternative to the now classical procedure of Donnan. The Donnan method is discussed in 5 2, and the McMillan-Mayer method in Q 3. In 3 4 the two methods are combined in a special case, and their limitations are discussed. A very condensed version of this paper has been published elsewhere,4 as has also an application of the McMillan-Mayer theory 1 9 5 to the binding of ions and molecules on proteins.6 The present work makes no pretence of being an exhaustive analysis of the Donnan membrane equilibrium problem from the McMillan-Mayer point of view.As will be apparent in Q 3, the detailed computa- tions will be different for each choice of the potential of average force. This will depend on molecular size, shape and charge distribution, on electrolyte concentration, etc. We confine ourselves here largely to ions represented by point charges. Also throughout the paper, the solution (in the osmotic equilibrium) containing diffusible ions only is assumed dilute enough to follow the Debye- Hiickel theory. 2. DONNAN METHOD A. GENERAL ELECTROLYTE-DILUTE SOLUTION.-on one side (the “ outside ”) Of a semipermeable membrane we have an aqueous solution of an electrolyte, the j-th species of which has a valence zj and a concentration (molecules/cm3) cj”.3132 THEORY OF DONNAN EQUILIBRIUM On the other side (the “ inside ”) of the membrane, thej-th species has a concentra- tion cp In addition, there is (on the inside) an ion of valence z and concentration p which cannot pass through the membrane. Let $in and #out be the potentials of the two sides, and t,b = +in - t,bOut; a,h is the membrane potential. Assuming the solutions are dilute (activity coefficients unity) and that all ions have negligible size (so that p Y terms may be omitted), cj = CJ exp (- X Z ~ ) = C; (1 - xzj + + ~ 2 ~ j 2 - . . .), (1) where x = c+[kT and E = I electronic charge I. We also have the neutrality conditions I;: C; zj = 0, (2) i and 2 cjzj + pz = 0, i and the osmotic pressure equation (3) where IIin is the osmotic pressure for the system : inside solution - membrane permeable to water only - water.flout has an analogous meaning for the outside solution. From eqn. (I), using eqn. (2), we find (to the term in x2) and hence The first term on the right-hand side of eqn. (6) is the contribution of the non- diffusible species while the second term (z Cj - c/”) is due to the different con- centrations of the diffusible ions on the two sides of the membrane. If eqn. (1) (to the term in x) is substituted for Cj in eqn. (3), we obtain, i so that eqn. (6) can also be written where K is the Debye-Hiickel parameter for the outside solution, i The above derivation of eqn. (8) is of course not new, but is included for reference below. ible electrolyte be uni-univalent with outside concentration c. On the inside, the positive ion of this electrolyte has a concentration c+ and the negative ion c-.We again use the Donnan method here, but introduce Debye-Huckel activity B. 1 : 1 ELECTROLYTE-DEBYE-Hi'r CKEL. ACTIVITY COEFFICIENTS.-Let the diffus-T. L. HILL 33 coefficients for both inside and outside solutions, again considering all ions as point charges. The Debye-Huckel parameters are ~2 (outside) = 8n&lDkT, Ki2 (inside) = (4&/DkT)(c+ + c- + pz2). (1 1) (12) We now equate the inside and outside electrochemical potentials for each of the two diffusible ions : On combining these equations, using the neutrality condition to eliminate c- , we have c- = c+ + z p C+C- = c+(c+ + zp) = c2 exp a { [(: f f g)' - I]} (16) - 11) (17) where a = &/DkT = (d/DkT)% (8nc)*.(1 8) We have written the linear form, eqn. (17), to be self-consistent, since the Debye- Huckel theory is valid only when 7 cc = &/DkT < 1 (outside) and &ci/DkT < 1 (inside). When a = 0, c+ = +[- zp + (z2p2 + 4c2)'], so we write for 0 Q a < 1, where 8 3 0 as cc -+ 0. If eqn. (1 9) is substituted for c I / c in eqn. (17) and we keep only linear terms in a and f , we find a i((!! + [(g)'+ lI))* - l}. (20) = 2[($ + 1 1 Eqn. (20), when substituted in eqn. (15) and (19), gives c+ and c- as functions of p. To obtain the osmotic pressure l7, we use = (.+ + c- + p - .I 24n That is, again to be self-consistent, we use the Debye-Huckel osmotic pressure expression for n i n and flout in eqn. (22). Introducing eqn. (1 l), (12), (15), (19) and (20) in eqn.(22), we obtain, I7 - = p + 2c[@2 + 1 1 4 - 2c - 'It2 + [(z)2 + l]*)i - l} kT 3 2c + ac *{t;+[@--+l]y-l}. B [(E)2 + 1134 THEORY OF DONNAN EQUILIBRIUM In the limit u -+ 0, the last two terms drop out and we have the usual Donnan result (1 : 1 electrolyte, dilute solution). In the limit c -+ 0, This is the osmotic pressure (according to the Debye-Hiickel theory) of a solution containing the non-diffusible ions and their counter-ions, the outside solution in this case being pure water. At the other extreme, when p is small, expansion of eqn. (23) yields 8 The term z2p2/4c agrees, of course, with eqn. (8). To find the membrane potential #, we write eqn. (14) in the form exp (E$/kT) = - exp - 5 DkT(K' - K) (26) " " Substitution of eqn. (15), (19) and (20) in eqn.(26) yields (to linear terms in a, as always) - (27) 1 exP (E#/kT) a((; -+ [@2 + 13")'- l}E [(3'+ 1]+ = (E + [($2 + 1 1 7 ,l - - As c + O , I # I 3 co. Asp +O, we find that The leading term on the right-hand side agrees, as it should, with eqn. (7). eqn. (13) and (14) we have here C. GENERAL ELECTROLYTE-DEBYE-HeCKEL ACTIVITY COEFFICIENTS.-In place O f where and K is given by eqn. (10). Now we write cj = C; + ajp + . . ., (3 1) E$/kT= A p + . . ., (32) where the aj and A are to be determined. From eqn. (lo), (30) and (31), we find where (34) On expanding the exponentials in eqn. (29) and using eqn. (33), there results so thatT. L. HILL Now we note, from eqn. (2), (3) and (31), that 35 or If eqn. (36) is multiplied through, first, by Zj and summed over j [using eqn.(37)] and, second, by zi2 and summed over j , we obtain two linear equations in A and 2: The solution of these equations gives and, from eqn. (36), If the " inside " Debye-Hiickel activity coefficient for then species j is denoted by Fj, The McMillan-Mayer activity coefficients (see Q 4 ~ ) satisfy If we let y/y" refer to the non-diffusible ion then we see from eqn. (43) that the coefficient of p in the expansion of y/y" in powers of p is obtained by putting z for zj in the expression for - [eqn. (41)J. Thus, from the (thermodynamic) argument of eqn. (83) through (87), the second virial coefficient is This agrees of course, with eqn. (8) when a = 0 and with eqn. (25) when the dif- fusible electrolyte is uni-univalent (Z(3) = 0). Since we have limited ourselves in this section to linear terms in p and a, eqn. (44) is believed to be exact to the linear term in cc.3. MCMILLAN-MAYER METHOD McMillan and Mayer showed that if the inside solution in an osmotic system contains a single non-diffusible species, then the osmotic pressure virial coefficients B,, (n/kT expanded in powers of p) are determined by the same formal expressions which Mayer 9 developed for the computation of the virial coefficients of a one- component imperfect gas. In a gas, the virial coefficients depend on the potential of the force between gas molecules ; in an osmotic system, the virial coefficients depend instead on the potential of the average force between non-diffusible mole- cules immersed in the outside solution (which is the same as the inside solution i n the limit p --f 0).36 THEORY OF DONNAN EQUILIBRIUM A.POINT cHARciEs.-We now apply this general result to the Donnan mem- brane equilibrium (i.e. to an osmotic system in which the non-diffusible particles are charged). We consider specifically the system of Q ZA and c with all ions regarded as point charges. The outside solution is assumed sufficiently dilute so that the Debye-Huckel theory is applicable. No such assumption need be made about the inside solution; furthermore, we can calculate the osmotlc pressure virial coefficients directly without considering at all quantities such as Ki, $, n i n , cj, etc. The required potential of average force in the present case (DebyeHiickel theory valid in the outside solution) for a pair of non-diffusible ions immersed in the outside solution is W(r) = z2d exp (- KY)/DY, (45) and for a set of n non-diffusible ions (n > 2) the total potential is a sum of pair potentials.The K in eqn. (45) is defined by eqn. (10). Although we shall calculate below correct virial coefficients (to linear terms in ol) for the potential of eqn. (43, as Mayer 10 has pointed out in another con- nection, these expressions are not necessarily the exact virial coefficients (to linear terms in a) for a system of point charges, since (unknown) higher terms in W(r) [omitted from eqn. (45)] may make additional contributions to the virial co- efficients. In fact, in Q 4 we shall see that the third and higher virial coefficients obtained here are certainly not exact in this sense. To avoid confusion, in the rest of this paper “correct” and “ exact” will be distinguished as in this paragraph.Let us write the osmotic pressure as n/kT=p+B2p2+B3p3+. . ., (46) (47) where Bn is the nth virial coefficient, and let us define hj = exp [- W(rij)/kT] - 1. where drl is the volume element for particle 1, etc., and the integrations are carried out over the volume V. On expanding the exponential in eqn. (47), we have Two terms in this expansion suffice to provide the linear term 11 in a = &c/DkT for B2, and only the first term is necessary for B3 and higher virial coefficients. Substituting eqn. (45) and (50) in eqn. (48), we find after elementary integrations (51) B2 = Bill + .Eli2) The first term, B;’), in eqn. (51) agrees with eqn.(44) while Bi2) also agrees with eqn. (44) when 12 Z(3) = 0. In the Donnan method B(i) is regarded as arising from the unequal diffusible ion distribution ; as an alternative but equivalent point of view, we see here that we may attribute B$’) to the repulsive forcesT. L. HILL 37 [eqn. (45)] between non-diffusible ions in the limit p -+ 0. The agreement of eqn. (51) with eqn. (8) [or (44)] as regards B$') is interesting because the Debye- Hiickel theory is used to obtain Bil) in the McMillan-Mayer method but not in the Donnan method. Although this appears to be a confirmation of the Debye-Hiickel limiting law, it is actually only a verification of the fact that electrical neutrality has been properly taken into account in the Debye-Hiickel theory (as it has in the Donnan treatment of the membrane equilibrium problem).This can be seen as follows.* Let W,&) be the potential of average force between ions of species i and j in the outside solution. We do not assume that Wij(r) has the form of the Debye-Hiickel potential, then is the local concentration of an ion of species j in the neighbourhood of an ion of species i. The total charge in the ion atmosphere of an ion of species i must be - ZiE (neutrality condition) : If we substitute eqn. (a) in eqn. (b), keep only the first two terms in the expansion of the exponential, and use eqn. (2) (neutrality condition), then where we have written Turning now to From eqn. (48), Wij(r) = zizj+b(r) + . . . (4 W(r) = zW$(r). (4 the calculation of &(I), the corresponding W(Y) here is (50) and (e), we find Putting the " neutrality relation ", eqn.(c) in eqn. (0, we obtain B$') E z2/22(2), ( g ) just as in eqn. (8) and (52). That is, we can derive eqn. (9) using the neutrality condition only (as in the Donnan method), and without committing ourselves as to the form of $(r). We may anticipate that when the correct potential of average force is used for any pair of molecules with a fixed charge z, regardless of how dilute or con- centrated the outside solution, B2 will consist of B$') (which is in dependent of T, D, molecular size and shape, etc.) plus other terms (not independent of these factors) ; see, for example, eqn. (66). The third virial coefficient follows from eqn. (49) and (50). The method of Bird, Spotz and Hirschfelder 13 may be used, or one may adopt the following alternative procedure.Write R = r12, s = ~ 1 3 , Y = r23 and introduce bipolar co-ordinates. Then, in eqn. (49), put dr3 = (2nsr/R) dsdr, r roo and J ( )drldr2 = V Jo ( )47~R2dR. v *The analysis in this paragraph was presented in the General Discussion, and was stimulated by the remarks of Prof. G. Scatchard (see Discussion remarks),38 THEORY OF DONNAN EQUILIBRIUM Thus ~3 = - Jrf(R)RdR Jr f(r)rdr S::Ir,f(s)sds. Inserting f = - W/kT, we obtain (54) This disagrees with the Donnan third virial coefficient in eqn. (25) (where there is an additional term in 24). One can be certain that the third virial coefficient in eqn. (25) is not exact since it is negative for small enough I z 1, which is impossible [from the nature of eqn.(49)] with strictly repulsive forces between non-diffusible ions. Also, as already mentioned, we shall see in $ 4 that eqn. (55) as well cannot be exact. The fourth and higher virial coefficients involve 9 integrals with several terms in the integrand instead of just one term as in eqn. (48) and (49). However, it is easy to show that, of the several terms, only one term for each B, (n > 3) gives a contribution to Bn which is linear in cc (using f = - W/kT for each pair interaction). The use of higher powers of l/kT in eqn. (50) or of other terms in the integrand, or both, leadst o contributions to B, involving am, where rn = 2, 3, . . . . The contribution to B,, linear in a, referred to above, arises from the “ cyclic ” term in the integrand ; for example [see also eqn.(49)], (56) and in general (n > 3) B, =(- A,/V) J (product of n f ’s) (product of n dr’s) = - A, 1 (product of n factors - W/kT)(product of (n - 1)dr’s) 2 2 9 = - An(- 1)” ( - DkT) S3J (product of n factors -- KR where A, and A,’ are positive constants [for example, A3’ = 1/24 in eqn. (55) and A4’ = 3/128 in eqn. (58)]. It is easy to calculate B4 but higher virial coefficients present a more serious problem, and are not discussed further [beyond eqn. (57)]. We rewrite eqn. (56) as ~4 = (- 3/8 v J fi4f24j23fi 3drld~zdr3dr4 9 and put dr3 = (27~xr/R)dsdr, dr4 = (2my/R)dxdy, Iv ( ) drldrz = V Then With f =- W/kT, 234 = - 3z80(/128(ZQ))3.T. L. HILL 39 In the special case of a 1 : 1 (diffusible) electrolyte with c: = c: = c (outside solution), as in 0 2 ~ , we have n a26 3 a28 kT -- - P + E(1- 7)]p2 + 9 j ~ 3 - s 3 p 4 + .. . . (5% B. IONS OF DIAMETER a.-Suppose all the ions, diffusible and non-diffusible, instead of being point charges, have a hard core of diameter a. Then, according to the Debye-Hiickel theory, the limiting potential of average force for a pair of non-diffusible ions immersed in the outside solution is W(r) = + GO, r < a a)1, r > a . - 2242 exp [- K ( r - - Dr(1 + Ka) We shall calculate B2 and B3 below for this potential, but we digress here to point out that eqn. (60) may also be regarded as the (approximate) potential of average force between a pair of non-diffusible particles of uniform surface charge z and diameter a, with the diffusible ions considered again as point charges.This is a useful model for charged, spherical colloidal particles or other large molecules (non-diffusible) where the electrolyte (diffusible) consists of ions of ordinary size. Venvey and Overbeek 14 discuss this model at length. Eqn. (60) is only a first approximation 14 to the potential in this case. B2 and B3, below, therefore have the additional significance of approximate virial coefficients for the model described in this papagraph. Essentially following Mayer,lo it is convenient to define w* and @ as follows : w w* kT - kT @? _ _ _ - w*lkT = 4- co , r < a = 0, r 2 a a) = 0, r < a, Also, we define - 1, r <a, 0, r > a ' k* = exp (- w*/kT) - 1 = = k * + @+%+. . . ) ( k * + l ) ( @2 Eqn. (48) and (65) (to the term in a)2) give where the first term is the second virial coefficient of a gas of hard spheres of radius a and the second term is the same as found for point charges [eqn.(52)]. The hard sphere term is negligible for small ions (a 3A) at ordinary electrolyte concentrations but may be important for large (colloidal) particles. Thus, the first term is of the same order of magnitude as the second term if a3 l/Z(2). For example, taking 2 3 2 ) = 0.1 M, a g 25 A.40 THEORY OF DONNAN EQUILIBRIUM We now consider B3. With R = yl2, s = ~ 1 3 and r = r23, the integral in eqn. (49) becomes (k*(s) + [@(s) + + W s ) + . . .])drldr2dr3 = k*(s)k*(r) k* (R) drldr2dr3 + 3 k*(s)k*(r)Q(R)dvldr2dr3 + 3 1 k*(s)@(r)~(~)drldY2dv3 + 1 @(s)~(r)Q(R)drldr2dr3 + . . . (67) Terms not listed in the last line of eqn.(67) can be shown to depend on a higher power of l/kT than 3J2 (linear in 01). The integrals in eqn. (67) are straight- forward but the limits require some care because of the intervaIs in which the functions k* and @ vanish. As an example, the third integral is [see eqn. ($411 The final result for B3, including terms in (l/kT)+, is B3 = 52 + &5[ 22E2 ](: - g K a -1. . .) 18 DkT(1 + .a) 2 exp(2Ka) [ Dk<y+ ~a)] K (1 + . .I where the order of terms corresponds to that in eqn. (67). The first term is the " hard sphere " term and the last should be compared with eqn. (55). For small ions (a E 3&, only the last term is important at ordinary electrolyte concentra- tions. For the first three terms to be of the same order of magnitude as the last, the criterion is again a3 g 1/Z(2).In the example already given, a g 2 5 A. 4. COMBINED DONNAN AND MCMILLAN-MAYER METHODS APPLIED TO The McMillan-Mayer theory, applied to the Donnan membrane equilibrium, gives the osmotic pressure directly. We cannot expect that purely thermodynamic manipulations on the expression for the osmotic pressure so obtained will permit a calculation of the membrane potential (and other details by-passed in the McMillan-Mayer method). This follows because the separation of the electro- chemical potential (a thermodynamic quantity which can be related to the osmotic pressure) into an " electrical " part and a " chemical *' part is an extra-thermo- dynamic procedure. 1 : 1 : 1-ELECTROLYTET. L. HILL 41 All ions are treated as point charges and the outside solution follows the Debye-Huckel theory.The inside solution contains singly charged diffusible ions with concentrations c+ and c- and the singly charged (z = + 1) non-diffusible ion with concentration p, while both diffusible ions have a concentration c in the outside solution. If we use (i) the McMillan-Mayer osmotic pressure, (ii) the fundamental Donnan equa- tions for the diffusible ions, and (iii) the extra-thermodynamic assumption (which is obviously correct on symmetry grounds) that the " usual " activity coefficients (denoted by Y k below) of the three ions in the inside solution are identical, it becomes possible to obtain the membrane potential and other details referred to above. The procedure below for the 1 : 1 : 1-case applies also (by redefining E) when 1 z I $: 1 provided all ions have the same absolute charge (2 : 2 : 2-, 3 : 3 : 3-, .. . electrolyte); Z(3) = 0. If the three ions do not have the same absolute charge, a further assumption must be introduced specifying the dependence of activity coefficient on absolute charge. We confine ourselves here to the sym- metrical case in order to avoid introduction of any approximations or guesses. A. ANALYSIS.-We now introduce the various activity coefficients required below. In any solution, McMillan and Mayer define an activity c'k of the k-th species as being proportional to exp (pk/kT) ( p k = electrochemical potential for a charged species) with a proportionality constant chosen so that Zk + p k , the concentration (number per unit volume) of the k-th species, as the system becomes infinitely dilute with respect to all species (perfect gas). The activity coefficient yk in the solution is then defined by ~k = Zk/pk.For the positive diffusible ion we have We consider here the system of § 2 ~ , taking z = + 1. F+ = c+y+ (inside, $in) = cy: (outside, $ouJ. (69) Let f+ be the limiting value of 7: when c -+ 0, keeping #out constant (all potentials are relative to the potential of the perfect gas used in the definition of zk). Then if we rewrite eqn. (69) as the quantity 7: = y"+yt for the outside solution is the " usual " concentration activity coefficient which approaches unity as c + 0. Since the outside solution is assumed to follow the Debye-Huckel theory, (71) - yy = exp (- E ~ K / ~ D ~ T ) = exp (- a/2) where K and cc are defined by eqn.(1 1) and (18). On the other hand, y+/yS, contains exp [($in - $,,t)/kT)] as well as ?+, so that y-/y: = 7- exp (- qh/kT). (74) We denote the McMillan-Mayer activity coefficient for the non-diffusible ion (no subscript) in the inside solution by y and in the outside solution by yo (that is, y -+ yo as p --f 0). Then, for the outside solution, yo = y:, ys = y: , (75) - yo = 7: = 7: = exp (- 4 2 ) , and for the inside solution, y = y + ,42 THEORY OF DONNAN EQUILIBRIUM Eqn. (76b) is the extra-thermodynamic assumption (3) referred to above. Thus the relation c+y+ = cy: becomes, after cancelling ys, (77) c+y exp (E$/kT) = c?', and c-7- = cy0 becomes, after cancelling yL9 Eqn. (77) and (78) correspond to eqn. (13) and (14) of 3 2B.c-7 exp (- qb/kT) = c r o . Eqn. (77) and (78) can be written as r+=r=-= c r exP ( E W n Y: Y O c+ 7" ¶ (79) and therefore c+ -+). c- To c c The general procedure may now be outlined. We can obtain y/yo as a power series in p from the osmotic pressure virial coefficients (as shown below). This gives [eqn. (79)] c/c+ and hence c+/c as power series in p. Since (neutrality of inside solution) (82) we also have c-/c and therefore [eqn. (Sl)] cyO/y)2 and r/ro as power series in p. Using this last result (with c/c+) in eqn. (79), we find Et,bJkT as a power series in p. The osmotic pressure may be expanded 5 in powers of z/yo(z/yo + p as p -+ 0) instead of p. Denote the coefficients by bj : c- = c+ + p , n/kT = 1 bj(S/y0)jy (bl = 1). i r l The thermodynamic relation 317/kT = Z ( - 3 ; - ) C T .then gives, P = 2 ibj (z/yo>J. 1 2 1 I f eqn. (84) is substituted for p in the virial expansion and the resulting series com- pared with eqn. (83), the bj can be related to the Bn. Eqn. (84) can then be inverted, (85) and the coefficients aj' also expressed 5v9 in terms of the Bn : al' = 1, a2' = 2B2, a3' = gB3 + 2B9, a4' = QB4 + 3B2B3 + %B23, etc. (86) Finally, since z = py, s/yo = al'p + a2'p2 + a3'p3 + . . .¶ yly" = al' + a2'p + a3'p2 + a4'p3 + . . . . (87) From eqn. (59), (86), and (87) we find (to linear terms in a) _ - y - c = 1 +(:-:):+ (!-??)(!?)2+ 8 64 c ( A - 2 ) p ) 3 + . 48 256 c ., (88) yo c+ and [see eqn. (82)]T L. HILL Then, using eqn. (81), (89) and (90), Finally, from eqn. (79), (88) and (91), 43 (91) (93) Eqn.(89), (90), (92) and (93) summarize the properties of the inside solution as a function of p. solution, N,, N-, N, n, A'" and r by : c+ = N+/V, c- = N-/V, p = N/V, Jlr = N+ + N- 4- N, n = X / V = 2c-, CORRECTION TO THE DEBYE-H6CKEL THEORY.-Let US define, for the inside 4 m 2 3 (N+ + N- + N ) r= (*) (12T)2 v ' (94) Let Fez be the contribution of interionic forces to the Gibbs free energy of the inside solution. Then, from dimensional considerations,~~ we may state that Fel/NkT should be a function of r only.16 In the Debye-Hiickel limit, this function is - r*. We therefore write - Fez/JVXT = r* + f(r), (95) where f(r) is a correction to the Debye-Huckel limiting expression. Writing Y = N,v, in eqn. (94), where N, and vs are the number and molecular volume of solvent (water) molecules in the inside solution, and defining Dez, the electrostatic contribution to IIin, by and Eqn.(97) and (98) can be rewritten in the form, In eqn. (99) and (loo), c-/c is given by eqn. (90) and In 7 by eqn. (92). Also we find IIel/kT from Since l7/kT and c-/c are known,44 THEORY OF DONNAN EQUILIBRIUM Eqn. (99) and (100) then become -r-=- df '"(p>, - + (a, _ _ - 3(3'. . . .) d r 32 c (103) f+rg=-z(c)2+ 1 5a p 3 + . . . . d r 32 c The term in (p/c)4 can also be found, as follows. In view of eqn. (57), let us write B5 = ccB/1280c4, where 0 is an unknown positive number. We now extend all the series starting with eqn. (88) to the term in (p/c)4, leaving 0 unspecified. We find eventually that eqn. (102) and (103) have added terms on the right-hand side of (- -& + !k 1024 + E ) ( 3 " a n d 12288 c ($ - respectively.Now, on adding eqn. (102) f = - " ( 3 3 + (- 64 c The thermodynamic self-consistency solving eqn. (102) for df/dp, integrating eqn. (105) : we substitute the relations and (103), 8 cancels and we have of the calculation can be checked by with respect to p, and again obtaining (; - g)($2 + . . .I, into eqn. (102) and find which, on integration with respect to p (f = 0 when p = 0), gives eqn. (105). If, instead of eqn. (95), we write - F,I/JC/lkT = G(F), (108) then a procedure analogous to that in eqn. (96) through (107) (or the use of G = f + F*) leads to B. DIscussIoN.-The McMillan-Mayer calculation would be exact (to linear terms in a) for a system of point charges if the exact potential were used in eqn.(45) (as already pointed out, higher terms which can affect the results are presumably omitted in this equation). The Donnan method (equating electrochemical poten- tials of diffusible ions) would, of course, also be exact if the exact osmotic pressure equation and activity coefficients were used (including higher than Debye-Huckel limiting terms where necessary). We have already seen that the Donnan method with Debye-Hiickel limiting expressions is not exact for third and higher virial coefficients, since B3 can be negative in eqn. (25).T. L. HILL 45 In 3 4A above, we have carried out a thermodynamically self-consistent cal- culation of the function f using the McMillan-Mayer method and eqn. (45). A necessary condition on f in eqn.(105), in order for the calculation to be exact, is that f should be expressible as a function of r only. It is clear from eqn. (106) that this is possible only through the term in p 2 ( f = 0 to p2). To arrive at the term in p3 in eqn. (105), one has to use the third virial coefficient. We can there- fore conclude that starting at least with the third virial coefficient [and with the terms in p 2 in eqn. (88) through (93) and (lol)] inexact results are obtained from eqn. (45). The discrepancy between eqn. (44) and (51) with respect to Bi2) when Z(3) $. 0 also appears to be due to eqn. (43, since eqn. (44) is believed to be exact (to the linear term in a). The self-consistency of the Donnan calculation of 5 2 can easily be checked; for simplicity we consider here a special case.Using eqn. (22), with expansions to p3, eqn. (25) gives, taking z = 1, 5a 9 6 c 2 B 3 = - - On the other hand, on expanding eqn. (19) to p2, with z = 1, we find c+ But, as in eqn. (88), c/c+ = y/yo so that the coefficients in eqn. (111) are a2' and a3'. The virial coefficients follow then from eqn. (86) and we find again eqn. (1 10). The method (in the Donnan case) based on the use of eqn. (86) is in general to be preferred since the virial coefficients can be obtained using series carried out to one less power of p than in the method based on eqn. (22). 1 McMillan and Mayer, J. Chem. Physics, 1945,13,276. 2 Zimm, J. Chem. Physics, 1946, 14, 164. 3 Onsager, Ann. N. Y. Acad. Sci., 1949, 51, 627. 4 Hill, J. Chern. Physics, 1954,22, 1251. 5 For a review of the McMillan-Mayer theory, see Hill, Statistical Mechanics (McGraw- 6 Hill, J. Chem. Physics, 1955, 23, 623, 2270. 7 Let Y(r) be the potential at a distance t from an ion in the outside solution. The Debye-Huckel assumption, cY(r)/kT< 1, when applied at t = 1 / ~ (the value of t at which the net charge in a shell of thickness dr is a maximum), is essentially dK/DkT 4 1. 8 The term in p2 is also contained in Hill, Faraday SOC. Discussions, 1953, 13, 132, eqn. (276). 9 Mayer and Mayer, Statistical Mechanics (John Wiley and Sons, New York, 1940). In neither case is it necessary to assume that the total intermolecular potential is the sum of pair potentials. Hill, New York, 1956). 10 Mayer, J. Chem. Physics, 1950, 18, 1426. 11 The linear term in CL corresponds to the term in (llk7')Q if the expansion is regarded 12 This relationship is discussed further in 9 4 ~ . 13 Bird, Spotz and Hirschfelder, J. Chern. Physics, 1950, 18, 1395. 14 Venvey and Overbeeck, Theory of the Stability of Lyophobic Colloids (Elsevier 15 Fowler and Guggenheim, Statistical Thermodynamics (Cambridge University Press, 16 For our special case, r is the same quantity as 7 3 of Berlin and Montroll, J. Chem. as one in powers of llkT. Publishing Co., Amsterdam, 1948). 1939), p. 384. Physics, 1952, 20, 75.

ISSN:0366-9033    

DOI:10.1039/DF9562100031

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年代:1956

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THE SIGNIFICANCE OF CONVECTION IN TRANSPORT PROCESSES ACROSS POROUS MEMBRANES BY R. SCHLOGL Max-Planck-Institut fur physikalische Chemie, Gottingen Bunsenstrasse 10 Received 26th January, 1956 For the treatment of transport phenomena across membranes according to the irrever- sible thermodynamics of" continuous systems ", the particle fluxes can be separated into a convection common to all particles, and fluxes relative to the local centre of gravity. The convection velocity represents an additional unknown quantity requiring a further known relationship ; this is provided by the balance of hydrodynamical forces. The separation of the convection term has proved itself useful both in the theoretical treatment of " anomalous osmosis " and in experimental investigations on current flow across ion- exchange membranes.A procedure by Kirkwood by which he obtains linear relation- ships between fluxes and forces will be considered from this viewpoint. The current theories on the transport of charged or uncharged particles across membranes can be roughly divided into the following groups. GROUP 1 considers the membrane as a surface of discontinuity setting up different resistances to the passages of the various molecular or ionic species.1-3 The driving forces are the diferences of the general chemical potential between the two outer media. (Differences of pressure or electrical chemical potential are included in the general chemical potential). GROUP 2 considers the membrane as a quasi-homogeneous intermediate phase of finite thickness in which the local gradients of the general chemical potential act as driving forces.4-15. Convection may also contribute to particle transport within the membrane. GROUP 3 considers the membrane as a series of potential energy barriers lying one behind the other, thus forming, in contrast to group 2, an inhomogeneous intermediate phase.16-18 An (irregular) spatial lattice is formed due to the higher probability of finding a particle in the positions between the activation thresholds.The driving forces arise from the differences between the transition probabilities in opposite directions perpendicular to the membrane. This grouping attempts to classify the various mathematical approaches, according to the ideal models on which they are based. It is in fact too schematic, as many theories occupy intermediate positions.No author is likely to take the view that one of these treatments is right and the others wrong. The various descriptions supplement each other, and depending on the system under considera- tion, one of the three will prove the most suitable. It may be shown, for example, that when the number of activation thresholds becomes very large, and the distance between the lattice points sufficiently small, then groups 3 and 2 merge into each other. A transition is also to be found between groups 1 and 2, and this will be dis- cussed later. Unlike group 3, groups 1 and 2 can be classified in the general scheme of irrever- sible thermodynamics. In 1 as well as in 2, linear relationships are assumed between the particle fluxes and the driving forces.Owing to the differing characters of the driving forces, 1 is treated according to the method of " discontinuous systems ", and 2 according to that of " continuous systems ' 7 . An integration in group 2 across the membrane does not as a rule yield a linear relationship between 46R. SCHLOGL 47 the flux and the general chemical potential differences. Only for sufficientlj small differences does group 2 merge into group 1 after integration. In this sense 2 is more general than 1. Group 2 is, however, inferior to group 1 in that a number of idealizations must be assumed before an explicit integration can be effected. In a recently published work,lg the chief interest of which lies in time-dependent integrals of equations of motion, Kirkwood finds a connection between groups 2 and 1.In our present discussion we are especially interested in this transition. Kirkwood's initial flux equation differs from that normally used in the treatment of " continuous systems " in irreversible thermodynamics. For the flux ja (Le., the number of moles of the molecular or ionic species a which are transported in unit time across the membrane cross-section), he writes : j , = - p c q B dik - (a, /3= 1,2, . . . , n). D d x a and /3 are the indices for the n species which participate in the transport. P p is the general chemical potential of the species /I. dj$dx is the potential gradient at the position x. Qd is a coefficient depending on x, but not on the forces d&/dx, and in addition satisfying the symmetry relationship fzap = Qp,.However, when evaluating the production of entropy, the irreversible thenno- dynamics of " continuous systems "20 distinguishes between the movement of the various species relative to each other, and the translational movement of the common (local) centre of gravity of all mobile particles. Thus, Here C, is the concentration of the species a, and v the velocity of the centre of gravity of all species. The coefficients Ld obey, as before, the symmetry relation- ship Lcq~ = Lp,, and are in addition linearly dependent upon one another, thus: Mu, Mp are the respective molar masses of the components a and /3. It is the aim of this paper to draw attention to the convection term C,v in (2), and to ascertain its significance in transport processes across membranes.At the same time we shall also discover under what conditions Kirkwood's eqn. (1) is equivalent to eqn. (2) for continuous systems. In one trivial case this equivalence is obvious, namely, in membrane systems with such high flow resistances that the velocity v of the centre of gravity vanishes. This is very likely the case in many biological membranes for which Kirkwood developed his theory. The equivalence is also possible, however, under more general conditions, as we shall see presently. The equations (2) contain v as an extra unknown quantity, and are therefore as such not integrable. To make the integration possible we must introduce the important relationship of the balance of hydrodynamical forces, The pressure gradient dp/dx and the electrical field d$/dx are assumed to constitute the forces driving the fluid across the membrane.,oe is the electrical space charge of a unit volume of fluid. K is a measure of the flow resistance of the membrane. An observable flow can take place especially in a membrane with porous structure. Now it can be shown that the equivalence of eqn. (I) with (2) and (4) is guaran- teed if K depends only on the membrane properties and the concentration Cp, but not on the velocities of the single components /3 relative to each other. In48 CONVECTION I N TRANSPORT PROCESSES general, this condition will not be strictly fulfilled. As is shown in the appendix, Kv takes the form IK,pp, where vp denotes the average particle velocity of the species /3, and Kp is a constant of matter (depending only on collisional cross- sections of the particles, the local concentration, and average pore cross-section). To confirm this statement we form the expression zCpdpD/dx, and with the use of the Gibbs-Duhem relationship obtain at once the equation which is, except for the signs, identical with the left-hand side of (4).Expressing v in (2) with the help of (4) and (5), we obtain Hence, we arrive at Kirkwood‘s eqn. (I), provided that K is a physical property of the system-that is, a space function which does not depend on vp. In practice this will always be a very good approximation, and any small deviations will almost certainly be insignificant compared with experimental errors. The relationship between SZll and the diffusion coefficient D, given by Kirkwood for binary systems, i.e.must, however, be re-written for a flow resistance K which is not infinite, thus forming a corresponding relationship bctween D and ,511. It is in any case only valid in this form (7) for sufficiently small concentrations C1 of the solute. With reference to the classification of membrane theories given in the introduc- tion, it would be profitable to make one more remark about the transition by which Kirkwood derives from eqn. (1) (which belongs to group 2) to an equation belonging to group 1. For this purpose he solves (1) with respect to the forces djip/dx, and integrates j, across the membrane, assuming steady-state conditions (ja independent of x). The differences of the values at either side of the membrane thus appear in place of the gradients of &.Solving again with respect to the fluxes j,, the formal linear relationships between the fluxes and the chemical potential differences are obtained, giving an equation of group 1. The coefficients now appear- ing, o c r p , again satisfy the symmetry relationships ; they are, however, dependent as Kirkwood emphasizes, not exclusively on the membrane properties, but also on the concentrations of all the components in the solutions. Generally speaking, a linear relationship of this type, which belongs to group 1, is not obtained by the integration of a group 2 equation. We can take as an example the integrals in Teorell’s theory 10 which are derived from the Nernst-Planck equations of motion. These equations are a very specialized form of the approach represented by group 2 : all coefficients LZp, excepting Lm, are assumed equal to zero, and since no convection is taken into consideration, K must be equated to CO.As is known, the integrals of these equations do not lead to a linear relationship between the fluxes and the (externally applied) chemical potential differences. This discrepancy can be explained as follows. The Kirkwood coefficients Wap depend also on the concentration profiles of all the species within the membrane. But as the profile itself depends on the electrical potential difference and the applied pressure difference, the wab terms are also functions of the applied “forces ”. The integrated equations are thus only apparently linear with respect to the forces, that is, they only appear to belong to group 1.However, the deductions drawn by Kirkwood in his paper remain valid for sufficiently small differences App, so that within this range, his theory belongs to group 1. We now return to the “ convection term ” in eqn. (2) and ask when the termR. SCHLOGL 49 C,CB/K in (6) becomes comparable with the term Lap. To my knowledge, no measurements have as yet been presented on the “ mixed ” coefficients L,p, for ct $; /3. All theories of group 2 which have attempted to make an explicit integra- tion of the equation of ionic motion have, for this purpose, equated the coefficients Lap to zero. This should in fact cause no serious error if the solvation shells are treated as belonging to the particles they surround.One can, however, arrive at an estimate of Lm with the help of eqn. (7), in which SZ, should be substituted by La,, if D is known. Investigations which we have made on membranes of ion-exchange material (phenolsulphonic acid) have revealed that the term Cz/K outweighs the term L,. It may be said in general that for porous membranes in concentrated solutions (over 0.1 M), the two terms are already comparable for pore sizes of 10 A. To illustrate the influence of convection on transport phenomena, I should like here to quote two examples taken from other papers.21.22 Fig. 1 shows the c.11 If c+ It c * (4 (b) FIG. 1 .-Calculated cation concentration profiles in a cation exchange membrane under the influence of electric current ; (a) positive current, (b) negative.DIDO is a measure of the flow resistance of the membrane. Boundary concentration C; = 1.5 (inside left) and C’; = 4 (inside right). (Z. plzysik. Chern. N.F., 1955, 5, 384.) steady-state concentration profiles within a cation exchange membrane when an electric current is applied ; each curve is calculated for a different flow resistance. The electrolyte is NaCl, the concentration of which at the left side of the membrane is 1 M and at the right side 3.5 M. D/& is a (dimensionless) measure of the flow resistance K. The profiles are calculated by means of the Nernst-Planck equations of motion, in which a convection term, corresponding to that in eqn. (2), is inserted. The diagram on the left is distinguished from that on the right by the direction of the applied current.Equal current densities are chosen for the two diagrams. The curves in which DID0 = 03 correspond to the theory of Teorell in which the convection vanishes, With diminishing flow resistance the curvature is inverted. The electro-osmotic liquid flow, whose direction in a cation exchanger coincides with that of the electric current, finally reverses the distribution completely. The contribution of convection to electrolyte transfer is, as the calculation shows, greater at points of higher concentration. S-shaped curves with an inflection point will be formed for membranes with average flow resistances. Fig. 2 shows concentration profiles measured by Schodel21 for phenolsulphonic acid membranes. The membranes used in the upper curves were strongly cross- linked, those in the lower curves weakly cross-linked.Comparison with the cal- culated curve indicates that the contribution of convection, rather than being insignificant, is actually quite considerable. The value of the flow resistance estimated from the measured concentration profile was in good agreement with the water permeability measured directly on the same membrane material. The contribution of convection to electrical conductivity lay roughly between 10 and 45 %.50 CONVECTION I N TRANSPORT PROCESSES As a further example22 we consider the same system, but with no electrical current. We assume a Donnan equilibrium at the two membrane surfaces. At these phase boundaries not only does there exist an electrical potential difference, but also, due to the different concentrations of the osmotically effective particles, the hydrostatic pressure within the membrane exceeds that in the adjacent solutions.Now the hydrostatic pressure within the membrane, as can be easily demonstrated, is higher on the more dilute side (left) than on the more concentrated side (right). FIG. 2.-Measured cation concentration profile in a phenolsulphonic acid membrane ; (a) and (b) cross-linked more strongly than (c) and ( d ) ; arrows show direction of electric current. Boundary concentrations differ somewhat from the values chosen in fig. 1. (2. physik. Chem.N.F., 1955, 5, 376.) The pressure difference at the phase boundary does not act as a driving force, for here we have assumed equilibrium. The pressure difference within the membrane, however, acts as a driving pump on the pore liquid, forcing it from the more dilute to the more concentrated solution. In other words if the contribution of the electric field vanishes in (4), a positive osmosis results due solely to the inner osmotic pressure difference of the membrane.In the example with an electric current investigated previously, the contribu- tion of the pressure term does not vanish, but the electrical term begins to pre- dominate at a rather low current density. In the case investigated above where there is no current, the pressure makes the chief contribution. Of course electrical fields also share in the process, their magnitude being calculable from the cation and anion mobilities. Without going into details, we should like to state the following consequences of the theory.If the cation is more mobile than, or as mobile as the anion, we find a positive osmosis. If the anion is much more mobile than the cation, we find a fluid transport from the concentrated to the dilute solu- tion, in other words a negative osmosis Taking the latter case and referring to eqn. (4), the contribution of the diffusion potential outweighs that of the innerK .F s CHLO GL 51 Osmotic pressure difference. Thus we arrive at a natural interpretation of the phenomenon of “ anomalous osmosis’’ and find that it yields to quantitative explanation. To summarize, it may be said that for membranes whose water permeability is not too low, among which can be reckoned ion exchangers with more than 65 % water content, convection effects can play a considerable role.When such systems are subjected to theoretical treatment, it is advantageous to split the ionic fluxes according to eqn. (2) and make use of the balance of hydrodynamical forces (eqn. (4)); this method is likely to lead to the clearest mathematical separation of the essential physical processes involved. APPENDIX THE BALANCE OF MECHANICAL FORCES FOR SEVERAL COMPONENTS In the molecular theory of viscosity it is shown that between two adjacent fluid1 ayer, moving in the x-direction with slightly different velocities v and v + dv, the exchangc of momentum in the direction normal to the surface (z-coordinate) results in an inter action given by the force f per unit surface area : dv 1 d V f = q - = -rnIwN - dz 3 dz’ where rn is the mass, I the mean free path, w the mean molecular velocity, and N thc number of molecules per unit volume.A complete analogue is found for various moleculat species /3 having various translational velocities vb. It should be noted that in this case vp = +rnplgwgNg depends, on account of Zg and wp on the concentrations of all species. When the concentrations Cg are very low, Zg and wi are for physical reasons independent of Cp Thus, because of the factor Ng, 70 becomes proportional to Cg as Cp-t 0. For the pressure gradient in a cylindrical tube, a perfect analogue to the Hagen-Poiseuille equation is found : where r = radial distance from cylinder axis. If we now assume that the particle concentration does not depend on Y, the fluid being homogeneously mixed over the cylinder cross-section, we find after integrating twice in the radial direction, where 5 p is the mean value of vg over the cylinder cross-section, and a the cylinder radius.The capillaries in a membrane deviate considerably from the cylindrical form (having statistically twisting and branching axes, and statistically changing cross-sectional forms), Taking the average over many pores yields, in place of the factor of 8/&, another numerical factor depending only on the membrane properties. If we now leave out the averaging bar over VB, we can write the general expression - dn L- = 1 K p g . dx B Here Kp depends only on the concentrations C, and on the membrane properties. over, for small concentrations Cp, Kp will be proportional to Cs. More-52 MEMBRANB POTENTIALS 1 Wiebenga, Rec. trao. chim., 1946, 65, 273. 2 Mazur and Overbeek, Rec. trav. chim., 1951,70, 83. 3 Staverman, Trans. Faraday SOC., 1952, 48, 176. 4 Teorell, Proc. SOC. Expt. Biol. Med., 1935, 33, 282. 5 Meyer and Sievers, Helv. chim. Acta, 1936, 19, 649, 665, 987 ; 1937, 20, 634. 6 Goldman, J. Gen. Physiol., 1943, 27, 37. 7 Hodgkin and Katz, J. Physiol., 1949, 108, 37. 8 Eriksson, Ann. Roy. Agric. Coll., Sweden, 1949, 16, 420. 9 Keynes, J. Physiol., 1951, 114, 119. 10 Teorell, Z. Elektrochem., 1951, 55, 445. 11 Schmid, 2. Elecktrochem., 1951, 55, 295 ; 1952, 56, 181. 12 Lorenz, J. Physic. Chem., 1952, 56, 775. 13 Scatchard, J. Amer. Chem. SOC., 1953, 75, 2883. 14 Schlogl, Z. physik. Chem. N.F., 1954, 1, 305. 15 Mackie and Meares, Proc. Roy. SOC. A., 1955, 232, 498. 16 Davison and Danielli, The Permeability of Natural Membranes (Cambridge, 1943, 17 Laidler and Shuler, J . Chem. Physic., 1949, 17, 851. 18 Zwolinski, Eyring and Reese, J. Physic. Clzem., 1949, 53, 1426. 19 Kirkwood, Ion Transport Across Membranes (Acad. Press, New York, 1954), p. 119. 20 De Groot, Thermodynamics of Irreversible Processes (Amsterdam, 1951), p. 94. 21 Schlogl and Schodel, 2. physik. Chem.N.F., 1955, 5, 372. 22 Schlogl, Z. physik. Chem. N.F., 1955, 3, 73. chapter 21 and appendix A).

ISSN:0366-9033    

DOI:10.1039/DF9562100046

出版商:RSC    

年代:1956

数据来源: RSC

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52 MEMBRANB POTENTIALS MEMBRANE POTENTIALS OF AN ION EXCHANGE MEMBRANE BY M. NAGASAWA AND I. KAGAWA Department of Applied Chemistry, Nagoya University Chikusa-ku, Nagoya, Japan Received 16th Junuary, 1956 By using the ion exchange membrane, Nepton CR-51, measurements were taken of the membrane potentials with different concentrations of simple electrolytes (NaCl, Na,SO,) and polyelectrolyte (sodium polyvinylsulphate), and a comparison made with theories already reported. It was observed that the membrane potential has a linear relationship with the logarithm of Na+ activity at lower concentrations with a slope slightly lower than RT/F. It is concluded that such results are due to the abnormal behaviour of ionic activities within membrane, and it is pointed out that they are important for determining an unknown activity of Na+ by the membrane potential method.The membrane potential of the rigid membrane, such as collodion, Cellophane ion exchange membranes and others, has been widely discussed by several authors on the basis of the theory of Meyer 1 and Teorell.2 Some years ago the more funda- mental equation of membrane potential, eqn. (l), was obtained by Schlogl and Helfferich 3 and, independently, by Nagasawa 4 : where the terms denote the average activities of ions within the membrane and I* their mobilities, and al, a2 the activities of the electrolyte on both sides of the membrane.M. NAGASAWA AND I . KAGAWA 53 If it is assumed that the ionic distribution between the outer and inner phases of the membrane is determined by the Donnan membrane equilibrium,l3 a: and a? in eqn.(1) may be approximately calculated from the following : - - in which A is the average concentration of counter ions of the membrane. Then, if eqn. (2) is introduced into eqn. (1) under the condition that A is constant, Meyer and Teorell’s equation (as already reported by Helfferich 5 ) can be derived from eqn. (1) as follows : I , - I- I+ + 1, u= - and x = (4a2 + &)*. Strictly speaking, it must be remembered, however, that the available range of eqn. (3) is considerably limited because the ionic distribution between two phases is given by the Donnan equilibrium only for membranes having homogeneous structure (see appendix), and also because the integration of eqn. (1) may be im- possible under the condition that A is constant if the activity coefficients of moveable ions within the membrane are not allowed to remain either constant during the variation of outer concentration of electrolyte, or equal to their activity coefficients in the outer solution.If the activity of ions within the membrane must be calculated from a relation other than the Donnan equilibrium, some other equation should be obtained. For the membrane having rigid porous structure, the following equation has already been given by Nagasawa and Kobatake 4 : E = [. log? - cc log (--) a1 + P + (“‘) log pQ)] F a2 a2 + 18 I+ i- 1- a;! + p 9 (4) where the relations were used for the calculation of membrane potential, and a, p and k’s are constant, depending upon the membrane and the electroIyte.Constants a and fi can be easily determined from the following linear relationship between transport number of cation and activity of electrolyte derived from equating eqn. (4) and Nernst’s equation of diffusion potential, Eqn. (4) was reported to be in good agreement with experiments using collodion, Cellophane, glass membrane, etc. In the present paper we show that the activities of ions in ion exchange membrane are better expressed by eqn. (5) than by eqn. (2) and that the observed values of membrane potential are in satisfactory agreement with calculated values from eqn. (4), despite the fact that ion exchange resins are usually supposed to have a comparatively homogenous structure. Moreover we stress the fact that the result thus obtained is mainly because of the abnormal behaviour of ionic activities within the membrane, and therefore we point out the importance of taking into account in full detail their abnormal behaviour for the purpose of discussing the theory of membrane potential and of determining an unknown ionic activity by the membrane potential method.54 MEMBRANE POTENTIALS In recently published papers it was shown that the transport of water with ions through membranes has considerable influence upon the membrane potentials. In the present paper the authors have neglected the discussion of water transport through membranes.Nevertheless, we find satisfactory agreement between experiments and theory. Therefore we may conclude that the deviation of mem- brane potential of ion exchange membranes from the potential of an ideal electrode is caused mainly by the presence of negative ions within the membrane and the abnormal behaviour of ionic activities.EXPERIMENTAL The essential part of the apparatus is shown in fig. 1. Electrolyte solutions wash the surfaces of the ion exchange membrane. The membrane potential appearing on both sides of the membrane was conducted by saturated KCl bridges and calomel electrodes, and measured by an ordinary potentiometer. If to electrode the flow of electrolyte solution is stopped, the value of the potential difference gradually decreases with time, probably because of the variation of electrolyte concentration in the thin layer near the membrane surface. The membrane used in this experiment is Nepton CR-51 which was kindly contributed by Dr.Wayne A. McRae. The electrolytes are NaCI, Na~S04, and Na-polyvinylsulphate (Na-PVS) prepared by the usual method. The Na+ activity of Na-PVS solution was determined by a Na-amalgam electrode, using the technique already reported by Lewis.7 In our experiments, however, the lower limit of activity which could be determined by this method was 0.001 N because the surface of the amalgam was continuously kept clear by dropping amalgam into Na-PVS solution drop-by-drop and the potential of the electrode was quickly determined using the vacuum tube voltmeter constructed of vacuum tube UX-54 and an ordinary potentiometer. A more precise description of the measurement of Na+ activity by the Na-amalgam electrode will be reported in another paper. Na+ activities in low molecular salt solutions were calcu- lated from the average activity coefficients of the salt in Landolt’s table, making use of Lewis’s hypothesis, that ions have the same activity coefficients if the ionic strength in the solutions are the same.rat, KC, bridqc membrane ‘---€ell for measurement Of membrane potential. RESULTS A series of experiments is shown in fig. 2 in which the membrane potential of different concentrations of NaCl were measured, maintaining the ratio of concentrations on both sides of the membrane at constant. Another series is shown in fig. 3 in which they were measured by maintaining the concentration on one side of the membrane constant. Inspection of fig. 3 shows that the membrane potential has an approximately linear relationship with log a1 at low activity of NaCl, but that it deviates from linearity at higher concentrations.The slope of the linear relationship between E and log a1 is nearly equal to but slightly lower than RVF. At activities of NaCl lower than 0.01 N, the relationship between membrane potential and log a1 can be given as (6) E = Eo - a(RT/F) log a1, where Eo is a constant depending upon the nature of the membrane and concentration of electrolyte used for the standard, and u is a constant nearly equal to unity, depending to a small degree upon the nature of the negative ion. TABLE RELATION BETWEEN a AND DEGREE OF ESTERIFICATXON OF Na-PVS no I I1 I11 w NaCl deg. of esterif. 0.740 0.71 1 043 1 0.301 a 0.816 0816 0883 0.927 0947M. NAGASAWA AND I. KAGAWA 55 Eqn.(6) in addition agrees fairly well with experimental results using electrolytes other than NaCI, i.e., Na2S04 and Na-PVS, if ON^+ is introduced into eqn. (6) instead of al. Here it is observed that the value of C( varies with the nature of the negative ion, and that as the degree of esterification of polyvinylsulphate decreases, the values of cc approach the value for NaCI. 0 0 - 5 I FIG. 2.-Membrane potential with NaCI, here C,/C, = const., temp. 25" C. (1) ExPt. values ; (2) values calc. from eqn. (4) ; (3) values of RT/F log (aib2)- E (mV) P FIG. 3.-Membrane potential with NaCl, here C2 = 0.1 N, temp. 25" C. (1) Values calc. from eqn. (4); (2) line of E = EO - (RT/F) log a1. There is a similar relation for H+, the activity of which can be easily determined by measuring the pH.The relation between membrane potential and H+ activity is shown in fig. 6. This behaviour of the membrane for H+ activity is exactly the same as that of a56 MEMBRANE POTENTIALS glass electrode.- fIt is usually found with the glass electrode that the membrane potential can be represented by an equation analogous to eqn. (6) and that it begins to deviate from linear relation at pH = 2, FIG. 4.-Linear relation between membrane potential and Naf activity of Na2SO4: here C2 is 0.1 N of NaC1, temp. 25" C. (1) Expt. values; (2) line of E = EO - (RT/F) log U N ~ + . FIG. 5.-Linear relation between membrane potential and Na+ activity of Na-PVS ; here C2 is approximately 0.01 N of NaCl, ~ temp. 25" C. (1) Expt. values; (2) lines of E = Eo - (RT/F) log UN*+.DISCUSSION If we consider that ion exchange equilibrium between resin phase and solution is based on the Donnan theory of membrane equilibrium as has been generally accepted, we should regard the structure of ion exchange resins as nearly homogene- ous. In this light, the present authors originally thought that experimental mem- brane potentials of ion exchange membrane should be compared with eqn. (3) of Meyer and Teorell. However, a satisfactory agreement between experiments and theory was not found. First, although the theory predicts that the membrane potential will approach lim (RTIF) log (al/a2) as the concentration of electrolyte decreases, the experimental membrane potential tends toward a value lower than lim (RT/F) log(al/a2), as indicated in fig. 2 and as already reported by others ; secondly, eqn.(3) can not explain the linear relationship between E and log al. The solid line in fig. 7 indicates the values calculated from eqn. (3) usingA = 0.1 and U = 1 which are most suitable for experi- ments. Here U has little effect on the calculated values except at higher NaCl concentrations. However, these calculated values are not in satisfactory agree- ment with experiments. Moreover as shown in fig. 8, the experimental values of fig. 2 do not agree with the values calculated using the same values of A and Uas in fig. 7. It is also difficult to find the suitable values of A and U for experiments represented in fig. 2 by the usual method. The linear relationship between E There are three principal points of disagreement. C+O c+oM .NAGASAWA A N D I. KAGAWA 57 and log a N+ in experiments using electrolytes other than NaCl could not be even qualitatively explained from eqn. (3) although, strictly speaking, such comparison between experimental results and theory is not valid. Thirdly, the value A = 0.1 may be too low for the activity of the counter ion in an ion exchange resin when compared with its analytical value even if the fact is taken into account,9~10 that the activity coefficient of sodium ion is usually lower within ion exchange resins than in the simple salt solution. FIG. 6.-Linear relation between membrane potential and H+ activity of polystyrene sulphonic acid ; here C2 is 0.00969 N HCI, temp. 35" C, (1) Expt. values; (2) line of E = EO + (RT'F)pH.FIG. 7.-Comparison between calculated values of eqn. (3) and experimental values (NaCl); here C2 = 0.1 N. (1) Expt. values; (2) calc. values. In contrast, comparing the experimental values with eqn. (4) and (6) derived for the porous, rigid membrane we can obtain a satisfactory agreement. We can see in fig. 9 a linear relation between E and a1 from which a = 0.924 and = 1.268 can be obtained by employing eqn (6). The values calculated from eqn. (4) by introducing a = 0-924-and fi = 1.268 are shown by solid lines in fig. 2 and 3.58 MEMBRANE POTENTIALS Here, we used the same value of l + / L within the membrane as that in the simple salt solution. The value of I + / L exerts little influence on the calculated values. That the experimental values are not consistent with eqn.(3) but satisfactorily so with eqn. (4), is due seemingly to the abnormal behaviour of the ionic activity in the resin, although it may be considered that this appears due to the porous, FIG. S.-Comparison between calculated values of eqn. (3) and experimental values (NaCl) ; here Cl/C:! = 2. (1) Expt. values; (2) values calc. using A = 0.1, U = 3 ; (3) values calc. using A = 0.1, u = 2. FIG. 9.-LLinear relation between E and al. rigid structure of the resin. That is to say, by measuring c$ and a& in the experi- ment of the ionic distribution between membrane phase and outer solution and, further by assuming that the activity coefficient of the anion is little affected by the resin, charge, as may be presumed from the published work of Kagawa and Katsuura,ll we can obtain the value of the activity coefficient of cation within the resin j-? and consequently of 3 using -- the following equation : f' +f c+ * c- +:=&.(8)M. NAGASAWA AND I. KAGAWA 59 The values of 3 so obtained along with the calculated values from eqn. (2) are shown in fig. 10. Thus it can be concluded that the Donnan equilibrium is not adequate in explaining the behaviour of 3, which is much more important than the behaviour of 2 for the purpose of discussing membrane potential. A further conclusion is that the linear approximation in eqn. (3, although not yet entirely satisfactory, may be better than eqn. (2). Similar abnormal behaviour of r;” or within ordinary ion-exchange resins has already been observed by Gregor,9 and also by Kanamaru, Nagasawa and Nakamura.10 FIG.10.-Abnormal behaviour of a? within the ion exchange membrane ; here (1) expt. values of e, (2) expt. values of a?; (3), (3) calc. values of a: and a? assuming A = 1 ; (4), (4)’ assuming A = 0 5 ; (9, (5)’ assuming A = 01. - - From the theoretical point of view it is impossible to prove quantitatively the linear relationship between membrane potential and Na+ activity of polyvinyl sulphate because the polymer negative ion cannot enter the membrane and therefore we cannot predict the effect of the polyelectrolyte upon the Na+ activity within membrane. Nevertheless, we can expect that the experiments with polyvinyl- sulphate at the lower concentration of polyelectrolyte are fairly well expressed by eqn. (6) for the three following reasons : (i) as > af within the ion exchange membrane, it can be seen from eqn.(1) that has greater importance than af for the membrane potential. Therefore, it may be expected that a1 and a2 in eqn. (3) and (4) are nearly equal to the activity of Na+ in the solution. (ii) A linear ap- proximation such as eqn. (5) has widest applicability for all kinds of behaviour of Na+ activity within the membrane. On the contrary, the following equation which is usually used for discussion of the membrane potential of an ion exchange mem- brane at low Na+ concentration can be derived only from the Donnan approxima- tion, the applicability of which is very limited : (9) It is natural to suppose that eqn. (6) is more useful than eqn. (9) for discussing the membrane potential of a Na+ solution of unknown activity. (iii) With the glass electrode, eqn.(7) is also consistent with the experiments with all electrolytes. Eqn. (6) may be important for the determination of Na+ activity by the mem- brane potential method. E = Eo - (RT/F) log aNa+.60 MEMBRANE POTENTIALS APPENDIX When we apply Donnan’s theory to the distribution of electrolyte between the membrane phase and the outer solution, we must assume two equations at the same time, i.e. a: at= a2, (10) where a$ denote the positive and negative ion activities at a point having an electrical poten- tial $ within the membrane phase, and a the average activity of electrolyte in the outer solution, so that If for the purpose of simplifying the following discussion, we assume the membrane phase to be composed of pores of radius r and also if we introduce a$/a = f ( r ) and aT/a = $(r) into eqn.(10) and (ll), we obtain a: = a exp (- qb/kT), af = a exp (E$/kT). (12) f ( r > * *(r) = 1, (13) ’(‘) * into eqn. (14), 1 *(r> Introducing f ( r ) = - obtained from eqn. (13), and K(r) = 1; $(r) . I’ dr we have finally From eqn. (15) we can obtain r2k2(r) - 4rk(r) + 4 = 0. k(r) = 2/r, that is, Moreover, it follows from eqn. (16) that $(r) = a exp (- et,h/kT) = constant. Therefore we should apply the Donnan equilibrium only to an electrolyte distribution between an outer solution and a membrane having a constant value of potential $ i.e. a homogeneous membrane. The authors thank Dr. Wayne A. McRae of Ionics, Incorporated, for his gift of the sample used in this study. Thanks are also due Mr. S. Shimoyama for experimental assistance. 1 Meyer and Sievers, Helv. chim. Acta, 1936, 19, 649, 665, 987. 2 Teorell, Proc. Soc. Expt. Biol., 1935,33, 282. 3 Schlogl and Helfferich, 2. Elektrochem., 1952, 56, 644. 4 Nagasawa, J. Chem. SOC. Japan (Pure Chem. Sect.), 1949,70, 160 5 Helfferich, 2. Elektrochem., 1952, 56, 644. 6 Spiegler, J. Electrochem. SOC., 1953, 100, 303 C. 7 Lewis and Kraus, J. Amer. Chem. SOC., 1910,32, 1459. 8 e.g., Bauman and Eichhorn, J. Amer. Chem. Soc., 1947, 69, 2830. 9 Gregor and Gottlieb, J. Amer. Chem. Soc., 1953, 75, 3539. loKanamaru, Nagasawa and Nakamura, J. Chem. SOC. Japan (Ind. Chem. Sect.), 11 Kagawa and Katsuura, J. Polymer Sci., 1952, 9, 405. 12 Marshall and Bergman, J. Amer. Chem. SOC., 1941, 63, 1911. Schindewolf and Bonhoeffer, 2. Elektrochem., 1953, 57, 216. Kressman, J . Appl. Chem., 1954, 4, 123. 13 Donnan and Guggenheim, 2. physik. Chem., 1932,162,346. Donnan, 2. physik. Chem., 1934,168, 369. Nagasawa and Kobatake, J. Physic. Chem., 1952, 56, 1017. 1953,56,435.

ISSN:0366-9033    

DOI:10.1039/DF9562100052

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

BI-IONIC POTENTIALS BY F. BERGSMA AND A. J. STAVERMAN Centraal Laboratorium T.N.O., Delft Received 18th January, 1956 Bi-ionic potentials (BIP) occur between two solutions containing ions of a different nature and separated by a membrane permeable to these ions and impermeable to ions of other sign. The theory of these potentials is reviewed. A large number of measurements is reported of BIP’s from 4 different ion pairs (Ag+ + H+, Na+ + Ag+, Na+ + H+ and Na+ + K+) and compared with transport measurements in mixtures of these ions. It is found that transport ratios in membranes may differ appreciably from those in free solution. Several discrepancies between experiment and theory show that in the simple theory one or more essential factors are omitted. It is well-known that potential differences are found between two solutions separated by a membrane if the two solutions contain the same electrolyte in different concentrations. These potentials are called Nernst potentials.It is equally well-known that potential differences are found if the two solutions contain electrolytes of a different nature. These potentials are of great interest in biology and acquire increasing interest in industrial practice. In this paper we will consider negative membranes of high selectivity and solu- tions of 1 : I-electrolytes differing in the nature of the cation. The potentials arising between these solutions are called bi-ionic potentials (BIP). Summarizing literature about these potentials can be found in a number of papers by Sollner 1 and by Wyllie.2 By “ negative membranes of high selectivity ” we mean membranes showing transport numbers for the cation which are near unity in the concentration range of interest.Such membranes can be prepared in different ways.3 While Nernst potentials are a measure of the selectivity of a membrane between ions of different sign, BIP’s are a measure of its selectivity between ions of equal sign. At present a large variety of membranes has been described showing nearly 100 % selectivity between ions of different sign. Selectivity between ions of equal sign has never been found to such an extent. The purpose of the work reported in this paper was to find out which factors govern the selectivity with respect to ions of equal sign. THEORY The first investigator who derived a relation between BIP and selectivity was Michaelis.4 Considering solutions of equal concentration but different in the nature of the permeating ions he derived the equation RT UI E = -1n- F ~ 2 ’ where E is the bi-ionic potential and u1 and u2 are the mobilities of the different permeating ions.Sollner 1 suggested replacing 4 and 112 the mobilities by tl and t 2 the transference numbers. Marshall 5 replaced the transference numbers by the products of activities and mobilities, whereupon Wyllie 2 remarked that the apparent mobility in a mixture of electrolytes not only depends upon the real mobility as can be cal- culated from conductivity measurements in pure electrolytes but also on the extent 6162 BI-IONIC POTENTIALS to which the membrane prefers one cation to the other i.e.on the ratio KpM of activity coefficients in the membrane. Thus he found for the BIP in which M and P indicate the critical ions, a' the activity in the solutions and u the real mobility. In these theoretical considerations various assumptions had to be made con- cerning the distribution of the ions in the stationary state. It would be much more satisfactory if an expression for the BIP could be derived without any additional assumptions. This has been shown to be possible for Nernst potentials which can be deduced from the transference numbers by general arguments based upon the thermodynamics of irreversible processes.6 However, a serious objection exists against the application of non-equilibrium thermodynamics to BIP's. That is the fact that this branch of thermodynamics deals exclusively with small deviations from equilibrium whereas in BIP measure- ments the thermodynamic potentials of the critical ions show large, theoretically infinite, differences between the two solutions.The most promising way of applying the thermodynamical theory in this case would be to consider layers parallel to the membrane plane and so thin that the change of the thermodynamic potential from one surface of the layer to the other is small. By calculating the potential differences between the surfaces of these layers and integrating from one membrane surface to the other the BIP could be found. However, this procedure implies some assumptions about the distribution of ions in the membranes. In fact it is identical with the careful treatment of Scatchard 7 who also finds the BIP by integration of the diffusion potential in the membrane.Scatchard writes generally for any potential difference between the membrane surfaces a and w : in which ti is the transference number and ai is the activity of ion i. Scatchard gave his final solution as a main term with some correction terms. Considering a negative membrane separating two solutions tc and w, he found that + [I t,dlna,, (4) *w tXZ: uimid In aiax + I , a Z$ujmj * where y = activity coefficient, t, = transference number of the negative ion, t , = transference number of water, s is a standard ion, ,Z+ is a summation of positive ions. The second term is a correction for the variation of the mobilities and activity coefficients in the membrane : the third term accounts for the transport of the nega- tive ion through the membrane : the last term is a correction for the water transport.For a negative membrane and only one kind of univalent cations in solution ct and solution w the main term gives ( & ) E = l n = + l n (ahJ (ws) - , ( 5 ) in which a; and a; are the activities in the solutions w and a respectively. principle this is the same formula as given by Sollner 1 and Wyllie.2 InF. BERGSMA A N D A . J . STAVERMAN 63 CHECKING THE THEORY Eqn. (5) can be checked in a variety of ways. The first check is to measure the BIP between one solution containing ion I and one solution containing the S and to calculate transference numbers tr and ts of these ions by means of (5).These transference numbers can also be measured immediately by passing a known amount of electricity through the membrane with solutions of identical composition con- taining both ions at both sides of the membrane and measuring the contribution of either kind of ions to the current. in the solution and further u for the mobility, c for the concentrations and y for the activity coefficient in the membrane, we have Indeed if we write a, and as for the activities in the membrane a,‘ and t1 UICI UIYS a_I t s uses USYI as a,la, = .,‘I& _ - - - = - By virtue of Donnan’s relation (6) can be written as (7) in which the same quantities appear as in (5). Another check is obtained by measuring the activities in the membrane separa- tely by exchange measurements and the mobilities by measurements of the conduc- tivity in pure electrolytes.Finally a more refined check can be obtained by measuring the transference number of water thus enabling to calculate the last term of the right-hand side in (4). In this paper experiments will be reported directed towards the first check of the theory. Experiments for further checking are in progress in our laboratory but are not reported here, EXPERIMENTAL * BI-IONIC POTENTIALS. The membrane was clamped between the ground-in flanges of two glass cells, containing salt solutions with different cations. These cells formed part of a circuit in which the solutions, volume 60 cm3, were circulated with a velocity of about 2 I/h. The potentials were measured with a lamp voltmeter with compensator (accuracy 0.1 mV).For the chloride solutions, calomel and silver chloride electrodes were used. For the solutions with silver nitrate we used calomel electrodes with a saturated ammonium nitrate bridge to prevent precipitation of Ag. We investigated five types of cation selective membranes, viz., I. 11. 111. IV. A 58, a Cellophane-type membrane with sulphonic acid groups, A 71, a Cellophane-type membrane with phosphonic acid groups, Stamex K, a polythene film with sulphonic acid groups, Dowex 50 + polythene ; a membrane prepared by mixing powdered Dowex 50 and polythene with a weight ratio of 2 to 1 and moulding at about 140” C , V. Amberlite IRC 50 treated with polythene in the same way as Dower 50. Amberlite IRC 50 is a cationic exchanger with carboxylic groups.Some data of the mem- branes are found in table 1. TABLE SO SOME DATA ON THE INVESTIGATED MEMBRANES membrane prepared according to cap. (mequiv./g dry weight) Dowex 50 Br.P. 719.315 2.0 Stamex K Dutch P. 180.986 1-1 Amberlite IRC 50 Br. P. 719.315 3.3 A 58 Br. P.733.100 0.27 A 71 Br. P. 733.100 0.42 * We acknowledge the collaboration in the experimental part of Mr. J. v. Wijngaarden and Mr. H. H. v. d. Berg.64 B I - 10 NI CZ P o TEN TI A L s The following combinations of ions have been studied : H+ and Na+, K+ and Na+, H+ and Ag+, Na+ and Ag+. In the presence of Ag+ ions, nitrate solutions were used, in the absence of Ag+ ions, chloride solutions. All measurements were made at 23 f 0.5" C. TRANSFERENCE NUMBERS. Transference numbers were measured in a multicel1 apparatus as shown in FIG.1 .-Multicell apparatus used for measurements of transference numbers (schema tical 1 y ) . The membrane (3 : 4) was the negative membrane to be tested. Membranes (2 : 3) and (4 : 5) were positive membranes with high selectivity intended to prevent the escape of cations from cells 3 and 4. In the beginning, cells 2, 3, 4 and 5 were filled with solutions of identical composition containing two kinds of cations in equal concentration and a total concentration of 0.1 N. Mean m>!aI a c t i v i ' j c s FIG. 2.-Bi-ionic potentials for HNO3 + AgNO3 solutions + - Stamex K - - - Dowex 50 membranes The cells 3 and 4 each form part of a circuit of 60 cm3 volume in which the solutions are circulated with a velocity of 2 l/h. Cells 2 and 5 are percolated by the same solution as is present in the beginning in cells 3 and 4.The electrode cells are rinsed with 0.1 N NaN03 solution. Membranes (1 : 2) and ( 5 : 6) are negative membranes with the exception of membrane (5 : 6) in Ag" solutions, where it was positive in order t~ prevent precipitation of silver. The area of each membrane was 40 cm2, and current density 0.5 mA/cm2.65 After passage of a known amount of electricity, the contents of cells 3 and 4. were transferred separately and quantitatively into standard flasks. The total amount of either kind of cation was determined. In this way true transference numbers were determined. F . BERGSMA A N D A . J . STAVERMAN Mean ~ o I J I ac;;.iiiies FIG. 3.-Bi-ionic potentials for HN03 + AgN03 solutions - - - - A58 A - - - - - - A 71 - - - - Amberlite IRC 50 membrane biean rnolal a c t i v i t i e s FIG.4.-Bi-ionic potentials for NaN03 + AgN03 solutions A - - - Dowex 50 membrane l a - - - - Amberlite IRC 50 membrane - - - - A 58 - Stamex K A - - - - - - A 71 In order to check the results a balance was made afterwards of the total amount of ions of either kind in cells 3 and 4 together. In this way we found a small loss of cations in the first experiments which disappeared after a number of experiments had been performed. Apparently the membranes absorb a small quantity of ions. C66 BI-IONIC POTENTIALS 0.1 0.01 0.00 I Mean molol a c t i v i t i e s FIG. 5.-Bi-ionic potentials for NaCl + HCl solutions + - Stamex K, measured with calomel electrodes 0 - Stamex K, measured with AgCl electrodes A _ - _ _ _ _ A 71, measured with calomel electrodes - - - A 71, measured with AgCl electrodes > E c a .- - m Mean rnolal a c t i v i t i r s FIG.6.-Bi-ionic potentials for NaCl + HCl solutions ' 9 - - - Dowex 50 membrane, measured with calomel electrodes 7 - - - Dowex 50 membrane, measured with AgCl electrodes I--- Amberlite IRC 50 membrane, measured with calomel electrodes 0 - - - Amberlite IRC 50 membrane, measured with AgCl electrodes 0 _ - _ _ A 58, measured with calomel electrodes 0 - - - - A 58, measured with AgCl electrodesF . BERGSMA AND A . J . STAVERMAN 67 t e j q f i ? ~ ! ~ l C C t ~ v i ~ ~ e F FIG. 7.-Bi-ionic potentials for NaCl + KCI solutions + - Stamex K, measured with calomel electrodes 0 -- Stamex K, measured with AgCl electrodes A - - - - A 71, measured with calomel electrodes i - - - - A 71, measured with AgCl electrodes t 4c + 2c > € 0 - a - m - 2c Meon molal cictiv!tt?q FIG.S.-Bi-ionic potentials for NaCl + KC1 solutions v - - - Dowex 50 membrane, measured with calomel electrodes v - - - Dowex 50 membrane, measured with AgCl electrodes --- Amberlite IRC 50 membrane, measured with calomel electrodes c] - - - Amberlite IRC 50 membrane, measured with AgCl electrodes Q - - - - A 58, measured with calomel electrodes 0 - - - - A 58, measured with AgCl electrodes68 BI-IONIC POTENTIALS In the mixture HN03 + AgN03, the amounts of cations were determined directly. In the mixtures HCI + KCl and AgNO3 + NaNO3, the first cation and the total amount of anion were determined and the second cation was calculated by subtraction.Hf, Ag+ and Cl- were determined by titration, NOT by means of a column of Dowex 50.8 In the mixture KClf NaCl the proportion of K+ and Na+ was determined spectrophotometrically. For checking the sum was compared with total C1-, found by titration. RESULTS The results of the BIP measurement are given in fig. 2-8. The BIP's have been measured as a function of the activity of one of the electrolytes following a procedure of Wyllie.2 From these plots the ratio of transference numbers in the membrane can be calculated. It is easily seen that at the point of intersection of the straight lines with the abscissa, the following relation holds since at that point the BIP vanishes In this way the " transport ratio " ~ ~ y ~ / u ~ y , can be calculated for all the combinations which are investigated.These quantities can be compared with those found from trans- port measurements. The results are given in tables 2-5. TABLE 2 transport ratio Ag+ + H+ ratio of limiting equivalent conductivities is 0-18 membrane transport measurement BIP Dowex 50 0.57 i 0.05 0.50 i 0.01 Stamex K 0.53 & 0.04 0.48 f 0-01 A 58 034 f 0.02 0-24 & 0.02 A 71 0.31 f 0.01 0.22 & 0.02 IRC 50 0.17 f 0.01 0.19 f 0.01 TABLE 3 transport ratio Na+ + Ag+ ratio of limiting equivalent conductivities is 0.8 1 membrane transport measurement BLP Dowex 50 0.62 f 0.02 0.76 5 0.04 Stamex K 0.40 f 0.01 0 5 5 f 0.03 A 58 0.65 f 0.05 0.52 & 0.02 A 71 0.66 f 0.04 0.81 & 0.01 IRC 50 0.53 f 0.04 0.52 & 0.02 TABLE 4 transport ratio Na+ 4- H+ ratio of limiting equivalent conductivities is 0.14 membrane transport measurement BIP Dowex 50 0.36 0.04 0.19 f 0-01 Stamex K 0.25 0.03 0.21 f 0.01 A 58 0.27 & 0.03 0.12 f 0.01 A 71 0-18 0.03 0.14 f 0.02 IRC 50 0.17 5 0.03 0.10 i 0.01 TABLE 5 transport ratio Na+ + K.+ ratio of limiting equivalent conductivities is 0.68 membrane transport measurement BIP Dowex 50 0-73 & 0-04 0.64 i 0.05 Stamex K 0-63 & 0.09 0.65 & 0.04 A 58 0.65 & 0.07 0.56 0.09 A 71 0.72 f 0.08 0.67 i 0.09 IRC 50 048 f 0.07 0.48 & 0.04F .BERGSMA AND A . J . STAVERMAN 69 DISCUSSION From these results the following conclusions can be drawn. (i) Marked differences are found between transport ratios in membranes and in free solutions.However, these differences do not exceed a factor of 2 or 3 and do not reach the high values found by Michaelis 4 in his pioneering work. Presumably Michaelis used membranes of a very low water content or with very narrow pores. (ii) Towards Na+ and K+ ions all membranes behave more or less in the same way. However, with respect to Ag+ and H+ ions the behaviour is different Qualitatively one can say that ions which are more specifically bound by an ion exchanger contribute more to the transport in a membrane made from these exchanges. This would mean, that a decreasing activity of a given ion in a given ion exchanger is not accompanied by a mobillity decreasing to the same extent. However, this point has to be investigated more thoroughly by separate measurements of u and y.In principle this effect can be used to separate ions of the same sign. (iii) Definite discrepancies are found between transport ratios from transport and from BIP measurement. Generally the transport ratios from BIP measurement are the lower but there are a few exceptions to this rule (Na+ + Ag+). These discrepancies indicate that one or more factors of importance are not accounted for in the approximate theoretical expression. One of these factors could be the water transport; experiments to check this assumption are in progress. (iv) An even more serious contradiction with the theory is afforded by the devia- tion of the experimental slopes of the plots for BIP against the logarithm of the activities from the theoretical value of 58 mV. In some instances it is as low as 25 mV. As the membranes are nearly 100 % selective at the concentrations used, it is improbable that this discrepancy results from permeation of anions. The fact that these deviations are particularly strong in hydrophilic membranes would point again to water transport as the cause, Also here measurements of water transport will be needed for a decision. Summarizing, we may say that bi-ionic potentials are neither theoretically nor experimentally sufficiently investigated and that various phenomena cannot be explained satisfactorily at present. 1 Sollner, J . Physic. Chem., 1949, 53, 121 1, 1226. 2 Wyllie, J. Physic. Chem., 1954, 58, 67, 73. 3 Wyllie and Patnode, J . Physic. Chem., 1950, 54, 204. Juda and McRay, J. Amer. 4 Michaelis, Naturwiss., 1926, 14, 33. 5 Marshall, J . Physic. Chem., 1948, 52, 1284. 6 Staverman, Trans. Faraclay SOC., 1952, 48, 176. 7 Scatchard, J. Anwr. Chem. SOC., 1953, 75, 2883. 8 Samuelson, Ion exchangers in analytical Chemistry (John Wiley and Sons, Tnc., New Chem. SOC., 1950, 72, 1044. Kressman, Nature, 1950, 165, 568. York, 1954), chap. 8, p. 117.

ISSN:0366-9033    

DOI:10.1039/DF9562100061

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

THE EFFECT OF STIRRING ON CELLS WITH CATION EXCHANGER MEMBRANES Ag(s) AgCl(s) BY G. SCATCHARD AND F. HELFFERICH Massachusetts Institute of Technology Cambridge 39 Massachusetts U.S.A. Max-Planck-Institut fur physikalische Chemie Gottingen Germany Received 20th January 1956 I solution 1 AgCl(s) Ag(s) (1 .l) cation-exchanger 1 membrane solution a We have measured the effect of stirring one or both solutions on the electrical potentials across cation exchanger membranes in concentration cells bi-ionic cells and cells with ions in the membrane which are not in either solution with dilute solutions containing HCl NaCl CaC12 or mixtures. Very large effects are obtained with systems containing two cations with different valences. With HCl + CaC12 bi-ionic cells changes up to 80 mV with reversal of sign have been observed.With CaC12 concentration cells and membranes containing Na+ the membrane potential is doubled when stirring is stopped. The quasi-thermodynamic equation for membrane potentials is integrated with some simplifying assumptions and the concentrations at the membrane surfaces are calculated from the electromotive force. The very large changes in electromotive force are related to the great preference for bivalent ions of the exchanger in contact with dilute solutions. When a cation-exchanger membrane is inserted between the two solutions in a concentration cell with transference the electromotive force of the cell is changed by a difference between the membrane potential EM and the liquid junction potential EL. If the ionic concentrations in the solutions are very much smaller than the concentration of fixed ions in the membrane the membrane shows prac-tically ideal permselectivity for cations and the membrane potential approaches the thermodynamic value for transfer of cations only.Membrane potentials smaller than the ideal value may be due to several causes, and have been discussed quantitatively.1-20 Potentials larger than the ideal can not be explained by a simple thermodynamic theory. Nevertheless such abnormal potentials ranging up to four times the ideal value have been reported by Wyllie,21 and by Coleman,22 and Scatchard23 for calcium chloride solutions and cation exchange membranes. They attributed the effect to sodium ion left in the membrane and found that the abnormal effect disappeared when the last trace of sodium was removed.The purpose of our investigation was to determine how the Na+ produced the effect. We find that the effect can be suppressed completely by violent stirring, and can be produced or suppressed at will by stopping or starting the stirring. We have measured the effect of stirring on both sides either side and neither side on the potentials of a number of cells of the type with solutions of NaCl HCl CaC12 or mixtures of two of them and with membranes equilibrated with these solutions or with packs of membranes equilibrated with different solutions. Symmetrical cells have a single cation throughout and the concentration of 0 is the same as that of p so the only difference is in the stirring. Concentration cells have a single cation throughout and the concentration of a is different from that of ,B (the ratio was 4 to 1 in most of our measurements).7 G . SCATCHARD AND F. HELFFERICH 71 Abnormal cells differ from symmetrical or concentration cells in that the mem-branes contain a different cation from the solutions. Bi-ionic cells have different cations in a and p but the same equivalent concentration. SYMBOLS a activity, E electric potential difference, F Faraday, rn molality, R gas constant, T absolute temperature, t transference number (negative for anions), u mobility (negative for anions), z ionic valence (negative for anions), y activity coefficient. Subscripts A B X refer to the ions A B and X ; subscript R to the fixed resin anion ; subscripts i j Ic refer to any ionic species i j k.Superscripts cc and j3 refer to the left and right solution a and b to the interfaces on the left and right side of the membrane ' and " to left and right sides of any phase. Bars denote quantities within the membrane. 2. EXPERIMENTAL CELL The membrane (or membrane pack) was clamped between two Plexiglass half cells 2 x 2 x 2 in. (fig. la) with circular holes of 8 mm diameter (or slits 8 x 1 mm for most of the experiments with membrane packs to ensure that the membranes were pressed tightly together with no aqueous pockets between). Thin rubber gaskets were used between the membrane and Plexiglass. The removable Plexiglass cover had four holes over each half cell for the solution inlet and outlet the electrode and a thermometer.The solutions were stirred violently by circulation through thermostatted glass turbines (fig. 16) in such a way that a jet of about 3 ft./sec was directed sideways across the membrane surface. This was found to be a most efficient way of agitation at the membrane surface The cell tem-perature was 25 & 0.2" C. Potential readings were made with a Leeds and Northrup type K-1 potentiometer and no. 2430 galvanometer or with a Ruhstrat " technischer Kompensator " Knick amplifier and Metrawatt microamperemeter. ELECTRODES Ag/AgCl electrodes were prepared by coating a previously annealed and etched Ag wire spiral cathodically with Ag-in KAg(CN)2 solution and then anodically with AgCI in NaCl solution. The spiral was then cut in half to give the two electrodes.The asymmetry potential of a pair of electrodes was nearly always less than 0-3 mV and usually less than 0-1 mV. In some of the measurements the electrodes were shielded from the turbulent stirring with glass tubes (see fig. la) though no difference was noted between shielded and unshielded electrodes. MEMBRANES The membranes were either Amberplex C-1 made by Rohm and Hass Co. Philadelphia, Pa. or phenolsulphonic acid-formaldehyde membranes prepared by us by the method of Schlogl and Schodel.24 The most important properties of the resins in the leached hydro-gen form except for one conductance are (with the Amberplex Iisted first each time): equivalents of fixed charge per kg of water = 5.1,0*85 ; % water = 43-0 74.3 ; thickness 0.65 0.45 mm ; specific conductance = 3.8 X 10-3 15.5 x 10-3 mhos ; specific conduc-tance of Na+ form25 = 0.48 X 10-3 mhos .. . ; water permeability = 6-27 x 10-9, 1.29 x 10-11 cm3 dyne-1 sec-1. Before each experiment except with abnormal cells the membranes were thoroughly equilibrated with the solution used or with a mixture of the two solutions 72 EFFECT OF STIRRING SOLUTIONS All solutions were prepared by dissolving analytical grade reagents (Malinckrodt or Merck) in conductivity water. The concentrations ranged from 9.5 x 10-5 to 2 x 10-2 N. a A n L P J b FIG. 1.-Apparatus. (a) The cell. In the front-view only solution inlet and outlet are shown in the left half cell, and only the electrode in the right half cell. In the top-view all equipment is omitted.A B C D E F G H J K L M N 0 P Q R S 3. RESULTS The membrane potential is the total cell potential minus potentials calculated as (RT/F) In (a&/&) assuming that ycl and ycl = y$ for CaC12. (b) The whole assembly. Plexiglass half cell rubber gaskets membrane Plexiglass cover . solution inlet (glass) solution outlet Ag/AgCl electrode electrode shielding clamps hole for solution inlet hole for solution outlet hole for electrode hole for thermometer thermostat vessel glass turbine motor thermometer stirrer the difference in electrode = YLt for HCI and NaCl CONCENTRATION CELLS The potentials obtained with CaC12 HCl and NaCl with stirring of both solutions of the more concentrated solution only of the more dilute solution only and with no stirring are listed in table 1.Stopping the stirring results in most cases in a decrease of the membrane potential which is usually more pronounced with the thin and more permeable membranes and on the side of the more dilute solution. There are however exceptions. Restarting the stirring of the more dilute solution causes an initial overshooting with a subsequent drop to the steady value. A representative potential against time curve is shown in fig. 2a. Membrane potentials between CaCl2 solutions containing up to 20 equiv. % of NaCl differ by no more than a few mV from those between pure CaClz solutions and show the same behaviour with respect to stirring. SYMMETRIC CELLS In a cell with two identical solutions separated by a membrane in ion-exchange equili-brium with the solution a potential usually arises when one solution is stirred.The result G. SCATCHARD AND F. HELFFERICH 73 are shown in fig. 2b and fig. 3. Except for the higher concentrations of NaCl and CaC12 the stirred solution is the more negative. The changes are somewhat slower than the changes with concentration potentials (fig.2b). FIG. 2.-Effect of stirring on concen-tration potentials and symmetrical potentials. The wavy line indicates that the pump is working on the respective side. Interruption of the wavy line corresponds to stopped Pump. Experimental c o n c en t r a t i o n potential, Experimental symmetrical poten-tial,-same concentration as more concentrated solution in 2a - - - same concentration as more dilute solution in 2a, concentration potential corrected for asymmetrical stirring [(2a) minus (26)].Although the potential changes are smaller than "Ol Membrane : phenosulphonic solutions CaC12, 6-020 x 10-3 - 1.505 X lO-3N. I t those with concentration cells they are no more reproducible. This is partly due to the fact that we have not reached a limiting value which would be unchanged by a further increase in stirring rate. Neither previous saturation of the solutions with AgCl or C02 nor shielding the electrodes changed the effect of stirring in the cases studied. TABLE 1 .-CONCENTRATION POTENTIALS concentrations membrane potential with stirring of theor-etical both conc. $2; neither limit-value equiv.11.mV mV mV mV mV solutions only ing membrane electrolyte zAma =AmB Amberplex CaC12 2.41 x 10-2 6.02 x 10-3 13.6 12.8 11.0 10-6 14.0 C-1 (single) 6.02 x 10-3 1-51 X 10-3 14.8 12.3 13.8 11.3 15.5 phenolsulphonic 2.41 x 10-2 6.02 X 10-3 13.2 9.6 3.5 -0.2 14.0 (single) 6.02 x 10-3 1.51 x 10-3 15.1 11.6 8.4 3.8 15.5 Amberplex HCl 2.46 x 10-2 6.14 x 10-3 33.3 32.3 32.1 32.9 34.1 C-1 (single) 6.14 x 10-3 1.54 x 10-3 33.1 31.8 33.7 32.9 34-6 1.54 x 10-3 3.84 x 10-4 32.8 31.0 34.5 33.1 35.1 A niberplex 2.46 x 10-2 6.14 x 10-3 33.4 29.9 34.4 31-2 34.1 C-1 (fourfold pack) 6.14 x 10-3 1-54 x 10-3 33.0 32-0 34.0 33.3 34.6 1.54 x 10-3 3.84 X 10-4 33.9 32.4 36.4 34.4 35.1 Amberplex NaCl 1.93 x 10-3 4-92 x 10-4 29.9 28.9 30.3 29.5 34.5 C-1 (single) ABNORMAL CELLS In solutions containing only univalent cations no abnormal effects of stirring are observed when a membrane between NaCl solutions has been equilibrated with KC1, or vice versa.Large effects are observed when a membrane equilibrated with CaCl2 i 74 EFFECT OF STIRRING inserted between solutions of NaC1 and very large effects are obtained when a membrane equilibrated with NaCl or with KCI is inserted between solutions of CaC12, (3.1) Ag AgCl I CaCl&za) I membrane (NaR) I CaCl;?(rnS) I AgC1 Ag, n V + 5 ’ 0 - 5 . - 5 -2 1 0 9 ( x i m i ) FIG. 3.-Potentials of systems symmetrical except for stirring. The potential is listed as positive when the unstirred solution is more positive than the stirred one. HCI 0 NaCl A CaClz Membrane Amberplex C-1 7 l e f t 2 0 4 0 60 8 0 100 200 5 0 0 mi n FIG.4.-Effect of stirring on the potential across a Na+ membrane between identical CaC12 solutions. The stirred solution is more negative than the unstirred solution. Membrane Amberplex C-1 ; concentration of solutions 9-24 x 10-4 N. m V + 2 0 , + 10. 0 ” -10. -20. I - ___y_______l - right - - w a m l e f t 2 0 4 0 6 0 8 0 100 100 3 0 0 1440 min FIG. 5.-Effect of stirring on the potential across a Ca2+ membrane between identical NaCl solutions. The stirred solution is more positive than the resting solution. Membrane, Amberplex C-1 ; concentration of solutions 9.84 x 10-4 N G . SCATCHARD AND F. HELFFERICH 75 When solutions x and are identical. the potential is zero if both solutions are stirred or if neither is. When only one solution is stirred the stirred solution becomes more negative.We have measured as much as 100 mV change on stirring. The effect decreases rapidly mV I FIG. 6.-Effect of stirring on the potential across a membrane which is /initially not in ion-exchange equilibrium with the solutions. Membrane Amberplex C-1 equilibrated with a mixture of 4 parts 1 N CaCb solution and Solutions mixtures of the same concentration ratio ~ c ~ / w z N ~ total concentrations 1 part 1 N NaCl solution and leached with conductivity water. 1.37 x 10-3 - 3-42 x 1 0 - 4 ~ . mV f 6 0 50 40 3 0 2 0 +I0 0 FIG. 7.-Effect of stirring on the potential in the system. 1.53 x lO-3N Ca2+ Ca2+ Na+ Ca2+ Ca2+ 3-82 x lO-4N CaC12 I membrane I membrane I membrane membrane I membrane 1 CaC12 0 Membrane potential with stirring on both sides A 0 0 A = " Na potential " B = " Ca potential " (The solutions were not stirred in the intervals between the measurements).with stirring of the more concentrated solution only with stirring of the more dilute solution only with no stirring at all. (RT/F) In (rnalrnb) (RT/2F) In (rna/rnb) with time. A typical potential against time curve is shown in fig. 4. A similar curve for a membrane equilibrated with CaC12 between identical solutions of sodium chloride is shown in fig. 5. The change is much smaller and the stirred solution is positive. Similar result 76 EFFECT OF STIRRING were obtained with membranes equilibrated with NaCl + CaC12 mixtures between solutions of CaC12 or of NaCl and with membranes equilibrated with 1 N solutions of NaCl 4- CaCl2 mixtures placed between dilute solutions with the same Na/Ca ratio which are not in ion exchange equilibrium because of the shift of equilibrium with concentration.When ma -+ mB in cell 3.1 the potential with both sides stirred is the same as with a membrane equilibrated with CaC12 When neither side is stirred the potential increases. Stopping the stirring on the more dilute side only gives a still greater increase and stopping the stirring on the concentrated side only gives a smaller decrease. This effect also decreases with time. In fig. 7 are shown measurements with CaC12 solutions w = 4mB and with a sandwich of five membranes. The middle one had been equilibrated with NaCI the others all with CaC12.Initially the potentials are the same as those of a simple concentration cell (without the Na+ membrane) and the potential with both sides stirred remains almost unchanged at A typical curve is shown in fig. 6. TABLE 2.-cHANGES OF BI-IONIC MEMBRANE POTENTIALS IN 2 MIN AFTER STOPPING STIRRING OF ONE SOLUTION ONLY single membrane single membrane mV mV mV mV membrane pack membrane pack concentration equiv.11. membrane solution not stirred (1) system HCl + NaCl HCI Amberplex 2.475 X 10-2 - 2 - 3 + 2 c- 1 6-19 x 10-3 - 1 - 7 + 3 1-55 x 10-3 - 2 -15 + 3 3-87 x 10-4 - 3 - 5 + 8 phenosulphonic 2.475 X 10-2 - 3 - 3.5 - 4 6-19 x 10-3 - 2.5 - 4 f O 1-55 x 10-3 - 2 - 9.5 & 0 3-87 x 10-4 - 3 -28 + 11 Amberplex c- I (2) system HC1 + CaC12 2.490 X 10-2 2.467 X 10-2 6.23 x 10-3 6.17 x 10-3 1-56 x 10-3 1-54 x 10-3 3.89 x 10-4 phenolsulphonic 2-490 x 10-2 2.467 X 10-2 6.23 x 10-3 6-17 x 10-3 1-56 X 10-3 1.54 x 10-3 3.89 x 10-4 3-86 x 10-4 (3) system NaCl + CaCl2 Amberplex 2.460 x 10-2 c-1 6.15 X 10-3 1.54 x 10-5 3.84 x 10-4 6-15 x 10-3 1-54 x 10-3 3.84 x 10-4 phenolsulphonic 2.460 x 10-2 CNal + 3 + 4 + 2.5 + 20 - 3.5 - 2 - 10 - 12 HC1 CaCl2 + 10 + 9 f O + 25 - 5 + 42 - 6 + 25 + 10 + 18 - 1 + 10 + 15 + 25 - 1 + 28 + 14 + 28 - 7 + 14 + 20 - 1 + 5 - 2 + 30 - 4 + 45 - 20 NaCl CaCI2 + 4 - 2 + 4 + 3 1 0 - 3 + 13 + 10 - 5 4-23 + 15 - 2 - 6 + 35 + 10 - 2 4- 11 + 13 + 8 - 1 + 14 +25 4-7 - 10 + 16 +35 + 2 3.1 G. SCATCHARD AND F. HELFFERICH 77 15 mV for 70 h.After about 20 h the potential without stirring increases about 23 mV, that with only the concentrated side stopped decreases about 17 mV and that with only the dilute side stopped increases about 40mV. These values also remain nearly constant until 70 h from the start and any of the four values may be obtained at will. I -3 -2 lop m -3 -2 log m > / / / / / / mV t 4 0 (dl 3 0 2 0 3 0 4 0 30 i tbo mV 1 ( f F 1 + 10 4 0 50 60 7 0 -:I -80 + 10 4 0 so 7 0 80 / / / 1 I - 3 - i loq(z;rn;) - 3 -2 log ( r . r n l ) FIG. S.-Bi-ionic potentials. (a) Membrane phenosulphonic solutions HCI (left) NaCl (right) (6) Amberplex C-1 9 9 7 7 (c) phenolsulphonic HCl (left) CaC12 (right) (4 Amberplex C-1 Y Y 97 (4 phenolsulphonic NaCl (left) ,,.(f) Amberplex C- 1 7 9 9 9 0 single membranes stirring on both sides, 0 membrane packs 9 9 9 , 0 single membranes without stirring, x membrane packs 3 7 ?) A = liquid junction potential in aqueous solution, B = theoretical bi-ionic potential 78 EFFECT OF STIRRING BI-IONIC CELLS We have studied bi-ionic cells Ag AgCl I AClzA(ma) I membrane I BCl,B(mB) I AgC1 Ag (3.2) with the three combinations HCI + NaCl HCl + CaC12 and NaCl + CaC12 with the equivalent concentrations the same in a and in ,B in two series. In the first series there is a ~MMM - HCI -- rur CaC12 I . . 10 2 0 3 0 4 0 5 0 6 0 I80 200 2 2 0 2 4 0 3 0 0 3 2 0 min FIG. 9.-Effect of stirring on the bi-ionic potential across a single membrane.Membrane, phenosulphonic ; solutions HCl (left) and CaC12 (right) 6.225 x 10-3 N. k c nwmw mmmuwey H C I MLTM llwmw COCI - 10 2 0 3 0 6 0 7 0 8 0 9 0 1 2 0 130 900910 920 min FIG. 10.-Effect of stirring on the bi-ionic potential across a membrane pack : HCl I membrane 1 membrane I membrane I membrane I CaC12 H' H+ Ca2f Ca2+ Membranes Amberplex C-1 ; solutions HCI (left) and CaC12 (right) 6-167 x 10-3 N. single membrane equilibrated with a solution half normal in each to the two solutions. In the second there is a pack of 4 membranes. The two on the cc side are equilibrated with the cation on the cc side and the two on the ,B side are equilibrated with the cation on the t9 side. The results after establishment of a steady state are shown in fig. 8 and in table 3 G .SCATCHARD A N D F . HELFFERICH 79 The bi-ionic potential HC1 + NaCl is fairly independent of the concentration and the effect of stirring is small. The bi-ionic potentials involving ions of different valence depend upon the concentration and are extremely sensitive to stirring. Stopping and restarting the stirring may result in potential changes as large as 80mV and to reversal of the sign of the e.m.f. In the experiments with a single membrane the effect of stirring is at its maximum in a few minutes. A typical potential against time curve is shown in fig. 9. In the experiment with a four membrane pack the potential with both sides stirred is nearly independent of the time but the effect of stopping stirring is negative at first as in a concentration cell and develops to the steady state value only after hours.A typical curve is shown in fig. 10. 4. SIMPLIFYING ASSUMPTIONS (i) The concentrations in the aqueous solutions are assumed to be always so small relative to the concentration of fixed ions in the membrane that the con-centration of anions in the membrane may be neglected and (ii) so smill absolutely that the change in free energy due to the transfer of water may be neglected. (iii) The activity coefficients and the ratios of the mobilities of any two ions are assumed to be independent of the composition and the mobilities are assumed to be independent of the total concentration in the small range in which that varies in a single phase. (iv) The boundaries between the membrane and the solutions are assumed to be sharp.(v) The concentration of fixed ions in the resin is assumed to be constant and any other effects of changes in swelling pressure are neglected. (vi) If there are two cations present it is assumed that the concentration of anion in each aqueous solution is constant. The first two assumptions and the third for all the ions univalent are probably quite exact for the concentrations we have used. The last three assumptions and the third for solutions containing CaZf are inexact approximations made for the sake of mathematical simplicity. EQUATION FOR THE ELECTROMOTIVE FORCE With the assumption of sharp boundaries (iv) it is convenient to split the general equation for liquid and membrane potentials EMFJRT - Eitid In ai (4.1 ) (4.2) into five parts two Donnan potentials and diffusion potentials in each solution and in the membrane J: ti == uimi/zjZjUjnlj, (4.3) We shall limit our discussion in this paper to the use of quasi-thermodynamics to determine approximately the changes in concentrations at the membrane-solution surfaces from the changes in membrane potential.A somewhat mor 80 EFFECT OF STIRKING precise and much more detailed picture is possible with the methods of the thermo-dynamics of irreversible processes.26 This will be presented in the subsequent paper by one of us.27 Our model is too simple to explain the symmetrical potentials of § 3. They may arise from the effect of stirring on a finite transition layer between membrane and solution (contrary to assumption (iv) or on a diffuse (Gouy) double layer, or from other causes.If the observed stirring effect on the concentration potential (fig. 2 4 is corrected for the potential change found with symmetrical systems (fig. 2b) a net effect is obtained (fig. 2 4 without the overshooting on starting stirring in the dilute solution. These results also show that the large effects of stirring in bi-ionic and in abnormal potentials must arise from other causes. CONCENTRATION CELLS With the assumptions of § 4 eqn. (4.3) for a concentration cell becomes With stirring on both sides our measurements correspond to the second term alone except for the decrease usually found in very dilute solutions. We assume therefore that stirring on the a side mades ma practically equal to rn and that stirring on the /3 side makes mb practically equal to- mg.It is then possible to calculate ma/rn or ~ n b ! r n ~ when stirring is stopped on one side only. For CaCl2, 6-02 - 1.53 x 10-3 N the measurements correspond to 103 rn& = 5.04 = 103 mE1 - 0.96 and 103 m& = 2.55 = 103 m& + 0-92. When stirring is stopped on both sides the change in potential is approximately the sum of the effects of stopping on a single side. The effect of stirring on con-centration cells with membranes has been discussed by Unmack 28 and by Brun.29 BI-IONIC CELLS For bi-ionic cells it is convenient to use cations A and B a s j and k respectively, and to regroup the terms to give with our simplifying assumptions The first term is the logarithm of the distribution ratio. We assume that stirring on the a side makes m; = rn and m," = Z," = 0 and that stirring on the /3 side makes irzf = m and mt = 7Zt = 0.This assumption has the further justification that in cells with multiple packs with stirring on both sides the potential is independent of time. For stirring on both sides then eqn. (4.5) reduces to -l I z A TB = In &) ( % ) I i z B - s" a 1,7j d In E 7 j - ($ - i) In 5. (4.6) mc1 Since mB is a linear function of mA and iTB of GA the integrals in eqn. (4.5) and (4.6) may be determined in any phase by the Henderson equation.30 So integrated, eqn. (4.6) may be obtained from the equation of Wyllie 31 for multi-ionic potentials, and it reduces €or Z = Z = 1 to the equation of Sollner.3 G. SCATCHARD AND F. HELFFERICH 81 From the values of MacTnnes 33 for the limiting ion conductances we obtain the following equations for the integral and the maximum values when x i = 1 and x i = 0 if xi = m>i/mkl at the left-hand side and xi = n z ~ i ' r n ~ at the right-hand side.H + Na 59.15 loglo (1 + 2.370 x&)/(l + 2.370 x;) 31.21 (4.7) H + Ca 65.21 loglo (1 + 2.137 xk)/(l + 2.137 x;) 32-40 (4.8) N a i Ca 128.25 loglo (1 + 0.069 ~ ; ~ ) / ( l + 0.069 x;,) 3.72 (4.9) In the Amberplex membrane we have used the conductance measurements in 5 2 to give ZIH/UN~ = 8 and the measurements with stirring on both sides in the H + Ca bi-ionic cell and the assumption that (YH/3/H)(?/Ca/YCa)' = 1 to give measurements of the H + Na and Na + Ca bi-ionic cells and the diffusion potentials : H + Na 59.15 loglo (1 + 7 xk)/(l f 7 Fg) 53-42 (4.10) H + Ca 61-12 loglo (1 + 15 %;)/(1 -I- 15 yz) 73.59 (4.1 1) UH/UCa 16- This gives (YNa5Na)(YH/YH) = (YNa/YNa)(YCa/YCa)' 2.From the Na + Ca 88.72 loglo (1 + xka)/(l + xGa) 26.70 (4.12) The H + Na potentials are nearly independent of the concentration and are but little changed when the stirring is stopped. Eqn. (4.6) indicates no change as the concentration changes. When the stirring is stopped the maximum change in potential corresponds to going from the change in composition being entirely in the membrane to its being entirely in the aqueous phases. The calculated change is 31.21 - (53.42 - 18.75) = - 3946mV. (4.13) However our assumption (vi) that the anion concentration is constant does not hold well here see ref. (27). When the ,8 cation is Ca2+ the membrane potential with both sides stirred becomes more negative as the concentrations decrease by about 30mV for each power of ten in agreement with eqn.(4.6). Again the maximum change on stopping stirring corresponds to going from the change being entirely in the membrane to its being entirely in the aqueous phases. It is (4.14) and 3-72 - [26.70 + 18.75 - 29.58 loglo (TtiR/mgl)] for Na + Ca. (4.15) For the ratio Gjm of 103 (6 N and 6 x 10-3 N) the maximum is about 45 mV for either. With such dilute solutions the preference of the resin for the bivalent ion is enormous and the changcs we observe are over periods very short compared with the time necessary to reach steady-state flow through the whole membrane, so all changes must be near the surface.When stirring is stopped on the a (uni-valent) side the increase in Ca2f is almost entirely in the resin where the relative change in concentration must be small so there is little change in potential. When stirring is stopped on the ,B (bivalent) side the decrease in Ca2f is almost entirely in the solution and the change in potential is large. It is not difficult to obtain a point on the curve for the variations of n;ga and iZga with potential by choosing an arbitrary value of that concentration which changes most calculating the other concentration from the equilibrium relation and then the change in membrane potential by substituting eqn. (4.8) and (4.11) or (4.9) and (4.12) in eqn. (4.5). With 6 x 10-3 N solutions a ratio iu$,/rn%a = + corresponds to a change of 28 and 10 mV for the H + Ca and Na + Ca cells respectively.The measured values after 2 min are 30 and 10 mV. 32.40 - [73.59 - 29.58 loglo (ZR/rn$,)] for H + C 82 EFFECT OF STIRRING ABNORMAL CELLS The cells with membranes containing Na+ between solutions of CaC12 behave like CaC12 concentration cells when both sides are stirred. When there is much Na+ in the membrane the effect of stopping stirring is the same as that of stopping stirring on the CaC12 side of the Na + Ca bi-ionic cell. In the sandwich-pack cell of fig. 7 the effect of stopping stirring on the side with 1-53 x 10-3 N CaC12 is 17 mV which corresponds to a izg,/mf.a ratio of about 1/3. The effect of stopping stirring on the side with 3.82 x 10-4 N CaCl2 is 50 mV as measured directly or 40 mV from the difference between stopping both sides and stopping the concentrated side only.This corresponds to a concentration ratio about 1/20 or about 1 /50. The change when stirring is stopped on both sides corresponds closely to the maximum change with both Na 4- Ca junctions in the aqueous phases which is marked sodium potential in fig. 7. This may be a coincidence as the change when stirring is stopped on either side is much less than the maximum change, -64 or +81 mV. We are indebted to Dr. R. Schlogl for helpful discussions. One of us (F. H). wishes to thank the Foreign Student Summer Project of the Massachusetts Institute of Technology for a grant which provided the opportunity to start this work. 1 Teorell Proc. SOC. Expt. Biol. 1935 33 282 ; Z.Elektrochem. 1951 55 460. 2 Meyer and Sievers Helv. chim. Acta 1936 19 649. 3 Marshall J. Physic. Chem. 1939 43 1155. 4 Sollner and Anderman J . Gen. Physiol. 1944 27 433. 5 Manecke and Bonhoeffer 2. Elektrochem. 1951 55 475. 6 Schmid and Schwarz Z. Elektrochenz. 1951 55 684. 7 Lorenz J. Physic. Chem. 1952 56 775. 8 Manecke 2. physik. Chem. 1952 201 193. 9 Schlogl and Helfferich Z. Elektrochem. 1952 56 644. 10 Schmid 2. Elektrochem. 1952 56 181. 11 Staverman Chem. Weekblad 1952 48 334 ; Trans. Faraday SOC. 1952 48 1.76. 12 Overbeek J. Colloid Sci. 1953 8 420. 13 Scatchard J. Amer. Chem. Sac. 1953 75 2883. 14 Schindewolf and Bonhoeffer 2. Elektrochem. 1953 57 216. 15 Spiegler J. Elektrochem. SOC. 1953 100 303 C. 16 Gregor and Sollner J . Physic. Chem. 1954 58 409. 17 Schlogl 2. physik. Chem. N.F. 1954 1 305. 18 Kirkwood Ion Transport Across Membranes (Acad. Press N.Y. 1954) p. 119. 19 Graydon and Stewart J. Physic. Chem. 1955 59 86. 20 Hills Kitchener and Ovenden Trans. Faraday SOC. 1955 51 719. 21 Wyllie private communication 1952. 22 Coleman Thesis (Mass. Inst. Tech. 1953). 23 Scatchard Ion Transport Across Membranes (Acad. Press N.Y. 1954) p. 128 ; Electrochemistry in Biology and Medicine (John Wiley and Sons Inc. New York, 1955) chap. 3. 24 Schlogl and Schodel 2. physik. Chem. 1955 5 372. 25 Spiegler and Coryell J. Physic. Chem. 1953 57 687. 26 Helfferich Thesis (Gottingen 1955). 27 Helfferich Faraday SOC. Discussions 1956 21 83. 28 Unmack Kgl. Danske Vid. Selsk. 1937 15 no. 5. 29 Brun Univ. Bergen Arb;k 1954 Nr. 15. 30 Henderson 2. physik. Chem. 1907 59 118 ; 1908 63 325. 31 Wyllie J. Physic. Chem. 1954 58 67. 32 Sollner J. Physic. Chem. 1949,53 121 1 and 1226 ; Sollner Dray Grim and Neihof, Ion Transport Across Membranes (Acad. Press N.Y. 1954) p. 155; Dray and Solher Biochim. Biophys. Acta 1955 18 341. 33 MacInnes J. Franklin Inst. 1938 225 661

ISSN:0366-9033    

DOI:10.1039/DF9562100070

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

BI-IONIC POTENTIALS BY F. HELFFERICH Max-Planck-lnstitut fur physikalische Chemie Gottingen Received 30th January 1956 Assuming steady-state conditions the Nernst-Planck equations can be used to deter-mine the concentration gradients which are found to exist across not only the membrane but also such adherent liquid “ films ” as are unaffected by stirring. By use of the inter-face concentrations thus obtained the membrane potential can be calculated. In contrast to concentration cells bi-ionic cells have a strong tendency towards film control which, in certain cases cannot be overcome even by violent stirring. Therefore with counter-ions of different valences a change in stirring conditions may give rise to very large membrane potential changes and to a reversal in sign of the potential.In addition the Nernst-Planck equations permit the calculation of the concentration profiles ; it is found that the slower ion is accumulated by the membrane. The calculated potentials are in fair agreement with experimental values obtained with and without stirring. 1. INTRODUCTION An ion exchange membrane separating two electrolyte solutions maintains across itself an electric potential difference which can be measured with suitable electrodes. Potentials between solutions of the same electrolyte but of different concentrations are customarily defined as concentration potentials and those between solutions of different electrolytes but of equal equivalent concentration as bi-ionic potentials : solution a membrane solution /I AX [ containingAandB 1 BX If the concentrations at the interfaces are known the bi-ionic potential can be cal-culated from the general equation for the e.m.f.of a Voltaic cell. In the preceding paper 1 Scatchard’s quasi-thermodynamic treatment 2 has been extended to systems having concentration gradients not only in the membrane but also in the solutions. Thus concentrations at the interfaces were calculated from experimental e.m.f. data. In this paper the Nernst-Planck flux equations are used to predict membrane potentials and concentration profiles which can be compared with experimental results. 2. PREVIOUS THEORIES (1.1) z*c = ZBC$ Bi-ionic potentials have been reported by Michaelis,3 Marshall et al.,4 Meyer and Bernfeld,s Sollner et a/.,6 7 Manecke,8 and Wyllie.9 Using the Henderson equation 10 for the liquid-junction potential and in it replacing concentrations by activities Marshall 4 derived equations for the bi-ionic potential.His approach however as Wyllie 9 pointed out later while leading to the diffusion potential within the membrane ignores interfacial “ Donnan ” potentials which make an essential contribution to the membrane potential especially where counter-ions of different valences are involved. The mechanism of the bi-ionic potential was considered in detail by Sollner.6.7 He found that not only was the relative mobility of the counter-ions important but also the selectivity of the membrane material played a significant role. According to his views when the membrane is in a bi-ionic cell one ion is preferred to the same extent as when the membrane is in equilibrium with a mixed solution containing 8 84 BI-IONIC POTENTIALS both counter-ions.His equation for the membrane univalent electrolytes), reflects the two factors relative mobility (DA/EB) in, ( y B / y A ) by the membrane.* potential (restricted to uni-(2.1) and preferential adsorption Wyllie 9 combines the theories of Sollner and Marshall. He uses the Henderson equation (with activities) for the diffusion potential in the membrane adds the Donnan potentials and as Sollner corrects for the assumed preferential adsorp-tion by multiplying the mobility ratio with the activity coefficient ratio. His equations are as is (2. l) in accordance with those derived quasi-thermodynamically (except for correction terms).It should be mentioned here that the Nernst-Planck treatment though it leads to basically the same equations indicates that any preferential adsorption taking place in bi-ionic cells is completely different from that in equilibrium systems and has no effect on the membrane potential the activity coefficient ratio in (2.1) being due to the difference in the Donnan potentials ; on the other hand in Wyllie’s approach (where Donnan potentials are included) the use of activity coefficients in the Henderson equation introduces a factor which is exactly compensated by his correction for the assumed preferential adsorption. The flux equations have been integrated in a general form by Goldmann,ll Teorell,l2 and for ions of different valences by Schlogl.13 Bi-ionic potentials are only a special case of this more general solution.However this procedure requires, as does any previous approach the knowledge of the concentrations at the inter-faces. 3. FLUX EQUATION TREATMENT In bi-ionic cells concentration gradients exist across both the membrane and adherent Nernst diffusion “ films ” which are unaffected by stirring.14 The flux equation treatment consists in calculating by use of the steady-state condition the concentrations at the interfaces and from these the diffusion potentials in films and membrane and the Donnan potentials at the interfaces and hence the membrane potential. (a) SIMPLIFYING ASSUMPTIONS treated (i) (ii) (iii) (iv) (4 (Vi) (vii) (viii) Only cation exchange membranes are discussed.Anion exchangers can be in the same way. Furthermore it is assumed that: The concentrations of the solutions are so small compared with the con-centration of fixed ions in the membrane that the concentration of anions in the membrane may be neglected (zx < C, C,). Transfer of solvent through the membrane may be neglected. The ratio of the diffusion constants of the counter-ions is independent of mole fraction (EA/OB = const.). The membrane/solution interfaces are sharp. Changes and gradients of swelling pressure may be neglected ; this implies a constant concentration of fixed ions in the membrane. The motion of the solution near the interface may be represented by a Nernst diffusion “ film ”. At the interfaces equilibrium is preserved between adjacent infinitesimal thin layers in membrane and film (i.e.no interfacial resistance to diffusion.) Only the steady state is considered. _ -* Heteroporosity is stressed as another important factor. Tn the forthcoming dis-cussion we account for this by using diffusion constants h experimentally determined by methods (self-diffusion or conductivity measurements) in which heteroporosity plays the same role as in bi-ionic cells F. HELFFERICH 85 Most of these assumptions have been made previously by other authors who discussed their validity in detail. If membranes with high water-permeability are used a considerable error may be introduced by (ii) despite the fact that in bi-ionic cells such as (1.1) the activity of the solvent is practically equal in both solutions .I5 The self-diffusion constants of ions in ion-exchange resins are known to depend on resin composition; however the ratio DJDB of the two diffusion constants in the same resin containing both counter-ions A and B is found to be reasonably constant and independent of mole fraction cA/(cA + cB),16 as assumed in (iii).Assumption (v) is certainly an oversimplification if counter-ions of different valence are involved. The error is larger with concentration profiles than with membrane potentials. (6) CALCULATION OF THE CONCENTRATIONS AT THE INTERFACES In contrast to concentration cells with dilute solutions where only a very small diffusion can occur we are concerned in bi-ionic cells with a continuous exchange of the counter-ions across the membrane i.e. with large ionic fluxes and corres-ponding large concentration gradients which may be located in both membrane and adherent films.In the steady state the fluxes $i of all ionic species i are constant throughout membrane and films i.e. the value of each flux is constant through all planes parallel to the interfaces no matter whether the planes are located in film or membrane i.e., According to. assumption (i) the membrane is impermeable to anions ; therefore - -4 i = 6 (3.1) $x = 0. (3 .a Electroneutrality requires that c Zi$i = 0. i (3.3) At the interfaces equilibrium is assumed : = KiCi/C (3.4) (C f CAZA + CBzB ; the partition coefficients K i are defined by (3.4) ; note that for zA + zB the ~i depend on C even in the ideal case.) By use of the Nernst-Planck flux equations (3.5) the concentrations at the interfaces can be calculated from (3.1-4).However a straightforward application of (3.5) leads to a complicated expression and is there-fore not a profitable line of approach. Instead we define integral diffusion con-stants DAB by 1 1 (C' and C" = concentrations at the left- and right-hand boundary respectively, of the considered layer (membrane or film) of thickness 1.) Using (3.6) instead of (3.5) we find for the concentrations at the interfaces a and b C," == (C - C:ZB)/Z 86 BI-IONIC POTENTIALS In the calculation the additional assumption has been made that CAZA + CBZB = C = const. (3.8) and thereby that Cx = const. Whereas in the membrane this follows from the assumptions (i) and (v) it is not strictly correct for the films because due to & = 0, the electric patential gradient acting on the anions has to be compensated for by a corresponding concentration gradient (see also footnote to 5 3c).If A and B are isotopes of the same cation (DA = DB = D) (3.7) reduces to This expression is exact as far as the film concept holds and it reveals more clearly than (3.7) the effect of the parameters D/E C / c and d/8 on the distribution of the concentration gradients. For DCd/b?8 > 1 we have C,” = Cb = C and Ci = C,” = 0 ; the concentration gradients are located completely within the membrane (ideal membrane control). For DCd/EC8 < 1 we have C = Ci = Cg = Cg = C/2 ; the concentration gradients are located completely within the films (ideal film control).The mechanisms correspond to what is known as “ par-ticle kinetics ” and “ film kinetics ” respectively in ion-exchange kinetics. For the evaluation of (3.7) approximate values of the DAB have to be estimated. This is done in the following way. We neglect gradients of activity coefficients and assume constant Di. d8/dx can now be eliminated from (3.5) by use of (3.3) and (3.8) giving As $x = 0 there are only two fluxes $A and +B. (3.10) The second term in (3.10) vanishes when the activity coefficients are independent of the mole fraction CA/(CA + CB) and thereby of the space coordinate x. Under this additional assumption (3.10) is readily integrated (again using (3.8)) for zA =+ z, an F. HELFFERICH 87 The limiting case ( 3 . 1 2 ~ ~ ) shows that the diffusion rate is essentially governed by the diffusion constant of the r a w ion.This rule which applies to any diffusion of two ionic species interrelated by the electroneutrality condition is inherent in the NernSt-Planck equations the electric term contains as a factor the concentration Cj of the species; the potential gradient produced by the diffusion process will therefore have a large effect on the species present in high concentrations but only a small effect on the species present in low concentration. In equilibrium with dilute solutions the membrane shows a pronounced pre-ference for the counter-ion of higher valence. This is evident from the equilibrium condition (aA/ZdZB = (aB/ZB)ZA (3.13) Hence in systenis with Z < z, if a concentration gradient builds up in the film situated on the cc side the membrane accumulates the ion B and the integral diffusion constant D A B approaches DA.On the other hand the concentration profile within the membrane remains relatively insensitive to concentration changes in the film on the p side. The evaluation of (3.7) requires furthermore the knowledge of the film thickness 6 and the partition coefficients Ki. The latter can be calculated directly from ion-exchange equilibria. 6 may be determined from one e.m.f. measurement-for a given stirring rate and cell geometry-and used for the prediction of all other e.m.f. values. In computing the concentrations at the interfaces (3.9) is used to make a first rough estimate which will often reveal that the system is practically membrane-controlled or film-controlled.In either case the membrane potential can be calculated directly from (3.17) or (3.1 8) respectively. If neither applies the first estimate-for counter-ions of different valences in combination with (3.13)-can be used to obtain approximate integral diffusion constants DAB from (3.12) or (3.11). Substituting these values in (3.17) gives a second approximation for the concentrations at the interfaces. It must be emphasized that this procedure leads to only a rough approximation for the concentrations at the interfaces. In most cases however the error thereby introduced into the calculation of the mem-brane potential does not exceed a few millivolts. (c) CALCULATION OF THE MEMBRANE POTENTIAL The membrane potential is the sum of the Donnan potentials at the interfaces and the diffusion potentials in membrane and films.The Donnan potentials are given by (3.14) (negative for side cc positive for side p). The diffusion potential can be obtained from the Henderson equation (without activity coefficients!) or if the necessary data are available from the Nernst-Planck equations. Using ( 3 . 9 (3.3) and (3.8) we obtain (3.15) (3.16 88 BI-IONIC POTENTIALS Except for the second term (3.16) is equivalent to the Henderson equation without activity coefficients. This becomes evident when C = CAZA + CBZB is substituted. Henderson's assumptions being granted (as is the case here since C = const.) the activity coefficients appear only in the correction term which makes a cohtribu-tion only if gradients of activity coefficients exist.Without giving a general equation for the membrane potential-which is readily obtained from (3-14) and (3.16) by substituting appropriate values for the interface concentrations-we would stress the two limiting cases. For ideal membrane control the diffusion potentials in the films vanish and the boundary conditions for the diffusion potential in the membrane become C~Z = C, and C~Z = 0. After substituting in (3.16) and adding the Donnan potentials we find the membrane potential The first and third terms arise from the diffusion potential and the others (including that containing the " preferential adsorption factor ") from the Donnan potentials. If we retain C = const. which particularly in this case is a rather forced assumption, the sum of the Donnan potentials vanishes also and we are left with For idealfilm control the diffusion potentials in the membranes vanish.which differs from the liquid-junction potential without membrane only in that the terms Dxzx under the logarithm are missing.* (d) CONCENTRATION PROFILES IN THE MEMBRANE Integrating (3.10) from x = 0 at the interface a to a variable value of x within the membrane (assuming constant Di) the concentration CA is obtained as a function of the space coordinate x. The resulting equation cannot be solved with respect to CA for z -+ z,. As in this case the evaluation is somewhat tedious the discussion below is for simplicity restricted to 2 = zB and to ideal membrane control. Activity coefficients enter (3.10) only in form of the expression [d In (Tp/e)ldx].The second term in (3.10) disappears when K is inde-To begin with we integrate (3.10) -zB yA/yB-= %A K is equivalent to the ion-exchange equilibrium constant defined by K G (CB/aB)"B (aAFJzA. pendent of mole fraction and thereby of x. under this additional assumption and obtain -= Cx/d. for DA = * The assumption C = const. is as (3.5) shows compatible with Dx = 0. Actually the diffusion potentials build up anion concentration films. A more detailed calculation which is omitted here shows that C, DB DB. (3.19) # = 0 only for gradients in both is far from being constant ; for the conditions Z = Z = z and K j independent of total concentration it is found that Cg = 2cE/[(&/D.$z + z x ) h -t- 11 and ci = 2c:/[(DAD,)(' +zx)lz~ f 11.For the potential however we obtain an expression identical with (3.18) except for a slight difference in the correction term. Thus the assumption C = const. is seen to introduce practically no error into the calculation of the membrane potential even for ideal film control where it is farthest from representing the actual conditions F . HELFFERICH 89 Eqn. (3.19) is plotted in fig. 2 for different values of D A / D B ; it is seen that the membrane accumulates the slower ion. Qualitatively this result follows from the rule that the ion present in smaller concentration governs the diffusion rate (3.12~). Near the interface a the diffusion _ _ FIG. 1 .-Characteristic con-centration profile for steady-state counter-diffusion of two ions.A and By with z < 2, and BB < 5 (schematically). The system is not completely membrane controlled hence the membrane accumulates the ion of higher valence. Due to DB < DAY the smaller CA/CB is the steeper is the profile. - _ solution d f i l m membrane f i l m solutron 3c FIG. 2.-Concentration pro-file of the ion A within the membrane for steady-state counter-diffusion with ideal membrane control Z = z,, and d In K/dx = 0. (a) D A I D B = 1, (b) = 2, (c) = 5, (4 = 15, - -constant of the slower ion B is effective (because of FB < zA) ; near the interface b this is true of the faster ion A. At the same time the steady-state condition requires that +i - const. Hence the concentration profile must be steeper near a than near b 90 BI-IONIC POTENTIALS Now we consider the effect of the quantity d In K/dx in (3.10) equating for simplicity D = D,.As the second term in (3.10) contains both FA and z,, it becomes equal to zero at both interfaces ; hence the slope of the profile is the same at each interface. If d1nKldx is a monotonic function as is usual S-shaped profiles are obtained which are steeper in the middle of the membrane than at the boundaries for d In K/dx > 0 and flatter for d In K/d? < 0 (fig. 3a). The profile develops a bulge when d In K/d% has a maximum or minimum (fig. 3b) ; which ion then predominates depends on whether the former or the latter is the case and not on whether In K is positive or negative so that the preference shown by the membrane in equilibrium systems is irrelevant.- -0 ) (b) FIG. 3.-Steady-state concentration profile of ion A for ideal membrane control and D = 5 schematically. -(a) d In K/dxB > 0 (b) d In K/dSi- has a minimum. Selectivity is a membrane property that can come into play only at the inter-faces. Thus if fixed boundary conditions are given at the interfaces-as is the case when ideal membrane control is assumed-the selectivity has no bearing on the concentration profiles. However the more the system changes over to film control the more the effect of the selectivity on the concentrations at the interfaces increases. In the limiting case of ideal film control Sollner’s assumption (pre-ferential adsorption the same as in equilibrium with a mixture of both solutions) is valid but now the membrane potential is given by quite a different expression which contains neither the preferential adsorption factor nor the intra-membrane mobility ratio.4. DISCUSSION AND EXPERIMENTAL EVIDENCE (a) THE FILM HYPOTHESIS The approach outlined above differs from any previous theory in that it can account quantitatively for partial or complete film control. The film hypothesis is therefore examined first. A rough estimate with eqn. (3.9) shows that deviations from ideal membrane control are to be expected for DCd/z& < 50 and that complete film control will occur for DCd/De8 < 0.1. Taking a characteristic ion-exchange membrane with C (ion-exchange capacity) w 1 N D / D = 5 and d w 0.1 cm we find that main-tenance of complete membrane control requires the reduction of film thickness 6 to less than 10-3 cm for solutions of 10-1 N 10-5 cm for 10-3 N and 10-7 cm for 10-5 N whereas complete film control must be anticipated for 8 > 0.5 cm, 5 x 10-3 cm and 5 x lO-5cmY respectively.Stirring by usual methods only F. HELFFERICH 91 reduces the films to about 10-3 cm and a reduction to below 10-4 cm is difficult to achieve Thus bi-ionic cells with dilute solutions are likely to be partially or completely film-controlled. In cells with zA = z the second term in (3.17) is equal to zero and the membrane potentials for both ideal membrane control and film control are seen to be fairly independent of concentration. Actually their values can be very similar when D,/D w DA/DB (compare fig. 8a and b in the preceding paper 1).This may account for the fact that with the exception of Sollner 697 and Manecke,8 the significance of film control escaped the notice of previous investigators. For Z =l= z, however, due to the second term in (3.17) the membrane-controlled potential is linearly dependent on log C where the potential changes by (z - zB)/zAzB X 59 mV for an increase in C by a factor of 10 whereas the film-controlled potential is again practically independent of concentration. It is therefore evident that both potentials may differ from each other considerably in absolute value and even in sign. In the preceding paper,l bi-ionic potentials obtained with HCl + CaC12 and NaCl + CaC12 were reported (fig. 8c-d and table 2). It is seen that violent stirring can maintain membrane control in most cases but not in all.In agreement with (3.9) and (3.7) deviations are more pronounced (i) with single membranes than with packs of four (ii) with the more permeable phenosulphonic than with the Amber-plex membranes (iii) with more dilute solutions than with more concentrated and (iv) in the system HC1 + CaC12 more than in the system NaCl + CaCli (in the former DAB/DAB is relatively small due to D A B + &+ according to (3.12~2)). Nearly all the experimental results reported in that paper with or without stirring on either or both sides agree to within & 5 mV with the calculated values using 6 = 5 x 10-5 cm with stirring and 6 m 5 x 10-2 cm without stirring." The film hypothesis is thus seen to account for the extreme sensitivity towards stirring of bi-ionic cells containing counter-ions of different valences and to explain those experimental potential values which disagree with previous theories.It has been pointed out that in bi-ionic systems with ideal membrane control the concentration profiles of the counter-ions are governed by the relative mobility of the ions and to a certain extent by the dependence of the equilibrium constant on mole fraction whereas the selectivity shown by the membrane in equilibrium systems (i.e. the absolute value of the equilibrium constant) is irrelevant. Ex-perimental evidence on this point has been obtained. Concentration profiles were measured directly by analysis of a multiple membrane pack between 0.1 m solution of NaCl and HC1 and of NaCl and KCI.In the system NaCl + HCl the equilibrium constant is very close to unity and independent of mole fraction. The profile shows that the slower ion Na+ is ac-cumulated to an extent corresponding roughly to a mobility ratio &/ENa= 6 (fig. 5). The ratio of the specific conductances of H+-resin and Naf-resin is 6.1. In the system NaCl + KCl the equilibrium constant decreases with increasing mole fraction of K+ the latter being preferred to a considerable degree. The profile shows the characteristic S-shape predicted by the theory for d In K/d%B < 0, the initial slopes at the phase boundaries corresponding to a mobility ratio The results are thus in excellent agreement with the predictions from the flux equation treatment and they rule out the hypothesis that in bi-ionic systems the counter-ions are present within the membrane in the same ratio as if the membrane were equilibrated with a solution prepared by mixing equal volumes of the two solutions of the bi-ionic system since this hypothesis would require absence of any accumulation in the system NaCl + HCl and a definite accumulation of K+ over Na+ in the system NaCl + KC1.Full details will be published elsewhere. - -&/ENa N 1.2 (fig. 4). * This is the distance for linear diffusion in the holes of the cell 92 B I - ION I C POT E N TI A L S (b) NON-STEADY STATE CONDITIONS The approach thus far has required the steady state. But since the integration leading to (3.16) is carried out over one variable (CJ only the potential difference between the two boundaries of the layer under consideration is determined solely by the boundary conditions and is independent of the concentration profile within the layer.Therefore the potential reaches the steady state value as soon as the concentrations at the interfaces assume the values corresponding to the steady state; usually this occurs long before the profile within the layer has become stationary (compare the results in the preceding paper ; 1 also the glass electrode seems to behave in a similar manner). For this same reason a relative abundance of one species within the membrane has no effect on the membrane potential. KCI x= 0 d FIG. 4. (C) GENERAL CONCLUSIONS Bi-ionic cells such as (1-1) represent an excellent tool for the study of ion-exchange kinetics they permit steady-state measurements under the simplest geometrical conditions (one-dimensional diffusion).The limiting cases (3.12) apply also to " particle kinetics " in granular ion exchange resins. Thus it becomes evident that the assumption of an " effective diffusion constant " DAB independent of composition (i.e. mole fraction) used in previous approaches,l7 cannot be upheld when %A is considerably different from 5,. From a modified eqn. (3.9) a rough but simple prediction can be made for ion exchange with granular resins as to whether " film kinetics " or " particle kinetics " is to be anticipated. 5. EXTENSIONS The treatment can be readily extended to (i) systems with different film thicknesses on either side of the membrane, (ii) systems with different total concentrations in both solutions (Ca + CP) an (iii) (iv) F .HELFFERICH 93 systems in which one or both solutions contain both counter-ions diffusion through the membrane of an electrolyte (as in concentration cells) or a non-electrolyte. / (Cf CB" =I= 0). Interfacial resistance to diffusion can be accounted for by introducing inter-The experiments however facial permeability parameters gi as defined by Scott.18 provide no evidence in favour of this phenomenon in ion exchange. NoCl x-0 d FIG. 5 . The method does not lend itself to systems with more than two permeating species i.e. with more than two counter-ions or with concentrations which permit anionic fluxes. In such cases either Wyllie's approach must be used or Schlogl's 13 which is more accurate but more time-consuming.Both however are restricted to ideal membrane control and neglect gradients of activity coefficients. The experiments on which this work is based were initiated at the Massachusetts Institute of Technology under the auspices of Professor G. Scatchard. The author is indebted to him and to Dr. R. Schlogl for advice and many helpful discussions. SYMBOLS a activity X mole fraction, C concentration (moles/I.) z ionic valence (negative for anions), d membrane thickness y activity coefficient, D diffusion constant 6 film thickness, E electric potential difference K partition coefficient, K ion-exchange equilibrium constant 0 electric potential, r (differential) transference number 4 ionic flux. x space coordinate normal to interfaces, Subscripts A and B refer to cations X to the anion i to any ionic species.Superscripts C( and p refer to the left and right solution a and b to the interfaces on the left and right side of the membrane. Bars denote quantities within the membrane 94 DIFFERENTIAL RATES OF PERMEATION 1 Scatchard and Helfferich this discussion p. 70. 2 Scatchard J. Amer. Chem. SOC. 1953 75 2883. 3 Michaelis Kolloid-Z. 1933 62 2. 4 Marshall and Krinbill J. Amer. Chem. SOC. 1942 64 1814 and later publications. 5 Meyer and Bernfeld Helv. chim. Acta 1945 28 962. 6 Sollner J. Physic. Chem. 1949 53 121 1 and 1226, 7 Sollner Dray Grim and Neihof Ion Transport Across Membranes (Acad. Press, N.Y. 1954) p. 144. Dray and Sollner Biochim. Biophys. Acta 1955 18 341. 8 Manecke 2. Elektrochern. 1951 55 672. 9 Wyllie J. Physic. Chem. 1954 58 67. 10 Henderson 2. physik. Chem. 1907 59 11 8. 11 Goldmann J. Gen. Pliysiol. 1943 27 37. 12 Teorell Z. Elektrochem. 1951 55 460. 13 Schlogl Z. physik. Chem. 1954 1 305. 14 The film concept was used in ion exchange reactions first by Boyd Adamson and 15 This effect is discussed by Schlogl Z. physik. Chem. 1955,3 73 and this Discussion. 16 See for instance Soldano and Boyd J. Amer. Chem. Soc. 1953 75 6107, 17 See for instance Kressman and Kitchener Faraday SOC. Discussioizs 1949 7 90. 18 Scott Tung and Drickamer J. Chem. Physics 1951 19 1075. Myers J. Amer. chem. Soc. 1947 69 2836. Reichenberg J. Amer. Chem. SOC. 1953 75 589

ISSN:0366-9033    

DOI:10.1039/DF9562100083

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

94 DIFFERENTIAL RATES OF PERMEATION THE PHYSICAL CHEMISTRY OF THE DIFFERENTIAL RATES OF PERMEATION OF IONS ACROSS POROUS MEMBRANES BY R. NEIHOF” AND K. SOLLNER Laboratory of Physical Biology National Institute of Arthritis and Metabolic Diseases National Institutes of Health Public Health Service U.S. Department of Health, Education, and Welfare Bethesda 14, Maryland, U.S.A. Received 12th January, 1956 A possible explanation of the differential uptake by living cells of various species of ions of the same charge by an essentially aqueous process is developed on the basis of the con- siderations which previously have led to the quantitative treatment of “ poIyionic” potentials across membranes of extreme ionic selectivity. Relative rates of exchange across such membranes of any two species of “ critical ” ions coexisting in solution 1 for any third species of ions of the same charge in solution 2 can be calculated from their relative activities in solution 1 and the “ bi-ionic ” potential arising with the same two species of ions across the same membrane.The predictions of the theory are confirmed with a variety of combinations of critical ions in systems with cation selective as well as in systems with anion selective permselective membranes of extreme ionic selectivity and low resistance. With these membranes the ratios of the fluxes of, for instance, Kf and Li+ (being at the same concentration in solution 1) are of the order of 6 : 1 ; of I- and C1-, 2.5 : 1 ; and of SCN- and Ac-, 33 : 1 . The mechanism of the differential uptake by living cells of various species of ions of the same charge from the surrounding milieu is one of the major open problems of physical biochemistry.In this paper we try to show that recent * present address : Physiological Institute, University of Uppsala, Uppsala, Sweden.R . NEIHOF AND K . SOLLNER 95 studies on the electromotive action of membranes of extreme ionic selectivity 1 * 2 lead to the prediction of the existence and the magnitude of an heretofore over- looked, easily demonstrable, physicochemical effect arising with porous membranes, which, if it should occur across the membranes of living cells and tissues, could readily account for the selective uptake by the latter of different ions of the same charge. Andr6 and Demoussy,3 according to Brooks,4 first realized that the preferential uptake of certain ions (for instance of K+ over Na+, or of I- over Cl-) by meta- bolizing cells must be connected with a state of non-equilibrium, now commonly believed to be a steady drift toward a Gibbs-Donnan membrane equilibrium.In this state of non-equilibrium, maintained by the continuous production of some electrolytic metabolites such as carbonic acid, the faster-permeating ions are present in the cell at a relatively higher concentration than the more slowly penetrating ones. Brooks has stressed the fact that numerous mechanisms could explain differential rates of permeation of ions of the same charge.4 The classical papers of Osterhout and his school consider the formation of some undissociated or weakly dissociated compounds in a protoplasmic membrane of an essentially nonaqueous character.Brooks proposed an essentially aqueous mechanism involving highly cation- or highly anion-selective membranes of porous character.4 On the basis of the infor- mation then available he suggested that digerences in the diffusion velocities of the various ions in water might be the determining factor. These differences, however, are much too small to account for the observed erTects. The lack of a demonstration in vifro of greatly differing rates of permeation of the various common univalent cations and anions across porous membranes of high ionic selectivity has remained one of the most serious difficulties of the various theories which assume essentially aqueous processes for the uptake of ions by living cells.The problem is one particular aspect of the dynamics of the exchange of ions across porous membranes in aqueous systems with three or more species of ex- changing ions of the same charge. The simplest systems of this type are those with membranes of extreme ionic selectivity, which (for exclusively cation-perme- able anion-impermeable membranes [ +@+ I ) are represented by system I : solution 1 1 membrane I solution 2 (system I) where a1 and a, are activities, and A+, B+, and L+- the exchangeable, " critical " cations ; X- are the nonexchanging anions. Anionic systems, with exclusively anion permeable membranes, I +-a+ I, are analogous. The systems sought would be characterized by a ratio in the rates of simul- taneous exchange of A+ for L+ and of B+ for L+, which is large compared with the ratio that might result from the differences in the diffusion velocities in water (which are proportional to the ionic mobilities) of the A+ and Bt ions.With the common ions these latter differences are relatively small, except for the H30f and OH- ions. For instance, the ratios of the diffusion velocities of K+, Na+ and Lii- are 1-00 : 0-68 : 0.53 ; of I-, C1-, SCN-, IO3-, and Ac- 1.01 : 1.00 : 0.86 : 0.54 : 0.54. There are no data in the literature concerning the kinetics of the exchange of ions between solutions across membranes in systems such as system I. However, the closely related problem of the origin of the electrical potentials which arise in systems of type I, and in numerous other more complex types of " polyionic " systems with membranes of high ionic selectivity, has recently been treated theoretically and experimentally in some detail.These potentials were interpreted in terms of relative intrinsic permeabilities of the different ions when present simultaneously in the same system. The concepts developed in this connection 19296 DIFFERENTIAL RATES OF PERMEATION are applicable to the problem on hand and lead, in combination with the empirical information on the electromotive behaviour of polyionic systems,S~ 6 to the pre- diction of the effect looked for and to the selection of appropriate experimental systems, as will be shown presently. The simplest polyionic systems are the " bi-ionic " systems in which a membrane of either extreme anionic or extreme cationic selectivity separates the solutions of two electrolytes at the same activities, al, having different " critical " ions, which are able to exchange across the membrane, and the same " noncritical " ion species for which the membrane is impermeable.l.2 Such bi-ionic membrane systems may be represented as shown here for a cationic system, system 11, (system 11) in which the univalent critical ions A+ and B+ exchange in equivalent quantities.The " bi-ionic " potentials arising in such systems, according to the nature of the membrane and the combinations of critical ions, may be 150 mV and more. The bi-ionic potential (b.i.p.) results from the different tendencies of the two species of critical ions to penetrate across the membrane and from the restriction that they can exchange only on a one to one basis.The more readily permeable species of critical ions impresses its charge on the other solution. The absolute magnitude of the b.i.p., Ebip, is a function of the relative contributions of the two species of critical ions toward the (virtual) transportation of electricity across the membrane, according to the equation where by definition T i + + r;+ = 1. TL+ + T;+ represent the transference numbers of critical ions A+ and B+ across the membrane. The sign of the potential refers to the charge of solution 2. The relative abundances of the two species of critical ions in the pores of a membrane multiplied by their relative diffusion velocities determine the ratio T ~ + / T % + . These ratios vary considerably according to the nature of the membranes.Typical figures (as given below for low resistance permselective membranes) are : rL1-/rYo3- = 7.1 ; r ~ l - / T ~ c - = 7.3 ; riCN-/TiC- = 39.0, etc. All such ratios are far in excess of, and in some instances in an order inverse to the ratios of the diffusion velocities of the various ions in water. With other membranes and combinations of ions the ratios may be much higher, of the order of 100 : 1 and more. The ratios T O in bi-ionic systems can be interpreted on the basis of the fixed charge theory of membrane behaviour, according to which the membranes are ion exchangers.1 If an ion exchanger is equilibrated with a solution containing two species of exchangeable ions, these ions compete as counter ions for positions of the fixed &sociable groups.In general, they are taken up to a different extent. The sequences of the relative adsorbabilities of the various ions are the two Hofmeister series, unless steric hindrance-the preferential screening out of some species of exchanging ions because of their size-comes into play. In explaining the mechanism of the origin of the bi-ionic potential two assumptions were made : (i) that the two species of critical ions are present within the membrane in the same ratio as if the membrane were equilibrated with a solu- tion prepared by mixing equal volumes of the two solutions of the bi-ionic system ; and (ii), that the ionic mobility of any species of ions within the membrane is independent of the presence or absence of other ions.In extending this approach to " polyionic " potentials across membranes of ideal ionic selectivity, in systems with more than two species of " critical " ions, rR+/rR,+ = 2.5 ; 7k+/Tli+ = 6.3 ; Tk,+/Te+ 2.6 ; 7' I- /TO c1- = 2.9 ; T&..N-/r&- = 6.2 ;R. NEIHOF AND K . SOLLNER 97 two additional assumptions were made ; (iii) the ratio of the adsorbed quantities of two species of ions is not changed by the presence of other competing species of ions; and (iv) the ratio of the adsorbed quantities of two competing species of ions is linearly proportional to their relative activities in the solutions.2 On the basis of these four assumptions it was possible to correlate quantitatively the poly- ionic potentials which arise in various polyionic systems with the same membrane and the same species of critical ions, The usefulness of this approach was confirmed by extensive experimental tests.6 Applying these assumptions to the exchange kinetics of polyionic membrane systems-the simplest of which is system I above-one concludes that the ratio of the rates of exchange across the membranes of two species of critical ions, A+ and B+ from solution 1 into solution 2 must be determined by the ratio of their relative abundances within the membrane times their respective mobilities.Thus, according to assumptions (i) to (iii), the ratio of the rates of exchange for A+ for L+ ions and of B f for L+ ions, $A+/~B+ in system I should be the same as the ratio T ~ + / T ; + in the corresponding bi-ionic system 11, independent of the nature or concentration of the L+ ions : Similarly, on the basis of assumptions (i) to (iv), the ratio of the rates of simul- taneous exchange of A+ and Bf across the same membrane can be predicted when these two ionic species are present in solution 1 at the different activities, a:; and a$>.We may write the general expression independent of the nature and activity of the L+ ions. Thus, our basic assumptions lead directly to the prediction of ratios of the rates of exchange, that is of the fluxes of two coexisting species of critical ions across porous membranes which are far in excess, in some instances in an inverse direction, of any flux ratios explainable by differences in the diffusion \,elocities of these ions in water. These considerations may be extended to any number of critical ions, A+, B+, Cf, etc., in solution 1 which exchange against one or several different species of ions L+, Mt, N+, etc., in solution 2.The ratios of +A+/$B+, #B+/$c+, #c+/#;, etc., for any pair of critical ions in solution 1 are defined by equations corres- ponding to eqn. (4). The experimental test of eqn. (4) is obvious: the bi-ionic potentials across a given membrane with several pairs of ions are determined and the corres- ponding T~+/T;+ , T ~ + / T E + , etc., ratios are computed. The initial rates of exchange of two or more ionic species, A+, B+, C+, etc., of known activities in solution 1 of a polyionic system (with the same membrane), against L+, M+, etc., ions of solution 2 are determined from the initial slopes, that is the slopes at zero time, of the curves in which the quantities of exchanged A+, B+, etc., ions are plotted against time.The ratios of each two of these initial flux rates ( ~ A + / $ B + ) ~ ~ ~ ~ . , ( $ B + / $ c + ) ~ ~ ~ ~ . , etc., are computed and compared with the ratios of the rates calculated from eqn. (4), ($~+/$~+)caic , ($~+/$~+)caic , etc. In the experiments reported below no attempt was made to select the experi- mental systems and conditions so that an optimum agreement between calculated and experimental 4 ratios would result. In all instances it must be considered that the idealized assumptions on which the calculated $ ratios are based are not neces- sarily strictly fulfilled, particularly over wide ranges of concentrations and con- centration ratios,51 6 and that a small error in the bi-ionic potentials from which a ro ratio is computed causes a relatively large error in this ratio since it appears in eqn.(1) as a logarithmic term. D98 DIFFERENTIAL RATES OF PERMEATION EXPERIMENTAL The experimental conditions for the study of dynamic membrane systems in general have recently been discussed and are not restated here.5 The membranes used were " perm- selective " collodion matrix membranes of almost ideal ionic selectivity.7. 8, 9 The permselective membranes are ion exchangers ; all ionic processes which occur across them are generally assumed to take place in the aqueous medium which fills their pores. Their absolute permeability (as measured by their electrolytic conductance) may be varied at will over a very wide range ; their water permeability is very low and can be disregarded in experiments of short duration. They were prepared according to methods previously described?, g Y 9 and tested by our standard methods (a) for their elec- trical resistance p * in 0.1 N KCI as an indication of the rates at which ions diffuse across them, and (b) for their electromotive properties in concentration cells 0.4 N KCl I membrane I 0-2 N KCl as a measure of their ionic selectivity.89 9 These potentials, corrected for the asymmetry of the liquid-junction potentials, were in the range of f 14.9 to rt 15.5 mV, the theoretical maximum potentials being & 15.95 mV, the plus sign referring to selec- tively cation-permeable, the minus sign to selectively anion-permeable membranes.The bi-ionic potentials, &p, with the various pairs of critical ions were measured at 25.0" by the Poggendorf compensation method, with an accuracy of f 2%, using saturated calomel half-cells with saturated KC1-agar bridges as reference electrodes.5 No correction was made for the asymmetry of the two liquid-junction potentials. Using eqn. (l), the corresponding ratios of the transference numbers T : + / T ~ + , 7;+/7e+, etc., and T ~ - / T & , %-IT%- , etc., were evaluated and used to compute the calculated flux ratios.* For the measurement of the rates of exchange a bag-shaped membrane was filled with 30 ml of solution 2 and immersed in 1 1. of solution 1 at 25.0" C. Both solutions were stirred at such rates that further increases in stirring did not increase the rates of the ex- change of ions.The effective membrane area in contact with the solutions was about 50 cm2 ; it was constant during a given experiment. To establish a steady-state condition across the membrane the inside solution was renewed repeatedly during the 1-2 h before starting the experiment proper at zero time when both solutions were renewed. At measured intervals small aliquots of solution 2 were removed and analyzed for the,ions A+, B+, C+, etc., or X-, Y-, Z-, etc., entering from solution 1. After the concentration of the critical ions initially present in solution 2 had decreased not more than 10 %, the experiment was interrupted, and a second run with fresh solutions started. (In a few systems rather large quantities of the " inside " solution were required for analysis ; in these instances several runs of different durations were made and the entire inside volume used for analysis at the end of each run.) These procedures were repeated until two succes- sive runs gave the same average rate of increase within k 5 % or less.All analyticaI determinations were carried out by standard (if necessary, suitably adapted) micro-methods,lo due regard being taken of the presence of other, potentially interfering electrolytes. The error in any individual analysis was never more than rt 5 %, in most cases less than rt 3 %. The rate of increase in concentration of a particular ionic species in the inside solution was determined by plotting concentration against time after correcting the measured concen- trations (after the first) for the withdrawal of previous samp1es.t The curves drawn through the plotted points were straight lines within experimental error up to at least 5 % depletion of the concentration of the ion in question in solution 2.Their slopes at zero time are the initial flux rates which were used in computing the experimental flux ratios ('#'A+/+B+)expt. Y (+B+/k+)expt. , . . . ($X-/+Y-)expt. . . . etc. * In view of the limitations of the assumptions on which eqn. (4) is based, and because of the similarity of the critical ions used, the calculated $ ratios were computed on the basis of concentrations without regard to the minor differences of the activity coefficients applic- able to the different ions in the various mixed solutions 1.t The formula used for computing the concentration Cn' corrected for withdrawal of previous samples was tn Cn cn' = t l + (v1/Y2) ( t 2 - t l ) + (YI/J'~) ( t 3 - 12) + - - (J'dVn) (tn - tn-1) ' where c, is the measured concentration at time tn when the total volume inside the membrane is V,. Vl, V2, V3, etc. and tl, t 2 , t 3 , etc. are the volumes and times, respectively, when the h t , second, third, etc. samples were withdrawn.R . NEIHOF AND K . SOLLNER 99 TABLE 1.-A COMPARISON OF THE CALCULATED AND EXPERIMENTAL RATIOS OF THE FLUXES OF TWO SPECIES OF COEXISTING CRITICAL IONS FROM SOLUTION 1 INTO SOLUTION 2 ACROSS PERMSELECTIVE MEMBRANES. ( t = 25.0" C) A.-SYSTEMS WITH CATION SELECTIVE MEMBRANES solution 1 (crit. ions A+ and B+) 0-1 N KCI 0.1 N LiCl 0.05 N KC1 0-05 N LiCl 0.3 N KCl 0-3 N LiCl 0.02 N KC1 0.2 N LiCl 0.2 N KCl 0-05 N LiCl 0.1 N KCI 0.1 N NaCl 0.1 N HCI 0.1 N NaCl solution 2 0.2 N NQCI 0.3 N NH4Cl 0.05 N NH4CI 0.2 N NHiCl 0.2 N NH4C1 0.2 N NH4Cl 0.2 N NH4C1 sulphonated polystyrene- oxidized collodion collodion membrane membrane 6.3a 6-3 6.8 7-lc 7.1 9-2 6.3a 6-3 6.2 7.lc 7.1 8.0 6 .3 ~ 25 28 7*lc 28 30 22b 22 24 a membrane with p* of 220 R cm2, b membrane with p* of 185 Q cm2, c membrane with p* of 295 L? cm2, dmembrane with p* of 325 L? cm2. K-SYSTEMS WITH ANION SELECTIVE MEMBRANES solution 1 (crit. ions solution 2 X- and Y-) KSCN 0.2N KN03 0.1 N KC1 0.05 N KCI KSCN 0.2N KN03 0.05 N KSCN 0.2 N KNo3 0-2 N KC1 0.05 N KSCN 0.3 N KN03 0.05 N KCI 0.1 N KSCN 0.2 KAc 0.1 N KCl 0.1 N KAc KBr 0.2 N KN03 KSCN 0.2 N KN03 0.1 N KAc KC' 0.2 N KN0-j 0.1 N KIO3 O.I KT 0 .2 ~ K N O ~ 0.1 N KCl 0.1 N KSCN 0.1 N KNO3 0.1 N KCI 0.1 N KAc poly-2-vinyl-N-methyl pyridinium protamine collodion collodion membrane membrane 8.2e 2.05 1.69 2.8g 0.70 0.70 8.2e 8.2 5.3 2.8g 2.8 2 7 12.9f 12.9 12-9 6.0h 6.0 6.8 39f 39 33 13.7h 13.7 15.3 7.1 7.1 8.6 4.3h 4.3 5.3 2.9f 2.9 2.4 1.62h 1.62 1.56 6.0f 6.0 4-5 3-1h 3.1 2.7 e membrane with p* of 170 R cm2, f membrane with p* of 11 5 R cm2 8 membrane with p* of 140 9 cm2, h membrane with p* of 150 52 cm2.100 DIFFERENTIAL RATES OF PERMEATION The probable error in these experimental flux ratios may be 3 % in the most favourable instances, and may reach 10 % under unfavourable conditions. ratios, an agreement of calculated and experimental q!~ ratios within 5 % is likely to be fortuitous or due to unusually favour- able conditions. In general, deviations of 10 to 15 % might be expected.Considering the uncertainties in the calculated RESULTS Tables 1 and 2 are self-explanatory. In the experiments of table 2 all species of critical ions in the solutions 1 were at the same concentration, so that the calculated 4 ratios are identical with the corresponding 7' ratios ; the latter are therefore omitted from the table. TABLE 2.-A COMPARISON OF THE CALCULATED AND EXPERIMENTAL RATIOS OF THE FLUXES OF THREE SPECIES OF COEXISTING CRITICAL IONS FROM SOLUTION 1 INTO SOLUTION 2 ACROSS solution 1 0.1 N KCl 0.1 N NaCl 0.1 N LiCl 0.1 N KCl 0.1 N NaCl 0.1 N LiCl solution 1 005 N KSCN 0.05 N KC1 0-05 N KAc 0.05 N KSCN 0.05 N KCl 0.05 N KAc solution 1 0-05 N KSCN 0.05 N KI 0.05 N KC1 0.05 N KSCN 0.05 N KI 0.05 N KCI PERMSELECTIVE MEMBRANES.(f = 25.0" C ) A.-SYSTEMS WITH CATION SELECTIVE MEMBRANES jk+- 4K+ +Na+ 4G membrane solution 2 calc. expt. calc. expt. sulphonated polystyrene 0.3 N NH4C1 2.5 2.8 6-4 7.1 collodion (p* = 185 52 cm2) oxidized (p* = 325 Qcm2) collodion 0.3 NNH4CI 3.0 3.2 7.1 9.5 B. SYSTEMS WITH ANION SELECTIVE MEMBRANES membrane solution 2 poly-2-vinyl-N- methyl pyridin- 0.15 N KN03 ium-collodion (p* = 115 L? cm2) protamine collodion 0-15 N KNO3 (p* = 150 s? cm2) membrane solution 2 poly-2-vinyl-N- methyl pyridin- 0.15 N KN03 ium-collodion (p* = 115 D cm2) protamine collodion 0-15 N KNO3 (p* = 150 12 cm2) 4SCN- 4SCN- dC1- $Ac- calc. expt. calc. expt. 6.0 4.8 39.0 42.0 3.1 2.7 13.5 14.9 4SCN- h C N - h- $CI- calc.expt. calc. expt. 1.98 1.80 6.0 4.6 1.86 1.78 3.1 2.7 DISCUSSION +Na+ G calc. expt. 2.6 2 4 2.4 3.0 d c l - calc. expt. 7.3 8.9 4.8 5.5 41- G- calc. expt. 2-9 2.6 1.63 1.52 The calculated and experimental 4 ratios in tables 1 and 2 demonstrate clearly the existence of the postulated effect and also show that its magnitude can be pre- dicted quantitatively on the basis of independent electrometric measurements in appropriate bi-ionic systems.R . NEIHOF AND K. SOLLNER 101 The agreement between the calculated and the experimental # ratios is in most instances within or near the estimated limits of the probable accuracy of the data. A discussion of the several larger deviations, of little importance with respect to the main purpose of this paper, may be left to a more comprehensive investigation of the general problem of ionic fluxes across permselective membranes.To what extent the effect demonstrated here plays a role in living cells and tissues is a problem outside the scope of this paper. One point, however, should be stressed here. The forces which regulate the chemical specificity of the various ions in exchange adsorption must be assumed to be of the same nature as those which determine ionic distribution equilibria between liquid phases. In micro- heterogeneous systems, in addition, steric hindrance may come into play. Thus it might be concluded that at least as great and varied degrees of ionic specificity can arise with micro-heterogeneous membranes as with homogeneous phase, " oil " membranes. The highly organized membranes of living cells and tissues might easily be much more effective in this respect than our synthetic membranes. 1 Sollner, J. Physic. Chem., 1949, 53, 1211, 1226. 2 Dray and Sollner, Biochim. Biophys. Acta, 1956, 21, 126. 3 Andr6 and Demoussy, Bull. SOC. Chim. biol., 1925, 8, 806. 4 Brooks, Protoplasma, 1929, 8, 389. 5 Dray and Sollner, Biochim. Biophys. Acta, 1955, 18, 341. 6 Dray and Sollner, Biochim. Biophys. Acta, 1956 (in press). 7 Sollner, J. Electrochem. SOC., 1950, 97, 139c ; Ann. N. Y. Acad. Sci., 1953, 57, 177 ; Electrochemistry in Biology and Medicine, ed. Shedlovsky (John Wiley and Sons, Inc., New York, 1955), Chap. 4, p. 33. 8 Neihof, J. Physic. Chem., 1954, 58, 916. 9 Gottlieb, Neihof and Sollner, J. Physic. Chem. (in press). 10 Kolthoff and Furman, Poterztiomefric Titrutions (John Wiley and Sons, Inc., New York), 2nd ed., 1931 ; Kolthoff and Stenger, Volumetric Analysis, vol. I1 (Inter- science Publishers, Inc., New York), 2nd ed., 1947 ; Snell and Snell, Colorimetric Methods of Analysis, vol. I1 (D. Van Nostrand Co., Toronto, New York, and London), 3rd ed., 1949.

ISSN:0366-9033    

DOI:10.1039/DF9562100094

出版商:RSC    

年代:1956

数据来源: RSC