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.