GENERAL DISCUSSION 117 GEhTERAL DISCUSSION Dr. T. L. Hill (Bethesda U.S.A.) said Both the Donnan and McMillan-Mayer methods can be applied to the more general situation in which one or more species are present on both sides of a membrane but have different electrochemical potentials on the two sides. Such a difference in electrochemical potential for any particular species might arise either (i) because the molecules or ions cannot pass through the membrane (e.g. protein molecules) or (ii) because the membrane does work to maintain the electrochemical potential difference (e.g. active trans-port of sodium ions). This extension of the present paper is discussed in more detail elsewhere.1 Prof. G. Scatchard (M.Z. T. Cambridge Mass.) said I am very much interested in Dr.Hill’s finding that the term in the second virial coefficient which the Donnan treatment attributes to unequal diffusible ion distribution is attributed by the MacMillan-Mayer method to repulsion between non-diffusible ions. This shows how dangerous it would have been to believe that the measurements prove either explanation to be correct. In this case a common basis of the two explanations is easy to find in that they both require that each solution be electrically neutral. Dr. B. A. Pethica (Cambridge University) said It is of interest to allow for the specific interaction of ions in the Donnan treatment of the equilibrium across a membrane impermeable to one charged species. The occurrence of ion pairing between the diffusible species introduces no special additional factors but if the non-diffusible species specifically binds gegenions the assumption that its charge is invariant with respect to the concentration of diffusible electrolyte is no longer valid.The Donnan correction for the “ excess osmotic pressure ” of the diffusible ions is still obtained however from the membrane potential directly as in the usual formula for small potentials. The question of specific interaction is of particular interest in systems involving for example the equilibrium of a detergent ion with a protein where the strong binding (even in dilute solutions) is measured by an equilibrium dialysis method. Prof. Teorell mentioned that it is possible to treat the ionic distribution at the boundary of a charged membrane by methods other than the Donnan.The use of the Donnan equilibrium in the fixed charge theory seems natural for thick membranes in which a volume charge density is a variable of choice. For a very thin charged membrane (e.g. Prof. Danielli’s bimolecular lipid membrane) it would seem preferable to treat the fixed charge in terms of a two-dimensional charge density. The Gouy and Stern theories are applicable in this case. As Davies and Rideal have shown 2 the simple Donnan treatment for a surface charge is closely related to a Gouy treatment. Similarly, it may be shown that the Stern method for surface charge is similar to a Donnan treatment in which specific interaction is allowed for It is hoped to give a fuller account of these points in due course. Ing. J. Straub (Utrecht) said I would like to add a personal tribute to the honours accorded to Prof.Donnan. I recall that Prof. Donnan realized that the Donnan equilibrium is always an imperfect equilibrium. Unless one of the liquids is put under a static pressure there remains in equili-brium a difference in total osmotic concentration that must cause a steady per-meation of water. A perfect equilibrium would be established only if on both sides of the membrane non-permeating ions of the same concentration but of different sign were present. This possibility has now been realized by my col-laborator P. Hirsch Ayalon. It is mentioned in a paper given by Dr. Hirsch in the International Congress on Polyelectrolytes at Rehoboth 1srael.j Prof. G. Scatchard (M.Z.T. Cambridge Mass.) said I believe that the differ-ences between Kirkwood’s treatment and Schlogl’s are probably even smaller 1 Hill J .Amer. Chem. SOC. (in press). 3 cp. also P. Hirsch Ayalon Rec. trav. chim. 1956 (in press). 2 J . Colloid Sci. 1948 3 3 13 118 GENERAL DISCUSSION than Dr. Schlogl indicates but that any discrepancy must be due to an error in Schlogl’s treatment rather than in Kirkwood’s. The fact that Kirkwood’s treatment leads to non-linear equations when the diffusion coefficients are not invariant is due to the nature of the systems and not to his treatment. The “ discontinuous ” method gives average values of these coefficients which must depend upon the detailed conditions. Moreover even in the simple cases in which each is the corresponding Gab at some point in the membrane there is no reason to suppose that this relation holds for any two of them at the same point.Prof. R. Schlogl (Guttingen) said In reply to Prof. Scatchard I would like to remark that I do not believe that there is any serious discrepancy between Kirkwood’s treatment and Schlsgl’s treatment. May I quote from my paper: “ In practice Kirkwood’s treatment will always be a very good approximation, and any small deviations will almost certainly be insignificant compared with experimental errors ”. More important than the difference between both approaches is the inter-pretation of Kirkwood’s coefficients wap. My objection to these coefficients (the calculation of which has been performed correctly by Kirkwood) is just what Prof. Scatchard mentions they are not invariant to the nature of the system (but rather depend on the applied “forces” APE) so that the flux equations become non-linear.Kirkwood in his paper states that the wag’s depend on the concentrations of the solutions as well as on the membrane properties. However, it seems to have escaped his attention that the wafi’s depend also on the forces, for example the applied pressure difference or the electric field; in any case he does not mention this in his paper. But I fear that this dependence deprives these coefficients of their practical value. (I mentioned in my paper that the dependence has no significance as long as the system is close to equilibrium. In this case however the integration across the membrane carried out by Kirkwood is unnecessary.) Dr.G. Manecke (Berlin) said As I understand the results of Dr. Schlogl, he found that the convection contribution to the total conductivity constituted between 7 and 45 %. Now by measuring the conductivity of cation exchangers of the same chemical composition and with a water content of 60-70 % we determined the composite mobility of potassium and chloride ions and found that the mobility of the cation is greater than that of the chloride ion. Does he consider it correct that one can calculate the share due to convection in the ion transport from the difference determined by measuring the conductivity and transference in the mobilities of K and C1 within the membrane ? In addition, it must be assumed that the true mobilities of K and C1 in the membrane are practically equal as is found in free solution.In such a case I would obtain from my experiments a contribution of approximately 25 % for the convection con-ductivity at an outer concentration of 0.1 M. Dr. R. Schlogl (G2ttingen) said Since the water content in the membranes studied by Manecke was relatively high it seems to me that the assumption of equal characteristic mobilities for K and C1 is sufficiently justified as an ap-proximation. In my opinion with this assumption Manecke’s method of calcula-tion of the convection part of the conductivity is correct. Schodel found for the concentration Manecke mentioned a convection contribution of about 30-40 % according to the degree of cross-linking. That would agree quite well with Manecke’s estimated value especially since his membranes possessed a somewhat smaller water content.Prof. G. Scatchard (M.I.T. Cambridge Mass.) said It is most unfortunate that neither Prof. Nagasawa nor Prof. Kagawa is here to discuss this paper. Everything which T can check in it seems to me wrong. Their eqn. (4) contains five unexplained parameters. Even if they are explained in previous papers they are apparently all determined from the membrane potential measurements. Th GENERAL DISCUSSION 119 fact that none of the five explicitly contains the water activity cannot be taken as proof that the water activity does not affect the potential. In fig. 8 the authors appear to permit no parameters in Teorell’s equation to be determined from the potential measurements and the values they choose seem to me most improbable.We know that the capacity of Nepton CR-51 is about 1.2 rather than 0.1 and that U can vary only between - 1 and + I with the probable value about + 0.25. Yet they use 2 and 3. Concerning the fact that their results are never close to the theoretical limit one can only say that other observers have approached it much more closely. Once the curve starts to rise with increasing activity it should continue rising with slope about equal to that at the inflection as drawn. Dr. M. Nagasawa and Dr. I. Kagawa (Japan) (communicated) Prof. Scatchard stated that our eqn. (4) contains five unexplained parameters. The five which he referred to may be kl k2 k3 a and p. Originally we had three parameters kl, k2 and k3 as was introduced in the previous paper where these three were finally reduced to cc and /3.Here is our explanation of their relationship : Curve ( 3 ) in fig. 2 does not correspond to the experimental results. k2(2+ + I-) + k3I+ ’ = kl(& + I-) Therefore we thought our task in the paper under discussion was to determine the values a and fi by experiments. As to the water activity we do not think it is essential to the membrane potential of ion-exchange membrane considering the good agreement between our experi-mental values and the values calculated without water activity. As pointed out by Prof. Scatchard the capacity of Nepton CR-51 is about 1.2 mequiv./cm3 resin or 1.7 mequiv./cm3 of water in the resin. To use this analytical concentration of counterion in the resin for A in our opinion would be,entirely in-correct because A concerns the activity of the counterion in the membrane.There-fore the appropriate value of A is to be determined from the experimental results. If A = 0.1 is used the considerable although not satisfactory agreement be-tween experimental and calculated values seems to be found in experiments in which the concentration of the solution on one side of the membrane is maintained constant as seen in our fig. 7. On the other hand in the experiments in which the ratio of concentrations on both sides is maintained constant we found it impossible to obtain the suitable values of A and U which would enable us to keep the agreement between observed and calculated values over the entire range of concentration. To bring out this feature we included fig.8 in which the cal-culated values were compared with the experimental values by the convenient use of A = 0.1 and 1+/1- = 2 or 3 . These results lead to our conclusion that the membrane potential of the ion-exchange membrane is characterized by the ab-normal behaviour of the ion activity in the resin phase which could never permit A = const. It is true that the symbol U was mistakenly used instead of l+//- in fig. 7 and 8, where it is well known that Curve (3) in fig. 2 is not the experimental results; the values of (RT/Fln (~*l/a*2) are calculated under the condition of Q/CZ = 2 to show the limiting values in an ideal case. Dr. P. Meares (Aberdeen University) said The abnormally low activity co-efficient of univalent counterions in a cation-exchange resin membrane in the absence of sorbed electrolyte is shown by Nagasawa and Kagawa to give rise to deviations from the Meyer and Teorell equation for membrane potentials .when this is derived on the basis of simple-assumptions regarding the activity coefficients.means (/+/I- - l)/(/+/I- + 1) 120 GENERAL DISCUSSION This unusual activity coefficient behaviour has been noticed by various authors and is usually attributed to binding of counterions into an electrical double layer around the polymer chains of the matrix. Thus in their appendix Nagasawa and Kagawa find as a necessary condition for normal activity coefficient behaviour that there must be a uniform electrical potential within the membrane. This would eliminate the tendency to double-layer formation.It has been noted 1 that for divalent counterions the activity coefficients of the ions in the membrane differ relatively little from those in free solution. Pre-sumably the double-layer effect is less important here as its thickness is inversely proportional to the valency of the counterions. It would be interesting to know whether any measurements have been made to test the adequacy of the Meyer and Teorell equation for calculating the membrane potentials obtained with solu-tions of such higher valence type electrolytes. Prof. Karl Sollner (Bethesda Maryland U S A .) said The potentiometric data of Dr. Bergsma and Dr. Staverman are similar to results obtained in our laboratory with anion-selective as well as with cation-selective permselective collodion matrix membranes.2sjs 4 With these membranes however lines with the theoretical slope of 59-1 mV fit the experimental points with only minor devi-ations at high concentrations.With reference to the very interesting electric ion transfer experiments of Dr. Bergsma and Dr. Staverman I should like to draw attention to the similarity in the reasoning in their paper and the paper by Dr. Neihof and myself.5 We have studied the ratios of the simultaneous exchange across permselective collodion matrix membranes of two or more species of ions A B C coexisting at various combinations of concentrations in one solution against another species of per-meable ions in the other solution. The ratios of the fluxes from solution 1 to solution 2 of the ions A B and C obtained in these experiments agree generally within 15 to 20 % in many instances considerably closer with those calculated from the bi-ionic potentials.In continuation of this work we have recently started in Bethesda experiments like those described by Dr. Bergsma and Dr. Staverman including some in which the competing ions under consideration are present in solution at concentration ratios other than 1 1. The preliminary results obtained thus far indicate satis-factory numerical agreement between the calculated and experimental transference ratios. In our first experiments along these lines we calculated for instance from the B.I.P. for K+ and Li+ when present at the same concentration a transfer ratio of 7.50 1 and found experimentally 7.85 1 ; with a concentration ratio of 1 5 the computed value is 1 1-50 the experimental value was 1 1.53; with a 5 1 ratio these ratios were 37.5 1 against 33.7 1.I have only a limited experience with commercial type ion-exchanger mem-branes but I am inclined to concur with the suggestion of Dr. Bergsma and Dr. Staverman that a good part of the numerical disagreement which they find between calculated and experimental values might be due to the transportation of water across these membranes which is much more copious than that across our much denser collodion matrix membranes. This conclusion is also supported by the potentiometric measurements of Wyllie and Kanaan with very dense cation exchanger membranes.6 1 Mackie and Meares Proc. Roy. SOC. A 1955 232,498. 2 Dray Ph. D.Thesis University of Minnesota Minneapolis Minn. 1954. 3 Sollner Dray Grim and Neihof Ion Transport across Membranes edited by H. T. Clarke and D. Nachmansohn p. 144 Academic Press Inc. New York 1954; EZectrochemistry in BioZogy and Medicine edited by T. Shedlovsky p. 65 John Wiley and Sons Inc. New York Chapman and Hall Ltd. London 1955. 4 Dray and Sollner Biochim. et Biophys. Acta in press. 5 Neihof and Sollner this Discussion. 6 Wyllie and Kanaan J. Physic. Chem. 1954 58 73 GENERAL DISCUSSION 121 Dr. F. L. Tye (The Permutit Co. Ltd. London) said Dr. Bergsma and Dr. Staverman have listed cation transport number ratios obtained directly for com-parison with ratios deduced from bi-ionic potentials. It should I think be made clear that the ratio they have determined directly is (1) where t; and t; are the transport numbers of cations X and Y through the central cation-selective membrane and t i and t,’ are the transport numbers of the same cations through an adjacent anion-selective membrane.The ratio really required for comparison with bi-ionic potentials is ( t - tcx)/(t - a , tilt;. (2) If the adjacent anion membrane is perfectly selective then t and t; are zero and the measured ratio (1) reduces to the desired ratio (2). However in two of the four combinations considered by the authors one of the cations is hydrogen and it is extremely difficult to prepare anion-selective membranes which are im-permeable to hydrogen ions-even at 0.05 N concentrations. Thus if Y is hydro-gen t$ could be appreciable and the measured ratio (1) would not be identical with the desired ratio (2).This doubt can be removed or its importance assessed if the authors were to list the quantity which should be obtainable from their measurements. If the quantity (3) is unity, then ratios (1) and (2) must be identical. If however quantity (3) is less than unity then the difference between (3) and unity gives the maximum possible value of t + ty+. Dr. A. Despid and Dr. G. J. Hills (Imperial College London) said With regard to the paper by Bergsma and Staverman we should like to draw attention to the two possible values of an ionic mobility in any one membrane system and to comment on their relevance to transport numbers and calculated flux ratios. The transport number of an ion in a membrane is defined as t i - t i + t; - t t (3) where c represents concentration and u ionic mobility in an applied electrical potential gradient.u = h/F where h is the measured ionic conductance. This transport number is distinct from a similar quantity I UiCi t’ = -W C ’ where u’ represents ionic mobility derived from a self-diffusion coefficient. In a membrane u and uf are different the relation between them being given by u = uf i- Au, where Au is the electro-osmotic mobility in the same direction as u. Similarly, there are two different flux ratios of two competing ions UiCi/Ujcj and u~ci/u~ci. Perhaps Dr. Bergsma and Dr. Staverman or any of the other authors concerned with membrane potential would comment on which of these ratios they consider to be relevant to bionic potentials and membrane potentials in general.When the flux ratio or mobility ratio of two counterions species in a membrane are discussed in relation to B.I.P. it is generally assumed that this ratio is constant, i.e. independent of the total or of the individual ionic concentrations and equal to the limiting mobility ratio in water. If the relevant mobility ratio is that in the absence of an external field this is in fact so. We have found that ionic mobilities derived from self-diffusio 122 GENERAL DISCUSSION coefficients obey a modified form of the Debye-Huckel-Onsager equation over the whole concentration range i.e., zc’ = (N/F)(l - K*dY)(A - VR), where A” is the limitingionic conductance in water a* is the Onsager coefficient for the time of relaxation effect I the ionic strength and ( A - VR) is a term taking into account the viscous resistance of the membrane phase.In any one membrane containing two mobile ionic species the mobility ratio will be given by and since K* dj and ( A - VR) are the same for both ions, Dr. F. Helfferich (Giittingen) said I believe that the deviations between experiment and theory found by Bergsma and Staverman can be explained quali-tatively if the following points are considered. (i) Because of the low flow rate the bi-ionic systems are likely to be partially film-controlled. If this is the case the Donnan potentials are lower than the theoretical values and the transference number ratio calculated from the BIP is too unfavourable for the ion preferred by the membrane.In all systems except for NaCl + KCl the deviations found by the authors show this tendency; as may be expected it is most pronounced in the system involving H+ and the weakly basic Amberlite IRC-50 membrane. The more dilute the solution of the ion not preferred by the membrane the more serious should be the deviation. (ii) The activity coefficient ratio ys/yI in the bi-ionic systems (eqn. (5)) is not identical with that in the transference systems (eqn. (6)). The latter involves the coefficients in equilibrium with the mixed solution used whereas in the former ys is in equilibrium with a pure solution of S and yr in equilibrium with a pure solution of I. If the ion exchange equilibrium constant depends on mole fraction, differences between the two ratios are to be expected.Furthermore in this case the full equation for the BIP contains correction terms for the variation of the yr through the membrane. (iii) The theory of the BIP assumes that co-ions (i.e. ions of the same sign as the fixed charges) are virtually excluded from the membrane phase. This is a good approximation for membranes with high concentration of fixed charges in contact with dilute solutions but it is not likely to hold for the low capacity membranes A-58 and A-71 (0.27 and 0-42 mequiv./g dry weight respectively) in the concentration range studied. This might explain the abnormally small slopes in the BIP curves found with these membranes. The higher the con-centrations used and the larger the absolute value of the diffusion potential within the membrane the more serious should be the deviation.A quantitative com-parison is of course not possible because the necessary data are lacking. It will be interesting to see the results of the investigation announced by the authors on the significance of water transfer. Dr. J. E. Salmon (Battersea Polytechnic London) said I note that in many papers both “ homogeneous ” and heterogeneous membranes are employed. It appears to be assumed that the theoretical treatment to be applied for the two cases should be identical but to what extent this is justified seems doubtful to me. With the so-called homogeneous membranes it is probably correct to assume that a Donnan effect will occur only at the two membrane-liquid sur-faces. With heterogeneous membranes however the structure consists essenti-ally of a series of resin beads located in a series of interconnected cavities in the hydrophobic matrix of the “filler”.Whilst the resin beads are effectively close packed they will be surrounded by and separated by a film of electrolyte throug GENERAL DISCUSSION 123 which electrical conduction from bead to bead must occur. Hence with the heterogeneous membranes a series of Donnan equilibria must be set up between each bead and its surrounding film of electrolyte and these must be affected by changes in (i) concentrations of the solutes in the electrolyte across the membrane (i.e. the concentration profile) (ii) in properties of the solvent (i.e. in degree of association and in dielectric constant) within the membrane (iii) polarization of solvent and solute molecules near the functional groups of the resin.Dr. R. J. P. Williams (Oxford University) said Many of the authors describing the study of bi-ionic potentials do not refer to the way in which their membranes are prepared. It is not clear that membranes will come into equilibrium with solutions rapidly for example see papers by Scatchard and Helfferich and by Hutchings and Williams. In experiments with bi-ionic cells and with the " ab-normal " cells of Scatchard and Helfferich we have shown that a steady potential may not be obtained for hours or even days. Such slow equilibria will be most important for ions which are strongly retained at the surface of the membrane. Systems of importance are bi-ionic cells in which one of the ions is a simple uni-valent ion such as sodium which equilibrates rapidly between the membrane and the solution and the other is a divalent ion such as barium.Perhaps the silver cation equilibrates slowly with the membrane and some of the observations of Bergsma and Staverman may be due to non-steady state conditions ? We feel that it would be advantageous if authors gave details of the preparation of the membranes and of the changes of properties with time. Dr. G. J. Hills (Imperid College) said With respect to the paper of Mackie and Meares I would like to emphasize that transport processes through a mem-brane are dependent upon at least three variables the swelling or pore size of the membrane the composition of solution in the membrane and the temperature. None of these can normally be varied independently and in studying for example, rates of permeation as a function of temperature the simultaneous variation of the other parameters must be taken into account.I would therefore like to ask these authors if their energies of activation are not in fact more complex quantities than they state ? Prof. Karl Sollner (Bethesda Maryland U.S.A.) said When I proposed the term bi-ionic potential (B.I.P.) several years ago this term was intended to denote the dynamic membrane potential which arises across membranes of extreme ionic selectivity separating the solutions of two electrolytes at the same concentration having different permeable ions which exchange across the membrane and the same nonpermeable ion.1 As the etymology of the word bi-ionic indicates this term is meant to refer to situations in which two and only two species of ions are of essential significance.This situation does not prevail if diffusion layers play a significant role.2 In this case one is really dealing with three-ionic systems with three effective transition zones in series as shown so ably by Dr. Helfferich. Under these conditions one of the basic assumptions concerning the nature of B.I.P. systems as originally defined is not fulfilled namely identity of the con-centrations in the two bulk solutions with the concentrations of the two liquid layers in contact with the membrane.2 Since it is of some importance to have the clear and well-defined original mean-ing associated with the term bi-ionic potential particularly in the discussion of polyionic potentials across membranes of extreme ionic selectivity and the exchange kinetics of such systems I should like to suggest that this term be used only in its original meaning.The B.I.P. so defined is for a given membrane and a given pair of critical (permeable) ions a characteristic constant which over a fairly wide range is independent of the concentration of the solutions used and of the nature of the nonpermeable ions. 1 Sollner J. Physic. Chem. 1949 53 121 1 1226. 2 Dray Ph.D. Thesis (University of Minnesota Minneapolis 1954). Dray and Sollner Biochim. Biophys. Acta 1955 18 341 1 24 GENERAL DISCUSSION Dr. A. M. Peers (Low Temperature Research Station Cambridge) (communi-cated) In order to calculate a bi-ionic potential by the method of Dr.Helfferich, one must first calculate 6 the diffusion-layer thickness from membrane potential measurements. An independent and more direct estimate of 6 may be obtained by observing the limiting current-density at the membrane. The simple theory which has been applied for example in polarographic studies is also applicable to a membrane + solution system for which one can accept the simplifying assumptions (i) and (ii) in Q 3 of Dr. Helfferich’s paper (i.e. negligible transport of water and neben-ions). For a cation-permeable membrane and a solution of a single uni-univalent salt at concentration c the total current-density i may be written i = t+i + id, where t+ is the cation transport number in the bulk solution and id is the “ diffusion current ” through the stationary layer.For the limiting-current case id = FDc/6, where D is the diffusion coefficient of the salt and the first equation yields i = ilim = FDc/t-8 where t- = (1 - t+). The following figure shows a current-voltage curve obtained with a Permutit, C-10 cation-exchange membrane bathed on both sides with (flowing) 0.01 N NaCl solutions. The-potential measurements were made with a high-impedance 0 I 2 3 4 5 A V = ( V i - l R i = o ) volts FIG. 1 valve voltmeter connected to a pair of AgCl “ probe ” electrodes situated on opposite sides of the membrane. The experimental arrangement was such that the concentration of the bulk solution was virtually independent of time and current density. (The current in excess of ilim was found to be carried partly by hydrogen ions but mostly by chloride.) A further remark concerning the transport number measurements of Bergsma and Staverman when using direct current to measure the combined transport numbers of two or more ions of the same sign the effect of the diffusion layer is to diminish preferentially the “ interfacial concentration ” of the ion whose transport number changes by the greater amount on passing from solution t GENERAL DISCUSSION 125 membrane.To obtain the ratio which would be observed in a membrane in equilibrium with the bulk solution the transport-number ratio may be plotted against current-density and the curve extrapolated to zero current. These con-siderations are consistent with the better agreement between “ experimental ’’ and “ calculated ” ratios obtained by Neihof and Sollner (whose measured flux-ratios are equivalent to those given by the zero-current intercept) and with the manner in which the “experimental” ratios of Bergsma and Staverman differ from those calculated from potential measurements.The above arguments are illustrated by the figures in the final column of the following table. flux ratio 100 (expt.-calc.) work of N. & S . expt. calc. calc. K+ - Naf 2.6 2.5 + 4 % H+ - Na+ 24.0 22.0 + 9 % transport no. ratio expt. calc. work of B. & S . K+ - Na+ 1.6 1.7 - 6 % H+ - Na+ 4-4 7.1 - 38 % Dr. F. Bergsma and Dr. A. J. Staverman (DelJt) (communicated) In reply to Dr. Helfferich we think it will be worth while to calculate the B.I.P. for the general case of combination of membrane diffusion and film diffusion combining the cal-culations of Helfferich with the technique of Wyllie and using the general formula for the B.I.P.(different concentrations on both sides of the membrane). We agree with his first remark. It is possible that closer agreement may be obtained if more attention was paid to changes in activity in the membrane. If leakage of the Cellophane membrane was the reason for the small slopes in the B.I.P. curves we should have found that the slope depended on the con-centration. This was not the case ; up to about 0.1 N we found a nearly constant slope. As the Cellophane-type membranes have a greater permeability I believe that film diffusion is responsible for the deviation In reply to Dr. Tye we used the arrangement sketched in our fig.1 to avoid the difficulties with reversible electrodes. It is possible especially if one of the cations is hydrogen that there is some leakage of these ions through the anion solution membranes. This should give too low a transport number for the hydrogen ion. We think it will be useful to investigate this effect. We can apply in cells 2 and 5 a suspension of an anion-exchange resin in distilled water by analogy with the experiments by Kressman and Tye. In reply to Dr. Peers in our transport number measurements we used a very low current-density (about 0.5 mA/sq. cm) and circulating solutions. Therefore we expect that the concentration ratio of the two cations in the diffusion layer did not differ very much from that in the bulk solution.Nevertheless it will be worth while to perform a series of transport measurements with varying current density extrapolating to zero current. In reply to Dr. Salmon for a heterogeneous membrane with a hydrophobe, non-conducting matrix exchange between the two solutions is possible only through ion-exchange beads in contact with each other (path 2 of the left-hand diagram of fig. 2 of the paper by Spiegler et d). In a bead of an ion-exchanger the pore-diameter is about lOA. If the distance between the two contact areas is of the same order of magnitude the membrane behaves as a homogeneous one. Dr. F. Hemerich (Giittingen) (communicated) It will prove very useful to have an independent method as that of Dr. Peers to measure the film thickness.Certainly the neglect of water transfer through the membrane is more serious with high current densities than in bi-ionic systems but since the film concept is an idealization anyhow the error introduced thereby will not affect the value of his method 126 GENERAL DISCUSSION Dr. P. Meares (Aberdeen University) (communicated) The studies of Manecke and Heller and of Mackie and Meares on the sorption of non-electrolytes by the sodium form of a phenol sulphonic acid + formaldehyde resin both indicate a partition of the non-electrolyte between an adsorbed layer on the resin matrix and free solution in the internal liquid. The authors appear to have reached slightly different conclusions regarding the equilibrium between the internal and external solutions. Closer examination of the data has resolved this matter satisfactorily.l o g c FIG. 1 .-Plot of Freundlich equation. la ethanol a r= 1.0 ; 16 ethanol a = 0.8 ; 2a acetone a = 1.0; 2b acetone a = 0.7. Using the nomenclature of Manecke and Heller the quantity a = C/c is equivalent to the salting-out coefficient between the internal solution which con-tains the counter-ions of the resin and the external solution containing no salt. a should therefore be almost independent of c over a reasonable concentration range but will vary with the non-electrolyte and with the concentration of counter-ions. The equilibrium between the internal solution and the adsorbed layer may be expected to follow a Freundlich type isotherm where x is the amount adsorbed and k and n are constants.The amount adsorbed by the matrix associated with 1 ml of imbibed solution is (Ctot - C) which can be written (Ctot - ac). If the degree of swelling is independent of c a condition which is justified experimentally for the concentration range studied the isotherm may be written Thus log (Ctot - ac) plotted against log c should be linear. The graph show-these plots for ethanol on Zeo-Karb 315 for a = 1.0 and a = 0.8 and for acetone on the resin of Manecke and Heller for a = 1-0 and a = 0.7. In each case the linear relation is not found for a = 1.0 but is obeyed for cc less than 1.0. The uncertainties attending the use of the Freundlich isotherm prevent this method being used for a more precise determination of a. None of the conclusions of Manecke and Heller is in any way affected by the foregoing considerations.x = kC1/", (Ctot - XC) = k'c'l"' GENERAL DISCUSSION 127 Dr. G. Manecke (Berlin) (communicated) We agree with Meares that a for acetone might have values less than 1.0. We had made that simplifying assumption as the value of cc has no bearing on our results. As it is not possible to determine the exact value for a it might be more convenient to transfer a to the left-hand side of our eqn. (8) so that it reads : P = Diak = (tan B) 2.303 1211212. 4 V l + 7J2) ’ with P defined in this way it is unnecessary to know the values of a in order to evaluate P. Our numerical values of P and our ultimate conclusions are not affected by this alteration. P has here the conventional definition for permeability of membranes it is the amount of substance transported in 1 sec through 1 cm* of surface of membrane 1 cm thick when the difference between the concentration of the solutions on the two sides of the membrane is 1 unit Dr.N. Krishnaswamy (India) (communicated) Studying two different mem-branes with three bound cations it has been shown that in the presence of acetone the sodium form of the membrane permits diffusion of the electrolyte to the same extent as in a solution without acetone. But the calcium and magnesium forms of the membrane are found to permit lower diffusion of the electrolyte in presence of acetone. From Manecke and Heller’s results in tables 1 and 2 it is shown that the swelling property of the sodium form of the membrane is governed by the external solution concentration while for the magnesium and calcium membranes change in the external concentration has little effect on their swelling property.Dr. Manecke and Dr. Heller have stated that the swelling behaviour of Na Mg and Ca membranes was determined at different acetone concentration of the external solution and the swelling capacity of the membrane remained constant. Does this mean that the swelling characteristics of the three forms of membranes depended on the external acetone concentration as with external electrolyte solution ? From fig. 5 in that paper it is shown that there is lower diffusion of electrolyte through the magnesium and calcium forms of the membrane and from the ob-served presence of more absorbed acetone in these membranes it is postulated that complex formation between magnesium and calcium ions with acetone may be responsible for the above findings.If complex formation is possible in the external solution phase also then the rate of diffusion of the electrolyte would be decreased through the membrane by the larger size of the complex ion. Hence besides the possible interaction between acetone and Mg2+ or Ca2f in the mem-brane as stated by these authors the interaction in the external solution also may be responsible for the lower diffusion. Dr. G. Manecke (Berlin) said In answer to Dr. N. Krishnaswamy the Na- Mg- and Ca membranes have a definite swelling capacity when they are in equilibrium with solutions of electrolytes. The addition of acetone did not alter that swelling capacity as we have stated within the experimental errors.The interaction in the external solution between acetone and Mg2+ and Ca2t-ions may also certainly be responsible for the lowering of the diffusion of those ions. As we have mentioned in our paper Herz and Knaebel observed an effect of MgCl2 and CaC12 on the capillary activity of acetone solutions. Prof. Karl SoIlner (Berlzesda Maryland U.S.A.) said The barrier function and separation action of ion exchange membranes can of course be studied and utilized in many situations other than the separation of electrolytes and non-electrolytes as described so clearly by Dr. Manecke and Dr. Heller. Just to mention a few situations involving permselective membranes,l electro-lytes and non-electrolytes may be separated by the simultaneous use of both cation-permeable and anion-permeable membranes of extreme ionic selectivity in exchange dialysis against the solution of an acid and a base respectively or in 1 Sollner J.Electrochem. Soc. 1950 97 139c; Ann. N. Y. Acad. Sci. 1953 57 177 128 GENERAL DISCUSSION an electrically short-circuited two-membrane three-compartment system or with greatly accelerated speed by electrodialysis in a three-cell outfit. The efficiency of this procedure particularly if carried out with dense non-swelling membranes, seems to be beyond doubt. Ions of the same charge may be separated selectively by the exchange of ions (or by electric transferences) across membranes of ion exchange character and high ionic selectivity,l the separation factors being calculable from the bi-ionic potentials across the same membrane arising with the ions under consideration, as is evident from the paper by Dr.Neihof and myself.2 Another interesting case the elaboration of a suggestion by Manegold,3 may be mentioned suppose we have a solution of an electrolyte A+B- and a non-electrolyte C a membrane of extreme ionic selectivity permeable to the A+ ions as well as to the non-electrolyte C and a second solution containing radioactively labelled A+*B-* at the same concentration as solution 1 . An exchange A+ + A+* will occur and C will diffuse from solution 1 to solution 2 while the membrane represents a definite barrier for any exchange of B- for B-*. If we were now to take a membrane composed of two superimposed layers one layer of extreme cationic selectivity permeable to A+ and A+* and to the C molecules and one layer of extreme anionic selectivity permeable to B- and B-* and to the non-electrolyte C.It is evident that the non-electrolyte can diffuse readily across such a layered membrane while it is an absolute barrier (like a wall of glass) to the penetration across its thickness of the ionic constituents of the two solutions. These and similar possibilities still await detailed experimental exploration. Prof. F. Runge and Dr. F. Wolf (Halle Saale Germany) said Dr. Manecke studied in his systems non-electrolytes such as acetone formaldehyde etc. In a similar manner we studied the behaviour of different phenols with the intention of separating the phenols from waste waters by means of ion-exchange resin mem-branes.On one side of the membrane was situated the phenolic aqueous solution, on the other a solvent such as methanol benzene or others. Qualitatively expressed the results were as follows. The different phenols diffuse and easily pass through the ion exchange membrane but after some hours the diffusion stops It is supposed that irreversible adsorption processes of the phenols in the resin phase together with possible shrinkage effects in the upper membrane surface layers on the side of the organic solvent are the reasons for this behaviour. The different steps of the diffusion processes were investigated. Dr. R. Schlogl (Gottingen) said In the paper by Mackie and Meares,4 (T was called “ the rate of osmotic or hydrostatic flow ”. As is implied in De Groot’s treatment of “ continuous systems ” (T must be the velocity of the centre of gravity of all components which make up the pore fluid.I agree entirely with the expres-sion “ rate of hydrostatic flow ” also with the expression “ rate of osmotic flow ” provided however that water is the dominant component of the pore fluid. I: I have understood correctly only dilute ethanol + water mixtures were used SO that this distinction will be of no consequence. However it seems to me incorrect to take values for (T measured for an arbitrary electrolyte and apply them to systems with other electrolytes or with non-electrolytes. As I have shown in my paper on anomalous osmosis,6 the factors responsible for the osmotic water transport are with electrolyte solutions not so much the osmotic difference between the two outer solutions as the pressure gradient and electrical field within the membrane.(+ can actually assume different signs with different electrolytes (negative and positive osmosis). Since for hydrochloric acid which was used in 1 Sollner J. Electrochem. SOC. 1950 97 139c ; Ann. N. Y. Acad. Sci. 1953 57 177. 2 Neihof and Sollner this Discussion, 3 Manegold Kapillar Systems vol. 1 (Strassenban Chemie and Technilc Verlags-4 Proc. Roy. SOC. A 1955,232,498. 5 Thermodynamics of Irreversible Processes (Amsterdam 1951) p. 119. 6 Z. physik. Chem. 1955 3 73. gesellschaft Heidelberg 1955) p. 637 GENERAL DISCUSSION 129 Meares' measurements the diffusion potentials arising are probably considerable, I believe that u will be appreciably larger in this system than in the ethanol + water system.A potential difference of 1 mV corresponds to approximately a pressure difference of 1 atm at room temperature. Dr. P. Meares (Aberdeen University) said In reply to Dr. Schlogl the quantity G is defined in the paper cited 1 as " the rate of osmotic or hydrostatic flow of the internal aqueous solution " ; the word solvent occurred in the defintion of (T in the pre-print of the present paper through an oversight. The rate of flow of solution was measured experimentally and was used in calculating the fluxes. I agree that the calculation of the small mass flow correction term ca has been greatly simplified and that there is a possibility of anomalous osmosis affecting results obtained with hydrochloric acid.Subsequent experiments 2 using only water and a hydrostatic pressure gradient gave the same flow rate per atmosphere, within 15 % as that calculated from the osmotic pressure of the hydrochloric acid solutions so that anomalous osmosis does not appear to have made an important contribution in the present case. I agree with Prof. Ubbelohde that it is difficult to distinguish between the interpretation suggested and the alternative possibility of a low diffusion coefficient for ethanol in the membrane. If this were to arise as suggested by Prof. Ubbelohde, from a reorientation of the hydrogen bonds in water and ethanol inside the mem-brane some effect on the energy of activation for diffusion and a heat of sorption would be expected but were not observed.Ideally one should measure the mobility of individual ethanol molecules in the internal solution to decide this question but no method has been devised for doing this. In reply to Dr. Hills the factors affecting the value of the overall activation energy for permeation Ep calculated for constant external concentrations are (i) the change in the surface concentrations within the membrane with temperature ; (iia) the change in membrane thickness due to increase of swelling with increase of temperature ; (iib) the change of diffusion path length due to increase of swelling ; (iii) the change of diffusion coefficient of ethanol in the internal solution with temperature. The sorption experiments show (i) to be negligible. Effects (iia) and (iib) tend to cancel one another ; allowance can be made for them using the membrane swelling data already published.3 This increases the value of E' by 0.033 kcal/mole.It may safely be concluded that the values of Ep represent within experimental error of & 0-2 kcal/mole the activation energies for diffusion of ethanol in the imbibed solution. Dr. E. Glueckauf (Harwell) said I wish to describe a new separation tech-nique based on the ion exclusion by semi-permeable membranes developed by G. P. Kitt and myself. Ionic transport in membranes is obviously dependent not only on the diffusivity but also on the concentration in which the ions are present in the membrane. If we have in the solution a univalent anion then the uptake of univalent cations is not dependent on concentration while that of poly-valent cations is.A simple mass law calculation shows that the distribution factor between uni- and divalent ions for a solution and an anion exchange resin, e.g. is given roughly by /?lilt ni;+ C capacity of resin m~2+ in;+ - m---N-=-ionic conc. in solution ' 1 Mackie and Meares Proc. Roy. SOC. A 1955 232,498. 2 Mackay unpublished work. 3 Mackie and Meares Proc. Roy. SOC. A 1955 232 510. 130 GENERAL DISCUSSION This is a considerable separation factor. Normally we cannot utilize this effect, because most of the ionic transport is done by the anions. But if we stop the anion transport by facing the anion exchange membrane with a cation exchange + -rll FIG. 1. membrane and apply a voltage then roughly half the current is carried by cations and then this separation effect comes into play.Fig. 1 shows schematically an arrangement. The electrolyte mixture to be separated is placed in the anode compartment the cathode side con-taining pure acid. Fig. 2 shows the transport across the membrane as function of time for an equimolar solution of K+ Ca2+ and Fe3+ nitrates of total concentration 0.12 N and the great preference for the transport of the univalent ion. When using ions of equal charge, the ion exclusion is dependent on the ratio of the activity coefficients and the effect is not as large as for differently charged cations. But it is still notice-able (fig. 3). The mechanism operating at moderately high current densities even in neutral solutions is far from simple.There are at least two distinct stages noticeable from the current-voltage curves. At very low voltages and current densities particularly in solutions above 0.3 N the ions of the electrolyte carry T i m e m l n u t e s FIG. 2. the current. At higher voltages across the membranes much current is trans-ported by H+ and OH- ions produced by dissociation of the water at the interface of the two membranes. A quantitative assessment of the process taking place has so far not been achieved. Mr. D. Reichenberg (C.R.L. Teddington) said I would like to refer to som GENERAL DISCUSSION 131 experimental work 1 on the sorption of organic compounds from aqueous solution by cation exchange resins. This sorption is molecular sorption not ion exchange, since the compounds studies were acetic propionic and n-butyric acids and ethyl, n-propyl and n-butyl alcohols.With the acids it was only possible to study their sorption by the resins (sulphonated polystyrenes of various degrees of cross-linking) in the H+ form; with the alcohols sorption by both the H+ and Na+ forms was studied. The degree of sorption has been found to be independent of the particle size of the resin showing that the phenomenon is one of true absorption and that T i m e . m i n u t e r FIG. 3. surface adsorption plays no appreciable part. The results may conveniently be expressed in terms of the molality of solute inside the resin phase divided by the molality in the outside solution. This quantity which we call the “ molality ratio ” is presumably equivalent to Dr.Manecke’s a’ and Dr. Meares’ C/c though both these authors speak of “ moles per litre of internal solution ” instead of the unambiguous “ moles per kilogram of sorbed water ” which we have used. The results .show that : (i) The molality ratio is not a constant for a given solute and a given resin in a given ionic form. In general it varies with the solute concentration. In most cases the molality ratio decreases with increasing solute concentration, in a few cases it is almost constant and with n-butyl alcohol in both the H+ and Naf forms of the resins it increases with increasing concentration. (ii) For a given solute at a given concentration and with the resin in a given ionic form (either Hf or Naf) the molality ratio has always been found to de-crease with increase of cross-linking over the range 5* to 15 % DVB.However, there are good grounds 1 for believing that at lower degrees of cross-linking some of the solutes at least must show an initial increase of molality ratio with increase of cross-linking. (iii) For a given resin in a given ionic form (either H+ or Na+) and a given concentration the molality ratio increases with the chain length of the solute molecule. Thus the molality ratio increases in the orders (a) acids; acetic < propionic < n-butyric; (b) alcohols ; ethyl < n-propyl < n-butyl. 1 Reichenberg and Wall submitted for publication J. Chem. Soc 132 GENERAL DISCUSSION (iv) For a given solute at a given concentration and a given degree of cross-linking the H+ form of a resin always absorbs much more of an alcohol than did the Na+ form.(About twice as much for the 5-4; % DVB and n-butyl alcohol.) Observation (iii) shows the contribution of London dispersion interactions between the hydrocarbon part of the organic solute and the benzene nuclei of the resin; (ii) shows a " salting-out " effect of the resin in both the H+ and Na+ forms; (iv) shows however that superimposed on this there is a " salting-in " effect of the polar groups when in the H+ form. This last effect is shown very strikingly by the increase in the miscibility of n-butyl alcohol and water brought about by HCl. Aqueous solutions of HC1 of molality 4.6 and higher are miscible in all proportions with n-butyl alcohol at 25" C. Both NaCl and LiCl cause a salting-out of n-butyl alcohol from water.However the miscibility of n-butyl alcohol with HCl solutions increases hardly at all until the HCl molality exceeds 1, when it increases very sharply. This may be of significance in connection with Dr. Meares' observation that there was no marked difference between the sorption of ethyl alcohol by the H+ and Na+ forms of his resin. His resin had a fixed charge concentration of about 0.5 molal whereas even our 5% % DVB resin had a fixed charge concentration of 3-6 molal in the H+ form. Making use of the effect of chain length on the degree of absorption I have separated 4.4 mg equiv. acetic acid and 2-7 mg equiv. n-butyric acid from a mixture of the two. The mixture was simply loaded on to the top of a column (85 cm X 0.79 cm2) of resin (53 % DVB sulphonated cross-linked polystyrene in Hf form-total capacity of column 100 mg equiv.) and eluted with water.The separation was nearly quantitative though I have not yet succeeded in getting a gap of pure water between the acetic acid band (which comes off the column first) and the n-butyric acid band. (The minimum total acid concentration between the two fronts was 0.01-0.02 N while the acetic acid peak was 0.8 N and the n-butyric acid peak 0-3 N). Prof. Karl Sollner (Bethesda Maryland U.S.A.) said I should like to make some remarks to the paper by Dr. Neihof and myself. First our theoretical predictions can be attained readily on a more general basis without reference to some of the specific assumptions made in our paper. The basic concept of transfer-ence numbers as pointed out some time ago is adequate for the handling of many problems related to bi-ionic potentials.19 2 Secondly our experiments may also be considered as the quantitative demon-stration of a selective separation process for ions of the same charge coexisting in solution somewhat similar to the separation of electrolytes and non-electrolytes described in the interesting paper by Dr.Manecke and Dr. Heller. The separation of various ions of the same charge can of course also be carried out by electro-dialysis.3 Thirdly the greatly different 4' ratios observed suggest the question of whether systems of the general type discussed in our paper show some interesting peculiarities in the kinetics of the exchange of ions while they drift towards equilibrium.4.5 1 Sollner J. Physic. Chem. 1949 53 121 1 1226. 2 Sollner Dray Grim and Neihof Ion Transport across Membranes ed. Clarke and Nachmansohn (Academic Press Inc. New York 1954) p. 144 ; Electrochemistry in Biology and Medicine ed. Shedlovsky (John Wiley and Sons Inc. New York, Chapman and Hall Ltd. London 1955) p. 65 ; Dray Ph.D. Thesis (University of Minnesota Minneapolis Minn. 1954) ; Dray and Sollner Biochim. Biophys. Acta., in press. 3 Sollner J. Electrochem. SOC. 1950 97 139c; Ann. N.Y. Acad. Sci. 1953 57 177. 4 Sollner and Neihof Arch. Biochem. Biophys. in press. 5 Neihof and Sollner J. Physic. Chem. (Colloid Symposium Issue 1956) in press GENERAL DISCUSSION 133 Consider a system with an exclusively cation-permeable membrane I +@-+ I, solution 1 solution 2 BfX- 0.01N +@+ C+X- 0*15N, A+X- 0.01 N C+X- 0.01 N where A+ Bf and C+ represent the exchangeable (permeable) ions and X- the non-exchangeable anions.Suppose the species of ions A+ in solution 1 (which is of infinite volume) exchanges across the membrane at a rate which is exceedingly high compared with the rates of exchange of Bf against C+ or A+. Apartial membrane equilibrium with respect to A+ and Cf ions will be virtually reached before a significant quantity of Bf ions have penetrated across the membrane.1 While this state of partid equilibrium prevails (in which the Bf ions do not participate) the concentration of both A+ and Cf ions in solution 2 will be 0.075 N according to the Donnan equation. During a further prolonged period the B+ ions will exchange across the membrane until our system reaches the state of the true final membrane equilibrium in which according to Donnan’s equation A+ Bf and C+ will be present in solution 2 at the same concentration 0.05 N.In other words the A+ ions reach temporarily in solution 2 a concentration in excess of that existing in the final true equilibrium state. Under suitable conditions the converse effect will arise-namely a transitory depletion of the concentration of some ionic species in solution 2. Overshooting the depletion effects of 50-85 % of those calculated for the partial equilibrium were observed.2 The overshooting of the equilibrium con-centration reached in some systems several hundred per cent as is evident from the graphs shown on the screen (which are in press elsewhere).2 Whether the overshooting and depletion effects play a significant role in the selective accumula-tion of ions by living cells is an entirely open question.However we feel that these effects should not be overlooked as possible factors. Fourthly the problem of the kinetics of the exchange of ions across membranes of extreme ionic selectivity in the genera1 case in which several species of exchanging ions exist in the two solutions in any arbitrary combination of concentrations can as it seems be attacked successfully along the same line of approach that we have taken in our paper for a very simple case. The kinetic interpretation of the equations for the polyionic potentials arising in such systems 3 seemingly provides the solution of this problem (on which a report will be presented at a later date).Dr. F. Helfferich and Dr. R. Schlogl (Gottingen) said In the derivation of the bi-ionic potential Neihof and Sollner have made the assumption that “ the two species of critical ions are present within the membrane in the same ratio as if the membranes were equilibrated with a solution prepared by mixing equal volumes of the two solutions of the bi-ionic system ”. It has been shown in this discussion that the application of the flux equations leads to a different picture and there is experimental evidence contrary to the above-mentioned assumption. But we wish to emphasize that our criticism of this assumption is not directed against the conclusions drawn by the authors.Both the quasi-thermodynamic treatment and 1 1 1 Donnan Chem. Rev. 1924 1 73. 2 Neihof and SoIlner J. Physic. Chem. (Colloid Symposium Issue 1956) in press. 3 Sollner Dray Grim and Neihof Ion Transport across Membranes ed. Clarke and Nachmansohn (Academic Press Inc. New York 1954) p. 144 ; Electrochemistry in Biology and Medieine ed. Shedlovsky (John Wiley and Sons Inc. New York, Chapman and Hall Ltd. London 1955) p. 62 ; Dray Ph.D. Thesis (University of Minnesota Minneapolis Minn. 1954) ; Dray and Sollner Biochem. Biophys. Acta., in press 134 GENERAL DISCUSSION the flux equation treatment lead without using the assumption in question to an equation for the B.T.P. which is identical with that of the authors except for correction terms. Also the relation given by the authors between the ratio of exchange fluxes #A/#B in system I and the B.I.P.in system I1 may be obtained from the flux equations assuming only constant mobilities constant activity coefficients and ideal permselectivity. The sum of the concentrations of the counterions A B and L in the membrane is equal to the concentration of fixed charges (concentration of co-ions is neglected) : ICi C A + C B + C L = C = const. (1) Z#i +A + +B + #L = 0. (2) The sum of the ionic fluxes is zero (no net transfer of charge) : The Nernst-Planck flux equations are Forming the sum of all fluxes and using (l), (4) In the steady state the left side of (4) is independent of the space co-ordinate x within the membrane. Hence due to C = const. the electric potential gradient is constant ‘ d’ - k = const.RTdx = Substituting (5) in (3) we obtain a linear differential equation for Ci which is readily integrated. By use of the boundary conditions c A = c;; c B = c;; c L = cL=o, at the left membrane surface; CA = c” = 0; c = c; = 0; CL = c” =z- c, at the right membrane surface ; the following solutions are found : c - A [ e x p (k(8 - x)) - 11, c -(6 = membrane thickness), A - kDA [exp {k(8 - x)) - 11 CL =- -[exp #L (- kx) - 11. - kDB kDL Inserting the boundary conditions for x = 0 and x = 6 respectively we obtain the following equations for the fluxes y$ : The exchange flux ratio 2 DACL’DBCi (7) obtained from (6) is identical with eqn. (4) in the paper of Neihof and Sollner (taking their eqn. (1) as a definition of the quantity T~C/T:+).Moreover the equation for the tri-ionic potential in system I is readily obtained from the above calculation. It is identical with that given previously by Wyllie GENERAL DISCUSSION 135 The diffusion potential within the membrane is obtained from (5) when the $i values in (2) are substituted according to (6) and the resulting equation is solved with respect to k6 : Assuming equilibrium at the interfaces membrane/solutions the Donnan potentials are given by The total membrane potential E is This calculation of the exchange flux ratio and of the membrane potential is easily extended to an arbitrary number of univalent counterions ccl cc2 . . . a on the left side and PI P2 . . . Pn on the right-side of the membrane : However this simple approach is not applicable to counter-ions of differing valence, since in this case d$/dx is no longer constant.For the same reason the Henderson formula cannot be used in such systems. Probably the most serious simplification in the above calculation is that the activity coefficients for every ionic species are assumed to be constant throughout the membrane i.e. independent of the mole fractions. This assumption cannot be accepted without some reservations for ion exchangers of pronounced selectivity which in this connection are of special interest. Perhaps the deviations found by the authors in the quantitative comparison of experimental and calculated fluxes can be explained in this way. Dr. R. Neihof (Uppsalu University) said I would like to point out that the use of collodion matrix membranes 1 9 2 in the experiments reported by us has made it possible to avoid certain difficulties which might otherwise have been en-countered with some of the more conventional ion-exchange resin membranes.They have relatively low water contents probably because of the swelling con-straint exerted by the matrix. The concentration of fixed dissociable groups in the membranes is high ; consequently their ionic selectivity is sufficiently great that the leak of non-critical ions can be neglected up to fairly high con-centrations of electrolytes. The ionic conductance of the membranes can be adjusted for the particular experimental conditions at hand so that with only moderate rates of stirring of the surrounding solutions diffusion processes occurring in the system are entirely membrane controlled.Due to the thinness of the membranes the unit-area ion-exchange capacity is small ; this is advantageous where it is important to have low capacities relative to the number of equivalents of ionic constituents in the surrounding solutions. 1 Neihof J. Physic. Chem. 1954 58 916. 2 Gottlieb Neihof and Sollner J. Physic. Chem. 1956 (in press) 136 GENERAL DISCUSSION Dr. R. D. Keynes (Cambridge University) said It is of considerable interest to biologists that Dr. Neihof and Dr. Sollner have succeeded in producing an artificial membrane capable of distinguishing to some extent between the various alkali metal ions. I think I should point out however the degree to which their membranes differ in selectivity both quantitatively and qualitatively from at any rate some cell membranes.The relative passive permeability of resting nerve and muscle membranes to group IA ions may be represented very approximately as Li = Na < K = Rb > Cs ; the difference between Na and K may be as much as 100 times while the membranes seem to be somewhat more permeable to Rb than to K in some cases and slightly less permeable in others. Quite apart from the fact that the selectivity towards Na and K can be suddenly reversed it would seem difficult to explain this complicated sequence by any process as straight-forward as a simple exaggeration of the differences in ionic mobility in free solu-tion arising from the greater hydration of the ions with smaller atomic weights.Prof. Teorell has quoted the relationship first derived by Behn and later by himself and Ussing between the ratio of labelled ion fluxes crossing a membrane in the two directions and the difference in electrochemical potential between the solutions on either side. This may be written as where E is the difference in electrochemical potential between the two solutions for the particular ion whose fluxes $12 and 421 are being measured. The basic assumption on which the derivation depends is that the ions cross the membrane independently ; with a constant potential difference the chances of an individual ion crossing the membrane in a given time interval are not affected by the other ions that are present. It has been shown for the passage of ions across some biological membranes (e.g.iodide and chloride in frog skin 192) that this equation is rather well obeyed but when Hodgkin and I used 42K to examine the passive movements of K+ ions between the inside and outside of Sepia axons,3 we found that the measured flux ratios were appreciably larger than the predicted ones, and that our results were fitted better by h 2 - nEF - exp-, $21 RT where n was about 2.5. We interpreted this deviation from the independence relationship as arising from an interaction between ions moving in one direction and those moving in the other possibly because the ions cross the membrane in single file through very narrow tubes or channels or pass over a bridge or chain of negatively charged sites. I wish to ask whether it has been verified that the movements of ions across artificial membranes of the types being discussed here are independent in the sense required for Behn’s relationship to hold.If any deviation from the predicted flux ratios were found it might throw an interesting light on the structure of these membranes and on the way in which ions move across them. Dr. R. Neihof (Bethesda) said in reply to Dr. Keynes’ remarks it is certainly true that the artificial membranes available now do not have the degree of selectivity for the alkali metal ions which is exhibited by certain biological membranes. The anion selective collodion matrix membranes on the other hand do show a high selectivity for certain anions. The selectivity of these membranes is due to chemical or adsorptive specificity and not to steric restriction of the ions having the larger hydrated size.Improved selectivities for particular alkali metal ions 1 Ussing Acta Physiol. Scand. 1949 19 43. 2 Koefoed Johnsen Levi and Ussing Acta Physiol. Scand. 1952 25 150. 3 Hodgkin and Keynes J. Physiol. 1955 128 61 GENERAL DISCUSSION 137 can be expected when materials having the necessary high chemical specificities become available. Such materials could or course be incorporated not only in microheterogeneous structures like the collodion matrix membranes discussed here but also in homogeneous phase “ oil ” membranes. Prof. A. R. Ubbelohde (Imperial College London) said Modern work in-dicates that the quasi-crystalline structure of liquids such as water or ethyl alcohol may undergo profound changes near a surface especially when the surface con-tains polar molecules as is the case for many membrane walls.One test of such changes of liquid structure arises from measurements of dielectric relaxation, which show that water molecules near the walls are much less free to rotate. In some ways the abnormal orientation imposed by membrane walls on the H20 dipoles nearest to them makes these boundary layers of solvent much nearer to a fluid like H2S than a strongly ionizing fluid like quasi-crystalline bulk H20. For example the effective dielectric constant is lowered. These changes in liquid structure are likely to be particularly important for molecules such as H20 or alcohols of low carbon content that form chains and networks of hydrogen bonds.For bulk water the co-ordination number is about 4 ; a very open structure is maintained by the hydrogen bonds. In the very strong polarizing fields near certain membrane walls a rise in co-ordination number and a decrease in ionizing power would be expected. Other solvents in which the co-ordination number is higher behave more nearly like assemblies of close-packed spheres; for such fluids any structural changes near to or within the membrane are likely to be much less marked. When flow of solvent through a membrane occurs these considerations indicate a number of consequences. For solvents which undergo marked changes of quasi-crystalline structure near membrane walls : (i) The effective viscosity of the modified solvent layers may be markedly different and may involve different entropies and energies of activation.(ii) The ratio of ion mobilities may be quite different from those in bulk solution particularly if ion solvation has a marked effect on the transport number in the bulk solvent. In the “modified” solvent close to the membrane walls, ion solvation is reduced by the competing polarization forces of the walls. These walls orient solvent dipoles along their own force fields which normally conflict with the centric fields due to individual ions. Relative to Kf both the ions Na+ and H3O+ which are very considerably more solvated will suffer substantial changes of mobility in the “ modified solvent ”. On the other hand two ions which are not extensively solvated such as K+ and Rb+ should preserve much the same relative properties in the modified layers.(iii) Ion activities may be appreciably changed in the modified solvent layers near membrane walls. This applies both in the “ diffusion layer” nearest the walls and in “ channels ” whatever their specific structure within the membrane itself. Some of the leading effects can be simply illustrated in relation to the Debye-Huckel expression for the limiting activity coefficient of an ion logf* = - A I z1z2 1 dr with A = 1.8246 x ~ O ~ / ( E T ) ~ / ~ ; I is the ionic strength.1 In the modified layers the effective dielectric constant E will be lowered for reasons described in the preceding section. In comparing the effect for two ions of the same charge a change in E merely leads to proportional changes. At rather higher ionic strengths the expression for log f* must be divided by the term (1 + Bad?) where a is the ionic diameter and B is a constant.At such con-centrations a more important influence may be the decrease in effective ionic radius a+ arising from desolvation in the modified layers. This influence will shift relative thermodynamic potentials of two ions such as K+ and Na+. 1 cf. Robinson and Stokes Electrolyte Solutions (Butterworth 1955) p. 228 138 GENERAL DISCUSSION (iv) On migrating from bulk solvent to modified solvent individual molecules require activation energy which may differ appreciably from the activation energy for migration within the bulk solvent. The change in co-ordination number which accompanies the change in quasi-crystalline structure of the solvent also involves a change in heat content.This change in heat content as the solvent molecules flow from bulk I -+ modified layer -+ bulk I1 must in some cases lead to appreciable heat transfer across the membrane if there is appreciable flow of solvent through the membrane. Ordinarily the thermal conductivity of the mem-brane will equalize any large temperature differences across it. For slow rates of solvent flow no large inequalities of temperature would seem likely. However, if membranes can be found which (i) permit rapid flow (ii) impose substantial modifications of structure on the solvent near the membrane walls appreciable cooling or heating may accompany solvent flow because of the accompanying substantial changes of heat content. Mr. D. Reichenberg (C.R.L.Teddington) said I would like to quote some experimental evidence in support of Prof. Ubbeolohde's view that conditions inside a resin cannot be treated as similar to those in an ordinary electrolyte solution even after the obvious differences due to fixed charges in the resin have been allowed for. At the Chemical Research Laboratory Mr. Selton has measured the equilibrium degree of penetration of HCl from aqueous solutions (0-03 molal up to 2.5 molal) into a commercial carboxylic acid resin Amberlite IRC 50 in the H+ form. Over the whole of this concentration range the molality inside the resin (i.e. mmoles HC1 absorbed per g of water inside the resin) was appreci-ably lower than that in the external solution the ratio rising with concentration from 0.45 0.10 (at 0.03 molal) to 0.67 f 0.03 (at 2-5 molal).The carboxylic acid groups of the resin would be almost completely in the undissociated state. Hence this " salting-out" could arise only from one or more of the following four causes : (i) a dielectric effect due to the hydrocarbon matrix of the resin; (ii) a dipole effect due to the undissociated carboxylic acid groups ; (iii) the water inside the resin being possibly in a different state of aggregation from that in the outside solution; (iv) an osmotic effect arising from constraints due to the cross-linking of the resin. However this last effect can probably be ruled out since it has been shown to be very small with most electrolytes in resins of normal degrees of cross-linking.1 Prof. G. Scatchard (M.I.T.Cambridge Mass.) said After Prof. Ubbelohde reminds me it seems to me that there must be an effect such as he suggests and that this effect must be related to the effect of the breadth of junction on the electro-motive force of cells with transference,2 which depends upon the heat of dilution. This effect at the membrane should also depend markedly upon the efficiency of heat transfer upon the rate of stirring etc. It may well enter into some of the effects of stirring noted in some papers presented at this Discussion. Prof. R. M. Barrer (Imperial College London) (communicated) Dr. Pethica has asked what is the relation between the diffusion expressed in terms of a chemical potential gradient dpldx and that expressed in terms of Fick's law. The relation is derived as follows.The force acting on a molecule at a point x is F cc - dp/dx. Thus the total force acting on all molecules at the point x is FT cc - Cdp/dx 1 Duncan. Proc. Roy. SOC. A 1952,214 344. 2 Scatchard and Buehrer J. Amer. Chem. Soc. 1931,53,574. Hamer J. Amer. Chem. SOC. 1935 57 662 GENERAL DISCUSSION 139 where C denotes the concentration at the point x. If the flux J is now assumed proportional to FT one has for the flux through unit area J = - [BC]dp/dx (1) where B is a coefficient measuring the mobility of the diffusing molecules. Since RT d In a = dp where a is the activity of the diffusing species at point x one may substitute in (1) and obtain BCRT da (2) J = - [4&’ and so J - - [,a]& BCRT da dC (3) But since in the Fick law equation, one has d In a d In C‘ D = BRT- (4) There is of course no reason why B or d In ald In C should not depend in a com-plex way on C or in inhomogeneous media on x.In some polymer systems it has moreover been discovered that on account of slow relaxation times of the polymer network D may for a given penetrant molecule depend also on time t. I would like to make a comment on the rather widespread use of the term “ affinity series ” revealed by the papers given in this Discussion to denote the extent of exchange of a series of ions with a given exchanger. This is a loose application of a term which should have a precise thermodynamic significance. In an exchange equilibrium where has in and Aaq + BZ + Baq + Az, the subscripts aq and 2 denote solution and exchanger respectively one terms of ion activity a, K = aB,qaAZ, aBZaAaq AGO = -RTln K.AGO measures the affinity of the reaction. If the ion B is kept the same and a series of ions A is used then the AGO values for the series will give the true affinity series. This has been measured for some ion pairs exchanging in chabazite.1 I would suggest that the term “ affinity series ” should be retained only in its true thermodynamic sense and should not as at present be incorrectly used to denote ion sequences indicating the extent of reaction. The latter series may not always coincide with the true affinity sequence. Dr. B. A. Pethica (Cambridge University) (communicated) Prof. Barrer’s simplified statement of the relation between the diffusion equations using Fick’s law and the chemical potential gradients is a useful addition to the discussion.The account is similar to that in his earlier publication,2 and should be compared 1 Barrer and Sammon J . Chem. SOC. 1955,2838. 2 Barrer Faraday SOC. Discussions 1948 4 68 140 GENERAL DISCUSSION to the fuller analysis given by de Groot 1 and others. My original remarks on eqn. (1) and (3) in the paper by Lorimer Boterenbrood and Hermans were in-tended to point out a certain degree of thermodynamic arbitrariness about the choice of forces in the flux equations as well as to draw attention to the Fick’s law equation. In the first place the separation of into chemical (p) and electrical potentials ( E ) is open to the well-known criticisms of Guggenheim,2 although since Lorimer et al. consider only small deviations from equilibrium the two sides of the membrane may be considered as of identical composition. In a simple diffusion system obeying Fick’s law it is clear that to write the diffusion in terms of “ chemical ” potential differences will involve a conjugate coefficient which is non-constant. This may be seen by comparing Barrer’s eqn. (1) with Lorimer’s eqn. (1) and (3). In making this point I was bearing in mind a paper by Denbigh 3 in which he considers the same question. Denbigh was principally concerned with the incorrect results obtained by Prigogine 4 on the thermodynamics of the stationary state in an open system involving chemical reaction showing that the errors arose from taking reaction rates as proportional to chemical potentials. In the diffusion case similar considerations will apply where chemical potential gradients are used if the conjugate coefficient is not constant (as when Fick’s law is obeyed). The question of the variation of the coefficients with p is left open by Lorimer et al. who have restricted themselves to small deviations from equilibrium. 1 De Groot Thermodynamics of Irreversible Processes (North Holland Publishing 2 Guggenheim J . Physic. Chem. 1929 33 842. 3 Denbigh Trans. Faruday Soc. 1952 48 389. 4 Prigogine Etude Thermodynamique des Phtnomdnes irriversible (Likge 1947). Co. Amsterdam 1952)