198 GENERAL DISCUSSION GENERAL DISCUSSION Dr. P. W. M. Jacobs (Imperial College London) (communicated) The pro-gramme described by Lorimer Boterenbrood and Hermans is similar to our own in that one of our aims has been to establish experimentally values for the pheno-menological coefficients. Using the form of the theory applicable to discontinuous systems they obtain eqn. (16) which can be tested by calculating t+ from dE’/d In a, allowing for solvent transport and comparing the calculated values with those measured directly. Since our results using membranes of polymethacrylic acid in KOH solution cover a wider concentration range than those recorded in their paper it is perhaps of interest to quote the results here. rn 0.00562 0-0 1 125 0.05624 0.1005 0.2010 0.4025 0.8078 1.013 f + (calc.) 0.998 0-991 0.988 0-986 0.957 0-90 1 0.794 0.765 t+ (obs.) 0.954 0.941 0-925 0.914 0-875 0.820 0.740 0-705 The calculated results are from 4-9 % too high whereas the observed values were reproducible to better than 1 %.Some of the discrepancy may be due to the errors inherent in the graphical differentiation of the plot of E’ against log (urr/ax), but there remains the suspicion that some more fundamental factor has been over-looked. This is not likely to be due to the authors’ use of the form of theory required for discontinuous systems for the same equation can be derived from pseudo-thermostatic arguments 1 and also by applying the thermodynamics of irreversible processes when the membrane is regarded as a continuous system.2 At least for membrane potentials there are no inherent theoretical difficulties, and one feels fairly safe in applying eqn.(16). The discrepancies observed are therefore all the more puzzling. Dr. J. W. Lorimer (Leiden University) (communicated) Two new techniques applicable to membranes which can be made in strip form are under development 1 Scatchard Ion Transport Across Membranes ed. Clarke (Academic Press 1954), 2 Hills Jacobs and Lakshminarayanaiah unpublished work. p. 134 GENERAL DISCUSSION 199 in our laboratory. The same cell (fig. 1) is used both for d.c. conductance and e.ni.f. measurements. It consists of two Plexiglas blocks B with electrode chambers C C’ D D’ and a channel A just slightly smaller than the membrane.For d.c. conductance measurements the membrane is placed in A and its equilibrium KCl solution in C and C’. A known current is passed through reversible electrodes in C and C’ and measurement of the potential between two reversible probe electrodes in D and D’ permits calculation of the cell re-sistance. Preliminary experiments using H FIG. 1. membranes of the type described earlier in this Discussion showed Ohm’s law was valid and gave conductance values agreeing within experimental error with those obtained from ax. measurements. For e.m.f. measurements a membrane is cut into two sections each of which is equilibrated in a different KC1 solution. The sections are placed in the cell, and meet at the dotted line. The appropriate equilibrium solutions and silver chloride electrodes are placed in C and C’.For 0.05-0.001 N KCI an e.m.f. of 134.8 mV was recorded at 15” C in excellent agreement with the value 134.4 mV obtained from flowing-junction cell experiments (8 B). Dr. K. S. Spiegler (Pittsburgh U.S.A.) (communicated) In their excellent discussion of transport processes across membranes Lorimer Boterenbrood and Hermans mentioned the experimental difficulties encountered as a result of un-wanted electrode reactions. Mr. J. G. McKelvey and I have met with similar difficulties and found a way to overcome them at least for certain systems. In the past our study dealt with transfer phenomena across commercial cation-exchange membranes (e.g. Permaplex C- 10 product of The Permutit Company Ltd., London).Our work too is based on the fundamental paper by Staverman.1 Since the transport numbers depend on the concentrations of the solutions separated by the membrane we determine the transport without changing appreci-ably the total solution concentration. No stirring is required. This is achieved by : (1) adding a radioactive tracer to one solution and (2) adding small amounts of appropriate ion-exchange resins to the solutions in the anode and cathode compartments. The resins act as “ concentra-tion buffers ” removing the unwanted products of the electrode reactions and balancing the ion concentrations in the two compartments. For instance in the determination of transfer phenomena in the Permaplex C-1 + sodium chloride system we used the following arrangement I NaCl + solution HR I Pt-cathode I membrane Pt-anode 1 + Na*:R Na*Cl solution where R represents the negative radical of the weakly acid cation-exchange resin Amberlite IRC-50 (product of the Rohm and Haas Co.Philadelphia Pennsylvania). The sodium ion in the anode compartment is traced with 2.6 y Na22 both in solution and on the resin. Upon passage of the electric current the platinum anode generates hydrogen ions which are immediately taken up by the resin since the solution in the electrode compartments is vigorously agitated by magnetic stirrers. At the same time the resin releases sodium ions most of which migrate through the membrane. At the cathode NaOH is formed and promptly adsorbed by the resin thus removing excess sodium ions approximately in the same amount as they migrated through the membrane.As a result the total concentrations of the solutions change 1 Trans. Faraday Soc. 1952 48 176 200 GENERAL DISCUSSION very little during current transfer. The transport numbers are calculated from the increase of the specific radioactivity of the solution and/or the minor change of the chloride concentration in the cathode compartment. The cell is made of Plexiglas. The gases produced by the electrode reactions escape through burettes inserted at the dome-shaped ceilings of the cell com-partments. The solvent transfer is calculated from the change of level in the burettes. Allowance is made for the small amount of water decomposed by electrolysis. This method might also be suitable for salts other than chlorides since it does not depend on the supply of anions from the cathode.With chlorides some chlorine evolution occurs at the anode but this does not seem to affect the results to any appreciable extent. A different method aimed at keeping the solution concentrations constant was used by Murakoshi 1 who measured ion and water transport in systems of KCl solutions and cation-exchange membranes. In these experiments potassium amalgam and mercury were used as anode and cathode respectively. Dr. F. L. Tye (The Permutit Co. Ltd. London) said Dr. Lorimer Miss Boterenbrood and Prof. Hermans write “ The good proportionality between resistance and length indicates that any refraction of the current lines in the area I I I / I I oo 0.1 0 - 1 0.3 a tcm, FIG.1. between the two Plexiglas plates is negligible . . .”. This statement is question-able and the evidence for it in their fig. 2 can be interpreted as being indicative of considerable current distortion between the Plexiglas plates. In fig. 1 cell resistance with membrane is plotted against membrane thickness and a smooth curve drawn through the points. The points are a repeat plot of the open circles shown in the authors’ fig. 2 except for the point at a = 0 1 private communication see also Kosaka J . Electrochem. SOC. Japan 1955 23 659 GENERAL DISCUSSION 201 which is shown in the authors’ fig. 2 as a half-filled circle. The curve convex to the resistance axis is the type one would expect if the effective area of conduction were increasing as the thickness of the membrane increased.Such an increasing area of conduction would of course result from distortion of current lines between the Plexiglas plates. An estimate of the effective area of conduction at any particular membrane thickness e.g. a = a1 can be obtained from the ratio of the slope of the tangential line at a = 0 to the slope of the line joining points a = 0 and a = a1 on the curve. This ratio gives the value of A/Ao where A is the effective area of conduction for a membrane of thickness al and A0 is the internal cell area. A plot of A/& against membrane thickness is shown in fig. 2. I I A/A I I I 1 a ( c m ) FIG. 2. The magnitude of the A/Ao values in the range of membrane thicknesses em-ployed demonstrates that distortion of current lines is far from negligible.The rather small internal diameter of the cell used by the authors has of course, emphasized the effect. The cell diameter is only four times greater than the thickest membrane used. It follows that had the internal cell area been used to calculate specific con-ductivities the results would have been considerably in error. However the authors have employed a comparative method which necessitates measurement of the resistance of KCl solution as a function of thickness. If it can be assumed that the amount of current distortion is the same for the KCl solution as it is for the membrane the final error in the specific conductivity results should be fairly small. It should be made clear that for this procedure to be at all justifiable the Plexi-glas rings inserted between the two halves of the cell to measure KCl solution resistance as a function of thickness must have internal diameters larger than the internal diameter of the cell so that full distortion of current lines is possible.The Plexiglas rings used by the authors did have much larger diameters than the internal bore of the cell.1 1 J. W. Lorimer private communication 202 GENERAL DISCUSSION Dr. J. W. Lorimer (Leiden University) (communicated) Dr. Tye’s remarks on the distortion of current lines in the conductance cell used in our research seem to demonstrate the importance of such effects. However two points must be settled before his method for finding the effective area of conduction proves acceptable. First the magnitude of the effect depends upon the slope of the tangent drawn at a = 0 in Dr.Tye’s fig. 1 and it is somewhat difficult to locate this line accurately. Secondly because there will always be some curvature of current lines in the solutions bathing the membrane there will be a refraction effect 1 at the membrane-solution interface. This effect should result in greater distortion in a KC1 solution layer than in a membrane layer of the same thickness, since the solution conductance is greater than that of the membrane. Our plots of resistance against thickness however all gave better straight lines for solutions than for membranes. This may indicate that distortion effects in the solutions next the cell electrodes are also important. Since this method for measuring membrane conductance is convenient and widely used an accurate analysis of the situation is highly desirable.Prof. G. Schmid (KoeZnlRhein Germany) said I cannot subscribe to the opinion of Dr. Hills when he says “The Schmid theory of electro-osmosis in charged membranes does not appear to be valid for this membrane system.” In its main deductions this theory makes a minimum of arbitrary assumptions. It is therefore hard to understand why it should not be valid for the membrane system under consideration. To be sure the basic formulae of my theory contain no information on pore radii or pore numbers these being obtainable only on the basis of quite arbitrary assumptions. Bjerrum and Manegold assume incorrectly of course a’system of random cylindrical pores and give the pore radius r as r = (24D~dv/W)# where DH is the water permeability of the membrane d its thickness and Wits water content.By use of the formula rrr2N = W the number of pores N can be calculated from the above assumption which is certainly incorrect. The basic formulae in my papers contain only the empirical quantities DH and W. To make them more comprehensible however I have also calculated “ pore radii ”. But here I have stressed that the pore radius r may be understood only as a numerical value which strictly speaking has no real meaning. The same is of course true for the number of pores N. The primary values which alone have a quantitative meaning are the water permeability DH and the water content W (or the resin content VR). Eqn. (6) of Dr. Hills is 1 0 3 ~ 2 ~ 2 (g) vR =-* ‘71 Dr.Hills is of the opinion that the right side of the expression is constant. He assumes that membranes with the same water content have also the same pore radius r and that if the water content or the resin content is kept constant, the pore radius must also be constant i.e. independent of ci. This idea seems plausible and may be valid to a certain extent for pore systems containing a great deal of mobile water. However for pore systems in which, due to fixed or mobile ions the amount of bound water is appreciable compared with that of unbound water the assumption certainly is not true. Even if the organic matrix and the water content remain unaltered an increase in fixed ion concentration can immobilize so much water that both the pore radius and the pore number are greatly altered.In general as the Bjermm-Manegold formula shows r is only constant provided not only VR but also DH is kept constant. In the system with which Dr. Hills works it is likely that the value DH decreases sharply with increasing ci even if the structure of the matrix and the value VR 1 Jeans The Mathematical Theory of EIectricity and Magnetism (Cambridge 5th ed., 1925) p. 346 GENERAL DISCUSSION 203 are kept constant. In the calculation of pore radii a decrease of r with increasing ci would then appear. The expression (g) VR must therefore decrease with increasing ci as has in fact been observed by Dr. Hills and Dr. Despi; and was represented in fig. 7. Furthermore I would like to say that I consider it somewhat unfortunate that the definition of the term electro-osmosis used by Dr.Hills does not include the transport of water of hydration. I would suggest that the term electro-osmosis should be defined purely phenomenologically and with no hypotheses from the total amount of transported water or solution as has nearly always been done until now as far as I am aware. For the treatment of electro-osmosis according to the thermodynamics of irreversible processes an unphenomenological definition would certainly be unsuitable. The distinction which Dr. Hills has made is of course completely correct in practice and indispensable for a theoretical inter-pretation of electro-osmosis. However the term electro-osmosis as such should not be encumbered with the uncertainties of theoretical interpretations as for example with hydration numbers.Prof. G. Scatchard (M.I.T. Cambridge Mass.) said If we consider the water as stationary the determination of primary solvation from the measurements of Despic and Hills is equivalent to the assumptions with ordinary solutions that self-diffusion gives the ‘< true transference ” number that from the difference between “ true ” and “ Hittorf ” transference the “ hydration ” of the ions may be de-termined and that this “ hydration ’’ is entirely the “ primary solvation ” of the cation. Many of us would be unwilling to make these assumptions. Dr. P. Meares (Aberdeen University) said When considering the change with concentration of equivalent conductance and self-diffusion coefficient of the counter-ions in an ion-exchange resin Despic and Hills include only the effects due to electro-osmosis and the c‘viscous effect of the matrix”.At constant volume fraction of resin they consider that the latter effect will be the same for conductance as for diffusion so that the difference between mobilities obtained by the two methods will give the electro-osmotic contribution. It appears however that a relaxation effect may also contribute to this difference. Confining attention for the present to the simple Onsager treatments neglecting the finite size of the ions the fractional decrease in the applied field A X / X caused by the relaxation effect in conduction is AX Z122e2K (1) X 3ckT 1 + l/q’ where z1 and z 2 are valencies e the electronic charge E the dielectric constant, k the Boltzman constant T the absolute temperature and K the Debye reciprocal length q for univalent ions is 3.Under the conditions of a self-diffusion experi-ment the reduction in the virtual force arising from the concentration gradient of tracer ions AFIF due to the relaxation effect is for univalent ions - - _ ~ ~ AF 1 + 2t F 3 ~ k T here t is the transport number of the ion of sign opposite to the tracer ions. For an ion-exchange resin t = 0. reduce to ~ _ _ Hence for the case here considered (1) and (2) e2K - 0.293 __ A x X 3 ~ k T AF e2K - = 0.500 --F 3&T (3) (4 204 GENERAL DISCUSSION Since (3) and (4) are not identical in the range of validity of the Onsager equations, the difference between and A’ of Despic and Hills will be due partly to electro-osmosis and partly to the relaxation effect.At higher concentrations such as were encountered in the resin phase the calculation of the relaxation effect in conduction can be improved by taking into account the finite size of the ions, as has been done by Falkenhagen Kelbg and Leist. No similar extension has been given for the self-diffusion theory but it seems necessary to admit the possibility that at high concentrations the difference between X and A’ may not give an uncomplicated measure of the electro-osmotic effect. Dr. A. DespiC and Dr. G. J. Hills (Imperial College London) said Prof. Schmid contends that constant VR does not imply a constant value for the Y or r2 because this is a hypothetical quantity introduced into his equations from DH, the hydrostatic diffusion coefficient which is dependent on concentration even at constant VR.This apparent anomaly emphasizes the need to consider the finite volume of the ions transported through the membrane. In Schmid’s equation where pe is the electro-osmotic pressure Df the electro-osmotic coefficient and i the current density the volume of solvent transported under a hydrostatic pressure is equated to the volume of solution transported electro-osmotically. This is only so on the basis that ions are point charges. Whenever the need arises to consider ions of finite size the appropriate form of this equation is peDs = Dii (1) where Ds is the hydrostatic diffusion coefficient of the solution notwithstanding the fact that this coefficient cannot be obtained in the same way as DH.Apart from the effect of concentration on the viscosity of the interstitial solution which we have neglected DS is not dependent upon ionic concentration but only upon r. We regard r2 as a purely geometrical quantity which on the basis that NO is con-stant is given unambiguously by eqn. (9) of our paper. On either argument constant VR does imply constant 9. It is this previous neglect of the finite volume of solvated ions which also leads to the anomaly in the definition of electro-osmosis. We agree with Prof. Schmid that the phenomenon of electro-osmosis has always referred to the total quantity of solvent transported through a membrane. In any consideration of the mechan-ism or theory of electro-osmosis however a distinction must be made between the water transported by the electro-osmotic mechanism and that migrating with the ions.Even if no experimental distinction were possible a distinction in principle should be made e.g., electro-osmosis = electro-convection + ionic solvation. pe DH = Dii , On this basis the mechanism and the various theories of electro-osmosis strictly refer to electro-convection. We used the word “ electro-osmosis ” and “ electro-osmotic transport ” in relation to the mechanism not the phenomenon. It is worth noting that where the electro-convection is very large and/or the solvation nil the anomaly disappears. In reply to the remarks of Dr. Meares we agree that the difference in the two relaxation effects could give rise to part of the difference between the observed mobilities or conductances but there is experimental evidence that this is apparently not so.As we pointed out earlier the variation of ionic mobility with ionic con-centration at constant VR obtained from self-diffusion coefficients is in accord with the equation (2) where A& is the limiting equivalent conductance of the counter-ion species in aqueous solution A is a constant equal to ( V R ) ~ = ~ and a* is the Onsager relaxation u’ = ( x ~ ~ / F ) ( I - a*dii)(A - I+) GENERAL DISCUSSION 205 parameter applicable to normal ionic conductance. Further if to this equation is added an equation similar to (10) of our paper the expression is obtained where B is the value of VR as AA -+ 0 and K = 103P/877-7No. A value for NO must be found from one experimental observation on the membrane material.Eqn. ( 3 ) which contains only terms for the normal conductance relaxation effect and electro-osmosis expresses the equivalent ionic conductance of all the alkali metal ions over a wide range of ci and VR values. It therefore does appear that the difference between u and u’ is due solely to electro-osmosis. Dr. G. A. H. Elton and Dr. D. I. Stock (Battersea Polytechnic London) (com-municated) We should like to raise some points concerning the work of Despik and Hills on electro-osmotic transport. The nature of the electrodes used is not stated but whether these were reversible or not the value of ANsolvent (anode) in table 5 is incorrect; if the electrodes were reversible to OH- the value of A Vsolvent (cathode) is also incorrect.With inert irreversible electrodes the result of the passage of 1 faraday is in respect of water the loss of 1 mole in the cathode compartment and a gain of 0.5 mole in the anode compartment. With reversible electrodes (e.g. Hg/HgO) the corresponding result is the loss of 0.5 mole in the cathode compartment and the gain of 0.5 mole in the anode compartment. In their calculations DespiL and Hill have assumed implicitly that 1 mole is lost in the cathode compartment and that 1 mole is gained in the anode compartment, Table 5 should then read : irreversible cathode 218 - 6 18 242 13.4 reversible cathode 218 - 6 18 233 12-9 electrodes {anode - 222 - 6 18 - 237 - 13.2 electrodes {anode - 222 - 6 18 - 237 - 13.2 These alterations lead to values of S N a of 8.7 (irreversible electrodes) and 8.5 (reversible electrodes).Dr. A. Despi; and Dr. G. J. Hills (Imperial College) (comniunicuted) In reply to Dr. Elton and Dr. Stock we should like to add that the electrodes were irre-versible (Pt) a fact which might have been deduced from our remarks concerning gas evolution. The need to use the appropriate correction for the volume of solvent lost at the electrodes was appreciated and the original typescript of our paper contained the following two equations which summarize the remarks of Dr. Elton and Dr. Stock : A Vcathode cathode solvent = Avobserved - ATNaOH f A/H,O 3 Nevertheless they are right in pointing out the arithmetical error in table 5 A Vszt should certainly be - 237 ml and A V s o ~ v t / A ~ ~ 2 0 - 13.2 and we thank them for making this clear.Dr. G. A. H. Elton (Buttersea Polytechnic London) (communicated) I should like to raise a few points concerning the paper by Despic and Hills The viscosity (va) of water in the narrow capillaries present in the ion-exchange material will probably differ considerably from the normal “ bulk ” viscosity (7). An approxim-ate estimate of y,/~ can be obtained from the equation 1 1 Elton and Hirschler Proc. Roy. SOC. A 1949 198 581 206 GENERAL DISCUSSION For solutions in the concentration range used by the authors the double layer will be compact and we may write (2) where Q is the surface charge per cm2 d is the effective thickness of the gegen-ion layer and the other symbols are defined by Despic and Hills.The value of d at 25" C is given by (3) €5 = 4 ~ 0 d = 2 x 10-3 Fcjrd, d = 3 x 1 O - S ~ i - i 19 whence 2% I + h' rl (4) For ci Q= 1 eqn. (4) should be fairly accurate for r > 25 A and should give a reasonable approximation for capillaries of rather smaller radii. (The equation cannot be used for low concentrations since in this case the double layer is not compact and d is not small compared with r.) Applying eqn. (4) to the values of ANa given by Despic and Hills we obtain the values of y,/r) shown in the table. TABLE 1.-vALUES OF '/,?a/q FOR VARIOUS VALUES OF Ci AND VR (FROM XNa DATA) VR ci = 1 C i = 2 C i = 3 C i = 4 0.2 2.0 2.2 2.5 2.9 0.3 2.4 2.7 3.0 3 *4 0-4 3.2 3.5 3.8 4.3 It might perhaps be argued that A' should be used in eqn.(4) instead of A, but this would lead to even higher values of y,/y (since A' < A). It would therefore appear that it is incorrect to assume that ~ ~ / r l is approximately unity for VR = 0.2 as Despid and Hills do in interpreting their results for A,. The values of q,/y in this system will be lower than those shown in the table (since A > ANJ but I think that the appropriate value should be calculated, and used in the estimation of r. As a result of the use of this correction a rather higher value of Y will be obtained; the correction will become more important as VR is increased. Since ya varies with Ci the author's eqn. (6) should be (5) A linear relation between (Ay)v and ci will therefore be obtained only if 1 O'P2r' 3(ci/y,) (%) = B ( T & is constant.This is not the case for the Na' system; the variation VR of (AA) v with Ci should therefore be described more satisfactorily by eqn. (5) above than by the authors' eqn. (6). In general a linear variation of (Ah), with ci will indicate that ci/ya varies linearly with ci over the range of ci studied and not necessarily that qa = The authors list three possible criticisms of their method of calculation of S N ~ ; a further point should also be considered. For a compact gegen-ion layer the electro-osmotic velocity of the more dilute solution further from the capillary wall may be greater than that of the more concentrated solution near the wall, so that a relatively greater amount of solvent may be transported ci being kept constant by osmotic forces.In this case the value of SNa calculated by the authors will be too high. Finally I should like to suggest that an investigation be made of the dependence of X on the a.c. frequency for systems of this type. It is to be expected that the electro-osmotic contribution to h will decrease fairly rapidly with increasing frequency due to inertial effects. If it should be found that the electro-osmotic contribution can be virtually eliminated by the use of a suitable frequency while = constant GENERAL DISCUSSION 207 leaving the electrolytic contribution practically unchanged this would provide a method of determining A’ independent of the use of radioactive species. Dr. A. Despi; and Dr. G. J. Hills (Imperial College) (communicated) We are grateful to Dr.Elton for his comments on the probable variation of the inter-stitial viscosity with ci and VR. Our elementary investigation of Schmid’s theory of electro-osmosis does not depend upon the assumption that 7 w ~ H ~ O but only that ( 7 ) ~ ~ m constant or (&; M constant (cf. Dr. Elton’s table 1). The value of Y = 7 A evaluated on the basis that 7 = ~ H ~ o was put forward simply to show that the value of (3X/JCi) vR = 0.2 was at least sensible. Dr. J. A. Kitchener (Imperial College London) said With a view to inter-preting membrane properties in terms of molecular structure it is desirable to work with homogeneous cross-linked polyelectrolyte gels rather than with hetero-geneous membranes or even deposited films of insoluble polymer with incorporated ionic substance (e.g.modified collodion membranes). Probably the best material of this class is the transparent polymethyl-methacrylate resin developed by Howe,l which seems to be ideal for fundamental studies. This is the material for which Dr. DespiC and Dr. Hills have now provided some remarkably accurate data covering conductivity self-diffusion and water-transport. Such data should give valuable information about the resin structure but some of the models at present proposed for treating electro-osmotic flow seem unrealistic-for example the treatment of pores as cylindrical capillaries. -. - ‘c / * # . 0 C a r b o n a t o m s COO- a n i o n s @ E r c h a n q o b l c c a t i o n s @ M o b i l e a n i o n s - i - ‘\ Diagrammatic representation of the structure of a pore in a polymethacryIate ion-exchange resin of about 10% cross-linking.The chains are nearly fully extended and the water-content is about 30 molecules of water per cation. Probably the best model for ion-exchange resins is a tangled network of flexible polymer chains permeated by a kind of 3-dimensional electrical double-layer, as shown schematically in the accompanying figure. It should be emphasized that the disposition of the counter-ions will depend on such factors as (i) charge density along the chains (e.g. higher with polymethacrylate resins than in sulphon-ated polystyrenes) (ii) valency and structure of the counter-ions (iii) presence of hydrophobic groups (e.g. aromatic nuclei) (iv) presence of non-ionic hydrophilic groups (e.g.-OH groups in phenol-sulphonic acid resins). An instantaneous picture would show a certain proportion of the counter-ions associated with the fixed charges (probably a minority with alkali-metal ions, varying of course with ionic radius but the majority in the case of the Ba2f salt of Howe’s resin 1). The remainder would be distributed in the pore-volume, 1 Howe and Kitchener J. Chew. SOC. 1955,2143 208 GENERAL DISCUSSION according to the potential gradient. The centre of a pore would be least concentrated in counter-ions and most concentrated in any diffusible " nebenions " present. An interesting piece of evidence in support of this model is provided by the work of Tetenbaum and Gregor 1 on self-diffusion of Kf counterions and C1-nebenions in a sulphonated polystyrene resin the latter moved almost twice as fast as the former whereas in water their mobilities are practically identical.The measured diffusion coefficient and equivalent conductivity of the counter-ions are clearly mean values for the ions in the different situations. Dr. DespiC and Dr. Hills have evaluated from their results a mean velocity of electro-osmotic transport of the counterions-i.e. a streaming of the medium superimposed on the electro-migration of the ions. This seems unobjectionable but it does not seem to be valid to assume that the mobile phase as a whole is moving with this velocity. When a field is applied the counterions in the centres of the pores will move most rapidly and impart momentum to the medium in their vicinity but those near the chains will be retarded and will transport less water.Thus the mean velocity of the water molecules cannot be identified with the quantity men-tioned above and it is not surprising to find cases where more water is transported than that assumption would indicate; in fact this is the result to be expected on the model suggested. Extension of these studies to other types of well-defined membrane should be extremely illuminating. Mr. D. K. Hale and Mr. D. J. McCauley (Chemical Research Laboratory, Teddington) said We have been investigating the properties of a series of ion-exchange membranes of the heterogeneous type containing sulphonated polystyrene resins of different degrees of cross-linking. The membranes were prepared by moulding a mixture of the finely divided ion-exchange resin (2 parts) and poly-ethylene powder (1 part).To obtain an intimate mixture of the two components, the ion-exchange resin and polyethylene were mixed in the presence of xylene which was subsequently removed by vacuum distillation. The powder obtained was then moulded into discs at a pressure of 2000 Ib.jsq. in. and a temperature of 140" C. The membranes swelled readily in water and had a high electrical conductivity (a membrane containing a resin cross-linked with 10 % divinyl-benzene (DVB) had a specific resistance of 136 ohm cm in 0.1 N NaCl solution). The permselective behaviour of these membranes has been studied by both direct and indirect methods. The e.m.f. of the cell has been measured using a technique similar to those described in the papers of Lorimer Boterenbrood and Hermans and Scatchard and Helfferich.The e.m.f. obtained was compared with that of a similar concentration cell without the membrane and the apparent transport numbers of the ions in the membrane calculated from the ratio of the two e.m.f.s and the transport numbers in solution. The results obtained with a mean sodium chloride concentration of 1.ON (c1 = 0.667 equiv./l. ; c2 = 1.333 equiv./l.) are given in table 1 and show the marked effect of the degree of cross-linking on the apparent transport number. TABLE 1 .-APPARENT TRANSPORT NUMBER OF SODIUM ION IN MEMBRANES CONTAINING RESINS OF DIFFERENT DEGREES OF CROSS-LINKING divinylbenzene content apparent transport of cation-exchange number of resin sodium ion 2 % 0,675 10 % 0-854 1 Tetenbaum and Gregor J.Physic. Chern. 1954 58 11 56. 5 % 0.808 15 % 0.88 GENERAL DISCUSSION 209 The apparent transport number (t;) should be equal to t+ - 0.018 mto where t+ is the true transport number nz the molality of the solution and to the transport number of the water.1 We are therefore determining the transport numbers of both the sodium ions and the water by a direct method. A known quantity of electricity is passed through a cell which contains sodium chloride solution and which is divided into two compartments by the membrane. The amounts of sodium ion and water which pass through the membrane are determined and the transport numbers calculated. Results obtained with a commercial membrane (Permaplex C-10) and a laboratory-prepared membrane (2 % DVB resin) and 1 N sodium chloride solutions are given in table 2 which also includes values for t+ calculated from the values of tl and fg.TABLE 2.-TRANSPORT NUMBERS OF SODIUM ION AND WATER IN CATION-EXCHANGE MEMBRANES Membrane f0 (moles per Faraday) t+ direct method ti-(calc. from t i and to) Permaplex C-I0 8 0-9 1 0.95 laboratory prepared membrane 12 0.8 1 0.89 (2 % DVB resin) The agreement between the values of f+ obtained by the two methods is not very good. The discrepancy in the results may be due to the approximate nature of the calculation of t + from the e.m.f. measurements or to errors which arise in the direct method because of concentration gradients which develop during the course of the experiment. FIG.1 .-Relationship between weight-swelling and resin content of heterogeneous membranes (a) expected (6) observed. We have also determined the weight-swelling in water and the density of a series of cation-exchange membranes containing different proportions of a sulphon-ated cross-linked polystyrene resin (5 % DVB) and polyethylene. At the higher resin contents the weight-swelling is greater than would be expected from the 1 Staverman Trans. Faraday SOC. 1952 48 176 210 GENERAL DISCUSSION weight-swelling of the resin alone (fig. l) and the density is less than would be expected from the densities of the wet resin and polyethylene (fig. 2). These results indicate that the swollen membranes contain interstices which are filled with water ; the interstices presumably develop when the dry membrane is allowed to swell in water.At the lower resin contents the weight swelling is lower and the density is higher than would be expected. This suggests that when the membranes contain a high proportion of polyethylene complete swelling of the resin is prevented. 0 2 5 5 0 7 5 100. Resin c o n t e n t b y v o l u m e ( % I FIG. 2.-Relationship between density and resin content of heterogeneous membranes, (a) expected (b) observed. These effects are likely to lead to considerable difficuIty in the detailed inter-pretation of results obtained with heterogeneous membranes and it will probably be necessary to interpret their electrochemical behaviour in terms of a model similar to that described in the paper by Spiegler Yoest and Wyllie.Dr. J. E. Salmon (Battersea Polytechnic London) (communicated) In a reply to my comment on the papers by Bergsma and Staverman and by Scatchard and Hemerich Prof. Scatchard suggested that since the porous plug described in the paper by Spiegler e f al. behaves like a membrane in some respects differences in behaviour between heterogeneous membranes which he likens to the porous plug and homogeneous membranes are not to be expected. Reference to the left diagram of fig. 2 in this paper shows however that there is little similarity between the heterogeneous membranes and porous plugs. The shaded region in this diagram (fig. 2) would for a heterogeneous membrane correspond to the hydro-phobic non-conducting matrix. Hence the alternative paths of conduction through bulk liquid with normal properties (of dielectric constant etc.) are not available in the heterogeneous membrane for which as I pointed out earlier electrical conduction between the beads is through films which are likely to have abnormal properties.Thus although the porous plug resembles the heterogeneous mem-brane in being " leaky " in other respects it is probably more like a " homogeneous " membrane. It still seems to me very doubtful if it is correct to assume that the behaviour of heterogeneous membranes is similar to that of " homogeneous " ones. Indeed the comments of Prof. Gregor Dr. Tye and others (in discussion) suggest that important differences in properties have already been observed GENERAL DISCUSSION 21 1 Dr. G. Scatchard (M.I. T. Cambridge Mass.) (communicated) When I said that the porous plug serves as an approximate model of a heterogeneous mem-brane and that there is no membrane which is not somewhat heterogeneous I was not using the term “ heterogeneous membrane ” in the sense of Dr.Salmon as a membrane with a non-conducting matrix but as what I will hereafter call a “ non-uniform membrane ”. Non-uniformity means a variation in “ pore size ” charge density etc. within the conducting region if the membrane is heterogeneous. I believe that non-uniformity is much more important than heterogeneity and that a heterogeneous membrane may be very uniform or a homogeneous membrane may be very non-uniform. If all the shaded area in fig 2 were non-conducting matrix the plug would represent a very uniform heterogeneous membrane.The original high pressure membranes of Wyllie and Patnode are probably of this type. If the matrix does not fill all the shaded area leaving conducting solution regions at the surfaces of the beads these regions will behave like large pores or cracks in a homogeneous membrane. For either one the model has to be modified to make the properties of the conducting solution different from that of the external solution. Although the mixed path (1) passes through a series of Donnan equilibria, they alternate in sense and the concentrations are so little different between two adjacent ones that all but the first and last are nearly cancelled out. Many of the properties of a very non-uniform membrane average out to appear much like those of a uniform membrane if the regions of non-uniformity are small relative to the thickness of the membrane.Dr. R. Schlogl (Guttingen) said The discussions on porous plugs and similarly constructed membranes are of particular interest to me as Herr Koschel 1 from our research group has recently completed physical measurements on ion exchangers of phenolsulphonic resins from which it is evident that even these optical clear materials possess an inhomogeneous granular structure. This conclusion follows both from recordings of stress-strain diagrams and from light-scattering measurements. According to these investigations the denser granular regions must in any case be smaller than about 10-5 cm i.e. roughly of the order of magnitude of normal colloids. Each of these dense regions is surrounded by electrical double layers and separated from the others by channels of lower density and lower membrane charge.This agrees well with the view put forward by Spiegler et a/. that even membranes which are apparently homogeneous show characteristics of porous plugs. Mr. W. D. Stein (King’s College London) said I should like to consider to what extent the porous plug system of Dr. Wyllie and Dr. Spiegler can be considered as a model for the membrane of the red blood cell. It is well known that the red cell manifests a high permeability towards certain anions e.g. chloride and bicarbonate and a far lower permeability (of the order of 104 lower) towards cations. Hence as a first approximation the red cell membrane may perhaps be regarded as a positively-charged ion-exchange membrane with a slight leakiness towards cations.In the first place it may be possible to compare the behaviour of the red cell membrane with that of cationic ion-exchange membranes of different charge density and containing different types of charged ions. In this way it may be possible to estimate the number and types of charged groups present in the red cell membrane and to compare this with the known molecular architecture of the membrane. Thus, insight into the nature of the cell membrane may be gained as well as possible confirmation of the cation-exchange model. Second studies on permselective membranes show that the selectivity between ions of opposite charge of such systems decreases with increasing concentrations of the bathing ions.It would be of interest to study the selectivity of cell membranes at varying concentrations of 1 publication being prepared. Several possibilities arise from this viewpoint 212 GENERAL DISCUSSION bathing electrolyte since such a study may confirm the proposed model. Finally, since the cations are here considered to be leaking through the ion-exchange membrane any selectivity between cations that the cell membrane manifests should be considered as a selectivity of leakiness rather than the conventional selectivity between readily permeating ions. Hence better models for cell membranes may be developed if the differential leakiness of synthetic ion-exchange membranes is considered rather than their differential Permeability. It is likely however, that such a model is far too simple and that we should regard the cell membrane, as far as its ion permeability is concerned as a mosaic of cationic and anionic permselective membranes.Dr. G. A. H. Elton (Battersea Polytechnic London) (communicated) The values of plug potentials calculated by Spiegler Yoest and Wyllie show greater deviations from the observed values at low concentrations than they do at high concentrations; this fact is contrary to the authors’ expectations. It seems to me that the deviations are due to the fact that it was assumed implicitly in deriving eqn. (21) that KR is a constant independent of uW. This seems unlikely as the specific conductance of an ion-exchange resin is usually a function of the activity of the solution with which it is in contact.It would appear likely therefore, that the value of KR will be 3.0 x 10-2 ohm-1 cm-1 only at the isoconductance point where the mean ion activity is 0.24 and not as the authors have assumed, over the whole activity range. It is seen from the authors’ table 1 that the difference between the observed and calculated potentials is within experimental error for the activity range 0.1 5 to 0.45 (which includes the isoconductance point) and also for the higher range 0.45 to 1-35. Although KR may not be 3.0 x 10-2 ohm-1 cm-1 in the latter range the error in potential introduced is small as most of the current is carried by the solution (element 3 in fig. 2 ~ ) . For moderately low activities (below the isoconductance point) errors in K~ become more important since an appreciable fraction of the current is carried by the resin.Finally at very low activities where uW becomes very small the plug potential approaches that of an ideally cation-permeable membrane; the actual value of KR then becomes unimportant so that the difference between the observed and calculated potentials should decrease again. These conclusions are confirmed by the results given in the authors’ table 1, which show that for activities below the isoconductance point the difference be-tween the observed and calculated plug potentials increases to a maximum and then falls again as very low activities are reached. To obtain agreement between the observed and calculated potentials it would be necessary to use values of K~ which decrease as K~ decreases although this might make the integration of eqn.(16) very diffcult. Although the experimental values of KO shown in fig. 3 agree with the line obtained by a calculation based on the assumption that KR is constant this does not justify the assumption as the equation used in the calculation (eqn. (2)) contains thee independently adjustable parameters while the form of the equation ensures that the line must pass through the isoconductance point. In order to interpret fully the data on plug conductance and plug potentials it will be necessary to know K~ as a function of K ~ . The required relationship could be determined experimentally e.g. by a method similar to that of Despic and Hills,l or might perhaps be obtainable from the existing values of KO and K ~ if suitable assumptions are made.For example it should be possible (except perhaps for very low values of K ~ ) to neglect the contribution to KO from element 2 ( fig. 2B) in view of the very low area of contact of the resin particles (actually equal to zero for perfect spheres). To do this b is set equal to zero so that only two independent constants (viz. c and d ) characteristic of the plug have to be determined. From eqn. (2), it is seen that c is equal to the limiting value to which the ratio K O / K ~ tends at high 1 DespiC and Hills this Discussion GENERAL DISCUSSION 21 3 values of K ~ . The constants c and d are related in a way which depends on the tortuosity factors for elements 1 and 3 (fig. 2 ~ ) so that d may be determined from c if the geometry of the plug packing is known (e.g.for close-packed spheres). Hence eqn. (2) can be used with b = 0 to determine KR as a function of K~ (and hence of activity in the solution) using the experimental values of KO shown in Dr. K. S. Spiegler (Pittsburgh) (cornrnunicated) In reply to Dr. Salmon in-asmuch as plugs of ion exchange resins have appreciable conductance even when they are immersed in distilled water (fig. 3 and ref. (5) (18) and (19) of our paper) it must be assumed that counter-ions alone can migrate from one bead to another at the point of contact and that the presence of mobile co-ions is not necessary to effect electrical conductance in this case. This mechanism of migration is also borne out by the phenomenon of " contact exchange " ; viz. the relatively rapid exchange of counterions between solid particles of an ion-exchange resin when the latter are stirred together in distilled water.It is believed that the small amounts of hydrogen and hydroxyl ions in distilled water play no important part in this transport. Ing. J. Straub (Utrecht) said Much work has also been done in the Nether-lands on transport numbers of ions in membranes in connection with the electro-dialysis of brackish water. These numbers are ratios of mobilities. Absolute numbers are given by experiments in which only one ion permeates. This can be effected by placing electrodes specific to the particular ion in front and behind the membrane and passing a constant direct current through the system. When a steady state has been reached only the specific ion moves and its concentration difference is a measure of its mobility in the membrane.Complications arise, if the concentrations are not sufficiently low. Such complications however, caused by lower activities or complex building are in themselves interesting in connection with specific phenomena occurring at membranes in living organisms. 1 Dr. F. Helfferich (Cuttingen) said As an explanation for the decrease in efficiency with decreasing current density encountered when current density is low Kressman and Tye suggest a " concentration diffusion " of NaCl across the membrane according to the equation (1) Eqn. (1) gives a linear relation between the diffusion flux QD and the concentration difference (Cl - C2) between the two solutions which is not obtained from the corresponding equations derived by Mackie and Meares,2 and Manecke and Heller.3 There are two possible mechanisms for electrolyte diffusion across a charged membrane.Mackie and Manecke deal with a single phase (" homo-geneous ") membrane in which the diffusion must occur through the resin itself; the rate is governed chiefly by the diffusion constant of the anion and the con-centration gradient within the membrane and should decrease faster than (C1- C,) with decreasing C1. For " heterogeneous " membranes consisting of resin par-ticles embedded in an inert binder an alternative mechanism is a diffusion which takes place through pockets of solution between resin and binder being thus unobstructed by fixed charges. The latter mechanism which is evidently assumed by the authors leads to a linear relationship as in eqn.(1). Actually both mechanisms should be effective in a " heterogeneous " membrane but the con-stancy of the quantity D (as seen from the linear plot in fig. 7) indicates that the second prevails in the membranes used by the authors. It is suggested however, that the quantity D be called a permeability constant rather than a diffusion constant the latter being defined conventionally by an equation similar to (1) but containing the fraction of area available for diffusion and a tortuosity factor. fig. 3. Q D = DA(C1 - C ~ ) / S . 1 Straub Chem. Weekblad. 1941 47 1041 ; 1956 52 in press. 2 Mackie and Meares Pruc. Roy. SOC. A 1955 232 510. 3 Manecke and Heller this discussion 214 GENERAL DISCUSSION Prof.Karl Sollner (Bethesda Maryland U.S.A.) said The conclusions of the paper by Hutchings and Williams seem to me to go too far. I refer to the state-ment " The study of both equilibrium potentials and the rate at which they are established suggests that the present membrane electrodes have little to recommend them for quantitative use ". While I certainly do not want to contend this con-clusion as far as it applies to the membrane electrodes with which the authors have worked I feel that no such sweeping statement applies to the various types of permselective collodion matrix membranes that were developed in our laboratory. If used judiciously these membranes are rather useful as membrane electrodes. 1 Of course I must also refer to the excellent quantitative pioneering work by Marshall and collaborators which was carried out with clay membranes,:! and Dr.Wyllie I hoped would make some remarks about his experience with membrane electrodes. In particular I should like to draw your attention to a fairly detailed study by Dr. Gregor and myself in which we have evaluated many points of interest in the practical use of membrane electrodes.3 The usefulness of these membranes as membrane electrodes seems to me evident also from such papers as those by Carr Johnson and Kolthoff,4 Chandler and McBaine,s Snell,6 and particularly the extensive studies by Carr and collaborators on the binding of ions by protein,7 and also from the recent similar work of Lewis.8 The ionic selectivity of the permselective collodion matrix membranes is ex-tremely high-with the most recent types of the order of 10,000 1 to 50,000 1 in 0-01 N KCl solution and 500 1 to more than 1500 1 in 0.1 N KCl solution.9 Their water permeability is so low as to cause seemingly no complications which would not be well within the range of normal analytical accuracy.The problem of gross leakage of bulk solution does not arise with the test-tube-shaped mem-branes which we use ; likewise contamination of the experimental solutions with material released by the membrane does not occur because of the rather low water content and the low exchange capacity of our membranes-about 1 p-equiv.lcm2. With properly prepared membranes final stable concentration potentials (at least with univalent ions) are obtained regularly within a few minutes in many instances virtually instantaneously.That these potentials very closely approach the theoretically possible value over wide ranges of concentration was shown in numerous papers. The current limitation of the ready applicability of permselective collodion matrix membranes as membrane electrodes aside from those inherent in any such electrometric measurements,3 lies in our inadequate knowledge of their behaviour with divalent polyvalent or very large ions. Nevertheless Carr has used such membranes extensively with good success in the study of the binding of alkali earth metal ions and so also did Lewis.* 1 Sollner J . Amer. Chem. SOC. 1943 65 2260. 2 Marshall J. Physic. Chem. 1939 43 1155 ; 1944 48 67. Marshall and Bergman, J.Amer. Chem. Sac. 1941 63 191 1 ; 1942 64 1814 ; J. Physic. Chem. 1942 46, 52 325. Marshall and Ayres J. Amer. Chem. SOC. 1948 70 1797 et seq. 3 Gregor and Sollner J. Physic. Chem. 1954 58 409. 4 Cam Johnson and Kolthoff J. Physic. Chem. 1947,51,636. 5 Chandler and McBaine J . Physic. Chem. 1949 53 930. 6 Snell Electrochemistry in Biology and Medicine ed. Shedlovsky (John Wiley and Sons Inc. New York Chapman and Hall Ltd. London 1955) p. 284. 7 Carr and Topol J. Physic. Chem. 1950 54 176. Carr Arch. Biochem. Biophys., 1952 40 286; 1953 43 147; 1953 46 417 424. Electrochemistry in Biology and Medicine ed. Shedlovsky (John Wiley and Sons Inc. New York; Chapman and Hall Ltd. London 1955) p. 266. 8 Lewis Ph.D. Thesis (Georgetown University Washington D.C.1955). 9 Neihof J. Physic. Chem. 1954 58 916. Gottlieb Neihof and Sollner J. Physic. Chem (Colloid Symposium Issue 1956) in press GENERAL DISCUSSION 21 5 I think that commercial-type ion-exchanger membranes (which after all are prepared in general for different purposes to fulfil different requirements) are not nearly as suitable as membrane electrodes as are the permselective collodion matrix membranes. Anyone interested in the solution of problems which might be solved by means of membrane electrodes should explore the usefulness of this latter type of membranes. Incidentally the word “ permselective ” which we coined quite some years ago,l has been used by now in a goodly number of papers ; it is not trade marked ; maybe we do not need the very similar term “ permiselective ”.Dr. T. R. E. Kressman (The Permutit Co. Ltd. London) (partly communicated) : I would like to correct two errors made by Hutchings and Williams in their interpretation of some statements in previous papers of Dr. Kitchener and myself. In their experimental section they refer (their ref. (6)) to our paper2 and state that we observed slow equilibrations between ion exchange granules and bivalent ions. A few lines below fig. 2 they quote the same reference as providing evidence for the weak affinity of sulphonic resins for Mg2+ as compared with H+. In fact both these effects were observed with a resin specially prepared to contain very few sulphonic groups which were consequently spaced widely apart. With normal resins including a sulphonated polystyrene (of composition virtually identical to the membrane used by Hutchings and Williams) rapid reaction and high affinity were observed with bivalent ions.A few lines above their fig. 3 they quote our same paper as giving the order of affinity Ba2+ > K+ > Na+ > Mg2+ in fact the order we observed was Ba2+ > Mg2+ > K+ > Na+ in the concentrations relevant to Hutchings and Williams’ work. All the evidence of our work is that Mg2+ behaves quite normally both as regards affinity and rate of attainment of equilibrium and does not support the apparent abnormality observed by Hutchings and Williams. Hutchings and Williams attempt to explain the abnormalities on the basis of the large size of the magnesium ion. However they state that the diethyl-ammonium ion behaves like the potassium ion (i.e.normally) yet the diethyl-ammonium ion is considerably larger than Mg2+ its major diameter 4 being 7.2A. Consequently their explanation does not appear to be valid. The ab-normal behaviour might be due to the unusual manner in which they have used the membrane viz. soaked with 0.1 N metal chloride solution which must inevitably diffuse out into the ambient electrolyte solutions and so affect the membrane potential. Hutchings and Williams remark upon the peculiar shape of curve I11 in their fig. 3. This is most probably due to the fact that the potential was measured with the membrane in the diethylammonium form and immersed in KC1 solution. Thus they had the system referred to by Scatchard and Helfferich in their paper as an “ abnormal cell ” whose potential is strongly dependent upon stirring among other factors.The shapes of the curves I I1 and IV are probably also influenced by this factor. I agree with Dr. Sollner that Hutchings and Williams are not justified from the results of their work in stating that “ the present membrane electrodes have little to recommend them for quantitative use ”. I believe their experimental technique is responsible for their disappointing results since other workers using membranes of this type and more orthodox techniques have obtained more satisfactory results. Dr. N. Krishnaswamy (India) said According to Dr. D. Hutchings and Dr. R. J. P. Williams there is a discrepancy noted for the membranes in the sodium magnesium forms when their equilibrium potentials and the rate of attain-ment of equilibrium are considered.Taking into consideration ionic size they This was supported by other work.3 1 Carr and Sollner J. Gen. Physiol. 1944 28 119. 2 J. Chem. SOC. 1949 1201. 3 Faraday SOC. Discussions 1949,7 90. 4 Kressman and Kitchener J. Chem. SOC. 1949 1209 216 GENERAL DISCUSSION studied a membrane with roseocobaltic ion comparable to the hydrated mag-nesium ion. They find that while the magnesium form of the membrane attained equilibrium quickly the membrane in the roseocobaltic form did not. This may be due to the inability of the potassium ion from the solution to displace the com-plex ion while it can easily displace sodium or magnesium ions. Working with salts of different valency an " abnormal cell " is set up as explained by Prof.Scatchard and Helfferich. Experiments with membranes of different porosity will help in explaining the influence of ionic size of the bound ions (simple and complex ions). Fig. 1 and 2 of the authors show the relationship between the membrane potential and ratio of the activity of potassium chloride on either side of the membrane. The larger deviations obtained with barium chloride are explained on the basis that the chloride ion is carrying part of the current perhaps as BaClf. It has been shown already 1 that cation-exchange membranes in different forms (i.e. with different bound cations) absorb different quantities of chloride ion, Thus for the same external concentration the barium form of the membrane absorbs more chloride ions than when it is in the lithium or sodium forms.In the alkali metal series the uptake is found to be in the order Cs > Rb > K > NH4 > Na > Li and in the alkaline earth group the order is Ba > Sr > Ca > Mg. An explanation for this difference in uptake in terms of the hydrated ionic radius of the bound cations has been provided.2 This study was conducted to predict how far the ideal permselective property of the membrane would be affected by different bound cations. The results obtained by Hutchings and Williams have confirmed our findings. Dr. F. Helfferich (G~ittingen) said The conclusions of Hutchings and Williams concerning the analytical application of ion exchange membranes seem somewhat too pessimistic when compared with numerous publications in which more encouraging results have been reported.Reference may be made to Schindewolf and Bonhoeffer,3 who discuss in detail the advantages and limitations of this method. The deviations found by the authors could be due at least partly to (i) the use of membranes primarily designed for other purposes (ii) the intro-duction of the liquid junction not necessary for potential measurements and (iii) the equilibration with 0.1 N solution previous to measurement. In the derivation of the theoretical potential values two assumptions are made equi-librium between the solutions and the adjacent membrane surfaces and steady state within the membrane. Generally this stage is reached faster and with less concentration change in the solutions when the membrane is equilibrated previous to measurement with a mixture of both solutions or when a twofold membrane sandwich is used each membrane being equilibrated previously with the solution with which it is in contact during the measurement.Dr. R. J. P. Williams (Oxford) said I am not sure that I understand the remark of Dr. Helfferich that the membranes we have studied were primarily designed for other purposes. Introducing these particular membranes Kressman 4 claimed that they were useful for the very purposes we had in mind during the experiments. The membranes were obtained from Dr. Kressman. I believe that the second point made by Dr. Helfferich is also misleading. The cell we described has three electrodes. It is possible to measure three poten-tials and one of these the membrane potential from direct measurement does not include a liquid junction.It is equivalent to a proper sum of the other two possible potentials. The use of the concentration cell potential which we measured also and which does include a liquid junction was that it enabled us to study any changes in the concentration of the solution bathing the membrane at the 1 Krishnaswamy J . Sci. Ind. Res. (India) By 1954 13 722 ; J . Physic Cliem. 1955 59 2 Krishnaswamy communicated for publication. 3 2. Elektrochem. 1953 57 216. 187 ; Current Sci. 1955 24 234. 4 Nature 1952 170 150 GENERAL DISCUSSION 217 same time as we measured the membrane potential. We found this precaution advisable although it is unusual. In all measurements we read the values of the three potentials in order to check the electrodes.The third point also raised by Dr. Kressman concerns the preparation of the membranes. Very little has been said on this topic in the discussion and yet I believe it is an important factor in the.study of membranes if high accuracy and reproducibility of potentials is wanted. We did not require to understand the origin of the potentials we obtained. We wished to have an analytical method. We could not prepare membranes by bathing them in very strong salt solutions for this leads to the absorption of neutral salt. Our method which appears to be very similar to that of many others was to treat the membranes with 0.1 molar salt until the washings were free from hydrogen ions. With the alkali metal cations this leads to the establishment of potentials very little different from those observed by many others but the method was still not analytically satisfactory.Dr. Helfferich is correct when he points out that it is advantageous to treat the membrane with mixtures of the salts under study but even in this case one side of a membrane in a bi-ionic cell will come to equilibrium before the other. It is easy to demonstrate slow rates of establishment of potentials even under the very rapid stirring we used throughout our measurements. I think that this also answers another of Dr. Kressman’s questions. If a membrane does not establish a potential rapidly it is unlikely to be of great practical value for the type of study we had in mind. I feel that there is not such a difference between our statements and those of Dr.Kressman as he would suggest. First we do not find slow equilibrium with magnesium ions. Secondly we make no comment on the absolute affinity of the resin for magnesium but we suggested that it is bound weakly (as compared with other cations) as an explanation of the peculiarities of the magnesium mem-branes. We used the reference to Dr. Kressman’s work as an illustration of parallel findings. Thirdly there is the point about the relative affinity for mag-nesium and sodium ions. The equilibrium constants which Dr. Kressman quotes in his paper were used as measures of affinity of ions for his exchangers. There is an arbitrary character in such a comparison but it does give the order we give. It must be remembered that we did not make a thorough study of exchange rates under different concentration conditions ; we only wished to know if a potential was established instantaneously.I do not understand Dr. Kressman’s remark about the concentration conditions relevant to our work for the concentration of magnesium ion in the membrane and in the solution were not measured by us. In the discussion of size factors and their effect on the uptake of cations Dr. Kressman has left out the fact that magnesium is divalent and diethyl ammonium ion univalent. It is readily shown that for ions of the same size the one of higher charge comes into equilibrium more slowly. This is made clear by the study with the cobaltic ion. Finally we have no comment to make upon the suitability of Dr.Sollner’s membranes. We have had no chance of studying them and they have many properties different from those of the membranes with which Dr. Kressman supplied us. We are quite convinced however that the latter membranes are not suitable for an accurate determination of activities of ions in solution. The data we have plotted in fig. 1 of our paper are very like those obtained by other workers in this field and are unsatisfactory. The data in fig. 3 were obtained under conditions of rapid stirring and they can be compared with the observations quoted by Dr. Helfferich under these conditions. Prof. Dr. K. F. Bonhoeffer (Giittifzgen) said I would like to mention some experiments carried out recently by Dr. Woermann in our laboratory. Since we are interested in membranes which show selectivity with respect to different alkali metal ions D.Woermann prepared membranes from an ion exchanger described In many cases it was not 218 GENERAL DISCUSSION by Skogseid,l which adsorbs K+ in preference to Na+. This ion exchanger con-tains a group with a configuration similar to dipicrylamine a precipitating agent for K+. Woermann prepared the membranes by embedding the powdered ex-changer in polyethylene ; the weight ratio exchanger/polyethylene was 6 4. The membranes are red opaque and brittle. In these membranes the self-diffusion coefficient for diffusion of K+ with the suggestion of K+ is-smaller than that of Na+ and the activation energy larger than that of Na+ (fig. 1). These results are consistent that K+ is more firmly held by the exchanger than Na+.FIG. 1. The experimental bi-ionic potential across these membranes between 0.1 N NaCl and KC1 solutions is 20 mV the NaCl solution being positive. If only the diffusion potential within the membrane would be responsible for the total mem-brane potential the higher mobility of Na+ within the membrane would lead to a potential of the opposite sign. However the total membrane potential is the sum of this diffusion potential and the difference of the two Donnan potentials at the phase boundaries. The preference of the membrane for K+ (which is equivalent to an activity coefficient within the membrane lower for K+ than for Na+) results in a Donnan potential on the side of the KC1 solution which is con-siderably smaller than that on the other side.The sign of the experimental potential is thus explained. Potentials across these membranes were also measured between a 0.1 N KC1 solution and KC1 + NaCl mixtures total concentration 0.1 N. The results are given below. They are compared with theoretical values calculated from the equation for multi-ionic potentials 2 assuming &a/& = const. = 1.2 (obtained from self-diffusion measurements) and r N a / r K = Const. = 2.7 (estimated from equilibrium data). potential (mV) expt. calc. left side right side 5 x 10-2 N KCl 5 x 10-2 N KC1 0 0 4 3.0 5 x 10-2 , 4 x 10-2 N KCl 1 x 10-2 N NaCl 10 8-4 5 x 10-2 , 2.5 X 10-2 N KCl 2.5 x 10-2 N NaCl 18 15.1 5 x 10-2 )) 1 x 10-2 N KCl 4 x 10-2 N NaCl 5 x 10-2 , 5 x 10-2 N NaCl 20 20.8 1 A.Skogseid Thesis (Oslo 1948), 2 R. Schlogl and F. HeHerich contribution to this Discussion GENERAL DISCUSSION 219 Prof. Dr. K. F. Bonhoeffer (Giittingen) (partZy communicated) G. Richter in our laboratory has recently succeeded in preparing membranes which behave very differently with respect to chlorine and bromine ions. The difference is so obvious that it may be observed without the aid of any measuring device. When the membranes contain chlorine ions they are voluminous soft, mechanically unstable and have a high water content and when they contain bromine ions they are dense rigid and stable and have only a small water content. Richter made use of the fact that soaps or generally speaking, amphipatic substances show a 6o remarkable power of discrimi- 2o H20 nation for similar ions.For example the different solubility of the ordinary potassium and 'O sodium soaps is very well known. The simplest way to prepare membranes containing amphi- 2o patic substances is to equilibrate a loosely cross-linked ion ex-changer with soap solution. For example we prepare a cation ex-acid with a small amount of P H 100 " 2 0 changer by polymerizing acrylic 2 . 0 4 . 0 6.0 divinylbenzene SO that the Pores FIG. 1.-The dependence on pH of water content of the exchanger are large enough of polyacrylic acid exchanger in a solution of to take up soap molecules such cetyltrimethylammonium chloride (CTAC) and as cetyltrimethylammonium cetyltrimethylammonium bromide (CTAB) resp. chloride or bromide.Now if we take this cation exchanger in the sodium form and immerse it in a solution of chlorine or bromine soap the sodium cations are exchanged by soap cations. In addition to these more soap molecules are adsorbed due to the van der Waals forces exerted by the soap ions already taken up by the exchanger and by the exchanger network itself. These newly adsorbed soap molecules carry halide anions with them for reasons of electroneutrality. As the soap cations are big and immobile compared with these anions the former cation exchanger is trans-formed into an anion exchanger. The new character of the exchanger can be shown by a reversal of the membrane potential between two alkali halide solutions of different concentration. This new anion-exchanger shows the above-mentioned discrimination between chlorine and bromine ions.It is intimately connected with the critical pheno-menon of micelle formation in soap solution. We have reason to assume that there exists in the interior of the exchanger a sort of critical concentration for the formation of soap micelles which is different from that in the external solution and lower for chlorine soap than for bromine soap. We may vary the soap concentration in the exchanger by varying the concentration of fixed charges, which in our case are carboxyl groups; this is easily done by varying the pH of the solution. Thus by altering the pH we alter the soap concentration in the exchanger. We believe that the two above-mentioned membrane types the one with high and the other with low water content differ from each other in that the mem-brane with low water content has shrunk due to the formation of soap micelles.I should like to show the results of some experiments of Richter in which an original cationic exchanger on a base of polyacrylic acid is transformed by 220 GENERAL DISCUSSION cationic soap namely cetyltrimethylammonium halide into an anionic exchanger. In the range of pH = 3 to pH = 4.5 this new anionic exchanger discriminates very remarkably between bromine and chlorine ions. The diagram shows the abrupt change in the water content at a critical pH, that is at a critical soap concentration different and characteristic for each halide ion. Here the water content changes from about 90 % to 25 % and we know other systems where the change is still greater.I need not mention that the change of water content means a change of all properties of permeability and conductivity, which will now be investigated. As the soap is firmly held by the exchanger the discrimination is found not only when the exchanger is immersed in soap solutions but also in salt solutions, provided these contain a small amount of soap. We believe that it is possible to synthesize corresponding membranes which behave differently with respect to sodium and potassium ions. Research is being made along these lines. Prof. H. Thiele (Kid University) (communicated) An important factor seems to be structure since artificial membranes are made up of disordered particles, but natural membranes have well-ordered particles in a particular type of fine structure as can be shown by electron micrographs.Gels with ordered particles could be built up by diffusion of gegenions into a solution of polyelectrolytes. These ionotropic gels represent a synthetic micellar structure and behave like gels in tissues. Since membranes are plate-shaped gels, this gives a method of preparing artificial membranes with well-ordered particles. A further step has been made by preparing gels and membranes with pores and capillary tubes of uniform size and shape. The gel formation formally follows the equation : 2 Na alginate + CuC12 $ Cu (a1ginate)z + 2 NaCl + water first phase second phase. polyelectrolyte + ions $ gel ionotrope + 2 reaction product. Na alginate and CuC12 yield the ionotropic gel or membrane-this gel now forms a special phase. The NaCl and water of dehydration form the second phase. The two phases are separated from another by a demixing of droplets. The water of dehydration arises from the transition from sol to gel. Now in the growing gel the second phase in the shape of droplets gives rise to a structure of many fine round tubes lying parallel to each other starting in a zone near the ions and ending in the sol. The gel forms the walls of the tubes and the second reaction product gels; the second phase as droplets gives rise to a structure of many fine round tubes lying parallel to each other starting in a zone near the ions and ending in the sol. The gel forms the walls of the tubes the second reaction product with the water of dehydration form the contents of the capillary tubes as shown in fig. 1 and 2. If our explanation is right then the pore size must depend on the concentra-tion of the second reaction product NaCl -t water. ' Indeed we found a strong de-pendence the diameter growing with increasing concentration of NaCl. The size of the pores depends on the gegenions giving the series C1 < Br < NO3 < SO4 < formate < acetate the other ions not being so important. Non-electrolytes and detergents have no effect on the pore size. H-ions and non-electrolytes do not yield pores at all. The diameter was found to vary between about 3 and 300 micron depending on the concentration of the polyelectrolyte. One can get tubes with a length varying from a few microns to 10 rnm. The membranes can be obtained simply by means of a Graham dialyser FIG. 1. FIG. 2. Capillary tubes of uniform size and shape by a droplet demixing from diffusing counterions in a polyelectrolyte during gel formation FIG. 1.-In directions of the diffusing FIG. 2.-Vertical section showing the ions x 25. uniform diameter and the parallelism, of the many thin tubes x 25. [To face page 220