GENERAL DISCUSSION Dr. L. M. Barclay (B.P. Ltd. Penarth) and Dr. R. H. Ottewill (University of Bristol) (communicated) In our paper we have reported mzasurements of the force of interaction between montmorillonite plates as a function of electrolyte concentra- tion and the distance of separation between the plate surfaces. The other model which is of interest theoretically is that for interaction between spherical particles. For this case the curve of potential energy Vagainst distance Ho of surface separation has the general form shown in fig. la. Three features of the curve are of particular interest the secondary minimum S the point of inflexion I and the primary maximum M. of inter- action between spherical particles leads to a curve of force (-aY/dH,) against Ho. This has the form shown in fig.lb and it is clear that the maximum force occurs at Differentiation of the appropriate expressions for potential energy I I I I FIG. 1.-Potential energy (a) and force (6) againt distance for interaction between two spherical particles (schematic). the distance at which the point of inflexion occurs on the potential energy curve; at the primary maximum and the secondary minimum the force is zero. Thus the interaction between spherical particles should lead experimentally to a force against distance curve showing these features the distances and magnitudes of the force being dependent on particle size and ionic strength. An extensive series of measure- ments have been made using the apparatus described in our paper with monodisperse E. J. W. Verwey and J. Th. G. Overbeek Theory of Stability of Lyophobic Colloids (Elsevier Amsterdam 1948).164 M GENERAL DISCUSSION 165 5 0 - n 6 8 4 0 - E u W VJ k 5 3 0 - 2 g 2 0 - .I d .I 0 10 - distance between surface of spheres in 8 diameter of particle = 1845 A. FIG. 2.-Pressure against distance between particle surfaces. Polystyrene latex at pH 10 and 25'C ; 100*0 volume % of latex FIG. 3.-Pressure against volume concentration of polystyrene latex at 25°C ; 0 1760 8 diam. ; 0,lO 990 A diam. 166 GENERAL DISCUSSION latex preparations as the disperse system. The results obtained with a latex having a modal diameter of 1845 A are shown in fig. 2. It is clear from this curve that very little pressure is exerted by the particles until the distance of surface separation is about 320A. The pressure then rises with decreasing distance and appears to reach a maximum at a separation distance of ca.230A. The distance axis on fig. 2 has been calculated on the basis of hexagonal close-packing between spherical particles. Although this assumption is supported by electron microscope examinations of highly compressed then dried latex dispersions it is not yet certain whether a com- pletely ordered hexagonal close-packed system is maintained at the various volume concentrations or whether ordered domains are formed at the lower pressures ; the packing is now being examined by optical methods. The effect of a change in diameter of the particles from 1760 to 10 990A is shown in fig. 3. The smaller particle size shows a gradual increase of pressure until a volume concentration of 64 % is reached ; then the pressure rises rapidly.The larger particle size material however shows a pressure rise at ca. 60 % volume concentration which is almost perpendicular to the volume concentration axis. The potential-energy curves for the smaller particle size latex at this ionic strength do not show a secondary minimum of any significance whereas those for the larger particles do. It therefore seems highly probable that the volume concentration at which the pressure starts to rise rapidly with distance could coincide with the ordering of the latex particles into a secondary minimum structure. From the theoretical calculations the force of repulsion rises very rapidly for particles with diameters of lO,OOOA whereas the rise for particles with diameters of the order of 1,000 A is gradual.The curves obtained bear a close resemblance to those expected theoretically. More quantitative conclusions can be reached for dispersions of spherically shaped particles once the distance of surface separation has been unequivocably established. Prof. J. Th. G. Overbeek (University of Utrecht) said One expects the best fit between theory and experiments for larger distances between the plates. According to fig. 5 (and fig. 4) of the paper by Ottewill et al. the calculated repulsion is larger than the one found in the experiments. The fit might be improved by introducing the Stern-correction which would lower the calculated repulsion. Did he try this and does it lead to reasonable values for the capacity of the Stern layer? Dr. R. H. Ottewill (University of Bristol) said In reply to Overbeek we have made some calculations of the force of interaction including an allowance for the Stern layer and this does improve the fit at long distances.Unfortunately this procedure does involve a somewhat arbitrary choice of the Stern adsorption potential. The capacity obtained for the inner layer is about 12 pF. Prof. G. M. Bell (Chelsea College) and Dr. S. Levine (Manchester University) said These comments on the work of Barclay and Ottewill may also have some relevance to other papers. Denoting the electrical van der Waals' and structural terms in the force per unit area between plane parallel surfaces by F' Fw and Fs respectively we agree with Barclay and Ottewill that Ps is not likely to be significant at separations of more than 50A and think that this limit could be considerably lower.Existing theoretical values of &+FW are far from exact and differences between these values and measured pressures are not reliable estimates of Fs. The remainder of our remarks will be concerned with F'. The DLVO evaluation of FE excludes the ionic environment (e.g. discreteness- of-charge) effects which depend on the difference between the actual situation in the GENERAL DISCUSSION 167 vicinity of an ion and the mean field situation. These include the image effect due to polarization of the dielectric interface by the ion field and the self-atmosphere effect which for a finite ion includes the “ cavity ” effect due to the displacement of mean charge by the ionic volume. The physical meaning of these omissions can be appreciated from the fact that for an uncharged air/electrolyte interface the DLVO theory would give uniform ionic concentrations and hence zero excess surface tension.Unfortunately the introduction of ionic environment and other corrections con- siderably complicates the DLVO theory and for two interacting charged interfaces adequate numerical values of FE are not so far available although calculations have been made by Sanfeld and others. Some idea as to possible effects may be obtained from the authors’ work on the force between uncharged plates in an electrolyte medium. This is based on a model like that of Onsager and Sarnara~,~ but with two interfaces instead of one and also uses local values of the Debye-Huckel constant K in the screening terms rather than the bulk value. It is found that where PI is the ideal osmotic pressure term while P2 and P3 are due directly to image-self-atmosphere effects.With a point-ion model the form of these terms is unaltered for symmetrically charged plates but the numerical values alter owing to the changed ionic concentrations. For charged or uncharged plates at separations 2h large compared with K-’ the terms P +P3 give an h-3 law repulsion. However the equivalent Hamaker constant is only 3 x 10-14 erg so that this repulsion will be cancelled by the van der Waals attraction unless retardation is appreciable. As pointed out by P e t h i ~ a ~ Pi is attractive for uncharged plates owing to the depletion of ionic concentration between the plates but for charged plates at sufficiently high potential it is repulsive as in DLVO theory where FE = P I .The sum P2+P3 is always repulsive and may account for the excess repulsion found by Barclay and Ottewill for 0.1 M electrolyte and at some separations for 0.0001 M electrolyte. Caution is necessary as to the overall effect since ionic depletion between the plates due to imaging will reduce the magnitude of the repulsive term P I . In a complete theory ionic volume and polarization effects would also have to be considered 1* 5 9 as well as the effect of the thinness of the plates on image potentials. The standard DLVO theory of F E assumes a “ reservoir ” large enough for the chemical potential of each species to remain effectively constant as the surfaces are moved. This does not seem to be the case in Barclay and Ottewill’s experiments where in the initial state nearly all the fluid is between the plates and is then “ squeezed out ”.Another point is that both the constant potential and the constant surface charge assumptions are artificial. However the use of a realistic adsorption isotherm would give results lying between the two curves so that if the latter are close together as in the calculations for 0.0001 M electrolyte the error is likely to be small. Fw = Pi +P +P3 Dr. L. Barclay (B.P. Penarth) and Dr. R. H. Ottewill (University of Bristol) said We appreciate the points made by Bell and Levine. We agree that the assumptions of constant charge and constant potential are somewhat artificial particularly as it A. Sanfeld Thermodynamics of Charged and Polarized Layers (Wiley-Interscience London 1968). G. M. Bell and S . Levine J. Chem. Phys. 1968,49 4584.L. Onsager and N. N. T. Samaras J . Chem. Phys. 1934 2 528. B. A. Pethica Expt. Cell. Res. Suppl. 1961 8 123. G. M. Bell and S . Levine Chemical Physics ofIonic Solutions B. E. Conway and R. G. Barradas ed. (John Wiley & Sons Inc. 1966). pp. 409-461. S. Levine and G. M. Bell Disc. Faraday Soc. 1966 42,69. 168 GENERAL DISCUSSION is conceivable that the extent of adsorption in the Stern layer could be a function of the distance of separation between the plates at distances as close as those studied. Prof. H. van Olphen (Amhem Netherlands) said With regard to the paper by Barclay and Ottewill the alternative approach to swelling measurements on expanding clay systems is to allow individual flakes to swell under no constraints and to obtain the equilibrium unit layer distance from X-ray diffraction patterns.1-3 As expected from double-layer theory equilibrium distances decrease with increasing electrolyte concentration of the medium. At each equilibrium distance repulsive and attractive forces must cancel each other. However the calculated double-layer repulsion at each equilibrium distance observed appears to be considerably greater than the van der Waals attraction. If a specific adsorption potential is assumed for the inter- layer counter ions to reduce the repulsion to equal the van der Waals attraction the adsorption potential would have to vary with electrolyte concentration which is unlikely. An alternative trivial explanation of the observations is that swelling is limited by cross-linking of parallel particles by non-parallel ones. Estimates of edge-to-face linking forces of bentonite particles derived from rheological observations show that relatively few cross-links would be necessary to limit the swelling as ob~erved.~ Dr.R. H. Ottewill (University of Bristol) said The procedure suggested by van Olphen is an interesting alternative to the one that we have employed but there may be some advantages in starting with a dilute system in which the particles are well dispersed. We consider that in the first compression edge-face links are broken down. However once the system has been subjected to a pressure of ca. SOatm then most of the plates would be likely to take up a parallel arrangement. This contention appears to be supported by the fact that after the first compression the pressure can be decreased to ca. 1 atm and then recompressed to a high value several times with a high degree of reproducibility in the results.It is probable that the whole system will not be composed of parallel plates ; rather that there will be domains with a parallel arrangement of plates. Negative adsorption measurements of the chloride ion gave a value of 690 m2/g which would suggest that a high degree of dispersion into fundamental plates had occurred. The possible variation of Stern potential with electrolyte concentration could be a deficiency of the theory and it would be interesting to calculate the force of interaction with allowance for the discreteness of the charges. Moreover it is conceivable that at such close distances of approach the extent of adsorption could he a function of the distance of plate separation.Dr. B. A. Pethica (Unilever Res. Port Sunlight) said Fundamental to the arguments of the paper by Barclay and Ottewill is the question as to whether the pressures measured by their apparatus reflect the characteristics of interacting plates every- where surrounded by the fluid phase or whether there is in the cell a gel-like matrix of interacting particles equivalent to a solid structure capable of resisting mechanical deformation. The question can be settled in a variety of ways the most direct being to relate the pressure-volume data directly to the vapour adsorption isotherm in the same colloid system. Similarly the general utility of the electrostatic repulsion calculations could be illuminated by a direct Donnan calculation using the same charge density assumptions as were made in the calculations given in the paper.K. Norrish Disc. Furuday SOC. 1954 18 120. K. Norrish and J. A. Rausell-Colom Clays and Clay Minerals 1962 10 123. D. E. Andrews P. W. Schmidt and H. van Olphzn Clays and Clay Min?rmls 1967,15 311. H. van Olphen J. Colloid Sci. 1962 17 660. GENERAL DISCUSSION 169 A further thermodynamic question relates to the effect of pressure on the c.m.c. of the polyoxyethylene surfactant which was used at 7 x M. The micelle point at atmospheric pressure is quoted as 7.25 x lo-’ M in one place and 7 x lo-’ M in another. In either case the concentration in the compression experiments is close to the c.m.c. and it would be necessary to know the effects of pressure on the c.m.c. and on the adsorption for a full analysis of the pressure effects in the suspensions.Dr. Th. F. Tadros (Plant Protection Ltd. Bracknell Berks) said Does the adsorp- tion of C12E6 on montmorillonite above the CMC correspond to vertically oriented chains or does Ottewill obtain adsorption of micelles? Has he measurements of equilibrium pressure in presence of C12E6 at high salt concentrations where the double layer repulsion term tends to zero leaving VA and AG,? Dr. L. M. Barclay (B.P. Penarth) and Dr. R. H. Ottewill (University of Bristol) said The first part of Pethica’s question has essentially been covered in the reply to van Olphen. Petbca is quite correct in stating that the same results should be obtained from measurements of water vapour adsorption on montmorillonite. The comparison is however not as easy as it might seem. First as observed by many author^,^'^ the water vapour adsorption isotherms on montmorillonites depend on the source of the montmorillonite.For example i n the work of Barshad a type I1 isotherm was obtained with a sodium montmorillonite from Otay California and a type 111 isotherm with a sodium montmorillonite from Clay Spur Wyoming. The results therefore are only meaningful if obtained on exactly the same material preferably on the same batch. A second problem with comparing published work on water adsorption with our data is that the pressure measurements have been made over a range which corresponds to p/po values in the range 0.9-1.0. The published isotherms are very short of data in this region and it is well known that it is a difficult range in which to measure adsorption. Conversion of published data into pressure against distance curves does give curves resembling our own but the adsorption data are not precise or extensive enough to allow a quantitative comparison.We have not carried out any Donnan calculations. Where the effects of pressure on c.m.c. have been measured the c.m.c. increases with pressure up to 1,000 atm. I am not aware of any similar measurements with non-ionics and we cannot measure this directly in our apparatus. It was possible to analyze C1&6 however in the solution expelled into the capillary. The concentra- tion of this was that expected from the isotherm and hence we concluded that the effect of pressure on the adsorption equilibrium in the range examined was negligible. Where the effects of pressure on c.m.c have been mea~ured,~.the c.m.c. increases with pressure up to 1,000 atm. Dr. L. Barclay (B.P. Penarth) and Dr. R. H. Ottewill (University of Bristol) said In reply to Tadros the adsorption isotherm for CI2E6 on montmorillonite is an interesting one since it differs in form from those found on hydrophobic substrates such as silver iodide,6 Graphon and polystyrene.* With these materials the I. Barshad 8th Nut. Conf. Clays and Clay Minerals 1959 8,84. W. A. White 3rd Nut. Con$ Clays and Clay Minerals 1955 3 186. A. C. Zettlemoyer G. J. Young and J. J. Chessick J . Phys. Chem.. 1955 59 962. R. F. Tuddenham and A. E. Alexander J. Phys. Chem. 1962 66 1839. S. D. Hamann J. Phys. Chem. 1962 66 1359. K. G. Mathai and R. H. Ottewill Trans. Faraday SOC. 1966 62 750 759. R. H. Ottewill and T. Walker Kolloid-Z. 2.Polymere 1968 227 108. ’ J. M. Corkill J. F. Goodman and J. R. Tate Trans. Faraday SOC. 1966 62 979. 170 GENERAL DISCUSSION isotherm reaches a saturation value close to the c.ni.c. With montmorillonite adsorption continues to increase above the c.m.c. despite the fact that constant activity of the solute is normally assumed to be reached at the c.m.c. In fact a limiting adsorption value of 2.5 x mol/g is only attained at about an equilibrium concentration of 3 x On the basis of a surface area of SO0 m2/g this corresponds to an area per molecule of 53 A2. It is tempting to conclude that this corresponds to a vertically oriented layer since this value compares favourably with the figure of 55A2 found for adsorption of CI2E6 of Graphon and one of 40 A2 obtained on polystyrene where it is clear that vertically orientated monolayers are formed.on the adsorption of C12E14 who used X-ray methods to determine the distance between the sheets two steps were found one at a distance of 4.4A and the other at S.4A. The first distance corre- sponded to a single layer of surface-active agent molecules lying flat on the surface and the second to a bi-layer of molecules. This evidence appeared to indicate attachment of the ethylene oxide groups to the hydrophilic silica layers and this would argue against reorientation to form a vertically orientated layer. It is probably possible for the hydrocarbon chains to associate however and thus form dimers on the surface and this would give an area per molecule not drastically different from M CI2E6. However in the work of Schott that found.64 62 6 0 58 5 6 54 volume concentration of latex (%) FIG. 1.-Equilibrium pressure against volume concentration for a latex with an adsorbed layer of dodecylhexaoxyethylene glycol monoether (CI2Es) 0 pH 10 without added sodium chloride ; 0 pH 9.6 with 0.5 M sodium chloride. We have not measured the interaction between montmorillonite sheets with However we have carried out an and the results are given in fig. 1. adsorbed CI2E6 at high salt concentrations. experiment of this type using polystyrene latices H. Schott Kolloici-Z. 1964 199 158. L. Barclay Ph.D. Thesis (University of Bristol 1970). GENERAL DISCUSSION 171 Two curves are presented one for particles having a diameter of 1,845 A and an adsorbed layer of CI2E6 at pH 10.0 without added salt and the other in the presence of 0.5 M sodium chloride.The addition of salt enables the particles to come closer together as would be expected from the decrease of electrical repulsion but there is still a very strong repulsion and there is a considerable increase in the gradient at low pressures. The fact that the system remains a stable dispersion can be attributed to “ steric stabilization ” and this is confirmed by kinetic studies of stability. However until we have precise measurements of the distances between the spherical particles we cannot tell whether overlap of the adsorbed layers actually occurs. Dr. G. Peschel (Universitdt Wiirzburg) said With regard to the paper by Ottewill et al. the disjoining pressure between colloidal particles in disperse systems might be sensibly dependent on the diameter of the particles as some evidence shows; e.g.Jura and Harkins in applying their well-known method for determining the surface area of powders condensed water from saturated water vapour in titanium dioxide particles which had a mean diameter in the ,LI region. The obtained layer thickness is of only 5 molecular diameters which cannot be regarded as a pronounced long-range orientation effect. Zorin on the other hand carried out a similar experi- ment but using a macroscopic flat glass surface. He found layer thicknesses of about 100 molecular diameters. Therefore additional information concerning the repelling forces between the particles might be gained by a variation of the particle diameters in Ottewill’s apparatus. Are such experiments possible ? Dr. A. L. Smith (Chem.Dept. Liverpool Polytechnic) said In the paper of Vincent and Lyklema it is stated that titration experiments yield true P.Z.C. values which might therefore (by implication) be expected to differ from the isoelectric points (i.e.p.) determined electrokinetically. However the (o,,E) plots from titrations will only have a common intersection point (used to determine the P.z.c.) when there is no specific adsorption in practice at low electrolyte concentrations. Under these circumstances the P.Z.C. and i.e.p. coincide. There thus seems to be a real experi- mental discrepancy between authors revealed by table 1 not explicable by specific adsorption. It does not seem necessary to invoke the adsorption of silver nitrate ion pairs of doubtful existence in bulk solution to explain the higher differential capacities observed on the positive side of the P.Z.C.and still less to explain the asymmetry of the P.Z.C. While some specific adsorption of nitrate ions is to be expected and is indeed revealed by the small shifts of the P.Z.C. to higher pAg values in 1 mol dm-3 KN03 the fluoride ion produces differential capacities on the positive side almost as high as those in the presence of nitrates even though no shifts in P.Z.C. can be detected.2 Specific adsorption of the strongly hydrated fluoride ion is more- over not expected and it is hardly likely that the fluoride and nitrate ions would have similar tendencies to form ion-pairs with the silver ion. The higher capacities on the positive side could be at least partly due to a con- tinuation on the positive side of the rise in capacity K of the Stern layer evident from all published capacity measurements as the AgT surface becomes less negatively charged.This variation of K which cannot on the negative side be an apparent effect due to specific adsorption (of cations) since this would only make the variation larger could have its origin in water dipole re-~rientation,~ variation in the thickness Z . A. M. Zorin and N. V. Churayev KolloidZhur. 1968,30 371. J. Lyklema Trans. Farahy SOC. 1963 59,418. S. Levine G. M. Bell and A. L. Smith J . Phys. Chem. 1969,73 3534. 172 GENERAL DISCUSSION and/or effective dielectric constant of the inner layer or possibly solid-state effects. The two effects cited as giving higher total differential capacities on the positive side viz. specific adsorption of anions or higher values of K will have opposite effects on the Stern plane potential +d the first decreasing t,9d and the second increasing it.This should be reflected in the electrokinetic 5 potential. Experimental electro- phoretic mobilities of positively charged AgI are not noticeably smaller than those on the negative side at the same value of I t,bo I and while not excluding some specific adsorption of nitrate ions are certainly not consistent with adsorption of Ag+ " largely in the associatcd form as AgN03 ". Dr. B. Vincent (University of Bristol) and Prof. J. Lyklema (Wageningen) said The first point Smith makes viz. that there is a real experimental discrepancy between P.Z.C. and i.e.p. measurements is virtually a restatement of our remark at the end of the paper. However we did not imply that this difference was due to specific adsorption of one of the added ions.In fact table 1 shows that there are some specific ionic effects but these are small as compared to the difference between P.Z.C. and i.e.p. In connection with the interpretation of the high capacitances on the positive side of the P.z.c. at 20°C the capacitance in KF is definitely lower than that in KNO,,' although even in KF it is much higher than on mercury. High capacities at the positive side of the P.Z.C. have also though to a lesser extent been observed by Iwasaki and De Bruyn for Ag,S (The high capacitances found on oxidic materials such as TiOz or Fe,O have a different cause and should not be considered in this connection.) Given the fact that there seems to exist a relationship between Ag+ as the potential-determining ion and high capacitances one is almost automatically led to an interpretation in terms of specific interactions in- volving Ag+ adatoms.As moreover the high surface charge does not produce a high [-potential (it is comparable to that at the negative side as confirmed by Smith in his remark) it is logical to postulate considerable counterion adsorption in the Stern-layer as well. If on the other hand an explanation is sought in terms of factors like dipole orientation and dielectric constant variation i.e. factors that are not primarily related to the presence of Ag+-adatoms it is not clear whether high capacitances are not observed on mercury as well. It was for these reasons and others given in the paper that we drew attention primarily to typical chemical effects occurring in the Stern layer thereby not excluding other but secondary possibilities.Finally the fact that we are concerned with a trend that is typical for AgI or at least for silver salts implies at the same time that we should not make recourse to bulk phenomena (like the extent of ion-pairing in solution) to interpret our experi- mental facts because if they were due to bulk phenomena they should occur in all double layers in disagreement with established facts. but not for mercury. Dr. Th. F. Tadros (Plant Protection Ltd. Bracknell Berks) said In the paper by Vincent and Lyklema they have assumed that Ag+ adsorbs at 20°C largely in an associated form i.e. as AgN03 whereas at O'C AgN03 ion-pairs are more dis- sociated. The association constant is given by the Fuoss equation KA = (4nNa3/3000) exp (e2 JDakT) E.P. Honig Tms. Furaduy Sac. 1969,65,2248. J. Lyklema and J. Th. G . Overbeek J. Colloid Sci. 1961 16 595. I. Iwasaki and P. L. de Bruyn J. Phys. Chem. 1958,62,594 fig. 8. GENERAL DISCUSSION 173 where a is the distance of closest approach between the paired ions and the other terms have their usual meaning. They mentioned in their paper that as a result of increased hydrogen-bonded structuring from 20 to O'C D increases from 7.5 1.5 to 8.0+ 1.5. However this increase in D does not outweigh the decrease in T and the final result would be higher KA at the lower temperature contrary to their explanation. Do I understand that they are speaking in terms of structure-stabilized ion-pairs Dr. B. Vincent (Bristol University) and Prof.J. Lyklema ( Wageningen) said We agree with Tadros that a decrease in ion pairing with decreasing temperature is not what one would intuitively expect. However the experimental facts do show a definite decrease in Ag+-adsorption with decreasing temperature and neither is this trend apriori expected at least not on the basis of classical energetic or electrical considerations. It was t h s trend in conjunction with a few auxiliary considerations that led us to thmk of increased structure formation with decreasing temperature. The anomalous behaviour of the association of Agi- and NO in the Stern layer as tentatively postulated by us must be looked upon in a similar fashion it is largely due to-presumably structural-causes that are not accounted for by the Fuoss equation.In this connection the slight increase of the inner layer dielectric constant with decreasing T (fig. 7d) in our paper applies to negatively charged AgI-surfaces whereas the structure formation takes place mainly at the positive side of the P.Z.C. Dr. S. Levine (Manchester University) and Dr. A. L. Smith (Liverpool College of Technology) (communicated) The tentative explanation given by Vincent and Lyklema for their increase with temperature in the pAg of the Agl suspension at the P.Z.C. is not convincing. Recently Honig has queried the neglect by colloid chemists of the diffuse layer in the solid AgT phase due to lattice (Frenkel) defects and a further study of this problem has been made by Levine et aL3 Some of the theory in these papers seems relevant to the shift with temperature in the pAg at the P.Z.C.We use the subscripts c b and s to denote the solid phasc the (surface) phase boundary and the aqueous solution phase respectively. Then the condition of uniform electrochemical potential pAg+ of the Ag+ ion yields the relations pAg+ = p,"-2.303kTpAg = ,uz+eO$b+kT In vb = ,u,"+e,\l/,+kT In n,. Here p pg and p,O are functions of pressure and temperature; $c and $b are the electrostatic potentials inside the AgI crystal and on the AgI surface (taking the potential zero in the interior of the solution) n is the volume density of Frenkel defects in the solid phase and vb the surface density of corresponding defects on the AgI surface (responsible for the excess or deficit of Ag+ ions on this surface) eo,k and T have their usual meanings. At the P.z.c. in the absence of specific adsorption of indifferent electrolyte we may assume $b = Xb (the X-potential) the potential drop at the P.Z.C.due to water dipole orientation mainly in the Stern inner region4 We note that t+bC # \l/b at the P.Z.C. because there would still be a surface charge equal in magnitude but opposite in sign to the diffuse layer charge inside the solid phase. The surface defects may have various origins e.g. vacancies in steps kinks on a step etc. and we assume such defects lead to an excess or deficit of both Agt and I- ions at the surface. Also Here nc vb and Xb will all be functions of temperature. e.g. R. M. Diamond J. Pliys. Clieni. 1963 67 2513. E. P. Honig Trans. Faraday Soc. 1969 65 224; Nature 1970 225 537. P. L. Levine S. Levine and A. L. Smith J. Colloid Interface Sci.1970 34 549. S. Levine G. M. Bell and A. L. Smith J . Phys. Clzern. 1969 73 3534. 174 GENERAL DlSCUSSION pz - p i which is partly due to the difference between the free energies of solvation of Agf ion in the solution and on the surface will depend on temperature. These considerations certainly suggest a dependence of pAg on temperature at the P.Z.C. Dr. B. Vincent (Bristol University) and Prof. J. Lyklema ( Wageningen) said We thank Levine for his suggestion to explain the observed shift in the P.Z.C. on the basis of a variation of n and v b with temperature. A quantitative study will be needed to evaluate to what extent the changes in the properties of the solid phase contribute to the observed shift. At any rate these changes must be reversible with change in teinperature because the P.Z.C.measurements were reversible as a function of T. At the same time variation of the solid state properties cannot be solely responsible for the observed trends. First there are definite lyotropic effects in the P.z.c. in the adsorption of potential-determining ions and in the interfacial excess entropy (not given in fig. 5 but mentioned in the text of our paper). This proves that at least a (great) part of the effects has to do with the properties of the Stern layer. Moreover the more or less pronounced transition around 20°C in e.g. the surface excess entropy and in the double-layer capacitance at the positive side of the P.z.c. is not reflected in the solubility product indicating that we are concerned not with a transition in the solid-phase properties but in the surface properties. In conclusion there is now ample evidence that we are concerned with interfacial effects. There is no indication for solid phase effects as well but their existence cannot be excluded a priori. Quantitative evaluation would be desirablc.