GENERAL DISCUSSION Prof. A. Vrij (Utrecht) said: On page 1 of their paper Everett and Stageman men- tion that preliminary experiments carried out by Dr. R. Bown indicated that the former approach (charge stabilization and dipolar repulsion I presume) was unpromising. Could you elaborate on this? Prof. D. H. Everett (Bristol) (communicated) : We did not expect charge stabilisa- tion by ionisation of surface groups to be effective in media of low dielectric constant. We did, however, consider the possibility that dipolar repulsion, for example, between OH-groups of adsorbed alcohols, might confer stability. Preliminary experiments in which gas mixtures of lower aliphatic alcohols and Ar or CH4 were co-condensed rapidly on various fine powders, and subjected to ultrasonics, appeared to give colloidal dispersions.However, similar dispersions were formed without ultrasonic treatment, when the gas mixtures were condensed alone : they were, presumably, dispersions of solid alcohol particles (microcrystals ?) of colloidal size. These appeared to flocculate slowly, the turbidity showing an exponential decrease with a half-life of about 40-60 min. The temperature dependence of the rate constant correlated with the viscosity change of the medium. No further experiments on these systems were carried out when attempts to prepare sterically stabilised dispersions were successful. Dr. B. Vincent (Bristol) said: I would like to emphasise two features of the results presented by Everett and Stageman, which we have also found1 for aqueous systems, i.e., neutral polystyrene latex particles, carrying terminally-anchored poly(ethy1ene oxide) chains, dispersed in aqueous electrolyte solutions.These are: (i) the non- correlation of the flocculation temperature with the &temperature of the correspond- ing polymer in solution; (ii) the apparent particle concentration dependence of the flocculation temperature (fig. 2 of the paper). Napper2 has reported that in most of his work there has always been a strong correlation between the flocculation tempera- ture and the &temperature and this view has been widely accepted as a general feature of sterically-stabilised dispersions. It would now seem that this condition only holds in the limit of high molecular weight stabilisers. With regard to the particle concentra- tion dependence of the flocculation temperature, I wonder if the authors would care to speculate on the reasons for this, and the theoretical significance, if any, of compar- ing values of the flocculation temperature extrapolated to zero particle concentration.I have in mind here the close resemblance of the " phase-separation " behaviour of sterically-stabilised particulate systems and that of polymer solutions. Prof. D. H. Everett and Dr. J. F. Stagernan (Bristol) (partly communicated): In reply to Vincent, the concentration dependence of the flocculation temperatures can be accounted for qualitatively using the following simplified arguments. We assume (i) that a chemical potential of the following form can be defined for dispersed parti- cles : C .Cowell, R. Li-In-On and B. Vincent, J.C.S. Faraday Z, 1978,74, 337. D. H. Napper, J. Colloid Znterface Sci., 1977, 58, 390.3 14 GENERAL DISCUSSION where c is a concentration variable, perhaps most appropriately the volume fraction of particles, and pesp(T) is a standard potential; (ii) that, to a first approximation, the chemical potential of a particle in a sufficiently large floc can be taken as a constant, Ilevf(T>. If the dispersed particles are in equilibrium with those in the floc at T,, and pelf(Tf) - peyp(Tf) = Afpe = RT, In c. dfp* is the standard free energy change accompanying the addition of a particle to the floc. If, as assumed in our paper, flocculation occurs as a result of a sudden deepen- ing of the minimum in the free energy of interaction of particles (i.e., dfpe) as the tem- perature is changed, then the concentration dependence of Tf is, accordng to eqn (2)’ given by If a(Afpe/T) aT < 0; i.e., if Afpe becomes more negative as the temperature rises, the flocculation temperature is an UFT and aT,/a In c < 0.Conversely, at an LFT a(dfp*/T>/aT > 0 and aTf/a In c > 0. Thus the sign of the observed concentration dependence of the flocculation temperature is correctly predicted. Moreover, the more rapid the change of Afye in the neighbourhood of T,, the smaller the concentra- tion dependence of T,. These arguments indicate that at an LFT dfhe is negative; while at an UFT, dfhe is positive and the negative value of A,pe must arise from a positive entropy change dfs*. These considerations give added point to Vincent’s question as to the validity of extrapolating Tf to zero concentration, which we adopted quite empirically.Eqn (3) suggests that if dfhe is constant, a linear relation between Tf and In c will be found over small temperature ranges, and that the range of thermal stability should expand indefinitely as c + 0. This would be consistent with the view of Long, Osmond and Vincent that at sufficiently low particle concentrations no flocculation should occur, while at higher concentrations singlet particles are in equilibrium with aggregates ; moreover Cowell, Li-In-On and Vincent2 have recently found linear Tf against In c relationships experimentally down to volume fractions of -2 x Although we have not explored the properties of exceedingly dilute dispersions, PCS studies in propane down to volume fractions -2 x show that the UFT for such dispersions is virtually identical with the value extrapolated from visual studies at higher concentrations.If further experiments confirm the absence of a logarithmic divergence at very low concentrations, then this must be attributed to a dependence of Afpe on Aoc size : A,pe must become more negative as the floc size decreases in such a way as to counteract the In c term in eqn (2). If the concentration dependence of ,up is given by eqn (l), then p e y f must become more negative as the floc size decreases. This is the reverse of what simple arguments might lead one to expect, so that more subtle factors would have to be examined. Dr. G. Taylor (Cambridge) and Dr.J. V. Dawkins (Loughborough) said: We have prepared and studied dispersions of polystyrene [PSI and poly(methy1 methacrylate) particles in aliphatic hydrocarbons stabilized by a surface layer of poly(dimethy1- siloxane) [PDMS]. The dispersant used in the preparation of such systems was an J. A. Long, D. W. J. Osmond and B. Vincent, J. Colloid Interface Sci., 1973,42, 545. C. Cowell, R. Li-In-On and B. Vincent, J.C.S. Faraday 1, 1978,74,337.GENERAL DISCUSSION 315 AB block copolymer of PS-PDMS having a narrow molecular weight distribution. The molecular weight of the PDMS block was varied from 2400 to 48 000. Thus, dis- persions of essentially monodisperse polymer particles having diameters in the range 400-47 000 A have been prepared with well-defined surface layers of PDMS.l The surface coverage was conveniently estimated from a silicon analysis of the dried particles.Thus, the mean chain spacing of the PDMS chains was calculated, assuming that each chain was terminally anchored on the particle surface at the centre of a regular hexagon. The mean chain separation was of similar magnitude to the radius of gyration calculated for an equivalent free PDMS chain in solution. Hence, an interaction between neighbouring chains on the particle surface would be expected. 50 40 30 \ &o 20 10 0 t 0 10 20 30 40 50 PDMS molecular weight x loe3 FIG. 1 .-Variation of the hydrodynamic thickness of the PDMS layer (6) with molecular weight; 0 from rheology studies; from surface coverage studies. The hydrodynamic thickness (6) of the PDMS surface layer was estimated from rheology studies, using capillary viscometry techniques similar to those described by Barsted et aL2 Fig.1 shows the variation of 6 with the molecular weight of the PDMS. The PDMS chains have a somewhat extended conformation over that of equivalent free PDMS chains in s~lution.~ Surface coverage studies have also led to an estima- tion of the hydrodynamic thickness of the PDMS layer,3 and the results are in agree- ment with those obtained from rheology (fig. 1). We have studied the stability of these dispersions under conditions of decreasing solvency of the dispersion medium, which was chosen to be a mixture of heptane and ethanol. The solvency was reduced by cooling at a rate of 10" h-l, and the tempera- ture at which flocculation was visually observed was recorded as the critical floccula- tion temperature (c.f.t.).The &temperature for PDMS in the same mixed solvent was determined under similar conditions, using homopolymers of PDMS of a narrow molecular weight distribution. The values obtained for c.f.t. were close to the 8- temperature for PDMS, and were independent of the molecular weight of the PDMS. J. V. Dawkins and G. Taylor, Paper presented at a Symposium of the Macromolecular Group of the Chemical Society, Polymer Surfaces (Durham University, March 1977). S. J. Barsted, L. J. Nowakowska, I. Wagstaff and D. J. Walbridge, Trans. Faraday Soc., 1971, 67, 3598. G. Taylor, PkD. Thesis (Loughborough University, 1977).316 GENERAL DISCUSSION Dr. A.E. Smith (Port Sunlight) said: Vincent has drawn attention to the discrep- ancy between flocculation temperatures and 8 temperatures for some systems. At the Unilever Port Sunlight Laboratory, Dr. Thompson has found that for polystyrene latex carrying adsorbed alkyl ethylene oxide surface active agent, the difference of these two temperatures decreases as the latex particle size decreases. In this case the dis- crepancy seems due to the van der Waals attraction between the underlying latex particles, which itself varies with size. Prof. A. Slberberg (Rehouot) said : The cases here investigated fall into the cate- gory of systems involving irreversibly adsorbed polymer layers. The results illustrate very elegantly that it is the characteristics of the soluble part of the irreversibly at- tached copolymers which now determine what Derjaguin terms phase stability.One has replaced the colloid by a strangely constituted but “ soluble ” polymer mole- cule whose solution stability is essentially determined by the usual Flory-Huggins considerations for this kind of polymer. It f o l l o ~ s that stability in this case is inde- pendent of “ steric compression ” and long range van der Waals attraction effects. This is as was to be expected2 and is indeed implicit already in the Hesselink et aL3 model which demonstrates that “ osmotic ” and not steric repulsion is dominant. Prof. D. H. Everett and Dr. J. I?. Stageman (Buistol) (partly communicated): We have also measured the surface coverage of our ABA block stabilisers on acrylonitrile latices by elemental microanalysis of the dried particles.Although this is probably less accurate than direct silicon analysis, we confirm Taylor and Dawkins’ finding that the mean chain spacing on the particle surface, assuming only terminal attachment, corresponds approximately to the root mean square radius of gyration of an equiva- lent PDMS chain in solution. Our measurements of adsorbed layer thickness, how- ever, gave values considerably larger than those quoted by Taylor for equivalent molecular weight PDMS stabilising chains. These differences may be ascribed either to the different techniques by which the thicknesses were measured, or possibly to actual differences in the surface chain configuration conferred by the AB and ABA structures of the respective stabilisers. Taylor and Dawkins’ observation of close correlation between the LFT and the 0-temperature in mixed solvents is interesting.We have not been able, in our systems, to compare the LFT with &temperatures derived from measurements of the UCST of bulk solutions, since solid polymer separated before the UCST was reached and the LFT seems to be closely related to the approach to this solubility limit. We did, however, observe that the UFT’s of dispersions of latex MM31 and the upper O-tem- peratures became more closely correlated the higher the molecular weight of the alkane, and for n-hexane were virtually identical (see our fig. 1). In agreement with the observations reported by Smith, the difference between the UFT of the smaller latex AN63 and the &temperature of the polymer in propane was much less than that for the larger latex MM31. As indicated in our paper, this re- flects the effect of both the smaller van der Waals forces and the thicker stabilising layer in AN63.We thus believe that a close correlation between dispersion stability and limiting bulk polymer solution phase behaviour may only be expected when the core particles are relatively small, the stabilising layer thickness relatively large, and when the configuration of individual adsorbed soluble chains is not too different from that en- ’ B. V. Derjaguin, paper at this Discussion. A. Silberberg, Puog. Colloid Polymer Sci., 1976, 59, 33. F. Th. Hesselink, A. Vrij and J. Th. G. Overbeek, J. P?iys. Chem., 1971,75,2094.GENERAL DISCUSSION 317 countered in free solution.forces become important. For larger particles and thinner layers van der Waals Dr. C. J. Martin (London) said: In fig. 1 of your paper, all the lower flocculation temperatures (LFT) are lower than the &temperatures of poly(dimethy1 siloxane) (BDMS). Such a lowering could only be attributed to the surface interacting with the PDMS segments, either directly or through the poly(styrene) anchor block of the co- polymer. The magnitude of the difference between the 8-temperature and the LFT would thus be a measure of the magnitude of the PDMS/surface interaction. Have you systematically studied such differences beyond the results presented in fig. 1, for example by changing the anchoring copolymer, using a large range of numbers of PDMS segments attached to the anchor, or using another " stabilising " polymer at- tached to the anchor block instead of PDMS ? Such a study may correlate the differ- ences with either the range of the surface forces or the strength of the binding between the surface and the polymer(s), and perhaps give some confirmation of the origins and range of surface forces suggested by existing theories such as the double layer theory, or the theory of van der Waals attractions.Prof, D. H. Everett and Dr. J. F. Stageman (Bristol) (communicated): In fig. 1 of our paper the UFT values all lie below the upper 0-temperatures of PDMS in the alkanes but the LFT values all lie above the lower 0-temperatures; these latter values are not experimentally attainable in the present systems since PDMS freezes out of solution as a solid before the lower 0-region is approached.This has led us to specu- late that the LFT values are a consequence of the surface attached PDMS molecules freezing out of the alkane and collapsing onto the particle surface. This collapse must be dependent on the nature and molecular weight of the stabilising chains, their rela- tive segment-segment attraction and adsorption forces, as you suggest. We have not yet performed any systematic studies to investigate the specific participation of ad- sorption forces in this process although it is interesting to note from our table 2 that the LFT is affected mainly by the nature of the stabiliser and is relatively independent of the size and nature of the core particle.A more complete study of the factors which affect the location of the LFT would be interesting in its own right, but there may be more direct ways of investigating adsorption forces and their effect on surface attached poly- mer molecules than by observations of colloidal instability. Dr. M. L. Hair (Ontario) said: Everett and Stageman report the preparation and properties of sterically stabilized polymer latex dispersions in liquid alkanes, point out that these latex dispersions exhibit both upper and lower flocculation temperatures and show that these correlate closely with the bulk phase properties of the stabilizing polymer in the same liquid. Although well discussed in the recent literature there are few (if any) systems described in which flocculations at both UCFT and LCFT are due solely to changes in polymer-solvent interaction (i.e.as distinct from, say, surface induced crystallization at LCFT). A system which supports the Everett-Stageman hypothesis, was described by Croucher at a recent American Chemical Society meet- ing. A poly(acrylonitri1e) latex, z0.2 pm diameter, was prepared by dispersion poly- merization techniques in n-butyl chloride in the presence of an amphipathic stabilizer previously prepared by grafting poly(acrylonitri1e) onto poly(or-methylstyrene). The resultant particles are stabilized by the poly (a-methylstyrene) and the stabiliz- ing moiety is grafted to the surface as distinct from being physically adsorbed. M. D. Croucher, Abstract #4, Division of Colloid and Surface Chemistry, American Chemical Society, Anaheim, California, March 13th 1978.31 8 GENERAL DISCUSSION Upper and lower critical solution temperatures for PmMS in tBC have been reported by Cowie and MacEwen.l The close agreement between LCFT, UCFT and 8,, 8= is readily seen from the accompanying table.The experimental accessibility of these temperatures suggests that this system might be useful as a model colloid. system 0 ° K LCFT/K UCFT/K poly (wMS) in n-C4H9Cl 263 412 PAN latices in n-C4H9Cl 254 403 Dr. E . Dickinson (Leeds) said : Arising from the interesting correlation2 between upper and lower flocculation temperatures in sterically-stabilised latex dispersions and lower and upper critical solution temperatures in solutions of the stabilising polymer, Stageman has indicated the need for phase equilibrium data on solutions of poly- dianethylsiloxane in the simple liquids.Dispersion media which might be considered in this context are hexamethyl- disiloxane (HMDS) or tetramethylsilane (TMS): HMDS is the shortest oligomer of the dimethylsiloxane series and its PVT behaviour is ~ell-known,~*~ and TMS, despite having no siloxane linkage, has been shown5 to be the natural “ monomer ’’ of the series. Using HMDS or TMS would be attractive from the theoretical viewpoint since results would be comparable directly with rigorous statistical mechanical theories of monomer (or dimer) + polymer systems. There is also the not inconsiderable practical advantage that both solvents are liquid at ambient temperature and pressure. The pressure dependence of the LCST of HMDS -+ polydimethylsiloxane has recently been investigatede6 Dr.E. L. Neustadter (Sunbury) said: I refer to our paper Mechanisms by which Dispersant Additives Stabilise Carbon Dispersions in Non-Aqueous Media.’ We studied the stabilkation of carbon dispersions in n-heptane with two very differ- ent stabilisers, a poly(alkylmethacry1ate) polymer (BP 45) of mol. wt. 500 000 contain- ing about 1% nitrogen as amine groups and a poly(isobuteny1 succinimide) (PV 30 TEPA) with a PIB chain of wt. average mol. wt. 1250. Ethanol was added as non- solvent to the sterically protected carbon dispersions and the dispersants dissolved in heptane and the critical flocculation volumes (CfV) and theta conditions determined. In the case of the BP 45 stabilised dispersions the ratio of the CfV of ethanol to its concentration in the corresponding theta solvent was significantly greater than unity.The surface density of adsorbed polymer was found to be much higher for the strongly terminally adsorbed FV 30 TEPA than for the BP 45 polymer. In the case of a high surface density of adsorbed polymer, there will be apparent agreement between flocculation conditions and theta conditions because of the logarithmic relationship between the precipitation volume of non-solvent and polymer volume fraction. We consider that flocculation of a sterically stabilised system occurs under condi- tions which lead to phase separation of the stabilising polymer in free solution at the same concentration as that of the adsorbed polymer.This means that there will be a Cowie and MacEwen, Polymer, 1974, 16, 244. D. H. Everett and J. F. Stageman, this Discussion. I. A. McLure, A. J. Pretty and P. A. Sadler, J. Chem. Eng. Data, 1977,22, 372, E. Dickinson, I. A. McLure, A. J. Pretty and P. A. Sadler, Chem. Phys., 1975,10, 17. I. A. McLure and J. F. Neville, J. Chern. Thermodynamics, 1977, 9, 957. P. A. Sadler, Ph.D. Thesis (University of Sheffield, 1971). 1975), vol. 1, p. 323. ’ R. J. R. Cairns and E. L. Weustadter, Proc. Int. ConJ Colloid Surface Sci. (Budapest, SeptemberGENERAL DISCUSSION 319 concentration dependence of CfV and that, in general, flocculation conditioiis will not correspond to theta conditions. Dr. B. Vincent (Bristol) said: I would agree with the general point being made by Neustadter that one should not expect a direct correlation between the critical flocculation concentration of a non-solvent for a sterically-stabilised dispersion and the corresponding &solvent conditions for the stabilising chains, except in special cases.Such cases would be exemplified by the types of dispersion which Napper et a2.l have in the main studied, where the stabilising polymer is a high molecular weight, termin- ally-anchored chain. Presumably the polyalkylmethacrylate (BP 45) stabiliser used in Cairn’s and Neustadter’s work is a random copolymer adsorbed from solution. We have shown,2 as indeed have Napper et aZ.,3 that for those cases where the polymer is adsorbed in a loop/train type of conformation, one can have stability in much worse- than4 solvents.One would not expect any necessary correlation between the thermo- dynamic properties of the polymer at the surface and in solution. In the case of the effectively, terminally-anchored low molar mass PIB stabiliser (PV30 TEPA), again I would think that any correlation of flocculation conditions with &conditions is for- tuitous. Everett and Stageman’s paper at this meeting and our own recent work4 have shown that interactions other than the so-called “ mixing ” contribution to the steric interaction have to be considered when one has low molar mass, high segment density polymer chains at the surface, i.e. the “ volume restriction ” term and the London dispersion forces. Dr. S. P. Stoylov (Soja) said: In his paper Scholten states that it was possible for him to control the occurrence of aggregation by a non-steady birefringence value at constant magnetic field and by trailing decay curve.This is true to some extent only for aggregation provoked by the magnetic field applied. First of all birefringence is not very sensitive to aggregation and secondly aggregation could also be important outside the period of application of the magnetic field on the suspensions. I should like to say that the work of Scholten is an excellent example how essentially new results can be obtained without the utilization of very complicated techniques. It is possible that the application of light scattering, which is more sensitive to aggrega- tion and of electro-optic methods might provide new information. Dr. P. C. Scholten (Eindhouen) said: Aggregates present before the experiments can be detected through their multi-domain behaviour.In the native state (or after demagnetization in a high frequency a.c. magnetic field), the magnetic dipoles of the particles in an aggregate generally form a closed loop, and the net dipole moment of the aggregate is small. After a short exposure to a strong magnetic field (exceeding the switching field HJ, the moments of the particles in the aggregate are aligned and the net moment of the aggregate is large. This shows up as an increased orientability in weak (<H,) fields. It is mainly these existing aggregates that show the field- induced aggregation. Light scattering would indeed provide a sensitive check for aggregation. With magnetic particles, electric orientation is less attractive than magnetic orientation ; one doesn’t ride a donkey when a horse is available.They can also be detected in electron micrographs. l D. H. Napper, e.g., J . Colloid Interface Sci., 1977, 58, 390. R. Lambe, Th. F. Tadros and B. Vincent, J. Colloid Interface Sci., 1978,66, 77. J. W. Dobbie, R. Evans, D. F. Gibson, J. B. Smitham and D. H. Napper, J . Colloid Irzterfuce Sci., 1973, 45, 557. C. Cowell, R. Li-In-On and B. Vincent, J.C.S. Farday I, 1978,74, 337.320 GENERAL DISCUSSION Dr. Th. F. Tadros (Jealott’s HiZZ) said: Do you know the molecular weight of the commercial polymers used in your studies? Have you determined the adsorption isotherms of these polymers and if so is the adsorption irreversible and what is the amount of adsorption ? Dr.P. C. Scholten (Eindhoven) said: Our primary interest was in the thickness of the layers that stabilized these particles in spite of their strong magnetic attraction. Molecular weight distributions and adsorption isotherms were not determined. With nitrocellulose, we found irreversible adsorption of about 3 mg mm2. This was also the minimum amount needed for stabilization. Dr. P. C. Scholten (Eindhoven) said: In the practice of stabilizing suspensions and emulsions in apolar media, it is often a mystery why some surfactants work and others don’t. This paper by Doroszkowski and Lambourne is a nice step towards elucida- tion of the relevant parameters. From the data presented, together with the common experience that mixtures of surfactants generally perform better than pure compounds, and that branched or kinked chains are superior to straight ones (e.g., oleic-stearic acid) I have the impression that there is a second requirement.Besides with segments, the outer layer should be packed with entropy. In other words, the randomness in the structure of the chains should make crystallization of single or overlapping layers impossible. Mr. A. Doroszkowski and Mr. R. Lambourne (Slough) said : We agree with Schol- ten’s comment and we should like to take it a little further. We think that not only should the loss of entropy be difficult to attain, on the interpenetration of adsorbed layers (ix., non crystallisation), but that the degree of branching of the adsorbed molecules is such that maximum localised surface concen- tration occurs at maximum inter particulate distance. Dr.H. N. Stein (Eindhouen) said: In fig. 2 of your paper, the logarithm of viscosity is plotted against D-” (D = velocity gradient). (a) Is the viscosity plotted the apparent viscosity (=shear stress/velocity gradient), or some other quantity? (b) Is the plotting of log against D-” based upon a theory which leads to a linear relationship between these quantities for the systems investigated, or is it just an em- pirical approach ? Mr. A. Doroszkowski and Mr. R. Lambourne (Slough) said: (a) Yes, the viscosity plotted is the apparent viscosity. (b) The (log r, D-*) plot is an empirical assessment of flocculation. We have found this approach more suitable than other conventional procedures, e.g., sedimen- tation rate or volume or changes in light scattering properties. However, there are a number of papers relating apparent viscosity with the degree of flocculation of small particles, for example those of Cassonl or Goodeve,2 where the apparent viscosity is considered to be due to a particle volume contribution along with a particle interaction factor.But we have found them insufficient to describe the rheological beliaviour of flocculated dispersions and prefer to use the above approach, provided certain precautions are taken. For instance, the cam- ’ N. Casson, RkeoZogy of Disperse Systenzs, ed. C. C. Mill (Pergamon Press, Oxford, 1959), p. 84. C. F. Goodeve, Trans. Favaday Soc., 1939, 35, 342.GENERAL DISCUSSION 321 parison of the degree of flocculation is only made at comparable disperse phase volumes, and that the continuous phase viscosity is also similar.For if the latter were very different, the energy dissipated at a given shear rate would entail putting in much more work in the case of the higher continuous phase viscosity sample. This would lead to a greater break up of floccules in a given velocity gradient and hence would not be a valid comparison in our assessment of flocculation, which is based on the devia- tion from Newtonian behaviour due to particle flocculation. Dr. J. Visser (Vlaardingen) said: (1) You used two completely different types of proteins: a globular and a fibrous protein having different functions. Could you go into a little bit more detail regarding the consequences for the interpretations of your measurements and say also what one could expect for a random coil protein like P-casein ? (2) Another question I would like to raise is related to the fact that the configura- tion of proteins is strongly dependent on ionic strength, pH, type of ions present and temperature.Did you consider this aspect when changing from pH = 8.9 to pH = 3.5, when diluting your system and when using literature data for interpreting your results ? Dr. A. van der Scheer (Amsterdam) said: (1) The two proteins investigated indeed have different functions in our blood. Albumin for maintaining the osmotic pressure and for many transport functions and fibrinogen for clot formation. It should be mentioned that fibrinogen itself does not formaclot before the so-called a- andb-peptides are split off by thrombin, the remaining molecule is called fibrin and fibrin monomers can polymerise to fibres causing a clot.Most authors place fibrinogen (not fibrin) and albumin both in the class of globular proteins. As can be seen from the instability regions shown in fig. 3 and 4 albumin is much more stable than fibrinogen. In our measurements it is shown that fibrinogen (outside the instability region) gives steric stabilisation at much lower protein concentrations than albumin does (fig. 7 and 9), indicating a stronger adsorption. For other differences between ad- sorbed albumin and fibrinogen layers we want to refer to our published work1 From our calculations and experiments we found a dependence of the reduction of the hydrodynamic interaction by the adsorbed protein molecules on the size of the protein molecules.For a random-coil protein like 8-casein it is very difficult to pre- dict the infiuence on the rate of flocculation (and thus the hydrodynamic interaction. This protein is not structured and, therefore, the size in the adsorbed state may be completely different from that in solution. It is even possible that it unfolds com- pletely upon adsorption at low concentrations, resulting in short tails and loops that hardly produce sensitization and thus hardly give any reduction in hydrodynamic interaction. (2) You are right that these factors influence the configuration of the proteins. The literature data which we used for the size of the protein molecules, however, show that even for the unstable fibrinogen [see ref.(47)-(49)] no major size differences occur at pH values from 5.9-11 at low and high ionic strengths. In our evaluation of the influence of molecular size on hydrodynamic interaction we used VR = 0 indicating high ionic strength. The size of the molecules is only used for experiments at pH = 8.9. So the data may be used in the interpretation. The interpretation of the results which we got at pH = 3.5 indeed do need more information on protein conformation, especially at low ionic strength. A. van der Scheer and C. A. Smolders, J. Colloid Interface Sci., 1978,63,7, and a following paper in the same journal.322 GENERAL DISCUSSION Dr. H. N. Stein (Eindhoven) said: In your paper, the hydrodynamic interaction between two coagulating particles is taken into account by a method introduced by Spielman and Honig et al.[your formula (7)]. In this formula, the distance from the phase boundary enters as the quotient u = R - 2a/a (a = radius of a spherical particle). In the limit of a - co (flat plates), u would become = -2 leading to p(u) = 0 and thus D = 0, irrespective of the mutual distance of the particles. Does the formula imply that the viscosity of the liquid medium becomes very high between two approaching par- ticles, or does it mean that the water cannot easily get away between two approaching particles even if it retains its normal viscosity? In the former case, use of the formula implies a large viscosity at a large distance from the phase boundary, and thus may be used only if we believe in " polywater ", at least near a phase boundary.My question is about the significance of this result. Dr. A. van der Scheer (Amsterdam) said : The formula implies that the water cannot easily get away between approaching particles although it retains its normal viscosity, so we do not believe in " poly water " but in viscous drag. Further you mention the quotient u = R - 2a/2n. The limit of this quotient for a + co is not -2 but 0 because R is not a constant but R = 2a 4- h, where h is the distance between the two phase boundaries and R the distance between the centres of the particles. The diffu- sion coefficient of particles with an infinite radius (a ---t co) is always 0 according to D = kT/6zqa and D(u) = l//?(u) . D also equals 0. It must be quoted here that formula (7) is an approximation of the exact formula for the viscous drag between two approaching equals spheres, as given by Brenner [ref.(37)], which has been tabulated by Honig et al. [ref. (32)]. This formula is valid, independent of particle size and particle distance, and shows the influence of viscous drag on the diffusion coefficient of the particles for motion along the line of centres, contrary to earlier derivations like that of Lorentzl which is only valid for small instantaneous values of a/h. Dr. W . Norde (Wageningen) said: Referring to the paper by van der Scheer, Tanke and Smolders, I would like to make two remarks. First, the authors suggest that at high pH, i.e., pH 8.9, the adsorbed albumin mole- cules have more or less retained their native dimensions, whereas at pH 3.5 albumin would adsorb in a much flatter conformation.From our experiments,2 most clearly from hydrogen ion titrations, we conclude that at pH values away from the iso- electric point (i.e.p.) of dissolved albumin, i.e., pH 4.7-4.8, the structure of the protein molecule changes as it adsorbs on polystyrene. The structural changes at the acid and the alkaline side of the i.e.p. seem to be comparable. This similarity indicates that the extent of structural alteration is primarily dependent on the stability of the structure of the protein molecule in solution, more specifically, on the relative contri- bution from intramolecular hydrophobic bonding to the stabilization of that structure. In the adsorbed state, the requirement of minimum exposure of hydrophobic groups to the aqueous phase does not necessarily involve burying of these groups in the in- terior of the protein molecule, but may also be realized by attaching them to the adsorbent surface.Hence, if under the conditions at which adsorption takes place, the net contribution of the interactions other than hydrophobic interaction would fav- Lorentz, Abh. Theor. Phys., 1907, 1, 23. W. Norde, Proteins at Interfaces, Comm. Agric. Univ. Wageningen 76-6, (1976).GENERAL DISCUSSION 323 our an expanded protein structure, such expansion is likely to occur during adsorp- tion. Obviously, both at the acid and the alkaline side of the i.e.p. the net coulombic interaction favours an expanded protein structure. Second, van der Scheer et al.point to the possible causality between the flat orien- tation of the protein molecule adsorbed at pH 3.5 and the electrostatic attraction be- tween the protein and the latex. From hydrogen ion titrations, we found that on the average the carboxyl groups are closer to the polystyrene surface than the amino groups. This would result in a large positive electrostatic contribution to the Gibbs energy of adsorption if not counteracted by the uptake of cations that are transferred from solution to the adsorbed protein layer. From titration and electrophoresis data, we have deduced that such an ion transfer does occur.1*2 It has also been confirmed by direct experiments (to be published), i.e., by radiotracer techniques using 22Na and by e m . using Mn. Then, accounting for the adsorbed ions, the electrostatic contribu- tion to the overall-Gibbs energy of adsorption is almost independent of pH, provided that the charge density at the polystyrene surface is not too high.It should be noted, however, that these comments refer to maximum saturation of the polystyrene surface by the protein, whereas van der Scheer et al. refer to very low degrees of surface coverage. Dr. H. M. Fijnaut (Utrecht) said: (1) The quantity A in fig. 2 of Lips’ paper is found as the difference between two relatively large quantities, namely the hydrodynamic radius r, of the latex with ad- sorbed polymer and Y, the radius of the pure latex. These radii are found from the measurement of diffusion coefficients. From your experiments you conclude for a maximum in the relation of A against added polymer.Can this maximum be explained by: firstly an increase in A by the addition of polymer, being increasingly adsorbed on the polymer ; secondly, upon further addition of polymer, you have a small number of large particles and a very high number of small particles, giving rise to a small increase in the apparent diffusion coefficient, but a relative large decrease in A ? You need a change of only 2 to 3 % in r, to explain your results . (2) How many photons must you detect in your scattering process to reach the high precision in A permitting the lines to be drawn as is done in fig. 2? Dr. A. Lips and Mr. E. J. Staples (Port Sunlight) (communicated): When first confronted with the unusual behaviour in fig. 2, we had in fact considered the first point raised by Fijnaut.Strictly, the measured correlation function is the sum of two exponentials, one from the slowly moving latex particles and the other from the poly- mer molecules. At fixed latex number concentration, the contribution from the polymer increases with concentration, and at concentrations kg dm-3 it can become significant. Our procedure then was to interpret the correlation function as the sum of two exponentials. An analysis consistent with the observed correlation profile of the polymer solution alone was so achieved. We have in fact done measure- ments at polymer concentrations > 1 x kg dm-3, and these suggest the layer thickness to increase again. We require, however, a much larger number of measure- ments to validate our preliminary findings, and the effect mentioned by Fijnaut is causing us some difficulty.Increasing the latex number concentration is not a solu- tion as excessive multiple scattering then renders the correlation measurement unreli- W. Norde, Pruteins at Interfaces, Comm. Agric. Univ. Wageningen 76-6, (1976). W. Norde and J. LyMema, Roc. Colston Symposium on the Behaviour of Ions in Macromole- 1 x lar and Biological Systems, Bnstol, 1977, (in press).324 GENERAL DISCUSSION able. It is worth also to point out that the necessity to uncouple the sum of two exponentials makes it important to use latices that are virtually free from complications of particle interactions. Regarding the second point made by Fijnaut, there is good reason for expecting a rapid increase in layer thickness in the region of polymer addition, 0.1 to 3 x kg dm-3, in fig. 2: a polymer addition of 3 x kg dm-3 is just sufficient to impart a surface coverage -3 mg m-z which is the expected maximum value.The behaviour in the range, 0.1 to 3 x kg dm-3, suggests that virtually all the added polymer is taken up by the latex particles. In our study so far we have concentrated on the region of negative slope. The results in this region together with the reasonable expectation of the initial increase at lower additions enable us to comment with confidence on the direction of the variation of layer thickness with concentration. The number of photons detected in our scattering process (> 100 per sample time) was indeed high primarily because of the strong scattering power of the latex particles.Photon flux and, relatedly, laser power was not, however, the main determinant of the precision of our measurement. More essential was the use of lasers whose noise content at low frequencies, especially at 50 Hz and multiples, was extremely low. It was also important continuously to monitor the time averaged scattering intensity to ascertain the absence of scattering from adventitious impurities in the cells during periods of data collection. Of course, to maximise statistical accuracy, the usual pro- cedure of taking many repeat samples at high photon flux, and where possible for long experiment times, was strictly adhered to. Dr. Th. F. Tadros (Jealott’s HiZZ) said: Although not mentioned by the authors in their paper, I presume the latex used in their study is the same as used by us.We have already measured the adsorbed layer thickness of the same PVA sample by several techniques including photon correlation spectroscopy. This work which has been published1 was not referred to by the authors. The results we obtained indicated that at concentrations corresponding to the plateau of the adsorption isotherm, the ad- sorbed layer thickness (6) remained constant. The value at the plateau of the iso- therm obtained by three independent methods for the same polymer sample used by the authors agree with each other and are shown below. ultracentrifugation intensity fluctuation slow speed method spectroscopy (IFS) centrifugation 8,hm 32.5 & 5.0 32.7 & 3.0 29.4 We are sure of the IFS measurements as they have been done in two different labora- tories, namely by Dr.P. Pusey (Royal Radar Establishment) and Dr. T. A. King (Manchester University). We are aware of the flocculation problem mentioned by the authors. That is why we have done measurements at concentrations corresponding to the plateau of the isotherm. In this region, there is no evidence of flocculation from the IFS measurements. Moreoever, in this region the latex shows the irides- cence colours which are maintained on centrifugation at 50 g to hexagonal close packed arrays. Thus, the results quoted by the present authors are anomalous and several factors can account for such an anomaly. (1) Non equilibrium: The time quoted by the authors, namely 20 min, is definitely not sufficient for completion of adsorption. Moreoever, the polymer coils rearrange resulting in change of thickness. M.J. Garvey, Th. F. Tadros and B. Vincent, J. Colloid Irzterface Sci., 1976,55,440.GENERAL DISCUSSION 325 (2) The polystyrene latex used by the authors has been prepared at least 5 years ago and when left for such a long time, possible hydrolysis of sulphate groups can lead to large changes in PVA adsorption. At least the authors should have checked the adsorption isotherm. (3) There is a large scatter in the data of fig. 2 and the error bars seem to be very large. I do not believe one can draw any line through the points obtained >lom5 kg dm’3. All the results show a much lower 6 than previously obtained by us. (4) The authors did not mention what volume of polymer solution they passed through the millipore filter paper.Experiments in our laboratory have clearly shown significant adsorption of PVA on the filter paper. Again the authors should have analysed their filtrate. One point worth mentioning is the size of the bare latex particles. In a recent papery1 we measured the size of the bare polystyrene latex particles using IFS and compared this with electron microscopy measurements. In that particular case the latex was prepared by dispersion polymerisation. The radius of the latex particles obtained from electron microscope pictures was 118 nm; that obtained from measure- ment of the diffusion coefficient of the particles by IFs was 119 & 1.5 nm. This again shows that the accuracy of 6 obtained by IFS is reasonable even if one uses the radius of the bare particle obtained from EM pictures.Dr. A. Lips and Mr. E. Staples (Port Sunlight) said: Both the polystyrene latex and the PVA sample were the same as that used in the study to which Tadros referred [ref, (l)]. In our view, the claim made by Tadros of having measured the adsorbed layer thickness 6 by three independent methods needs considerable qualification. First, a value of 6 = 29.4 nm was determined by slow speed centrifugation on the assumption that the particles packed in hexagonal close packed arrays. However, ref. (2) clearly indicates that the sedimentation in this particular case was not accompanied by the formation of iridescent structure. The strong sensitivity of the value of 6 inferred by this technique to the type of packing, in the direction of 6 decreasing with increasing randomness of packing, leads one then to expect the true value of 6 to be considerably less than 29.4 A.In principle it could be as low as 17 nm which is of the order of the value we obtain by phton correlation spectroscopy (PCS). In view of its strong sensi- tivity to the mode of packing, slow speed centrifugation can easily be open to mis- interpretation. Even in cases of observed iridescence, a detailed diffraction analysis may be necessary to establish accurate packing fractions. Another technique which Tadros mentions is ultra centrifugation. In this case a smaller latex size was employed than in the slow speed centrifugation measurements and in both his and our light scattering studies.The actual value obtained was 22.6 nm which again is much closer to our values obtained by PCS. Tadros, however, argues that this value needs to be corrected to an “ equivalent thickness ” appropriate to the size of the latex particles used in the light scattering and slow speed centrifuga- tion work. The justification for this large correction, from 22.6 to 32.5 nm, is argued to derive from studies based on PCS. The manner in which these measurements were performed is of some concern to us and even if our reservations prove to be unfounded we cannot agree with Tadros that ultra centrifugation, appearing to require a large correction based on another type of measurement, affords one in this case an independent method of measuring thickness. Our central objection to the work referred to by Tadros is that in none of the Th.van den Boomgaard, T. A. King, Th. F. Tadros, H. Tang and B. Vincent, J. Colloid Interface Sci., in press. M. J. Garvey, Th. F. Tadros and B. Vincent, J. Colloid Interface Sci., 1976,55,440.326 GENERAL DISCUSSION methods described, including PCS, a direct difference measurement was performed. It was assumed that the bare particles were unaggregated and estimates of layer thick- ness were calculated on the basis of the electron microscope diameter of the particles. It is our experience that even freshly prepared latices can suffer from pre-aggregation, the degree of which can be assessed most easily by PCS or by a light scattering method which one of us deve1oped.l The preparation of a truly unaggregated latex is the ex- ception rather than the rule. Now it is obvious that pre-aggregation will distort the estimate of thickness, in the direction of giving much larger values.In view of this, one should be inclined to accept the lowest reported values. In our study we have taken great care to ascertain that the latex, at least at the con- centrations corresponding to the PCS measurement, was virtually free from aggrega- tion. To achieve this, it was essential to subject the latex to careful filtration. We also filtered the polymer solutions prior to adding them to the sols. This step was desirable but not essential as we were able to show that the thickness was unaffected by the filtration of the polymer solutions.We see no possibility of our results, at least those corresponding to high polymer coverage, being anomalous: we have rigorously adhered to a difference method and have shown by low angle light scattering that there is no significant change in particle interaction following the addition of polymer. It is worth considering whether the discrepancy between our conclusions and those of Tadros et al. is the result of differences in the mode of application of polymer to the latex. In our experiments a large excess of polymer was added directly to a very dilute latex dispersion in the scattering cell. In the experiments of Tadros the polymer was added to a relatively large concentration of latex and the system equilibrated for 48 h, the latex was then diluted by a factor of 100 into mol dm-3 electrolyte solution.In our case, equilibration times 220 min were adequate as no significant change in ihickness could be detected on much longer equilibration times (24 h). The justifica- tion for the procedure of Tadros is the observation of negligible desorption of polymer on dilution of the latex; while this may undoubtedly be true on kinetic grounds it has to be recognised that the polymer system is then strictly under non-equilibrium condi- tions. The equilibrium demands that polymer should utimately desorb, and at least an initial response of rearrangement of the polymer on the surface is to be expected. In view of this we would suggest to Tadros that our conditions of measurements are far more representative than his of the equilibria of adsorption.In an attempt to resolve the discrepancy between the results of Tadros and our own, we have measured the adsorbed layer thickness by light scattering using a 0.255 pni polystyrene latex and following both procedures of applying polymer. Direct addi- tion of polymer to a dilute andfihered latex of number concentration -5 x lo8 c ~ n - ~ , to a polymer concentration of -1 x kg dm-3, gave a value 6 = 22 nm. This is close to the corresponding value in our paper (fig. 2) obtained for a larger particle size. The bare particle size of filtered latex was close to the electron microscope diameter. The same value was obtained following the procedure of Tadros provided that the latex was carefully filtered on dilution. The filtration ensured the removal of aggre- gates and rendered more reasonable the assumption of the bare latex size being repre- sented by the electron microscope diameter.When we measured the diffusion coefficients of unfiltered diluted latex in the presence and absence of polymer we ob- tained effective particle sizes which in both cases were -20 nm greater than those measured for the corresponding filtered sols. This clearly shows that aggregated latex particles are not deflocculated by polymer and that it is necessary to employ a direct difference method to obtain a reliable value for the hydrodynamic thickness. A. Lips and E. Willis, J.C.S. Faraday I, 1973,69, 1226.GENERAL DISCUSSION 327 Though the difference method to a large degree overcomes the difficulties caused by pre-aggregation, it is essential for precise measurements to employ latices that are virtually free from aggregation.We note that in the work of Tadros et al. hardly any attention has been paid to the central issue in this type of measurement of hydro- dynamic thickness. In our view, therefore, their conclusions regarding the dependence of layer thickness on particle size should be treated with caution. Prof. R. H. Ottewill (Bristol) said: I should like to comment on the time dependent properties of polystyrene latices found by Lips. It has been our experience with latices prepared using sodium persulphate as the initiator, which therefore have sul- phate groups on the surface, that the latter hydrolyse with time to form hydroxyl groups. Consequently, over a period of years, there can be a substantial loss of charge.Dr. C. A. Young (Bristol) said : Lips reports lower adsorbed layer thicknesses for PVA (Alcotex 88/10} on polystyrene latex particles than reported by Garvey et al.' I I I I I 100 200 300 LOO 500 equilibrium PVA concentration /p.pm. FIG. 1 .-Adsorption isotherms by several workers-see table 1. TABLE DETAILS OF LATICES USED number diameter/nm initiator surfactant purification reference I 236 potassium TI 200 azobisisobutyr. persulphate amidinium chloride persulphate IT1 190 potassium TV 3 30 potassium persulphate none dialysis 2, 3 none dialysis 2 none steam stripping 2 (100 "C); then dialysis 2 sulphate dialysis 1 sodium dodecyl M. J. Garvey, Th. F. Tadros and B. Vincent, J. Colloid Interface Sci., 1974,49,74. C. A. Young, unpublished work.Th. van den Boomegaard, T. A. King, Th. F. Tadros, H. Tang and B. Vincent, J. Colloid Infer- face Sci., 1978, in press.328 GENERAL DISCUSSION It is worth pointing out that the amount adsorbed and, therefore, presumably the ad- sorbed layer thickness, depends strongly on the nature of the latex used. In fig. 1 are collected adsorption isotherms by several workers ; details of the corresponding latices are given in table 1. All isotherms were measured using the method described in ref. (1). It can be seen that the latices prepared without surfactant show a higher affinity for PVA than latex IV which had surfactant present. Even exhaustive dialysis pre- sumably does not remove all the surfactant (a proportion of the sodium dodecyl- sulphate seems to become hydrolysed to dodecanol which is virtually insoluble in water).2 The result is a more hydrophobic surface, leading to lower PVA adsorption. Steam stripping also leads to reduced adsorption.It is not clear at the moment why this is so; possibly some form of surface hydrolysis occurs. Changing the nature of the surface groups from sulphate to amidine does not alter the adsorption significantly. Dr. A. Lips and Mr. E. J. Staples (Port Sunlight) said: Ottewill, Tadros and Young all refer to the problem of loss of surface charge by hydrolysis of polymer latex con- taining sulphate groups. It seems reasonable that this would be accompanied by a decrease in the stability of latices and in changes in the adsorption of polymers such as PVA. More recent measurements in our laboratory of the adsorption of PVA on the latex used in our study has given a value for adsorption at the platea which is in good agreement with the value previously reported by Garvey et aZ.l On the subject of aggregation of latices on storage, we should like to comment that it is our experience that even fresh latices can suffer from appreciable aggregation and that the aggregates are generally extremely stable to dilution forces which suggests that primary minimum forces are implicated.Prof. A. Silberberg (Rehovot) said : A non-monotonic dependence of adsorbed polymer layer thickness for some molecular weight fractions has also been observed by us in the adsorption of polystyrene from toluene onto glass but is probably of different origin.3 The effect occurs at a much lower concentration than here observed and is believed by us to demonstrate the transition from a " tail " dominated adsorbed layer to a " loop " dominated adsorbed layer as the molecular weight increases.Mr. F. A. Waite (Slough) said: This contribution is not only relevant to the paper of Lips but also to those of Lyklema, Smitham and Vincent and to the contributions by the numerous other speakers who have taken part in the discussions relating to the behaviour of PVA at an interface. The Discussion has included several papers in which measurements relating to the adsorbed layer thickness of and steric forces exhibited by PVA at interfaces were described. The results have been discussed in relation to each other and to current theories both of polymer adsorption and steric stabilisation.In order to do this sensi- bly the structure of PVA must be considered very carefully. The material generally referred to as PVA or polyvinyl alcohol is not a homopoly- M. J. Garvey, Th. F. Tadros and €3. Vincent, J. Colloid Interface Sci., 1974,49,74. J. W. Goodwin, personal communication. Z. Riel and A. Silberberg, J. Polymer Sci. in press, also quoted in A. Silberberg, Colloques Internationaux du C.N.R.S. No. 233, PoZym2res et Lubrificution, 1975, p. 81.GENERAL DISCUSSION 329 mer. It is, in fact, partially hydrolysed polyvinyl acetate, the hydrolysis being carried out in such a manner, that the product is a " good commercial surface active polymer ". Herein lies the problem. As Lyklema indicates in his paper the material is a block copolymer.The polymer chains contain blocks of acetate groups which associate with hydrophobic surfaces and blocks, rich in hydroxyl, which remain extended to some degree in the aqueous phase. In order to discuss the behaviour of " polyvinyl alco- hol " at an interface the average number of acetate groups in a block and the distribu- tion of these blocks in the polymer chain must be known. Fractionation of the com- mercial polymer with respect to molecular weight does not alleviate the problem. Although the acetate content of each fraction is rather similar it is not known whether the block size and/or block number change with molecular weight. Since this informa- tion is not available the relevance of the experimental work presented at this confer- ence to the theories of polymer adsorption and steric stabilisation is minimal.Further, comparing the properties of the whole polymer in solution with those of the solvated component of the adsorbed layer does not appear to be justified. At least some of the acetate blocks will be at the surface, effectively in a separate phase, i.e. the chemical composition of the solvated adsorbed layer is not the same as that of the whole polymer. Ottewill said that " polyvinyl alcohol ", as a polymer for study, was far from ideal. Since it is of the essence of current theories of polymer adsorption that the adsorbing species is a homo-polymer, the ideal polymer for related experimental work is a true homo-polymer. On the other hand steric stabilisation, in the practical sense, derives in the main from polymers which are indifferent to the surface but which are attachedl anchored at the surface at one or a few points on the chain.A convenient way of achieving this is to use block or graft copolymers, containing at least one component capable of associating with the surface and at least one component which is indifferent to the surface and is solvated by the medium. Ideally, the structure of such a block or graft copolymer should be known with some degree of certainty. This cannot be said of PVA. Indeed, all that can be said of PVA in this context is that it is cheap and commercially available. Mr. D. J. W. Osmond (SZough) said: Waite has said that cost and availability are the only virtues of" PVA "; I suggest that its popularity may also be because, in many cases, it is the only " homo-polymer " which adsorbs strongly enough to provide any useful degree of steric stability, but the only reason for this is that it is not actually a homo-polymer at all, but a poorly defined amphipathic block copolymer! This suggests that the subject of the adsorption of homopolymers in the absence of any strong anchoring points, as discussed by Fleer yesterday, and as distinct from the analysis of Levine, for example, warrants some further thought.A decade ago, when the subject became suddenly popular in the hands of Roe, DiMarzio, McCracken and so on, the systems studied implied (though rarely stated) that the polymer was in an atherma2 solvent and that the molar volume of the polymer segments and the solvent molecules were very similar. This implies, for all except specially contrived models, that the segment and solvent are chemically similar, i.e., we are normally discussing systems such as polystyrene in ethyl benzene or xylene.At the same time, enthalpies of adsorption per segment of many kT were considered. However, all surface sites not yet occupied by polymer segments are filled by solvent molecules, which have to be displaced for polymer adsorption to occur; but we have just agreed that usually the composition of the two is very similar, so that the net enthalpy of segment-adsorption (after subtracting the work of desorption of the solvent330 GENERAL DISCUSS ION molecule) must tend to zero! Values for the enthalpy of adsorption per segment, large compared to kT, are obviously impossible. Of course, in modern analyses, the thermodynamic quality of the solvent for the polymer is explicitly taken into account (usually via the x parameter) and there is also a correction for the work of solvent-desorption.Yet nevertheless, it still seems desir- able to point out that, although not implicit in the algebra, in the real world these three quantities, the polymer/solvent, the polymer/surface and the solvent/surface enthalpies of interaction, are not totally free and independent variables. Having arbitrarily defined any two, there are, for most physically real systems, severe con- straints on the possible values for the third. As a result, segmentlsurface interaction with net enthalpic gains larger than a small fraction of kT are not usually found for strictly athermal polymer solutions ; equally, reasonable strong adsorption is normally found only in the case of solutions in thermodynamically rather poor solvents, nearer the 0 than the athermal regime.This is of course in accord with common experimental observation. Homopoly- mers are rarely very good steric stabilisers for particles having homogeneous surfaces, but are least bad broadly mid-way between the 8 and athermal limits, the fall-off at one end being due to inadequate solubility as opposed to inadequate adsorption at the other. The point has been made twice already at this meeting; Ottewill has described how the adsorption of polyethylene glycol from water on to polymethyl methacrylate sur- faces is too weak to allow meaningful measurement of the repulsion and Robb has mentioned the feeble adsorption of the higher aliphatic hydrocarbons from their lower homologues in the absence of surface crystalline associations. One therefore concludes that, while the adsorption of ideal homo-polymers at ideal surfaces may well be a worthwhile theoretical and experimental study in its own right, it is not very relevant to the study of practical levels of steric stabilisation.Prof. J. Lyklema and Dr. T. van Vliet (Wageningen) said: Although qualitatively we agree that one must be careful in generalizing results, obtained with block co-poly- mers to random homo-polymers and in identifying polymer properties in solution with those in the adsorbed stage, quantitatively the differences are less than Waite antici- pates.First, the great similarity between properties of adsorbed and free macro- molecules has been proven by us l s 2 for a polyelectrolyte undergoing a conformational transition as a function of pH. The transition range was very similar for the adsorbed and the dissolved polyelectrolyte, and as this range is certainly dictated by subtle details in the spatial configuration, this is a sensitive test in support of conformational analogy. Unless the contrary is proven, there is no reason to assume that PVA would behave differently. Considering the blockiness of our PVA-samples, in our PVAs 205 and 217 the average lengths of the blocks are 10 and 8, re~pectively.~ In the adsorbed state the acetate contents in loops and tails are lower because of preferential adsorption in trains.The crucial question is then what value to assign to a for tails. According to Scholtens’ analysis a in tails exceeds V. in bulk by maximally 0.08. As a occurs in the equation for steric repulsion four eqn (5)] as (a2 - 1) and as u is of the order of 1.1 (table l), this would lead to an uncertainty in the mixing term of the order of 1.7-2.4. The influence on the volume restriction term is zero and the influence on the sum is at most a factor 2. However, inspection of fig. 3 shows that this difference would T. van Vliet and J. Lyklema, Int. Conf. Colloid Surface Sci. (Budapest, 1975), vol. 1, p. 197. T. van Vliet and J. Lyklema, J. Colloid Interface Sci., 1978,63, 97. B. J. R. Scholtens, Meded. Landbouwhogeschool Wageningen, 1977,77,7.GENERAL DISCUSSION 33 1 already be accounted for by allowing 5% more segments to be present in tails, so that this uncertainty does by no means detract from our conclusions.Prof. A. Silberberg (Rehovot) said: Arising from a general comment by Osmond, there is no question but that protection by physical adsorption is optimally achieved by a suitable copolymer, but terminal (covalent) attachment of a highly soluble polymer is best. When I published my first two papers on polymer adsorption in 1962, I already emphasized the independent contribution of polymer solubility as embodied in x and polymer surface interaction as embodied in xs. Not only the athermal case was considered. It was stressed that adsorption is a displacement of an adsorbed solvent molecule by a polymer segment [see eqn (4), (11) and (12) of my present paper].The main burden of my 1962 papers, however, was that xs could be small, of order 1, but in excess of its critical value and adsorption would nevertheless be strong, essen- tially complete. The energy levels e,,, E,, and epo occur both in x and xs but the latter also depends upon E=, and cap. There are thus five quantities involved (four differ- ences) which can vary independently. Solvent power is a guide but not the only reason why xs may be large or small. The second important conclusion of that early paper was that the behaviour of concentrated surface phases was very different from the behaviour of the isolated macromolecules on the surface and that studies of the latter case whether by analytical or by computer techniques, give only the poorest insight into the real case.Treatments such as the one presented by Levine and by Fleer and the earlier work on which they are based have fortunately now moved away from the isolated chain case. A proper understanding of the cases treated by these analyses is thus essential and must logically precede the special theoretical problems created when practically more valuable materials such as special copolymers or surface crystallizable materials, are employed. Dr. J. M. H. M. Scheutjens and Dr. G. J. Fleer (Wageningen) said: In reply to Osmond we would like to point out that the fact that polymers in good solvents can have only very small net adsorption enthalpies per segment does not necessarily mean that no adsorption can occur from good solvents.First, the solvent quality (X-para- meter) and segment-surface interaction &,-parameter) contain in addition to an en- thalpy contribution also entropy terms which are not necessarily the same for the exchange of a segment with sovent in bulk and with solvent on the surface. Secondly, the size ratio between segments and solvent molecules is not unambiguously defined. This also has consequences for the entropy change of mixing and that of adsorption (e.g., if a segment is exchanged against several solvent molecules on the surface) and will generally not be the same for the two cases. Admittedly this last effect cannot yet adequately be accounted for in theoretical treatments, but certainly needs further attention.Finally, the theories for polymer adsorption are not only relevant for steric stabilisation but also for the destabilisation of colloidal systems by polymers. As to Osmond’s point that copolymers are better stabilizers than homopolymers, we mention that at present we are extending our theory to (random and block) copolymers. Results will be reported shortly. Dr. A. Lips (Port Sunlight) said: I agree with most of the remarks made by Waite on the suitability of PVA as a model polymer for studies of adsorption or steric stabilisation. I am little concerned, however, by the appearingly exclusive emphasis which is placed in so many studies on the steric aspect of polymer mediated effects. Polymer bridging by comparison is a relatively poorly researched, let alone quantified phenomenon. We know, however, that homopolymers, under good Solvent condi-332 GENERAL DISCUSSION tions far removed from the theta point, can be excellent flocculants, particularly so at intermediate surface coverage.At the highest surface concentrations achievable with a particular polymer, the osmotic term usually wins but is the bridging contribution then truly negligible. Existing theories and experiment do not really enable one to make a reasonable judgement, and we should not lose sight therefore of the possibility that polymer mediated effects with model homopolymers may be a delicate interplay of competing bridging and osmotic contributions even at fairly high surface concentra- tions, in which case it would not be permissible to discuss measurements in relation to theories of the steric contribution in isolation.Dr. J. F. Padday (Harrow) said: Vincent et al. have indicated in their paper that the adsorption isotherm were indeed reversible and that the same point may be reached first by approaching the equilibrium first by increasing the concentration in solution and then, in a further experiment, by decreasing the concentration in solution resulting in desorption. Have the authors attempted the same reversibility experiments by changing the ionic strength? If so, what results were obtained? Dr. B. Vincent (Bristol) said: Padday has raised a very interesting point. We have recently in fact carried out experiments to determine the degree of reversibility of the high affinity isotherms on changing the ionic strength, at fixed total particle number concentration.To this end we selected the system in which both sets of latex particles were covered with an adsorbed layer of PVA 24 000 and in which the electrolyte con- centration had been adjusted to rnol dm'3 NaCI. Three parallel sets of ad- sorption experiments (a, b and c) were set up. After equilibration, series (a) was used as a control set, in the sense that the previous particle adsorption isotherms was re- established. The ionic strength in series (b) was adjusted to rnol dm-3 by the addition of the necessary quantity of solid NaCl; that in series (c) was adjusted to rnol dm-3 by dialysing against a large excess of NaCl solution at that concentra- tion. In both cases, after re-equilibration, it was found that the adsorption isotherm changed to that found previously for the adjusted electroyte concentration.Thus, at rnol dm-3, which had been previously found to correspond to a low affinity iso- therm, small particles had desorbed from the large particles. Also at rnol d ~ l l - ~ , which had been found to correspond to a high affinity isotherm (but having a lower plateau level than mol dm-3), again desorption of small particles occurred, sug- gesting that the lateral repulsion forces between nearest neighbours are stronger than the normal attraction forces by the large particles in these systems. Thus, one con- cludes that, although, in the case of the high affinity isotherms, the adsorption is apparently irreuersibk when the particle concentration is diminished at the same ionic strength, the adsorption is reversible to changes in ionic strength.Dr. I. D. Robb (Port Sunlight) said: If the slope of an adsorption isotherm changes abruptly or adsorption takes place only above a finite concentration of adsorbate, it implies that the adsorption (at the point of abrupt change) is a cooperative process. Such isotherms are shown in fig. 1 of your paper at higher salt concentrations and it suggests that the small positive particles adsorb in clusters on the large negative ones. Measurements of the flocculation of the small positive particles on their own would determine whether these clusters existed in solution prior to adsorption or whether the surface of the negative particles acted as a nucleating site for the clusters.Dr. B. Vincent (Bristol) said: We detected no flocculation of the small positive latex particles alone in the presence of 10-1 mol dmm3 NaCI, when there was an adsorbedGENERAL DISCUSSION 333 PVA layer on the particle. (However, these particles did coagulate at this electrolyte concentration in the absence of PVA. This point is referred to in the paper). The two-dimensional appearance of the clusters [fig. 6(b)] of small particles on the large particles would also suggest a cooperative adsorption process at the surface, rather than pre-aggregation in the continuous phase. Prof. T. W. Healy (Melbourne) said: I refer to the [c, log (NaCl concentration)] isotherm of fig. 8 for the " bare latex ". The reported potentials at loe2 mol dm-3 are of the order of twice that usually reported for materials similar to latex A of the present paper.Again, one might expect a reduction in [-potential from, say, -40 to -50 mV at to -20-35 mV at lo-' rnol drne3. At such high salt concentra- tions, surface conductance effects will be minimal. Could the authors comment on such anomalously large potentials for bare latex A? Again, if the PVA-coated latex reflects the electrostatic properties of PVA or bound PVA itself, the positive latex colloids coated with PVA might be expected to show [-potentials in 10-2-10-1 mol dmm3 of 3 -10 to -15 mV. Was such an effect observed? Alternatively, did the PVA at high concentrations reverse the sign of the c-potential of positive latex sols ? Dr. B. Vincent (Bristol) said: The electrophoresis data for the large (3 pm) nega- tive bare latex particles shown in fig.8 are, I agree, unusual, in the sense that it is not what one might intuitively expect. However, very similar results have been found by another group at Bristoll working with similar large, high surface density latices. There is, on the other hand, a slow ageing effect in that the zeta potential does drop slowly with time; this is thought to be due to the gradual hydrolysis of surface sul- phate groups. (Latices can suffer from old age!) With regard to the implicit suggestion that PVA itself is charged: there is no ex- perimental evidence for this. Fleer and Lyklema? for example, have made a detailed study of this point. As we report in the paper, it was very difficult to obtain reliable, consistent electrophoresis results with the small positive latex particles, but the data we did obtain always indicated that the zeta potentials of these particles remained positive in the presence of PVA.Since the paper was submitted, however, we have been able to obtain electrophoresis data on small negative latex particles (i.e., latex B in the paper) ; these have a very similar particle size and magnitude of surface charge density to the small positive particles (latex C) reported in the paper. The data are given in fig. 1 shown here. As may be seen, the trends with ionic strength could be considered more " normal ". Moreoever, because of the much higher adsorbed layer thickness/particle radius ratio with this latex, there is now a definite trend of zeta potential with molar mass of PVA (in the direction expected), compared to the case of the larger latex (fig.8). Prof. J. Lyklema (Wageningen) said: In cases like the one studied by Vincent et al., where steric repulsion and double layer interaction are simultaneously operative the electric repulsion equation to be used should be based on interaction at constant Outer Helmholtz Plane (OHP) potential $vd. That interaction should be interpreted at constant potential follows from the rela- tively long interaction times, permitting the double layers to adjust themselves com- pletely. R. Buscall and J. W. Goodwin, personal communication. See e.g., G. Fleer, PhD. Thesis (Wageningen, 1971), p. 20.334 90 r GENERAL DISCUSSION -5 -4 -3 -2 log c FIG.1.4alculated zeta potentials, That, for the potential, Wd should be used and not < is because of the fact that the ions in part of the double layer between the OHP and the slipping plane (or slipping region) are still quite mobile. As a first approximation the ionic mobilities are not influenced at all by the low volume fraction of polymer segments in that layer. In that case the charge distribution would satisfy the unperturbed Poisson-Boltzmann law. The starting point of the diffuse part of the double layer part being the OHP, the potential to be used in the equations is vd. Obviously, it is not easy to find a value for this parameter in the presence of ad- sorbed polymer. It is clearly not justified to use for tyd the electrokinetic potential in the absence of adsorbed polymer because the potential drop over the Stern-layer is affected by the adsorption of train segments.Perhaps the best chance is to obtain 'y, from the effective hydrodynamic thickness d and the electrokinetic potential in the presence of polymer. Equations for this are avai1able.l Dr. B. Vincent (Bristol) said: We would certainly agree that, given the relatively long equilibration times in these experiments, the assumption of constant potential is more valid than that of constant charge for the electrical double layer interactions. However, it is presumably the surface potential that remains unchanged when two charged particles come together during an equilibrium encounter. It is possible that both the OHP potential ( ~ 8 ) and the zeta potential change as the ion distribution in the double layer changes during such an encounter.In the current case the situation is L. K. Koopal and J. Lyklema, Faruday Disc. Chern. SOC., 1975,59,230.GENERAL DISCUSSION 335 even more complex, because it is difficult to define the electrical double layer structure at high coverage of the small positive particles around one large negative particle (cf. the comment by Goodwin and our reply). However, we agree that changes in the OHP potential are likely to be less than those in the zeta potential, and formally, it may be better to use the former in any calculations. We would stress again, on the other hand, that these calculations were meant to be only illustrative and semi-quantita- tive in order to show trends with ionic strength.Exact calculations would need to take account of the many-body nature of the interactions. Dr. J. W. Goodwin (Bristol) said: (a) The results of the calculation of the electrostatic interactions between positively charged particles at a negatively charged surface are shown in fig. 10 of the paper. At low values of rca (e.g., 7ca < 10) this calculation is not as simple as indicated in the paper. For example, if we consider the schematic representation in fig. 9, the over- lapping electrical double layer of the positive particles are existing within the double layer of the negatively charged surface. How was this taken into account in the calculation ? (b) Following Silberberg’s informal comment to Lyklema with regard to the experiments of Brooks and Seaman.It is interesting to note that Brooks, Goodwin and Seaman1 found that the coagulation/redispersion boundary occurred at a critical l,-potential over a wide range of ionic strengths for erythrocytes with adsorbed low molecular weight dextran. Dr. B. Vincent (Bristol) said: Goodwin is quite correct when he asserts that the calculated interaction energy curves shown in fig. 10 may be based on an oversimplifi- cation of the true situation. As we stress in the paper, however, these calculations are only intended as a semi-quantitative guide to the trends in the normal and lateral interactions with ionic strength. The main problem arises, as he points out, at low ionic strengths (corresponding to the high affinity isotherms), at coverages where lateral interactions become really significant (i.e., in particular in the plateau regions of these isotherms).One essentially has a many-body problem (fig. 9 illustrates the 3-body situation). It may prove more profitable to discard the formal division into normal and lateral interactions and to try to calculate instead the free energy change in bringing a small positive particle up to the surface of big particles as a function of separa- tion, and as a function of coverage. Dr. D. B. Hough (Strathclyde) said: The origin in the maximum in the curve of zeta potential against log (NaCl concentration) in fig. 8 for the uncoated polystyrene particles has been questioned. The effect, rather than requiring a physical explana- tion, may be explained in terms of the use of the tabulated mobility data of Wiersema et al.Curves of mobility against log rca at various values of zeta potential, drawn from the tables used by Vincent et al., are shown in fig. 1. If Wiersema’s solutions are accepted as representing the practical system then in this region of K a and under conditions of high zeta potential, where electrical double layer relaxation effects are important, small errors in mobility or 7ca will result in a large degree of uncertainty of derived zeta potential. The mobility data of the authors are superimposed on fig. 1 together with the stated -&lo% error bars. It is observed that the curve of zeta potential against log (NaC1 D. E. Brooks, J. W. Goodwin and G . V. F. Seaman, Biorlzeology, 1974,11, 69.336 GENERAL DISCUSSION I / I I I 1 I I I I 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2 logK a 3 Fro.1 .-Electrophoretic mobilities as a function of log rca for different values of zeta potential (mv) using the tabulated data of Wiersema et al. 0, Experimental points of Vincent et ul. reproduced by permission of the authors. concentration) could in fact be drawn to show a plateau in the region of -110 to - 120 mV rather than a maximum as in fig. 8. A further degree of uncertainty would be similarly introduced if KU of the measured particles is not accurately known. Thus, the natural tendency to measure the mobili- ties of the larger, brighter particles in the field of view will result in the true values of rca being larger than those calculated from the mean particle radius. However, the above conclusions do not explain the excessively large zeta potentials obtained for the uncoated sol particles.Dr. B. Vincent (Bristd) (communicated) : Hough is correct in pointing out the rela- tively large errors in zeta potential values derived from mobility data in this region of Ka. With regard to the ‘‘ excessively large ” zeta potentials he refers to, I would reiterate the remarks we made in connection with Healy’s comment that similar results had been found by other workers. Dr. P. Richmond (Port Sunlight) said: A couple of years ago I was working on theories of wetting. Specifically I was interested in understanding the relation between the adsorption isotherms, onset of multilayer wetting and the underlying intermolecu-GENERAL DISCUSSION 337 lar and molecule-substrate interaction potentials.To analyse the problem I used the Percus-Yevick approximation to handle correlations between the particles and the interparticle potential consisted of a hard core plus a short attraction. By appropriate limiting procedures the range of the attraction was taken to be zero, this enabled an analytic solution to be obtained and isotherms of types I and I11 in the B.E.T. classi- fication were obtained according to the relative magnitudes of the potential para- meters.le2 Replacing the above potential by a more realistic potential will yield other isotherms in addition to types I and 111. Specifically using the appropriate potential, it should be possible to understand the results presented by Vincent, Young and Tadros. It should also be noted that correlation of particles of the sort referred to by Robb (above) are automatically (albeit approximately uia the Percus-Yevick method) included in this treatment.Dr. B. Vincent (Bristol) said: We thank Richmond for bringing his theory to our attention and will certainly look into the possibility of fitting OUT data to his equations. We would just add that we did try to fit the particle adsorption isotherms to the Hill- de Boer equation, in a suitably modified form, following a suggestion by Lyklema. The Hill-de Boer equation, which predicts both type I and type I1 isotherms, is based essentially on a two-dimensional gas model, taking into account lateral interactions on the surface, i.e. in linearised form: ' + In (&@} - In 9 = In Kl + K28 1 - where Kr and K2 incorporate the normal and lateral interactions, respectively.Its application at low ionic strengths is, however, questionable because of the irreversible nature of the adsorption. In the high ionic strength region, non-linear plots were ob- tained. Dr. S. Levine and Mr. I. S. Jones (Manchester) said in part: The question of inter- preting the electrophoretic measurements in terms of the zeta potential when the particles are coated with polymer can be answered, at least qualitatively, by the following simplified theory. We imagine the charged surface of a (large) polystyrene particle to be planar, at potential ( and covered with a polymer layer of thickness d. We use the linear Debye-Huckel expression for the potential in the diffuse layer t , ~ = where IC'~ is the characteristic Debye thickness and z is distance measured normal from the polystyrene surface. On applying a uniform electric field E in the x direction paral- lel to the surface, the electro-osmotic velocity u may be identified with the electro- phoretic velocity.In the region 0 < z < d of the polymer film, the x component of Stokes hydrodynamic equation reads where ,u is the viscosity of the fluid, u the fluid velocity in the x direction, p the diffuse layer charge density, N the number density of segments of the polymer andf the fric- P. Richmond, Phys. Chem. Liquids, 1976,5,251. * P. Richmond, J.C.S. Faruduy 11, 1977,73,251.338 GENERAL DISCUSSION tion coefficient of a segment. This equation follows from Debye and Bueche,' Kirkwood and Riseman' and more recently Felderhof and D e ~ t c h .~ Substituting where E is the dielectric constant, and applying the no-slip condition u = 0 at the boun- dary z = 0, we can write the solution of eqn (2) in the form where u2 = NAp and B is a constant of integration. In the region z > d, we omit the factor Nfu in eqn (2) and so obtain as solution noting that u = U at z =; co. The two constants B and U are determined by applying the conditions that u and duldz are continuous at z = d. This yields the electro- osmotic velocity where Us = -(E4/47r,u) is the Smoluchowski formula. It has been assumed that the diffuse layer charge distribution is not affected by the polymer layer. If we choose a Stokes resistance law f = 6npa where a is the effective radius of a segment, then for typical values a = 1 nm N = 5 x lOI9 (about 5% volume fraction of polymer segments) and 0.1 mol dm-3 of a 1 - 1 electrolyte, u % K.For a > K, U E Use-Kd which means that the shear plane is practically at z = d and the zeta potential calculated from the Smoluchowski formula refers to the outer boundary of the polymer layer. For a < K, U E Use-ad and if further ud < 1 then U z Us and use of the Smoluchowski formula yields the potential at the polystyrene surface. Obviously these are the two extreme cases. Dr. J. W. Goodwin and Prof. R. H. Ottewill (Bristol) (communicated) : Following our recent work on the preparation of monodisperse polystyrene latices of various s i ~ e s , ~ * ~ in the absence of added surface active agents, using as initiators both 2-azo- bis-(2-methylpropamidinium) dichloride and 2-azo-bis-(2 -isopropyliminazolium) dichloride, these latices have been used to study the heterocoagulation of cationic polystyrene latices with anionic polystyrene particles.These studies have included particle size effects and electrolyte concentration effects but have not included the addition of surface active or macromolecular species to the systems. It has been our impression from these studies that lateral interactions between the adsorbed particles are not of great importance. For example, in studies by Mr. S. Cheung using 2 pm diameter anionic polystyrene particles and 0.5 ,um diameter catio- nic particles in dilute electrolyte solutions scanning electron microscopy indicated that the cationic particles invariably close-packed on the larger anionic one.This is illus- P. Debye and A. M. Bueche, J. Chem. Phys., 1948,16,573. J. G. Kirkwood and J. Riseman, J. Chem. Phys., 1948,16,565. B. U. Felderhof and J. M. Deutch, J. Chem. Phys., 1975,62.2391. R. Pelton, Ph.D. Thesis (University of Bristol, 1976). J. W. Goodwin, R. H. Ottewill and R. Pelton, Colloid Polymer Scieirce, 1978, in press.FIG. 1 .-Scanning electron micrographs of the heterocoagulation of cationic latex partic (a) anionic latex particles-full coverage, (6) anionic latex particles-partial coverage, (c) on : glass surface-partial coverage. [To face page 338GENERAL DISCUSSION 339 trated in fig. 1, where micrograph (a) shows the close-packing at essentially full cover- age and (b) the close-packing which occurs even at partial coverage of the surface.It was also found even with planar glass surfaces (negatively charged) and dilute cati- onic latex dispersions that when adsorption occurred the latex particles tended to close-pack in small groups as shown in fig. l(c). Dr. P. Richmond (Port Sunlight) said : The measurements of van der Waals forces between metals are very interesting. Recently Chan and I looked at the problem of van der Waals forces between metal surfaces and found that effects of spatial dispersion in such systems causes the inter- action to deviate from that given by the usual Lifshitz theory? We computed the results for aluminium shown in fig. 1. The dotted line is the result obtained by con- ventional Lifshitz theory. At small separations, the Hamaker ‘‘ constant ” is con- stant; at large separations it drops in magnitude due to retardation. The solid line shows the effect of taking into account spatial dispersion via the dielectric permittivity. Clearly the difference becomes quite marked at distances less than -50 A. At small distances (-4/kF, where kF is the Fermi wavenumber for the metal) we expect our results will start to become inaccurate due to overlap of electronic charge distribu- LO Y d d E LA 1 ‘kF 10 100 1000 separation /A FIG. 1.-Hamaker “ constant ” for aluminium in units of kT. tions. Nevertheless, at this distance, which for our example is 12 A, spatial dispersion has resulted in a 20% reduction in the Hamaker constant. Results for platinum and gold should be qualitatively similar and I would be interested to know if the experi- mental method of Deryaguin can be used to study accurately the small distance regime. Prof. B. V. Derjaguin (Moscow) (communicated) : In deriving the ionic electro- static repulsion using the Gibbs-Duhern equation, let us consider a system made LIP of two parallel metal plates each having an area equal to unity, the metal plates being immersed in an electrolyte solution having a concentration of y mol ~ m - ~ ; the electrolyte contains n1 cations having charges zle and n2 anions having charges z2e, where e is the electron charge. Relative to infinitely remote places in the solution, the potentials of plates y1 and w2 are maintained constant, owing to two sources of electromotive forces and to an electrode which has been placed in infinity. However, this does not alter the fact that a part of the potential (or the whole potential) of each plate is set up by the specific adsorption of ions. D. Chan and P. Richmond, J. Phys. C. : Solid State Phys., 1976,9,153.340 GENERAL DISCUSSION The Gibbs-Duhem equation generalized with due regard to the electric work of charging the interfaces may be written in the following form: dG + S dT - V dp + 2 T'i dpi + I7 dh + 01 dvl + 02 dy/2 = 0, (1) i where G is the thermodynamic potential including terms -cl )y, and -c2y2; I', indicates the adsorptions of ions ; pi indicate their chemical potentials ; S the entropy ; T is the temperature ; h is the gap between the plates, and I7 is the disjoining pressure set up by the overlapping of double ionic layers in the interlayer h. Being interested in the overlapping effects, we shall consider a, and c2 as the charges on the internal surfaces of the plates, whose values depend on h. In a general case, the adsorption values in the system under consideration depend on h. Now, we shall not discuss other, non-electrostatic components of disjoining pressure. From eqn (l), it follows that at T = const, p = const, pi = const, y, = const, In order to calculate a@), it will be necessary to apply the Poisson-Boltzmann equa- tion where a = 81~10 enlz,y, b = e]kT, D is the permittivity of the electrolyte solution; y is the concentration in mol crnB3; x is the coordinate which is read off, the internal surface of plate 1, in the direction of the normal to it. Defining by -C the integra- tion constant (see fig. l), the first integral of eqn (3) gives the following expression: Atx=O,wehavey=y/l,al=- - (9) ; hence it follows: 4~ dx x = o Using a well-known identity: and an obvious relationship (see fig. 1):GENERAL DISCUSSION 341 db h we derive from eqn (5'): From this expression and from eqn (2) and (4'), we obtain by integrating and taking into account that at h = 00, 17 == 0, and owing to eqn (4") C = 0, the well known ex- pression : (9) D 17 = C = kTy[n,(ezlbvl - 1) + nZ(e-Z2bwl - l)] - 8n E: . 8Zb The first term expresses the hydrostatic pressure, and the second one expresses the Maxwell electrostatic tension. We see that the value of 17 derived depends only on the potentials applied to the boundaries of an electrolyte interlayer at the given moment, hence cannot depend on what will occur, when its thickness h varies in a real process nor on the material and the electrical conductivity of plates.