GENERA L DISCUSSION Mr. D. W. J. Osmond (I.C.Z. Ltd. Slough) said My colleagues and I have been very interested in the paper of Andrews et al. We have been concerned with the behaviour of sterically stabilized particles in concentrated solutions and ‘‘ melts ”. There are now semi-quantitative theories for the action of polymeric steric barriers in low molecular weight environments. These theories suggest that a large part of the repulsion arises from the non-ideal osmotic pressure generated by the increased concentration of polymer segments in the region in which the barriers have overlapped. Clearly however this change in segment concentration and hence excess osmotic pressure is much reduced in concentrated solutions of unadsorbed stabilizing polymer in the low molecular weight solvent and disappears altogether in an environment which comprises solely molten polymer.F. A. Waite and I have considered the problem of particle stability in such cases and have concluded first that the concentra- tion of segments of stabilizing (adsorbed) polymer chains in the barrier will rise in the limiting case of the melt to 100 % and secondly that these concentrated barriers will be stiffer and stronger than the more diffuse barrier formed in low mole- cular weight solvents. We propose that where the particle surface has free access to more stabilizing molecules and there are no packing limitations of the anchor groups at the surface more stabilizer will be adsorbed to maintain the barrier of similar thickness to that of the barrier in low molecular weight solvent. Where these conditions cannot be fully met the additional rise in concentration must be met by contraction of the barrier back towards the surface.In some preliminary experiments we have demonstrated that stable dispersions of polymethyl methacrylate stabilized by polymethyl methacrylate/poly( 12 OH stearic acid) graft copolymers can be prepared in molten methyl ester of poly(l2 OH stearic acid). In these dispersions the amount of stabilizer adsorbed per unit area of particle surface appears to be several times that adsorbed from low molecular weight aliphatic hydrocarbon continuous phases. In the latter case the effective barrier thickness is believed to be about lOOA (10 nm) and the mean stabilizing segment concentration about 10-15 %. In the melt therefore the segment density may be about 50 % with a barrier still of 100 8 (10 nm) or more probably the segment density may be near 100 % with the barrier contracted to about 50A (5 nm) thickness.The experimental techniques of Dr. Haydon and his colleagues are far more refined than ours and they support our ideas closely. It would be of interest if the work could be repeated with higher molecular weight soluble chains. In this case the lower segment densities in low molecular weight solvents would allow a much larger rise in concentration as the solvent molecular weight was raised and freed from the limitation of anchor group spacing which may operate with oleyl mono- glyceride the predicted increase in adsorption might also be observed. Dr. H. E. Ries (Chicago) said Although the interesting studies of Andrews Manev and Haydon were performed on systems considerably different from those investigated in our laboratories the overall results and their implications are strikingly different from the stand-point of chain-length compatibility in mixtures of polar and non-polar compounds.In our work we have found that (a) mixed films of stearic acid and n-hexadecane at the water/air interface retain considerable hydrocarbon in the monolayer when subjected to elevated surface pressures ; and (b) radiotracer 75 76 GENERAL DISCUSSION adsorption experiments at the solid/liquid interface indicate the formation of mixed films of stearic acid and n-hexadecane. In the latter experiments radiostearic acid is adsorbed directly from n-hexadecane solutions on vapour-deposited metal films on the window of a Geiger tube.Moreover studies of rust-preventive films clearly demonstrate strong interaction and chain-length compatibility in thin films of fatty acids and hydrocarbons. Fatty acids and hydrocarbons of the same length and geometry apparently form stronger mixed films and thus provide better rust protection,2 as well as greater resistance to scuffing in four-ball studies by Cameron and other^.^ Dr. H. Sonntag (Deutsche Akademie der Wissenschaften Berlin) said With regard to the paper by Haydon et al. did the thickness of the hydrocarbon region change reversibly or irreversibly with applied potential ? We obtained with the same method the thickness of oil layers between mercury droplets reversibly up to a certain applied potential and we could calculate the elasticity of the adsorbed layer which was unaffected by the thickness and had a value for oleic acid layers (thickness 54 A) of lo6 d y n / ~ r n ~ .~ Above this potential the thickness altered irrever- sibly. From Haydon’s measurements we calculated an elasticity of 10’- lo6 dyn/cm,2 which is of the same order as our values. It it possible that the change of elasticity with applied potential could be explained by an alteration of the film diameter? We measured an increasing diameter of the film with increasing applied potentials in water/oil emulsions. Prof. J. Th. G. Overbeek (University of Utrecht) said The sharp c.m.c. in the presence of 0.1 M NaCl and the much wider transition region in the presence of saturated NaCl (see fig. 3 of the paper by Haydon et aZ.) point to small aggregates formed with saturated NaCl and larger ones with the more dilute solution.It is worth while to look for a confirmation by light scattering or ultracentrifugation. The difference in aggregate size might be connected with the difference in water activity if water is a necessary partner in at least the bigger aggregates ; or the small aggregates might be formed around ions solubilized in the oil phase. The latter explanation would require an increased conductance of the oil phase in contact with saturated NaCl. Dr. D. A. Haydon (PhysioZogicaZLab. Cambridge) said In reply to Osniond we have been interested for some time in the possibility of working with black lipid films stabilized by molecules of chain lengths both longer and shorter than that of the oleyl derivatives. A limited investigation has been reported using chain lengths between n-C, and n-C, but owing to the nature of the stabilizing molecules a detailed interpretation of the results was not possible.It is hoped however to find satisfactory stabilizers of chain length greater than CZ2. The problem of steric stabilization in one component liquids such as polymer melts to which Osmond draws attention underlines the necessity to develop further the formulation of the configurational free energy along the lines attempted by Mackor and van der Waals and now by Findenegg and Ash.‘ H. D. Cook and H. E. Ries Jr. J. Phys. Chem. 1959,63 226. H . E. Ries Jr. and J. Gabor Chem. and Ind. 1967,1561. A. Cameron and R. F. Crouch Nature 1963 198,475. Tenside 1969 6 61. J. L. Taylor and D. A. Haydon Disc. Faraday SOC. 1966,42 51. this Discussion.GENERAL DISCUSSION 77 In reply to Ries the spread films of stearic acid and n-hexadecane at the air/water interface and the adsorption of stearic acid from n-hexadecane on to metal-coated mica surfaces should perhaps not be compared too closely with the adsorbed mono- layers of glyceryl mono-oleate at the n-hexadecane/water interface. In the spread film experiment the n-hexadecane is presumably squeezed out from between the stearic acid molecules as the compression proceeds. Towards the end of the com- pression (where from Ries’s graph the surface pressure becomes constant) it is not clear where the hexadecane is. estimated that the maximum adsorption of stearic acid at the n-heptane/water interface (at ca. 0.02 mol/l.) corresponded to ca. 60 A2/molecule. The results reported in our paper for glyceryl mono-oleate and adsorption studies on n-alkanols do not indicate any great influence of the solvent on the adsorption and it seems probable that 60A2 per molecule would hold also for n-hexadecane.If this is so the space available for n-hexadecane in the monolayer would be substantially greater than in the glyceryl mono-oleate systems where thc area per molecule is ca. 30A2. A similar situation appears to exist in the metal- coated mica systems examined by Ries. The data indicate a maximum area per molecule for stearic acid adsorbed from n-hexadecane of ca. 65 A2. Again there is apparently considerable space available for solvent. The inclusion of n-hexadecane into such stearic acid monolayers does not therefore seem in any way remarkable and it would be expected that shorter chain solvents would be included to a similar or even greater extent.This does not exclude the possibility that in hexadecane the monolayers may have exceptional mechanical properties. In reply to Sonntag under the conditions described in our paper the thickness of the hydrocarbon region of the film changed reversibly with applied potential. As stated however the equilibrium condition was for some systems established only after considerable time. For higher applied potentials the films tended to rupture. Jn all membranes the application of a potential caused an increase in the diameter of the film. This effect was allowed for in the calculation of the specific capacitance of the film and it is not thought that it could account for the change of compressibility with applied potential.In reply to Overbeek no attempt was made to examine in detail the aggregation of the glyceryl mono-oleate at high concentrations in the hydrocarbons. Neverthe- less for the oleate in n-heptane at 25°C (equilibrated with saturated NaCl) the vapour pressure curve was measured to concentrations (ca. 1.2 x M) at which it became roughly linear. In this region the aggregation number was ca. 26. The interfacial tension curves certainly suggest that at lower concentrations at least the aggregates formed in systems equilibrated with saturated NaCl are smaller than in those equilibrated with 0.1 M NaCl. While no conclusive evidence is available miscellaneous observations during the course of the experiments indicated that the presence of water in the hydrocarbon phase favoured the formation of larger aggregates.Dawson Dr. G. H. Findenegg (University of Vienna Austria) said In relation to the stability of thin liquid films I would like to mention some theoretical work by Ash and myself.2 We have considered a solution of chain molecules between two plane interfaces. The chain molecules have an “ active ” end-group which is preferentially adsorbed to the interfaces. The calculations are based on a multi-layer lattice model for Dawson Ph.D. Thesis (Cambridge 1963). S. G. Ash and G. H. Findenegg Trans. Faraduy SOC. to be published. 78 GENERAL DISCUSSION adsorption from monomer + r-mer solutions. Different chain-conformations are allowed for by considering a number of configurational species of r-mer according to the sequence of their segments in the lattice 1ayers.l We have calculated for r-mers up to r = 4 the concentrations of the adsorbed configurational species the Gibbs adsorption of r-mer and the configurational Helmholtz free energy F, as a function of the following parameters the thickness of the liquid film ; the concentration of r-mers (in a bulk solution at equilibrium with the liquid film); the strength of preferential adsorption of the active end-groups ; and the segment interchange energy of active and non-active segments (monomers are energetically equivalent to non-active segments of r-rners).Many features of this model are in agreement qualitatively with the properties of non-compressed lipid films in aqueous media as reported by Haydon et al. We find that only a fraction of the r-mers are in their fully extended form normal to the interface and hence the concentration of r-mer chain segnients decreases towards the centre of the film.The surface excess of the configurational free energy F has a (shallow) minimum at a thickness of the film equal to twice the extended form of r-mer (8 layers for r = 4). F," then increases with decreasing thickness hence there exists a repulsive force. At a given film thickness F," increases with increasing chain length and concentration of r-mer as well as by an increase in the preferential adsorption of active segments and the interchange energy. For films consisting of monomers + homogeneous r-mers (all its segments preferentially adsorbed to the interfaces) we find a decrease in F," with decreasing film thickness hence such films should not be stable.Dr. B. Vincent (I.C.I. Ltd. Slough) said I would suggest some data and calcula- tions that could help resolve the apparent discrepancy between the results presented by Sonntag at this meeting on oil droplets in water and those of Ottewill and Walker on aqueous polystyrene latex dispersions both systems containing ethylene oxide (E.O.) stabilizers but showing different trends in stability as the stabilizer concentra- tion is increased. I have recently determined some Haniaker constant values by the method of Gregory using refractive index data. Values relevant to this work are material A x l O z o J octane 5.3 polystyrene 7.8 poly(ethy1ene oxide) 6.9 water 3.8 Appropriate models were set up (flat-plates for octane ; spheres for the polystyrene latices) in which the thickness of and ethylene oxide concentration in the adsorbed layer together with the surface separation of the particles were allowed to vary.The relevant equations for the attraction energy V l (flat plates) and V i (spheres) were derived from eqn (2) of Sonntag's paper and the equation of V ~ l d ~ respectively. Retardation effects were neglected for the purposes of these calculations. Fig. 1 indicates how the Hamaker constant A 3 of the adsorbed layer varies as a function of the wt fraction w of E.O. in the layer. Fig. 2 and 3 show how V i varies as a function S. G. Ash D. H. Everett and G. H. Findenegg (a) Trans. Faraday SOC. 1968,64,2645 ; (b) 1970 66 708. R. H. Ottewill and T. Walker Kolloid-Z. Polymere 1968 227 108. J . Gregory Adv. Colloid Itirerface Sci. 1969,2 396. M.J. Vold J. Colloid Sci. 1961 16 1 . GENERAL DISCUSSION 79 W FIG. 1.-Hamaker constant of adsorbed layer A3 as a function of wt fraction 10 of ethylene oxide in the adsorbed layer. 8.2 0.4 0.6 - 06 Q L- W FIG. 2.-Attraction energy between two aqueous polystyrene latex particles (radius 25 nm) covered with adsorbed layer thickness a3 as a function of ethylene oxide wt fraction w ; surface separation h = 0.2nni. 80 GENERAL DISCUSSION of w for various thicknesses d3 of the adsorbed layer. In fig. 2 the surface separation h between the particles (core and adsorbed layer) is 0.2 nm (effectively the two particles are in contact i.e. held apart by Born repulsion forces) In fig. 3 h = 10nm. The general form of fig. 2 and 3 is the same only the magnitude of V i being signifi- cantly different.The two points labelled A and B in fig. 2 indicate the values of V i when there is no surface-active agent present and when there is a monolayer of adsorbed surface-active agent present respectively. (It can be shown from the adsorption isotherm that w is about 0.7 at monolayer coverage of n-dodecyl hexa- ethylene oxide on polystyrene latex. Also the thickness of the E.O. layer is about 2.5 nm). Between these two points one would expect the actual locus of points for V; curve 111 to be between the two extreme curves I and 11 in fig. 2. Curve I I 0 2 0.4 0.6 0.8 W FIG. 3.-As for fig. 2 but h = 10 nm. corresponds to the case where the thickness of the E.O. layer gradually increases but that its E.O. content (after the initial addition) remains virtually constant. This corresponds to a gradual change from a “ horizontal ” to a “ vertical ” configuration of the E.O.molecules at the surface. Curve I1 represents the case where there is a gradual increase in E.O. concentration in the adsorbed layer the thickness remaining more or less constant (i.e. vertical configuration throughout). The real curve 111 would indicate that there is probably a gradual decrease in V i as stabilizer is added to the system as was suggested by Ottewill and Wa1ker.l Fig. 4 and 5 show the corresponding V i curves for Sonntag’s system again for Iz = 0.2 and 10 nm respectively. The maximum thickness of the E.O. layer in this case would be expected to be in the range 5-10 nm and again assuming the maximum value for w is about 0.7 the corresponding two points A and B may be plotted (fig.5). This time the case h = 10 nm is arbitrarily considered since in this system the electrical double layer repulsion will contribute to the equilibrium separation. However again the general form of the curves in fig. 4 and 5 is similar although for h = 0.2 nm the curves for d3 are virtually coincidental. (This results from the r6 dependence GENERAL DISCUSSION 81 W FIG. 4.-Attraction energy between two octane droplets in water having an adsorbed layer thickness s3 as a function of ethylene oxide wt fraction w ; surface separation h = 0.2 nm. 4 0 0.6 0.8 0.4 0 . 2 W FIG. 5.-As for fig. 4 but h = 10 nm. 82 GENERAL DISCUSSION of the inter-molecular attraction forces-neglecting retardation.) In this case unlike the polystyrene latex V (B)> V (A). The two extreme loci discussed above are represented by curves I and I1 again.Here the most probable locus (curve 111) indicates that after the initial addition of stabilizer V i increases on further addition of stabilizer as Sonntag has suggested. This would appear to resolve the apparent discrepancy. The main reason underlying these two apparently different trends in the attractive force lies in the relative Hamaker constant values for the sheaths and cores in the two cases. In the Ottewill and Walker case the core Hamaker constant is greater than that of the sheath and vice-versa in the case of Sonntag. The exact way in which V varies as stabilizer is added will depend on exactly how its configuration and concentration varies in the adsorbed layer. Dr. H. Sonntag (Berlin-Adlershof) said In reply to Vincent his calculations are correct but nevertheless incorrect.He chose as the distance between the particles the spacing from one adsorbed layer to the other. If this is done he will indeed find a reduction of dispersion forces if the Hamaker constant of the adsorbed material is less than that of the particles or vice versa. But we measured the distance from particle to particle because the polar groups are strongly solvated and the refractive index changes most rapidly at the particle surface. In this case one always obtains increasing dispersion foices independent of A3 < A or A3 > A l . Only if the Hamaker constant of the adsorbed material is less than that of the water phase can one calculate decreasing dispersion forces. Unfortunately the discrepancy between 0 ttewill's and our paper cannot be explained so easily.Dr. B. Vincent (University of Bristol) said I agree partly with Sonntag but I am also wondering if he has missed the main point of my argument. We are both looking I think for an explanation in terms of increased inter-particle attraction of why the spacings in his experiments decrease on increasing the stabilizer concentration. In terms of the Hamaker constant values I quoted it is largely irrelevant in the case of his experiments as to whether one considers constant surface-surface separation or constant adsorbed layer-adsorbed layer separation. The latter case corresponds to the situation I had previously described. The former case would correspnd to one of the fixed Even for increasing adsorbed layer thickness at constant surface-surface separation this would lead to increasing attraction.In both cases the attraction increases as stabilizer is added (in the latter case continuously in the former case probably only after some stabilizer has initially been added). In Ottewill's experiments however it is very relevant as to whether one takes constant surface-surface separation or constant adsorbed layer-adsorbed layer separation (see e.g. fig. 2). In the former case again one would again have to take a fixed 6 (again probably 25A) and this would lead to increasing attraction on adding stabilizer. My reasons for taking the constant adsorbed layer-adsorbed layer (or perhaps a better definition is constant " outer " surface-" outer " surface) separation is that Ottewill was considering particle flocculation (under conditions where the electrical double layer repulsion is eliminated) and in this case it is necessary to take the origin of the attractive forces as being at the outer surface of the particles.In this case as I showed previously (and as Mrs. Vold has shown) the most probable result is a decrease in attraction on adding stabilizer. curves in fig. 5 (say 6 = 25 A). That is what is required to explain his results. Prof. A. Scheludko (Sofia) said The paper of Sonntag Netzel and Unterberger First the use of a porous is a further step in the investigation of emulsion films. GENERAL DISCUSSION 83 plate as a modification of Mysels’ porous ring method is of considerable interest. In this particular case the role of the porous walls is to fix the film to the holder something which until now has been difficult to achieve in a smooth-walled glass cell and which represented a major obstacle.This method makes it possible to vary over a wide range the capillary pressure which although not made use of in their work in fact was its original purpose.2 Also this is the first application in real emulsion films of the microscopic method of measuring the contact angle film/bulk l i q ~ i d . ~ As with foam films the contact angle reaches significant values after transition to the Perrin films obtained in this case at sufficiently high electrolyte concentration (5 x lo-’ M MgS04). The reported values of the contact angle at low concentration (a few hundredths of a degree) are greater than the sensitivity of the method. The observed influence of the surfactant concentration on the equilibrium thickness is somewhat unexpected.According to these observations the equilibrium thickness decreases with increase of the surfactant concentration. This corresponds to the negative component of the disjoining pressure prevailing over the positive component. In fact the effect is even greater than can be seen in fig. 2 because the surface tension and therefore the outer capillary pressure decrease when the surfactant concentration is increased. We however cannot agree with their generalization of the effect to any dispersion system since in other cases as e.g. with some foam films the opposite effect of the surfactant has been observed. Thus in ref. (3) the deviations from the DVO theory were in the direction of the positive disjoining pressure prevailing over the negative component for sufficiently thin films.The influence of the surfactant on foam films was directly demonstrated in the investigation of the critical thickness of r ~ p t u r e . ~ In the latter a decrease of the critical thickness at high surfactant concentration was obtained which meant an increase of the positive disjoining pressure i.e. the reverse of the effect described in their paper. Unfortunately the curves of equilibrium thickness against electrolyte concentra- tion in the paper are not interpreted according to the DVO theory with the simplest assumption that IIvw is inversely proportional to the third power of the film thickness. Tt is hardly appropriate to take into account the thickness of the adsorption layers (in fact merely the thickness of the polar “ heads ”) when considering films with such a large total thickness (200-550 A).The thickness of the polar groups is of the order of magnitude of the experimental error. That is why their interpretation does not appear convincing. Dr. H. Sonntag (Deutsche Akademie der Wissenschaften Berlin (communicated) In reply to Scheludko one finds an alteration of the critical thickness of rupture with increasing surfactant concentration until only cb is reached. Above this concentra- tion the rupture thickness remains constant. We always measured the equilibrium thicknesses above cb and therefore a comparison of his results with ours is impossible. On the other side his coworker Exerowa also found a decrease of equilibrium thick- ness with increasing concentration of non-ionic surfactant.Prof. J. Lyklema (Wageningen Netherlands) said In looking for an explanation for the effect of surfactant concentration on the equilibrium thickness as shown in D. Exerowa and S. Scheludko Cumpt. Rend. Acad. Bulg. Sci. in press. K. Mysels J. Phys. Chem. 1964 68 3741. A. Scheludko B. Radoev and T. Kolarov Trans. Faraduy SOC. 1968 64 2213 ; T. Kolarov A. Scheludko and D. Exerowa Trans. Faruduy Suc. 1968,64,2864. I . Ivanov B. Radoev E. Manev and A. Scheludko Trans. Faraduy Soc. 1970,66,1262. 84 GENERAL DISCUSSION fig. 2 of Sonntag et aI.’s paper one could also think of a kind of “ tele-entropic ” stabilization mechanism according to the following principle. If two emulsion drop- lets each covered with surfactant molecules and bearing at least some charge approach each other the diffuse double layers start to overlap and counterions are transferred from the Gouy-layer to the Stern-layer.When the degree of occupancy of the liquid/liquid interface with surfactant molecules is low it is possible that these counterions are pressed in between these molecules which could reduce their con- figurational entropy and hence constitute a repulsion. The more compact the surfactant layer becomes the less this effect and at sufficiently high degrees of occupancy this repulsive entropic term is completely absent. Thus the model can account for a repulsion that is only operative at low surfactant concentrations. Dr. H. Sonntag (Deutsclie Akademie der Wissenschafien Berlin) said With regard to the paper by Padday the rupture of liquid films on solid surfaces is a very complicated example of hetero-coalescence.I think his measuring device is not sufficiently sensitive to decide what happens at the rupture process because the thickness of the film is inhomogeneous before breaking. We investigated the rupture process of aqueous films on cyclohexane with the apparatus described in our paper. The thickness of rupture decreased with increasing concentration of surface-active agent from several 1000 A to 300 A. Above a certain concentration the thickness of rupture remained unaltered and we obtained a stable film whose thickness depended only on the electrolyte concentration. Dr. J. F. Padday (Kodak Ltd. Harrow) In reply to Sonntag in subsequent experi- ments described in the appendix of my paper I have pointed out that high-speed cine photographs revealed an indentation or dimple in the surface of my experiments.Thus the critical thickness between the liquid-air and solid-liquid interfaces inay well be of the same order as Sonntag’s rupture thickness because the thickness I have measured is that of h in the fig. 8 whereas Sonntag measures h’. Dr. R. G. Picknett (C.D.E. Porton Down Wilts) said Padday has given a modificd form of the Kelvin equation which relates capillary pressure disjoining pressure and vapour pressure Deryaguin made it clear that for thin liquid layers the curvature is not constant but varies with a m thickness in accordance with the disjoining pressure Thus in applying eqn (I) to liquid in a capillary or at the point of contact of sphere and plane it is incorrect to calculate I3 from the total liquid thickness; instead it must be evaluated for each point on the liquid surface This has been done for water between a 720 pm dim.glass sphere and plane the work being part of an adhesion investiga- tion by Cross and myself. The surfaces were assumed to be smooth and the vertical profile of the water/air interface was calculated using I’I values derived from the work of Deryaguin and Zorin.2 The adsorbed water film far from the point of contact was so thin that it had only a negligible effect. The maximum thickness obtained for the water annulus is shown in fig. l(a) as a function of PIP it is larger than the thickness calculated from the simple Kelvin equation by a factor of 1.2-1.3. Knowing the surface profile the adhesion due to the surface tension of the water B. V. Deryaguin Proc.2nd Int. Congr. Surface Activity (London 1957) 2 153. B. V. Deryaguin and Z. M. Zorin Proc. 2nd Int. Congr. Surface Activity (London) 1957,2,145. GENERAL DISCUSSION 85 can be obtained as a function of PIP,. These adhesions are shown in fig. l(b) and l(c) as solid lines the diagrams referring to two different separations h of sphere and plate corresponding to different degrees of surface roughness. Experimental adhesions were measured using plates with artificially-induced roughness and are represented in fig. l(b) and l(c) by crosses. The experimental values lie well below the solid curves derived from eqn (I) and in fact lie more closely on the broken curves which were derived from the simple Kelvin equation. The discrepancy is thought to be significant and indicates that eqn (1) does not apply to the sphere+plane system.The explanation may well lie in the assumption used in eqn (1) that the (4 (b) (c) 40p n 0 d h E 30- s 20- --- .d 4 10- h=SO i f 0.7 - 0.8 0.9 1 0.7 0.8 0.9 0,- PIPS PIPS PIPS FIG. 1. capillary pressure and the disjoining pressure are additive. If instead of this assump- tion allowance is made for change in surface tension as well as for disjoining pressure then better agreement with experiment may well be found. Dr. J. F. Padday (Kodak Ltd. Harrow) said I am grateful to Picknett for pointing out to me that Deryaguin in 1957 proposed a modification to the Kelvin equation that took into account the effects of disjoining forces on the condensation of liquid within a pore. This equation is general in principle but is difficult to apply particularly to the system of liquid condensing between the ball and plate of Picknett's experiments.In applying either form of the Kelvin equation modified for thin film effect Picknett has made two assumptions. The first is that the surface tension is a constant value at both the thin and thick parts of the meniscus and that therefore the angle of contact between thin and thicker film is zero. This assumption is reasonably well justified because the force of adhesion is predominantly a surface pressure term and in the results quoted in the comments depends on the " bulk " surface tension and the radii of curvature at the neck of the liquid bridge. The second assumption concerns the effect of geometry of the axisymmetric liquid bridge on the disjoining pressure at any element of liquid between the solid/liquid and liquid/air interfaces.I understand that Picknett calculated the data of fig. 1 by first deriving the shape of the liquid bridge using a graphic integration method with eqn (6) of my paper. The sum of the II terms were derived from the values given by Deryaguin and Zorin and the integration process produced a shape from which shape parameters such as the two principle radii of curvature at the narrowest point at the neck of the liquid-air interface were obtained. The sum of these curvatures multiplied by the " bulk " surface tension was then it appears used to calculate both the adhesion force and the vapour pressure in equilibrium with it. In applying these calculations one must assume that the disjoining pressure measurements of Deryaguin and Zorin for disjoining of a thin layer of liquid between two flat parallel surfaces are equally suitable when the 86 GENERAL DISCUSSION two surfaces deviate appreciably from parallelism.Both van der Waals' and electric- double layer forces appear to be sufficiently sensitive to the angle between the two surfaces bounding the thin film to suggest that at the neck where the angle is nearly go" the value of the disjoining pressure would be greatly reduced and thereby explain Pickett's results. Dr. L. M. Dormant (Bristol University) said Process C of Padday's paper can be examined in a more quantitative manner. The equilibrium shape of a very large drop in a gravity field leading to the Young and Duprb equation was solved by Adamson and Ling.2 The final state of process C is just the inverse of this configura- tion so that any height less than a (1 -cos O)+ where a is the capillary constant and a' = 2y/pg will be unstable.A few values-those for which the contact angle 0 was readily obtained 3-are compared with Padday's results in table 1. All of the experimental results are in the region of predicted instability. Exact agreement cannot be expected unless the radius of the patch is very large. It is not sufficient to show that the system is unstable; one needs to discuss mechanisms for rupture. Even though the results (that the critical rupture thickness is different for Teflon and paraffin wax) seem to show that this thickness is dependent on the solid used I cannot (yet) accept the implied concept that a S/L interface can exert an influence on an L/A interface at a distance of 1 to 5 x lo6 A.lo2 A yes ; 103A maybe ; 106A NO! It would be simpler to imagine some extra-thermodynamic disturbance bringing the L/A interface to within a short (N10A) distance of the S/A interface. At this distance one could acceptably assume long-range interactions thereby forcing the L/A interface to remain there and thus forming the dimple that Padday described. TABLE 1 .-THERMODYNAMIC AND EXPERIMENTAL RUPTURE THICKNESSES benzene/Teflon 14.7 46 1.4 0.16 decane/Teflon 6.73 24 0.7 0.26 water/paraffin 6.34 106 4.3 0.31 water/Teflon 6.34 108 4.4 0.21 (a) a' = 2y/pg ; (b) from ref. (3) ; (c) from h" = a(1 -cos 813 ; ( d ) from table 1 and 2 of Padday. The mechanism which might help to explain this postulated disturbance is the formation of capillary gravity waves and the subsequent amplification of certain wavelengths due to the geometry of the system.One could make a somewhat dubious analogy to the placing of the more dense of two immiscible liquids on top of the less dense liquid. The primary mode of rupture for such bulk phases is that some of the wavelengths are selectively amplified until rupture OCCU~S.~ This system is only stable to wavelengths less than &a. The analogy is useful in so far as it poses three other questions (i) what would happen if instead of a large piece of Teflon a sample a few m2 or less was used and (ii) what would happen if his trough was only a few cm wide? These experiments could show whether Padday W. A. Zisman Ado. Chern. no. 43 (Amer. Chem. SOC. Washington D.C. 1964) p. 11. A. W. Adamson and I. Ling Adu.Chern. no. 43 (Amer. Chem. SOC. Washington. D.C.. 1964) p.72.. A. W. Adamson Physical Chemistry of Surfaces (Intersci. N . Y . 1967) p. 364. 389. R. Bellman and R. H. Bennington Quat. Appl. Math. 1954 12. 151. GENERAL DISCUSSION 87 is indeed measuring a fundamental property or only some property connected with the geometry of the system. The amplification step may take a considerable time (the time factor was not mentioned) and leads to the remaining. questions what would happen if the system was kept slightly above the critical rupture thickness but held there a factor of 10 times longer than the remainder of the experiments? Also what would happen if vibrations were deliberately induced? The question of impurity has already been brought up. Judging from fig. 6 it seems that a small concentration of impurity would have a negligible effect.Impurities should be negligible if the mechanism is a long-range effect. Yet ,if a wave pheno- menon was involved a surface tension gradient of 0.01 dynlcm (N/km) could have pronounced effects perhaps explaining the difference between Teflon and paraffin. Similar conceptual difficulties occur with the salt and surfactant solutions. The double layer thickness of a M solution is approximately lo2 A so that it would be difficult to postulate effects at distances of lo4 times the double-layer thickness regardless of the charge on the Teflon surface. On the other hand the damping of waves by the addition of a surface-active agent leading to greater stability is a common phenomenon.2 I do not believe that a negative damping coefficient has ever been previously observed.Dr. J. F. Padday (Kodak Ltd. Harrow) said I disagree with the first comment of Dormant by which it is implied that any thin film at a solid surface with a thickness less than (2y (1 - cos O)/pg)% is unstable. For water on wax this thickness is about 4.5 mm and all experiments show clearly that layers between 1 and 4.5 mm in thickness are stable over many days. Column 3 of the table in his remarks is thus not relevant as there is no instability. Layers in this region of thickness may have a degree of metastability but this will depend much more on the forces that give rise to dimple formation than to the contact angle properties of a wetting meniscus. As pointed out in the appendix the dimple once formed is resistant to low energy vibrations or ripples at the liquid-air interface.The process by which the dimple first forms could possibly be the trapping of a wave form at the point where the liquid is thinnest but the high speed cine films do not show this. The geometry of the vessel and to some extent the solid surface has been altered and this does not appear to vary the process described. As the phenomenon is also observed on a vibration-free mounting surface effects arising from very small surface tension gradients induced by waves may be discounted. The apparent electrical effects do not necessarily operate over large distances because the dimple reduces the interaction distance. Negative damping coefficients do not have to be invoked although they are well knowq4 because it is believed that the dimple is in an asymmetric force field.Dr. G. Frens (Philips Res. Lab. Eindhoven) said Padday’s work may explain why layers of (aggregated) particles form at the surface of perfectly stable gold and silver sols (and of many other colloidal dispersions). Let us suppose that Brownian motion brings a particle with a hydrophobic surface near the surface of the disper- sion. Padday shows there is a chance for the water layer between the particle and the surface to break. Then the particle will rise and despite its larger density it will be kept afloat by surface tension forces. Now let us consider the coagulation M. van den Tempel private communication. E. H. Lucassen-Reynders and J. Lucassen Adv. Colloid Znt. Sci.. 1970,2,347. J. F. Padday Proc. 2nd Znt. Congr. Surface Activity 1957,3,136 187.J. T. Davies and E. K. Rideal Znterfuciul Phenomena (Academic Press London 1961) p. 360. 88 GENERAL DISCUSSION of two such hydrophobic particles. Instead of meeting the surface they approach each other in a Brownian collision. The water layer between the two particles will break if only because the two particles come in close contact. If the water layer is broken at some point the capillary forces will push the water back from the narrow pores of the aggregate until the radius of curvature of the newly created interface becomes large enough to be in equilibrium with the hydrostatic pressure outside the aggregate. There is a close analogy between this situation inside a floc in a hydro- phobic sol and that in mercury porosimetry @ and the work of Kruyt and van Selms on dispersions in mixed solvents (one wetting the other non-wetting) comes to mind as well as that of Vanderhoff et al.on the coalescence of latex particle^.^ In general it can be concluded that an aggregate of hydrophobic particles should be a three-phase instead of a two-phase system. This will have consequences for the properties of such aggregates e.g. for their repeptization since the situation inside these aggregates will be greatly influenced by the addition of surface-active agents to the dispersion medi~m,~ and to a far lesser extent by agents which might influence the electrical properties of the interface between the original particles and the solution. Dr. J. F. Padday (Kodak Ltd. Harrow) said In reply to Frens in principle the process of rupture described in part 2 of my paper could explain the coagulation of two or more hydrophobic particles which approach each other at some critical rupturing distance when embedded in a non-wetting liquid.A similar explanation was used to account for the driving force that gives rise to the aggregation of two cyanine dye ions to form dimers against electrostatic repulsion forces. However by invoking such an explanation the very small particles may well give rise to rupture and cohesion forces that are very different from those of my experiments because the reciprocal of the radius of curvatures in the two cases differ by more than an order of magnitude. The reverse explanation i.e. that hydrophobic particles near the surface of the liquid gives rise to the dimple does not appear to be possible because the strong disjoining action of a " pillar " of small hydrophobic particles would lead to immediate rupture and not the intermediate formation of the dimple. R. P. Iczkowski Ind. Eng. Chem. Fund. 1966 516. R. P. Mayer and R. A. Stowe J . Phys. Chem. 1966,70,3867. H. R. Kruyt and F. G. van Selms Rec. Trav. Chim. 1943 62,407. J. W. Vanderhoff H. L. Tarkowski M. C. Jenkins and E. B. Bradford J . Mucvomol Clzem. 1966,1 361. E. J. Clayfield and E. C. Lumb Disc. Furaduy SOC. 1966,42,285. J. F. Padday J . Phys. Chem. 1968,72 1259.