Direct Measurements of the Interaction between Adsorbed M acromolecular Layers BY FREDERICK w. GAIN,* RONALD H. OTTEWILL AND JAMES B. SMITHAM School of Chemistry, University of Bristol, Bristol BS8 ITS Received 28th December, 1977 Experimental methods have been developed for determining, as a function of their separation distance, the force of interaction between two macroscopic surfaces coated with adsorbed layers. The central element of the apparatus was two hemi-spherically capped silicone rubber cylinders. With the surfaces far apart, an aqueous solution of poly(viny1 alcohol) was placed between the caps to allow adsorption to occur. Under the influence of a normally applied pressure, the surfaces were forced together so that the liquid layer thinned and the adsorbed layers interacted.The rate of film thinning was measured by a reflectance technique and the distance of surface separation by multiple beam interferometry. The interaction pressure between the layers appeared to commence at a surface separation distance of 160 31: 20 nm and increased to about 1.5 x lo4 N m” at a distance of 70 nm. At shorter distances, the pressure rose steeply with decrease in distance and suggested the formation of a film with a high concentration of PVA between the surfaces. One of the principal ways of ensuring the stability of a colloidal dispersion is to coat the particle surfaces with a protective co1loid.l The latter is usually a macro- molecule; gelatin has frequently been used for this purpose. More recently the classical term “ protected colloids ” has been replaced by the term “ sterically stabil- ised ” dispersions. The latter name, in fact, first appears to have been used by Heller and Pugh2 to denote the fact that uncharged particles could be prevented from floc- culating by the addition of macromolecules.As pointed out by N a ~ p e r , ~ however, the term “ steric ’’ is used in this context with a broad thermodynamic connotation rather than with the restricted meaning its use has in organic chemistry. Knowledge of the forces which control steric stabilisation is still somewhat un- certain; evaluation of the force of steric repulsion as a function of the distance of separation between the surfaces has not yet reached the same quantitative experimental level as that achieved in the case of electrostatic and van der Waals forces, where direct measurements have been made using macroscopic surface^.^-^ In the case of steric stabilisation only a few direct attempts at measuring the forces have been made, one using a 2-dimensional compression at the oil-water i n t e r f a ~ e , ~ , ~ and others using a 3-dimensional compression method.l0-l2 One of the major developments in techniques for making direct measurements between macroscopic surfaces in liquids came with the work of Roberts and Tabor.4 These authors used an optically smooth spherical cap of transparent rubber, which was pressed against a flat glass surface in an electrolyte solution to give a thin liquid film between the glass and the rubber.The rubber deformed easily over local pro- trusions so that in the compression region, essentially parallel surfaces were formed with liquid between them.A more sensitive form of this apparatus was developed * Present address : Department of Chemical Engineering, University College of Swansea, Swansea SA2 8PP.34 ADSORBED LAYER INTERACTION in our laboratories5 and used to measure the pressure arising from electrostatic repul- sion as a function of the distance of surface separation. In this paper we describe our preliminary attempts to develop this technique in order to make direct measurements of the repulsive pressure developed between two surfaces with adsorbed polymer layers as these two surfaces approach to close dis- tances in the interactive region. The surfaces were essentially sterically stabilised by the adsorption of a polyvinyl alcohol-polyvinyl acetate copolymer from an aqueous solution.EXPERIMENTAL MATERIALS All water used was twice distilled from an all-Pyrex apparatus. The poly(vinylalcoho1)-poly(viny1acetate) copolymer (PVA) used was kindly supplied by Dr. T. Tadros, ICI, Plant Protection Division and was an Alcotex 88/10 originally made by Revertex Ltd. The poly(viny1acetate) content was 12% w/w and the weight average molecular weight determined by ultracentrifugation, was quoted as 45 000. A fractionation of the raw material by Dr. M. J. Garvey13 gave weight average molecular weights for the highest and lowest fractions as 67 000 and 8000 respectively. The cloud point in water was 52 "C. REFLECTANCE APPARATUS The principal part of the apparatus consisted of two silicone rubber cylinders with spherical caps submerged in a solution of PVA.The two rubbers A and B were mounted so that B was vertically above A as shown in fig. 1 . The rubber B was securely held by a clamp C so that it remained rigid during an experiment; this support was quite independent of the mechanism holding A. The latter was connected to the drive movement D of a micrometer unit (L. S . Starrett Co.). Lockable joints within the drive assembly allowed the spherical surface of the rubber to be both rotated around the drive axis and to be tilted. The micrometer drive, attached to a slotted beam, enabled movement of the rubber in the vertical direction to be obtained in a very precisely controlled manner. The base could be fixed in position using locking screws.The aqueous PVA solution was placed in the cup E with the spherical rubber surfaces maintained at such a distance that no distortion of the rubber occurred at zero applied pressure. A thin liquid film between the rubber surfaces was formed by driving the rubber A upwards using the drive unit D so that the rubber surfaces became distorted in the central region to a flat disc as shown in fig. l(b). Distortion of the rubber, as shown by changes in the Newton's rings, was observed through the eyepiece of the microscope G. In addition to a viewing eyepiece, the projector end of the microscope could be equipped with either a camera for photographing the films, or with a photomultiplier to monitor the intensity of light reflected from the film.PREPARATION OF THE RUBBER SURFACES These were prepared using Sylgard 184 resin kits as supplied by Dow Corning Ltd, Barry, Glamorgan ; the kits consisted of resin, methylvinylpolysiloxane and a curing agent, hydrogenmethylpolysiloxane. The resin and the curing agent were mixed together in the ratio of ten to one by weight. A metal cylinder was used as a mould and in the bottom of this was placed a plano-concave lens of focal length -3.6 cm with a diameter of 2.05 cm. After pouring the mixed resin and curing agent into the mould, the mixture was left until all the bubbles formed during mixing and pouring had disappeared. The mixture was then cured at 70°C for a period of 15 h. The silicone rubber cylinder, still with the lens attached,F . W. CAIN, R . H .OTTEWILL AND J . B . SMITHAM 35 E - n (a) ( b ) FIG. 1 .-(a) Schematic diagram of reflectance apparatus for measuring intereaction between adsorbed layers. A and B, silicone rubbers with spherical caps; C , clamp for rubber B; D, micrometer drive for movement of rubber A; E, cup for PVA solution; F, beam-splitter; G, microscope. (b) Dia- gram illustrating flattening of rubber surfaces under applied pressure. was then removed from the mould. The refractive index of the rubber, as determined by ellipsometry, was found to be 1.430 at a wavelength of 632.8 nm. Fuller and TaborI4 estimated the surface energy of the rubber as 40 mJ mW2 and the Young's modulus as 1.68 & 0.06 x lo6 N m-2. MULTIPLE BEAM INTERFEROMETRIC APPARATUS The basic lay-out of the multiple beam interferometric apparatus is shown in fig.2. The apparatus and arrangements for clamping the silicone rubbers remained as shown in fig. 1. However, for interferometry, white light was used as a source of illumination and the beam was passed through rubber lenses A and B at normal incidence uia a prism, P, mounted underneath the rubbers. The emergent ray was split by the beam splitter F, one portion passing into a viewing eyepiece G and the other portion being focused onto the slit of a Hilger and Watts D187 prism spectrograph. A major difference in this method of measurement was the preparation of silicone rubbers with a metal coating on the spherical surface. The initial procedure was exactly as described previously up to the point at which the lenses were removed from the mould.The rubbers were then mounted in pairs and silver deposited on to the spherical surfaces to give a silver film with a thickness of about 50 nm. A thin layer (= 5 pum) of poly(methylmethacry1ate) was then deposited on to the silver layer. This was carried out by evaporation of the solvent from dilute solutions of polymer using the method of Carnell.15 A 3.8% w/w solution of Perspex was prepared in redistilled acetone and placed inside a covered container. The silvered rubbers were mounted carefully in a cradle and lowered into the solution using a hand winch. After five minutes the rubbers were slowly raised and allowed to drain in a saturated acetone vapour atmosphere for a further 15 min. A cross-sectional view of the completed lens is shown in fig.2(b).36 ADSORBED LAYER INTERACTION H F G- f- $ f-- light ( a ) ( b ) FIG. 2 . 4 ~ 2 ) Schematic diagram of multiple beam interferometric apparatus for measuring inter- action between adsorbed layers. A and B, coated silicone rubbers; C, clamp for rubber B; D, micrometer drive for movement of rubber A; E, cup for PVA solution; F, beam-splitter; G, viewing eyepiece; €3, prism spectroscope; P, prism. (b) Cross-section of coated silicone rubber. T, poly- (methylmethacrylate) ; S, silver layer; R, silicone rubber. PROCEDURE FOR OBSERVATIONS ON THIN FILMS With the rubbers A and €3 in their respective holders (see fig. 1 and 2) the lower rubber was raised by the micrometer drive so that it was approximately 1 mm below the upper rubber. At this point both the rubbers were adjusted until the observed Newton's rings were concen- tric around the optic axis of the viewing microscope G.Rubber B was then tilted slightly until the reflection from its upper surface appeared in the field of view; it was then deliber- ately tilted through a small angle to ensure that the reflection moved out of the field of view. The centre of the Newton's rings was then rechecked for alignment and readjustment made if required. In the multiple beam apparatus tilting of the beam was not required. A contact area between the rubbers was then formed by moving the rubber A gently upwards. The contact area was accurately focused and the rubbers separated by a small distance. At this point a PVA solution was added to the cup. After allowing a period of time for adsorption equilibration to occur, rubber A was slowly advanced towards B so that a thin film was formed between the two surfaces.When the reflectance technique was used the reflected light intensity was observed with time as the liquid film drained to its equilibrium position. The film was taken to be at equilibrium when the reflected light intensity did not change for a period of at least 25 min. In the equilibrium position, the diameter of the film formed was determined using a graticule in the microscope eyepiece. The lower rubber was then moved upwards a small distance by the micrometer drive and a new position of equilibrium found at an increased applied pressure. In this way it was possible to obtain an estimate of the thickness of the liquid film as a function of the applied pressure.DETERMINATION OF FILM THICKNESS: (a) BY LIGHT REFLECTANCE MEASUREMENTS Light from a 2 mW helium-neon laser (wavelength = 632.8 nm) was directed on to the semi-silvered mirror F which was inclined at an angle of 45" to the horizontal (see fig. 1). Part of the light beam was transmitted by the mirror and was then baffled by a RayleighF. W. CAIN, R . H. OTTEWILL AND J . B . SMITHAM 37 horn whilst the reflected light was directed on to the thin liquid film between the rubbers. The light reflected back from the centre of the film passed into the microscope G and thence on to a photomultiplier. The current from the latter was converted into a voltage and output on a chart recorder in order to obtain a trace of the signal as a function of time. The reflected intensity was converted into a film thickness using the equation of Caballero.16 (b) BY MULTIPLE BEAM INTERFEROMETRY Interference of the incident beam of white light occurred in the thin sandwich, poly- (methylmethacrylate)-thin liquid film-poly(methylmethacry1ate) between the two silver layers as shown in fig.2. The emergent light after focusing onto the slit of a spectrograph pro- duced fringes of equal chromatic order (FEC0).17 The methods by which FECO can be used to measure the thickness of films sandwiched between silver-backed transparent sub- strates has been described in detail by Israelachvili.18 Initially, a contact area was formed between the rubber surfaces in the absence of polymer solution and the wavelengths of the FECO were obtained by comparison with a mercury reference spectrum.The contact was then broken, polymer solution added and a pressure applied as described previously. The shift in wavelength of the FECO for the odd order fringes enabled the total distance between the poly(methylmethacry1ate) surfaces to be calculated18 at each applied pressure. DETERMINATION OF THE FILM PRESSURE The change in contact area under a known applied load was measured independently using a beam apparatus of the type described by Lewis.lg This gave a calibration curve of average pressure against contact area. The thin film area was always measured in a com- pression experiment and the average pressure obtained from the calibration curve. The pressures quoted in this paper are average pressures and not Hertzian pressures.20 RESULTS REFLECTANCE MEASUREMENTS A typical curve of reflected intensity against time is shown in fig.3. This was obtained with an 0.2 g/100 cm3 solution of PVA between the rubber surfaces when subjected to an average pressure of 2 x lo4 N mW2. Rapid drainage between the surfaces occurred at this pressure but the first bright interference fringe which occurs at A0/4n, where Lo = wavelength of light in vacuo and n = the refractive index of the solution, is clearly visible. After the initial rapid drainage the intensity decreased gradually with time, passed through a minimum after about 10 min and then increased again. The minimum is illustrated in the expanded inset in fig. 3(a) and it can be observed that at this point the intensity became equal to the background and it thus corresponded to a point of zero reflectance.Since the condition for zero reflectance is that the refractive index of the film should be equal to that of the substrate, the minimum indicated that the refractive index of the solution phase had become equal to the refractive index of the silicone rubber, namely 1.430. Thus it was possible to calculate the concentration of PVA at this point from the relationship, where no = refractive index of water and dn/dc = the refractive index of PVA (taken as 0.160 cm3 g-1).21 This indicated that the concentration of PVA in the film was of the order of 0.55 g ~ m - ~ . Beyond the minimum point the intensity rose slightly and then became constant with time indicating that the liquid film had reached an equilibrium position at the38 ADSORBED LAYER INTERACTION pressure applied.It can also be inferred that in this position the PVA concentration was higher than 0.55 g ~ m - ~ . Although the reflectance measurements located the position of the minimum and hence established the polymer concentration in the film, it was not possible to calculate the thickness at this point since it corresponded to the position of zero reflectance. I I I I 1 I X, 12 14 16 18 20 t imel min 0 1 2 3 4 5 5 7 8 9 10 tirne/rnin FIG. 3.-Reflected intensity as a function of time for drainage of a 0.2 g/lOO cm4 PVA solution between silicone rubber surfaces. Inset : enlarged view showing minimum in reflected intensity ; --- , background intensity. However, an attempt was made to obtain an estimate of the total film thicknesses at the equilibrium positions using an optical sandwich model composed of, rubber- adsorbed layer-solution-adsorbed layer-rubber and the equation of Cabellero.16 Estimates of the adsorbed layer thickness made independently give values of the order of 40 nm.13*22 Hence, using this value and an adsorbed layer concentration of 0.55 g ~ m - ~ approximate values were obtained for the film thickness as a function of applied pressure.These are given in fig. 4. For comparison, a second curve is given assuming a much lower concentration in the adsorbed layer, i.e., 0.2 g ~ m - ~ . The different assumptions did not, in fact, alter the gradient of the pressure against dis- tance curve, but they did displace it laterally along the abscissa.It is, therefore, considered that these results do reflect the form of the curve. However, a difficulty exists with the reflectance method in that as a consequence of the very high concentra- tion of polymer in the thin film it was not possible to obtain a unique determination of film thickness without an independent determination of the film refractive index. Moreover, these data indicated that lower applied pressures were required in order to determine the initial steric stabilisation overlap region. MULTIPLE BEAM INTERFEROMETRIC MEASUREMENTS The multiple beam apparatus (see fig. 2) enabled the distance between the poly- (methylmethacrylate) surfaces to be obtained without assumptions being made about the adsorbed layer thickness and concentration and also allowed lower pressures to be applied. The results obtained with this apparatus are shown in fig.5. TheF. W. CAIN, R. H. OTTEWILI, AND J . B. SMIT€IAM 39 initial PVA solution used was 0.2 g/100 cm-3 and results were obtained with both water and 0.1 mol dm-3 sodium chloride solution as solvents for the PVA. The results obtained in the presence and absence of salt were identical, indicating that electrostatic interaction did not make a significant contribution to the interaction pressure. Compression-decompression experiments were also carried out and since the points fell on the same curve, it can be concluded that the interaction is a reversible one. 7 6 N 'E 5 '0 c 4 z \ * X $ 3 !! n 2 1 2- 20 40 60 80 100 b Inm FIG. 4.-Pressure against distance of surface separation, h, obtained from reflectance measurements using a 0.2 g/lOO cm3 solution of PVA.Data calculated taking a polymer adsorbed layer thickness of 40 nm. - -, assuming a PVA concentration of 0.2 g ~ m - ~ in the adsorbed layer; -0-, assuming a PVA concentration of 0.5 g ~ m - ~ in the adsorbed layer. The data presented in fig. 5 show a slow rise in applied pressure at the longer separation distances and then a steep increase as the distance of separation approaches 60 nm. At the latter distance, the curve becomes almost vertical and confirms the steep rise observed by the reflectance technique. These data also agree with those from reflectance measurements calculated on the assumption of ~ 0 . 5 5 g ~ m - ~ PVA in the film, and hence confirm the high polymer concentrations formed in the film.DISCUSSION Basic measurements of interaction forces demand either a molecularly smooth surface, eg., r n i ~ a , ~ , ~ or elastic materials whose surfaces deform to approach closely smooth surfaces under an applied p~essure.~*~ Earlier work had shown that poly(is0- butylene) rubbers could be used to produce an optically smooth spherical surface and that such a surface could be used in conjunction with an optically polished glass surface to study electrostatic interaction force^.^^^ The disadvantage of this method was that it involved the use of two different adsorbing surfaces. In order to avoid this problem in the nresent work. two silicone rubber lenses were used. It was also40 ADSORBED LAYER INTERACTION 1 I I I 1 I I 20 LO 60 60 100 120 140 h /nm FIG.5.-Pressure against distance of surface separation, h, obtained using multiple beam interfero- metry and a 0.2 g/lOO cm3 solution of PVA. --& in water; 0, in 0.1 mol dmW3 sodium chloride sodion. found that these were easier to mould, more reproducible in moulding and had a better optical transparency than the poly(-isobutylene) rubbers. The surfaces of the silicone rubbers are presumably mainly composed of siloxane and methyl groupings although the surface energy of 40 mN m-l estimated by Fuller and Tabor l4 suggests a fairly polar surface. The poly(-methylmethacrylate) surface coatings which were necessary to form the multiple lenses required for interferometry also had the advantage of producing a polar surface for the adsorption of PVA.The macromolecular adsorbate chosen was PVA because a characterised sample was available and because it is frequently used as a disper~ant.~~ Despite the many limitations of this material in terms of heterodispersity, both with regard to degree of substitution and molecular weight, the fact that it is essentially a block copolymer ensures that it adsorbs on relatively inert surfaces. The material used, Alcotex 88/10, had a weight average molecular weight of 45 000 and according to Garvey et aZ.,13 after fractionation, the highest fraction had a weight average molecular weight of 67 000. It is clear, therefore, that this material could contain even higher molecular weight material, lo5 or greater, and that under the low surface area and relatively long equilibration times used in the present experiments there is a high probability that the highest molecular weight material would be preferentially adsorbed.Initially, following on previous work5 a reflectance method was used to estimate the form of the applied pressure against distance curves. This established that the concentration of PVA in the thin liquid film formed between the rubber surfaces had a concentration of m0.55 g cm-3 or higher. At this high concentration it was not possible to establish uniquely the distance between the rubber surfaces owing to the rapid change in refractive index with distance from that of the initial solution. How- ever, the high gradient of the (pressure, distance) curve which was independent of the absolute determination of distance, indicated that the compressibility modulus of the thin film was very high, becoming comparable with the elastic modulus of the rubber.F .W . CAIN, R . H . OTTEWILL AND J . B . SMITHAM 41 This observation, together with the high PVA concentration, indicated the possible formation of an elastic gel between the surfaces. However, the long-term stability of the film under pressure and the reversibility on removing the pressure, indicated that the polymer molecules remained firmly adsorbed on the surfaces. The development of the multiple beam interferometric apparatus established that the rapidly rising pressure (>2 x lo4 N m-2) occurred at a distance of ~ 6 0 nm. In the high pressure region the gradient of the interferometric data was identical with that of the reflectance data, thus establishing the mutual compatibility of the two sets of data.With the interferometric technique the results were also extended to longer dis- tances of surface separation and lower pressures. At the lowest pressure measured, 5.5 x lo3 N m-2, the distance between the poly(-methylmethacrylate) surfaces was m 120 nm and extrapolation to the zero pressure axis, to obtain the distance of initial interaction, ho, gave a value of 160 & 20 nm. This would suggest, if interaction begins at the periphery of the adsorbed layers, a distance of about 80 nm for the thickness of the adsorbed layers. This appears to be of the same order of magnitude but a little longer than some of the values quoted for thicknesses obtained by different method^.^^*^^*^^ Inevitably, in these cases, the thickness is defined by the method of measurement ; it is clear, however, that the thicknesses are not necessarily physically equivalent.In fact, using a PVA sample with a molecular weight of 86000, van Vliet 25 found an h, value of 100 nm from measurements on aqueous foam films. This would suggest 50 nm as the extension of the adsorbed layer (h0/2), a value consideraby larger than the figure of 20 nm found by ellip~ometry~~ for the optical thickness of an adsorbed layer of PVA (number average molecular weight = 30 000) at the air-water interface. Garvey et aZ.,13 using PVA adsorbed on polystyrene latices, obtained a value from hydrodynamic measurements for the adsorbed layer thickness of 38.2 & 3.0 nm with a PVA fraction having a weight-average molecular weight of 67000.The latter authors also obtained data on the variation of adsorbed layer thickness with molecular weight, which give for a molecular weight of 87 000 & 6000 an adsorbed layer thickness of 80 10 nm. If it is remembered that the present technique would allow the high molecular weight fraction to adsorb preferentially at the interface and that, as suggested by van Vliet,2s some of the polymer tails could extend a substantial distance into the solution, then the value of h0/2 obtained in the present work is not unreasonable. The compressibility of the thin film as expressed by, Y = -(aP/a In h)h where P = applied pressure, was found to have a value of 1.2 x lo4 N m-2 at h = 100 nm.This, if interpreted as an elasticity modulus, would suggest the formation of a weak visco-elastic gel. However, whether this is due to the overlap of adsorbed layers, either monolayer or polylayer, to the entrapment of molecules in the layer during drainage or the variation in the physical properties of PVA solutions with volume fraction, is not at present clear. Under the conditions of the present experiments, the van der Waals attractive forces are essentially negligible between two rubber surfaces separated by about 100 nm in a liquid of similar refractive index. Moreover, the experiments carried out in 0.1 mol dmW3 sodium chloride solution gave the same results as those in water hence indicating the absence of electrostatic forces arising from the overlap of electrical double layers.We therefore consider that fig. 5 represents the form of the inter- action curve for two surfaces in the presence of a macromolecular solution where it is known that the inacromolecule adsorbs strongly to the surface,42 ADSORBED LAYER INTERACTION The present indications are that for PVA the interaction behaviour depends very markedly on the rheological properties of the thin films, i.e., the variation in the visco- elastic properties with composition. It would seem that to investigate the region of steric stabilization covered by most current theories the investigation must be extra- polated to lower pressures and to longer distances. We will defer, therefore, a comparison with theory until such experiments have been successfully accomplished.Our thanks are due to the S.R.C. for the award of a CASE studentship to F. W. C. and a post-doctoral research assistantship to J. B. S. J. B. S. also acknowledges with thanks the award of an Eleanor Sophia Wood travelling fellowship from the Uni- versity of Sydney. The CASE studentship was held in conjunction with B.P. Limited, Sunbury, and we are grateful to Dr. R. J. R. Cairns for many helpful discussions. H. Freundlich, Colloid and Capillary Chemistry (Methuen, London, 1926). W. Heller and T. L. Pugh, J. Chem. Phys., f954,22, 1778. D. H. Napper, Ind. Eng. Chem. (Product Res. Des.), 1970, 9,467. A. D. Roberts and D. Tabor, Proc. Roy. SOC. A, 1971,325, 323. D. B. Hough and R. H. Ottewill, Colloid and Interface Science, ed. M. Kerker, Hydrosols and Rheology (Academic Press, N.Y., 1976), vol. IVY p. 45. J. N. Israelachvili and G. E. Adams, Nature, 1976,262,774; J.C.S. Faraday I, 1978,74, 975. J. N. Israelachvili and D. Tabor, Prog. Surface Membrane Sci., 1973, 7, 1. A. Doroszkowski and R. Lambourne, J. Polymer Sci., 1971, C34,253. A. Doroszkowski and R. Lambourne, J . Colloid Interface Sci., 1973, 43, 97. lo L. Barclay and R. H. Ottewill, Spec. Disc. Faraday Soc., 1970,1, 169. R. J. R. Cairns, R. H. Ottewill, D. W. J. Osmond and I. Wagstaff, J. Colloid Interface Sci., 1976, 54, 45. l2 A. Homola and A. A. Robertson, J. Colloid Interface Sci., 1976, 54, 286. l3 M. J. Gamey, Th. F. Tadros and B. Vincent, J. Colloid Interface Sci., 1976, 55, 440. l4 K. N. G. Fuller and D. Tabor, Proc. Roy. Soc. A, 1975,345, 327. l6 D. Caballero, J. Opt. SOC. Amer., 1947, 37, 176. l7 S. Tolansky, Multiple Beam Interferometry of Surfaces and Films (Oxford University Press, l8 J. N. Israelachvili, J. Colloid Interface Sci., 1973, 44, 259. l9 P. A. Lewis, Ph.D. Thesis (University of Bristol, 1973). 2o H. Hertz, Miscellaneous Papers (Macmillan, London, 1966). 21 Polymer Handbook, ed. J. Bandrup and E. H. Immergut (Interscience, New York, 1966). 22 F. W. Cain, Ph.D. Thesis (University of Bristol, 1978). 23 Th. F. Tadros, Particle Growth in Suspensions, ed. A. L. Smith (Academic Press, London, 1973), p. 221. 24 E. L. Zichy, J. G. Morley and F. Rodriguez, Chemie, physikalische Chemie irnd Anwendungs- technik der grendachenaktiven Stofe (Carl Hanser Verlag, 1973), p. 241. 25 T. van Vliet, Mededelingen Landboidwhogeschool, Wageningen, 1977,77, 1. P. H. Carnell, J. Appl. Polymer Sci., 1965, 9, 1863. London, 1949).