Measurement of Forces between Colloidal Particles BY L. M. BARCLAY AND R. H. OTTEWILL School of Chemistry University of Bristol Bristol England Received 30th April 1970 Apparatus has been constructed for the measurement of the pressure created by disperse systems as a function of the volume concentration of the disperse phase. Experiments with sodium mont- morillonite as the colloidal system have enabled the force to be obtained as a function of the distance between the plates down to distances of the order of 108,. The results have been compared with those expected theoretically on the basis of the DLVO theory. The forces obtained at distances of less than 50 8 are much greater than those predicted by the theory and the additional force appears to arise from solvation effects in the thin liquid film between the particles.This has been confirmed by carrying out measurements in the presence of a non-ionic surface-active agent a known stabilizing agent where the repulsive forces due to solvation are enhanced. Information on the stability of disperse systems can be obtained by both kinetic le3 and equilibrium method^.^-^ In kinetic studies the electrolyte is added to the system and the rate at which the stability is lost is examined i.e. the rate of flocculation is determined.8 Although this approach has provided considerable information the interpretation of the kinetic data is limited. There are therefore considerable advantages to studying a disperse system in its own environment under essentially equilibrium conditions. One method of carrying out such a study is to measure the pressure developed in the system as a function of the distance of separation of the particles.Some swelling pressure studies 4-9 have been used hitherto to obtain information of this sort. The type of apparatus previously used has been considerably refined and the present communication describes the apparatus used and some studies carried out using sodium montmorillonite dispersions in the presence and absence of a non-ionic surface active agent. Studies carried out using monodisperse polystyrene latex particles will be described in a later publication. EXPERIMENTAL MATERIALS The distilled water used was doubly-distilled from an all-Pyrex apparatus. Sodium chloride was B.D.H. A.R. material which was roasted before use. n-Dodecyl hexaoxyethylene glycol monether (C 2E 6) was prepared by the Williamson ether synthesis.l o The critical micelle concentration determined by surface tension measure- ments was 7.25 x The montmorillonite was a sample of montmorillonite no. 26 (Bentonite) from Clay Spar Wyoming as prepared for the American Petroleum Institute Clay Mineral Standards Project no. 49. About 30 g of the dry material was dispersed in 1 1. of distilled water contain- ing 1 ml of 30 % v/v hydrogen peroxide per 100 g of clay. After standing for 24 h the sample was centrifuged to remove impurities such as silica particles. Conversion to sodium montmorillonite was achieved by redispersing the clay particles in molar sodium chloride 138 M at 25°C (compare 7.8 x lo-’ M ll). L . M . BARCLAY A N D R . H . OTTEWILL 139 solution and allowing the dispersion to stand for several days.The sodium montmorillonite was separated by centrifugation at 38,000 g for 1 h. For compression studies the centrifuged material was dispersed in M sodium chloride solution and then dialyzed against that solution for a long period. or ADSORPTION STUDIES A dispersion of ca. 1.5 % w/w sodium montmorillonite which had been extensively dialyzed against twice-distilled water was used as a stock dispersion. Various weights ranging from 0.4 to 1.5 g of this stock dispersion were added to a series of CIZE6 solutions having concentrations in the range 10-4-10-3 M and a volume of 25 ml ; these solutions uere contained in stoppered tubes. The mixtures were equilibrated at 2510.05"C for 3 days with frequent shaking. The surface tension of the mixture was used to determine the equilibriumconcentration of C12ES.A comparison of the surface tensions of the supernatants of a series of mixtures which had been centrifuged at 38,OOOg with those of the original mixtures showed them to be identical. Hence the centrifugation procedure was dispensed with in later experiments. APPARATUS FOR COMPRESSION STUDIES The cell used for pressure measurements which was constructed of stainless steel is shown diagrammatically in fig. 1. All sharp edges were rounded off to prevent damage DISPERSION CASTOR OIL MILLIPORE FILTER RUBBER D I APH RAG M FIG. 1 .-Cross-sectional diagram of compression cell. occurring to the rubber diaphragm and the Millipore filters. Similarly the end of the glass capillary which was inserted into the cell was bevelled in order to avoid chipping the tip when assembling and dismantling the cell.A PTFE O-ring placed between the capillary tip and the end of the steel orifice also minimized damage to the capillary. The capillaries were constructed from calibrated lengths of 3 mm diam. (inside) Viridia glass tubing. The stainless steel disc (porosity no. 3) fitted exactly into a recess in the top of the cell. Samples of rubber latex for the cell diaphragm were selected from a large sheet 0.007- 0.010 in. thick (Holdfast Rubber Dam) by stretching pieces in front of a light source. Only 140 FORCES BETWEEN COLLOIDAL PARTICLES sections free from bubbles within the rubber were used. A calibration curve was constructed 'for each diaphragm' of the force applied by the stretched rubber to the sol. Millipore MF filters (47 mm diam.0.1 p pore diam.) were used as membranes ; the Viskase dialysis tubing used by some authors was found to be unsuitable as a membrane and led to a very slow attainment of equilibrium. Before use approximately 4 1. of distilled water at 60°C were passed through each filter in order to remove impurities such as non-ionic surface-active agents and polyhydric alcohols. The removal of surface-active material was monitored by measuring the surface tension of the filtrate. After thorough washing the filters were dried at 7OoC between filter papers held between perforated metal plates. In order to generate pressure in the system a Budenberg hydraulic gauge tester was used with caster oil as the hydraulic fluid. The pressure applied was read directly on direct mounting Budenberg bronze tube Bourdon gauges.The gauges were used to cover the ranges 0-20 0-160 and 0-1600p.s.i. The 0-2Op.s.i. gauge was calibrated in position on the complete apparatus by connecting a mercury manometer to the hydraulic system. The other two gauges were calibrated using a dead weight tester. In order to maintain the selected pressure constant a pressure compensating mechanism was built into the apparatus so that compensation occurred as the dispersion medium was forced out of the sol compartment. For this purpose the pressure gauges were used as regulators. A knife-edge metal contact was attached to the glass face of each gauge and a platinum contact to each of the gauge needle-pointers. For each gauge the knife-edge contact and a suitable point on the chassis of the gauge were connected to an electric motor (Parvalux 2 rev/min) which by means of a chain drive mechanism could rotate the piston drive wheel and so increase the pressure.The electric motor drive spindle was connected to a drive shaft via a chain and sprocket. The rotation of this shaft was transmitted via another chain and sprocket set fixed to the threaded piston rod. The piston could be operated manually by retracting a spring-loaded pin (fixed to one sprocket on the drive shaft) from the key-way on the drive shaft so that the sprocket rotated freely about the shaft (see plate 1). The major section of the apparatus including the cell and capillary was fitted into a tight-fitt ing air-thermostat box which was maintained at a temperature of 25.0f0.05"C. In order to load the cell for measurements the diaphragm recess volume was initially adjusted to ca.6 ml by retracting the piston and approximately 5 ml of the degassed sol to be used was introduced into this. The pressure was then slowly increased in the system until the meniscus of the sol was slightly above the rim of the cell. A clean millipore filter was placed on top of the liquid surface without trapping air bubbles underneath it. The cell was then assembled. Tnitially a small pressure of less than 1 p.s.i. was applied so that the dispersion medium slowly emerged from the cell interior forcing most of the air out of the sintered disc into the capillary. More air was released by raising and lowering the pressure repeatedly over a period of about 1 h. The " dead space " above the membrane which included the pore volume of the sintered disc and the volume of the exit aperture in the top of the cell was determined from values of the initial and final solid contents in con- junction with the volume of the supernatant in the capillary.Usually at the beginning of each run a fairly large volume of dispersion medium was forced from the cell from a compara- tively dilute sol. For montmorillonite about 4 g of approximately 2.5 % w/w dispersions were used ; higher concentrations were not practicable as the material gelled at concentrations above 3 "/ w/w. Since a relatively large volume of liquid had to be removed on the first compression the first equilibrium pressure reading often took up to 24 h. The meniscus of the liquid in the capillary was observed with a cathetometer and equilibrium at a given pressure occurred when there was no further change in the position of the meniscus.The whole apparatus was mounted rigidly on a steel frame. RESULTS COMPRESSION STUDIES WITH MONTMORILLONITE The curves of equilibrium pressure against distance of plate separation for and 10-1 M sodium chloride solutions are shown in fig. 2. montmorillonite in Plate 1 Photograph of apparatus showing cell and compression mechanism. [To face page 140. L . M. BARCLAY AND R. H. OTTEWILL 141 Experimentally the first compression on each sample gave a larger repulsion at a given distance up to a pressure in the region of 20atm. After the first compression however subsequent compression and decompression experiments gave coincident results as can be seen from fig. 2. The distance between the plate surfaces H, was calculated assuming a specific surface area of 800 m2/g and using the expression Ho = 2V/mA distance between plates (A) FIG.2.-Equilibrium pressure against distance between plate surfaces for sodium moiitmorilloriite dis- persions at 25°C. In M sodium chloride solution 0 first compression ; V decompression ; 0 subsequent recompression. In 10-1 M sodium chloride solution 0 first compression ; v dc- compression ; A subsequent recompression. where V = volume of liquid in a sol containing m g of clay and A = specific surface area. A check on the interplate separation distance was obtained by carrying our a low-angle X-ray diffraction examination * of two vacuum concentrated samples. The particles in these samples had not been deliberately orientated and hence the distances obtained were probably the interparticle distances in oriented domains.The X-ray results are compared with those obtained from the surface area in table 1. TABLE 1 .-INTERPARTICLE SPACING DISTANCES % wlw of HO HO montmorillonite calc. from first calc. from in sample order X-ray pattern surface area 37.4 40.8 A 42.0 8 34.2 45.5 A 48.2 8 The X-ray results based on a plate thickness of 8.5 A are in good agreement with those calculated using a surface area of 800 m*/g. * We thank Dr. S Clunie for this determination. 1 42 FORCES BETWEEN COLLOIDAL PARTICLES ADSORPTION OF C12E6 ON MONTMORILLONITE The adsorption isotherm obtained for the adsorption of C12E6 onto mont- morillonite from water at 25°C is shown in fig. 3. The adsorption of C12E6 continued equilibrium concentration of C12E6 ( x lo4 M) FIG.3.-Adsorption of CI2E6 on sodium montmorillonite at 25"C from solution. M sodium chloride t critical 0 centrifuged at 38,000 g ; 0 centrifuged at 12,500 g ; A not centrifuged. micelle concentration. to increase above the critical micelle concentration and did not reach a steady value at or just below this concentration as has been observed with silver iodide l2 and polystyrene 1atices.l However the isotherm is essentially similar to that found by Schott l3 in studies of the adsorption of C12E14 on montmorillonites. At the critical micelle Concentration (7 x M) the adsorption of CI2E6 was 1.16 x mol/g which on the basis of a surface area of 800 m2/g corresponds to an area per adsorbed molecule of 144 A.2 This would correspond to a horizontal extended orientation of the CI2E6 molecule.COMPRESSION CURVES FOR MONTMORILLONITE IN THE PRESENCE OF C12E6 The equilibrium pressure against distance curves obtained for montmorillonite in the presence of 7 x M sodium chloride are given in fig. 4. A pronounced difference occurred between the first and second compression curves but subsequent compression and decompression points all fell on the same curve. A feature of the curves is that although the electrolyte concentration was maintained at M at pressures below 20 atm the equilibrium distance was reduced in the presence of C12E6. Above 20 atm the system was more expanded in the presence M C12E6 and of C12E6. DISCUSSION The two basic problems encountered in the present work were the accurate measurement of the equilibrium pressure and the estimation of the interparticle spacing.The use of a servo-mechanism allowed the applied pressure to be maintained accurately until the liquid expelled from the cell had reached an equilibrium height L. M. BARCLAY AND R . H. OTTEWILL 143 in the capillary. However the pressures observed in the compression of a sodium montmorillonite dispersion for the first time were always higher than those observed on subsequent compression and decompression cycles. This effect was attributed to a grain pressure in which edge-face contacts between the clay plates occurred leading to a card-house structure of the type described by~anO1phen.l~ At the high pressures presumably the plates re-aligned to a parallel arrangement although the possibility of some domains could not be excluded. The hysteresis was largest at low equilibrium pressures for both the electrolyte concentrations examined.The displacement at ~~~~ 5 0 100 150 2 0 0 250 3 0 0 distance between plates (A) FIG. 4.-Equilibrium pressure against distance between plate surfaces for sodium montmorillonite in M sodium chloride solution in the presence of an equilibrium concentration of 7 x lo-’ M CI2E6. . . . . . . first compression ; A non-equilibrium decompression ; 0 subsequent recompression. - - - curve in M sodium chloride solution. 0.1 atm pressure was 130 A in 10-1 M sodium chloride solution and 90 8 in M sodium chloride solution ; the larger electrical repulsion in M sodium chloride solution clearly aided the dispersion. In all the experiments the second and sub- sequent compression curves gave the same results and there was good agreement between the results obtained with different samples.We assume therefore that the grain pressure was largely eliminated after the first compression. Since separation of the montmorillonite layers into basic sheets occurs the surfaces can be considered as molecularly smooth. On the basis of a sheet thickness of 8 A the low angle X-ray diffraction results agreed closely with those calculated from the surface area. The agreement was sufficiently satisfactory (table 1) to conclude that although some error is involved in the determination of the interparticle spacing, 1 4 4 FORCES BETWEEN COLLOIDAL PARTICLES this is probably small. Thus the experimental evidence suggests that the system studied involved flat plate-flat plate interactions through the liquid medium.Hence it is of considerable interest to compare the results obtained with those expected on the basis of the theory of colloid stability put forward by Deryaguin and Landau l 5 and Verwey and Overbeek.16 The theory involves a consideration of the electro- static repulsion FR and the van der Waals attraction FA acting between the plates so that the total force can be written F = FR+ FA. The force of electrostatic repulsion per cm2 of plate is given by F R = 2nkT (cosh u- l) where rz = number of ions per ml and u = ve$,,/,lkT. $ H o / 2 is the potential mid-way between the plates taking Ho as the interplate distance which can be evaluated for a particular potential on the plate $o or surface charge using the integral This integral can be evaluated from tables 14* l6 taking K = Debye-Huckel reciprocal length and z = vet,h6/kT.If the potential at any distance other than at the surface or the mid-point is given by $ then y = ve$/kT. The curves for the force of repulsion against distance of plate separation calculated for conditions of both constant potential and constant surface charge density in loF4 M sodium chloride solution are shown in fig. 5. The surface charge of the clay surface was taken to be 3.53 x lo4 e.s.u./cm2. The difference between the two curves is small except at close distances. The force of attraction between flat plates of thickness 6 is given by the expression16 A 1 1 2 6n Eli (H0+26)3 ( H + C ~ ) ~ FA = -(- + The net Hamaker constant A was calculated from A = ( J A i i - JA22)' where A l l = Hamaker constant of the particle and A22 that of the medium.A was taken as 2 . 0 ~ erg the value for silica,l' and the value for water (A2') was taken as 5 . 6 ~ 10-13 erg.18 The thickness of the montmorillonite plates was taken as 8.0A. Calculations showed that the attractive energy became very small for such thin plates at interparticle distances greater than 30A and that the effect of retardation calculated using the expression developed by Hunter l9 was negligible. The curve of total force against interparticle distance is also shown in fig. 5 which shows that the force at a distance greater than 40A arises solely from electrostatic repulsion. At a distance of ca. 158 there is a maximum in the curve and hence at shorter distances than this the van der Waals force of attraction should predominate and the plates would coagulate into a primary minimum.This however was not observed experimentally. Up to the highest pressures exerted (approximately 100 atm) it was always possible to decompress and retrace the original compression curve thus indicating the reversibility of the system. The pressure continued to increase with decreasing distance and in M sodium chloride the distance between the plates at an applied pressure of 100 atm was only 17.5 A. Thus no evidence is L . M. BARCLAY AND R . H . OTTEWILL 145 found for the primary minimum effects expected and it seems therefore that an additional force of repulsion has to be considered for such systems. Deryaguin and Greene-Kelly 2o have suggested that structural boundary layers of water 30-200 8 thick exist between the silicate layers of swollen montmorillonite and contribute to the stabilisation of the particles at close distances.van Olphen 21 and Briant 22 have also indicated that hydration forces cannot be neglected in clay systems and evidence for hydration forces in stable black soap films has been given by Goodman et aZ.23 The resemblance between the present results and those obtained by Goodman and coworkers is striking and would suggest that the effects observed at high pressures distance between plates (A) FIG. 5.-Pressure against distance between plates in M sodium chloride solution. - theoretical curve for electrical repulsion at constant potential (250 mV) ; - . - . - theoretical curve for electrical repulsion at constant charge (3.53 x lo4 e.s.u./cm*) ; . . . total force between plates assuming a plate thickness of 8 A.- - - - experimental curve in M sodium chloride solution. in view of their reversibility are due to solvation forces and not to grain pressure. An alternative possibility is that in the model of the electrostatic repulsion the electrical situation at close distances has been oversimplified. At distances greater than 50A it is reasonable to postulate that the repulsion arises solely from electrostatic repulsion ; this is in agreement with previous workers.4* 9 9 24* 2 5 9 26 In the present work the predicted values of the pressure are larger than those found experimentally in M sodium chloride solutions at distances greater than 150& but are less than those measured at distances of less than 150A. In 10-1 M sodium chloride solutions the measured pressures were larger over the whole range examined than those predicted theoretically for the same 146 FORCES BETWEEN COLLOIDAL PARTICLES distance of separation ; this is not unexpected in view of the difficulties of the theory in the more concentrated electrolyte solutions.RESULTS I N THE PRESENCE OF C12E6 The results shown in fig. 4 indicate that at an applied pressure of less than 20 atm the interparticle spacing is considerably less in the presence of CI2E6. Although electrokinetic experiments were not possible with the montmorillonite plates with silver iodide sols l2 and with polystyrene latex dispersions l1 a considerable drop in the electrokinetic potential occurs on the adsorption of C12E6. This would appreci- ably reduce the electrostatic repulsion and hence allow the plates to approach more closely.At pressures greater than 20 atm the curve is displaced to larger distances than those found in M sodium chloride solution alone and at the highest pressures there is a displacement of ca. 9A. The adsorption isotherm indicates that at the concentration of C12E6 used the non-ionic inolecule is adsorbed in a horizontal orientation on the clay surface. It would seem likely that this orientation was maintained under pressure since an analysis of the liquid expelled into the capillary for C12E6 gave the expected equilibrium concentration. The flat lying orientation of the C12E6 molecule is also in agreement with the X-ray studies of Schott l3 011 the adsorption of CI2El4 on sodium and calcium montmorillonite. His results clearly indicated a flat orientation and he suggested either that the ethylene oxide groups were bound to the silica sheets by secondary valence forces or that the poly- oxyethylene glycol chain tended to pack into the holes between the oxygen atoms of the silica surface to give a close fit.The adsorbed layer of C12E6 would reduce the van der Waals attraction between the sheets 27* 28 and also act as an effective dispersing agent for the sodium montmorillonite since ethylene oxide/water contacts are preferred to ethylene oxidelethylene oxide contacts at ambient temperatures. Under these conditions card-house floc formation would be minimized and since the electrical repulsion has also been reduced the increased gradient of the pressure against distance curve at high pressures can only be a consequence of the strong repulsive forces arising from the interaction of the hydrated layers.We thank the University of Bristol for the award of a Graduate Scholarship to L. M. B. H. 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