Measurement of Forces between Surfaces Immersed in Electrolyte Solutions BY JACOB N. ISRAELACHVILI Research School of Physical Sciences and Research School of Biological Sciences, Institute of Advanced Studies, The Australian National University, Canberra, A.C.T. 2600, Australia Received 30th November, 1917 The forces between two mica surfaces immersed in various aqueous electrolyte solutions have been measured. From 200 nm down to contact separations four different types of force are operating. First, there are attractive van der Waals forces; these are non-retarded up to about 6.5 nm with a Hamaker constant of (2.2 f 0.3) x J. The van der Waals forces appear to be slightly stronger than expected from the Lifshitz theory. Second, there are repulsive double-layer forces. In lo-' mol dm-3 1 : 1,2 : 1 and 2 :2 electrolytes these are well accounted for by theory but at concentrations above mol dm-3 there are discrepancies with theory, especially for 2 : 1 electrolytes.Third, there are repulsive " hydration " forces; these decay exponentially with distance with the characteristic decay length of about 1 .O nm. Their magnitude varies from mica to mica and is largely independent of ionic strength. They are negligible at separations above 7.5 nm. Fourth, there are adhesion forces; these are complex and depend on a host of factors such as pH, type of electrolyte cations, mica orientation, etc., and are not simply given by extrapolating the long-range forces down to separations of the order of interatomic spacings. The forces measured are those between two crossed cylindrical sheets of molecu- larly smooth mica of radius R w 1 cm.The apparatus is similar to earlier models used for measuring the van der Waals force between mica surfaces in air and in vacuum,l the optical properties of liquid and monomolecular films,2 and in adhesion and boundary friction ~tudies.~ A short account of the experimental technique and some initial results were reported ear lie^.^ Forces may be measured to within &(3-5) x N, and distances to within k(O.1-0.2) nm. In general, the forces measured in dilute solutions were exponentially repulsive, whereas in more concen- trated solutions an attractive region (secondary minimum) often preceded the onset of repulsion. At very small separations, below about 5 nm, the repulsion often peaked (force barrier), below which the net force became attractive and resulted in the surfaces jumping into strong adhesive contact (primary minimum).The results show that at least four different, though not necessarily independent, types of force are operating between mica surfaces in aqueous solutions : van der Waals forces, double-layer forces, " hydration " forces and adhesive forces. These will be described and discussed in turn. EXPERIMENTAL RESULTS VAN DER WAALS FORCES The attractive van der Waals forces were studied in two ways. First, at high electrolyte concentrations, when double-layer repulsions are weak, the van der Waals forces may be measured in the region of a secondary minimum. Second, at small separations the surfaces often jump into molecular contact from a position, the forceJ .N. ISRAELACHVILI 21 barrier, where the repulsion is maximum. By noting the position and force at the jump an estimate may be made of the attractive force needed to bring about the jump into contact. Both methods require some extrapolation of the repulsive forces and between them provided information of the van der Waals forces in the range 1-1 5 nm. The van der Waals forces were found to be effectively non-retarded from -1 to -6.5 nm, with a Hamaker constant of A = (2.2 5 0.3) x J. Above 6.5 nm retardation effects set in and the forces decay more rapidly with increasing separation. The van der Waals forces were found to be largely independent of the type and concentration of electrolyte and of the strength and nature of the repulsive forces.Measurements of the refractive index of water and of aqueous solutions between two mica surfaces yielded values within 1% of bulk values for surface separations in the range 2-100 nm; we conclude that in theoretical calculations of van der Waals dispersion forces, the bulk refractive indices should be adequate for calculations of these forces down to separations of 2 nm. The following approximate expression, derived from the Lifshitz the or^,^ may be used to obtain a theoretical estimate of the dispersion force contribution to the non- retarded Hamaker constant : where n, = refractive index of water = 1.33, n2 = refractive index of mica = 1.60, and where oo = characteristic adsorption frequency for mica and water (which are the same) = 1.90 x 1OI6 rad s-,. Substituting these values into eqn (1) yields A,,,,.= 1.85 x 10”O J. A more detailed theoretical analysis has been carried out by Dr L. R. White, using a computer program to solve the Lifshitz equation as described earlierY6 who found that the non-retarded Hamaker constant is A N, 2.0 x J, but that retardation sets in at smaller separations than was observed. DOUBLE-LAYER FORCES In dilute KNOJ and NaCl solutions (lo4 - mol dm4), the measured double- layer repulsive forces are in remarkably good agreement with theory (i.e., exact solutions to the non-linear Poisson-Boltzmann equation) at separations ranging from five Debye lengths down to 0.2 Debye lengths. The interaction occurs at constant surface potential both as the surfaces approach each other and as the concentration is changed.The surface potential does not depend on the type of electrolyte (to 5 1 0 mV), and is weakly dependent on pH in the pH range 10-6, but falls rapidly at lower pH, reaching about a third of the high pH value at pH 3. The surface potential appears to be determined by the nature of the mica: micas of different chemical composition exhibited different potentials; these varied from 50 to 130 mV, but were usually between 70 and 100 mV, in the pH range 6 - 7. Lower potentials were associ- ated with a high K/Na ratio at the cleavage plane. In more concentrated 1 : 1 electrolyte solutions - 10-1 mol dnr3) the measured double-layer forces begin to deviate from theoretical expectations. The forces still decay exponentially with distance, but the exponential decay lengths are now x 20% higher than the theoretical Debye lengths.The surface potentials still remain con- stant, or fall slightly, at these higher concentrations. In dilute solutions of 2: 1 electrolytes Ca(NO,),, CaCl,, MgC1, and BaC1, the double-layer forces are much reduced from those in 1 : 1 electrolytes at the same con- centration (the surface potentials in 2: 1 electrolytes are smaller than those in 1 : 1 electrolytes, and the interaction appears to be intermediate between constant charge22 FORCES BETWEEN SURFACES IN ELECTROLYTES and constant potential). In mol dm-3 solutions the forces are in fairly good agreement with exact solutions of the Poisson-Boltzmann equation in the range 5 - 0.3 Debye lengths; but in mol dmm3 solutions the forces decay faster with distance than expected from theory; the mean exponential decay lengths being 20 - 45% lower than the theoretical Debye lengths.At concentrations of mol dm-3 and above, the double-layer forces for 2:l electrolytes were too weak to be accurately measured. In one experiment with the 2:2 electrolyte MgS04 at mol dm-3, the double-layer forces were in good agreement with theory. We conclude that the behaviour of symmetric 1 :1 electrolytes is well described by the Poisson-Boltzmann equation, but that asymmetric 2 : 1 electrolytes are not well described by the Poisson-Boltzmann equation already at concentrations as low as IW3 rnol dm-3. The Outer Helmholtz Plane (OHP), i.e., the plane where the diffuse double-layer starts, is not necessarily at the mica-water interface but may be as far as 2.5 nm beyond this interface.As two mica surfaces are brought towards each other for the first time in a given solution, the OHPs are irreversibly shifted towards the mica surfaces. The shifts commence once the surfaces are sufficiently close together (closer than -10 nm), and there are indications that the shifts occur at a constant pressure (between two flat surfaces, calculated according to the Deryaguin approxi- mation)’ of -lo4 N r r 2 , or 4 . 1 atmospheres. These irreversible shifts of the OHPs lead to hysteresis effects in that the repulsive forces appear to be reduced after the first approach. Similar effects have been known to occur in swelling pressure studies on clay sheets, notably between montmorillonite sheets in water and NaCl so1utions.8-10 Our results indicate that such hysteresis effects are real and not a bothersome artifact due to the forced alignment of edges or non-parallel sheets on the first compression, as has been suggested.Our results may further be interpreted as furnishing evidence that a structured aqueous region exists near a mica surface (whose refractive index is nevertheless very close to that of bulk water). This region may extend as far as 2.5 nm beyond each surface with the OHP located at its outer bound- ary. Beyond this there is little or no structuring, the dielectric constant of water is now very close to the bulk value of E = 80, and diffuse double-layer theory holds [any significant deviation of e from 80 would have shown up in the slopes of the (double- layer force, distance) curves].When two mica surfaces are forced to approach each other the shifts of the OHPs probably reflect the progressive breakdown of the struc- tured aqueous regions as the surfaces come together. Hysteresis effects were rarely ob- served in dilute mol dm-3 solutions, and they could be brought about by increasing the electrolyte concentration. The existence and extent of hysteresis varied from mica to mica, and it therefore depends on the nature of the mica in addition to that of the electrolyte. Our observations are not inconsistent with the many “ anomalous ” surface and colloidal properties of clay mineral, silica and other oxide “HYDRATION” FORCES Apart from the normal van der Waals and double-layer forces, there is also an additional long range repulsive force. The magnitude of this force varies from mica to mica; in all cases where it was large enough to be accurately measurable it was found to be roughly exponential in the range 1.0-6.0 nm with a characteristic decay length of about 1 .O nm.This force is largely independent of the electrolyte concentra- tion, the pH and the mutual crystallographic orientation of the two mica surfaces. It appears to depend mainly on the nature of the mica and, to a lesser extent, on the cations present in the solution. The effectiveness of this third force depends on theJ . N. ISRAELACHVILI 23 strength of the van der Waals and double-layer forces, but it is negligible at separations above 7.5 nm.At low electrolyte concentrations, when double-layer forces are strong, its influence may be negligible right down to the force barrier which is de- termined solely by the DLVO forces. At high electrolyte concentrations, when double-layer forces are weak, this force may determine the position and depth of the secondary minimum as well as that of the force barrier. It is probably due to this force that silica dispersions are sometimes stable at very high ion strengths and undergo reversible coagulation. Our findings are consistent with those of Olejnik and White19 who measured the self-diffusion of water in thin layers between clay mineral surfaces of vermiculite and montmorillonite, and found that in the range 0.5-6.0 nm this decayed exponentially away from the surface with a characteristic decay length of -1 .O nm.* Hunter and Leyemdekkers22 found a similar exponential decay length ( -1.1 nm) for the viscosity of water between clay mineral surfaces. Further, a number of other unrelated experimental and theoretical (empirical) studies on water23 have also indicated an exponential " coherence length " for bonding in liquid water of z 1 nm. We conclude that (i) hydration forces exist, and that their effective range may extend to surface separations of -7.5 or -4 nm beyond each surface; (ii) there appear to be at least two different types of hydration force, characterised by different exponential decay lengths [see also ref. (24)], and (iii) more generally, any deviations from bulk values of such liquid properties as the self-diffusion, viscosity, molecular mobility, etc., near surfaces appears to be accompanied by a force between two such surfaces (this has recently been substantiated on theoretical grounds by MarEelja and coworkers in their theoretical analyses of " structural " force^).^^-^' ADHESION FORCES Previous studies of adhering mica surfaces using multiple beam interferometry have yielded valuable information on the fundamental mechanisms underlying adhesion and f r i ~ t i o n .~ ~ ~ ~ - ~ ~ The advantage of using multiple beam interference fringes is that both the shapes of the contacting surfaces and their separation may be accurately monitored. The theory of the adhesion of deformable solids is in dispute. According to the theory of Johnson et aZ.31r28 the pull-off force (adhesive force) at which two adhering surfaces come apart, P, is related to the adhesion energy per unit area, y, by P = 3nRy, (2) where R is the radius of curvature of the surfaces, which may be equated with the radius of the curved mica surfaces used in our experiments.The radius of the contact zone at pull-off rp is finite and is related to the contact radius under zero external force ro by According to the theory of Deryaguin et aZ.32 the pull-off force is P = 4nRy, and rp = 0, i.e., the surfaces come apart when the contact radius has fallen to zero. Our results show that at pull-off the contact radius is always finite, and that for pull-off in air rJr0 = 0.56 & 0.05, while in aqueous solutions rp/ro = 0.64 0.10. These * A similar study of the diffusion of water between ammonium perfluoro-octanoate bilayers20 yielded a characteristic decay length of 0.2 nm. This result is particularly interesting in view of some recent measurements of the forces between lecithin bilayers in water," where an exponentially decaying hydration force was measured at separations below 2 nm with a characteristic decay length of 0.19 nm.rp/ro = (1/4)'13 = 0.63. (3)24 FORCES BETWEEN SURFACES IN ELECTROLYTES results support the conclusions of Taborz8 that the Johnson theory gives a better description of adhesion than the Deryaguin theory. However, both theories predict that y cc P cc r;, and while we did observe that larger contact radii ro were accom- panied by larger pull-off forces P, a dependence of the form P cc r,3 was not obtained.Eqn (2) allows us to determine the adhesion energy y from the pull-off force P and the radius R, which are easily measurable. The range of values we have obtained for adhesion energies y in aqueous electrolyte solutions were enormous, ranging from -10 mJ rnm2 (erg cm-2) to below 0.01 mJ-2. 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