(430c) Ion Exchange and DLVO Theory

A crowning acheivement of the Isrealachvili surface forces apparatus is the first direct confirmation of DLVO theory, as illustrated in Figure 12.13¹ showing the measured force between mica sheets immersed in a dilute KNO₃ aqueous electrolyte (symbols) compared to DLVO theory (solid line).¹ Charge densities of the mica surface used to fit the diffuse-layer overlap contribution¹ are near 1 e/ 50 nm². Conversely, mica exchanges 1:1 alkali cations with a large cation exchange capacity (CEC) of over 0.4 mequiv/g (i.e., 1 e/ 0.5 nm²)² The meaning gleaned from Figure 12.13¹ and interpretation of the ion-exhange isotherms is that less than a few percent of the mica surface charge resides in the diffuse layer. Essentially all surface-charge neutralization occurs directly at the mica surface and is not reflected by SFA measurements.

To unify measurement of ion-exchange isotherms, zeta potentials, and surface forces for 1:1 aqueoues alkali cations, we adopt a simple triple-layer ion-complexation picture with ion complexing in the inner Helmholtz plane followed by a diffuse layer commencing at the outer Helmholtz plane. Inner and outer-layer capacitances are set physically by ion size and local dielectric permittivity. An ion-complexing equilibrium constant is imposed or each cation species. We fit the ion-binding equilibrium constants from measured ion-exchange isotherms and measured zeta potentials. Surface forces are predicted a priori with no adjustment of physcial parameters.

At low ionic strengths, we find good agreement between theory and experiment for all three measurement sets within the precision of the data, including the effect of pH. The relative concentrations of cations present and their ion-binding constants modulate the fraction of surface charge neutralized by specific ion binding versus by the diffuse layer. At higher ionic strengths, beyond about 10^-2 M, there is significant deviation from theory for measured surface forces. Since surface forces gauge the diffuse region, this suggests deviation from the Poisson-Boltzmann expression at high ionic strengths.

1. Israelachvili, J. N., Intermolecular and surface forces. Academic press: 2011.
2. Osman, M. A.; Moor, C.; Caseri, W. R.; Suter, U. W., Alkali Metals Ion Exchange on Muscovite Mica. J. Colloid Interface Sci. 1999, 209 (1), 232-239.
3. Pashley, R. M., DLVO and hydration forces between mica surfaces in Li+, Na+, K+, and Cs+ electrolyte solutions: A correlation of double-layer and hydration forces with surface cation exchange properties. J. Colloid Interface Sci. 1981, 83 (2), 531-546.
4. Scales, P. J.; Grieser, F.; Healy, T. W., Electrokinetics of the muscovite mica-aqueous solution interface. Langmuir 1990, 6 (3), 582-589.