ELECTROSTATIC INTERACTIONS OF BODIES BEARING THIN DOUBLE-LAYERS .1. GENERAL FORMULATION

The modified Poisson-Boltzmann (PB) equation was formulated for a system of flat dissimilar double-layers by considering the excluded volume effect. Limiting solutions of the modified PB equation derived for an isolated plate, and for two-plate system at large and small separations and arbitrary electrolyte composition were discussed. Results obtained for the parallel-plate geometry were generalized to regularly shaped bodies (either convex or concave around their contact point) bearing thin double-layers by applying the surface integration procedure analogous to the Derjaguin summation method. The excluded volume effect proved to be important for the dimensionless parameter beta larger than 10(-2) leading to a considerable increase of the potential difference across double-layers and to a slight increase of the interaction force between bodies at large separations. At small separations, however, the force remains finite due to the excluded volume effect (in the constant charge model) in contrast to previous results predicting that the force should tend to infinity in this limit. It was also predicted that the presence of trace amount of polyvalente ions (e.g., Al3 + ion) decreased considerably the force between bodies immersed in a 1-1 electrolyte.