Dressed ion theory for electric double layer structure and interactions; an exact analysis

Abstract

Dressed ion theory, an exact statistical mechanical formalism for electrolyte systems in the primitive model, is extended to electric double layer systems in various geometries. In this theory an exact equation that has the same form as the linearized Poisson–Boltzmann (PB) equation is set up, in which ‘dressed ions’ take the same role in the exact theory as the bare ions have in the PB approximation. Various distribution functions are expressed in terms of the dressed ion charges. Exact asymptotic results for large particle separations are obtained for the distribution functions, the average electrostatic potential and the interaction free energies in colloid dispersions and for planar double layer systems. A practical method is derived for evaluating the effective surface charge densities of the particles. The question of whether double layer interactions between equally charged colloid particles must be repulsive at large separations (as suggested by the PB approximation) or whether they can be attractive there is treated in some detail.