Electrical forces between particles with arbitrary fixed surface charge distributions in ionic solution

Abstract

An expression is derived for the change in free energy of interaction of two colloid particles immersed in electrolyte due to the presence on their surfaces of an arbitrary fixed charge distribution. The treatment is based on linearization of the Poisson–Boltzman equation.

For a quasi periodic overall neutral distribution of charge the energy may be attractive or repulsive according to the relative orientation of the two plates. Typically for hydrocarbon plates immersed in 0.01 mol kg^–1 aqueous electrolyte and having a mean ion number density of 10¹⁷ m^–2 the attractive energy is comparable at small separations with the van der Waals interaction energy between particles with Hamaker constant H∼10^–21 J.