Discrete charge effects on the Donnan potential and surface potential of a soft particle

Abstract

The Donnan potential and surface potential of soft particles (i.e., polyelectrolyte-coated hard particles) in an electrolyte solution play an essential role in their electric behaviors. These potentials are usually derived via a continuum model in which fixed charges inside the surface layer are distributed with a continuous charge density. In this paper, for a plate-like soft particle consisting of a cubic lattice of fixed point charges, on the basis of the linearized Poisson–Boltzmann equation, we derive expressions for the electric potential distribution in the regions inside and outside the surface layer. This expression is given in terms of a sum of the screened Coulomb potentials produced by the point charges within the surface layer. We show that the deviation of the results of the discrete charge model from those of the continuous charge model becomes significant as the ratio of the lattice spacing to the Debye length becomes large.