Numerical solution of a modified Poisson-Boltzmann equation for 1 : 2 and 2 : 1 electrolytes in the diffuse layer

Abstract

A modified Poisson-Boltzmann (MPB) equation for an unsymmetrically charged electrolyte in the diffuse part of the electric double layer at a plane charged wall is solved numerically using a quasi-linearization procedure. Computations are carried out for 1 : 2 and 2 : 1 restricted primitive model electrolytes with no imaging and for a metallic wall and the results compared with the classical Gouy-Chapman-Stern theory. Except for negligible surface charge, the system with a divalent counter ion is the most sensitive to any change in its physical parameters. In general the MPB mean electrostatic potential, in contrast to the Gouy-Chapman-Stern potential, is not a monotonic decreasing function. The asymptotic behaviour of the MPB equation implies charge oscillations above a critical electrolyte concentration (≳0·23 M) while below this concentration imaging or surface charge-ion interactions can produce a charge inversion. Charge separation is found for no surface charge with a metallic wall. The point ion limit is briefly considered.