Electrostatic and entropic interactions between parallel interfaces separated by a glassy film

Abstract

A simple classical density functional model is set up to describe the electrostatic and entropic interactions between two parallel planar charged interfaces separated by a thin film of a phase (the glass) containing a distribution of charged ions. The total charge in the system is zero. Three cases are treated: (1) the two interfaces carry a fixed surface charge; (2) the first interface carries a fixed surface charge, simulating a ceramic, while the second is held at zero potential, simulating a metal; and (3) both interfaces are held at zero potential. A discretized form of the nonlinear Poisson-Boltzmann equation is derived and solved by a Newton-Raphson method. The continuum approximation is compared with a model in which the ions are only allowed to occupy discrete planes. The effect of correlation among the ions is included within the local density approximation. Inserting parameters appropriate to the copper-alumina interface, we find that the attractive image force between the ceramic and metal dominates the entropic (DLVO) repulsive force in the 1-2 nm range.