Interaction Free Energy between Plates with Charge Regulation: A Linearized Model

Abstract

The linearized Poisson-Boltzmann theory is used to calculate the electrical double layer interaction free energy between two parallel charged plates for the case in which charge regulation due to the dissociation of surface groups may be modelled by the linearized regulation model that specifies a linear relationship between the surface charge and the surface potential. This charge regulation model is characterized by a constant—termed the regulation capacitance of the surface. Analytic expressions for the force per unit area, the interaction free energy per unit area as well as the interaction free energy between two nonidentical spheres in the Deryaguin limit are given for the general case of nonidentical surfaces. An expression for the interaction free energy, applicable to any geometry, is obtained by thermodynamic arguments. Numerical comparisons for the case of identical amphoteric surfaces show that linearizing the charge regulation boundary conditions produces little error in the resultant interaction free energy.