A new potential for the numerical simulations of electrolyte solutions on a hypersphere

Abstract

We propose a new way of performing numerical simulations of the restricted primitive model of electrolytes—and related models—on a hypersphere. In this new approach, the system is viewed as a single component fluid of charged bihard spheres constrained to move at the surface of a four dimensional sphere. A charged bihard sphere is defined as the rigid association of two antipodal charged hard spheres of opposite signs. These objects interact via a simple analytical potential obtained by solving the Poisson–Laplace equation on the hypersphere. This new technique of simulation enables a precise determination of the chemical potential of the charged species in the canonical ensemble by a straightforward application of Widom’s insertion method. Comparisons with previous simulations demonstrate the efficiency and the reliability of the method.