Monte Carlo simulations of restricted primitive model (RPM) electrolytes in non-Euclidean geometries

Abstract

Canonical ensemble ( NVT) Monte Carlo simulations of 1:1 and 2:2 restricted primitive model (RPM) electrolytes on the 3D ‘surface’ of a 4D hypersphere are reported here. We investigated the effects of system size ( N), concentration ( c), solvent permittivity ( ε) and temperature ( T) on the mean internal energy ( U), mean ionic activity coefficient ( γ ±) and pair correlation function (pcf). Thermodynamic properties of the system in the non-Euclidean geometries were almost independent of the system size, N. However, these properties depended upon the values of c, q, ε and T. Comparison of our results with those of 3D Euclidean simulations reported in the literature showed very good agreement. We also compared our results with theoretical predictions of the Debye–Huckel model. The internal energies, mean ionic activities and screening lengths agreed well with the predictions of the Debye–Huckel theory. We calculated the nearest neighbour distributions for the distances between an ion and its first five nearest neighbours, regardless of charge. From studying the nearest neighbour distribution of ionic separations, we concluded that the first nearest neighbouring ion to a given ion is closer than would be expected for a random arrangement, but the second to fifth nearest neighbours are randomly arranged on average. The use of non-Euclidean geometries for the simulation of electrolytes is a very good alternative to Euclidean geometries with periodic boundary conditions.