Monte Carlo simulations of restricted primitive electrolytes in a 2D non-Euclidean geometry

Abstract

Monte Carlo simulations of a restricted primitive model (RPM) electrolyte on the 2D surface of a sphere are reported. The initial quasi-random ion positions were generated using a Halton sequence. Equilibration of the system from the quasi-random starting configuration was quite rapid and typically required less than 10 successful moves per particle. The internal energy, U, and ln γ_±, where γ_± is the ionic activity coefficient, did not depend upon N, the total number of ions, but the heat capacity, C_v, did. The internal energy also scaled linearly with r_±⁻¹, where r_± is the ionic radius. The internal energy, as a function of concentration for 1:1 and 2:2 electrolytes agreed unusually well with the energies calculated from 3D cubic geometries, especially when differences in the ionic radii were accounted for. The ln γ_± values agreed reasonably with the values from 3D cubic geometries at lower concentrations, but the reported 3D values exhibit an unrealistic upward curvature at higher concentrations which our 2D results did not. The cause was found to be the use of the particle insertion method. The hybrid particle method was found to give more consistent and realistic values. The internal energy also depended upon the charge product (q_iq_j) and inversely upon the solvent permittivity, although neither relationship was purely linear. Distributions of ion numbers lying within the Bjerrum distance and pair correlation functions clearly indicated ion association and the formation of strings or chains of ions with alternating charge. These structures were confirmed by plotting the ion positions on the surface of the sphere. The fact that dimensionality and curvature had no apparent effect upon the results may be due partly to the fact that ion association gives rise to predominantly 1D structures (chains) which will not be seriously affected by 2D or 3D spaces.