MONTE-CARLO SIMULATIONS OF RESTRICTED PRIMITIVE ELECTROLYTES IN A 2D NON-EUCLIDEAN GEOMETRY

Monte Carlo simulations of a restricted primitive model (RPM) electrol yte on the 2D surface of a sphere are reported. The initial quasi-rand om 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 particl e. The internal energy, U, and In gamma(+/-), where y(+/-) is the ioni c activity coefficient, did not depend upon N, the total number of ion s, but the heat capacity, C-v, did. The internal energy also scaled li nearly with r(+/-)(-1), where r(+/-) is the ionic radius. The internal energy, as a function of concentration for 1 : 1 and 2 : 2 electrolyt es agreed unusually well with the energies calculated from 3D cubic ge ometries, especially when differences in the ionic radii were accounte d for. The In y(+/-) values agreed reasonably with the values from 3D cubic geometries at lower concentrations, but the reported 3D values e xhibit an unrealistic upward curvature at higher concentrations which our 2D results did not. The cause was found to be the use of the parti cle insertion method. The hybrid particle method was found to give mor e consistent and realistic values. The internal energy also depended u pon the charge product (q(i) q(j)) and inversely upon the solvent perm ittivity, although neither relationship was purely linear. Distributio ns of ion numbers lying within the Bjerrum distance and pair correlati on functions clearly indicated ion association and the formation of st rings 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 upo n the results may be due partly to the fact that ion association gives rise to predominantly 1D structures (chains) which will not be seriou sly affected by 2D or 3D spaces.