Direct Derivation of the Interfacial Free Energy of Charged Colloids from (N,V,T) Monte Carlo Simulations

Abstract

(N,V,T) Monte Carlo simulations are used to simulate the equilibrium distribution of the neutralizing monovalent counterions condensed in the vicinity of two charged colloids of various shapes (spheres, disks, and cylinders). The corresponding configurational entropy is used, in addition to the total electrostatic energy, to estimate the free energy of a pair of colloids at different distances and relative orientations (in the case of nonspherical colloids). By calculating the balance between energetic and entropic contributions to the total free energy of charged colloids, this study illustrates the large influence of the entropy on the net repulsion between colloids carrying electric charges of the same sign and neutralized by monovalent counterions. This procedure leads also to an effective pair potential useful for describing dispersions of charged colloids in the one-component plasma framework, implicitly including the contribution of the labile counterions. The treatment is based on a pairwise additivity of the effective potential. The validity of this hypothesis is carefully examined for the case of three charged cylinders.