A mean field approach for computing solid-liquid surface tension for nanoscale interfaces

The physical properties of a liquid in contact with a solid are largely determined by the solid-liquid surface tension. This is especially true for nanoscale systems with high surface area to volume ratios. While experimental techniques can only measure surface tension indirectly for nanoscale systems, computer simulations offer the possibility of a direct evaluation of solid-liquid surface tension although reliable methods are still under development. Here we show that using a mean field approach yields great physical insight into the calculation of surface tension and into the precise relationship between surface tension and excess solvation free energy per unit surface area for nanoscale interfaces. Previous simulation studies of nanoscale interfaces measure either excess solvation free energy or surface tension, but these two quantities are only equal for macroscopic interfaces. We model the solid as a continuum of uniform density in analogy to Hamaker's treatment of colloidal particles. As a result, the Hamiltonian of the system is imbued with parametric dependence on the size of the solid object through the integration limits for the solid-liquid interaction energy. Since the solid-liquid surface area is a function of the size of the solid, and the surface tension is the derivative of the system free energy with respect to this surface area, we obtain a simple expression for the surface tension of an interface of arbitrary shape. We illustrate our method by modeling a thin nanoribbon and a solid spherical nanoparticle. Although the calculation of solid-liquid surface tension is a demanding task, the method presented herein offers new insight into the problem, and may prove useful in opening new avenues of investigation.