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

C. C. Chiu, R. J. K. U. Ranatunga, D. T. Flores, D. V. Perez, P. B. Moore,
__W. Shinoda__, and S. O. Nielsen

J. Chem. Phys. 132, 054706 (2010).

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 make an approximation which 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.