Monte Carlo Calculations of Effective Surface Tension for Small Clusters

Abstract

In this study we have calculated configurational Helmholtz free energy differences between n and n – 1 molecule water clusters and nand n – 1 atom argon clusters using classical effective atom-atom pair potentials and the Bennett–Metropolis Monte Carlo technique. When plotted versus n^{–1/ 3} the slope of the free energy differences yields an effective surface tension, σ. It is found that these slopes display a universal (material independent) property related to the excess surface entropy / κ per molecule (or atom), Ω. For most materials (in the bulk liquid state) the latter quantity is about 2. The results indicate that clusters as small as n = 10 display bulk surface free energy properties. The temperature dependence of the effective surface tension for the model water clusters is also investigated and is consistent with a simple scaled form, σ / κTρ^2/3_liquid ≈ Ω(T_c /T – 1), where T_c = 647 K and Ω = 1·9.