Reducing Uncertainty in Simulation Surface Tension Estimates Through a Two-Scale Finite-Size Analysis: Thicker is Better
Jack F. Douglas, Jose Rivera
Recent simulation studies of the surface tension γ, and other properties of thin free-standing films, have revealed unexpected finite size effects in which the variance of these properties vary monotonically with the in-plane width of the films, complicating the extrapolation of estimates of film properties to the thermodynamic limit. We carried out molecular dynamics simulations to determine the origin of this phenomenon, and to address the practical problem of developing a more reliable methodology for estimating γ in the thermodynamic limit. We find that there are two distinct finite size effects that must be addressed in a finite size analysis of γ in thin films. The first finite size scale is the in-plane width of the films and the second scale is the simulation cell size in the transverse direction. Increasing the first scale enhances fluctuations in γ, measured by the standard deviation of their distribution, while increasing the second reduces γ fluctuations due to a corresponding increased freedom of the film to fluctuate out of plane. We find that by using progressively large simulation cells in the transverse direction, while keeping the film width fixed, allows us to obtain a smooth extrapolation to the thermodynamic limit, enabling a reduction in the γ uncertainty to a magnitude on the order of 1 % for systems having a reasonable large size, i.e., O(1 micron).