Reducing Uncertainty in Simulation Estimates of the Surface Tension Through a Two-Scale Finite-Size Analysis: Thicker is Better

TL;DR

This study investigates finite size effects in molecular dynamics simulations of surface tension in thin films, proposing a two-scale analysis that improves the accuracy of thermodynamic limit estimates by adjusting simulation cell dimensions.

Contribution

The paper introduces a two-scale finite size analysis method that separates in-plane width and transverse cell size effects to reliably estimate surface tension in the thermodynamic limit.

Findings

Increasing transverse cell size reduces surface tension fluctuations.

Large simulation cells enable smooth extrapolation to the thermodynamic limit.

Uncertainty in surface tension estimates can be reduced to about 1%.

Abstract

Recent simulation studies of the surface tension, and other properties of thin free-standing films, have revealed unexpected finite size effects in which the variance of the 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 the surface tension in the thermodynamic limit. We find that there are two distinct finite size effects that must be addressed in a finite size analysis of the surface tension 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 the surface tension, measured by the standard deviation of their distribution, while increasing the second reduces the surface tension 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 to an extent in which the full bulk liquid zone is developed, allows us to obtain a smooth extrapolation to the thermodynamic limit, enabling a reduction of the surface tension uncertainty to a magnitude on the order of 1% for systems having a reasonable large size, i.e., O(1 micrometer).