Reducing uncertainty in simulation estimates of the surface tension through a two-scale finite-size analysis: thicker is better

Abstract

Recent simulation studies of the surface tension , and other properties of thin freestanding 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 in the thermodynamic limit. We find that there are two distinct finite size effects that must be addressed in a finite size analysis of 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 , measured by the standard deviation of their distribution, while increasing the second reduces 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 uncertainty to a magnitude on the order of 1 % for systems having a reasonable large size, i.e., O IntroductionLongford et al. 1 recently studied the vapor/liquid equilibrium of Lennard-Jones atoms (Ar) and water molecules, using thin liquid films surrounded by coexisting vapor phases, and found unexpected finite-size effects for the variance of as the width of the simulated film was varied. This result is important because it suggests that extrapolation of the film properties by increasing the film in-plane extent may not lead to reliable thermodynamic limit estimates of and other film properties. For Lennard-Jones systems with liquid and vapor lengths, and dimensions in the transverse directions of between 15 $%&$% and 35 $%&$% ( $%&$% being the diameter of a single Argon atom), temperatures between 85 K and 135 K, a short reduced-cutoff radius, ( * , of » 3 $%&$% , with long-range corrections to the properties, and a large timestep of 2 fs, the variance of the surface tension grows with the length of the layers in a linear fashion. Schmitz et al. 2,3suggested that these unexpected size effects are due to a 'domain broadening' caused by density fluctuations in the bulk liquid. In a previous study, we found that bulk and some interfacial properties of narrow layers vary with the size of the simulation cell in the transverse directions, and that the average property values and their distribution narrow as the transverse area of the simulation cell is increased. 4 Here, we perform simulations aimed to understand these unexpected finite size effects, also observed of Langford et al. 1 , in order to develop a more reliable approach for the precise estimation of the thermodynamic properties of thin films.In...

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