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Recent simulation studies of the surface tension, and other properties ofthin free-standing films, have revealed unexpected finite size effects in whichthe variance of the properties vary monotonically with the in-plane width ofthe films, complicating the extrapolation of estimates of film properties tothe thermodynamic limit. We carried out molecular dynamics simulations todetermine the origin of this phenomenon, and to address the practical problemof developing a more reliable methodology for estimating the surface tension inthe thermodynamic limit. We find that there are two distinct finite sizeeffects that must be addressed in a finite size analysis of the surface tensionin thin films. The first finite size scale is the in-plane width of the filmsand 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 thesecond reduces the surface tension fluctuations due to a correspondingincreased "freedom" of the film to fluctuate out of plane. We find that byusing progressively large simulation cells in the transverse direction, whilekeeping the film width fixed to an extent in which the full bulk liquid zone isdeveloped, allows us to obtain a smooth extrapolation to the thermodynamiclimit, enabling a reduction of the surface tension uncertainty to a magnitudeon the order of 1% for systems having a reasonable large size, i.e., O(1micrometer).

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