  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).
