Capillary condensation in the two-dimensional lattice gas: A Monte Carlo test of fluctuation corrections to the Kelvin equation

A two-dimensional lattice gas model with nearest-neighbour attractive interaction confined in a strip of width L between two parallel boundaries at which an attractive short-range force acts is studied by Monte Carlo simulations, for cases where the system is in the wet phase near the critical wetting transition line for L --> infinity. We study the shift of the chemical potential mu of the transition in the strip as a function of L by thermodynamic integration methods, Delta mu = mu(c)(L) - mu(c)(infinity), and also obtain the thickness l(c) of the wetting film at the chemical potential mu(c)(L) at which capillary condensation occurs. In the range 32 less than or equal to L less than or equal to 120 the data are consistent with a variation according to the Kelvin equation, Delta mu proportional to L-1, as well as with a shifted Kelvin equation, Delta mu proportional to (L - L-0)(-1), with a constant L-0. Thus, we find no evidence for the fluctuation correction {Delta mu proportional to (L - 3l(c))(-1)} predicted by Parry and Evans. This failure is traced back to the fact that in this range of linear dimensions there are not yet any well developed wetting layers at coexistence, and the prediction l(c) proportional to L-1/3 from the theory of complete wetting does not hold in this range either. Instead we empirically find a relation l(c) proportional to ln L + constant over the whole range of system sizes we studied.