Finite-size scaling study of the vapor-liquid critical properties of confined fluids: Crossover from three dimensions to two dimensions

We perform histogram-reweighting grand canonical Monte Carlo simulations of the Lennard-Jones fluid confined between two parallel hard walls and determine the vapor-liquid critical and coexistence properties in the range of σH6σ and 10σ L_x, L_y 28σ, where H is the wall separation, L_x = L_y is the system size and σ is the characteristic length. By matching the probability distribution of the ordering operator, P (M), to the three-dimensional (3D) and two-dimensional (2D) Ising universality classes according to the mixed-field finite-size scaling approach, we establish a "phase diagram" in the (H,L) plane, showing the boundary between four types of behavior: 3D, quasi-3D, quasi-2D, and 2D. In order to facilitate 2D critical point calculation, we present a four-parameter analytical expression for the 2D Ising universal distribution. We show that the infinite-system-size critical points obtained by extrapolation from the apparent 3D and 2D critical points have only minor differences with each other. In agreement with recent reports in the literature [Jana, J. Chem. Phys. 130, 214707 (2009)], we find departure from linearity in the relationship between critical temperature and inverse wall separation, as well as nonmonotonic dependence of the critical density and the liquid density at coexistence upon wall separation. Additional studies of the ST2 model of water show similar behavior, which suggests that these are quite general properties of confined fluids.