Molecular simulation of phase coexistence: Finite-size effects and determination of critical parameters for two- and three-dimensional Lennard-Jones fluids

The subject of this paper is the investigation of finite-size effects and the determination of critical parameters for a class of truncated Lennard-Jones potentials. Despite significant recent progress in our ability to model phase equilibria in multicomponent mixtures from direct molecular simulations, the accurate determination of critical parameters remains a difficult problem. Gibbs ensemble Monte Carlo simulations with systems of controlled linear system size are used to obtain the phase behavior in the near-critical region for two- and three dimensional Lennard-Jones fluids with reduced cutoff radii of 3, 3.5, and 5. For the two-dimensional systems, crossover of the effective exponent for the width of the coexistence curve from mean field (β = 1/2 in the immediate vicinity of the critical point to Ising-like (β= 1/8) farther away is observed. Critical parameters determined by fitting the data that follow Ising-like behavior are in good agreement with literature values obtained with finite-size scaling methods. For the three-dimensional systems, no crossover to mean field-type behavior was apparent. Extrapolated results for the critical parameters are consistent with literature estimates for similar fluids. For both two- and three-dimensional fluids, system size effects on the coexistence curves away from the critical point are small, normally within simulation statistical uncertainties.