Critical point and phase behavior of the pure fluid and a Lennard-Jones mixture

Monte Carlo simulations in the grand canonical ensemble were used to obtain liquid-vapor coexistence curves and critical points of the pure fluid and a binary mixture of Lennard-Jones particles. Critical parameters were obtained from mixed-field finite-size scaling analysis and subcritical coexistence data from histogram reweighting methods. The critical parameters of the untruncated Lennard-Jones potential were obtained as $Tc*=1.3120±0.0007$⁠, $ρc*=0.316±0.001$ and $pc*=0.1279±0.0006.$ Our results for the critical temperature and pressure are not in agreement with the recent study of Caillol [J. Chem. Phys. 109, 4885 (1998)] on a four-dimensional hypersphere. Mixture parameters were $ε1=2ε2$ and $σ1=σ2,$ with Lorentz–Berthelot combining rules for the unlike-pair interactions. We determined the critical point at $T*=1.0$ and pressure-composition diagrams at three temperatures. Our results have much smaller statistical uncertainties relative to comparable Gibbs ensemble simulations.