Phase equilibria and critical behavior of square-well fluids of variable width by Gibbs ensemble Monte Carlo simulation

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Abstract
The vapor–liquid phase equilibria of square‐well systems with hard‐sphere diameters σ, well‐depths ε, and ranges λ=1.25, 1.375, 1.5, 1.75, and 2 are determined by Monte Carlo simulation. The two bulk phases in coexistence are simulated simultaneously using the Gibbs ensemble technique. Vapor–liquid coexistence curves are obtained for a series of reduced temperatures between about Tr=T/Tc=0.8 and 1, where Tc is the critical temperature. The radial pair distribution functions g(r) of the two phases are calculated during the simulation, and the results extrapolated to give the appropriate contact values g(σ), g(λσ−), and g(λσ+). These are used to calculate the vapor‐pressure curves of each system and to test for equality of pressure in the coexisting vapor and liquid phases. The critical points of the square‐well fluids are determined by analyzing the density‐temperature coexistence data using the first term of a Wegner expansion. The dependence of the reduced critical temperature T*c=kTc/ε, pressure P*c=Pcσ3/ε, number density ρ*c=ρcσ3, and compressibility factor Z=P/(ρkT), on the potential range λ, is established. These results are compared with existing data obtained from perturbation theories. The shapes of the coexistence curves and the approach to criticality are described in terms of an apparent critical exponent β. The curves for the square‐well systems with λ=1.25, 1.375, 1.5, and 1.75 are very nearly cubic in shape corresponding to near‐universal values of β (β≊0.325). This is not the case for the system with a longer potential range; when λ=2, the coexistence curve is closer to quadratic in shape with a near‐classical value of β (β≊0.5). These results seem to confirm the view that the departure of β from a mean‐field or classical value for temperatures well below critical is unrelated to long‐range, near‐critical fluctuations.