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

Abstract

The vapor-liquid phase equilibria of square-well systems with hard-sphere diameters o, welldepths E, and ranges il = 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 T,. = T/T, = 0.8 and 1, where T, 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(a), g(/Za-), and g(;la-I-). 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 squarewell 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 Tr = kT,/q pressure P r = P,o-'/E, number density p: = pE d, and compressibility factor Z = P /(pkT), on the potential range il, 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 8. The curves for the square-well systems with il = 1.25, 1.375, 1.5, and 1.75 are very nearly cubic in shape corresponding to near-universal values ofp (flzO.325). This is not the case for the system with a longer potential range; when ;1 = 2, the coexistence curve is closer to quadratic in shape with a nearclassical value of p (PzO.5). These results seem to confirm the view that the departure of fl from a mean-field or classical value for temperatures well below critical is unrelated to longrange, near-critical fluctuations.

Gas-liquid coexistence for the boson square-well fluid and theHe4binodal anomaly

“…If we choose λ * = 1/100 and P = 2, M q = 1 (in this case the advance-recede move cannot occur) we find that our algorithm gives results close to the ones of Vega [10] obtained with the classical statistical mechanics (λ * = 0) algorithm of Panagiotopoulos [6] [15]. As we diminish the time-step ǫ * = 1/P T * at a given temperature we can extrapolate to the zero time-step limit P → ∞ as shown in Fig.…”

“…λ * = λ/(Aσ 2 ) ≪ 1 we are in the classical limit. The classical fluid has been studied originally by Vega et al [10] who found that the critical point of the gas-liquid coexistence moves at lower temperatures and higher densities as ∆ gets smaller. The quantum mechanical effects on the thermodynamic properties of nearly classical liquids can be estimated by the de Boer quantum delocalization parameter Λ = √ 2λ * .…”

“…In this communication we will apply the QGEMC method to the fluid of square well bosons in three spatial dimensions as an extension of the work of Vega et al [10] on the classical fluid. The de Boer quantum delocalization parameter Λ = /σ(mE) 1/2 , with E and σ measures of the energy and length scale of the potential energy, can be used to estimate the quantum mechanical effects on the thermodynamic properties of nearly classical liquids [11].…”

“…A situation comparable to the square well case with λ * = 1/10. We use N = 128 and the Aziz HFDHE2 [10] at λ * = 0 and our results in the P → ∞ limit for λ * = 1/100, 1/10. In the simulations we used N = 50 and for the extrapolation to the zero time-step limit up to P = 20 for λ * = 1/100 and P = 500 for λ * = 1/10.…”

Calculation of high-order virial coefficients for the square-well potential

“…The calculated virial coefficients are expressed in reduced form as Increasingly positive values of f correspond to square-well potentials of greater well depth, and for f > f c a bulk liquid phase is possible [27], where f c = exp(1 / T c * ) − 1…”