Fourth virial coefficients of asymmetric nonadditive hard-disk mixtures

Abstract

The fourth virial coefficient of asymmetric nonadditive binary mixtures of hard disks is computed with a standard Monte Carlo method. Wide ranges of size ratio (0.05 ≤ q ≤ 0.95) and nonadditivity (-0.5 ≤ Δ ≤ 0.5) are covered. A comparison is made between the numerical results and those that follow from some theoretical developments. The possible use of these data in the derivation of new equations of state for these mixtures is illustrated by considering a rescaled virial expansion truncated to fourth order. The numerical results obtained using this equation of state are compared with Monte Carlo simulation data in the case of a size ratio q = 0.7 and two nonadditivities Δ = ±0.2.

Virial coefficients, equation of state, and demixing of binary asymmetric nonadditive hard-disk mixtures

“…Similar results were observed in Ref. 31 in the case of the coefficients D ijkℓ for positive nonadditivities.…”

“…In fact, as we observed in Ref. 31, the RVE EoS performs better than the SHY EoS in the case of negative nonadditivity.…”

“…In this subsection we will recall two theoretical EoSs for NAHD mixtures whose performance with respect to numerical values of the fourth virial coefficients and compressibility factor was proved to be reasonably good in Ref. 31. These are the one proposed by Hamad 18,[36][37][38] (which we will label with a superscript H) and one proposed by three of us in 2005 23 (labeled with the superscript SHY).…”

“…(2.21) In Ref. 31 we assessed the merits of the above approximations with respect to the partial fourth virial coefficients. We will do the same with the fifth virial coefficients in Sec.…”

“…29 In 2011, another of us 30 computed the fourth virial coefficient of symmetric NAHD mixtures (σ 2 = σ 1 ) over a wide range of nonadditivity and compared the fluid-fluid coexistence curve derived from two EoSs built using the new virial coefficients with some simulation results. More recently, four of us 31 extended the previous study to asymmetric NAHD mixtures, (i.e., mixtures such that the size ratio q = σ 2 /σ 1 is different from unity), while three of us 32 reported values of the fifth virial coefficient and studied the EoS and the equilibrium behavior of a symmetric NAHD mixture.…”