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

Abstract

Values of the fifth virial coefficient, compressibility factors, and fluid-fluid coexistence curves of binary asymmetric nonadditive mixtures of hard disks are reported. The former correspond to a wide range of size ratios and positive nonadditivities and have been obtained through a standard Monte Carlo method for the computation of the corresponding cluster integrals. The compressibility factors as functions of density, derived from canonical Monte Carlo simulations, have been obtained for two values of the size ratio (q = 0.4 and q = 0.5), a value of the nonadditivity parameter (Δ = 0.3), and five values of the mole fraction of the species with the biggest diameter (x = 0.1, 0.3, 0.5, 0.7, and 0.9). Some points of the coexistence line relative to the fluid-fluid phase transition for the same values of the size ratios and nonadditivity parameter have been obtained from Gibbs ensemble Monte Carlo simulations. A comparison is made between the numerical results and those that follow from some theoretical equations of state.

Structural and Thermodynamic Properties of Hard-Sphere Fluids

“…We should also mention that the ideas presented here in connection with the EOS for additive multicomponent HS mixtures have also been used for nonadditive systems and for hard-hypersphere systems with arbitrary spatial dimensions. 126,177,180,[226][227][228] Finally, it should be clear that there are many facets of the equilibrium and structural properties of many other hard-core systems that may be studied following the ideas presented here but that up to now have not been considered. For instance, the generalization of the RFA approach to square-well or square-shoulder mixtures and the surplus mapping of the single-component EOS to that of nonadditive HS mixtures appear as interesting challenges.…”

Surface Free Energy of a Hard-Disk Fluid at Curved Hard Walls: Theory and Simulation

“…The excess free energy density f ex is obtained by integration of the excess compressibility factor The solvation free energy of species 1 in the pure fluid of species 2 is given by which combined with eq 61 gives where the coefficients 12 (2) , 122 (3) , 1222 (4) , etc. have been calculated by Fiumara et al 29 The surface free energy can then be obtained from B ̃n is the nth virial coefficient of the bulk fluid from eq 28.…”

“…The total number density is given by ρ = ρ 1 + ρ 2 , and the mole fractions of species 1 and 2 are x 1 = ρ 1 /ρ and x 2 = ρ 2 /ρ, respectively. The virial expansion of the pressure can be expressed as a power series in the total density where the coefficients in eq can be in turn written in terms of composition-independent coefficients The excess free energy density f ex is obtained by integration of the excess compressibility factor The solvation free energy of species 1 in the pure fluid of species 2 is given by which combined with eq gives where the coefficients , , , etc. have been calculated by Fiumara et al . The surface free energy can then be obtained from where V = πR 2 and A = 2 πR for ρ = ρ 2 and p is described by the virial expression given in eq .…”

“…The surface free energy can then be obtained from where V = πR 2 and A = 2 πR for ρ = ρ 2 and p is described by the virial expression given in eq . γ is then which can be generalized as B̃ n is the n th virial coefficient of the bulk fluid from eq . The first and second terms from eq can be evaluated exactly using the expressions for , , and B̃ 2 given in Fiumara et al; however, the higher-order terms (for example, ) must be estimated from numerical results. The coefficients and were numerically evaluated by Saija et al .…”

Demixing and tetratic ordering in some binary mixtures of hard superellipses

“…The competing different structures give rise to strong segregation and even demixing between identical phases [34]. In two dimensions the simplest binary mixture, which exhibit demixing transition is the nonadditive mixture of hard disks [35][36][37][38][39][40][41]. The positive nonadditivity is responsible for the fluid-fluid demixing transition, because it reduces the available room for both components upon mixing.…”