Simulations in ternary hard sphere mixtures

The Monte Carlo method was used to determine the compression factors and radial distribution functions (rdf) of ternary hard-sphere mixtures with hard-sphere diameters σA=1, σB=0.6, σC=0.3 at several packing fractions (y=0.35, 0.40 and 0.45) and mole fractions (xA=xB=xC=1/3 or xA=1/6, xB=1/3, xC=1/2). The obtained values of the compression factor were employed to test the equations of state of hard-sphere mixtures. Fair agreement was found in all the cases. Also the obtained contact values of rdfʹs, gij(σij), compare well with the theoretical values. Simulation results for the dependence of the rdfʹs on distance were compared with values determined from a simple relation devised recently for calculation of gij(x̄) in ternary and multi-component systems. In all the cases, a satisfactory agreement was found for distances close to the contact values. Larger deviations were found in the range of distances close to the first minimum of gij. The magnitude of deviations increases with the increasing differences between σij and σA. In the case of considerably different values of σij and σA, the proposed theoretical method overestimates gij for x̄≥x̄min.