Structure and thermodynamics of non-additive hard sphere mixtures

Abstract

We present a reliable analytic expression for equation of state of non-additive hard sphere (NAHS) mixtures with equal diameters. A unique feature of the present work is that positive and negative NAHS mixtures are both well expressed within a single equation of state regardless of their composition. To get exact equation of state data for fitting and checking the analytic expression, we have done extensive Monte Carlo simulations for binary NAHS mixtures with equal diameters and different composition [i.e., (x$_$, x$_2$) = (0.5,0.5), (0.25,0.75), and (0.1,0.9)]. The new analytic expression shows good agreements (less than 1\% of discrepancy) with the Monte Carlo results over wide range of density and collision diameter d$_{12}$ regardless of the composition of NAHS mixtures. We also check the validity of Ballone et al.``s modified [Molec. Phys. 59, 275 (1986)] integral equation of Martynov and Sarkisov [Molec. Phys. 49, 1495 (1983)] for compositionally asymmetric ($\mbox{x_1\neq{x_2}}$) NAHS mixtures. An equimolar mixture of hard spheres with equal diameter d, having an unequal collision diameter d$_{12}$ between unlike species, favors a heterocoordinated arrangement if d$_{12}$ lies between 0.65d and d, and a homocoordinated packing below d$_{12}$ = 0.65d. At $d_{12} < 0.65d$, hard spheres of one type move increasingly unaffected by the presence of hard spheres of the other type. This conclusion was drawn from Monte Carlo simulations over large ranges of density and d$_{12}$ and originates in the fact that collisions between like-species at d prevent collisions of unlike-species at shorter distance $d_{12} < d$. The observed shift of hetero- to homo-coordination affects equation-of-state data as well. Additionally, a test of the van der Waals one-fluid model of mixtures by the Monte Carlo data shows that this model significantly overestimates the pressure at high density, hence, less suitable for non-additive hard sphere mixtures. As expected, the MC data sug...