Nonadditive hard-sphere fluid mixtures: A simple analytical theory

We construct a nonperturbative fully analytical approximation for the thermodynamics and the structure of nonadditive hard-sphere fluid mixtures. The method essentially lies in a heuristic extension of the Percus-Yevick solution for additive hard spheres. Extensive comparison with Monte Carlo simulation data shows a generally good agreement, especially in the case of like-like radial distribution functions.

Figure 1

Plane $\Delta$ vs ${\sigma }_2/{\sigma }_1$ showing the shaded region $-{\sigma }_2/({\sigma }_1+{\sigma }_2)\le \Delta \le 2{\sigma }_2/({\sigma }_1+{\sigma }_2)$ where the first two singularities of $g_{ij}\left(r\right)$, according to approximation $\text{RFA}$, are ${\sigma }_{ij}$ and ${\sigma }_{ik}-a_{kj}$ with $k\ne j$. The circles denote the systems analyzed in Sec. 5.

Figure 2

Compressibility factor as a function of the nonadditivity parameter for a symmetric binary mixture of NAHSs at $\rho {\sigma }^3=0.2$ and two different compositions. The MC data are taken from Refs. [36, 37].

Figure 3

Compressibility factor as a function of the nonadditivity parameter for an equimolar asymmetric binary mixture of NAHSs with a size ratio ${\sigma }_2/{\sigma }_1=1/3$ at a packing fraction $\eta =0.5$. The symbols [v] and [c] stand for the virial and compressibility routes, respectively. The MC data are taken from Ref. [38].

Figure 4

Compressibility factor as a function of the size ratio ${\sigma }_2/{\sigma }_1$ for binary asymmetric NAHS mixtures with $x_2=\frac{1}{2}$, $\Delta =-0.05$, and $\eta =0.5$ (top panel); $x_2=\frac{1}{4},\frac{1}{2}$, $\Delta =0.2$, and $\eta =0.2$ (middle panel); $x_2=\frac{1}{4},\frac{1}{2}$, $\Delta =0.5$, and $\eta =0.075$ (bottom panel). In the bottom panel only the theoretical data obtained from the virial route are shown since they practically coincide with those obtained from the compressibility route. The MC data are taken from Ref. [38].

Figure 5

RDF for system A of Table .

Figure 6

RDF for system B of Table .

Figure 7

RDF for system C of Table .

Figure 8

RDF for system D of Table .

Figure 9

RDF for system E of Table .

Figure 10

RDF for system F of Table .

Figure 11

RDF for the WR model at $\rho {\sigma }_{12}^3=0.28748$. The MC data are taken from Ref. [43].

Figure 12

RDF for the WR model at $\rho {\sigma }_{12}^3=0.4$. The MC data are taken from Ref. [43].

Figure 13

Plane $\Delta$ vs $R\equiv {\sigma }_2/{\sigma }_1$ showing the regions with different ordering of the distances ${\sigma }_1$, ${\sigma }_2$, ${\sigma }_{12}-a_{12}$, ${\sigma }_{12}+a_{12}$, $2{\sigma }_{12}$, and ${\sigma }_1+{\sigma }_2$.