Mixtures of Hard Spheres with Nonadditive Diameters: Some Exact Results and Solution of PY Equation

Abstract

We investigate the properties of binary mixtures of hard‐sphere fluids with nonadditive diameters: calling $R_{\mathrm{ij}}$ the distance of closest approach between particles of species $i$ and $j$ we assume $R_{12}\mathrm{\hspace{0.17em}=\hspace{0.17em}}\frac{1}{2}{\mathrm{(R}}_{11}{\mathrm{\hspace{0.17em}+\hspace{0.17em}R}}_{22}\mathrm{)\hspace{0.17em}+\hspace{0.17em}\alpha }$ with $\text{α\hspace{0.17em}≠\hspace{0.17em}0}$ . We find the exact correlation functions as well as the solution of the Percus–Yevick integral equation for this system with $\text{0\hspace{0.17em}≤\hspace{0.17em}α\hspace{0.17em}≤\hspace{0.17em}}\frac{1}{2}{\mathrm{(R}}_{22}{\mathrm{\hspace{0.17em}-\hspace{0.17em}R}}_{11})$ , in one dimension. For the three‐dimensional case the Percus–Yevick equation is solved partially.