An analysis of the direct correlation functions $c_{ij}\left(r\right)$ of binary additive hard-sphere mixtures of diameters ${\sigma }_s$ and ${\sigma }_b$ (where the subscripts $s$ and $b$ refer to the “small” and “big” spheres, respectively), as obtained with the rational-function approximation method and the WM scheme introduced in previous work [S. Pieprzyk et al., Phys. Rev. E 101, 012117 (2020)], is performed. The results indicate that the functions $c_{ss}(r<{\sigma }_s)$ and $c_{bb}(r<{\sigma }_b)$ in both approaches are monotonic and can be well represented by a low-order polynomial, while the function $c_{sb}(r<\frac{1}{2}({\sigma }_b+{\sigma }_s))$ is not monotonic and exhibits a well-defined minimum near $r=\frac{1}{2}({\sigma }_b-{\sigma }_s)$, whose properties are studied in detail. Additionally, we show that the second derivative $c_{sb}^{\prime \prime }\left(r\right)$ presents a jump discontinuity at $r=\frac{1}{2}({\sigma }_b-{\sigma }_s)$ whose magnitude satisfies the same relationship with the contact values of the radial distribution function as in the Percus-Yevick theory.

• Received 27 September 2021
• Accepted 17 November 2021

DOI:https://doi.org/10.1103/PhysRevE.104.054142