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An analysis of the direct correlation functions $c_{ij} (r)$ of binaryadditive hard-sphere mixtures of diameters $\sigma_s$ and $\sigma_b$ (where thesubscripts $s$ and $b$ refer to the "small" and "big" spheres, respectively),as obtained with the rational-function approximation method and the WM schemeintroduced in previous work [S.\ Pieprzyk \emph{et al.}, Phys.\ Rev.\ E {\bf101}, 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 monotonicand 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 welldefined minimum near $r=\frac{1}{2}(\sigma_b-\sigma_s)$, whose properties arestudied in detail. Additionally, we show that the second derivative$c_{sb}''(r)$ presents a jump discontinuity at$r=\frac{1}{2}(\sigma_b-\sigma_s)$ whose magnitude satisfies the samerelationship with the contact values of the radial distribution function as inthe Percus-Yevick theory.

Structural properties of additive binary hard-sphere mixtures. III. Direct correlation functions