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

An analysis of the direct correlation functions c(ij)(r) 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 < 1/2 (sigma(b) + sigma(s))) is not monotonic and exhibits a well-defined minimum near r = 1/2 (sigma(b) - sigma(s)), whose properties are studied in detail. Additionally, we show that the second derivative c ''(sb)(r) presents a jump discontinuity at r = 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.