Direct correlation function from the consistent fundamental-measure free energies for hard-sphere mixtures

In a recent paper [Phys. Rev. E 86, 040102(R) (2012)], Santos presented a self-consistency condition that can be used to limit the possible forms of fundamental measure theory. Here, the direct correlation function, resulting from the Santos functional, is derived, and it is found to be very close to the result of the White Bear density functional, except near the origin where it diverges.

Figure 1

The direct correlation function as calculated using the full line: Percus-Yevik approximation; dotted line: the White Bear approximation; and dashed line: Eq. (6) with $\Lambda \left(y\right)=[1-(y/2)-\ln (1+y)/y]/3$ [1]. The left panel is for a low-density fluid with packing fraction $\eta =0.1$, and the right panel is for a high-density fluid with $\eta =0.5$. At low densities, the Percus-Yevik result is quite accurate, and at high densities, the White Bear result is in good agreement with the simulations [3].