Test particle limit for the pair structure of quenched-annealed fluid mixtures

A density functional route to the pair structure of quenched-annealed fluid mixtures is presented. The bulk two-body partial pair correlation functions of the mixture are identified with the one-body density distributions in an external potential that models a fixed test particle. Quenched-annealed (replica) density functional theory is used to calculate the inhomogeneous one-body density distributions. A closed theory is obtained by using an exact sum rule that equates two different expressions for the cross pair correlation function between unlike species. Results for binary quenched-annealed hard sphere mixtures are found to agree well with computer simulation data, improving over results from the replica Ornstein-Zernike equations using the direct correlation functions, obtained as second functional derivatives of the quenched-annealed excess free energy functional, as input. The proposed framework allows for the independent determination of the blocked part of the fluid-fluid partial pair correlation function.