Free-energy model for charged Yukawa mixtures: Asymptotic strong-coupling limit and a nonlinear mixing rule

A free-energy model for mixtures of charged particles interacting through the Yukawa repulsive potential is derived analytically from the Onsager-type exact lower bound for the free energy of the system. It takes the form of a ``nonlinear mixing rule,'' which relates the configurational free energy of the mixture to that of the one-component Yukawa system. This scaling law holds, under broad assumptions, for the exact Madelung (i.e., asymptotic strong-coupling) energy term for the fluid; within the hypernetted-chain approximation, it is very accurate also for conditions of intermediate and weak coupling. The physics relating this mixing rule with the well-known volume-additivity rule for the Thomas-Fermi mixing of elements is revealed.