Generalized Linear Mixing Rule for Classical Coulomb Mixtures

It is shown that the Coulomb energy U of fully ionized ionic mixture can be written as a sum over partial contributions of ion species j: U = T ∑ j Nju(Γj , yj) (generalized linear mixing rule). In contrast to the traditional linear mixing rule ULM = T ∑ j NjuOCP(Γj), applicable for strong coupling, the partial contribution function u depends not only on Γj , but on an additional parameter yj = (rD/r D ) 2 also. Here rD and r D are Debye radiuses in the mixture and in the one component plasma at coupling parameter Γj , correspondingly. The parameter yj does not depend on a specific composition of the mixture, but on the Debye radius rD only, making function u(Γj , yj) universal. The generalized linear mixing rule can be applied at any coupling parameter, if ionic mixture is not crystallized. It reproduces results of the Debye-Hückel theory at weak coupling and traditional linear mixing rule at strong coupling. It can be easily applied to the complicated mixtures, composed of a large number of ion species. Since yj is temperature independent, the Coulomb contribution to Helmholtz free energy of the mixture can also be presented in a form of generalized linear mixing rule.