Global order parameters and Antonoff’s rule in multicomponent regular and related solutions

Abstract

The global phase diagram of multicomponent mixtures is obtained in mean field theory from minimizing a function Φ of many variables. It is shown that by subjecting the variational parameters (global order parameters) in Φ to linear transformations, the number of parameters can often be greatly reduced. Simple criteria are constructed that guarantee the reduction to a single global order parameter. In this case the mixture is globally equivalent to the Landau theory with a single order parameter, and Antonoff ’s rule is often valid in these mixtures. Examples are furnished by regular solutions, multicomponent van der Waals mixtures, and Flory–Huggins mixtures if the interaction energies aij approximately satisfy the geometric mean rule aij=(aiiajj)1/2.