Subregular model for multicomponent solutions

The subregular Margules model is applied here to quaternary solutions in order to derive equations for excess properties (G^xs, V^xs, etc.) and partial molar excess properties (RT ln γ_i, etc.) for components in the mixture. Formulae generalizing the subregular model to arbitrary numbers of components and expressions for higher derivatives of the free energy, for use in binode and spinode location, are also presented. The derivation indicates that ternary mixing parameters exist independent of their component binaries. It is therefore impossible to estimate ternary interaction coefficients having knowledge only of the mixing properties of the binaries. Quaternary and higher-order coefficients are not required for multicomponent subregular solutions. -Authors