Critical phenomena in binary mixtures

Abstract

Critical phenomena in binary mixtures are investigated on the basis of a fresh approach. The empirical formulae which hold in the critical region are considered to be approximations only. They are replaced by new approximations from which mathematical expressions are derived which describe exactly the behaviour of coexisting phases as the temperature approaches and reaches the critical value.

The new model is valid within the temperature range 0.9 T_c≲T⩽T_c. However, when the composition parameters are expressed in more appropriate units (e.g. as molar ratios instead of molar fractions) the model is applicable over the whole range of coexistence.

The model has inherent extrapolative power making it possible to determine the critical parameters x_c and T_c from measurements outside the critical region.

The model links the properties of coexisting phases α₁ and α₂ by an unusual mathematical symmetry, i.e. x₁(composition of α₁)=g(T)/ƒ(T), x₂(composition of α₂)=g(T)ƒ(T) where g(T) is the re-defined “rectilinear diameter” and ƒ(T)=(1–P) where P behaves like an “order parameter.”

The applicability of the model to liquid, solid and gaseous binary mixtures is demonstrated.