Analysis of miscibility gaps based on the Redlich–Kister polynomial for binary solutions

The conditions for miscibility gaps are examined for the binary solutions of which the excess molar Gibbs energy is described by the Redlich–Kister polynomials of the terms, L A , B ( n ) x A x B ( x A − x B ) n (n=0, 1, 2, …, v), and L A , B ( n ) is given by A A , B ( n ) + B A , B ( n ) T . For the binary solutions specified by the first three R–K terms, the domains of miscibility gaps and of no miscibility gap at 0 K have been successfully defined on the coordinate plane of L A , B ( 2 ) / L A , B ( 0 ) vs. L A , B ( 1 ) / L A , B ( 0 ) . For the binary regular solution at high temperatures ( | A A , B ( 0 ) | ≪ | B A , B ( 0 ) T | ), the domain of miscibility gap with lower critical points and that with upper critical points have been successfully defined on the coordinate plane of A A , B ( 0 ) vs. B A , B ( 0 ) for the first time. For the case of single R–K terms at high temperatures, a rough guiding range of B A , B ( n ) for no miscibility gap is found to be given by − 2 R ≤ B A , B ( n ) ≤ 2 R . Both analytical approaches and numerical calculations were exploited in the present study.