Decorated Lattice Model of a Binary Mixture

Abstract

A binary lattice gas model is described whose properties can be exactly transformed into those of a reference one‐component lattice gas. The model lattice contains regular lattice sites occupied by one component and decorated bond sites occupied by the second component. Multiple occupancy of sites is not allowed. All other interactions between like molecules are zero but there is a finite repulsion between unlike nearest neighbors. The complete two‐phase region of the binary system is described by means of the two‐phase behavior of the reference system. The two‐phase region in a constant temperature plane is enclosed in a closed‐loop binodal curve with two plait points. The binodal curve near the plait point is found to be of degree (1‐α′) / β while the degree of the top of the coexistence surface is 1 / β , where α′ and 1 / β are the exponents of the divergence of the constant volume heat capacity in the two‐phase region and the degree of the coexistence curve, respectively, of the reference system. The heat capacity at constant volume and composition in the one‐phase region is found to remain finite near the plait point and to diverge as the −α power of the distance from the top of the coexistence surface at the critical composition. Fluctuations in the composition in the one‐phase region diverge as the −γ / (1 − α) power of the distance from the plait point and as the −γ power of the distance from the top of the coexistence surface, where −γ is the power of the divergence of the reference system compressibility in the one‐phase region near the critical point.