Plait Points in Two- and Three-Component Liquid Mixtures

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Abstract
It is pointed out that the plait‐point (isothermal critical‐mixing‐point) phenomenon in a three‐component liquid system of fixed pressure and temperature is identical in character to that in a two‐component liquid system of fixed temperature but variable pressure. A lattice‐gas model of a two‐component liquid system is described. The intermolecular forces are all postulated to be infinitely strong repulsions, as between hard cores, but the model system nevertheless undergoes first‐order phase transitions with an associated plait point. The behavior of the system with varying densities ρ1 and ρ2 of its two components, at fixed temperature, is shown to be exactly transcribable, with only a change of language, from the behavior of a reference one‐component lattice gas of varying density and temperature, in which the interaction between neighboring molecules is attractive. The critical point of the reference one‐component system is mapped into a plait point in the isothermal ρ1, ρ2 plane of the binary system. The two‐phase coexistence curve (binodal curve) in the isothermal ρ1, ρ2 plane of the binary system is found to be of algebraic degree (1—α′)/β near the plait point, where α′ and 1/β are the index of the divergence of the constant‐volume specific heat in the two‐phase region of the reference system, and the algebraic degree of the reference system's temperature—density coexistence curve, respectively. Fluctuations in ρ1 and ρ2 in the one‐phase region of the binary system are found to diverge as the —γ/(1—α) power of the distance from the plait point, where α and γ are the indices of the divergence of the constant‐volume specific heat and of the compressibility, respectively, in the one‐phase region of the reference system.

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