Local composition and preferential solvation in two-component systems

4 Local composition and preferential solvation in two-component systems 

In the previous section, we discussed the theory of preferential solvation of a solute s in a two-component system. In the traditional concept of solvation thermodynamics, only very dilute solutions could be treated. Therefore, the minimum number of components required for such a study are three a solute and a two-component solvent. However, the question of PS can also be asked in a two-component system, say of A and B. At any composition xA, we may focus on an A solvaton and ask what is the PS of A with respect to the two components A and B. Likewise, we may focus on a B solvaton and ask the same, but independent question of the PS of B with respect to the two components A and B. In this sense, the treatment of the two-component system is a generalization of the corresponding three-component system, as discussed in the previous section. 

Let Ra be any arbitrary radius, and let Va = 4nR3a/3 be the corresponding sphere, the center of which coincides with the center of an A solvaton. The local composition in the volume Va is defined as (see section 8.2) 

Clearly, in a two-component system, there is only one local composition around A, xA (and xjj = 1 — x A). Likewise, there is one local composition around B which we choose to define as 

Since there are only two components around either an A solvaton or a B solvaton, we have only one PS of A and one PS of B. For reasons of symmetry, 

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