Preferential solvation in three-component systems

In the previous section, we have defined the concepts of the local composition and the preferential solvation for any mixture. In a three-component system of s, A, and B, we can define three local compositions around each of the molecules, e.g., x (s),x (s) and x s(s). 

However, since the sum of these is unity (provided we have chosen the same correlation volume for the three cases), we have only two independent quantities for each type of solvaton. Altogether, we have six independent local compositions xf(j) in the system. Likewise there are three PS(j/s)  

As in the general case discussed in section 8.2, for any choice of a volume Va which is at least the size of correlation volume Vc, one can obtain all the KB integrals from the inversion of the KB theory. Hence, we can compute all the local compositions as well as the preferential solvation around any species in the system. To the best of our knowledge, such a complete computation has not been undertaken for any three-component system. However, there exists abundant information, both experimental and theoretical, on a three-component system where one solute say, s, is very dilute in the mixed solvents of A and B. Although one can define the local composition and PS around s, A and B, only one of these has been studied, the component s which is diluted in the mixed solvent. It is worthwhile noting that in the traditional approach to solvation thermodynamics, only very dilute solutions could be studied, i.e., a dilute solution of s in a mixed solvent of two components was a minimal requirement for studying PS. We shall see in the next section that PS can be studied in a two-component system as well. 

From now on we focus on the solute s and define the local composition around it. Since 0, we have from (8.9) 

PS(A s) is the preferential solvation of s with respect to A. A positive value of 

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