Preferential Solvation in Binary and Ternary Systems

As mentioned previously, one of the major advantages of FST is that it provides information on local density fluctuations. An alternative approach to this problem involves the concepts of local composition and preferential solvation (Ben-Naim 2006). To do this we first note that the average number of j particles in a region of spherical volume siurounding a central particle i is 

The above expressions depend explicitly on the spherical volume of interest. This volume must be large enough to ensure all RDFs are unity and therefore that Equation 1.81 is valid. Unfortunately, the distance beyond which the RDFs are unity is generally unknown. It will certainly depend on the species and specific composition, as well as the values of T and p. There are two solutions to this problem. First, one can attempt to estimate the volume and thereby provide quantitative values for the preferential solvation. This is described in Chapters 3 and 4. Alternatively, one can take the approach of Ben-Naim and expand the above expression in powers of to give (Ben-Naim 2006) 

The numerator then provides the sign of the preferential solvation as we decrease the value of 1., from that of an infinite region in a closed system to that of an open local region of the solution. The magnitude of the effect is therefore unimportant, but 

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