Distribution Functions in Mixtures Definitions

In this section we generalize the concepts of MDF to multicomponent mixtures. As in the case of pure liquids, the fundamental molecular quantities required to determine the MDF are the intermolecular interactions. For pairwise additive systems we need the pair potential function for each pair of species as a function of their relative configurations. 

We denote by C/ (X, X ) the work required to bring two molecules of species A and B from infinite separation to the final configuration X, X . (We adopt the convention that the first vector, X, describes the configuration of the first species, A similarly, X describes the configuration of the second species, B. This convention will be applied to any other pairwise function as well.) 

For spherical molecules, l/ (R, R ) is a function of the separation = R - R only. Hence, it is clear that 

In principle, the function Uab R) does not have to bear any resemblance to the corresponding functions Uaa R) and Ubb R) of the pure substances A and B, respectively. However, it is convenient when working with simple molecules—say, Lennard-Jones 

The situation becomes more complex when dealing with nonspherical particles, in which case there is no simple way of relating Uab to Uaa and Ubb- This is certainly true for aqueous solutions where very little is known about the pair potential for the various species. 

Relation (4.2) is expected to be exact for hard spheres. We adopt 

12 coordinates X, X . However, six of these are redundant since we can always translate and rotate the pair, keeping the relative configuration fixed.) 

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