Solvent-Induced Interactions and Forces

In the previous four sections we have dealt with some aspects of very dilute aqueous solutions. From the formal point of view, it is sufficient to study the solvation properties of one solute j in a pure solvent. We now proceed to the next step and study a pure solvent with two solutes. In the absence of a solvent, two-particles-in-a-system determines the second virial coefficient in the density expansion of the pressure (section 1.8). Likewise, two-solute-in-a-solvent determines the second virial coefficient of the osmotic pressure (section 6.11). This quantity is expressed in terms of the pair correlation function by 

In general we shall be interested in the six-dimensional function where X2 = 

CI2 are measured relative to a fixed configuration of the first solute. In (7.14.1), however, we can integrate over Xi and over all orientations of the second solute to obtain 

If the system is not infinitely dilute with respect to s, then the analogue quantity is the Kirkwood-Buff integral 

Instead of studying the pair correlation function we can equivalently study the corresponding potential of average force, i.e., 

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