Ligand Correlation Mediated by the Solvent

We use the model of section 3.1 to introduce the ligand-ligand correlation mediated by the solvent. We use here the same notation as in Chapter 3. Direct correlation due to direct interaction is denoted by S. Indirect correlation mediated by the polymer only was denoted by y. In this section we introduce a new source of indirect correlation between the ligands. In order to stress this new correlation due to the solvent, we have chosen the model of section 3.1, i.e., no conformational change, hence y = 1. 

The pair correlation function for two ligands on the same polymer is related to the work, here simply the energy, required to convert two singly occupied polymers into one 

The total ligand-ligand pair correlation function is now, in generalization of (3.1.24), 

FIGURE 8.2. A cyclic process corresponding to Eq. (8.5.2). Instead of performing the reaction (8.5.1) in the liquid phase, we first transform the two polymers (O.l) to the gaseous phase. We perform the conversion (8.5.1) and reintroduce the new polymers (0, 0) and (1,1) into the liquid. 

In order to focus on the origin of this new correlation we rewrite each of the solvation Gibbs energies as 

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