A Simple Solvable Model

We present here a simple model where long-range and nonadditivity of the correlations can be studied explicitly in terms of the ligand-ligand, and ligand-site interactions. With this model we can clearly see the different behavior of the three models discussed in previous sections and, by generalization, we shall see that the same mechanism applies for correlations between particles in the liquid state. 

The three variants of this model are described in Fig. 5.9. The ligands are simple Lennard-Jones particles, at the center of which a point dipole of strength d is embedded. The orientation of the ligand on the site is always the same, say upward, as in Fig. 5.9. The adsorbent macromolecule consists of three subunits denoted by a, b, and c, each of which has one binding site to which we also refer as a, b, and c. Near each site the macromolecule has a dipole of strength D, which can be oriented either upward or downward. The orientation of the dipole D is determined 

If the long-range interaction 17(1, 3) can be neglected compared with 1/(1, 2), the (direct) triplet correlations can be written as  

The LJ part of the binding energies is of no importance for the indirect correlation only the difference - Ufj enters into the correlation. Note the different orientations of the dipoles D in the two states L and H (Fig. 5.9b). 

we see the fundamental differences between the direct and indirect correlations. First, all three indirect pair correlations are equal and independent of the distance R. They do depend on r (through h), but not on the ligand-ligand distance. 

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