Microscopic modelling of association

In a reformulation and extension of our earlier published work, exact equations which relate the cavity function to excess solvation free energies and equilibrium association constants are rederived by using a thermodynamic cycle. A zeroth-order approximation, derived previously by us as a simple interpolation scheme, is found to be very accurate if the associative bonding occurs on or near the surface of the repulsive core of the interaction potential. If the monomeric bonding radius is substantially less than the core radius, our zeroth-order approximation overestimates the association degree and association constant, and an alternative approach is found advantageous. In the case of the association A+B ⇌ AB, it is based on a calculation of the thermodynamics of a mixture of A, B, and AB species, with the species concentrations regarded as independent. From this, near-exact analytic results for binary hard-sphere association into RISM molecules are obtained. Solvent effects on binary hard-sphere association and ionic association are also investigated, and a theory of particle-particle correlation is given to supplement the above purely thermodynamic study. It reveals the sense in which the complete-association limit is like a critical point.