Limit Of Complete Association Research Articles

A perturbation density-functional theory for polyatomic fluids. I. Rigid molecules

We present a density-functional theory of nonuniform fluids composed of polyatomic species. It is derived from Wertheim’s first-order perturbation theory of polymerization by taking the limit of complete association. In the case of the uniform fluid, an explicit expression of the complete angle-dependent pair distribution function is obtained which shows that the theory yields nontrivial results for the intermolecular structure. However, features of the long-wavelength structure, such as the existence of an orientational order, are not described. Illustrative applications of the theory are given in the case of diatomic and linear tetra-atomic molecules formed by tangent hard spheres of the same diameter.

Microscopic modelling of association

Abstract 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.

A model for weak electrolytes

The structural and thermodynamic properties of a model electrolyte in which oppositely charged ions bind at a distance L through a delta function interaction are reviewed. The sticky electrolyte model (SEM), as it is called, mimics the behavior of a weak electrolyte and requires a theory (or approximations) for the stickiness (or bonding) between the ions and for the electrical interactions between them. Analytic solutions for charged hard spheres of diameter σ with L = σ/n where n=1, 2, 3, 4, and 5 have been obtained when the hypernetted chain (HNC) approximation was used for the correlation functions inside the hard core and the mean spherical approximation (MS) was employed outside this region. Numerical solutions to the HNC approximation applied to both these regions show only small changes in the internal energy and the degree of association as a function of the concentration. The effect of a solvent on the association of a weak electolyte is assessed from the analytic solutions to the HNC/MS approximation in the presence of a hard sphere solvent and a dipolar solvent. It is found that the degree of association of the weak electrolyte is considerably enhanced by the packing effect of a solvent and is decreased by ion solvation. In the limit of complete association, the system consists of dumbells with extended dipoles provided L<σ/2 when polymerization is averted by the repulsion between the hard cores of like ions. The energies of the systems of extended dipoles are found to have a simple analytic form when they are calculated according to the mean spherical approximation.