MULTIDENSITY INTEGRAL-EQUATION THEORY FOR HIGHLY ASYMMETRIC ELECTROLYTE-SOLUTIONS

Integral equation theory based on a recently developed multidensity formalism [Mol. Phys. 78, 1247 (1993)] is proposed to study highly asymmetric electrolyte (polyelectrolyte) solutions. The system studied consists of large and highly charged polyions and small counterions having one or two elementary charges. The potential energy of interaction between counterions and polyions is separated into two parts, a strongly attractive part responsible for the association and a nonassociative part. Due to the strong asymmetry in size we can treat each counterion as bondable to a limited number of polyions n, while each polyion can bond arbitrary number of counterions. In our cluster expansion appropriate to the problem the diagrams appearing in the activity expansion of the one-point counterion density are classified in terms of the number of associating bonds incident upon the labeled white counterion circle. The corresponding diagrams for the one-point polyion density are classified in the usual way. A generalized version of the Ornstein-Zernike equation, which involves n + 1 counterion densities and one polyion density, together with hypernetted-chain-like (HNC) closure conditions are derived. The simplest two-density version of the theory yields very good agreement with new and existing computer simulations for both thermodynamical and structural properties of these systems. This good agreement extends into the region of parameter space where the ordinary HNC approximation does not have a convergent solution. © 1995 American Institute of Physics.