Ionic effects beyond Poisson-Boltzmann theory

Polyelectrolytes are electrolytes asymmetric both in charge and size. Their properties in solution are dominated by Coulombic forces, and without a detailed understanding of these interactions, no interpretation of experimental data is possible. This paper is a review of recent developments in the theory of highly asymmetric electrolytes of spherical shape resembling surfactant micelles. Three different models are discussed: (a) the cell model, which is focused on the small ion-macroion interaction; (b) the model that treats the solution as an effective one-component fluid of macroions; and (c) the isotropic model, where the solution is represented as a mixture of charged spheres. Traditionally, the electrostatic interactions are accounted for via the solution of the Poisson-Boltzmann equation. This theory, however, ignores the fluctuations around the most probable distribution and may yield poor results for systems with multivalent ions. This paper focuses on developments beyond the Poisson-Boltzmann theory; the results of computer simulations and integral equation theories represent the major part of the review.