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 de tailed understanding of these interactions, no interpretation of experiment al data is possible. This paper is a review of recent developments in the t heory of highly asymmetric electrolytes of spherical shape resembling surfa ctant micelles. Three different models are discussed: (a) the cell model, w hich is focused on the small ion-macroion interaction; (b) the model that t reats the solution as an effective one-component fluid of macroions; and (c ) the isotropic model, where the solution is represented as a mixture of ch arged spheres. Traditionally, the electrostatic interactions are accounted for via the solution of the Poisson-Boltzmann equation. This theory, howeve r, ignores the fluctuations around the most probable distribution and may y ield poor results for systems with multivalent ions. This paper focuses on developments beyond the Poisson-Boltzmann theory; the results of computer s imulations and integral equation theories represent the major part of the r eview.