Exact asymptotic expansions for the cylindrical Poisson-Boltzmann equation

G. Tellez 1, E. Trizac 2, 3

Journal of Statistical Mechanics: Theory and Experiment 1 (2006) P06018

The mathematical theory of integrable Painleve/Toda type systems sheds new light on the behavior of solutions to the Poisson-Boltzmann equation for the potential due to a long rod-like macroion. We investigate here the case of symmetric electrolytes together with that of 1:2 and 2:1 salts. Short and large scale features are analyzed, with a particular emphasis on the low salinity regime. Analytical expansions are derived for several quantities relevant for polyelectrolytes theory, such as the Manning radius. In addition, accurate and practical expressions are worked out for the electrostatic potential, which improve upon previous work and cover the full range of radial distances.

  • 1. Departamento de Fisica,
    Universidad de Los Andes
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 3. Center for Theoretical Biological Physics (CTBP),
    University of San Diego