Exact asymptotic expansions for the cylindrical Poisson-Boltzmann equation

Abstract

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.

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• High Order Coherent Control Sequences of Finite-Width Pulses
• Nonlinear screening of charged macromolecules
• Charge inversion of colloids in an exactly solvable model
• Renormalized Surface Charge Density for a Strongly Charged Plate in Asymmetric Electrolytes: Asymptotic Exact Results in Poisson Boltzmann Theory
• Free energy of cylindrical polyions: analytical results