The Poisson-Boltzmann Theory for Two Parallel Uniformly Charged Plates

Abstract

We solve the nonlinear Poisson-Boltzmann equation for two parallel and likely charged plates both inside a symmetric elecrolyte, and inside a 2 : 1 asymmetric electrolyte, in terms of Weierstrass elliptic functions. From these solutions we derive the functional relation between the surface charge density, the plate separation, and the pressure between plates. For the one plate problem, we obtain exact expressions for the electrostatic potential and for the renormalized surface charge density, both in symmetric and in asymmetric electrolytes. For the two plate problems, we obtain new exact asymptotic results in various regimes.

17 pages, 9 eps figures

References in corpus (3)

• Statics and Dynamics of Strongly Charged Soft Matter
• Variational approach for electrolyte solutions: from dielectric interfaces to charged nanopores
• Bound Pairs: Direct Evidence for Long-range Attraction between Like-Charged Colloids

Cited by in corpus (8)

• Calculating potential of mean force between like-charged nanoparticles: a comprehensive study on salt effects
• Electrostatic Interactions and Electro-osmotic Properties of Semipermeable Surfaces
• The Correlation Potential of a Test Ion Near a Strongly Charged Plate
• Renormalized Surface Charge Density for a Strongly Charged Plate in Asymmetric Electrolytes: Asymptotic Exact Results in Poisson Boltzmann Theory
• Electric Fields Near Undulating Dielectric Membranes
• Dynamical effects of long-range interaction revealed in screened Coulomb interacting ring systems
• Near- and far-field expansions for stationary solutions of Poisson--Nernst--Planck equations
• The Poisson-Boltzmann Theory for The Two-Plates Problem: Some Exact Results