Poisson-Boltzmann model in a solvent of interacting Langevin dipoles

¹  Department of Physics, North Dakota State University - Fargo, ND 58108-6050, USA
²  Faculty of Health Sciences, University of Ljubljana - Poljanska 26a, 1000 Ljubljana, Slovenia, EU

Corresponding author: sylvio.may@ndsu.edu

Received: 7 August 2009
Accepted: 29 September 2009

Abstract

We incorporate a solvent model of interacting Langevin dipoles into the Poisson-Boltzmann formalism of mobile point-like ions close to a single charged surface. Our model aims at understanding the interplay between the diffuse double layer and the polarization of water due to a surface-induced dipolar ordering. We account for interactions between the Langevin dipoles, which leads to an intrinsic spatial decay length of the solvent polarization. An analytical solution of the free energy in the weak perturbation limit is presented and compared with the nonlinear regime. From our analytical results we derive conditions for the optimal polarization at the surface and for the sign inversion of the electrostatic potential.