Theory of inhomogeneous rod-like Coulomb fluids

TL;DR

This paper develops a field theoretic model for inhomogeneous rod-like Coulomb fluids, deriving coupled equations and providing explicit solutions near charged surfaces, revealing nematic ordering effects on electrostatic profiles.

Contribution

It introduces a novel field theoretic framework combining Coulomb and nematic interactions, solving for inhomogeneous systems with explicit analytical solutions.

Findings

Explicit profiles of nematic order parameter, counterion density, and electrostatic potential near charged surfaces.

Generalization of Gouy-Chapman theory to include nematic ordering effects.

Identification of nematic wetting layer behavior with a Donnan potential.

Abstract

A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact {\sl via} long range Coulomb and short range nematic interactions. The field theory is then solved on a saddle-point approximation level, leading to a coupled system of Poisson-Boltzmann and Maier-Saupe equations. Explicit solutions are finally obtained for a rod-like counterion-only system in proximity of a charged planar wall, generalizing the standard Gouy-Chapman results. The nematic order parameter profile, the counterion density profile and the electrostatic potential profile are interpreted within the framework of a nematic wetting layer with a (Donnan) potential difference.