The one dimensional Coulomb lattice fluid capacitor

TL;DR

This paper presents an exact solution for a one-dimensional Coulomb lattice fluid capacitor model, revealing phenomena like over-screening, density oscillations, and capacitance oscillations, which are not captured by mean field theory.

Contribution

The study provides an exact analytical solution using transfer operator methods for a 1D Coulomb lattice fluid, highlighting complex phenomena in a simplified model.

Findings

Over-screening and density oscillations near capacitor plates

Capacitance exhibits strong oscillations with applied voltage

Mean field theory fails to capture key effects

Abstract

The one dimensional Coulomb lattice fluid in a capacitor configuration is studied. The model is formally exactly soluble via a transfer operator method within a field theoretic representation of the model. The only interactions present in the model are the one dimensional Coulomb interaction between cations and anions and the steric interaction imposed by restricting the maximal occupancy at any lattice site to one particle. Despite the simplicity of the model, a wide range of intriguing physical phenomena arise, some of which are strongly reminiscent of those seen in experiments and numerical simulations of three dimensional ionic liquid based capacitors. Notably we find regimes where over-screening and density oscillations are seen near the capacitor plates. The capacitance is also shown to exhibit strong oscillations as a function of applied voltage. It is also shown that the corresponding mean field theory misses most of these effects. The analytical results are confirmed by extensive numerical simulations.