# The system of mobile ions in lattice models: Screening effects, thermodynamic and electrophysical properties

## TL;DR

This paper develops a lattice fluid model with Coulomb interactions to analyze screening effects, thermodynamic properties, and electric double layer characteristics, revealing how boundary conditions influence capacitance and system stability.

## Contribution

It introduces a lattice model incorporating both short and long-range Coulomb interactions and analytically examines their effects on screening and electric properties.

## Key findings

- Debye length depends on concentration and boundary effects.
- Coulomb contribution to free energy is derived analytically.
- Capacitance diverges and can become negative, indicating potential instability.

## Abstract

The lattice fluid model of the system with short range and long range Coulomb interactions is suggested. In the framework of the collective variables method, the screening of the Coulomb interactions in the bulk is considered. It is shown that the Debye length includes additional concentration dependence inversely proportional to the square root of the mean concentration of vacant sites like what is known at the plane boundary. The Coulomb interaction contribution to the free energy of the system is calculated in the approach close to the mean spherical approximation and is given in an analytical form. The influence of the variation of the crystal field near the system boundary on the structure and characteristics of the electric double layer is investigated. As compared to the system with equal crystal potentials at the lattice sites throughout the system the pronounced difference for the electric capacitance appears at low absolute values of the surface potential and it is more pronounced for negative electric potentials. The capacitance diverges as the potential values at which the electric field tends to zero and attains negative values in regions of the surface potentials depending on their polarity and values of the surface crystal potential. Negative values of the capacitance may indicate the thermodynamic instability of the system that can result from neglecting the short range interaction contribution.

---
Source: https://tomesphere.com/paper/1901.07941