Non-electrostatic interactions as random fields in charged liquids

TL;DR

This paper introduces a complex Poisson-Boltzmann equation incorporating non-electrostatic interactions as random fields, enabling easier simulation of effects like ion sterics in charged liquids using finite element methods.

Contribution

It presents a novel complex equation that models both electrostatic and non-electrostatic interactions in charged liquids through random fields, facilitating simulations.

Findings

Steric effects are effectively captured by the new equation.

The finite element method successfully solves the complex equation.

Non-electrostatic interactions are represented as random fields for simplified simulation.

Abstract

We derive an equation capable of treating both the electrostatic and non-electrostatic interactions in the charged liquids. The equation derived is a complex version of the Poisson-Boltzmann equation, in which the non-electrostatic interactions are transformed to complex random fields by the field theory. Thus, the non-electrostatic interactions of the ions in the charged liquids can be simulated easily by generating random numbers according to the random fields. To solve the equation, the finite element method has been applied. The non-electrostatic interactions treated in the equation are general. In this study, we take the steric effect of ions as an example. Results show that the steric effect can be clearly caught by the equation.