A Monte-Carlo approach to Poisson-Boltzmann like free energy functionals

TL;DR

This paper introduces a Monte-Carlo method for efficiently computing equilibrium ion distributions from Poisson-Boltzmann free energy functionals, simplifying numerical analysis of complex ionic systems.

Contribution

It presents a novel Monte-Carlo simulation technique that uses the free energy as a Hamiltonian, offering an easier and more general alternative to solving differential equations.

Findings

Successfully applied to valence mixtures

Effectively modeled hard core ion interactions

Demonstrated ease of implementation

Abstract

A simple technique is proposed for numerically determining equilibrium ion distribution functions belonging to free energies of the Poisson-Boltzmann type. The central idea is to perform a conventional Monte-Carlo simulation using the free energy as the "Hamiltonian" entering the Metropolis criterion and the spatially discretized density as degrees of freedom. This approach is complementary to the possibility of numerically solving the differential equations corresponding to the variational problem, but it is much easier to implement and to generalize. Its utility is demonstrated in two examples: valence mixtures and hard core interactions of ions surrounding a charged rod.