Approaching the thermodynamic limit of a bounded one-component plasma

TL;DR

This study uses molecular dynamics to analyze the bounded one-component plasma, extrapolating to the thermodynamic limit and providing a wide-range ionic equation of state for testing simulations.

Contribution

It introduces a method to estimate the thermodynamic limit of a bounded OCP and proposes an improved cutoff radius for interionic forces in MD simulations.

Findings

Estimated the electrostatic energy per ion in the thermodynamic limit with 0.1% error.

Calculated energies align with Monte Carlo data at high Coulomb coupling.

Proposed an improved cutoff radius affecting the phase transition in MD simulations.

Abstract

The classical one-component plasma (OCP) bounded by a spherical surface reflecting ions (BOCP) is studied using molecular dynamics (MD). Simulations performed for a series of sufficiently large BOCP's make it possible to establish the size dependencies for the investigated quantities and extrapolate them to the thermodynamic limit. In particular, the total electrostatic energy per ion is estimated in the limit of infinite BOCP in a wide range of the Coulomb coupling parameter $\Gamma$ from 0.03 to 1000 with the relative error of the order 0.1%. Calculated energies are by about 0.5% lower as compared to the modern Monte Carlo (MC) simulation data obtained by different authors at $\Gamma<30$ and almost coincide with the MC results at $\Gamma>175$. We introduce two more converging characteristic energies, the excess interatomic electrostatic energy and the excess ion-background electrostatic energy, which enable us to calculate the ionic compressibility factor inaccessible in conventional MC and MD simulation of the OCP with periodic boundary conditions. The derived wide-range ionic equation of state can be recommended for testing OCP simulations with various effective interaction potentials. Based on this equation, we propose an improved cutoff radius for the interionic forces implemented in LAMMPS and perform MD simulation of the OCP to demonstrate that location of the metastable region of the fluid-solid phase transition depends sensitively on this radius.