Statistical mechanics of a 2D material in a gas reservoir

TL;DR

This paper develops a statistical mechanics framework for low-dimensional materials interacting with a gas reservoir, validated through molecular dynamics simulations, highlighting environmental effects on 2D materials like graphene.

Contribution

It introduces a new partition function formulation for nanoscale systems interacting with a heat bath, validated via MD simulations, extending traditional thermodynamics models.

Findings

Interactions with the heat bath significantly affect 2D material properties.

The developed MD algorithm accurately models low-dimensional systems in a gas reservoir.

Environmental effects alter the fluctuations and behavior of 2D materials.

Abstract

We derive and validate a partition function for low-dimensional systems interacting with a heat bath, addressing the general issue of thermodynamic modeling of nanoscale systems. In contrast to bulk systems in the canonical (NVT) ensemble where the partition function is solely determined by the Hamiltonian of the system and the temperature of the heat bath, our formulation demonstrates that accounting for the interactions with the heat bath is essential for describing the statistical mechanics of low-dimensional materials. To validate our theoretical findings, we develop a molecular dynamics (MD) algorithm for directly modeling the heat bath as a gas reservoir. We first validate our approach using a 1D harmonic oscillator, calculating its length distribution through explicit numerical integration and confirming these results with MD simulations. We then extend our method to investigate the out-of-plane fluctuations of a 2D graphene monolayer immersed in a gas at finite temperature and pressure. Comparisons with conventional NVT ensemble simulations controlled by a thermostat reveal that environmental interactions significantly influence the properties of the 2D material system.