Systematic Coarse-Graining in Nucleation Theory

TL;DR

This paper introduces an extended state space approach to nucleation theory that incorporates internal energy and momentum, resolving discrepancies between atomistic simulations and traditional models, and enabling more accurate predictions.

Contribution

The authors develop a nonequilibrium statistical mechanics framework for nucleation in an extended state space, improving agreement with molecular dynamics simulations and allowing richer order parameters.

Findings

Extended model explains discrepancies in nucleation rate predictions.

Nucleus temperature naturally emerges and obeys fluctuation law.

Framework allows extension to more complex order parameters.

Abstract

In this work we show that the standard method to obtain nucleation rate-predictions with the aid of atomistic Monte-Carlo simulations leads to nucleation rate predictions that deviate $3-5$ orders of magnitude from the recent brute-force molecular dynamics simulations [J. Diemand, R. Ang\'{e}lil, K. K. Tanaka, and H. Tanaka, J. Chem. Phys. \textbf{139}, 074309 (2013)] conducted in the experimental accessible supersaturation regime for Lennard-Jones argon. We argue that this is due to the truncated state space literature mostly relies on, where the number of atoms in a nucleus is considered the only relevant order parameter. We here formulate the nonequilibrium statistical mechanics of nucleation in an extended state space, where the internal energy and momentum of the nuclei is additionally incorporated. We show that the extended model explains the lack in agreement between the molecular dynamics simulations by Diemand et al.\ and the truncated state space. We demonstrate additional benefits of using the extended state space; in particular, the definition of a nucleus temperature arrises very naturally and can be shown without further approximation to obey the fluctuation law of McGraw and Laviolette. In addition, we illustrate that our theory conveniently allows to extend existing theories to richer sets of order parameters.