Reconsidering the structure of nucleation theories

TL;DR

This paper derives an exact non-equilibrium equation for nucleation size distribution from microscopic dynamics, compares memory effects to Markovian assumptions, and confirms non-Markovian behavior through simulations of Lennard-Jones crystal nucleation.

Contribution

It provides a novel, exact derivation of the nucleation equation of motion from microscopic dynamics, highlighting non-Markovian effects.

Findings

Memory effects influence nucleation dynamics.

Simulation confirms non-Markovian behavior.

Equation of motion derived without approximations.

Abstract

We discuss the structure of the equation of motion that governs nucleation processes at first order phase transitions. From the underlying microscopic dynamics of a nucleating system, we derive by means of a non-equilibrium projection operator formalism the equation of motion for the size distribution of the nuclei. The equation is exact, i.e. the derivation does not contain approximations. To assess the impact of memory, we express the equation of motion in a form that allows for direct comparison to the Markovian limit. As a numerical test, we have simulated crystal nucleation from a supersaturated melt of particles interacting via a Lennard-Jones potential. The simulation data show effects of non-Markovian dynamics.