Transient Nucleation near the Mean-Field Spinodal

TL;DR

This paper investigates transient nucleation near the pseudospinodal in a one-dimensional $$ model, deriving time-dependent droplet profiles and nucleation rates, and comparing theoretical predictions with simulations.

Contribution

It introduces the concept of transient nucleation near the spinodal and provides a theoretical framework for analyzing time-dependent nucleation processes.

Findings

Transient critical droplets are more compact than equilibrium droplets.

Nucleation times show a nonstationary distribution with a peak.

Theoretical results align with computer simulations.

Abstract

Nucleation is considered near the pseudospinodal in a one-dimensional $\phi^4$ model with a non-conserved order parameter and long-range interactions. For a sufficiently large system or a system with slow relaxation to metastable equilibrium, there is a non-negligible probability of nucleation occurring before reaching metastable equilibrium. This process is referred to as transient nucleation. The critical droplet is defined to be the configuration of maximum likelihood that is dynamically balanced between the metastable and stable wells. Time-dependent droplet profiles and nucleation rates are derived, and theoretical results are compared to computer simulation. The analysis reveals a distribution of nucleation times with a distinct peak characteristic of a nonstationary nucleation rate. Under the quench conditions employed, transient critical droplets are more compact than the droplets found in metastable equilibrium simulations and theoretical predictions.