Fokker-Planck Equations for Nucleation Processes Revisited

TL;DR

This paper introduces a thermodynamics-based approach to derive Fokker-Planck equations for nucleation, providing a unified framework that recovers existing models and offers new equations for crystallization processes.

Contribution

It develops a novel non-equilibrium thermodynamics method to derive Fokker-Planck equations for nucleation, including a new kinetic equation for the crystallization order parameter.

Findings

Derived a new kinetic equation for a global crystallization order parameter

Recovered existing Fokker-Planck equations for nucleation

Proved the scheme's consistency in quasi-stationary conditions

Abstract

We present a new approach to analyze homogeneous nucleation based on non-equilibrium thermodynamics. The starting point is the formulation of a Gibbs equation for the variations of the entropy of the system, whose state is characterized by an internal coordinate or degree of freedom. By applying the method of non-equilibrium thermodynamics we then obtain the entropy production corresponding to a diffusion process in the internal space. The linear laws together with the continuity equation lead to a kinetic equation of the Fokker-Planck type. By choosing properly the degree of freedom we are able to obtain a new kinetic equation for a global crystallization order parameter (used in recent simulations), and also we recover some of the existing equations. The consistency of the scheme we propose is proved in the quasi-stationary case. Finally, we also outline the way in which our formalism could be extended to more general situations.