Unification of classical nucleation theories via unified It\^o-Stratonovich stochastic equation

TL;DR

This paper unifies classical nucleation theories by deriving a stochastic differential equation framework that encompasses different kinetic equations, providing a consistent approach and new expressions for induction time under various mass-transport mechanisms.

Contribution

It introduces a unified stochastic differential equation framework that recovers various classical nucleation theory expressions and aligns with recent updates, offering new formulas for induction time.

Findings

Unified CNT derived from a stochastic differential equation.

Recovered existing CNT expressions as special cases.

Provided new induction-time formulas for different mass-transport mechanisms.

Abstract

Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g. Zeldovich-Frenkel or Becker-D\"oring-Tunitskii equations. Starting from a phenomenological stochastic differential equation a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that from a recent update of CNT [J.F. Lutsko and M.A. Dur\'an-Olivencia, J. Chem. Phys., 2013, 138, 244908] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios. In particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion or interface transfer.