Classical nucleation theory of ice nucleation: second-order correction of thermodynamic parameters

TL;DR

This paper enhances classical nucleation theory for ice by deriving second-order analytical formulas for key thermodynamic parameters using molecular dynamics simulations, reducing uncertainties in nucleation rate estimates.

Contribution

It introduces second-order corrections to the Gibbs-Thomson equation and provides analytical formulas for thermodynamic parameters in ice nucleation, improving accuracy.

Findings

Second-order formulas accurately describe temperature dependence of parameters.

Enhanced estimates of chemical potential difference and interfacial free energy.

Reduced uncertainty in ice nucleation rate calculations.

Abstract

Accurate estimate of nucleation rate is crucial for the study of ice nucleation and ice-promoting/anti-freeze strategies. Within the framework of Classical Nucleation Theory (CNT), the estimate of ice nucleation rate is very sensitive to thermodynamic parameters, such as chemical potential difference between water and ice $\Delta \mu$ and ice-water interfacial free energy $\gamma$. However, even today, there are still many contradictions and approximations in the estimating of these thermodynamic parameters, introducing large uncertainty to the estimate of the ice nucleation rate. Herein, starting from the basic concepts, for a general solid-liquid crystallization system, we expand the Gibbs-Thomson (GT) equation to second order, and derive the second-order analytical formulas of $\Delta \mu$, $\gamma$ and nucleation barrier $\Delta G$ with combining molecular dynamics (MD) simulations. These formulas describe well the temperature dependence of these thermodynamic parameters. Our results can provide a method of estimating $\Delta \mu$, $\gamma$ and $\Delta G$.