Classical nucleation theory of ice nucleation: Second-order corrections to thermodynamic parameters

Abstract

Accurately estimating the nucleation rate is crucial in studying ice nucleation and ice-promoting and anti-freeze strategies. In classical nucleation theory, estimates of the ice nucleation rate are very sensitive to thermodynamic parameters, such as the chemical potential difference between water and ice Δμ and the ice-water interfacial free energy γ. However, even today, there are still many contradictions and approximations when estimating these thermodynamic parameters, introducing a large uncertainty in any estimate of the ice nucleation rate. Starting from basic concepts for a general solid-liquid crystallization system, we expand the Gibbs-Thomson equation to second order and derive second-order analytical formulas for Δμ, γ, and the nucleation barrier ΔG*, which are used in molecular dynamics simulations. These formulas describe well the temperature dependence of these thermodynamic parameters. This may be a new method of estimating Δμ, γ, and ΔG*.