Classical Nucleation Theory Of Ice Nucleation

Water freezing is a very common crystallization phenomenon in the natural world.It always affects the climate,human life and production activities.In order to find icepromoting and anti-freeze strategies to control the icing and use it for human life and production,it is crucial to understand the mechanism of freezing and control the freezing rate.The most widely used theory to describe the freezing of water is the classical nucleation theory.The concept of nucleation rate in this theory is a essential parameter that can quantitatively describe how fast water freezes.Moreover,the nucleation rate is very sensitive to thermodynamic parameters,such as the chemical potential difference between water and ice,and the water-ice interfacial free energy.However,even today,there are still many contradictions and approximations when estimating these thermodynamic parameters,introducing a large uncertainty in estimate of the ice nucleation rate.Therefore,in this work,starting from basic concepts for a general solid-liquid crystallization system,we expanded the Gibbs-Thomson equation to second order.Then,we derived the analytical formula of the second-order chemical potential difference between water and ice.Combined with molecular dynamics simulation,the second-order analytical formula of the water-ice interfacial free energy was derived.These second-order expressions describe the relationship between these thermodynamic parameters and the supercooling well.Finally,combined with the classical nucleation theory,we got the second-order nucleation barrier expression.Compared with the previous first-order nucleation barrier expression,it can estimate the nucleation barrier more accurately.Our results provide a new method for estimating these thermodynamic parameters,and also provide theoretical guidance for other solid-liquid crystallization systems research.