Temperature Dependence of Homogeneous Nucleation in Ice

Ice nucleation is a process of great relevance in physics, chemistry, technology, and environmental sciences; much theoretical effort has been devoted to its understanding, but it still remains a topic of intense research. We shed light on this phenomenon by performing atomistic based simulations. Using metadynamics and a carefully designed set of collective variables, reversible transitions between water and ice are able to be simulated. We find that water freezes into a stacking disordered structure with the all-atom transferable intermolecular potential with 4 points/ice (TIP4P/ice) model, and the features of the critical nucleus of nucleation at the microscopic level are revealed. We have also estimated the ice nucleation rates along with other nucleation parameters at different undercoolings. Our results are in agreement with recent experimental and other theoretical works, and they confirm that nucleation is preceded by a large increase in tetrahedrally coordinated water molecules.

Figure 1

Free energy surface in terms of collective variables $s_X$ and $s_S$ with TIP4P/ice model. (a) Free energy surface at 230 K for a system of 1600 water molecules. (b) Probability distribution of the cubicity of the nucleated ice structure obtained from simulations.

Figure 2

Features of critical nucleus of ice nucleation. (a) Reweighted free energy at 230 K as a function of ice cluster size $n^{1/3}$ for a system with $N=896$, 1600, and 2880 water molecules. (b)–(c) Typical critical ice nucleus and idealized crystalline model of it. Here, $h$ and $c$ refer to the hexagonal and cubic sequences of $I_{\mathrm{sd}}$. (d) Possible crystal shape of $I_{\mathrm{sd}}$ with a threefold rotational symmetry.

Figure 3

Temperature dependence of ice nucleation behavior. (a) Reweighted free energy as a function of ice cluster size $n^{1/3}$ for a range of temperatures from 215 to 240 K. (b) Ice nucleation rate ${\log }_{10}J$ as a function of the supercooling temperature $\mathrm{\Delta }T$ (difference between the melting temperature and the temperature of interest) obtained in this work and comparison with experimental [48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60] and other theoretical results [19, 47]. Theoretical results denoted as FFS and seeding were estimated with forward-flux sampling [19] and a seeding technique [47], respectively.

Figure 4

Homogeneous ice nucleation process. Configuration snapshots at different stages of nucleation of (a) tetrahedral-like atoms and (b)–(c) solidlike atoms. (d) Relationship between the numbers of solidlike atoms $\mathrm{\Delta }{N}_{\mathrm{ice}}$ and tetrahedral-like atoms $\mathrm{\Delta }{N}_{\text{tetra}}$. Here, $\mathrm{\Delta }{N}_{\text{tetra}}$ is the difference between the tetrahedral-like atoms number of the current state and the tetrahedral-like atoms number of the liquid state.The dashed line is drawn only to guide the eyes.