Thermodynamics of Ice Nucleation in Liquid Water

Abstract

We present a density functional theory approach to investigate the thermodynamics of ice nucleation in supercooled water. Within the theoretical framework, the free-energy functional is constructed by the direct correlation function of oxygen-oxygen of the equilibrium water, and the function is derived from the reference interaction site model in consideration of the interactions of hydrogen-hydrogen, hydrogen-oxygen, and oxygen-oxygen. The equilibrium properties, including vapor-liquid and liquid-solid phase equilibria, local structure of hexagonal ice crystal, and interfacial structure and tension of water-ice are calculated in advance to examine the basis for the theory. The predicted phase equilibria and the water-ice surface tension are in good agreement with the experimental data. In particular, the critical nucleus radius and free-energy barrier during ice nucleation are predicted. The critical radius is similar to the simulation value, suggesting that the current theoretical approach is suitable in describing the thermodynamic properties of ice crystallization.

The barrier to ice nucleation in monatomic water

“…This is consistent with the present findings for the cut-and-shifted LJ model, though only not too far from coexistence. Subsequent studies of LJ nucleation [40,70] have indicated that precritical clusters are rich in randomly stacked hexagonal planes, hence in hcp-like particles. Again, the same is found in the present investigation of the cut-and-shifted LJ model, where in the deep metastable region there is a large amount of hcp-like particles in the nuclei.…”

“…Indeed, a lot of work has been done already, on a variety of classical water models: ST2 [27], TIP4P (in its various declinations) [28][29][30][31][32][33], and monatomic water (mW) [28,31,[34][35][36][37][38][39]. Also the methods employed to investigate ice nucleation have been the most varied: umbrella sampling [27,31,36], seeding approach [28,30,37], mean first passage time [34], metadynamics [32], density-functional theory [40], forward-flux sampling [29,33,38], and aimless shooting [39]. While all studies agree on the main picture (i.e., that the nucleation cluster is polymorphic rather than structurally homogeneous), divergence persists on the critical size, nucleation rate, interface free energy, and importance of the various ice polymorphs in the first stages of crystallization.…”

Icephobic materials: Fundamentals, performance evaluation, and applications

“…Under the thermodynamic driving force, ice nucleation will occur once a sufficient number of relatively long-lived hydrogen bonds spontaneously develop at the same location to form a compact nucleus. Subsequently, the nucleus alters the shape and size until reaching a stage that allows the rapid expansion, and finally causes crystallization of the entire system [152,153,155]. As shown by the molecular dynamics simulation in Fig.…”

Crystal nucleation as the ordering of multiple order parameters

“…There are also many interests on how ice polymorphs are selected upon ice nucleation [227,228,[230][231][232]. Besides this problem of polymorph selection, the estimation of the barrier height and critical nucleus size is also an important issue and recently there have been many efforts toward this direction [229,[232][233][234][235][236][237]. A link between the so-called Widom line [238], or the thermodynamic anomalies associated with the liquidliquid transition, and the ice nucleation process was also suggested [239].…”