On the time required to freeze water

Abstract

By using the seeding technique the nucleation rate for the formation of ice at room pressure will be estimated for the TIP4P/ICE model using longer runs and a smaller grid of temperatures than in the previous work. The growth rate of ice will be determined for TIP4P/ICE and for the mW model of water. Although TIP4P/ICE and mW have a similar melting point and melting enthalpy, they differ significantly in the dynamics of freezing. The nucleation rate of mW is lower than that of TIP4P/ICE due to its higher interfacial free energy. Experimental results for the nucleation rate of ice are between the predictions of these two models when obtained from the seeding technique, although closer to the predictions of TIP4P/ICE. The growth rate of ice for the mW model is four orders of magnitude larger than for TIP4P/ICE. Avrami's expression is used to estimate the crystallization time from the values of the nucleation and growth rates. For mW the minimum in the crystallization time is found at approximately 85 K below the melting point and its value is of about a few ns, in agreement with the results obtained from brute force simulations by Moore and Molinero. For the TIP4P/ICE the minimum is found at about 55 K below the melting point, but its value is about ten microseconds. This value is compatible with the minimum cooling rate required to avoid the formation of ice and obtaining a glass phase. The crossover from the nucleation controlled crystallization to the growth controlled crystallization will be discussed for systems of finite size. This crossover could explain the apparent discrepancy between the values of J obtained by different experimental groups for temperatures below 230 K and should be considered as an alternative hypothesis to the two previously suggested: internal pressure and/or surface freezing effects. A maximum in the compressibility was found for the TIP4P/ICE model in supercooled water. The relaxation time is much smaller than the crystallization time at the temperature at which this maximum occurs, so this maximum is a real thermodynamic feature of the model. At the temperature of minimum crystallization time, the crystallization time is larger than the relaxation time by just two orders of magnitude.

Theoretical prediction of the homogeneous ice nucleation rate: disentangling thermodynamics and kinetics

“…For example, with the Φ-based Gibbs dividing surface we estimated n ≈ 550 molecules, and in Ref. 41 the estimate is 688 molecules, which implies that the estimated rate would differ by about 8 orders of magnitude using the original CNT expression. It is worth pointing out that our framework eliminates this ambiguity in the determination of the critical nucleus and the nucleation rate, making the classical nucleation theory much more rigorous.…”

“…can be obtained numerically from the nucleation free energy profile G(n s (Φ)) in Figure 3. The addition rate f + can be computed as a diffusion coefficient from the mean square displacement of the cluster size after it is released at the top of the nucleation barrier [40,41]. However, this approach assumes that dG(n s )/dn s is effectively zero when running multiple trajectories, is influenced by the choice of the initial configuration, and by the latent heat created when the solid nucleus changes size [42].…”

Navigating at Will on the Water Phase Diagram

“…The kinetic barriers are however generally too large to allow an efficient exploration of the configuration space within typical MD timescales. Hence, so far it has been necessary to introduce (i) simplistic interaction models [14] and/or (ii) seeding techniques [15]. Another approach consists in using enhanced sampling techniques that accelerate the occurrence of rare events by focusing on low-dimensional order parameters, also called collective variables (CV) [16].…”

Crystalline clusters in mW water: Stability, growth, and grain boundaries

“…For unbiased simulations, we use the seeding technique [81][82][83][84], which consists in the insertion of perfect crystalline nuclei in the melt in order to determine at which conditions the nucleus is critical, and then use Classical Nucleation Theory to estimate parameters like the surface tension and the crystallization rate. While being successful in the estimation of the crystallization rate of water at moderate supercooling, with critical nuclei composed of several thousand molecules and where the approximations of Classical Nucleation Theory are most likely to hold, potential problems with the extension of this technique to deeply supercooled conditions have been recently highlighted [85].…”