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

Abstract

Estimating the homogeneous ice nucleation rate from undercooled liquid water is at the same time crucial for understanding many important physical phenomena and technological applications, and challenging for both experiments and theory. From a theoretical point of view, difficulties arise due to the long time scales required, as well as the numerous nucleation pathways involved to form ice nuclei with different stacking disorders. We computed the homogeneous ice nucleation rate at a physically relevant undercooling for a single-site water model, taking into account the diffuse nature of ice-water interfaces, stacking disorders in ice nuclei, and the addition rate of particles to the critical nucleus. We disentangled and investigated the relative importance of all the terms, including interfacial free energy, entropic contributions and the kinetic prefactor, that contribute to the overall nucleation rate. There has been a long-standing discrepancy for the predicted homogeneous ice nucleation rates, and our estimate is faster by 9 orders of magnitude compared with previous literature values. Breaking down the problem into segments and considering each term carefully can help us understand where the discrepancy may come from and how to systematically improve the existing computational methods.

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

“…Ignoring the bulk free energy difference makes our value an upper bound to the true surface penalty, so overall our estimate is in agreement with the results of Ref. [94].…”

“…No free energy difference was indeed found in similar studies [20,95]. The difference in nucleation barriers between an hexagonal and cubic nucleus at T = 240 K was also found to be negligibly small, 2 ± 2 J mol −1 [94], which is equivalent to a difference of about 1 k B T . Figure 5 shows the result for our calculations of the nucleation barriers at T = 218 K with the Umbrella Sampling method detailed in the Methods section.…”

“…Nucleation of the stable Ice I phase in the mW model has been extensively addressed in previous studies [40,44,50,52,83,[92][93][94]. The free energy difference between the two polytypes, cubic and hexagonal ice, was found to be very small, ∆G ch = 2 ± 1.5 J mol −1 at T = 200 K [40].…”

Ab initio thermodynamics of liquid and solid water

“…At the quantummechanical level ∆µ Ih→Ic is close to zero at 200-250 K and increases to 0.2 ± 0.2 meV/H 2 O at 300 K, suggesting ice Ih is more stable after all. For comparison, at the classical level, the monoatomic water model [52] which omits hydrogen atoms -predicts a negligible difference (∆µ Ih→Ic (240 K) = 0.032 ± 0.002 meV [53]), while the MB-pol forcefield [54], which includes many-body terms fitted to the coupled-clusters level of theory, predicts a small negative value (−0.4 meV/H 2 O) (see SI Appendix for further detail). Assuming that the heat of transition from ice Ic to ice Ih is approximately constant over the temperature range 200-300 K, the temperature dependence of ∆µ Ih→Ic implies (using a TI with respect to T analogous to (2)) a transition enthalpy of H Ic − H Ih = 1.0 ± 0.5 meV/H 2 O, consistent with the wide experimental range 0.1 − 1.7 meV/H 2 O [55].…”

Non-classical nucleation pathways in stacking-disordered crystals

“…They crystallize in two different polytypes: either fcc or hcp for HS, and either cubic ice (I c ) or hexagonal ice (I h ) for water. Importantly, in both cases the difference in all thermodynamic relevant quantities (such as free-energy difference, nucleation barrier, and solid/melt surface tension) between the competing polytypes are negligibly small (within 10 −3 k B T per particle for all cases) [1,5,[17][18][19][20][21]. For example, in the mW water model [16] the stacking fault between the ice I c and I h has been estimated as low as 0.16 ± 0.05 mJ m −2 at T = 218 K [4].…”