Homogeneous ice nucleation rates for mW and TIP4P/ICE models through Lattice Mold calculations

Abstract

Freezing of water is the most common liquid-to-crystal phase transition on Earth; however, despite its critical implications on climate change and cryopreservation among other disciplines, its characterization through experimental and computational techniques remains elusive. In this work, we make use of computer simulations to measure the nucleation rate ( J) of water at normal pressure under different supercooling conditions, ranging from 215 to 240 K. We employ two different water models: mW, a coarse-grained potential for water, and TIP4P/ICE, an atomistic nonpolarizable water model that provides one of the most accurate representations of the different ice phases. To evaluate J, we apply the Lattice Mold technique, a computational method based on the use of molds to induce the nucleus formation from the metastable liquid under conditions at which observing spontaneous nucleation would be unfeasible. With this method, we obtain estimates of the nucleation rate for ice Ih and Ic and a stacking mixture of ice Ih/Ic, reaching consensus with most of the previously reported rates, although differing with some others. Furthermore, we confirm that the predicted nucleation rates obtained by the TIP4P/ICE model are in better agreement with experimental data than those obtained through the mW potential. Taken together, our study provides a reliable methodology to measure nucleation rates in a simple and computationally efficient manner that contributes to benchmarking the freezing behavior of two popular water models.

The limit of macroscopic homogeneous ice nucleation at the nanoscale

“…For each W, the range of critical cluster sizes (indicated in parentheses) is obtained by splitting its data set into three. The range for J(W) is calculated using the largest and smallest values for n ‡ cl for a given W in eqn (6) (Dm/k B = 122 K and r = 33.3774 nm −3 ), and is also reported in parentheses from a simulation of bulk water under periodic boundary conditions-agrees well with that previously reported by Sanchez-Burgos et al 63 at T = 220 K and p = 1 bar. The biggest drawbacks of the seeding method are that it presupposes the nucleation mechanism and relies upon CNT to compute J.…”

“…3d we present J ( W ) for the different film thicknesses investigated (see also Table 1). As a check of our implementation, our result for J (∞)—obtained from a simulation of bulk water under periodic boundary conditions—agrees well with that previously reported by Sanchez-Burgos et al 63 at T = 220 K and p = 1 bar. The biggest drawbacks of the seeding method are that it presupposes the nucleation mechanism and relies upon CNT to compute J .…”

“…Taking the volume of an mW water molecule in the liquid phase as 1/ r z 3 × 10 −29 m 3 we nd that 6000 water molecules occupy 1.8 × 10 −25 m 3 . Dividing our calculated freezing rates by this volume we obtain values of J entirely consistent with previous literature values 29,35,63,74 for mW (see ESI †). However, obtaining J in this fashion is made possible as we know the exact number of water molecules used in our simulations.…”

Mold: a LAMMPS package to compute interfacial free energies and nucleation rates

“…In the bottom part of Figure 1 we depict a schematic picture of the Lattice Mold technique, showing the different simulation steps to compute the nucleation rate of the system (see Sanchez-Burgos et al (2022) for further details). The nucleation free energy to form a sub-critical cluster is calculated from the well-occupancy vs well depth curve for each well radius.…”

“…To date, the Mold Integration method has been widely used to calculate solid-liquid interfacial free energy of hard spheres (Espinosa et al, 2014), pseudo-hard spheres (Sanchez-Burgos, Sanz, et al, 2021), Lennard-Jones (Espinosa et al, 2014), SPC/E water with JC NaCl (Sanchez-Burgos & Espinosa, 2023), NaCl (Tosi-Fumi) (Espinosa et al, 2015), ice-water interfaces for TIP4P, TPI4P/2005 TIP4P/Ice and mW models , and CO 2 hydrate water interfacial energy (Algaba et al, 2022;Romero-Guzmán et al, 2023;Zerón et al, 2022). The Lattice Mold method has been used to calculate the nucleation rate of pseudo-hard spheres and NaCl from its melt (Espinosa, Sampedro, et al, 2016), and mW and TIP4P/Ice water models (Sanchez-Burgos et al, 2022). All these simulations have been carried out with GROMACS v4.6.7 (Abraham et al, 2015) and using a tabulated potential for the square-like attractive interaction between the wells and the fluid particles.…”