On the time required to freeze water

The limit of macroscopic homogeneous ice nucleation at the nanoscale

Nucleation in small volumes of water has garnered renewed interest due to the relevance of pore condensation and freezing under conditions of low partial pressures of water, such as in the upper troposphere. Molecular simulations can in principle provide insight on this process at the molecular scale that is challenging to achieve experimentally. However, there are discrepancies in the literature as to whether the rate in confined systems is enhanced or suppressed relative to bulk water at the same temperature and pressure. In this study, we investigate the extent to which the size of the critical nucleus and the rate at which it grows in thin films of water are affected by the thickness of the film. Our results suggest that nucleation remains bulk-like in films that are barely large enough accommodate a critical nucleus. This conclusion seems robust to the presence of physical confining boundaries. We also discuss the difficulties in unambiguously determining homogeneous nucleation rates in nanoscale systems, owing to the challenges in defining the volume. Our results suggest any impact on a film's thickness on the rate is largely inconsequential for present day experiments.

Molecular simulation of the confined crystallization of ice in cement nanopore

Freezing of water under nanoconfinement exhibits physical peculiarities with respect to the bulk water. However, experimental observations are extremely challenging at this scale, which limits our understanding of the effect of confinement on water properties upon freezing. In this study, we use molecular dynamic simulations to investigate how confinement affects the kinetics of growth of ice and the thermodynamic equilibrium of ice-liquid coexistence. TIP4P/Ice water model and CSH-FF model were applied to simulate ice crystallization in a confined cement system at temperatures down to 220 K. We adapted an interface detection algorithm and reparameterized the CHILL/CHILL+ algorithm to capture ice growth. The confinement leads to a shift of the maximum growth rate of ice to a higher temperature than for bulk water. Both the confinement and surface impurities contribute to slowing down the ice growth. For the ice-liquid coexistence at equilibrium, we derive a formulation of Thomson's equation adapted to statistical physics quantities accessible by molecular simulation, and we show that this adapted equation predicts accurately the melting line of bulk and confined ice Ih as a function of pressure. The confinement decreases systematically the melting temperature of ice of about 5 K compared with bulk ice Ih. A premelted water film about 1 nm thick is observed between the solid wall and ice, and its thickness is found to decrease continuously as temperature is lowered. We note that the surface impurities are key to the formation of the premelted water nanofilm when the temperature is lower than 250 K.

Charged Ice Particle Beams with Selected Narrow Mass and Kinetic Energy Distributions

Small ice particles play an important role in atmospheric and extraterrestrial chemistry. Circumplanetary ice particles that are encountered by space probes at hypervelocities play a critical role in the determination of surface and subsurface properties of their source bodies. Here we present an apparatus for the generation of low-intensity beams of single mass-selected charged ice particles under vacuum. They are produced via electrospray ionization of water at atmospheric pressure and undergo evaporative cooling when transferred to vacuum through an atmospheric vacuum interface. m/z selection is achieved through two subsequent quadrupole mass filters operated in the variable-frequency mode within a range of m/z values between 8 × 10⁴ and 3 × 10⁷. Velocity and charge of the selected particles are measured using a nondestructive single-pass image charge detector. From the known electrostatic acceleration potentials and settings of the quadrupoles the particle masses could be obtained and be accurately controlled. It has been shown that the droplets are frozen within the transit time of the apparatus such that ice particles are present after the quadrupole stages and finally detected. The demonstrated correspondence between particle mass and specific quadrupole potentials in this device allows preparation of beams of single particles with a repetition rate between 0.1 and 1 Hz with various diameter distributions from 50 to 1000 nm at 30-250 eV of kinetic energy per charge. This corresponds to velocities and particle masses quickly available between 600 m/s (80 nm) and 50 m/s (900 nm) and particle charge numbers (positive) between 10³ and 10⁴[e], depending upon size.

Minimum in the pressure dependence of the interfacial free energy between ice Ih and water

Despite the importance of ice nucleation, this process has been barely explored at negative pressures. Here, we study homogeneous ice nucleation in stretched water by means of molecular dynamics seeding simulations using the TIP4P/Ice model. We observe that the critical nucleus size, interfacial free energy, free energy barrier, and nucleation rate barely change between isobars from -2600 to 500 bars when they are represented as a function of supercooling. This allows us to identify universal empirical expressions for homogeneous ice nucleation in the pressure range from -2600 to 500 bars. We show that this universal behavior arises from the pressure dependence of the interfacial free energy, which we compute by means of the mold integration technique, finding a shallow minimum around -2000 bars. Likewise, we show that the change in the interfacial free energy with pressure is proportional to the excess entropy and the slope of the melting line, exhibiting in the latter a reentrant behavior also at the same negative pressure. Finally, we estimate the excess internal energy and the excess entropy of the ice Ih-water interface.

Homogeneous nucleation rate of methane hydrate formation under experimental conditions from seeding simulations

In this work, we shall estimate via computer simulations the homogeneous nucleation rate for the methane hydrate at 400 bars for a supercooling of about 35 K. The TIP4P/ICE model and a Lennard-Jones center were used for water and methane, respectively. To estimate the nucleation rate, the seeding technique was employed. Clusters of the methane hydrate of different sizes were inserted into the aqueous phase of a two-phase gas-liquid equilibrium system at 260 K and 400 bars. Using these systems, we determined the size at which the cluster of the hydrate is critical (i.e., it has 50% probability of either growing or melting). Since nucleation rates estimated from the seeding technique are sensitive to the choice of the order parameter used to determine the size of the cluster of the solid, we considered several possibilities. We performed brute force simulations of an aqueous solution of methane in water in which the concentration of methane was several times higher than the equilibrium concentration (i.e., the solution was supersaturated). From brute force runs, we infer the value of the nucleation rate for this system rigorously. Subsequently, seeding runs were carried out for this system, and it was found that only two of the considered order parameters were able to reproduce the value of the nucleation rate obtained from brute force simulations. By using these two order parameters, we estimated the nucleation rate under experimental conditions (400 bars and 260 K) to be of the order of log₁₀ (J/(m³ s)) = -7(5).

Refractive Index of Supercooled Water Down to 230.3 K in the Wavelength Range between 534 and 675 nm

Knowledge of the refractive index of water in the deeply supercooled metastable liquid state is important, for example, for an accurate description of optical reflection and refraction processes occurring in clouds. However, a measurement of both the temperature and wavelength dependence of the refractive index under such extreme conditions is challenging. Here, we employ Raman spectroscopy in combination with microscopic water jets in vacuum to obtain the refractive index of supercooled water to a lowest temperature of 230.3 K. While our approach is based on the analysis of Mie resonances in Raman spectra measured by using a single excitation wavelength at 532 nm, it allows us to obtain the refractive index in a wide visible wavelength range from 534 to 675 nm. Because of a direct link between the refractive index and density of water, our results provide a promising approach to help improve our understanding of water's anomalous behavior.

Revealing the Mechanism of Irreversible Binding of Antifreeze Glycoproteins to Ice

Antifreeze glycoproteins (AFGPs) are a special kind of antifreeze proteins with strong flexibility. Whether their antifreeze activity is achieved by reversibly or irreversibly binding to ice is widely debated, and the molecular mechanism of irreversible binding remains unclear. In this work, the antifreeze mechanism of the smallest AFGP isoform, AFGP8, is investigated at the atomic level. The results indicate that AFGP8 can bind to ice both reversibly through its hydrophobic methyl groups (peptide binding) and irreversibly through its hydrophilic disaccharide moieties (saccharide binding). Although peptide binding occurs faster than saccharide binding, free-energy calculations indicate that the latter is energetically more favorable. In saccharide binding, at least one disaccharide moiety is frozen in the grown ice, resulting in irreversible binding, while the other moieties significantly perturb the water hydrogen-bonding network, thus inhibiting ice growth more effectively. The present study reveals the coexistence of reversible and irreversible bindings of AFGP8, both contributing to the inhibition of ice growth and further provides molecular mechanism of irreversible binding.

Solubility of Methane in Water: Some Useful Results for Hydrate Nucleation

In this paper, the solubility of methane in water along the 400 bar isobar is determined by computer simulations using the TIP4P/Ice force field for water and a simple LJ model for methane. In particular, the solubility of methane in water when in contact with the gas phase and the solubility of methane in water when in contact with the hydrate has been determined. The solubility of methane in a gas-liquid system decreases as temperature increases. The solubility of methane in a hydrate-liquid system increases with temperature. The two curves intersect at a certain temperature that determines the triple point T₃ at a certain pressure. We also determined T₃ by the three-phase direct coexistence method. The results of both methods agree, and we suggest 295(2) K as the value of T₃ for this system. We also analyzed the impact of curvature on the solubility of methane in water. We found that the presence of curvature increases the solubility in both the gas-liquid and hydrate-liquid systems. The change in chemical potential for the formation of hydrate is evaluated along the isobar using two different thermodynamic routes, obtaining good agreement between them. It is shown that the driving force for hydrate nucleation under experimental conditions is higher than that for the formation of pure ice when compared at the same supercooling. We also show that supersaturation (i.e., concentrations above those of the planar interface) increases the driving force for nucleation dramatically. The effect of bubbles can be equivalent to that of an additional supercooling of about 20 K. Having highly supersaturated homogeneous solutions makes possible the spontaneous formation of the hydrate at temperatures as high as 285 K (i.e., 10K below T₃). The crucial role of the concentration of methane for hydrate formation is clearly revealed. Nucleation of the hydrate can be either impossible or easy and fast depending on the concentration of methane which seems to play the leading role in the understanding of the kinetics of hydrate formation.

Screening and collective effects in randomly pinned fluids: a new theoretical framework

We propose a theoretical framework for the dynamics of bulk isotropic hard-sphere systems in the presence of randomly pinned particles and apply this theory to supercooled water to validate it. Structural relaxation is mainly governed by local and non-local activated process. As the pinned fraction grows, a local caging constraint becomes stronger and the long range collective aspect of relaxation is screened by immobile obstacles. Different responses of the local and cooperative motions results in subtle predictions for how the alpha relaxation time varies with pinning and density. Our theoretical analysis for the relaxation time of water with pinned molecules quantitatively well describe previous simulations. In addition, the thermal dependence of relaxation for unpinned bulk water is also consistent with prior computational and experimental data.

Homogeneous ice nucleation in an ab initio machine-learning model of water

Molecular simulations have provided valuable insight into the microscopic mechanisms underlying homogeneous ice nucleation. While empirical models have been used extensively to study this phenomenon, simulations based on first-principles calculations have so far proven prohibitively expensive. Here, we circumvent this difficulty by using an efficient machine-learning model trained on density-functional theory energies and forces. We compute nucleation rates at atmospheric pressure, over a broad range of supercoolings, using the seeding technique and systems of up to hundreds of thousands of atoms simulated with ab initio accuracy. The key quantity provided by the seeding technique is the size of the critical cluster (i.e., a size such that the cluster has equal probabilities of growing or melting at the given supersaturation), which is used together with the equations of classical nucleation theory to compute nucleation rates. We find that nucleation rates for our model at moderate supercoolings are in good agreement with experimental measurements within the error of our calculation. We also study the impact of properties such as the thermodynamic driving force, interfacial free energy, and stacking disorder on the calculated rates.

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

Water freezing 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 240K. We employ two different water models, mW, a coarse-grained potential for water, and TIP4P/ICE, an atomistic non-polarizable 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, 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 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 which contributes to benchmarking the freezing behaviour of two popular water models.

Is It Possible to Follow the Structural Evolution of Water in "No-Man's Land" Using a Pulsed-Heating Procedure?

The anomalous increase in compressibility and heat capacity of supercooled water has been attributed to its structural transformation of into a four-coordinated liquid. Experiments revealed that κ_T and C_p peak at T_W^thermo ≈ 229 K [Kim et al. Science 2017, 358, 1589; Pathak et al. Proc. Natl. Acad. Sci. 2021, 118, e2018379118]. Recently, a pulsed heating procedure (PHP) was employed to interrogate the structure of water, reporting a steep increase in tetrahedrality around T_W^PHP = 210 ± 3 K [Kringle et al. Science 2020, 369, 1490]. This discrepancy questions whether water structure and thermodynamics are decoupled, or if the shift in T_W is an artifact of PHP. Here we implement PHP in molecular simulations. We find that the stationary states captured at the bottom of the pulse are not representative of the thermalized liquid or its inherent structure. Our analysis reveals a temperature-dependent distortion that shifts T_W^PHP to ∼20 K below T_W^thermo. We conclude that 2 orders of magnitude faster rates are required to sample water's inherent structure with PHP.

Impact of surface nanostructure and wettability on interfacial ice physics

Ice accumulation on solid surfaces is a severe problem for safety and functioning of a large variety of engineering systems, and its control is an enormous challenge that influences the safety and reliability of many technological applications. The use of molecular dynamics (MD) simulations is popular, but as ice nucleation is a rare event when compared to simulation timescales, the simulations need to be accelerated to force ice to form on a surface, which affects the accuracy and/or applicability of the results obtained. Here, we present an alternative seeded MD simulation approach, which reduces the computational cost while still ensuring accurate simulations of ice growth on surfaces. In addition, this approach enables, for the first time, brute-force all-atom water simulations of ice growth on surfaces unfavorable for nucleation within MD timescales. Using this approach, we investigate the effect of surface wettability and structure on ice growth in the crucial surface-ice interfacial region. Our main findings are that the surface structure can induce a flat or buckled overlayer to form within the liquid, and this transition is mediated by surface wettability. The first overlayer and the bulk ice compete to structure the intermediate water layers between them, the relative influence of which is traced using density heat maps and diffusivity measurements. This work provides new understanding on the role of the surface properties on the structure and dynamics of ice growth, and we also present a useful framework for future research on surface icing simulations.

Crystallisation and polymorph selection in active Brownian particles

We explore crystallisation and polymorph selection in active Brownian particles with numerical simulation. In agreement with previous work (Wysocki et al. in Europhys Lett 105:48004, 2014), we find that crystallisation is suppressed by activity and occurs at higher densities with increasing Péclet number ([Formula: see text]). While the nucleation rate decreases with increasing activity, the crystal growth rate increases due to the accelerated dynamics in the melt. As a result of this competition, we observe the transition from a nucleation and growth regime at high [Formula: see text] to "spinodal nucleation" at low [Formula: see text]. Unlike the case of passive hard spheres, where preference for FCC over HCP polymorphs is weak, activity causes the annealing of HCP stacking faults, thus strongly favouring the FCC symmetry at high [Formula: see text]. When freezing occurs more slowly, in the nucleation and growth regime, this tendency is much reduced and we see a trend towards the passive case of little preference for either polymorph.

The microscopic mechanism of bulk melting of ice

We study the initial stages of homogeneous melting of a hexagonal ice crystal at coexistence and at moderate superheating. Our trajectory-based computer simulation approach provides a comprehensive picture of the events that lead to melting, from the initial accumulation of 5+7 defects, via the formation of L-D and interstitial-vacancy pairs, to the formation of a liquid nucleus. Of the different types of defects that we observe to be involved in melting, a particular kind of 5+7 type defect (type 5) plays a prominent role as it often forms prior to the formation of the initial liquid nucleus and close to the site where the nucleus forms. Hence, like other solids, ice homogeneously melts via the prior accumulation of defects.

Crystallization kinetics of amorphous acetonitrile nanoscale films

We measure the isothermal crystallization kinetics of amorphous acetonitrile films using molecular beam dosing and reflection adsorption infrared spectroscopy techniques. Experiments on a graphene covered Pt(111) substrate revealed that the crystallization rate slows dramatically during long time periods and that the overall kinetics cannot be described by a simple application of the Avrami equation. The crystallization kinetics also have a thickness dependence with the thinner films crystallizing much slower than the thicker ones. Additional experiments showed that decane layers at both the substrate and vacuum interfaces can also affect the crystallization rates. A comparison of the crystallization rates for CH₃CN and CD₃CN films showed only an isotope effect of ∼1.09. When amorphous films were deposited on a crystalline film, the crystalline layer did not act as a template for the formation of a crystalline growth front. These overall results suggest that the crystallization kinetics are complicated, indicating the possibility of multiple nucleation and growth mechanisms.

Structural relaxation and crystallization in supercooled water from 170 to 260 K

The origin of water's anomalous properties has been debated for decades. Resolution of the problem is hindered by a lack of experimental data in a crucial region of temperatures, T, and pressures where supercooled water rapidly crystallizes-a region often referred to as "no man's land." A recently developed technique where water is heated and cooled at rates greater than 10⁹ K/s now enables experiments in this region. Here, it is used to investigate the structural relaxation and crystallization of deeply supercooled water for 170 K < T < 260 K. Water's relaxation toward a new equilibrium structure depends on its initial structure with hyperquenched glassy water (HQW) typically relaxing more quickly than low-density amorphous solid water (LDA). For HQW and T > 230 K, simple exponential relaxation kinetics is observed. For HQW at lower temperatures, increasingly nonexponential relaxation is observed, which is consistent with the dynamics expected on a rough potential energy landscape. For LDA, approximately exponential relaxation is observed for T > 230 K and T < 200 K, with nonexponential relaxation only at intermediate temperatures. At all temperatures, water's structure can be reproduced by a linear combination of two, local structural motifs, and we show that a simple model accounts for the complex kinetics within this context. The relaxation time, τ _rel , is always shorter than the crystallization time, τ _xtal For HQW, the ratio, τ _xtal /τ _rel , goes through a minimum at ∼198 K where the ratio is about 60.

Homogeneous Freezing of Water Using Microfluidics

The homogeneous freezing of water is important in the formation of ice in clouds, but there remains a great deal of variability in the representation of the homogeneous freezing of water in the literature. The development of new instrumentation, such as droplet microfluidic platforms, may help to constrain our understanding of the kinetics of homogeneous freezing via the analysis of monodisperse, size-selected water droplets in temporally and spatially controlled environments. Here, we evaluate droplet freezing data obtained using the Lab-on-a-Chip Nucleation by Immersed Particle Instrument (LOC-NIPI), in which droplets are generated and frozen in continuous flow. This high-throughput method was used to analyse over 16,000 water droplets (86 μm diameter) across three experimental runs, generating data with high precision and reproducibility that has largely been unrepresented in the microfluidic literature. Using this data, a new LOC-NIPI parameterisation of the volume nucleation rate coefficient (JV(T)) was determined in the temperature region of -35.1 to -36.9 °C, covering a greater JV(T) compared to most other microfluidic techniques thanks to the number of droplets analysed. Comparison to recent theory suggests inconsistencies in the theoretical representation, further implying that microfluidics could be used to inform on changes to parameterisations. By applying classical nucleation theory (CNT) to our JV(T) data, we have gone a step further than other microfluidic homogeneous freezing examples by calculating the stacking-disordered ice-supercooled water interfacial energy, estimated to be 22.5 ± 0.7 mJ m-2, again finding inconsistencies when compared to theoretical predictions. Further, we briefly review and compile all available microfluidic homogeneous freezing data in the literature, finding that the LOC-NIPI and other microfluidically generated data compare well with commonly used non-microfluidic datasets, but have generally been obtained with greater ease and with higher numbers of monodisperse droplets.

Anomalous Behavior in the Nucleation of Ice at Negative Pressures

Ice nucleation is a phenomenon that, despite the relevant implications for life, atmospheric sciences, and technological applications, is far from being completely understood, especially under extreme thermodynamic conditions. In this work we present a computational investigation of the homogeneous ice nucleation at negative pressures. By means of the seeding technique we estimate the size of the ice critical nucleus N_{c} for the TIP4P/Ice water model. This is done along the isotherms 230, 240, and 250 K, from positive to negative pressures until reaching the liquid-gas kinetic stability limit (where cavitation cannot be avoided). We find that N_{c} is nonmonotonic upon depressurization, reaching a minimum at negative pressures in the doubly metastable region of water. According to classical nucleation theory we establish the nucleation rate J and the surface tension γ, revealing a retracing behavior of both when the liquid-gas kinetic stability limit is approached. We also predict a reentrant behavior of the homogeneous nucleation line. The reentrance of these properties is related to the reentrance of the coexistence line at negative pressure, revealing new anomalies of water. The results of this work suggest the possibility of having metastable samples of liquid water for long times at negative pressure provided that heterogeneous nucleation is suppressed.

Antifreeze proteins and homogeneous nucleation: On the physical determinants impeding ice crystal growth

Antifreeze proteins (AFPs) are biopolymers capable of interfering with ice growth. Their antifreeze action is commonly understood considering that the AFPs, by pinning the ice surface, force the crystal-liquid interface to bend forming an ice meniscus, causing an increase in the surface free energy and resulting in a decrease in the freezing point ΔT^max. Here, we present an extensive computational study for a model protein adsorbed on a TIP4P/Ice crystal, computing ΔT^max as a function of the average distance d between AFPs, with simulations spanning over 1 µs. First, we show that the lower the d, the larger the ΔT^max. Then, we find that the water-ice-protein contact angle along the line ΔT^max(d) is always larger than 0°, and we provide a theoretical interpretation. We compute the curvature radius of the stable solid-liquid interface at a given supercooling ΔT ≤ ΔT^max, connecting it with the critical ice nucleus at ΔT. Finally, we discuss the antifreeze capability of AFPs in terms of the protein-water and protein-ice interactions. Our findings establish a unified description of the AFPs in the contest of homogeneous ice nucleation, elucidating key aspects of the antifreeze mechanisms and paving the way for the design of novel ice-controlling materials.

Seeding approach to nucleation in the NVT ensemble: The case of bubble cavitation in overstretched Lennard Jones fluids

Simulations are widely used to study nucleation in first order phase transitions due to the fact that they have access to the relevant length and time scales. However, simulations face the problem that nucleation is an activated process. Therefore, rare event simulation techniques are needed to promote the formation of the critical nucleus. The Seeding method, where the simulations are started with the nucleus already formed, has proven quite useful in efficiently providing estimates of the nucleation rate for a wide range of orders of magnitude. So far, Seeding has been employed in the NPT ensemble, where the nucleus either grows or redissolves. Thus, several trajectories have to be run in order to find the thermodynamic conditions that make the seeded nucleus critical. Moreover, the nucleus lifetime is short and the statistics for obtaining its properties is consequently poor. To deal with these shortcomings we extend the Seeding method to the NVT ensemble. We focus on the problem of bubble nucleation in a metastable Lennard Jones fluid. We show that, in the NVT ensemble, it is possible to equilibrate and stabilise critical bubbles for a long time. The nucleation rate inferred from NVT-Seeding is fully consistent with that coming from NPT-Seeding. The former is quite suitable to obtain the nucleation rate along isotherms, whereas the latter is preferable if the dependence of the rate with temperature at constant pressure is required. Care should be taken with finite size effects when using NVT-Seeding. Further work is required to extend NVT seeding to other sorts of phase transitions.

Interfacial free energy of a liquid-solid interface: Its change with curvature

We analyze the changes in the interfacial free energy between a spherical solid cluster and a fluid due to the change of the radius of the solid. Interfacial free energies from nucleation studies using the seeding technique for four different systems, being hard spheres, Lennard-Jones, and two models of water (mW and TIP4P/ICE), were plotted as a function of the inverse of the radius of the solid cluster. In all cases, the interfacial free energy was a linear function of the inverse of the radius of the solid cluster and this is consistent with Tolman's equation. This linear behavior is shown not only in isotherms but also along isobars. The effect of curvature on the interfacial free energy is more pronounced in water, followed by hard spheres, and smaller for Lennard-Jones particles. We show that it is possible to estimate nucleation rates of Lennard-Jones particles at different pressures by using information from simple NpT simulations and taking into account the variation of the interfacial free energy with the radius of the solid cluster. Neglecting the effects of the radius on the interfacial free energy (capillarity approximation) leads to incorrect values of the nucleation rate. For the Lennard-Jones system, the homogeneous nucleation curve is not parallel to the melting curve as was found for water in previous work. This is due to the increase in the interfacial free energy along the coexistence curve as the pressure increases. This work presents a simple and relatively straightforward way to approximately estimate nucleation rates.

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.

Characterizing key features in the formation of ice and gas hydrate systems

Crystallization in liquids is critical to a range of important processes occurring in physics, chemistry and life sciences. In this article, we review our efforts towards understanding the crystallization mechanisms, where we focus on theoretical modelling and molecular simulations applied to ice and gas hydrate systems. We discuss the order parameters used to characterize molecular ordering processes and how different order parameters offer different perspectives of the underlying mechanisms of crystallization. With extensive simulations of water and gas hydrate systems, we have revealed unexpected defective structures and demonstrated their important roles in crystallization processes. Nucleation of gas hydrates can in most cases be characterized to take place in a two-step mechanism where the nucleation occurs via intermediate metastable precursors, which gradually reorganizes to a stable crystalline phase. We have examined the potential energy landscapes explored by systems during nucleation, and have shown that these landscapes are rugged and funnel-shaped. These insights provide a new framework for understanding nucleation phenomena that has not been addressed in classical nucleation theory. This article is part of the theme issue 'The physics and chemistry of ice: scaffolding across scales, from the viability of life to the formation of planets'.

Ice formation and solvent nanoconfinement in protein crystals

Ice formation within protein crystals is a major obstacle to the cryocrystallographic study of protein structure, and has limited studies of how the structural ensemble of a protein evolves with temperature in the biophysically interesting range from ∼260 K to the protein-solvent glass transition near 200 K. Using protein crystals with solvent cavities as large as ∼70 Å, time-resolved X-ray diffraction was used to study the response of protein and internal solvent during rapid cooling. Solvent nanoconfinement suppresses freezing temperatures and ice-nucleation rates so that ice-free, low-mosaicity diffraction data can be reliably collected down to 200 K without the use of cryoprotectants. Hexagonal ice (Ih) forms in external solvent, but internal crystal solvent forms stacking-disordered ice (Isd) with a near-random stacking of cubic and hexagonal planes. Analysis of powder diffraction from internal ice and single-crystal diffraction from the host protein structure shows that the maximum crystallizable solvent fraction decreases with decreasing crystal solvent-cavity size, and that an ∼6 Å thick layer of solvent adjacent to the protein surface cannot crystallize. These results establish protein crystals as excellent model systems for the study of nanoconfined solvent. By combining fast cooling, intense X-ray beams and fast X-ray detectors, complete structural data sets for high-value targets, including membrane proteins and large complexes, may be collected at ∼220-240 K that have much lower mosaicities and comparable B factors, and that may allow more confident identification of ligand binding than in current cryocrystallographic practice.

Ice Ih vs. ice III along the homogeneous nucleation line

The melting and the homogeneous nucleation lines of the TIP4P/Ice water model closely resemble the experimental ones. Computer simulations show that a change in the nucleating ice polymorph from ice Ih to ice III justifies the slope sign inversion of the homogeneous nucleation line.

Nucleation of pseudo hard-spheres and dumbbells at moderate metastability: appearance of A15 Frank–Kasper phase at intermediate elongations

Crystal nucleation of repulsive hard-dumbbells from the sphere to the two tangent spheres limit is investigated at moderately high metastability by brute-force molecular dynamics simulations.

Bridging solution properties to gas hydrate nucleation through guest dynamics

By investigating the aqueous solution properties of several hydrate guests with molecular simulations, we find that with increasing guest concentration, the guest's hydration shell becomes more ordered and the system entropy decreases. A common critical value of the self-diffusion coefficient of different guest molecules is identified, below which hydrates will nucleate very readily.

Phase boundaries, nucleation rates and speed of crystal growth of the water-to-ice transition under an electric field: a simulation study

We investigate with computer simulations the effect of applying an electric field on the water-to-ice transition. We use a combination of state-of-the-art simulation techniques to obtain phase boundaries and crystal growth rates (direct coexistence), nucleation rates (seeding) and interfacial free energies (seeding and mold integration). First, we consider ice Ih, the most stable polymorph in the absence of a field. Its normal melting temperature, speed of crystal growth and nucleation rate (for a given supercooling) diminish as the intensity of the field goes up. Then, we study polarised cubic ice, or ice Icf, the most stable solid phase under a strong electric field. Its normal melting point goes up with the field and, for a given supercooling, under the studied field (0.3 V nm^-1) ice Icf nucleates and grows at a similar rate as Ih with no field. The net effect of the field would then be that ice nucleates at warmer temperatures, but in the form of ice Icf. The main conclusion of this work is that reasonable electric fields (not strong enough to break water molecules apart) are not relevant in the context of homogeneous ice nucleation at 1 bar.

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

We computed the homogeneous ice nucleation rate, and disentangled and investigated all the relevant physical quantities.

Navigating at Will on the Water Phase Diagram

Despite the simplicity of its molecular unit, water is a challenging system because of its uniquely rich polymorphism and predicted but yet unconfirmed features. Introducing a novel space of generalized coordinates that capture changes in the topology of the interatomic network, we are able to systematically track transitions among liquid, amorphous, and crystalline forms throughout the whole phase diagram of water, including the nucleation of crystals above and below the melting point. Our approach, based on molecular dynamics and enhanced sampling or free energy calculation techniques, is not specific to water and could be applied to very different structural phase transitions, paving the way towards the prediction of kinetic routes connecting polymorphic structures in a range of materials.

How Water's Properties Are Encoded in Its Molecular Structure and Energies

How are water's material properties encoded within the structure of the water molecule? This is pertinent to understanding Earth's living systems, its materials, its geochemistry and geophysics, and a broad spectrum of its industrial chemistry. Water has distinctive liquid and solid properties: It is highly cohesive. It has volumetric anomalies-water's solid (ice) floats on its liquid; pressure can melt the solid rather than freezing the liquid; heating can shrink the liquid. It has more solid phases than other materials. Its supercooled liquid has divergent thermodynamic response functions. Its glassy state is neither fragile nor strong. Its component ions-hydroxide and protons-diffuse much faster than other ions. Aqueous solvation of ions or oils entails large entropies and heat capacities. We review how these properties are encoded within water's molecular structure and energies, as understood from theories, simulations, and experiments. Like simpler liquids, water molecules are nearly spherical and interact with each other through van der Waals forces. Unlike simpler liquids, water's orientation-dependent hydrogen bonding leads to open tetrahedral cage-like structuring that contributes to its remarkable volumetric and thermal properties.

Role of Salt, Pressure, and Water Activity on Homogeneous Ice Nucleation

Pure water can be substantially supercooled below the melting temperature without transforming into ice. The achievable supercooling can be enhanced by adding solutes or by applying hydrostatic pressure. Avoiding ice formation is of great importance in the cryopreservation of food or biological samples. In this Letter, we investigate the similarity between the effects of pressure and salt on ice formation using a combination of state-of-the-art simulation techniques. We find that both hinder ice formation by increasing the energetic cost of creating the ice-fluid interface. Moreover, we examine the widely accepted proposal that the ice nucleation rate for different pressures and solute concentrations can be mapped through the activity of water [ Koop , L. ; Tsias , P. Nature , 2000 , 406 , 611 ]. We show that such a proposal is not consistent with the nucleation rates predicted in our simulations because it does not include all parameters affecting ice nucleation. Therefore, even though salt and pressure have a qualitatively similar effect on ice formation, they cannot be quantitatively mapped onto one another.