Role of stacking disorder in ice nucleation

The Mechanism of Heterogeneous Ice Nucleation by Fatty Alcohol Monolayers

Organic ice nucleating substances (INSs) are thought to play an essential role in cloud formation and, hence, precipitation and climate. Organic INSs are an important but poorly understood class of INSs in the atmosphere. To study organic INSs with exposed hydroxylated surfaces, researchers have previously used fatty alcohol monolayers as model systems. For alcohol monolayers, ice nucleation temperatures increase with increasing alkyl chain length and show a high-low oscillation following the number (odd-even) of carbon atoms in the alkyl chains. We employ atomistic models, together with molecular dynamics simulations, to investigate ice nucleation by C20H41OH, C30H61OH, and C31H63OH monolayers. As expected, we find that ice nucleation by alcohol monolayers depends on the lattice match to ice, and a poorer lattice match can at least partially account for the reduced ice nucleation ability of C20H41OH monolayers compared to monolayers of the longer chain alcohols. More interestingly, our simulations identify a limited range of alcohol configurations that readily nucleate ice via the basal plane. For configurations outside this range, ice nucleation did not occur on the time scale of our simulations (i.e., 5000 ns). The configurational feature that crucially influences ice nucleation is the angle between the alcohol C-O bond and the interfacial plane. C-O bonds directed sharply toward or away from the water phase strongly inhibit ice nucleation. In contrast, ice nucleation is easily observed for a relatively narrow band of C-O bond orientations centered about the surface plane. For comparable surface configurations, the ice nucleating abilities of C30H61OH and C31H63OH monolayers are practically identical, but the existence of a narrow band of ice-compatible surface configurations can perhaps explain why odd-chain alcohol monolayers are better INSs than even-chain alcohol monolayers. Earlier simulations have shown that for alcohols differing by a single carbon atom, the odd-chain monolayer is less rigid than the even-chain monolayer. This suggests the possibility that for odd-chain alcohol monolayers, the orientation of the C-O bonds can more easily adjust into the ice-compatible range than their even-chain counterparts, accounting for their enhanced ice nucleating ability.

Bridging classical nucleation theory and molecular dynamics simulation for homogeneous ice nucleation

Water freezing, initiated by ice nucleation, occurs widely in nature, ranging from cellular to global phenomena. Ice nucleation has been experimentally proven to require the formation of a critical ice nucleus, consistent with classical nucleation theory (CNT). However, the accuracy of CNT quantitative predictions of critical cluster sizes and nucleation rates has never been verified experimentally. In this study, we circumvent this difficulty by using molecular dynamics (MD) simulation. The physical properties of water/ice for CNT predictions, including density, chemical potential difference, and diffusion coefficient, are independently obtained using MD simulation, whereas the calculation of interfacial free energy is based on thermodynamic assumptions of CNT, including capillarity approximation among others. The CNT predictions are compared to the MD evaluations of brute-force simulations and forward flux sampling methods. We find that the CNT and MD predicted critical cluster sizes are consistent, and the CNT predicted nucleation rates are higher than the MD predicted values within three orders of magnitude. We also find that the ice crystallized from supercooled water is stacking-disordered ice with a stacking of cubic and hexagonal ices in four representative types of stacking. The prediction discrepancies in nucleation rate mainly arise from the stacking-disordered ice structure, the asphericity of ice cluster, the uncertainty of ice-water interfacial free energy, and the kinetic attachment rate. Our study establishes a relation between CNT and MD to predict homogeneous ice nucleation.

Correlating Ultrastability with Fragility and Surface Mobility in Vapor Deposited Tetrahedral Glasses

Several experiments on molecular and metallic glasses have shown that the ability of vapor deposition to produce ultrastable glasses is correlated to their structural and thermodynamic properties. Here we investigate the vapor deposition of a class of tetrahedral materials (including silicon and water) via molecular dynamics simulations of the generalized Stillinger-Weber potential. By changing a single parameter that controls the local tetrahedrality, we show that the emergence of ultrastable behavior is correlated with an increase in the fragility of the model. At the same time, while the mobility of the surface compared to the bulk shows only slight changes at low temperature, with increasing the tetrahedrality, it displays a significant enhancement toward the glass transition temperature. Our results point toward a strong connection between bulk dynamics, surface dynamics, and glass-ultrastability ability in this class of materials.

Two-dimensional bilayer ice in coexistence with three-dimensional ice without confinement

Icing plays an important role in various physical-chemical process. Although the formation of two-dimensional ice requires nanoscale confinement, two-dimensional bilayer ice in coexistence with three-dimensional ice without confinement remains poorly understood. Here, a critical value of a surface energy parameter is identified to characterize the liquid-solid interface interaction, above which two-dimensional and three-dimensional coexisting ice can surprisingly form on the surface. The two-dimensional ice growth mechanisms could be revealed by capturing the growth and merged of the metastable edge structures. The phase diagram about temperature and pressure vs energy parameters is predicted to distinguish liquid water, two-dimensional ice and three-dimensional ice. Furthermore, the deicing characteristics of coexisting ice demonstrate that the ice adhesion strength is linearly related to the ratio of ice-surface interaction energy to ice temperature. In addition, for gas-solid phase transition, the phase diagram about temperature and energy parameters is predicted to distinguish gas, liquid water, two-dimensional ice and three-dimensional ice. This work gives a perspective for studying the singular structure and dynamics of ice in nanoscale and provides a guide for future experimental realization of the coexisting ice.

Interplay between the Formation of Colloidal Clathrate and Cubic Diamond Crystals

Controlling the valency of directional interactions of patchy particles is insufficient for the selective formation of target crystalline structures due to the competition between phases of similar free energy. Examples of such are stacking hybrids of interwoven hexagonal and cubic diamonds with (i) its liquid phase, (ii) arrested glasses, or (iii) clathrates, all depending on the relative patch size, despite being within the one-bond-per-patch regime. Herein, using molecular dynamics simulations, we demonstrate that although tetrahedral patchy particles with narrow patches can assemble into clathrates or stacking hybrids in the bulk, this behavior can be suppressed by the application of external surface potential. Depending on its strength, the selective growth of either cubic diamond crystals or empty sII clathrate cages can be achieved. The formation of a given ordered network depends on the structure of the first adlayer, which is commensurate with the emerging network.

Heterogeneous Coprecipitation of Nanocrystals with Metals on Substrates

ConspectusThe heterogeneous coprecipitation of nanocrystals with metals on substrates plays a significant role in both natural and engineered systems. Due to the small dimensions and thereby the large specific surface area, nanocrystal coprecipitation with metals, which is ubiquitous in natural settings, exerts drastic effects on the biogeochemical cycling of metals on the earth's crust. Meanwhile, the controlled synthesis of nanocrystals with metal doping to achieve tunable size/composition enables their broad applications as adsorbents and catalysts in many engineered settings. Despite their importance, complex interactions among aqueous ions/polymers, nanocrystals, substrates, and metals are far from being well-understood, leaving the controlling mechanisms for nanocrystal formation with metals on substrates uncovered.In this Account, we discuss our systematic investigation over the past 10 years of the heterogeneous formation of representative nanocrystals with metals on typical substrates. We chose Fe(OH)3 and BaSO4 as representative nanocrystals. Mechanisms for varied metal coprecipitation were also investigated for both types of nanocrystals (i.e., Fe, Al, Cr, Cu, and Pb)(OH)3 and (Ba, Sr)(SO4, SeO4, and SeO3)). Bare SiO2 and Al2O3, as well as those coated with varied organics, were selected as geologically or synthetically representative substrates. Through the integration of state-of-the-art nanoscale interfacial characterization techniques with theoretical calculations, the complex interactions during nanocrystal formation at interfaces were probed and the controlling mechanisms were identified.For BaSO4 and Fe(OH)3 formation on substrates, the local supersaturation levels near substrates were controlled by Ba2+ adsorption and the electrostatic attraction of Fe(OH)3 monomer/polymer to substrates, respectively. Meanwhile, substrate hydrophobicity controlled the interfacial energy for the nucleation of both nanocrystals on (in)organic substrates. Metal ions' (i.e., Cr/Al/Cu/Pb) hydrolysis constants and substrates' dielectric constants controlled metal ion adsorption onto substrates, which altered the surface charges of substrates, thus controlling heterogeneous Fe(OH)3 nanocrystal formation on substrates by electrostatic interactions. The sizes and compositions of heterogeneous (Fe, Cr)(OH)3 and (Ba, Sr)(SO4, SeO4, SeO3) formed on substrates were found to be distinct from those of homogeneous precipitates formed in solution. The substrate (de)protonation could alter the local solution's pH and the substrates' surface charge; substrates could also adsorb cations, affecting local Fe/Cr/Ba/Sr ion concentrations at solid-water interfaces, thus controlling the amount/size/composition of nanocrystals by tuning their nucleation/growth/deposition on substrates. From slightly supersaturated solution, homogeneous coprecipitates of microsized (Ba, Sr)(SO4, SeO4, SeO3) formed through growth, with little Sr/Se(VI) incorporation due to higher solubilities of SrSO4 and BaSeO4 over BaSO4. While cation enrichment near substrates made the local solution highly supersaturated, nanosized coprecipitates formed on substrates through nucleation, with more Sr/Se(VI) incorporation due to lower interfacial energies of SrSO4 and BaSeO4 over BaSO4. The new insights gained advanced our understanding of the biogeochemical cycling of varied elements at solid-water interfaces and of the controlled synthesis of functional nanocrystals.

Data-Driven Path Collective Variables

Identifying optimal collective variables to model transformations using atomic-scale simulations is a long-standing challenge. We propose a new method for the generation, optimization, and comparison of collective variables that can be thought of as a data-driven generalization of the path collective variable concept. It consists of a kernel ridge regression of the committor probability, which encodes a transformation's progress. The resulting collective variable is one-dimensional, interpretable, and differentiable, making it appropriate for enhanced sampling simulations requiring biasing. We demonstrate the validity of the method on two different applications: a precipitation model and the association of Li+ and F- in water. For the former, we show that global descriptors such as the permutation invariant vector allow reaching an accuracy far from the one achieved via simpler, more intuitive variables. For the latter, we show that information correlated with the transformation mechanism is contained in the first solvation shell only and that inertial effects prevent the derivation of optimal collective variables from the atomic positions only.

Using machine learning with atomistic surface and local water features to predict heterogeneous ice nucleation

Heterogeneous ice nucleation (HIN) has applications in climate science, nanotechnology, and cryopreservation. Ice nucleation on the earth's surface or in the atmosphere usually occurs heterogeneously involving foreign substrates, known as ice nucleating particles (INPs). Experiments identify good INPs but lack sufficient microscopic resolution to answer the basic question: What makes a good INP? We employ molecular dynamics (MD) simulations in combination with machine learning (ML) to address this question. Often, the large amount of computational cost required to cross the nucleation barrier and observe HIN in MD simulations is a practical limitation. We use information obtained from short MD simulations of atomistic surface and water models to predict the likelihood of HIN. We consider 153 atomistic substrates with some surfaces differing in elemental composition and others only in terms of lattice parameters, surface morphology, or surface charges. A range of water features near the surface (local) are extracted from short MD simulations over a time interval (≤300 ns) where ice nucleation has not initiated. Three ML classification models, Random Forest (RF), support vector machine, and Gaussian process classification are considered, and the accuracies achieved by all three approaches lie within their statistical uncertainties. Including local water features is essential for accurate prediction. The accuracy of our best RF classification model obtained including both surface and local water features is 0.89 ± 0.05. A similar accuracy can be achieved including only local water features, suggesting that the important surface properties are largely captured by the local water features. Some important features identified by ML analysis are local icelike structures, water density and polarization profiles perpendicular to the surface, and the two-dimensional lattice match to ice. We expect that this work, with its strong focus on realistic surface models, will serve as a guide to the identification or design of substrates that can promote or discourage ice nucleation.

Comparing brute force to transition path sampling for gas hydrate nucleation with a flat interface: comments on time reversal symmetry

Fluid to solid nucleation is often investigated with the rare event method transition path sampling (TPS). I claim that the inherent irreversibility of solid nucleation, even at stationary conditions, calls into question TPS's applicability for determining solid nucleation mechanisms, especially for pre-critical behavior. Even when applied to a phenomenon which displays time reversal asymmetry like solid nucleation, TPS is a good means of exploring phase space and giving trends in post-critical structure, and its ability to facilitate nucleation rate and free energy calculations remains outstanding. Forward-only splitting and ratcheting methods such as forward flux sampling are more attractive for understanding nucleation mechanisms as they do not require time reversal symmetry, but at low driving forces may suffer from the same limitations as brute force: they may never make it to the first ratchet. Here I briefly summarize the TPS method and gas hydrate nucleation simulation literature, focusing on topics within both to facilitate a comparison of brute force hydrate nucleation to transition path sampling of hydrate nucleation. Perhaps anecdotally, the brute force technique results in more crystalline trajectories despite having higher driving forces than TPS. I maintain this difference is because of the inherent irreversibility of hydrate nucleation, meaning its pre-critical behavior cannot accurately be determined by the melting trajectories that comprise approximately half of the configurations in TPS's path ensemble.

Spiers Memorial Lecture: Water at interfaces

In this article we discuss current issues in the context of the four chosen subtopics for the meeting: dynamics and nano-rheology of interfacial water, electrified/charged aqueous interfaces, ice interfaces, and soft matter/water interfaces. We emphasize current advances in both theory and experiment, as well as important practical manifestations and areas of unresolved controversy.

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.

Observing growth and interfacial dynamics of nanocrystalline ice in thin amorphous ice films

Ice crystals at low temperatures exhibit structural polymorphs including hexagonal ice, cubic ice, or a hetero-crystalline mixture of the two phases. Despite the significant implications of structure-dependent roles of ice, mechanisms behind the growths of each polymorph have been difficult to access quantitatively. Using in-situ cryo-electron microscopy and computational ice-dynamics simulations, we directly observe crystalline ice growth in an amorphous ice film of nanoscale thickness, which exhibits three-dimensional ice nucleation and subsequent two-dimensional ice growth. We reveal that nanoscale ice crystals exhibit polymorph-dependent growth kinetics, while hetero-crystalline ice exhibits anisotropic growth, with accelerated growth occurring at the prismatic planes. Fast-growing facets are associated with low-density interfaces that possess higher surface energy, driving tetrahedral ordering of interfacial H2O molecules and accelerating ice growth. These findings, based on nanoscale observations, improve our understanding on early stages of ice formation and mechanistic roles of the ice interface.

Multiscale Molecular Dynamics Simulations of Ice-Binding Proteins

Ice-binding proteins (IBPs) are a diverse class of proteins that are essential for the survival of organisms in cold conditions. IBPs are diverse in their function and can prevent or promote ice growth and selectively bind to specific crystallographic planes of the growing ice lattice. Moreover, IBPs are widely utilized to modulate ice crystal growth and recrystallization in the food industry and as cryoprotectants to preserve biological matter. A key unresolved aspect of the mode of action is how the ice-binding sites of these proteins distinguish between ice and water and interact with multiple crystal facets of the ice. The use of molecular dynamics (MD) simulation allows us to thoroughly investigate the binding mechanism and energetics of ice-binding proteins, to complement and expand on the mechanistic understandings gained from experiments. In this chapter, we describe a series of molecular dynamics simulation methodologies to investigate the mechanism of action of ice-binding proteins. Specifically, we provide detailed instructions to set up MD simulations to study the binding and interaction of ice-binding proteins using atomistic and coarse-grained simulations.

Resolving Temperature-Dependent Hydrate Nucleation Pathway: The Role of "Transition Layer"

Understanding the nucleation of natural gas hydrate (NGH) at different conditions has important implications to NGH recovery and other industrial applications, such as gas storage and separation. Herein, vast numbers of hydrate nucleation events are traced via molecular dynamics (MD) simulations at different degrees of supercooling (or driving forces). Specifically, to precisely characterize a hydrate nucleus from an aqueous system during the MD simulation, we develop an evolutionary order parameter (OP) to recognize the nucleus size and shape. Subsequently, the free energy landscapes of hydrate during nucleation are explored by using the newly developed OP. The results suggest that at 270 K (or 0.92 Tm supercooling, where Tm is the melting point), the near-rounded nucleus prevails during the nucleation, as described from the classical nucleation theory. In contrast, at relatively strong driving forces of 0.85 and 0.88 Tm, nonclassical nucleation events arise. Specifically, the pathway toward an elongated nucleus becomes as important as the pathway toward a near-rounded nucleus. To explain the distinct nucleation phenomena at different supercoolings, a notion of a "transition layer" (or liquid-blob-like layer) is proposed. Here, the transition layer is to describe the interfacial region between the nucleus and aqueous solution, and this layer entails two functionalities: (1) it tends to retain CH4 depending on the degrees of supercooling and (2) it facilitates collision among CH4, which thus promote the incorporation of CH4 into nucleus. Our simulation indicates that compared to the near-rounded nucleus, the transition layer surrounding the elongated nucleus is more evident with the higher collision rate among CH4 molecules. As such, the transition layer tends to promote the elongated nucleus pathway, while offsetting the cost of larger surface free energy associated with the elongated nucleus. At 0.92 Tm, however, the transition layer gradually disappears, and classical nucleation events dominate. Overall, the notion of "transition layer" offers deeper insight into the NGH nucleation at different degrees of supercooling and could be extended to describe other types of hydrate nucleation.

Surface premelting of ice far below the triple point

Premelting of ice, a quasi-liquid layer (QLL) at the surface below the melting temperature, was first postulated by Michael Faraday 160 y ago. Since then, it has been extensively studied theoretically and experimentally through many techniques. Existing work has been performed predominantly on hexagonal ice, at conditions close to the triple point. Whether the same phenomenon can persist at much lower pressure and temperature, where stacking disordered ice sublimates directly into water vapor, remains unclear. Herein, we report direct observations of surface premelting on ice nanocrystals below the sublimation temperature using transmission electron microscopy (TEM). Similar to what has been reported on hexagonal ice, a QLL is found at the solid-vapor interface. It preferentially decorates certain facets, and its thickness increases as the phase transition temperature is approached. In situ TEM reveals strong diffusion of the QLL, while electron energy loss spectroscopy confirms its amorphous nature. More significantly, the premelting observed in this work is thought to be related to the metastable low-density ultraviscous water, instead of ambient liquid water as in the case of hexagonal ice. This opens a route to understand premelting and grassy liquid state, far away from the normal water triple point.

Crystallization of FAPbI3: Polytypes and stacking faults

Molecular dynamics simulations are performed to study the crystallization of formamidinium lead iodide. From all-atom simulations of the crystal growth process and the δ-α-phase transitions, we try to reveal the formation of various stack-faulted intermediate defected structures and report various polytypes of formamidinium lead iodide that are observed from simulations.

Microstructure and crystal order during freezing of supercooled water drops

Supercooled water droplets are widely used to study supercooled water1,2, ice nucleation3-5 and droplet freezing6-11. Their freezing in the atmosphere affects the dynamics and climate feedback of clouds12,13 and can accelerate cloud freezing through secondary ice production14-17. Droplet freezing occurs at several timescales and length scales14,18 and is sufficiently stochastic to make it unlikely that two frozen drops are identical. Here we use optical microscopy and X-ray laser diffraction to investigate the freezing of tens of thousands of water microdrops in vacuum after homogeneous ice nucleation around 234-235 K. On the basis of drop images, we developed a seven-stage model of freezing and used it to time the diffraction data. Diffraction from ice crystals showed that long-range crystalline order formed in less than 1 ms after freezing, whereas diffraction from the remaining liquid became similar to that from quasi-liquid layers on premelted ice19,20. The ice had a strained hexagonal crystal structure just after freezing, which is an early metastable state that probably precedes the formation of ice with stacking defects8,9,18. The techniques reported here could help determine the dynamics of freezing in other conditions, such as drop freezing in clouds, or help understand rapid solidification in other materials.

Pursuing colloidal diamonds

The endeavor to selectively fabricate a cubic diamond is challenging due to the formation of competing phases such as its hexagonal polymorph or others possessing similar free energy. The necessity to achieve this is of paramount importance since the cubic diamond is the only polymorph exhibiting a complete photonic bandgap, making it a promising candidate in view of photonic applications. Herein, we demonstrate that due to the presence of an external field and delicate manipulation of its strength we can attain selectivity in the formation of a cubic diamond in a one-component system comprised of designer tetrahedral patchy particles. The driving force of such a phenomenon is the structure of the first adlayer which is commensurate with the (110) face of the cubic diamond. Moreover, after a successful nucleation event, once the external field is turned off, the structure remains stable, paving an avenue for further post-synthetic treatment.

Characterizing Surface Ice-Philicity Using Molecular Simulations and Enhanced Sampling

The formation of ice, which plays an important role in diverse contexts ranging from cryopreservation to atmospheric science, is often mediated by solid surfaces. Although surfaces that interact favorably with ice (relative to liquid water) can facilitate ice formation by lowering nucleation barriers, the molecular characteristics that confer icephilicity to a surface are complex and incompletely understood. To address this challenge, here we introduce a robust and computationally efficient method for characterizing surface ice-philicity that combines molecular simulations and enhanced sampling techniques to quantify the free energetic cost of increasing surface-ice contact at the expense of surface-water contact. Using this method to characterize the ice-philicity of a family of model surfaces that are lattice matched with ice but vary in their polarity, we find that the nonpolar surfaces are moderately ice-phobic, whereas the polar surfaces are highly ice-philic. In contrast, for surfaces that display no complementarity to the ice lattice, we find that ice-philicity is independent of surface polarity and that both nonpolar and polar surfaces are moderately ice-phobic. Our work thus provides a prescription for quantitatively characterizing surface ice-philicity and sheds light on how ice-philicity is influenced by lattice matching and polarity.

Analysis of Vibrational Spectra of Tetrafluoroethane Glasses Deposited by Physical Vapor Deposition

This paper presents the results obtained in the study of structural phase transitions in thin films of R134A. The samples were condensed on a substrate by physical deposition of R134A molecules from the gas phase. Structural phase transformations in samples were investigated by observing the changes in characteristic frequencies of Freon molecules in the mid-infrared range with the help of Fourier-transform infrared spectroscopy. The experiments were carried out in the temperature range from 12 to 90 K. A number of structural phase states, including glassy forms, were detected. The changes in thermogram curves at fixed frequencies of half-widths of absorption bands of R134A molecules were revealed. These changes indicate a large bathochromic shift of these bands at frequencies of ν = 842 cm^-1, ν = 965 cm^-1, and ν = 958 cm^-1 and a hypsochromic shift of the bands at frequencies of ν = 1055 cm^-1, ν = 1170 cm^-1, and ν = 1280 cm^-1 at temperatures from T = 80 K to T = 84 K. These shifts are related to the structural phase transformations in the samples.

Continuous transition of colloidal crystals through stable random orders

Randomly stacked 2D hexagonal close-packed (RHCP) layer structures are frequently observed in colloids and other material systems but are considered metastable. We report a stable RHCP phase domain of poly(butadiene-b-ethylene oxide) (PB-PEO) diblock copolymer micellar colloids in water. The stable RHCP colloidal crystals emerge in the middle of a continuously transiting phase domain of close-packed PB-PEO colloids from a face-centered cubic (FCC) polytype to a HCP polytype. We attribute the stability of RHCP structures to two competing contributions, entropic preference for FCC lattices and long PEO corona chains stabilizing HCP lattices. When these two contributions become comparable in the phase space, thermal fluctuation randomizes the stacking order of the 2D-HCP layers, and RHCP orders are stabilized. The continuously transiting close-packed structures of PB-PEO colloids with stable RHCP states suggest that similar structural transitions and equivalent RHCP states may occur in other polytypic crystal systems because polytypic crystals have the common crystal construction rule, i.e., stacking 2D-HCP lattice layer groups in different orders.

RSeeds: Rigid Seeding Method for Studying Heterogeneous Crystal Nucleation

Heterogeneous nucleation is the dominant form of liquid-to-solid transition in nature. Although molecular simulations are most uniquely suited to studying nucleation, the waiting time to observe even a single nucleation event can easily exceed the current computational capabilities. Therefore, there exists an imminent need for methods that enable computationally fast and feasible studies of heterogeneous nucleation. Seeding is a technique that has proven to be successful at dramatically expanding the range of computationally accessible nucleation rates in simulation studies of homogeneous crystal nucleation. In this article, we introduce a new seeding method for heterogeneous nucleation called Rigid Seeding (RSeeds). Crystalline seeds are treated as pseudorigid bodies and simulated on a surface with metastable liquid above its melting temperature. This allows the seeds to adapt to the surface and identify favorable seed-surface configurations, which is necessary for reliable predictions of crystal polymorphs that form and the corresponding heterogeneous nucleation rates. We demonstrate and validate RSeeds for heterogeneous ice nucleation on a flexible self-assembled monolayer surface, a mineral surface based on kaolinite, and two model surfaces. RSeeds predicts the correct ice polymorph, exposed crystal plane, and rotation on the surface. RSeeds is semiquantitative and can be used to estimate the critical nucleus size and nucleation rate when combined with classical nucleation theory. We demonstrate that RSeeds can be used to evaluate nucleation rates spanning many orders of magnitude.

Tracking cubic ice at molecular resolution

Ice is present everywhere on Earth and has an essential role in several areas, such as cloud physics, climate change and cryopreservation. The role of ice is determined by its formation behaviour and associated structure. However, these are not fully understood1. In particular, there is a long-standing debate about whether water can freeze to form cubic ice-a currently undescribed phase in the phase space of ordinary hexagonal ice2-6. The mainstream view inferred from a collection of laboratory data attributes this divergence to the inability to discern cubic ice from stacking-disordered ice-a mixture of cubic and hexagonal sequences7-11. Using cryogenic transmission electron microscopy combined with low-dose imaging, we show here the preferential nucleation of cubic ice at low-temperature interfaces, resulting in two types of separate crystallization of cubic ice and hexagonal ice from water vapour deposition at 102 K. Moreover, we identify a series of cubic-ice defects, including two types of stacking disorder, revealing the structure evolution dynamics supported by molecular dynamics simulations. The realization of direct, real-space imaging of ice formation and its dynamic behaviour at the molecular level provides an opportunity for ice research at the molecular level using transmission electron microscopy, which may be extended to other hydrogen-bonding crystals.

Nucleation and growth of crystalline ices from amorphous ices

We here review mostly experimental and some computational work devoted to nucleation in amorphous ices. In fact, there are only a handful of studies in which nucleation and growth in amorphous ices are investigated as two separate processes. In most studies, crystallization temperatures T_x or crystallization rates R_JG are accessed for the combined process. Our Review deals with different amorphous ices, namely, vapor-deposited amorphous solid water (ASW) encountered in many astrophysical environments; hyperquenched glassy water (HGW) produced from μm-droplets of liquid water; and low density amorphous (LDA), high density amorphous (HDA), and very high density amorphous (VHDA) ices produced via pressure-induced amorphization of ice I or from high-pressure polymorphs. We cover the pressure range of up to about 6 GPa and the temperature range of up to 270 K, where only the presence of salts allows for the observation of amorphous ices at such high temperatures. In the case of ASW, its microporosity and very high internal surface to volume ratio are the key factors determining its crystallization kinetics. For HGW, the role of interfaces between individual glassy droplets is crucial but mostly neglected in nucleation or crystallization studies. In the case of LDA, HDA, and VHDA, parallel crystallization kinetics to different ice phases is observed, where the fraction of crystallized ices is controlled by the heating rate. A key aspect here is that in different experiments, amorphous ices of different "purities" are obtained, where "purity" here means the "absence of crystalline nuclei." For this reason, "preseeded amorphous ice" and "nuclei-free amorphous ice" should be distinguished carefully, which has not been done properly in most studies. This makes a direct comparison of results obtained in different laboratories very hard, and even results obtained in the same laboratory are affected by very small changes in the preparation protocol. In terms of mechanism, the results are consistent with amorphous ices turning into an ultraviscous, deeply supercooled liquid prior to nucleation. However, especially in preseeded amorphous ices, crystallization from the preexisting nuclei takes place simultaneously. To separate the time scales of crystallization from the time scale of structure relaxation cleanly, the goal needs to be to produce amorphous ices free from crystalline ice nuclei. Such ices have only been produced in very few studies.

Real-time TEM observations of ice formation in graphene liquid cell

The study of ice nucleation and growth at the nanoscale is of utmost importance in geological and atmospheric sciences. However, existing transmission electron microscopy (TEM) approaches have been unsuccessful in imaging ice formation directly. Herein, we demonstrate how radical scavengers - such as TiO₂ - encased with water in graphene liquid cells (GLCs) facilitate the observation of ice nucleation phenomena at low temperatures. Atomic-resolution imaging reveals the nucleation and growth of cubic ice-phase crystals at close proximity to TiO₂-water nanointerfaces at low temperatures. Interestingly, both heterogeneously and homogeneously nucleated ice crystals exhibited this cubic phase. Ice crystal nuclei were observed to be more stable at the TiO₂-water nanointerface, as compared with crystals in the bulk liquid (homogeneous nucleation), suggesting the radical scavenging efficacy of TiO₂ nanoparticles mitigating the electron beam by-products. The present work demonstrates that the use of radical scavengers in GLC TEM shows great promise towards unveiling the nanoscale pathways for ice nucleation and growth dynamic events.

Order-disorder phase transition driven by interlayer sliding in lead iodides

A variety of phase transitions have been found in two-dimensional layered materials, but some of their atomic-scale mechanisms are hard to clearly understand. Here, we report the discovery of a phase transition whose mechanism is identified as interlayer sliding in lead iodides, a layered material widely used to synthesize lead halide perovskites. The low-temperature crystal structure of lead iodides is found not 2H polytype as known before, but non-centrosymmetric 4H polytype. This undergoes the order-disorder phase transition characterized by the abrupt spectral broadening of valence bands, taken by angle-resolved photoemission, at the critical temperature of 120 K. It is accompanied by drastic changes in simultaneously taken photocurrent and photoluminescence. The transmission electron microscopy is used to reveal that lead iodide layers stacked in the form of 4H polytype at low temperatures irregularly slide over each other above 120 K, which can be explained by the low energy barrier of only 10.6 meV/atom estimated by first principles calculations. Our findings suggest that interlayer sliding is a key mechanism of the phase transitions in layered materials, which can significantly affect optoelectronic and optical characteristics.

Ice crystallization under cryogenic cooling in lipid membrane nanoconfined geometry: Time-resolved structural dynamics

Time-resolved structural investigations of crystallization of water in lipid/protein/salt mesophases at cryogenic temperatures are significant for comprehension of ice nanocrystal nucleation kinetics in lipid membranous systems and can lead to a better understanding of how to experimentally retard the ice formation that obstructs the protein crystal structure determination. Here, we present a time-resolved synchrotron microfocus X-ray diffraction (TR-XRD) study based on ∼40,000 frames that revealed the dynamics of water-to-ice crystallization in a lipid/protein/salt mesophase subjected to cryostream cooling at 100 K. The monoolein/hemoglobin/salt/water system was chosen as a model composition related to protein-loaded lipid cubic phases (LCP) broadly used for the crystallization of proteins. Under confinement in the nanoscale geometry, metastable short-living cubic ice (I_c) rapidly crystallized well before the formation of hexagonal ice (I_h). The detected early nanocrystalline states of water-to-ice transformation in multicomponent systems are relevant to a broad spectrum of technologies and understanding of natural phenomena, including crystallization, physics of water nanoconfinement, and rational design of anti-freezing and cryopreservation systems.

Kinetics and Mechanisms of Pressure-Induced Ice Amorphization and Polyamorphic Transitions in a Machine-Learned Coarse-Grained Water Model

Water glasses have attracted considerable attention due to their potential connection to a liquid-liquid transition in supercooled water. Here we use molecular simulations to investigate the formation and phase behavior of water glasses using the machine-learned bond-order parameter (ML-BOP) water model. We produce glasses through hyperquenching of water, pressure-induced amorphization (PIA) of ice, and pressure-induced polyamorphic transformations. We find that PIA of polycrystalline ice occurs at a lower pressure than that of monocrystalline ice and through a different mechanism. The temperature dependence of the amorphization pressure of polycrystalline ice for ML-BOP agrees with that in experiments. We also find that ML-BOP accurately reproduces the density, coordination number, and structural features of low-density (LDA), high-density (HDA), and very high-density (VHDA) amorphous water glasses. ML-BOP accurately reproduces the experimental radial distribution function of LDA but overpredicts the minimum between the first two shells in high-density glasses. We examine the kinetics and mechanism of the transformation between low-density and high-density glasses and find that the sharp nature of these transitions in ML-BOP is similar to that in experiments and all-atom water models with a liquid-liquid transition. Transitions between ML-BOP glasses occur through a spinodal-like mechanism, similar to ice crystallization from LDA. Both glass-to-glass and glass-to-ice transformations have Avrami-Kolmogorov kinetics with exponent n = 1.5 ± 0.2 in experiments and simulations. Importantly, ML-BOP reproduces the competition between crystallization and HDA→LDA transition above the glass transition temperature T_g, and separation of their time scales below T_g, observed also in experiments. These findings demonstrate the ability of ML-BOP to accurately reproduce water properties across various regimes, making it a promising model for addressing the competition between polyamorphic transitions and crystallization in water and solutions.

Stability and Metastability of Liquid Water in a Machine-Learned Coarse-Grained Model with Short-Range Interactions

Coarse-grained water models are ∼100 times more efficient than all-atom models, enabling simulations of supercooled water and crystallization. The machine-learned monatomic model ML-BOP reproduces the experimental equation of state (EOS) and ice-liquid thermodynamics at 0.1 MPa on par with the all-atom TIP4P/2005 and TIP4P/Ice models. These all-atom models were parametrized using high-pressure experimental data and are either accurate for water's EOS (TIP4P/2005) or ice-liquid equilibrium (TIP4P/Ice). ML-BOP was parametrized from temperature-dependent ice and liquid experimental densities and melting data at 0.1 MPa; its only pressure training is from compression of TIP4P/2005 ice at 0 K. Here we investigate whether ML-BOP replicates the experimental EOS and ice-water thermodynamics along all pressures of ice I. We find that ML-BOP reproduces the temperature, enthalpy, entropy, and volume of melting of hexagonal ice up to 400 MPa and the EOS of water along the melting line with an accuracy that rivals that of both TIP4P/2005 and TIP4P/Ice. We interpret that the accuracy of ML-BOP originates from its ability to capture the shift between compact and open local structures to changes in pressure and temperature. ML-BOP reproduces the sharpening of the tetrahedral peak of the pair distribution function of water upon supercooling, and its pressure dependence. We characterize the region of metastability of liquid ML-BOP with respect to crystallization and cavitation. The accessibility of ice crystallization to simulations of ML-BOP, together with its accurate representation of the thermodynamics of water, makes it promising for investigating the interplay between anomalies, glass transition, and crystallization under conditions challenging to access through experiments.

Phase Transition between Crystalline Variants of Ordinary Ice

Water is one of the most abundant molecules on Earth. However, this common and "simple" material has more than 18 different phases, which poses a great challenge to theoretically study the nature of water and ice. We designed two reaction coordinates that can distinguish between water and various ice states and used them to efficiently sample all possible states of the system in all-atom molecular dynamics simulation at ambient temperature and pressure. Various structural and thermodynamics properties, including the water-ice phase diagrams, can thus be calculated. We also present a simple model that successfully explains the thermodynamic stability of different ice states. Our work provides effective methods and data for theoretical studies of different phases of water and ice.

The Possible Mechanism of Amyloid Transformation Based on the Geometrical Parameters of Early-Stage Intermediate in Silico Model for Protein Folding

The specificity of the available experimentally determined structures of amyloid forms is expressed primarily by the two- and not three-dimensional forms of a single polypeptide chain. Such a flat structure is possible due to the β structure, which occurs predominantly. The stabilization of the fibril in this structure is achieved due to the presence of the numerous hydrogen bonds between the adjacent chains. Together with the different forms of twists created by the single R- or L-handed α-helices, they form the hydrogen bond network. The specificity of the arrangement of these hydrogen bonds lies in their joint orientation in a system perpendicular to the plane formed by the chain and parallel to the fibril axis. The present work proposes the possible mechanism for obtaining such a structure based on the geometric characterization of the polypeptide chain constituting the basis of our early intermediate model for protein folding introduced formerly. This model, being the conformational subspace of Ramachandran plot (the ellipse path), was developed on the basis of the backbone conformation, with the side-chain interactions excluded. Our proposal is also based on the results from molecular dynamics available in the literature leading to the unfolding of α-helical sections, resulting in the β-structural forms. Both techniques used provide a similar suggestion in a search for a mechanism of conformational changes leading to a formation of the amyloid form. The potential mechanism of amyloid transformation is presented here using the fragment of the transthyretin as well as amyloid Aβ.

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.

Manipulating Reaction Intermediates to Aqueous-Phase ZnSe Magic-Size Clusters and Quantum Dots at Room Temperature

It is not resolved which model describes better the aqueous-phase nucleation and growth of semiconductor quantum dots (QDs), the classical one-step one or the nonclassical multi-step one. Here, we design a room-temperature reaction to trap reaction intermediates in the prenucleation stage of ZnSe QDs (as a model system). We show that the trapped intermediate can transform to magic-size clusters (MSCs) via intra-molecular reorganization and can fragment to enable the growth of QDs. The MSCs exhibit a sharp optical absorption peaking at 299 nm, labelled MSC-299. The intermediate, the precursor compound (PC-299) of MSC-299, is optically transparent at 299 nm and to longer wavelengths. This intermediate forms in various Zn and Se reaction systems. The present study provides unambiguous evidence that the nonclassical and classical pathways are both necessary to explain the nucleation and growth of aqueous-phase QDs, with the former pathway favored more by high reaction concentrations.

Normalizing flows for atomic solids

We present a machine-learning approach, based on normalizing flows, for modelling atomic solids. Our model transforms an analytically tractable base distribution into the target solid without requiring ground-truth samples for training. We report Helmholtz free energy estimates for cubic and hexagonal ice modelled as monatomic water as well as for a truncated and shifted Lennard-Jones system, and find them to be in excellent agreement with literature values and with estimates from established baseline methods. We further investigate structural properties and show that the model samples are nearly indistinguishable from the ones obtained with molecular dynamics. Our results thus demonstrate that normalizing flows can provide high-quality samples and free energy estimates without the need for multi-staging.

The role of structural order in heterogeneous ice nucleation

The freezing of water into ice is a key process that is still not fully understood. It generally requires an impurity of some description to initiate the heterogeneous nucleation of the ice crystals. The molecular structure, as well as the extent of structural order within the impurity in question, both play an essential role in determining its effectiveness. However, disentangling these two contributions is a challenge for both experiments and simulations. In this work, we have systematically investigated the ice-nucleating ability of the very same compound, cholesterol, from the crystalline (and thus ordered) form to disordered self-assembled monolayers. Leveraging a combination of experiments and simulations, we identify a “sweet spot” in terms of the surface coverage of the monolayers, whereby cholesterol maximises its ability to nucleate ice (which remains inferior to that of crystalline cholesterol) by enhancing the structural order of the interfacial water molecules. These findings have practical implications for the rational design of synthetic ice-nucleating agents.

The freezing of water into ice is still not fully understood. Here, we investigate the role of structural disorder within the biologically relevant impurities that facilitate this fundamental phase transition.

Following the Crystallization of Amorphous Ice after Ultrafast Laser Heating

Using time-resolved wide-angle X-ray scattering, we investigated the early stages (10 μs–1 ms) of crystallization of supercooled water, obtained by the ultrafast heating of high- and low-density amorphous ice (HDA and LDA) up to a temperature T = 205 K ± 10 K. We have determined that the crystallizing phase is stacking disordered ice (I_sd), with a maximum cubicity of χ = 0.6, in agreement with predictions from molecular dynamics simulations at similar temperatures. However, we note that a growing small portion of hexagonal ice (I_h) was also observed, suggesting that within our timeframe, I_sd starts annealing into I_h. The onset of crystallization, in both amorphous ice, occurs at a similar temperature, but the observed final crystalline fraction in the LDA sample is considerably lower than that in the HDA sample. We attribute this discrepancy to the thickness difference between the two samples.

The physics of empty liquids: from patchy particles to water

Empty liquids represent a wide class of materials whose constituents arrange in a random network through reversible bonds. Many key insights on the physical properties of empty liquids have originated almost independently from the study of colloidal patchy particles on one side, and a large body of theoretical and experimental research on water on the other side. Patchy particles represent a family of coarse-grained potentials that allows for a precise control of both the geometric and the energetic aspects of bonding, while water has arguably the most complex phase diagram of any pure substance, and a puzzling amorphous phase behavior. It was only recently that the exchange of ideas from both fields has made it possible to solve long-standing problems and shed new light on the behavior of empty liquids. Here we highlight the connections between patchy particles and water, focusing on the modelling principles that make an empty liquid behave like water, including the factors that control the appearance of thermodynamic and dynamic anomalies, the possibility of liquid-liquid phase transitions, and the crystallization of open crystalline structures.

Heterogeneous Ice Growth in Micron-Sized Water Droplets Due to Spontaneous Freezing

Understanding how ice nucleates and grows into larger crystals is of crucial importance for many research fields. The purpose of this study was to shed light on the phase and structure of ice once a nucleus is formed inside a metastable water droplet. Wide-angle X-ray scattering (WAXS) was performed on micron-sized droplets evaporatively cooled to temperatures where homogeneous nucleation occurs. We found that for our weak hits ice grows more cubic compared to the strong hits that are completely hexagonal. Due to efficient heat removal caused by evaporation, we propose that the cubicity of ice at the vicinity of the droplet’s surface is higher than for ice formed within the bulk of the droplet. Moreover, the Bragg peaks were classified based on their geometrical shapes and positions in reciprocal space, which showed that ice grows heterogeneously with a significant population of peaks indicative of truncation rods and crystal defects. Frequent occurrences of the (100) reflection with extended in-planar structure suggested that large planar ice crystals form at the droplet surface, then fracture into smaller domains to accommodate to the curvature of the droplets. Planar faulting due to misaligned domains would explain the increased cubicity close to the droplet surface.

Crystallization kinetics of atomic crystals revealed by a single-shot and single-particle X-ray diffraction experiment

Crystallization is a fundamental natural phenomenon and the ubiquitous physical process in materials science for the design of new materials. So far, experimental observations of the structural dynamics in crystallization have been mostly restricted to slow dynamics. We present here an exclusive way to explore the dynamics of crystallization in highly controlled conditions (i.e., in the absence of impurities acting as seeds of the crystallites) as it occurs in vacuum. We have measured the early formation stage of solid Xe nanoparticles nucleated in an expanding supercooled Xe jet by means of an X-ray diffraction experiment with 10-fs X-ray free-electron laser (XFEL) pulses. We found that the structure of Xe nanoparticles is not pure face-centered cubic (fcc), the expected stable phase, but a mixture of fcc and randomly stacked hexagonal close-packed (rhcp) structures. Furthermore, we identified the instantaneous coexistence of the comparably sized fcc and rhcp domains in single Xe nanoparticles. The observations are explained by the scenario of structural aging, in which the nanoparticles initially crystallize in the highly stacking-disordered rhcp phase and the structure later forms the stable fcc phase. The results are reminiscent of analogous observations in hard-sphere systems, indicating the universal role of the stacking-disordered phase in nucleation.

Facile self-assembly of colloidal diamond from tetrahedral patchy particles via ring selection

The self-assembly of colloidal diamond–a classic example of an open crystal with the low coordination number of four and much sought after due to its applications in visible light management–from designer spherical colloidal particles has proved challenging over the years. The formation of the diamond lattice from tetrahedral patchy particles is hampered by the propensity to form competing open periodic structures for narrow patches or dynamically arrested states for wider patches, leaving a narrow window in design space where diamond crystals may be realized. Our two-component system of designer tetrahedral patchy particles supports a significantly wider range for patch sizes for programmed self-assembly, thus facilitating experimental fabrication, and offers fundamental insight into crystallization into open lattices.

Diamond-structured crystals, particularly those with cubic symmetry, have long been attractive targets for the programmed self-assembly of colloidal particles, due to their applications as photonic crystals that can control the flow of visible light. While spherical particles decorated with four patches in a tetrahedral arrangement—tetrahedral patchy particles—should be an ideal building block for this endeavor, their self-assembly into colloidal diamond has proved elusive. The kinetics of self-assembly pose a major challenge, with competition from an amorphous glassy phase, as well as clathrate crystals, leaving a narrow widow of patch widths where tetrahedral patchy particles can self-assemble into diamond crystals. Here we demonstrate that a two-component system of tetrahedral patchy particles, where bonding is allowed only between particles of different types to select even-member rings, undergoes crystallization into diamond crystals over a significantly wider range of patch widths conducive for experimental fabrication. We show that the crystallization in the two-component system is both thermodynamically and kinetically enhanced, as compared to the one-component system. Although our bottom-up route does not lead to the selection of the cubic polytype exclusively, we find that the cubicity of the self-assembled crystals increases with increasing patch width. Our designer system not only promises a scalable bottom-up route for colloidal diamond but also offers fundamental insight into crystallization into open lattices.

Advances in the study of supercooled water

In this review, we report recent progress in the field of supercooled water. Due to its uniqueness, water presents numerous anomalies with respect to most simple liquids, showing polyamorphism both in the liquid and in the glassy state. We first describe the thermodynamic scenarios hypothesized for the supercooled region and in particular among them the liquid-liquid critical point scenario that has so far received more experimental evidence. We then review the most recent structural indicators, the two-state model picture of water, and the importance of cooperative effects related to the fact that water is a hydrogen-bonded network liquid. We show throughout the review that water's peculiar properties come into play also when water is in solution, confined, and close to biological molecules. Concerning dynamics, upon mild supercooling water behaves as a fragile glass former following the mode coupling theory, and it turns into a strong glass former upon further cooling. Connections between the slow dynamics and the thermodynamics are discussed. The translational relaxation times of density fluctuations show in fact the fragile-to-strong crossover connected to the thermodynamics arising from the existence of two liquids. When considering also rotations, additional crossovers come to play. Mobility-viscosity decoupling is also discussed in supercooled water and aqueous solutions. Finally, the polyamorphism of glassy water is considered through experimental and simulation results both in bulk and in salty aqueous solutions. Grains and grain boundaries are also discussed.

Hyperactive Antifreeze Proteins Promote Ice Growth before Binding to It

The antifreeze mechanism of antifreeze proteins (AFPs) evolved by organisms has been widely studied. However, detailed knowledge of the synergy between AFPs and ice crystals still remains fragmentary. In the present contribution, the cooperative effect of the hyperactive insect antifreeze protein TmAFP and ice crystals on the interfacial water during the entire process of inhibiting ice growth is systematically investigated at the atomic level and compared with its low activity mutant and a nonantifreeze protein. The results indicate a significant synergy between TmAFP and ice crystals, which enables the TmAFP to promote the ice growth before adsorbing on the surfaces of the ice crystals, while the mutant and the nonantifreeze protein cannot promote the ice growth due to the lack of this synergy. When TmAFP approaches the ice surface, the interfacial water is induced by both the AFP and the ice crystals to form the anchored clathrate motif, which binds TmAFP to the ice surface, resulting in a local increase in the curvature of the ice surface, thereby inhibiting the growth of ice. In this study, three stages, namely, promotion, adsorption, and inhibition, are observed in the complete process of TmAFP inhibiting ice growth, and the synergistic mechanism between protein and ice crystals is revealed. The results are helpful for the design of antifreeze proteins and bioinspired antifreeze materials with superior performance.

Effect of Graphene on Ice Polymorph

Recently, ice with stacking disorder structure, consisting of random sequences of cubic ice (Ic) and hexagonal ice (Ih) layers, was reported to be more stable than pure Ih/Ic. Due to a much lower free energy barrier of heterogeneous nucleation, in practice, the freezing process of water is controlled by heterogeneous nucleation triggered by an external medium. Therefore, we carry out molecular dynamic simulations to explore how ice polymorphism depends on the lattice structure of the crystalline substrates on which the ice is grown, focusing on the primary source of atmospheric aerosols, carbon materials. It turns out that, during the nucleation stage, the polymorph of ice nuclei is strongly affected by graphene substrates. For ice nucleation on graphene, we find Ih is the dominant polymorph. This can be attributed to structural similarities between graphene and basal face of Ih. Our results also suggest that the substrate only affects the polymorph of ice close to the graphene surface, with the preference for Ih diminishing as the ice layer grows.

Fcc vs. hcp competition in colloidal hard-sphere nucleation: on their relative stability, interfacial free energy and nucleation rate

Hard-sphere crystallization has been widely investigated over the last six decades by means of colloidal suspensions and numerical methods. However, some aspects of its nucleation behaviour are still under debate. Here, we provide a detailed computational characterisation of the polymorphic nucleation competition between the face-centered cubic (fcc) and the hexagonal-close packed (hcp) hard-sphere crystal phases. By means of several state-of-the-art simulation techniques, we evaluate the melting pressure, chemical potential difference, interfacial free energy and nucleation rate of these two polymorphs, as well as of a random stacking mixture of both crystals. Our results highlight that, despite the fact that both polymorphs have very similar stability, the interfacial free energy of the hcp phase could be marginally higher than that of the fcc solid, which in consequence, mildly decreases its propensity to nucleate from the liquid compared to the fcc phase. Moreover, we analyse the abundance of each polymorph in grown crystals from different types of inserted nuclei: fcc, hcp and stacking disordered fcc/hcp seeds, as well as from those spontaneously emerged from brute force simulations. We find that post-critical crystals fundamentally grow maintaining the polymorphic structure of the critical nucleus, at least until moderately large sizes, since the only crystallographic orientation that allows stacking close-packed disorder is the fcc (111) plane, or equivalently the hcp (0001) one. Taken together, our results contribute with one more piece to the intricate puzzle of colloidal hard-sphere crystallization.