Effects of surface interactions on heterogeneous ice nucleation for a monatomic water model

Unraveling Ice-Solid Interface Rupture Dynamics: Insights from Molecular Dynamics Simulations

Unwanted icing on exposed surfaces poses significant risks, driving the quest for effective anti-icing mechanisms. While fracture mechanics concepts have been developed for designing coatings that weaken the ice-solid interface on soft surfaces, the factors that dictate ice adhesion strength and its counterpart, ice removal force, on hard surfaces remain poorly understood. In this study, we employ molecular dynamics simulations to investigate the interface rupture between ice and a hard solid substrate. The results indicate that the ice adhesion strength is contingent on the length of the ice cube. By examining the shearing behavior, we reveal a nanoscale critical force-bearing length. The shear force required to detach the ice scales proportionally with the length of the ice cube when it is smaller than the critical length. Once the ice cube length exceeds the critical length, the shear force stabilizes at a constant maximum value, revealing the existence of a maximum ice-removal force. The results align with the so-called strength versus toughness-controlled deicing regimes and are in agreement with cohesive zone modeling at the continuum length scale and recent experimental results. Our results extend this understanding to the nanoscale, confirming consistency between macro and micro scales. This consistency suggests that the toughness of the ice-solid interface is intrinsically governed by ice-surface interactions. By unraveling key intrinsic factors and their scale-dependent effects on the interface rupture of ice on surfaces, this study lays a solid theoretical foundation for the design and fabrication of next-generation anti-icing surfaces.

Effect of substrate mismatch, orientation, and flexibility on heterogeneous ice nucleation

Heterogeneous nucleation is the main path to ice formation on Earth. The ice nucleating ability of a certain substrate is mainly determined by both molecular interactions and the structural mismatch between the ice and the substrate lattices. We focus on the latter factor using molecular simulations of the mW model. Quantifying the effect of structural mismatch alone is challenging due to its coupling with molecular interactions. To disentangle both the factors, we use a substrate composed of water molecules in such a way that any variation on the nucleation temperature can be exclusively ascribed to the structural mismatch. We find that a 1% increase in structural mismatch leads to a decrease of ∼4 K in the nucleation temperature. We also analyze the effect of orientation of the substrate with respect to the liquid. The three main ice orientations (basal, primary prism, and secondary prism) have a similar ice nucleating ability. We finally assess the effect of lattice flexibility by comparing substrates where molecules are immobile to others where a certain freedom to fluctuate around the lattice positions is allowed. Interestingly, we find that the latter type of substrate is more efficient in nucleating ice because it can adapt its structure to that of ice.

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.

Phase diagrams-Why they matter and how to predict them

Understanding the thermodynamic stability and metastability of materials can help us to, for example, gauge whether crystalline polymorphs in pharmaceutical formulations are likely to be durable. It can also help us to design experimental routes to novel phases with potentially interesting properties. In this Perspective, we provide an overview of how thermodynamic phase behavior can be quantified both in computer simulations and machine-learning approaches to determine phase diagrams, as well as combinations of the two. We review the basic workflow of free-energy computations for condensed phases, including some practical implementation advice, ranging from the Frenkel-Ladd approach to thermodynamic integration and to direct-coexistence simulations. We illustrate the applications of such methods on a range of systems from materials chemistry to biological phase separation. Finally, we outline some challenges, questions, and practical applications of phase-diagram determination which we believe are likely to be possible to address in the near future using such state-of-the-art free-energy calculations, which may provide fundamental insight into separation processes using multicomponent solvents.

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.

Multivalent Surface Cations Enhance Heterogeneous Freezing of Water on Muscovite Mica

Heterogeneous ice nucleation is a crucial phenomenon in various fields of fundamental and applied science. We investigate the effect of surface cations on freezing of water on muscovite mica. Mica is unique in that the exposed ion on its surface can be readily and easily exchanged without affecting other properties such as surface roughness. We investigate freezing on natural (K⁺) mica and mica in which we have exchanged K⁺ for Al³⁺, Mg²⁺, Ca²⁺, and Sr²⁺. We find that liquid water freezes at higher temperatures when ions of higher valency are present on the surface, thus exposing more of the underlying silica layer. Our data also show that the size of the ion affects the characteristic freezing temperature. Using molecular dynamics simulations, we investigate the effects that the ion valency and exposed silica layer have on the behavior of water on the surface. The results indicate that multivalent cations enhance the probability of forming large clusters of hydrogen bonded water molecules that are anchored by the hydration shells of the cations. These clusters also have a large fraction of free water that can reorient to take ice-like configurations, which are promoted by the regions on mica devoid of the ions. Thus, these clusters could serve as seedbeds for ice nuclei. The combined experimental and simulation studies shed new light on the influence of surface ions on heterogeneous ice nucleation.

Hydrogen polarity of interfacial water regulates heterogeneous ice nucleation

Using all-atomic molecular dynamics (MD) simulations, we show that the structure of interfacial water (IW) induced by substrates characterizes the ability of a substrate to nucleate ice. We probe the shape and structure of ice nuclei and the corresponding supercooling temperatures to measure the ability of IW with various hydrogen polarities for ice nucleation, and find that the hydrogen polarization of IW even with the ice-like oxygen lattice increases the contact angle of the ice nucleus on IW, thus lifting the free energy barrier of heterogeneous ice nucleation. The results show that not only the oxygen lattice order but the hydrogen disorder of IW on substrates are required to effectively facilitate the freezing of top water.

One-dimensional water nanowires induced by electric fields

Self-aggregation of water vapour molecules under external electric fields is systemically investigated by using molecular dynamics simulations. It is found that small water clusters aggregate into one-dimensional water nanowires along the electric field direction. The electric field strength plays a crucial role in tuning the nanowire structure. Under relatively weak electric fields such as E = 0.1 V Å^-1, square and pentagonal prism-like structures are preferred; when intermediate strength electric fields are applied (E = 1.0 V Å^-1), water nanowires featuring a disordered mixture of four-, five- and six-membered rings are formed; and an open ordered structure which is reminiscent of two-dimensional (2D) ice is observed when the field strength becomes very high (E > 3.0 V Å^-1). Bond parameter analysis based on density-functional theory calculations shows that the electric field affects anisotropically the conformation of water molecules as well as the hydrogen-bond properties. Along the electric field, the H-O bond is stretched and the hydrogen bond shrinks with field strength in contrast to the changes perpendicular to the electric field. As a result, the hydrogen bonding is enhanced along the electric field. Under very high electric fields, the anisotropic hydrogen-bond network opens up via breaking of the bonds perpendicular to the electric field and ultimately relaxes into a loose quasi-2D ordered network.

Unravelling the origins of ice nucleation on organic crystals

Organic molecules such as steroids or amino acids form crystals that can facilitate the formation of ice - arguably the most important phase transition on earth. However, the origin of the ice nucleating ability of organic crystals is still largely unknown. Here, we combine experiments and simulations to unravel the microscopic details of ice formation on cholesterol, a prototypical organic crystal widely used in cryopreservation. We find that cholesterol - which is also a substantial component of cell membranes - is an ice nucleating agent more potent than many inorganic substrates, including the mineral feldspar (one of the most active ice nucleating materials in the atmosphere). Scanning electron microscopy measurements reveal a variety of morphological features on the surfaces of cholesterol crystals: this suggests that the topography of the surface is key to the broad range of ice nucleating activity observed (from -4 to -20 °C). In addition, we show via molecular simulations that cholesterol crystals aid the formation of ice nuclei in a unconventional fashion. Rather than providing a template for a flat ice-like contact layer (as found in the case of many inorganic substrates), the flexibility of the cholesterol surface and its low density of hydrophilic functional groups leads to the formation of molecular cages involving both water molecules and terminal hydroxyl groups of the cholesterol surface. These cages are made of 6- and, surprisingly, 5-membered hydrogen bonded rings of water and hydroxyl groups that favour the nucleation of hexagonal as well as cubic ice (a rare occurrence). We argue that the phenomenal ice nucleating activity of steroids such as cholesterol (and potentially of many other organic crystals) is due to (i) the ability of flexible hydrophilic surfaces to form unconventional ice-templating structures and (ii) the different nucleation sites offered by the diverse topography of the crystalline surfaces. These findings clarify how exactly organic crystals promote the formation of ice, thus paving the way toward deeper understanding of ice formation in soft and biological matter - with obvious reverberations on atmospheric science and cryobiology.

Heterogeneous seeded molecular dynamics as a tool to probe the ice nucleating ability of crystalline surfaces

Ice nucleation plays a significant role in a large number of natural and technological processes, but it is challenging to investigate experimentally because of the small time scales (ns) and short length scales (nm) involved. On the other hand, conventional molecular simulations struggle to cope with the relatively long time scale required for critical ice nuclei to form. One way to tackle this issue is to take advantage of free energy or path sampling techniques. Unfortunately, these are computationally costly. Seeded molecular dynamics is a much less demanding alternative that has been successfully applied already to study the homogeneous freezing of water. However, in the case of heterogeneous ice nucleation, nature's favourite route to form ice, an array of suitable interfaces between the ice seeds and the substrate of interest has to be built, and this is no trivial task. In this paper, we present a Heterogeneous SEEDing (HSEED) approach which harnesses a random structure search framework to tackle the ice-substrate challenge, thus enabling seeded molecular dynamics simulations of heterogeneous ice nucleation on crystalline surfaces. We validate the HSEED framework by investigating the nucleation of ice on (i) model crystalline surfaces, using the coarse-grained mW model, and (ii) cholesterol crystals, employing the fully atomistic TIP4P/ice water model. We show that the HSEED technique yields results in excellent agreement with both metadynamics and forward flux sampling simulations. Because of its computational efficiency, the HSEED method allows one to rapidly assess the ice nucleation ability of whole libraries of crystalline substrates-a long-awaited computational development in, e.g., atmospheric science.

Hybrid Monte Carlo with LAMMPS

We describe a strategy for performing canonical and isothermal-isobaric ensemble hybrid Monte Carlo (HMC) simulations with the widely-used Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) molecular dynamics (MD) software package. The overall workflow for the HMC simulations is handled using an external Python driver script, which invokes LAMMPS’ library interface to perform numerically intensive tasks such as MD integration. We document several rigorous consistency checks that have been used to validate our HMC implementation. We also demonstrate that our approach can be readily extended to implement biased HMC sampling schemes for computing free energies. Codes and input files from the documented examples are available on the web.

Is Water at the Graphite Interface Vapor-like or Ice-like?

Graphitic surfaces are the main component of soot, a major constituent of atmospheric aerosols. Experiments indicate that soots of different origins display a wide range of abilities to heterogeneously nucleate ice. The ability of pure graphite to nucleate ice in experiments, however, seems to be almost negligible. Nevertheless, molecular simulations with the monatomic water model mW with water-carbon interactions parameterized to reproduce the experimental contact angle of water on graphite predict that pure graphite nucleates ice. According to classical nucleation theory, the ability of a surface to nucleate ice is controlled by the binding free energy between ice immersed in liquid water and the surface. To establish whether the discrepancy in freezing efficiencies of graphite in mW simulations and experiments arises from the coarse resolution of the model or can be fixed by reparameterization, it is important to elucidate the contributions of the water-graphite, water-ice, and ice-water interfaces to the free energy, enthalpy, and entropy of binding for both water and the model. Here we use thermodynamic analysis and free energy calculations to determine these interfacial properties. We demonstrate that liquid water at the graphite interface is not ice-like or vapor-like: it has similar free energy, entropy, and enthalpy as water in the bulk. The thermodynamics of the water-graphite interface is well reproduced by the mW model. We find that the entropy of binding between graphite and ice is positive and dominated, in both experiments and simulations, by the favorable entropy of reducing the ice-water interface. Our analysis indicates that the discrepancy in freezing efficiencies of graphite in experiments and the simulations with mW arises from the inability of the model to simultaneously reproduce the contact angle of liquid water on graphite and the free energy of the ice-graphite interface. This transferability issue is intrinsic to the resolution of the model, and arises from its lack of rotational degrees of freedom.

Heterogeneous Ice Nucleation: Interplay of Surface Properties and Their Impact on Water Orientations

Ice is ubiquitous in nature, and heterogeneous ice nucleation is the most common pathway of ice formation. How surface properties affect the propensity to observe ice nucleation on that surface remains an open question. We present results of molecular dynamics studies of heterogeneous ice nucleation on model surfaces. The models surfaces considered emulate the chemistry of kaolinite, an abundant component of mineral dust. We investigate the interplay of surface lattice and hydrogen bonding properties in affecting ice nucleation. We find that lattice matching and hydrogen bonding are necessary but not sufficient conditions for observing ice nucleation at these surfaces. We correlate this behavior to the orientations sampled by the metastable supercooled water in contact with the surfaces. We find that ice is observed in cases where water molecules not only sample orientations favorable for bilayer formation but also do not sample unfavorable orientations. This distribution depends on both surface-water and water-water interactions and can change with subtle modifications to the surface properties. Our results provide insights into the diverse behavior of ice nucleation observed at different surfaces and highlight the complexity in elucidating heterogeneous ice nucleation.

Lattice-Matched Epitaxial Growth of Organic Heterostructures for Integrated Optoelectronic Application

Development of nanowire photonics requires integration of different nanowire components into highly ordered functional heterostructures. Herein, we report a sequential self-assembly of binary molecular components into branched nanowire heterostructures (BNHs) via lattice-matched epitaxial growth, in which the microribbon backbone of 2,5-Bis(5-tert-butyl-2-benzoxazolyl)thiophene (BBOT) functions as blue-emitting microlaser source to pump the nanowire branches of BODIPY. By constructing Au electrodes on both branch sides and measuring the photocurrent in them, we successfully realize the integration of an organic laser and a power meter in a single device. This work provides a new insight into the integration of 1D organic nanostructures into BNHs for realizing organic multifunctional photonic devices.

Ice Nucleation Efficiency of Hydroxylated Organic Surfaces Is Controlled by Their Structural Fluctuations and Mismatch to Ice

Heterogeneous nucleation of ice induced by organic materials is of fundamental importance for climate, biology, and industry. Among organic ice-nucleating surfaces, monolayers of long chain alcohols are particularly effective, while monolayers of fatty acids are significantly less so. As these monolayers expose to water hydroxyl groups with an order that resembles the one in the basal plane of ice, it was proposed that lattice matching between ice and the surface controls their ice-nucleating efficiency. Organic monolayers are soft materials and display significant fluctuations. It has been conjectured that these fluctuations assist in the nucleation of ice. Here we use molecular dynamic simulations and laboratory experiments to investigate the relationship between the structure and fluctuations of hydroxylated organic surfaces and the temperature at which they nucleate ice. We find that these surfaces order interfacial water to form domains with ice-like order that are the birthplace of ice. Both mismatch and fluctuations decrease the size of the preordered domains and monotonously decrease the ice freezing temperature. The simulations indicate that fluctuations depress the freezing efficiency of monolayers of alcohols or acids to half the value predicted from lattice mismatch alone. The model captures the experimental trend in freezing efficiencies as a function of chain length and predicts that alcohols have higher freezing efficiency than acids of the same chain length. These trends are mostly controlled by the modulation of the structural mismatch to ice. We use classical nucleation theory to show that the freezing efficiencies of the monolayers are directly related to their free energy of binding to ice. This study provides a general framework to relate the equilibrium thermodynamics of ice binding to a surface and the nonequilibrium ice freezing temperature and suggests that these could be predicted from the structure of interfacial water.

Heterogeneous Nucleation of an n-Alkane on Tetrahedrally Coordinated Crystals

Heterogeneous nucleation refers to the propensity for phase transformations to initiate preferentially on foreign surfaces, such as vessel walls, dust particles, or formulation additives. In crystallization, the form of the initial nucleus has ramifications for the crystallographic form, morphology, and properties of the resulting solid. Nevertheless, the discovery and design of nucleating agents remains a matter of trial and error because of the very small spatiotemporal scales over which the critical nucleus is formed and the extreme difficulty of examining such events empirically. Using molecular dynamics simulations, we demonstrate a method for the rapid screening of entire families of materials for activity as nucleating agents and for characterizing their mechanism of action. The method is applied to the crystallization of n-pentacontane, a model surrogate for polyethylene, on the family of tetrahedrally coordinated crystals, including diamond and silicon. A systematic variation of parameters in the interaction potential permits a comprehensive, physically based screening of nucleating agents in this class of materials, including both real and hypothetical candidates. The induction time for heterogeneous nucleation is shown to depend strongly on crystallographic registry between the nucleating agent and the critical nucleus, indicative of an epitaxial mechanism in this class of materials. Importantly, the severity of this registry requirement weakens with decreasing rigidity of the substrate and increasing strength of attraction to the surface of the nucleating agent. Employing this method, a high-throughput computational screening of nucleating agents becomes possible, facilitating the discovery of novel nucleating agents within a broad "materials genome" of possible additives.

Silicon-wall interfacial free energy via thermodynamics integration

We compute the interfacial free energy of a silicon system in contact with flat and structured walls by molecular dynamics simulation. The thermodynamics integration method, previously applied to Lennard-Jones potentials [R. Benjamin and J. Horbach, J. Chem. Phys. 137, 044707 (2012)], has been extended and implemented in Tersoff potentials with two-body and three-body interactions taken into consideration. The thermodynamic integration scheme includes two steps. In the first step, the bulk Tersoff system is reversibly transformed to a state where it interacts with a structureless flat wall, and in a second step, the flat structureless wall is reversibly transformed into an atomistic SiO₂ wall. Interfacial energies for liquid silicon-wall interfaces and crystal silicon-wall interfaces have been calculated. The calculated interfacial energies have been employed to predict the nucleation mechanisms in a slab of liquid silicon confined by two walls and compared with MD simulation results.

Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations

The nucleation of crystals in liquids is one of nature's most ubiquitous phenomena, playing an important role in areas such as climate change and the production of drugs. As the early stages of nucleation involve exceedingly small time and length scales, atomistic computer simulations can provide unique insights into the microscopic aspects of crystallization. In this review, we take stock of the numerous molecular dynamics simulations that, in the past few decades, have unraveled crucial aspects of crystal nucleation in liquids. We put into context the theoretical framework of classical nucleation theory and the state-of-the-art computational methods by reviewing simulations of such processes as ice nucleation and the crystallization of molecules in solutions. We shall see that molecular dynamics simulations have provided key insights into diverse nucleation scenarios, ranging from colloidal particles to natural gas hydrates, and that, as a result, the general applicability of classical nucleation theory has been repeatedly called into question. We have attempted to identify the most pressing open questions in the field. We believe that, by improving (i) existing interatomic potentials and (ii) currently available enhanced sampling methods, the community can move toward accurate investigations of realistic systems of practical interest, thus bringing simulations a step closer to experiments.

Can Ice-Like Structures Form on Non-Ice-Like Substrates? The Example of the K-feldspar Microcline

Feldspar minerals are the most common rock formers in Earth's crust. As such they play an important role in subjects ranging from geology to climate science. An atomistic understanding of the feldspar structure and its interaction with water is therefore desirable, not least because feldspar has been shown to dominate ice nucleation by mineral dusts in Earth's atmosphere. The complexity of the ice/feldspar interface arising from the numerous chemical motifs expressed on the surface makes it a challenging system. Here we report a comprehensive study of this challenging system with ab initio density functional theory calculations. We show that the distribution of Al atoms, which is crucial for the dissolution kinetics of tectosilicate minerals, differs significantly between the bulk environment and on the surface. Furthermore, we demonstrate that water does not form ice-like overlayers in the contact layer on the most easily cleaved (001) surface of K-feldspar. We do, however, identify contact layer structures of water that induce ice-like ordering in the second overlayer. This suggests that even substrates without an apparent match with the ice structure may still act as excellent ice nucleating agents.

The Many Faces of Heterogeneous Ice Nucleation: Interplay Between Surface Morphology and Hydrophobicity

What makes a material a good ice nucleating agent? Despite the importance of heterogeneous ice nucleation to a variety of fields, from cloud science to microbiology, major gaps in our understanding of this ubiquitous process still prevent us from answering this question. In this work, we have examined the ability of generic crystalline substrates to promote ice nucleation as a function of the hydrophobicity and the morphology of the surface. Nucleation rates have been obtained by brute-force molecular dynamics simulations of coarse-grained water on top of different surfaces of a model fcc crystal, varying the water-surface interaction and the surface lattice parameter. It turns out that the lattice mismatch of the surface with respect to ice, customarily regarded as the most important requirement for a good ice nucleating agent, is at most desirable but not a requirement. On the other hand, the balance between the morphology of the surface and its hydrophobicity can significantly alter the ice nucleation rate and can also lead to the formation of up to three different faces of ice on the same substrate. We have pinpointed three circumstances where heterogeneous ice nucleation can be promoted by the crystalline surface: (i) the formation of a water overlayer that acts as an in-plane template; (ii) the emergence of a contact layer buckled in an ice-like manner; and (iii) nucleation on compact surfaces with very high interaction strength. We hope that this extensive systematic study will foster future experimental work aimed at testing the physiochemical understanding presented herein.

Molecular simulations of heterogeneous ice nucleation. II. Peeling back the layers

Coarse grained molecular dynamics simulations are presented in which the sensitivity of the ice nucleation rate to the hydrophilicity of a graphene nanoflake is investigated. We find that an optimal interaction strength for promoting ice nucleation exists, which coincides with that found previously for a face centered cubic (111) surface. We further investigate the role that the layering of interfacial water plays in heterogeneous ice nucleation and demonstrate that the extent of layering is not a good indicator of ice nucleating ability for all surfaces. Our results suggest that to be an efficient ice nucleating agent, a surface should not bind water too strongly if it is able to accommodate high coverages of water.

Molecular simulations of heterogeneous ice nucleation. I. Controlling ice nucleation through surface hydrophilicity

Ice formation is one of the most common and important processes on earth and almost always occurs at the surface of a material. A basic understanding of how the physicochemical properties of a material's surface affect its ability to form ice has remained elusive. Here, we use molecular dynamics simulations to directly probe heterogeneous ice nucleation at a hexagonal surface of a nanoparticle of varying hydrophilicity. Surprisingly, we find that structurally identical surfaces can both inhibit and promote ice formation and analogous to a chemical catalyst, it is found that an optimal interaction between the surface and the water exists for promoting ice nucleation. We use our microscopic understanding of the mechanism to design a modified surface in silico with enhanced ice nucleating ability.

Ice Nucleation Properties of Oxidized Carbon Nanomaterials

Heterogeneous ice nucleation is an important process in many fields, particularly atmospheric science, but is still poorly understood. All known inorganic ice nucleating particles are relatively large in size and tend to be hydrophilic. Hence it is not obvious that carbon nanomaterials should nucleate ice. However, in this paper we show that four different readily water-dispersible carbon nanomaterials are capable of nucleating ice. The tested materials were carboxylated graphene nanoflakes, graphene oxide, oxidized single walled carbon nanotubes and oxidized multiwalled carbon nanotubes. The carboxylated graphene nanoflakes have a diameter of ∼30 nm and are among the smallest entities observed so far to nucleate ice. Overall, carbon nanotubes were found to nucleate ice more efficiently than flat graphene species, and less oxidized materials nucleated ice more efficiently than more oxidized species. These well-defined carbon nanomaterials may pave the way to bridging the gap between experimental and computational studies of ice nucleation.

Stacking disorder in ice I

Traditionally, ice I was considered to exist in two well-defined crystalline forms at ambient pressure: stable hexagonal ice (ice Ih) and metastable cubic ice (ice Ic). However, it is becoming increasingly evident that what has been called cubic ice in the past does not have a structure consistent with the cubic crystal system. Instead, it is a stacking-disordered material containing cubic sequences interlaced with hexagonal sequences, which is termed stacking-disordered ice (ice Isd). In this article, we summarise previous work on ice with stacking disorder including ice that was called cubic ice in the past. We also present new experimental data which shows that ice which crystallises after heterogeneous nucleation in water droplets containing solid inclusions also contains stacking disorder even at freezing temperatures of around -15 °C. This supports the results from molecular simulations, that the structure of ice that crystallises initially from supercooled water is always stacking-disordered and that this metastable ice can transform to the stable hexagonal phase subject to the kinetics of recrystallization. We also show that stacking disorder in ice which forms from water droplets is quantitatively distinct from ice made via other routes. The emerging picture of ice I is that of a very complex material which frequently contains stacking disorder and this stacking disorder can vary in complexity depending on the route of formation and thermal history.

Ice nucleation on carbon surface supports the classical theory for heterogeneous nucleation

The prevalence of heterogeneous nucleation in nature was explained qualitatively by the classical theory for heterogeneous nucleation established over more than 60 years ago, but the quantitative validity and the key conclusions of the theory have remained unconfirmed. Employing the forward flux sampling method and the coarse-grained water model (mW), we explicitly computed the heterogeneous ice nucleation rates in the supercooled water on a graphitic surface at various temperatures. The independently calculated ice nucleation rates were found to fit well according to the classical theory for heterogeneous nucleation. The fitting procedure further yields the estimate of the potency factor, which measures the ratio of the heterogeneous nucleation barrier to the homogeneous nucleation barrier. Remarkably, the estimated potency factor agrees quantitatively with the volumetric ratio of the critical nuclei between the heterogeneous and homogeneous nucleation. Our numerical study thus provides a strong support to the quantitative power of the theory and allows understanding ice nucleation behaviors under the most relevant freezing conditions.