Melting the ice: on the relation between melting temperature and size for nanoscale ice crystals

Freezing of water and melting of ice: theoretical modeling at the nanoscale

Freezing of water and melting of ice at the nanoscale play critical roles in science and technology fields, including aviation systems, infrastructures, and other broad spectrum of technologies. To cope with the icing challenge, nanoscale anti-icing surface technology has been developed. The freezing and melting temperatures can be tailored by manipulating the size (the radius of water or ice); however, it lacks systemic research. In this work, the size effect on the melting temperature of ice nanocrystals was first established, which considered the variation of bond energy and equivalent heat energy from the perspective of the force-heat equivalence energy density principle. Based on the heterogeneous nucleation mode and by further considering the size and temperature effects on the interface energy involved solid-liquid energy and liquid-vapor energy as well as the above developed melting temperature model, another model is established to accurately predict the freezing temperature of water nanodroplets. The parameters required by the two models established in this paper have a clear physical meaning and establish the quantitative relationships among freezing temperature, melting temperature, surface stress, interface energy, and other thermodynamic parameters. The agreement between model prediction and experimental simulation data confirms the validity and universality of the established models. The higher prediction accuracy of this work compared to the other theoretical models, due to the more detailed consideration and the reference point, captures the errors introduced by the experiment or simulation. This study contributes to a deeper understanding of the underlying mechanism of freezing of water and melting of ice nanocrystals and provides theoretical guidance for the design of cryopreservation systems and anti-icing systems for aviation.

Preferential Ordering and Organization of Hydration Water Favor Nucleation of Ice by Ice-Nucleating Proteins over Antifreeze Proteins

Bacteria containing ice-nucleating proteins (INPs) evolved in nature to nucleate ice at the high sub-zero ambiance. The ability of the INPs to induce order in the hydration layer and their aggregation propensity appear to be key factors of their ice nucleation abilities. However, the mechanism of the process of ice nucleation by INPs is yet to be understood clearly. Here, we have performed all-atom molecular dynamics simulations and analyzed the structure and dynamics of the hydration layer around the proposed ice-nucleating surface of a model INP. Results are compared with the hydration of a topologically similar non-ice-binding protein (non-IBP) and another ice-growth inhibitory antifreeze protein (sbwAFP). We observed that the hydration structure around the ice-nucleating surface of INP is highly ordered and the dynamics of the hydration water are slower, compared to the non-IBP. Even the ordering of the hydration layer is more evident around the ice-binding surface of INP, compared to the antifreeze protein sbwAFP. Particularly with increasing repeat units of INP, we observe an increased population of ice-like water. Interestingly, the distances between the hydroxyl groups of the threonine ladder and its associated channel water of the ice-binding surface (IBS) of INP in the X and Y direction mimic the oxygen atom distances of the basal plane of hexagonal ice. However, the structural synergies between the hydroxyl group distances of the threonine ladder and its associated channel water of the IBS of sbwAFP and oxygen atom distances of the basal plane are less evident. This difference makes the IBS of the INP a better template for ice nucleation than AFP, although both of them bind to the ice surface efficiently.

Salt Enrichment and Dynamics in the Interface of Supercooled Aqueous Droplets

The interconversion reaction of NaCl between the contact-ion pair (CIP) and the solvent-separated ion pair (SSIP) as well as the free-ion state in cold droplets has not yet been investigated. We report direct computational evidence that the lower is the temperature, the closer to the surface the ion interconversion reaction takes place. In supercooled droplets the enrichment of the subsurface in salt becomes more evident. The stability of the SSIP relative to the CIP increases as the ion-pairing is transferred toward the droplet's outer layers. In the free-ion state, where the ions diffuse independently in the solution, the number density of Cl^- shows a broad maximum in the interior in addition to the well-known maximum in the surface. In the study of the reaction dynamics, we find a weak coupling between the interionic NaCl distance reaction coordinate and the solvent degrees of freedom, which contrasts with the diffusive crossing of the free energy barrier found in bulk solution modeling. The H₂O self-diffusion coefficient is found to be at least an order of magnitude larger than that in the bulk solution. We propose to exploit the enhanced surface ion concentration at low temperature to eliminate salts from droplets in native mass spectrometry ionization methods.

Premelting layer during ice growth: role of clusters

The premelting layer plays an important role in ice growth, but there is a significant gap in our knowledge between the atomistic premelting surface structure and the macroscopic growth mechanism. In this work, using large-scale molecular dynamics simulation, we reveal the existence of clusters on the premelting surface, as an intermediate feature bridging the gap. We show the spontaneous formation and evolution of clusters, and they form a stable distribution determined by the growth rate. We demonstrate how this stable distribution is related to the growth mode of ice, connected by the growth of clusters. We come to a bilayer-by-bilayer growth mode at simulation-reachable high growth rates, but another mechanism, namely "cluster stacking", is speculated to exist at lower growth rates. This work builds a connection between the microscopic structure of the premelting layer and the macroscopic growth of ice, making a step forward toward the full understanding of premelting and ice growth.

How do interfaces alter the dynamics of supercooled water?

The structure of liquid water in the proximity of an interface can deviate significantly from that of bulk water, with surface-induced structural perturbations typically converging to bulk values at about ∼1 nm from the interface. While these structural changes are well established it is, in contrast, less clear how an interface perturbs the dynamics of water molecules within the liquid. Here, through an extensive set of molecular dynamics simulations of supercooled bulk and interfacial water films and nano-droplets, we observe the formation of persistent, spatially extended dynamical domains in which the average mobility varies as a function of the distance from the interface. This is in stark contrast with the dynamical heterogeneity observed in bulk water, where these domains average out spatially over time. We also find that the dynamical response of water to an interface depends critically on the nature of the interface and on the choice of interface definition. Overall these results reveal a richness in the dynamics of interfacial water that opens up the prospect of tuning the dynamical response of water through specific modifications of the interface structure or confining material.

Clathrate Adhesion Induced by Quasi-Liquid Layer

The adhesive force of clathrates to surfaces is a century-old problem of pipeline blockage for the energy industry. Here, we provide new physical insight into the origin of this force by accounting for the existence of a quasi-liquid layer (QLL) on clathrate surfaces. To gain this insight, we measure the adhesive force between a tetrahydrofuran clathrate and a solid sphere. We detect a strong adhesion, which originates from a capillary bridge that is formed from a nanometer-thick QLL on the clathrate surface. The curvature of this capillary bridge is nanoscaled, causes a large negative Laplace pressure, and leads to a strong capillary attraction. The microscopic capillary bridge expands and consolidates over time. This dynamic behavior explains the time-dependent increase of measured capillary forces. The adhesive force decreases greatly upon increasing the roughness and the hydrophobicity of the sphere, which founds the fundamental basics for reducing clathrate adhesion by using surface coating.

A high-accuracy machine-learning water model for exploring water nanocluster structures

Water, the most important molecule on the Earth, possesses many essential and unique physical properties that are far from completely understood, partly due to serious difficulties in identifying the precise microscopic structures of water. Hence, identifying the structures of water nanoclusters is a fundamental and challenging issue for studies on the relationship between the macroscopic physical properties of water and its microscopic structures. For large-scale simulations (at the level of nm and ns) of water nanoclusters, a calculation method with simultaneous accuracy at the level of quantum chemistry and efficiency at the level of an empirical potential method is in great demand. Herein, a machine-learning (ML) water model was utilized to explore the microscopic structural features at different length scales for water nanoclusters with a size up to several nm. The ML water model can be employed to efficiently predict the structures of water nanoclusters with a similar accuracy to that of density functional theory and with substantially lower computational resource demands. To validate the low-lying structure search results with experimental spectral results, an ML water model combined with velocity autocorrelation function analysis was used to simulate the vibrational spectra of water nanoclusters with up to thousands of water molecules. By comparing the simulated and experimentally recorded vibrational spectra, the atomic structures determined by a simulation based on the ML water model are all verified. To demonstrate its ability to represent water's structural evolution at large length and time scales, the ML water model was employed to model the structural evolution during the crystal-liquid transition, and the phase transition temperatures of water clusters with different sizes were precisely predicted. The ML water model provides an efficient theoretical calculation tool for exploring the structures and physical properties of water and their relationships, especially for clusters with relatively large sizes and processes with relatively long durations.

Edge premelting of two-dimensional ices

The surface of a three-dimensional ice crystal naturally has a quasi-liquid layer (QLL) at temperatures below its bulk melting point, due to a phenomenon called surface premelting. Here, we show that the edges of a two-dimensional (2D) bilayer hexagonal ice adsorbed on solid surfaces undergo premelting as well, resulting in the formation of quasi-liquid bands (QLBs) at the edges. Our extensive molecular dynamics simulations show that the QLB exhibits structure and dynamics indistinguishable from the bilayer liquid phase, acting as a lower-dimensional analog of the QLL on the bulk ice. We further find that at low temperatures, the width of the QLBs at armchair-type edges of the 2D ice is almost identical to that at zigzag-type edges but becomes far greater than the latter at temperatures near the melting point. The chirality-dependent edge premelting of 2D ices should add an important new ingredient to the heterogeneity of premelting.

Water Mobility in the Interfacial Liquid Layer of Ice/Clay Nanocomposites

At solid/ice interfaces, a premelting layer is formed at temperatures below the melting point of bulk water. However, the structural and dynamic properties within the premelting layer have been a topic of intense debate. Herein, we determined the translational diffusion coefficient Dt of water in ice/clay nanocomposites serving as model systems for permafrost by quasi-elastic neutron scattering. Below the bulk melting point, a rapid decrease of Dt is found for charged hydrophilic vermiculite, uncharged hydrophilic kaolin, and more hydrophobic talc, reaching plateau values below -4 °C. At this temperature, Dt in the premelting layer is reduced up to a factor of two compared to supercooled bulk water. Adjacent to charged vermiculite the lowest water mobility was observed, followed by kaolin and the more hydrophobic talc. Results are explained by the intermolecular water interactions with different clay surfaces and interfacial segregation of the low-density liquid water (LDL) component.

Flash Brillouin Scattering: A Confocal Technique for Measuring Glass Transitions at High Scan Rates

Glass transition temperatures T _g are most commonly measured by differential scanning calorimetry, a method that has been extended to the flash scanning calorimetry (FSC) regime by reducing sample volumes. However, significant manual preparation effort can render FSC impractical for, e.g., local probing of spatially heterogeneous specimens. Another strategy can be to select a small volume by focusing down a laser beam, where Brillouin Light Scattering (BLS) is a proven method for confocal T _g measurement. Here, we introduce Flash Brillouin Scattering, which extends BLS to fast scan rates, achieved by periodically heating the probed region with an infrared laser. For comparison with conventional BLS, we first characterize T _g of pure glycerol, and show how rapid quenching produces a less packed glass with downshifted sound velocity. We then turn toward its aqueous solutions, which crystallize too fast for a nonflash approach, and demonstrate scan rates in excess of 10⁵ K/s. These results are of interest not only because glycerol is a model system for hydrogen-bonded glass formers, but also because of its applications as a cryoprotectant for frozen biological samples. Light scattering studies of the latter, currently limited to cryo-Raman spectroscopy, are likely to be complemented by the technique introduced here.

Anomalous Freezing of Low-Dimensional Water Confined in Graphene Nanowrinkles

Various properties of water are affected by confinement as the space-filling of the water molecules is very different from bulk water. In our study, we challenged the creation of a stable system in which water molecules are permanently locked in nanodimensional graphene traps. For that purpose, we developed a technique, nitrocellulose-assisted transfer of graphene grown by chemical vapor deposition, which enables capturing of the water molecules below an atomically thin graphene membrane structured into a net of regular wrinkles with a lateral dimension of about 4 nm. After successfully confining water molecules below a graphene monolayer, we employed cryogenic Raman spectroscopy to monitor the phase changes of the confined water as a function of the temperature. In our experiment system, the graphene monolayer structured into a net of fine wrinkles plays a dual role: (i) it enables water confinement and (ii) serves as an extremely sensitive probe for phase transitions involving water via graphene-based spectroscopic monitoring of the underlying water structure. Experimental findings were supported with classical and path integral molecular dynamics simulations carried out on our experimental system. Results of simulations show that surface premelting of the ice confined within the wrinkles starts at ∼200 K and the melting process is complete at ∼240 K, which is far below the melting temperature of bulk water ice. The processes correspond to changes in the doping and strain in the graphene tracked by Raman spectroscopy. We conclude that water can be confined between graphene structured into nanowrinkles and silica substrate and its phase transitions can be tracked via Raman spectral feature of the encapsulating graphene. Our study also demonstrated that peculiar behavior of liquids under spatial confinement can be inspected via the optical response of atomically thin graphene sensors.

Evidence of disruption of Si-rich microstructure in engineering-lightweight Al-12.2at.%Si alloy melt above liquidus temperature

The exploration of microstructures in high temperature alloy melts is important for manufacturing of metallic components but extremely challenging. Here, we report experimental evidence of the disruption of Si-rich microstructure in engineering-lightweight Al–12.2at.%Si alloy melt at 1100 °C, via melt-spinning (MS) of Al_1−xSi_x (x = 0.03,0.07,0.122,0.2) alloy melts from different initial melt temperatures, 800 °C and 1100 °C, under the super-high cooling rate of ~ 10⁶ °C/s, in cooperation with the small angle neutron scattering (SANS) measurement. Si particles in 1100 °C MS alloys are abnormally smaller and increased in number at Al–12.2at.%Si, compared with 800 °C MS alloys, which demonstrates the disruption of Si-rich microstructure in Al–12.2at.%Si alloy melt at 1100 °C. SANS experiment verifies that large quantities of small (0–10 nm) Si-rich microstructures and small quantities of large (10–240 nm) Si-rich microstructures exist in Al–12.2at.%Si alloy melt, and the large Si-rich microstructures disrupt into small Si-rich microstructures with increasing of melt temperature from 800 to 1100 °C. Microstructure analysis of the MS alloys indicates that the large Si-rich microstructures in Al–12.2at.%Si alloy melt are probably aggregates comprising multiple small Si-rich microstructures. This work also provides a pathway for the exploration of microstructures in other high temperature alloy melts.

Tailoring electric field standing waves in reflection-absorption infrared spectroscopy to enhance absorbance from adsorbates on ice surfaces

The spectroscopic detection of molecules adsorbed onto ice surfaces at coverages similar to those encountered under typical environmental conditions requires high surface selectivity and sensitivity that few techniques can afford. An experimental methodology allowing a significant enhancement in the absorbance from adsorbed molecules is demonstrated herein. It exploits Electric Field Standing Wave (EFSW) effects intrinsic to grazing incidence Reflection-Absorption Infrared (RAIR) spectroscopy, where film thickness dependent optical interferences occur between the multiple reflections of the IR beam at the film-vacuum and the substrate-film interfaces. In this case study, CH₄ is used as a probe molecule and is deposited on a 20 ML coverage dense amorphous solid water film adsorbed onto solid Ar underlayers of various thicknesses. We observe that, at thicknesses where destructive interferences coincide with the absorption features from the CH stretching and HCH bending vibrational modes of methane, their intensity increases by a factor ranging from 10 to 25. Simulations of the RAIR spectra of the composite stratified films using a classical optics model reproduce the Ar underlayer coverage dependent enhancements of the absorbance features from CH₄ adsorbed onto the ice surface. They also reveal that the enhancements occur when the square modulus of the total electric field at the film's surface reaches its minimum value. Exploiting the EFSW effect allows the limit of detection to be reduced to a coverage of (0.2 ± 0.2) ML CH₄, which opens up interesting perspectives for spectroscopic studies of heterogeneous atmospheric chemistry at coverages that are more representative of those found in the natural environment.

Interfacial premelting of ice in nano composite materials

We present a quantitative description of ice premelting in permafrost model systems. Experimental data on the interfacial premelting in ice/clay nano composites was obtained by high energy X-ray diffraction.

Enhanced structural disorder at a nanocrystalline ice surface

Enhanced structural disorder at the surface of nanocrystalline ice is studied by heterodyne-detected sum-frequency generation spectroscopy.

Why Is It So Difficult to Identify the Onset of Ice Premelting?

Premelting of ice at temperatures below 0 °C is of fundamental importance for environmental processes. Various experimental techniques have been used to investigate the temperature at which liquid-like water first appears at the ice-vapor interface, reporting onset temperatures from -160 to -2 °C. The signals that identify liquid-like order at the ice-vapor interface in these studies, however, do not show a sharp initiation with temperature. That is at odds with the expected first-order nature of surface phase transitions, and consistent with recent large-scale molecular simulations that show the first premelted layer to be sparse and to develop continuously over a wide range of temperatures. Here we perform a thermodynamic analysis to elucidate the origin of the continuous formation of the first layer of liquid at the ice-vapor interface. We conclude that a negative value of the line tension of the ice-liquid-vapor three-phase contact line is responsible for the continuous character of the transition and the sparse nature of the liquid-like domains in the incomplete first layer.

Thermodynamic and structural anomalies of water nanodroplets

Liquid water nanodroplets are important in earth's climate, and are valuable for studying supercooled water because they resist crystallisation well below the bulk freezing temperature. Bulk liquid water has well-known thermodynamic anomalies, such as a density maximum, and when supercooled is hypothesised to exhibit a liquid-liquid phase transition (LLPT) at elevated pressure. However, it is not known how these bulk anomalies might manifest themselves in nanodroplets. Here we show, using simulations of the TIP4P/2005 water model, that bulk anomalies occur in nanodroplets as small as 360 molecules. We also show that the Laplace pressure inside small droplets reaches 220 MPa at 180 K, conditions close to the LLPT of TIP4P/2005. While the density and pressure inside nanodroplets coincide with bulk values at moderate supercooling, we show that deviations emerge at lower temperature, as well as significant radial density gradients, which arise from and signal the approach to the LLPT.

Thermodynamic, structural, and dynamical properties of nano-confined water using SPC/E and TIP4P models by molecular dynamics simulations

Different morphologies of water molecules are confined between two parallel graphene surfaces.

Control of ice nucleation: freezing and antifreeze strategies

Water freezing remains a perennial topic of great relevance to many important aspects of our lives; from the climate to human society and from economics to medicine, frozen water profoundly influences our living environment and life activities.

Excess Hydrogen Bond at the Ice-Vapor Interface around 200 K

Phase-resolved sum-frequency generation measurements combined with molecular dynamics simulations are employed to study the effect of temperature on the molecular arrangement of water on the basal face of ice. The topmost monolayer, interrogated through its nonhydrogen-bonded, free O-H stretch peak, exhibits a maximum in surface H-bond density around 200 K. This maximum results from two competing effects: above 200 K, thermal fluctuations cause the breaking of H bonds; below 200 K, the formation of bulklike crystalline interfacial structures leads to H-bond breaking. Knowledge of the surface structure of ice is critical for understanding reactions occurring on ice surfaces and ice nucleation.

Premelting-Induced Smoothening of the Ice-Vapor Interface

We perform computer simulations of the quasiliquid layer of ice formed at the ice-vapor interface close to the ice Ih-liquid-vapor triple point of water. Our study shows that the two distinct surfaces bounding the film behave at small wavelengths as atomically rough and independent ice-water and water-vapor interfaces. For long wavelengths, however, the two surfaces couple, large scale parallel fluctuations are inhibited, and the ice-vapor interface becomes smooth. Our results could help explain the complex morphology of ice crystallites.

Water at Interfaces

The interfaces of neat water and aqueous solutions play a prominent role in many technological processes and in the environment. Examples of aqueous interfaces are ultrathin water films that cover most hydrophilic surfaces under ambient relative humidities, the liquid/solid interface which drives many electrochemical reactions, and the liquid/vapor interface, which governs the uptake and release of trace gases by the oceans and cloud droplets. In this article we review some of the recent experimental and theoretical advances in our knowledge of the properties of aqueous interfaces and discuss open questions and gaps in our understanding.

The microscopic features of heterogeneous ice nucleation may affect the macroscopic morphology of atmospheric ice crystals

It is surprisingly difficult to freeze water. Almost all ice that forms under "mild" conditions (temperatures > -40 degrees C) requires the presence of a nucleating agent--a solid particle that facilitates the freezing process--such as clay mineral dust, soot or bacteria. In a computer simulation, the presence of such ice nucleating agents does not necessarily alleviate the difficulties associated with forming ice on accessible timescales. Nevertheless, in this work we present results from molecular dynamics simulations in which we systematically compare homogeneous and heterogeneous ice nucleation, using the atmospherically important clay mineral kaolinite as our model ice nucleating agent. From our simulations, we do indeed find that kaolinite is an excellent ice nucleating agent but that contrary to conventional thought, non-basal faces of ice can nucleate at the basal face of kaolinite. We see that in the liquid phase, the kaolinite surface has a drastic effect on the density profile of water, with water forming a dense, tightly bound first contact layer. Monitoring the time evolution of the water density reveals that changes away from the interface may play an important role in the nucleation mechanism. The findings from this work suggest that heterogeneous ice nucleating agents may not only enhance the ice nucleation rate, but also alter the macroscopic structure of the ice crystals that form.

Size dependence of phase transitions in aerosol nanoparticles

Phase transitions of nanoparticles are of fundamental importance in atmospheric sciences, but current understanding is insufficient to explain observations at the nano-scale. In particular, discrepancies exist between observations and model predictions of deliquescence and efflorescence transitions and the hygroscopic growth of salt nanoparticles. Here we show that these discrepancies can be resolved by consideration of particle size effects with consistent thermodynamic data. We present a new method for the determination of water and solute activities and interfacial energies in highly supersaturated aqueous solution droplets (Differential Köhler Analysis). Our analysis reveals that particle size can strongly alter the characteristic concentration of phase separation in mixed systems, resembling the influence of temperature. Owing to similar effects, atmospheric secondary organic aerosol particles at room temperature are expected to be always liquid at diameters below ~20 nm. We thus propose and demonstrate that particle size should be included as an additional dimension in the equilibrium phase diagram of aerosol nanoparticles.

Although phase transitions are fundamental for understanding aerosol particles, current models are insufficient to explain observations at the nanoscale. Here, the authors present a method for investigating droplets, suggesting particle size is a key determinant in the phase diagram of nanoparticles.

Crystallization of confined water pools with radii greater than 1 nm in AOT reverse micelles

Freezing of water pools inside aerosol sodium bis(2-ethylhexyl) sulfosuccinate (AOT) reverse micelles has been investigated. Previous freezing experiments suffer from collision and fusion of AOT micelles and resultant loss of water from the water pool by shedding out during the cooling process. These phenomena have restricted the formation of ice to only when the radius of the water pool (Rw) is below 1 nm, and only amorphous ice has been observed. To overcome the size limitation, a combination of rapid cooling and a custom-made cell allowing thin sample loading is applied for instantaneous and homogeneous freezing. The freezing process is monitored with attenuated total reflection infrared spectroscopy (ATR-IR) measurements. A cooling rate of ca. -100 K/min and a sample thickness of ca. 50 μm overcomes the limitations mentioned above and allows the crystallization of water pools with larger radii (Rw > 1 nm). The corresponding ATR-IR spectra of the frozen water pools with Rw < 2.0 nm show similar features to the spectrum of metastable cubic ice (Ic). Further increase of the radius of the water pool (Rw > 2.0 nm), unfortunately, drastically decreased the integrated area of the ν(OH) band observed just after freezing, indicating the breakup of the micellar structure and shedding out of the water pool. In addition, it was revealed that Ic ice can also be formed in flexible organic self-assembled AOT reverse micelles for at least Rw ≤ ca. 2 nm, as well as in inorganic and solid materials with a pore radius of ca. 2 nm. The dependence of the phase transition temperature on the curvature of the reverse micelles is discussed from the viewpoint of the Gibbs-Thomson effect.

25th anniversary article: exploring nanoscaled matter from speciation to phase diagrams: metal phosphide nanoparticles as a case of study

The notions of nanoscale "phase speciation" and "phase diagram" are defined and discussed in terms of kinetic and thermodynamic controls, based on the case of metal phosphide nanoparticles. After an overview of the most successful synthetic routes for these exotic nanomaterials, the cases of InP, Ni2 P, Ni12 P5 and Pdx Py are discussed in detail to highlight the relationship between composition, structure, and size at the nanoscale. The influence of morphology is discussed next by comparing the behavior of Cu3 P nanophases with those of Nix Py , FeP/Fe2 P, and CoP/Co2 P. Perspectives provide the reader with methodological guidelines for further investigation of nanoscale "phase diagrams", and their use for optimized synthesis of new functional nanomaterials.

Sandwich crystals of butyl paraben

Sandwich crystals: one polymorph. Opaque middle layer: 0.1 μm scale size pores. Parallel outer layer: translucent crystalline layers.

Ice nucleation at the nanoscale probes no man's land of water

At a given thermodynamic condition, nucleation events occur at a frequency that scales with the volume of the system. Therefore at the nanoscale, one may expect to obtain supercooled liquids below the bulk homogeneous nucleation temperature. Here we report direct computational evidence that in supercooled water nano-droplets ice nucleation rates are strongly size dependent and at the nanoscale they are several orders of magnitude smaller than in bulk water. Using a thermodynamic model based on classical nucleation theory, we show that the Laplace pressure is partially responsible for the suppression of ice crystallization. Our simulations show that the nucleation rates found for droplets are similar to those of liquid water subject to a pressure of the order of the Laplace pressure within droplets. Our findings aid the interpretation of molecular beam experiments and support the hypothesis of surface crystallization of ice in microscopic water droplets in clouds.

Size of a crystal nucleus in the isothermal crystallization of supercooled liquid

We present an alternative to classical nucleation theory (CNT). We introduce a size-dependent surface energy into the total Gibbs free-energy of formation of a crystal (ΔG). We consider the free-energy in the core part of the total volume of crystal and the free-energy in the surface-layer part of it, separately, for the evaluation of ΔG. As a result, we present an explicit model to evaluate a characteristic size of an initial nucleus that differs from the critical nucleus of CNT, but whose temperature dependence agrees well with that reported for the temperature dependency initial fold length of isotactic polystyrene and polyethylene in the literature. Our model has fitted the experimental data in the literature with only one adjustable parameter that is defined as nucleation constant. The nucleation constant is the Gibbs free-energy difference between the crystal and supercooled liquid phases for the volume of initial nucleus. We also present an expression to approximate the evolution of free-energy in the surface-layer part of crystal during the crystal growth.