Ice Nucleation Rate Research Articles

Homogeneous Ice Nucleation Under Shear.

Homogeneous ice nucleation involving a water flow is subject to shear, which may greatly affect the ice nucleation rate. In this work, we investigate the homogeneous ice nucleation rate under shear through molecular dynamics simulations. It is found that the ice nucleation rate changes nonlinearly with varying shear rates and reaches a maximum at an intermediate shear rate. Such a behavior is determined by two distinct effects of shear rates. On the one hand, shear increases the free energy barrier for the nucleation, which hinders the ice nucleation. On the other hand, shear enhances the diffusion of water molecules, assists the adsorption of water molecules on the ice nucleus, and consequently promotes the growth of ice nucleus. The latter effect dominates at low shear rates, while the former effect becomes significant at high shear rates. The competition between these two effects leads to a non-monotonic dependence of the ice nucleation rate on the shear rate.

Technical note: Fundamental aspects of ice nucleation via pore condensation and freezing including Laplace pressure and growth into macroscopic ice

Abstract. Pore condensation and freezing (PCF) is an ice nucleation mechanism that explains ice formation at low ice supersaturation. It assumes that liquid water condenses in pores of solid aerosol particles below water saturation, as described by the Kelvin equation, followed by homogeneous ice nucleation when temperatures are below about 235 K or immersion freezing at higher temperatures, in case the pores contain active sites that induce ice nucleation. Porewater is under tension (negative pressure) below water saturation as described by the Young–Laplace equation. This negative pressure affects the ice nucleation rates and the stability of the pore ice. Here, pressure-dependent parameterizations of classical nucleation theory are developed to quantify the increase in homogeneous ice nucleation rates as a function of tension and to assess the critical diameter of pores that is required to accommodate ice at negative pressures. Growth of ice out of the pore into a macroscopic ice crystal requires ice supersaturation. This supersaturation as a function of the pore opening width is derived, assuming that the ice phase first grows as a spherical cap on top of the pore opening before it starts to expand laterally on the particle surface into a macroscopic ice crystal.

Bias‐Free Estimation of Ice Nucleation Efficiencies

AbstractIce nucleation efficiencies, expressed in terms of either the active site density or the ice nucleation rate coefficient, are widely used to estimate ice formation rates in atmospheric models. Most estimates are, however, subject to bias since composition and surface area variation between particles is commonly neglected. This may amount to several orders of magnitude error in active site densities and introduce substantial error in cloud freezing temperatures impacting the accuracy of atmospheric models. Here it is shown that by performing droplet freezing experiments, varying mean particle surface area along with the temperature removes such a bias. The proposed method offers, for the first time, a solution to the long‐standing problem of differentiating the “freezing rate” from the ice nucleation rate, or the apparent and the actual active site density of a material, and will likely improve the estimation of ice crystal formation rates in clouds.

Microscopic mechanism of ice nucleation: The effects of surface rough structure and wettability

It is significant to inhibit the formation of ice on solid surface under some occasions in industry. The origin of ice formation on solid surface is the heterogeneous ice nucleation, which has drawn a lot of research attention in the last decade. In this work, we investigated the effects of surface fraction, pillar height, and solid surface wettability on ice nucleation using molecular dynamics simulation. Compared with that of smooth surface, the ice nucleation rates on rough surface can be enhanced or inhibited depending on the groove size, which can be attributed to the status of water molecules confined between pillars. In addition, it is found that the ice nucleation rate can be significantly weakened by reducing the solid surface free energy. More importantly, when the surface free energy is low enough, a quenching-induced mobility of nanodroplet is observed, including wandering on the solid surface or jumping away. These findings can address the importance of the coupling effect of the gap width and height of pillars, together with the quenching-induced mobility, which we believe will be helpful to understand more molecular mechanisms of heterogeneous ice nucleation.

Investigation of Heterogeneous Ice Nucleation on the Micro-Cubic Structure Superhydrophobic Surface for Enhancing Icing-Delay Performance

The aim of this study is to explore the heterogeneous ice nucleation behavior based on controllable micro-cubic array structure surfaces from the statistic perspective. To this end, we firstly constructed a group of micro-cubic array structures on silicon substrates by a selective plasma etching technique. After grafting low-free-energy substance, the as-constructed micro-cubic array structure surfaces exhibited higher non-wettability with the water contact angle being up to 150°. On this basis, 500 cycles of freezing and melting processes were accurately recorded to analyze the instantaneous ice nucleation behavior according to the statistical results of freezing temperature. As a consequence, the statistical freezing temperature of the sample with micro-spacing distance of 40 μm is as low as −17.13°C. This microstructure configuration (conforming to Cassie-Baxter wetting regime) not only could entrap more air pockets, but also achieved lower solid-liquid contact area, resulting in lower ice nucleation rate (~2–3 orders of magnitude less than that on the flat substrate). Furthermore, the gradually increasing micro-spacing distance to 60 μm would induce the transition from CassieBaxter to Wenzel wetting state, leading to higher freezing probability and ice nucleation rate. The complete understanding on microstructure configuration improving the ice nucleation will lay the foundation stone for the microstructure design of ice-repellent materials.

Atomistic Simulation of Ice Nucleation on Silver Iodide (0001) Surfaces with Defects

Small particles of silver iodide (AgI) are known to have excellent ice nucleating capabilities and have been used in rain seeding applications. It is widely believed that the silver-terminated (0001) surface of β-AgI acts as a template for the basal plane of hexagonal ice. However, the (0001) surface of ionic crystals with the wurtzite structure is polar and will therefore exhibit reconstructions and defects. Here, we use atomistic molecular dynamics simulations to study how the presence of defects on AgI(0001) affects the rates and mechanism of heterogeneous ice nucleation at moderate supercooling at −10 °C. We consider AgI(0001) surfaces exhibiting vacancies, step edges, terraces, and pits and compare them to simulations of the corresponding ideal surface. We find that, while point defects have no significant effect on ice nucleation rates, step edges, terraces, and pits reduce both the nucleation and growth rates by up to an order of magnitude. The reduction of the ice nucleation rate correlates well with the fraction of the surface area around the defects where perturbations of the hydration layer hinder the formation of a critical ice nucleus.

Toward Improved Cloud-Phase Simulation with a Mineral Dust and Temperature-Dependent Parameterization for Ice Nucleation in Mixed-Phase Clouds

Abstract Mixed-phase clouds are frequently observed in the atmosphere. Here we present a parameterization for ice crystal concentration and ice nucleation rate based on parcel model simulations for mixed-phase stratocumulus clouds, as a complement to a previous parameterization for stratus clouds. The parcel model uses a singular (time independent) description for deposition nucleation and a time-dependent description for condensation nucleation and immersion freezing on mineral dust particles. The mineral dust and temperature-dependent parameterizations have been implemented in the Geophysical Fluid Dynamics Laboratory atmosphere model, version 4.0 (AM4.0) (new), while the standard AM4.0 (original) uses a temperature-dependent parameterization. Model simulations with the new and original AM4.0 show significant changes in cloud properties and radiative effects. In comparison to measurements, cloud-phase (i.e., liquid and ice partitioning) simulation appears to be improved in the new AM4.0. More supercooled liquid cloud is predicted in the new model, it is sustained even at temperatures lower than −25°C unlike in the original model. A more accurate accounting of ice nucleating particles and ice crystals is essential for improved cloud-phase simulation in the global atmosphere.

Low-voltage and -surface energy SWCNT/poly(dimethylsiloxane) (PDMS) nanocomposite film: Surface wettability for passive anti-icing and surface-skin heating for active deicing

Icing is a multiphase/multiscale/multiparameter physical process, and is of frequent occurrence when suitable conditions with temperature, pressure and humidity are met. In the present work, we prepared a series of PDMS-matrix nanocomposite films with different SWCNT contents, which were endowed with hydrophobicity based on the low-surface-energy PDMS matrix and the conductivity on the SWCNT filler. Furthermore, by etching the pillar-textured structure on its surface, the nanocomposite with 5.0 wt% SWCNT was given the superhydrophobicity. These nanocomposites can be easily switched from a hydrophobic anti-icing mode to an electro-thermal deicing mode by supplying a low voltage. Using non-contact infrared thermometry, we presented an analysis of the freezing phase transition process of a single water droplet on cooling surfaces with different wettability, and investigated their ice nucleation rate and macroscopic growth velocity on these surfaces. The ice-retarding capability of superhydrophobic nanocomposite surface subjected to lots of condensed droplets was also confirmed, and understanding in light of weak contact interaction with droplets. Also under consideration is the icephobicity after freezing in terms of ice shear strength. In addition, we performed a statistical analysis about the Joule heat distribution on nanocomposite surface, the results of which demonstrated that the nanocomposite could supply a suitable heating function for active deicing, demonstrating with an energy-input deicing experiment subsequently.

Temperature Dependence of Homogeneous Nucleation in Ice.

Ice nucleation is a process of great relevance in physics, chemistry, technology, and environmental sciences; much theoretical effort has been devoted to its understanding, but it still remains a topic of intense research. We shed light on this phenomenon by performing atomistic based simulations. Using metadynamics and a carefully designed set of collective variables, reversible transitions between water and ice are able to be simulated. We find that water freezes into a stacking disordered structure with the all-atom transferable intermolecular potential with 4 points/ice (TIP4P/ice) model, and the features of the critical nucleus of nucleation at the microscopic level are revealed. We have also estimated the ice nucleation rates along with other nucleation parameters at different undercoolings. Our results are in agreement with recent experimental and other theoretical works, and they confirm that nucleation is preceded by a large increase in tetrahedrally coordinated water molecules.

Homogeneous ice nucleation rates and crystallization kinetics in transiently-heated, supercooled water films from 188 K to 230 K.

The crystallization kinetics of transiently heated, nanoscale water films were investigated for 188 K < Tpulse < 230 K, where Tpulse is the maximum temperature obtained during a heat pulse. The water films, which had thicknesses ranging from approximately 15-30 nm, were adsorbed on a Pt(111) single crystal and heated with ∼10 ns laser pulses, which produced heating and cooling rates of ∼109-1010 K/s in the adsorbed water films. Because the ice growth rates have been measured independently, the ice nucleation rates could be determined by modeling the observed crystallization kinetics. The experiments show that the nucleation rate goes through a maximum at T = 216 K ± 4 K, and the rate at the maximum is 1029±1 m-3 s-1. The maximum nucleation rate reported here for flat, thin water films is consistent with recent measurements of the nucleation rate in nanometer-sized water drops at comparable temperatures. However, the nucleation rate drops rapidly at lower temperatures, which is different from the nearly temperature-independent rates observed for the nanometer-sized drops. At T ∼ 189 K, the nucleation rate for the current experiments is a factor of ∼104-5 smaller than the rate at the maximum. The nucleation rate also decreases for Tpulse > 220 K, but the transiently heated water films are not very sensitive to the smaller nucleation rates at higher temperatures. The crystallization kinetics are consistent with a "classical" nucleation and growth mechanism indicating that there is an energetic barrier for deeply supercooled water to convert to ice.

Ice formation and solvent nanoconfinement in protein crystals.

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

Enhancing and Impeding Heterogeneous Ice Nucleation through Nanogrooves

In this work, we investigate the effects of nanogrooves on heterogeneous ice nucleation (HIN) through molecular dynamics simulations. It is found that nanogrooves on a surface significantly alter the ice nucleation rate by more than 2 orders of magnitude. Depending on the width of the grooves, the nucleation rate can be enhanced or impeded compared with that on flat surfaces. For relatively large grooves, ice nucleation enhancement is observed when the effective groove width is a multiple of the ice lattice constant, for which ice crystal nucleus forms in the groove. For narrow grooves, strong confinements lead to the formation of solid-like layered structures, which may or may not enhance ice nucleation, depending on their structural match with ice crystal. The findings in this work provide critical information for surface designs in controlling HIN.

Homogeneous Ice Nucleation Rate in Water Droplets

To predict the radiative forcing of clouds it is necessary to know the rate with which ice homogeneously nucleates in supercooled water. Such rate is often measured in drops to avoid the presence of impurities. At large supercooling small (nanoscopic) drops must be used to prevent simultaneous nucleation events. The pressure inside such drops is larger than the atmospheric one by virtue of the Laplace equation. In this work, we take into account such pressure raise in order to predict the nucleation rate in droplets using the TIP4P/Ice water model. We start from a recent estimate of the maximum drop size that can be used at each supercooling avoiding simultaneous nucleation events [Espinosa et al. J. Chem. Phys., 2016]. We then evaluate the pressure inside the drops with the Laplace equation. Finally, we obtain the rate as a function of the supercooling by interpolating our previous results for 1 and 2000 bar [Espinosa et al. Phys. Rev. Lett. 2016] using the Classical Nucleation Theory expression for the rate. This requires, in turn, interpolating the ice-water interfacial free energy and chemical potential difference. The TIP4P/Ice rate curve thus obtained is in good agreement with most droplet-based experiments. In particular, we find a good agreement with measurements performed using nanoscopic drops, that are currently under debate. The successful comparison between model and experiments suggests that TIP4P/Ice is a reliable model to study the water-to-ice transition and that Classical Nucleation Theory is a good framework to understand it.

A simulation study of homogeneous ice nucleation in supercooled salty water

We use computer simulations to investigate the effect of salt on homogeneous ice nucleation. The melting point of the employed solution model was obtained both by direct coexistence simulations and by thermodynamic integration from previous calculations of the water chemical potential. Using a seeding approach, in which we simulate ice seeds embedded in a supercooled aqueous solution, we compute the nucleation rate as a function of temperature for a 1.85 NaCl mol per water kilogram solution at 1 bar. To improve the accuracy and reliability of our calculations, we combine seeding with the direct computation of the ice-solution interfacial free energy at coexistence using the Mold Integration method. We compare the results with previous simulation work on pure water to understand the effect caused by the solute. The model captures the experimental trend that the nucleation rate at a given supercooling decreases when adding salt. Despite the fact that the thermodynamic driving force for ice nucleation is higher for salty water for a given supercooling, the nucleation rate slows down with salt due to a significant increase of the ice-fluid interfacial free energy. The salty water model predicts an ice nucleation rate that is in good agreement with experimental measurements, bringing confidence in the predictive ability of the model. We expect that the combination of state-of-the-art simulation methods here employed to study ice nucleation from solution will be of much use in forthcoming numerical investigations of crystallization in mixtures.

Ice nucleation rates near ∼225 K.

We have measured the ice nucleation rates, Jice, in supercooled nano-droplets with radii ranging from 6.6 nm to 10 nm and droplet temperatures, Td, ranging from 225 K to 204 K. The initial temperature of the 10 nm water droplets is ∼250 K, i.e., well above the homogeneous nucleation temperature for micron sized water droplets, TH ∼235 K. The nucleation rates increase systematically from ∼1021 cm-3 s-1 to ∼1022 cm-3 s-1 in this temperature range, overlap with the nucleation rates of Manka et al. [Phys. Chem. Chem. Phys. 14, 4505 (2012)], and suggest that experiments with larger droplets would extrapolate smoothly the rates of Hagen et al. [J. Atmos. Sci. 38, 1236 (1981)]. The sharp corner in the rate data as temperature drops is, however, difficult to match with available theory even if we correct classical nucleation theory and the physical properties of water for the high internal pressure of the nanodroplets.

Suppressing Ice Nucleation of Supercooled Condensate with Biphilic Topography

Preventing or minimizing ice formation in supercooled water is of prominent importance in many infrastructures, transportation, and cooling systems. The overall phase change heat transfer on icephobic surfaces, in general, is intentionally sacrificed to suppress the nucleation of water and ice. However, in a condensation frosting process, inhibiting freezing without compromising the water condensation has been an unsolved challenge. Here we show that this conflict between anti-icing and efficient condensation cooling can be resolved by utilizing biphilic topography with patterned high-contrast wettability. By creating a varying interfacial thermal barrier underneath the supercooled condensate, the biphilic structures tune the nucleation rates of water and ice in the sequential condensation-to-freezing process. Our experimental and theoretical investigation of condensate freezing dynamics further unravels the correlation between the onset of droplet freezing and its characteristic radius, offering a new insight for controlling the multiphase transitions among vapor, water, and ice in supercooled conditions.

Freezing of micrometer-sized liquid droplets of pure water evaporatively cooled in a vacuum.

Freezing processes are reported for pure-water droplets generated in a vacuum in the size range of 49-71 μm in diameter. The process is characterized for each size by measurement of a freezing curve, where the fraction of frozen droplets is evaluated as a function of time. The 49 μm droplet was found to freeze at a time between 7.0 and 7.9 ms after being generated at room temperature, where the fraction of frozen droplets increased from 5% to 95%; the freezing time was thus distributed statistically within 1 ms. The freezing time was retarded by about 3 ms as the size increases from 49 to 71 μm, while the rise time of the freezing curve was almost unchanged. Numerical simulation of a cooling curve, i.e., the temperature of a droplet as a function of time, revealed that the droplets in the present size range are frozen at almost the same temperature between 233 and 236 K. The freezing curves measured in the experiment were well reproduced by numerical simulation based on the simulated cooling curves combined with the temperature dependence of the volume-based homogeneous ice nucleation rates of pure water reported previously. It was also found that a droplet is disintegrated into a few fragments upon freezing, which suggests formation of a frozen shell in the outer region of a droplet.

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

Estimating the homogeneous ice nucleation rate from undercooled liquid water is crucial for understanding many important physical phenomena and technological applications, and challenging for both experiments and theory. From a theoretical point of view, difficulties arise due to the long time scales required, as well as the numerous nucleation pathways involved to form ice nuclei with different stacking disorders. We computed the homogeneous ice nucleation rate at a physically relevant undercooling for a single-site water model, taking into account the diffuse nature of ice-water interfaces, stacking disorders in ice nuclei, and the addition rate of particles to the critical nucleus. We disentangled and investigated the relative importance of all the terms, including interfacial free energy, entropic contributions and the kinetic prefactor, that contribute to the overall nucleation rate. Breaking down the problem into pieces not only provides physical insights into ice nucleation, but also sheds light on the long-standing discrepancy between different theoretical predictions, as well as between theoretical and experimental determinations of the nucleation rate. Moreover, we pinpoint the main shortcomings and suggest strategies to systematically improve the existing simulation methods.

Soluble Oligomeric Nucleants: Simulations of Chain Length, Binding Strength, and Volume Fraction Effects.

Recent theories and simulations suggest that molecular additives can bind to the surfaces of nuclei, lower the surface energy, and accelerate nucleation. Experiments have shown that oligomeric and polymeric additives can also modify nucleation rates of proteins, ice, and minerals; however, general design principles for oligomeric or polymeric promoters do not yet exist. Here we investigate oligomeric additives for which each segment of the oligomer can bind to surfaces of nuclei. We use semigrand canonical Monte Carlo simulations in a Potts lattice gas model to study the effects of oligomer chain length, volume fraction, and binding strength. We find that increasing each of those parameters lowers the nucleation barrier. At extremely low oligomer concentrations, the nucleation kinetics can be modeled as though each oligomer is a heterogeneous nucleation site in solution.

Homogeneous Nucleation of Ice in Transiently-Heated, Supercooled Liquid Water Films.

We have investigated the nucleation and growth of crystalline ice in 0.24 μm thick, supercooled water films adsorbed on Pt(111). The films were transiently heated with ∼10 ns infrared laser pulses, which produced typical heating and cooling rates of ∼109-1010 K/s. The crystallization of these water films was monitored with infrared spectroscopy. The experimental conditions were chosen to suppress ice nucleation at both the water/metal and water/vacuum interfaces. Furthermore, internal pressure increases due to curvature effects are precluded in these flat films. Therefore, the experiments were sensitive to the homogeneous ice nucleation rate from ∼210 to 225 K. The experiments show that Jmax, the maximum for the homogeneous ice nucleation rate, J(T), needs to be ≥1026 m-3 s-1 and is likely to be ∼1029±2 m-3 s-1. We argue that such large nucleation rates are consistent with experiments on hyperquenched glassy water, which typically have crystalline fractions of ∼1% or more.