Ice Nucleation Kinetics Research Articles

Kinetics model of crystal nucleation and growth in supercooled water for designing ice-templating soft matter scaffold

Ice-templating technology has recently attracted extensive attention to achieve programed structure-property relationships in porous soft matter scaffolds. However, there is a huge gap existed between theoretical understanding and practical applications of nucleation kinetics and growth of ice crystals in supercooled water. This paper establishes a nucleation kinetics model of crystal growth in supercooled water, for designing ice-templating soft matter scaffolds with programmable structure-property relationship. A phase transition model was firstly formulated to characterize liquid-liquid phase transition of supercooled water, based on a two-state model and free-volume theory. Effects of diffusion coefficient and density of the supercooled water on ice nucleation kinetics and crystal growth were investigated, based on the classic nucleation theory. Analytical results showed excellent agreement with experimental data, with correlation indices of R2=90.7 % for diffusion coefficients and R2=94.0 % for densities, respectively. The model predicted a nucleation rate of 31.7 m−3∙s−1 at 200 K and peak nucleation rate and crystal growth rates appearing at 183 K and 227 K. Constitutive relationships among mechanical behaviors, ice nucleus radius, nucleation ratio, and crystallization growth rate, were developed for the ice-templating scaffolds, based on the affine model theory and verified with finite element analysis results (R2= 99.9 %) and experimental results (R2 = 95.8 %). Finally, the prediction results using the proposed model were further verified using the experimental data reported in the literature. This study provides a new methodology to describe the nucleation kinetics and growth of ice crystals in supercooled water and programmable structure-property relationships in ice-templating soft matter scaffolds.

Thermodynamics Explains How Solution Composition Affects the Kinetics of Stochastic Ice Nucleation.

The freezing of aqueous solutions is of great relevance to multiple fields, yet the kinetics of ice nucleation, its first step, remains poorly understood. The literature focuses on the freezing of microdroplets, and it is unclear if those findings can be generalized and extended to larger volumes such as those used in the freezing of biopharmaceuticals. To this end, we study ice nucleation from aqueous solutions of ten different compositions in vials at the milliliter scale. The statistical analysis of the approximately 6,000 measured nucleation events reveals that the stochastic ice nucleation kinetics is independent of the nature and concentration of the solute. We demonstrate this by estimating the values of the kinetic parameters in the nucleation rate expression for the selected solution compositions, and we find that a single set of parameters can describe quantitatively the nucleation behavior in all solutions. This holds regardless of whether the nucleation rate is expressed as a function of the chemical potential difference, of the water activity difference, or of the supercooling. While the chemical potential difference is the thermodynamically correct driving force for nucleation and hence is more accurate from a theoretical point of view, the other two expressions allow for an easier implementation in mechanistic freezing models in pharmaceutical manufacturing.

Characterizing and measuring the ice nucleation kinetics of aqueous solutions in vials

Characterizing and measuring the ice nucleation kinetics of aqueous solutions in vials

Anomalous Vapor and Ice Nucleation in Water at Negative Pressures: A Classical Density Functional Theory Study.

In contrast to the abundance of work on the anomalous behavior of water, the relationship between the water's thermodynamic anomalies and kinetics of phase transition from metastable water is relatively unexplored. In this work, we have employed classical density functional theory to provide a unified and coherent picture of nucleation (both vapor and ice) from metastable water at negative pressure conditions. Our results suggest a peculiar nonmonotonic temperature dependence of vapor-liquid surface tension at temperatures where vapor-liquid coexistence is metastable with respect to the ice phase. The vapor nucleation barrier on isochoric cooling also shows a nonmonotonic temperature dependence. We further report that, for low density isochores, the temperature of the minimum vapor nucleation barrier does not coincide with the temperature of maximum density (TMD) where metastability is maximum. The difference between the and the TMD, however, decreases with increasing the density of the isochore. The vapor nucleation barrier along isobars shows an interesting crossover behavior in the vicinity of the Widom line on lowering the temperature. Our results on the ice nucleation suggest an anomalous retracing behavior of the nucleation barrier along isotherms at negative pressures and theoretically validate the recent findings that the reentrant ice(Ih)-liquid coexistence line can induce a drastic change in the kinetics of ice nucleation. Thus, this study establishes a direct connection between the metastable water's thermodynamic anomalies and the (vapor and ice) nucleation kinetics. In addition, this study provides deeper insights into the origin of the isothermal compressibility maximum on isochoric cooling.

Stochastic ice nucleation governs the freezing process of biopharmaceuticals in vials

Biopharmaceuticals commonly require freezing to ensure the stability of the active pharmaceutical ingredients (APIs). At commercial scale, freezing is typically carried out over the course of days in pallets comprising tens of thousands of vials. The selected process conditions have to ensure both complete freezing in all vials and a satisfactory manufacturing throughput. Current process design, however, is mainly experimental, since no mechanistic understanding of pallet freezing and its underlying phenomena has been achieved so far. Within this work, we derive a mechanistic modeling framework and compare the model predictions with engineering run data from the Janssen COVID-19 vaccine. The model qualitatively reproduced all observed trends and reveals that stochastic ice nucleation governs both process duration and batch heterogeneity. Knowledge on the ice nucleation kinetics of the formulation to be frozen thus is required to identify suitable freezing process conditions. The findings of this work pave the way towards a more rational design of pallet freezing, from which a plethora of frozen drug products may benefit. For this reason, we provide open source access to the model in the form of a python package (Deck et al., 2021).

Repurposing superhydrophobic surfaces into icephobic surfaces

Ice accretion on surfaces is a major economic concern in the energy and transportation industries, particularly due to the need of frequent maintenance. In contrast to the traditional de-icing approaches involving the use of electrical, mechanical, chemical or a combinatorial approach, the use of icephobic surfaces inspired by nature is a more environmentally friendlier solution. Understanding the fundamentals of the interaction of liquid with solid surfaces at low temperatures is at the core of this topic which motivated the need of this review. While shedding light on the ice nucleation kinetics and ice accretion on solid surfaces, this review provides an overview of icephobicity and provide a pathway to repurpose superhydrophobic surfaces for their use as icephobic surfaces.

Stochastic shelf-scale modeling framework for the freezing stage in freeze-drying processes

Freezing and freeze-drying processes are commonly used to improve the stability and thus shelf life of pharmaceutical formulations. Despite strict product quality requirements, batch heterogeneity is widely observed in frozen products, thus potentially causing process failure. Such heterogeneity is the result of the stochasticity of ice nucleation and the variability in heat transfer among vials, which lead to unique freezing histories of individual vials.We present for the first time a modeling framework for large-scale freezing processes of vials on a shelf and publish an open source implementation in the form of a python package on pypi. The model is based on first principles and couples heat transfer with ice nucleation kinetics, thus enabling studies on batch heterogeneity. Ice nucleation is assumed to be an inhomogeneous Poisson process and it is simulated using a Monte Carlo approach. We applied the model to understand the individual pathways leading to batch heterogeneity. Our simulations revealed a novel mechanism how ice nucleation leads to heterogeneity based on thermal interaction among vials. We investigated the effect of various cooling protocols, namely shelf-ramped cooling, holding steps and controlled nucleation, on the nucleation and solidification behavior across the shelf. We found that under rather general conditions holding schemes lead to similar solidification times, as in the case of controlled nucleation, thus identifying a potential pathway for freezing process optimization.

Designing Anti‐Icing Surfaces by Controlling Ice Formation

AbstractUnderstanding the formation of ice from supercooled water on a surface is a matter of fundamental importance and general use. Kinetics of ice nucleation and ice growth on solid surfaces are actively studied, based on which effective anti‐icing surfaces are designed. This review introduces one major breakthrough of experimental estimation of the critical ice nucleus size in heterogenous ice nucleation (HIN). Besides that, targeted anti‐icing strategies are summarized according to the icing steps: suppression of ice nucleation, regulation of ice growth, and reducing ice adhesion. Factors such as crystal lattice match, charge, and ions, etc., are found to have determined effects on the HIN in specific circumstances. This promotes the study of surfaces with ice nucleation inhibition properties. Recent research about distinct ice growth patterns on hydrophobic and hydrophilic surfaces provides a new insight of designing icephobic surfaces by regulating ice growth or spreading processes. At last, effective surfaces including lubricated surface, low interfacial toughness surface, and superhydrophobic surface are developed to significantly reduce ice adhesion strength. The robustness, cost, and manufacture complexity can be problems that need to be considered for the widespread practice of anti‐icing surfaces.

Deep Undercooling of Aqueous Droplets on a Superhydrophobic Surface: The Specific Role of Cation Hydration.

An extraordinary prolonged freezing delay was detected for the first time for deeply undercooled sessile droplets of aqueous solutions of alkali metal chlorides deposited onto a superhydrophobic surface. Accounting for the variation in the hydration energy of ions, their distribution in the vicinity of charged interfaces of solution/air and solution/superhydrophobic surface allows qualitative description of the observed ice nucleation kinetics and ionic specificity in freezing phenomena.

Energetics of ice nucleation in mesoporous titania using positron annihilation spectroscopy.

The low temperature behavior of water and kinetics of ice nucleation in titania mesopores have been probed by positron annihilation lifetime spectroscopy as a function of pore filling. It is revealed that water undergoes complete freezing at around 220 K when more than 50% of the pore volume is filled and such freezing is hindered at lower hydration levels. A model describing progressive trapping of positronium by ice nuclei in liquid water during the phase transition is employed to estimate the energy associated with the nucleation under confinement. It is observed that the energy for ice nucleation in confinement is less than the activation energy for nucleation in bulk water because of the surface assisted nucleation inside the pore. Interestingly, energy for nucleation is seen to decrease with the lowering of hydration level and ascribed to the curtailed hydrogen bonding network of water at lower pore filling.

Analysis of isothermal and cooling-rate-dependent immersion freezing by a unifying stochastic ice nucleation model

Abstract. Immersion freezing is an important ice nucleation pathway involved in the formation of cirrus and mixed-phase clouds. Laboratory immersion freezing experiments are necessary to determine the range in temperature, T, and relative humidity, RH, at which ice nucleation occurs and to quantify the associated nucleation kinetics. Typically, isothermal (applying a constant temperature) and cooling-rate-dependent immersion freezing experiments are conducted. In these experiments it is usually assumed that the droplets containing ice nucleating particles (INPs) all have the same INP surface area (ISA); however, the validity of this assumption or the impact it may have on analysis and interpretation of the experimental data is rarely questioned. Descriptions of ice active sites and variability of contact angles have been successfully formulated to describe ice nucleation experimental data in previous research; however, we consider the ability of a stochastic freezing model founded on classical nucleation theory to reproduce previous results and to explain experimental uncertainties and data scatter. A stochastic immersion freezing model based on first principles of statistics is presented, which accounts for variable ISA per droplet and uses parameters including the total number of droplets, Ntot, and the heterogeneous ice nucleation rate coefficient, Jhet(T). This model is applied to address if (i) a time and ISA-dependent stochastic immersion freezing process can explain laboratory immersion freezing data for different experimental methods and (ii) the assumption that all droplets contain identical ISA is a valid conjecture with subsequent consequences for analysis and interpretation of immersion freezing. The simple stochastic model can reproduce the observed time and surface area dependence in immersion freezing experiments for a variety of methods such as: droplets on a cold-stage exposed to air or surrounded by an oil matrix, wind and acoustically levitated droplets, droplets in a continuous-flow diffusion chamber (CFDC), the Leipzig aerosol cloud interaction simulator (LACIS), and the aerosol interaction and dynamics in the atmosphere (AIDA) cloud chamber. Observed time-dependent isothermal frozen fractions exhibiting non-exponential behavior can be readily explained by this model considering varying ISA. An apparent cooling-rate dependence of Jhet is explained by assuming identical ISA in each droplet. When accounting for ISA variability, the cooling-rate dependence of ice nucleation kinetics vanishes as expected from classical nucleation theory. The model simulations allow for a quantitative experimental uncertainty analysis for parameters Ntot, T, RH, and the ISA variability. The implications of our results for experimental analysis and interpretation of the immersion freezing process are discussed.

Kinetics of Ice Nucleation Confined in Nanoporous Alumina.

The nucleation mechanism of water (heterogeneous/homogeneous) can be regulated by confinement within nanoporous alumina. The kinetics of ice nucleation is studied in confinement by employing dielectric permittivity as a probe. Both heterogeneous and homogeneous nucleation, obtained at low and high undercooling, respectively, are stochastic in nature. The temperature interval of metastability extends over ∼4 and 0.4 °C for heterogeneous and homogeneous nucleation, respectively. Nucleation within a pore is spread to all pores in the template. We have examined a possible coupling of all pores through a heat wave and a sound wave, with the latter being a more realistic scenario. In addition, dielectric spectroscopy indicates that prior to crystallization undercooled water molecules relax with an activation energy of ∼50 kJ/mol, and this process acts as precursor to ice nucleation.

Anomalous Behavior of the Homogeneous Ice Nucleation Rate in "No-Man's Land".

We present an analysis of ice nucleation kinetics from near-ambient pressure water as temperature decreases below the homogeneous limit TH by cooling micrometer-sized droplets (microdroplets) evaporatively at 103–104 K/s and probing the structure ultrafast using femtosecond pulses from the Linac Coherent Light Source (LCLS) free-electron X-ray laser. Below 232 K, we observed a slower nucleation rate increase with decreasing temperature than anticipated from previous measurements, which we suggest is due to the rapid decrease in water’s diffusivity. This is consistent with earlier findings that microdroplets do not crystallize at <227 K, but vitrify at cooling rates of 106–107 K/s. We also hypothesize that the slower increase in the nucleation rate is connected with the proposed “fragile-to-strong” transition anomaly in water.

040 Metastable vitrification of cryoprotectant solutions

Vitrification is a phenomenon in which liquids take on the physical properties of a solid while retaining the structure of a liquid on a molecular scale. When aqueous solutions vitrify, a solid state is achieved without phase separation or crystallization. Cytoplasmic vitrification is believed to occur during almost all forms of cryopreservation. Metastable vitrification is a cryopreservation process in which both cells and surrounding medium are supercooled, vitrified, and then rewarmed without significant freezing of water. Metastable vitrification relies on solutes to reduce the activity of water and slow the kinetics of ice nucleation and growth so that ice avoidance can be achieved at cooling and warming rates compatible with the size of the sample being cryopreserved. For small samples that can be cooled and rewarmed at rates of thousands of degrees per minute, dilute solutions can be sufficient to achieve practical vitrification. On the other end of the metastable vitrification spectrum, organ cryopreservation has necessitated the development of solutions of low water content and low melting points sufficient for vitrification at cooling and warming rates less than one degree Celsius per minute. In any vitrification solution, the temperature of maximum ice growth rate is above the temperature of maximum ice nucleation rate. In dilute solutions, there is broad overlap between ice growth and ice nucleation temperature zones, while in concentrated solutions the zones are more narrow and separated. In either case, ice nucleation during vitrification tends to occur at cold temperatures during the later stages of cooling and early stages of warming. Consequently more ice nuclei are present during warming than cooling. Therefore ice growth (“devitrification”) during warming is a more serious problem than ice growth during cooling, making warming rate the most important rate parameter of vitrification. If a solution is only marginally vitrifiable at a given cooling rate, devitrification during warming will tend to be severe unless the warming rate is even faster. In some circumstances it may be possible to escape the adverse biological consequences of devitrification if ice recrystallization can be avoided. Successful vitrification therefore requires understanding and navigating the landscape of ice nucleation, ice growth, and ice recrystallization when applicable. A complicating factor is that solutions and cell interiors with the same water activity can have different vitrification tendencies due to different solute composition so that cells may escape ice formation even if surrounding solution does not. Source of funding: This research was supported by 21st Century Medicine, Inc. Conflict of interest: None declared. wowk@21cm.com

A water activity based model of heterogeneous ice nucleation kinetics for freezing of water and aqueous solution droplets

Immersion freezing of water and aqueous solutions by particles acting as ice nuclei (IN) is a common process of heterogeneous ice nucleation which occurs in many environments, especially in the atmosphere where it results in the glaciation of clouds. Here we experimentally show, using a variety of IN types suspended in various aqueous solutions, that immersion freezing temperatures and kinetics can be described solely by temperature, T, and solution water activity, a(w), which is the ratio of the vapour pressure of the solution and the saturation water vapour pressure under the same conditions and, in equilibrium, equivalent to relative humidity (RH). This allows the freezing point and corresponding heterogeneous ice nucleation rate coefficient, J(het), to be uniquely expressed by T and a(w), a result we term the a(w) based immersion freezing model (ABIFM). This method is independent of the nature of the solute and accounts for several varying parameters, including cooling rate and IN surface area, while providing a holistic description of immersion freezing and allowing prediction of freezing temperatures, J(het), frozen fractions, ice particle production rates and numbers. Our findings are based on experimental freezing data collected for various IN surface areas, A, and cooling rates, r, of droplets variously containing marine biogenic material, two soil humic acids, four mineral dusts, and one organic monolayer acting as IN. For all investigated IN types we demonstrate that droplet freezing temperatures increase as A increases. Similarly, droplet freezing temperatures increase as the cooling rate decreases. The log10(J(het)) values for the various IN types derived exclusively by Tand a(w), provide a complete description of the heterogeneous ice nucleation kinetics. Thus, the ABIFM can be applied over the entire range of T, RH, total particulate surface area, and cloud activation timescales typical of atmospheric conditions. Lastly, we demonstrate that ABIFM can be used to derive frozen fractions of droplets and ice particle production for atmospheric models of cirrus and mixed phase cloud conditions.

Isothermal Ice Crystallization Kinetics in the Gas-Diffusion Layer of a Proton-Exchange-Membrane Fuel Cell

Nucleation and growth of ice in the fibrous gas-diffusion layer (GDL) of a proton-exchange membrane fuel cell (PEMFC) are investigated using isothermal differential scanning calorimetry (DSC). Isothermal crystallization rates and pseudo-steady-state nucleation rates are obtained as a function of subcooling from heat-flow and induction-time measurements. Kinetics of ice nucleation and growth are studied at two polytetrafluoroethylene (PTFE) loadings (0 and 10 wt %) in a commercial GDL for temperatures between 240 and 273 K. A nonlinear ice-crystallization rate expression is developed using Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory, in which the heat-transfer-limited growth rate is determined from the moving-boundary Stefan problem. Induction times follow a Poisson distribution and increase upon addition of PTFE, indicating that nucleation occurs more slowly on a hydrophobic fiber than on a hydrophilic fiber. The determined nucleation rates and induction times follow expected trends from classical nucleation theory. A validated rate expression is now available for predicting ice-crystallization kinetics in GDLs.

Effects of solution composition on the theoretical prediction of ice nucleation kinetics and thermodynamics

Predictions by various mathematical models of intracellular ice formation (proposed by Mazur, Pitt, Toner, and Karlsson, respectively) were compared to the known thermodynamic and kinetic behavior of ice formation in supercooled aqueous systems. The older models (Mazur, Pitt, and Toner) significantly underestimated the magnitude of colligative nonequilibrium freezing point depression in response to increased concentration of solutes, such as salts or cryoprotectants. Furthermore, kinetics predicted using phenomenological models (by Mazur and Pitt) exhibited implausible temperature-dependence, with the probability of intracellular ice formation being allowed to increase even at temperatures below the glass transition point. The Toner model, on the other hand, produced invalid results at temperatures below −48 °C. The Karlsson model was the only model that consistently yielded realistic predictions over a wide range of temperatures and solute concentrations, especially in the presence of cryoprotectant additives. To facilitate adoption of the Karlsson model of intracellular ice nucleation, the complete set of model equations has been collected and described in detail.

Evidence of enhanced local order and clustering in supercooled water near liquid–vapor interface: Molecular dynamic simulations

Molecular dynamic (MD) simulations have been performed to compare the local order in a thin film and the bulk liquid of supercooled water. We found that the density fluctuations and the average size of low density domains (‘ice-like’ clusters) in supercooled water in the presence of the interface are noticeably higher than those of the bulk liquid. The present simulation results support the concept of surface-stimulated nucleation. This may have a significant impact on the ice nucleation kinetics in the atmosphere, where the total volume and the surface area of typical (micron-size) aerosol particles have comparable values.

The nucleation rate of crystalline ice in amorphous solid water.

The kinetics of crystalline ice nucleation and growth in nonporous, molecular beam deposited amorphous solid water (ASW) films are investigated at temperatures near 140 K. We implement an experimental methodology and corresponding model of crystallization kinetics to decouple growth from nucleation and quantify the temperature dependence and absolute rates of both processes. Nucleation rates are found to increase from approximately 3x10(13) m(-3) s(-1) at 134 K to approximately 2x10(17) m(-3) s(-1) at 142 K, corresponding to an Arrhenius activation energy of 168 kJ/mol. Over the same temperature range, the growth velocity increases from approximately 0.4 to approximately 4 A s(-1), also exhibiting Arrhenius behavior with an activation energy of 47 kJ/mol. These nucleation rates are up to ten orders of magnitude larger than in liquid water near 235 K, while growth velocities are approximately 10(9) times smaller. Crystalline ice nucleation kinetics determined in this study differ significantly from those reported previously for porous, background vapor deposited ASW, suggesting the nucleation mechanism is dependent upon film morphology.

Infrared Spectroscopic Evidence for the Ice Formation Mechanisms Active in Aerosol Flow Tubes

Interest in quantifying processes of ice formation in the atmosphere has led to the recent development of new laboratory techniques, including an aerosol flow tube (AFT) reactor employed for the study of the ice nucleation kinetics of suspended submicrometer aqueous particles. The AFT technique employs an infrared (IR) beam along the flow tube axis. Spectral changes between 700 and 6000 cm−1 indicate the formation of ice at sufficiently cool temperatures. Apparent freezing temperatures are determined as a function of condensed-phase mole fraction composition. A typical aqueous chemical system is (NH4)2SO4/H2O. The mole fraction composition of the condensed-phase of this aerosol is determined by the ratio of the integrated spectroscopic bands for H2O and SO42–. A key uncertainty in the AFT-IR technique is the freezing mechanism, and knowledge of the mechanism is essential to estimate homogeneous nucleation rates ( J, cm−3 s−1) from observed apparent freezing temperatures. The current work provides observational and modeling spectral evidence, based upon changes in the scattering component of the recorded IR extinction spectra with temperature, that observed ice freezing events at warmer temperatures arise from the following mechanism: relatively few particles in the aerosol freeze (e.g., 1 in 106) and this primary event is followed by rapid scavenging of water vapor to grow the few ice particles into large ice particles observed in the IR spectra. Correspondingly, the remaining aqueous particles partially evaporate. In contrast, the spectral evidence provides support that a modified mechanism is operative at cooler temperatures: the ice freezing event consists of the freezing of a much larger fraction of the particles (e.g., 1 in 10) accompanied by a much less important vapor-phase mass transfer event.