scholarly journals Thermodynamic derivation of the energy of activation for ice nucleation

2015 ◽  
Vol 15 (13) ◽  
pp. 18151-18179
Author(s):  
D. Barahona
Keyword(s):  
Activation Energy ◽  
Nucleation Rate ◽  
Phenomenological Model ◽  
Ice Nucleation ◽  
Liquid Interface ◽  
Experimental Results ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Water Molecules ◽  
Molecular Rearrangement

Abstract. The activation energy controls the flux of water molecules from the bulk of the liquid to the solid during the early stages of ice formation. In most studies it is estimated by direct association with the bulk properties of water, typically viscosity and self-diffusivity. As the environment in the ice–liquid interface may differ from that of the bulk this approach may introduce bias in calculated nucleation rates. In this work a phenomenological model is proposed to describe the transfer of water molecules across the ice–liquid interface. Within this framework the activation energy naturally emerges from the combination of the energy required to break hydrogen bonds in the liquid, i.e., the bulk diffusion process, and the work dissipated from the molecular rearrangement of water molecules within the ice–liquid interface. The new expression is introduced into a generalized form of classical nucleation theory. Even though no nucleation rate measurements are used to fit any of the parameters of the theory the predicted nucleation rate is in good agreement with experimental results, even at temperature as low as 190 K where it tends to be underestimated by most models. It is shown that the activation energy has a strong dependency on temperature and a weak dependency on water activity. Such dependencies are masked by thermodynamic effects at temperatures typical of homogeneous freezing of cloud droplets, however may affect the formation of ice in haze aerosol particles. The phenomenological model introduced in this work provides an independent estimation of the activation energy and the homogenous ice nucleation rate, and it may help to improve the interpretation of experimental results and the development of parameterizations for cloud formation.

scholarly journals Thermodynamic derivation of the activation energy for ice nucleation

2015 ◽  
Vol 15 (24) ◽  
pp. 13819-13831 ◽  
Author(s):  
D. Barahona
Keyword(s):  
Activation Energy ◽  
Nucleation Rate ◽  
Ice Nucleation ◽  
Liquid Interface ◽  
Experimental Results ◽  
Nucleation Theory ◽  
Cloud Formation ◽  
Classical Nucleation Theory ◽  
Water Molecules ◽  
Molecular Rearrangement

Abstract. Cirrus clouds play a key role in the radiative and hydrological balance of the upper troposphere. Their correct representation in atmospheric models requires an understanding of the microscopic processes leading to ice nucleation. A key parameter in the theoretical description of ice nucleation is the activation energy, which controls the flux of water molecules from the bulk of the liquid to the solid during the early stages of ice formation. In most studies it is estimated by direct association with the bulk properties of water, typically viscosity and self-diffusivity. As the environment in the ice–liquid interface may differ from that of the bulk, this approach may introduce bias in calculated nucleation rates. In this work a theoretical model is proposed to describe the transfer of water molecules across the ice–liquid interface. Within this framework the activation energy naturally emerges from the combination of the energy required to break hydrogen bonds in the liquid, i.e., the bulk diffusion process, and the work dissipated from the molecular rearrangement of water molecules within the ice–liquid interface. The new expression is introduced into a generalized form of classical nucleation theory. Even though no nucleation rate measurements are used to fit any of the parameters of the theory the predicted nucleation rate is in good agreement with experimental results, even at temperature as low as 190 K, where it tends to be underestimated by most models. It is shown that the activation energy has a strong dependency on temperature and a weak dependency on water activity. Such dependencies are masked by thermodynamic effects at temperatures typical of homogeneous freezing of cloud droplets; however, they may affect the formation of ice in haze aerosol particles. The new model provides an independent estimation of the activation energy and the homogeneous ice nucleation rate, and it may help to improve the interpretation of experimental results and the development of parameterizations for cloud formation.

scholarly journals Analysis of the effect of water activity on ice formation using a new thermodynamic framework

2014 ◽  
Vol 14 (14) ◽  
pp. 7665-7680 ◽  
Author(s):  
D. Barahona
Keyword(s):  
Water Activity ◽  
Nucleation Rate ◽  
Ice Nucleation ◽  
Nucleation Theory ◽  
Cloud Formation ◽  
Classical Nucleation Theory ◽  
Solid Matrix ◽  
Effect Of Water ◽  
Thermodynamic Framework ◽  
New Framework

Abstract. In this work a new thermodynamic framework is developed and used to investigate the effect of water activity on the formation of ice within supercooled droplets. The new framework is based on a novel concept where the interface is assumed to be made of liquid molecules "trapped" by the solid matrix. It also accounts for the change in the composition of the liquid phase upon nucleation. Using this framework, new expressions are developed for the critical ice germ size and the nucleation work with explicit dependencies on temperature and water activity. However unlike previous approaches, the new model does not depend on the interfacial tension between liquid and ice. The thermodynamic framework is introduced within classical nucleation theory to study the effect of water activity on the ice nucleation rate. Comparison against experimental results shows that the new approach is able to reproduce the observed effect of water activity on the nucleation rate and the freezing temperature. It allows for the first time a phenomenological derivation of the constant shift in water activity between melting and nucleation. The new framework offers a consistent thermodynamic view of ice nucleation, simple enough to be applied in atmospheric models of cloud formation.

scholarly journals Parameterizing ice nucleation rates using contact angle and activation energy derived from laboratory data

2008 ◽  
Vol 8 (24) ◽  
pp. 7431-7449 ◽  
Author(s):  
J.-P. Chen ◽  
A. Hazra ◽  
Z. Levin
Keyword(s):  
Activation Energy ◽  
Contact Angle ◽  
Thermodynamic Parameters ◽  
Laboratory Data ◽  
Ice Nucleation ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Curvature Effects ◽  
Ice Nuclei ◽  
Cloud Models

Abstract. The rate of ice nucleation in clouds is not easily determined and large discrepancies exist between model predictions and actual ice crystal concentration measured in clouds. In an effort to improve the parameterization of ice nucleating in cloud models, we investigate the rate of heterogeneous ice nucleation under specific ambient conditions by knowing the sizes as well as two thermodynamic parameters of the ice nuclei – contact angle and activation energy. Laboratory data of freezing and deposition nucleation modes were analyzed to derive inversely the two thermodynamic parameters for a variety of ice nuclei, including mineral dusts, bacteria, pollens, and soot particles. The analysis considered the Zeldovich factor for the adjustment of ice germ formation, as well as the solute and curvature effects on surface tension; the latter effects have strong influence on the contact angle. Contact angle turns out to be a more important factor than the activation energy in discriminating the nucleation capabilities of various ice nuclei species. By extracting these thermodynamic parameters, laboratory results can be converted into a formulation that follows classical nucleation theory, which then has the flexibility of incorporating factors such as the solute effect and curvature effect that were not considered in the experiments. Due to various uncertainties, contact angle and activation energy derived in this study should be regarded as "apparent" thermodynamics parameters.

Thermodynamic and Kinetic controls to the ice nucleation rate

2020 ◽  
Author(s):  
Donifan Barahona
Keyword(s):  
Nucleation Rate ◽  
Anthropogenic Activities ◽  
Ice Nucleation ◽  
Nucleation Theory ◽  
Cloud Formation ◽  
Classical Nucleation Theory ◽  
Limited Information ◽  
Atmospheric Conditions ◽  
Theoretical Approaches ◽  
Cloud Models

<p>Ice nucleation is a necessary step for the formation of ice clouds in the atmosphere. It has become clear that its correct representation is critical for the accurate description of atmospheric processes, and for the reliable prediction of the effect of anthropogenic activities on climate. This is accomplished in most cases using empirical models. Although a simple way to parameterize ice nucleation they provide limited information on the nature of ice formation and may not represent all atmospheric conditions.  Theoretical approaches used in cloud models are typically based on the Classical Nucleation Theory (CNT).  There is however a large uncertainty in key parameters of the theory which in most cases are fitted to reproduce observed rates. This talk details recent efforts to go beyond the formulation of CNT to describe ice nucleation. It shows that it is possible to define uncertain parameters like the ice-liquid interfacial tension and the activation energy over a pure thermodynamic basis, hence only as a function of the bulk thermodynamic properties of water. This approach is extended to describe heterogeneous ice nucleation mediated by immersed ice nucleating particles (INPs). It is shown that INPs that significantly reduce the work of ice nucleation also pose strong limitations to the growth of the nascent ice germs. This leads to the onset of a new ice nucleation regime, called spinodal ice nucleation, where the dynamics of ice germ growth instead of the ice germ size determines the nucleation rate. Nucleation in this regime is characterized by an enhanced sensitivity to particle area and cooling rate. Finally a new approach to extract intrinsic nucleation rates from droplet-freezing experiments is used to compare of predicted ice nucleation rates against experimental measurements, for a diverse set of species relevant to cloud formation. This comparison suggests that spinodal ice nucleation may be common in nature, and shows a considerable skill of the new theory in predicting measured ice nucleation rates. </p>

scholarly journals Parameterizing ice nucleation rates for cloud modeling using contact angle and activation energy derived from laboratory data

2008 ◽  
Vol 8 (4) ◽  
pp. 14419-14465 ◽  
Author(s):  
J.-P. Chen ◽  
A. Hazra ◽  
Z. Levin
Keyword(s):  
Activation Energy ◽  
Contact Angle ◽  
Thermodynamic Parameters ◽  
Laboratory Data ◽  
Ice Nucleation ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Curvature Effects ◽  
Ice Nuclei ◽  
Cloud Models

Abstract. The rate of ice nucleation in clouds is not easily determined and large discrepancies exist between model predictions and actual ice crystal concentration measured in clouds. In an effort to improve the parameterization of ice nucleating in cloud models, we investigate the rate of heterogeneous ice nucleation under specific ambient conditions by knowing the sizes as well as two thermodynamic parameters of the ice nuclei – contact angle and activation energy. Laboratory data of freezing and deposition nucleation modes were analyzed to derive inversely the two thermodynamic parameters for a variety of ice nuclei, including mineral dusts, bacteria, pollens, and soot particles. The analysis considered the Zeldovich factor for the adjustment of ice germ formation, as well as the solute and curvature effects on surface tension, the latter effects have strong influence on the contact angle. Contact angle turns out to be a more important factor than the activation energy in discriminating the nucleation capabilities of various ice nuclei species. By extracting these thermodynamic parameters, laboratory results can be converted into a formulation that follows classical nucleation theory, which then has the flexibility of incorporating factors such as the solute effect and curvature effect that were not considered in the experiments.

scholarly journals Low-temperature nucleation anomaly in silicate glasses shown to be artifact in a 5BaO·8SiO2 glass

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Xinsheng Xia ◽  
D. C. Van Hoesen ◽  
Matthew E. McKenzie ◽  
Randall E. Youngman ◽  
K. F. Kelton
Keyword(s):  
Nucleation Rate ◽  
Experimental Approach ◽  
Cluster Formation ◽  
Heating Time ◽  
Silicate Glasses ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Real Phenomenon ◽  
Satisfactory Answer ◽  
Over 40 Years

AbstractFor over 40 years, measurements of the nucleation rates in a large number of silicate glasses have indicated a breakdown in the Classical Nucleation Theory at temperatures below that of the peak nucleation rate. The data show that instead of steadily decreasing with decreasing temperature, the work of critical cluster formation enters a plateau and even starts to increase. Many explanations have been offered to explain this anomaly, but none have provided a satisfactory answer. We present an experimental approach to demonstrate explicitly for the example of a 5BaO ∙ 8SiO2 glass that the anomaly is not a real phenomenon, but instead an artifact arising from an insufficient heating time at low temperatures. Heating times much longer than previously used at a temperature 50 K below the peak nucleation rate temperature give results that are consistent with the predictions of the Classical Nucleation Theory. These results raise the question of whether the claimed anomaly is also an artifact in other glasses.

scholarly journals Brief Overview of Ice Nucleation

Molecules ◽  
2021 ◽  
Vol 26 (2) ◽  
pp. 392
Author(s):  
Nobuo Maeda
Keyword(s):  
Molecular Level ◽  
Ice Nucleation ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Radiation Balance ◽  
Feature Article ◽  
Aircraft Wings ◽  
Food Engineering ◽  
Research Activities ◽  
Important Field

The nucleation of ice is vital in cloud physics and impacts on a broad range of matters from the cryopreservation of food, tissues, organs, and stem cells to the prevention of icing on aircraft wings, bridge cables, wind turbines, and other structures. Ice nucleation thus has broad implications in medicine, food engineering, mineralogy, biology, and other fields. Nowadays, the growing threat of global warming has led to intense research activities on the feasibility of artificially modifying clouds to shift the Earth’s radiation balance. For these reasons, nucleation of ice has been extensively studied over many decades and rightfully so. It is thus not quite possible to cover the whole subject of ice nucleation in a single review. Rather, this feature article provides a brief overview of ice nucleation that focuses on several major outstanding fundamental issues. The author’s wish is to aid early researchers in ice nucleation and those who wish to get into the field of ice nucleation from other disciplines by concisely summarizing the outstanding issues in this important field. Two unresolved challenges stood out from the review, namely the lack of a molecular-level picture of ice nucleation at an interface and the limitations of classical nucleation theory.

scholarly journals Efficiency of immersion mode ice nucleation on surrogates of mineral dust

2007 ◽  
Vol 7 (19) ◽  
pp. 5081-5091 ◽  
Author(s):  
C. Marcolli ◽  
S. Gedamke ◽  
T. Peter ◽  
B. Zobrist
Keyword(s):  
Contact Angle ◽  
Active Sites ◽  
Quantitative Agreement ◽  
Ice Nucleation ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Aqueous Suspensions ◽  
Freezing Temperatures ◽  
Good Agreement ◽  
Heterogeneous Ice Nucleation

Abstract. A differential scanning calorimeter (DSC) was used to explore heterogeneous ice nucleation of emulsified aqueous suspensions of two Arizona test dust (ATD) samples with particle diameters of nominally 0–3 and 0–7 μm, respectively. Aqueous suspensions with ATD concentrations of 0.01–20 wt% have been investigated. The DSC thermograms exhibit a homogeneous and a heterogeneous freezing peak whose intensity ratios vary with the ATD concentration in the aqueous suspensions. Homogeneous freezing temperatures are in good agreement with recent measurements by other techniques. Depending on ATD concentration, heterogeneous ice nucleation occurred at temperatures as high as 256 K or down to the onset of homogeneous ice nucleation (237 K). For ATD-induced ice formation Classical Nucleation Theory (CNT) offers a suitable framework to parameterize nucleation rates as a function of temperature, experimentally determined ATD size, and emulsion droplet volume distributions. The latter two quantities serve to estimate the total heterogeneous surface area present in a droplet, whereas the suitability of an individual heterogeneous site to trigger nucleation is described by the compatibility function (or contact angle) in CNT. The intensity ratio of homogeneous to heterogeneous freezing peaks is in good agreement with the assumption that the ATD particles are randomly distributed amongst the emulsion droplets. The observed dependence of the heterogeneous freezing temperatures on ATD concentrations cannot be described by assuming a constant contact angle for all ATD particles, but requires the ice nucleation efficiency of ATD particles to be (log)normally distributed amongst the particles. Best quantitative agreement is reached when explicitly assuming that high-compatibility sites are rare and that therefore larger particles have on average more and better active sites than smaller ones. This analysis suggests that a particle has to have a diameter of at least 0.1 μm to exhibit on average one active site.

scholarly journals A semi-analytical method for calculating rates of new sulfate aerosol formation from the gas phase

2007 ◽  
Vol 7 (1) ◽  
pp. 2169-2196 ◽  
Author(s):  
J. Kazil ◽  
E. R. Lovejoy
Keyword(s):  
Steady State ◽  
Gas Phase ◽  
Nucleation Rate ◽  
Atmospheric Modeling ◽  
Sulfate Aerosol ◽  
Nucleation Theory ◽  
Rate Coefficients ◽  
Classical Nucleation Theory ◽  
Aerosol Formation ◽  
Aerosol Model

Abstract. The formation of new sulfate aerosol from the gas phase is commonly represented in atmospheric modeling with parameterizations of the steady state nucleation rate. Such parameterizations are based on classical nucleation theory or on aerosol nucleation rate tables, calculated with a numerical aerosol model. These parameterizations reproduce aerosol nucleation rates calculated with a numerical aerosol model only imprecisely. Additional errors can arise when the nucleation rate is used as a surrogate for the production rate of particles of a given size. We discuss these errors and present a method which allows a more precise calculation of steady state sulfate aerosol formation rates. The method is based on the semi-analytical solution of an aerosol system in steady state and on parameterized rate coefficients for H2SO4 uptake and loss by sulfate aerosol particles, calculated from laboratory and theoretical thermodynamic data.

scholarly journals A new temperature- and humidity-dependent surface site density approach for deposition ice nucleation

2015 ◽  
Vol 15 (7) ◽  
pp. 3703-3717 ◽  
Author(s):  
I. Steinke ◽  
C. Hoose ◽  
O. Möhler ◽  
P. Connolly ◽  
T. Leisner
Keyword(s):  
Contact Angle ◽  
Relative Humidity ◽  
Active Surface ◽  
Ice Nucleation ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Aerosol Size Distribution ◽  
Surface Site ◽  
Linear Behavior ◽  
Temperature And Humidity

Abstract. Deposition nucleation experiments with Arizona Test Dust (ATD) as a surrogate for mineral dusts were conducted at the AIDA cloud chamber at temperatures between 220 and 250 K. The influence of the aerosol size distribution and the cooling rate on the ice nucleation efficiencies was investigated. Ice nucleation active surface site (INAS) densities were calculated to quantify the ice nucleation efficiency as a function of temperature, humidity and the aerosol surface area concentration. Additionally, a contact angle parameterization according to classical nucleation theory was fitted to the experimental data in order to relate the ice nucleation efficiencies to contact angle distributions. From this study it can be concluded that the INAS density formulation is a very useful tool to describe the temperature- and humidity-dependent ice nucleation efficiency of ATD particles. Deposition nucleation on ATD particles can be described by a temperature- and relative-humidity-dependent INAS density function ns(T, Sice) with ns(xtherm) = 1.88 ×105 · exp(0.2659 · xtherm) [m−2] , (1) where the temperature- and saturation-dependent function xtherm is defined as xtherm = −(T−273.2)+(Sice−1) ×100, (2) with the saturation ratio with respect to ice Sice >1 and within a temperature range between 226 and 250 K. For lower temperatures, xtherm deviates from a linear behavior with temperature and relative humidity over ice. Also, two different approaches for describing the time dependence of deposition nucleation initiated by ATD particles are proposed. Box model estimates suggest that the time-dependent contribution is only relevant for small cooling rates and low number fractions of ice-active particles.

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