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

2014 ◽  
Vol 14 (2) ◽  
pp. 1525-1557
Author(s):  
D. Barahona
Keyword(s):  
Water Activity ◽  
Freezing Temperature ◽  
Cloud Formation ◽  
Solid Matrix ◽  
Effect Of Water ◽  
Thermodynamic Framework ◽  
Novel Concept ◽  
First Time ◽  
Nucleation Work ◽  
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. Using this concept 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. Comparison against experimental results shows that the new theory is able to reproduce the observed effect of water activity on nucleation rate and 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.

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 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 Immersion freezing of water and aqueous ammonium sulfate droplets initiated by humic-like substances as a function of water activity

2013 ◽  
Vol 13 (13) ◽  
pp. 6603-6622 ◽  
Author(s):  
Y. J. Rigg ◽  
P. A. Alpert ◽  
D. A. Knopf
Keyword(s):  
Water Activity ◽  
Active Sites ◽  
Melting Curve ◽  
Contact Angles ◽  
Ice Nucleation ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Surface Areas ◽  
Immersion Freezing ◽  
Freezing Temperatures

Abstract. Immersion freezing of water and aqueous (NH4)2SO4 droplets containing leonardite (LEO) and Pahokee peat (PP) serving as surrogates for humic-like substances (HULIS) has been investigated. Organic aerosol containing HULIS are ubiquitous in the atmosphere; however, their potential for ice cloud formation is uncertain. Immersion freezing has been studied for temperatures as low as 215 K and solution water activity, aw, from 0.85 to 1.0. The freezing temperatures of water and aqueous solution droplets containing LEO and PP are 5–15 K warmer than homogeneous ice nucleation temperatures. Heterogeneous freezing temperatures can be represented by a horizontal shift of the ice melting curve as a function of solution aw by Δaw = 0.2703 and 0.2466, respectively. Corresponding hetrogeneous ice nucleation rate coefficients, Jhet, are (9.6 ± 2.5)×104 and (5.4 ± 1.4)×104 cm−2 s−1 for LEO and PP containing droplets, respectively, and remain constant along freezing curves characterized by Δaw. Consequently predictions of freezing temperatures and kinetics can be made without knowledge of the solute type when relative humidity and ice nuclei (IN) surface areas are known. The acquired ice nucleation data are applied to evaluate different approaches to fit and reproduce experimentally derived frozen fractions. In addition, we apply a basic formulation of classical nucleation theory (α(T)-model) to calculate contact angles and frozen fractions. Contact angles calculated for each ice nucleus as a function of temperature, α(T)-model, reproduce exactly experimentally derived frozen fractions without involving free-fit parameters. However, assigning the IN a single contact angle for the entire population (single-α model) is not suited to represent the frozen fractions. Application of α-PDF, active sites, and deterministic model approaches to measured frozen fractions yield similar good representations. Furthermore, when using a single parameterization of α-PDF or active sites distribution to fit all individual aw immersion freezing data simultaneously, frozen fraction curves are not reproduced. This implies that these fitting formulations cannot be applied to immersion freezing of aqueous solutions, and suggests that derived fit parameters do not represent independent particle properties. Thus, from fitting frozen fractions only, the underlying ice nucleation mechanism and nature of the ice nucleating sites cannot be inferred. In contrast to using fitted functions obtained to represent experimental conditions only, we suggest to use experimentally derived Jhet as a function of temperature and aw that can be applied to conditions outside of those probed in laboratory. This is because Jhet(T) is independent of time and IN surface areas in contrast to the fit parameters obtained by representation of experimentally derived frozen fractions.

scholarly journals Deposition-mode ice nucleation reexamined at temperatures below 200 K

2015 ◽  
Vol 15 (4) ◽  
pp. 1621-1632 ◽  
Author(s):  
E. S. Thomson ◽  
X. Kong ◽  
P. Papagiannakopoulos ◽  
J. B. C. Pettersson
Keyword(s):  
Substrate Surface ◽  
Ice Nucleation ◽  
Nucleation Theory ◽  
Cloud Formation ◽  
Classical Nucleation Theory ◽  
Careful Examination ◽  
Contradictory Result ◽  
Experimental Conditions ◽  
Water Ice ◽  
Atmospheric Nucleation

Abstract. The environmental chamber of a molecular beam apparatus is used to study deposition nucleation of ice on graphite, alcohols and acetic and nitric acids at temperatures between 155 and 200 K. The critical supersaturations necessary to spontaneously nucleate water ice on six different substrate materials are observed to occur at higher supersaturations than are theoretically predicted. This contradictory result motivates more careful examination of the experimental conditions and the underlying basis of the current theories. An analysis based on classical nucleation theory supports the view that at these temperatures nucleation is primarily controlled by the rarification of the vapor and the strength of water's interaction with the substrate surface. The technique enables a careful probing of the underlying processes of ice nucleation and the substrate materials of study. The findings are relevant to atmospheric nucleation processes that are intrinsically linked to cold cloud formation and lifetime.

scholarly journals Exploring the Mechanisms of Ice Nucleation on Kaolinite: From Deposition Nucleation to Condensation Freezing

2013 ◽  
Vol 71 (1) ◽  
pp. 16-36 ◽  
Author(s):  
André Welti ◽  
Zamin A. Kanji ◽  
F. Lüönd ◽  
Olaf Stetzer ◽  
Ulrike Lohmann
Keyword(s):  
Water Saturation ◽  
Particle Surface ◽  
Ice Nucleation ◽  
Mixed Phase ◽  
Nucleation Theory ◽  
Cloud Formation ◽  
Classical Nucleation Theory ◽  
Appreciable Amount ◽  
Nucleation Mechanisms ◽  
Ice Nucleation Activity

Abstract To identify the temperature and humidity conditions at which different ice nucleation mechanisms are active, the authors conducted experiments on 200-, 400-, and 800-nm size-selected kaolinite particles, exposing them to temperatures between 218 and 258 K and relative humidities with respect to ice (RHi) between 100% and 180%, including the typical conditions for cirrus and mixed-phase-cloud formation. Measurements of the ice active particle fraction as a function of temperature and relative humidity with respect to ice are reported. The authors find enhanced activated fractions when water saturation is reached at mixed-phase-cloud temperatures between 235 and 241 K and a distinct increase in the activated fraction below 235 K at conditions below water saturation. To provide a functional description of the observed ice nucleation mechanisms, the experimental results are analyzed by two different particle-surface models within the framework of classical nucleation theory. Describing the ice nucleation activity of kaolinite particles by assuming deposition nucleation to be the governing mechanism below water saturation was found to be inadequate to represent the experimental data in the whole temperature range investigated. The observed increase in the activated fraction below water saturation and temperatures below 235 K corroborate the assumption that an appreciable amount of adsorbed or capillary condensed water is present on kaolinite particles, which favors ice nucleation.

scholarly journals Ice nucleation from aqueous NaCl droplets with and without marine diatoms

2011 ◽  
Vol 11 (3) ◽  
pp. 8291-8336 ◽  
Author(s):  
P. A. Alpert ◽  
J. Y. Aller ◽  
D. A. Knopf
Keyword(s):  
Surface Area ◽  
Water Activity ◽  
Nucleation Rate ◽  
Particle Production ◽  
Ice Nucleation ◽  
Nucleation Theory ◽  
Rate Coefficients ◽  
Freezing Temperatures ◽  
Aqueous Volume ◽  
Heterogeneous Ice Nucleation

Abstract. Ice formation in the atmosphere by homogeneous and heterogeneous nucleation is one of the least understood processes in cloud microphysics and climate. Here we describe our investigation of the marine environment as a potential source of atmospheric IN by experimentally observing homogeneous ice nucleation from aqueous NaCl droplets and comparing against heterogeneous ice nucleation from aqueous NaCl droplets containing intact and fragmented diatoms. Homogeneous and heterogeneous ice nucleation are studied as a function of temperature and water activity, aw. Additional analyses are presented on the dependence of diatom surface area and aqueous volume on heterogeneous freezing temperatures, ice nucleation rates, ωhet, ice nucleation rate coefficients, Jhet, and differential and cumulative ice nuclei spectra, k(T) and K(T), respectively. Homogeneous freezing temperatures and corresponding nucleation rate coefficients are in agreement with the water activity based homogeneous ice nucleation theory within experimental and predictive uncertainties. Our results confirm, as predicted by classical nucleation theory, that a stochastic interpretation can be used to describe this nucleation process. Heterogeneous ice nucleation initiated by intact and fragmented diatoms can be adequately represented by a modified water activity based ice nucleation theory. A horizontal shift in water activity, Δaw, het = 0.2303, of the ice melting curve can describe median heterogeneous freezing temperatures. Individual freezing temperatures showed no dependence on available diatom surface area and aqueous volume. Determined at median diatom freezing temperatures for aw from 0.8 to 0.99, ωhet ~ 0.11+0.06−0.05 s−1, Jhet ~ 1.0+1.16−0.61 × 104 cm−2 s−1, and K ~ 6.2+3.5−4.1 × 104 cm−2. The experimentally derived ice nucleation rates and nuclei spectra allow us to estimate ice particle production which we subsequently use for a comparison with observed ice crystal concentrations typically found in cirrus and polar marine mixed-phase clouds. Differences in application of time-dependent and time-independent analyses to predict ice particle production are discussed.

scholarly journals Immersion freezing of water and aqueous ammonium sulphate droplets initiated by Humic Like Substances as a function of water activity

2013 ◽  
Vol 13 (2) ◽  
pp. 4917-4961
Author(s):  
Y. J. Rigg ◽  
P. A. Alpert ◽  
D. A. Knopf
Keyword(s):  
Water Activity ◽  
Active Sites ◽  
Melting Curve ◽  
Contact Angles ◽  
Ice Nucleation ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Surface Areas ◽  
Immersion Freezing ◽  
Freezing Temperatures

Abstract. Immersion freezing of water and aqueous (NH4)2SO4 droplets containing Leonardite (LEO) and Pahokee peat (PP) serving as surrogates for Humic Like Substances (HULIS) has been investigated. Organic aerosol containing HULIS are ubiquitous in the atmosphere, however, their potential for ice cloud formation is uncertain. Immersion freezing has been studied for temperatures as low as 215 K and solution water activity, aw, from 0.85–1.0. The freezing temperatures of water and aqueous solution droplets containing LEO and PP are 5–15 K warmer than homogeneous ice nucleation temperatures. Heterogeneous freezing temperatures can be represented by a horizontal shift of the ice melting curve as a function of solution aw, Δaw, by 0.2703 and 0.2466, respectively. Corresponding heterogeneous ice nucleation rate coefficients, Jhet, are (9.6 ± 2.5)×104 and (5.4 ± 1.4)×104 cm−2 s−1 for LEO and PP containing droplets, respectively, and remain constant along freezing curves characterized by Δaw. Consequently predictions of freezing temperatures and kinetics can be made without knowledge of the solute type when relative humidity and IN surface areas are known. The acquired ice nucleation data are applied to evaluate different approaches to fit and reproduce experimentally derived frozen fractions. In addition, we apply a basic formulation of classical nucleation theory (α(T)-model) to calculate contact angles and frozen fractions. Contact angles calculated for each ice nucleus as a function of temperature, α(T)-model, reproduce exactly experimentally derived frozen fractions without involving free fit parameters. However, assigning the IN a single contact angle for entire population (single-α model) is not suited to represent the frozen fractions. Application of α-PDF, active sites, and deterministic model approaches to measured frozen fractions yield similar good representations. Thus, from fitting frozen fractions only, the underlying ice nucleation mechanism and nature of the ice nucleating sites cannot be inferred. In contrast to using fitted functions obtained to represent experimental conditions only, we suggest to use experimentally derived Jhet as a function of temperature and aw that can be applied to conditions outside of those probed in laboratory. This is because Jhet(T) is independent of time and IN surface areas in contrast to the fit parameters obtained by representation of experimentally derived frozen fractions.

scholarly journals Ice nucleation from aqueous NaCl droplets with and without marine diatoms

2011 ◽  
Vol 11 (12) ◽  
pp. 5539-5555 ◽  
Author(s):  
P. A. Alpert ◽  
J. Y. Aller ◽  
D. A. Knopf
Keyword(s):  
Surface Area ◽  
Water Activity ◽  
Nucleation Rate ◽  
Particle Production ◽  
Ice Nucleation ◽  
Nucleation Theory ◽  
Rate Coefficients ◽  
Freezing Temperatures ◽  
Aqueous Volume ◽  
Heterogeneous Ice Nucleation

Abstract. Ice formation in the atmosphere by homogeneous and heterogeneous nucleation is one of the least understood processes in cloud microphysics and climate. Here we describe our investigation of the marine environment as a potential source of atmospheric IN by experimentally observing homogeneous ice nucleation from aqueous NaCl droplets and comparing against heterogeneous ice nucleation from aqueous NaCl droplets containing intact and fragmented diatoms. Homogeneous and heterogeneous ice nucleation are studied as a function of temperature and water activity, aw. Additional analyses are presented on the dependence of diatom surface area and aqueous volume on heterogeneous freezing temperatures, ice nucleation rates, ωhet, ice nucleation rate coefficients, Jhet, and differential and cumulative ice nuclei spectra, k(T) and K(T), respectively. Homogeneous freezing temperatures and corresponding nucleation rate coefficients are in agreement with the water activity based homogeneous ice nucleation theory within experimental and predictive uncertainties. Our results confirm, as predicted by classical nucleation theory, that a stochastic interpretation can be used to describe the homogeneous ice nucleation process. Heterogeneous ice nucleation initiated by intact and fragmented diatoms can be adequately represented by a modified water activity based ice nucleation theory. A horizontal shift in water activity, Δaw, het = 0.2303, of the ice melting curve can describe median heterogeneous freezing temperatures. Individual freezing temperatures showed no dependence on available diatom surface area and aqueous volume. Determined at median diatom freezing temperatures for aw from 0.8 to 0.99, ωhet~0.11+0.06−0.05 s−1, Jhet~1.0+1.16−0.61×104 cm−2 s−1, and K~6.2+3.5−4.1 ×104 cm−2. The experimentally derived ice nucleation rates and nuclei spectra allow us to estimate ice particle production which we subsequently use for a comparison with observed ice crystal concentrations typically found in cirrus and polar marine mixed-phase clouds. Differences in application of time-dependent and time-independent analyses to predict ice particle production are discussed.

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.

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