Homogeneous ice nucleation from aqueous inorganic/organic particles representative of biomass burning: water activity, freezing temperatures, nucleation rates

Homogeneous ice nucleation plays an important role in the formation of cirrus clouds with subsequent effects on the global radiative budget. Here we report on homogeneous ice nucleation temperatures and corresponding nucleation rate coefficients of aqueous droplets serving as surrogates of biomass burning aerosol. Micrometer-sized (NH(4))(2)SO(4)/levoglucosan droplets with mass ratios of 10:1, 1:1, 1:5, and 1:10 and aqueous multicomponent organic droplets with and without (NH(4))(2)SO(4) under typical tropospheric temperatures and relative humidities are investigated experimentally using a droplet conditioning and ice nucleation apparatus coupled to an optical microscope with image analysis. Homogeneous freezing was determined as a function of temperature and water activity, a(w), which was set at droplet preparation conditions. The ice nucleation data indicate that minor addition of (NH(4))(2)SO(4) to the aqueous organic droplets renders the temperature dependency of water activity negligible in contrast to the case of aqueous organic solution droplets. The mean homogeneous ice nucleation rate coefficient derived from 8 different aqueous droplet compositions with average diameters of ～60 μm for temperatures as low as 195 K and a(w) of 0.82-1 is 2.18 × 10(6) cm(-3) s(-1). The experimentally derived freezing temperatures and homogeneous ice nucleation rate coefficients are in agreement with predictions of the water activity-based homogeneous ice nucleation theory when taking predictive uncertainties into account. However, the presented ice nucleation data indicate that the water activity-based homogeneous ice nucleation theory overpredicts the freezing temperatures by up to 3 K and corresponding ice nucleation rate coefficients by up to ～2 orders of magnitude. A shift of 0.01 in a(w), which is well within the uncertainty of typical field and laboratory relative humidity measurements, brings experimental and predicted freezing temperatures and homogeneous ice nucleation rate coefficients into agreement. The experimentally derived ice nucleation data are applied to constrain the water activity-based homogeneous ice nucleation theory to smaller than ±1 order of magnitude compared to the predictive uncertainty of larger than ±6 orders of magnitude. The atmospheric implications of these findings are discussed.     

Homogeneous ice nucleation from supercooled water

Homogeneous ice nucleation from supercooled water was studied in the temperature range of 220-240 K through combining the forward flux sampling method (Allen et al., J. Chem. Phys., 2006, 124, 024102) with molecular dynamics simulations (FFS/MD), based on a recently developed coarse-grained water model (mW) (Molinero et al., J. Phys. Chem. B, 2009, 113, 4008). The calculated ice nucleation rates display a strong temperature dependence, ranging from 2.148 ± 0.635 × 10(25) m(-3) s(-1) at 220 K to 1.672 ± 0.970 × 10(-7) m(-3) s(-1) at 240 K. These rates can be fitted according to the classical nucleation theory, yielding an estimate of the effective ice-water interface energy γ(ls) of 31.01 ± 0.21 mJ m(-2) for the mW water model. Compared to experiments, our calculation underestimates the homogeneous ice nucleation rate by a few orders of magnitude. Possible reasons for the discrepancy are discussed. The nucleating ice embryo contains both cubic ice Ic and hexagonal ice Ih, with the fraction of each structure being roughly 50% when the critical size is reached. In particular, a novel defect structure containing nearly five-fold twin boundaries is identified in the ice clusters formed during nucleation. The way such defect structure is formed is found to be different from mechanisms proposed for the formation of the same defect in metallic nanoparticles and thin film. The quasi five-fold twin boundary structure found here is expected to occur in the crystallization of a wide range of materials with the diamond cubic structure, including ice.     

Homogeneous nucleation and growth of melt in copper

Molecular dynamics simulations are conducted to investigate homogeneous nucleation and growth of melt in copper described by an embedded-atom method (EAM) potential. The accuracy of this EAM potential for melting is validated by the equilibrium melting point obtained with the solid-liquid coexistence method and the superheating-supercooling hysteresis method. We characterize the atomistic melting process by following the temperature and time evolution of liquid atoms. The nucleation behavior at the extreme superheating is analyzed with the mean-first-passage-time (MFPT) method, which yields the critical size, steady-state nucleation rate, and the Zeldovich factor. The value of the steady-state nucleation rate obtained from the MFPT method is consistent with the result from direct simulations. The size distribution of subcritical nuclei appears to follow a power law similar to three-dimensional percolation. The diffuse solid-liquid interface has a sigmoidal profile with a 10%-90% width of about 12 A near the critical nucleation. The critical size obtained from our simulations is in reasonable agreement with the prediction of classical nucleation theory if the finite interface width is considered. The growth of melt is coupled with nucleation and can be described qualitatively with the Johnson-Meh-Avrami law. System sizes of 10(3)-10(6) atoms are explored, and negligible size dependence is found for bulk properties and for the critical nucleation.     

Freezing water in no-man's land

We report homogeneous ice nucleation rates between 202 K and 215 K, thereby reducing the measurement gap that previously existed between 203 K and 228 K. These temperatures are significantly below the homogenous freezing limit, T(H)≈ 235 K for bulk water, and well within no-man's land. The ice nucleation rates are determined by characterizing nanodroplets with radii between 3.2 and 5.8 nm produced in a supersonic nozzle using three techniques: (1) pressure trace measurements to determine the properties of the flow as well as the temperature and velocity of the droplets, (2) small angle X-ray scattering (SAXS) to measure the size and number density of the droplets, and (3) Fourier Transform Infrared (FTIR) spectroscopy to follow the liquid to solid phase transition. Assuming that nucleation occurs throughout the droplet volume, the measured ice nucleation rates J(ice,V) are on the order of 10(23) cm(-3) s(-1), and agree well with published values near 203 K.     

Heterogeneous ice nucleation in aqueous solutions: the role of water activity

Heterogeneous ice nucleation experiments have been performed with four different ice nuclei (IN), namely nonadecanol, silica, silver iodide and Arizona test dust. All IN are either immersed in the droplets or located at the droplets surface. The IN were exposed to various aqueous solutions, which consist of (NH4)2SO4, H2SO4, MgCl2, NaCl, LiCl, Ca(NO3)2, K2CO3, CH3COONa, ethylene glycol, glycerol, malonic acid, PEG300 or a NaCl/malonic acid mixture. Freezing was studied using a differential scanning calorimeter and a cold finger cell. The results show that the heterogeneous ice freezing temperatures decrease with increasing solute concentration; however, the magnitude of this effect is solute dependent. In contrast, when the results are analyzed in terms of the solution water activity a very consistent behavior emerges: heterogeneous ice nucleation temperatures for all four IN converge each onto a single line, irrespective of the nature of the solute. We find that a constant offset with respect to the ice melting point curve, Deltaaw,het, can describe the observed freezing temperatures for each IN. Such a behavior is well-known for homogeneous ice nucleation from supercooled liquid droplets and has led to the development of water-activity-based ice nucleation theory. The large variety of investigated solutes together with different general types of ice nuclei studied (monolayers, ionic crystals, covalently bound network-forming compounds, and a mixture of chemically different crystallites) underlines the general applicability of water-activity-based ice nucleation theory also for heterogeneous ice nucleation in the immersion mode. Finally, the ice nucleation efficiencies of the various IN, as well as the atmospheric implication of the developed parametrization are discussed.     

Dynamics of ice nucleation on water repellent surfaces

Prevention of ice accretion and adhesion on surfaces is relevant to many applications, leading to improved operation safety, increased energy efficiency, and cost reduction. Development of passive nonicing coatings is highly desirable, since current antiicing strategies are energy and cost intensive. Superhydrophobicity has been proposed as a lead passive nonicing strategy, yet the exact mechanism of delayed icing on these surfaces is not clearly understood. In this work, we present an in-depth analysis of ice formation dynamics upon water droplet impact on surfaces with different wettabilities. We experimentally demonstrate that ice nucleation under low-humidity conditions can be delayed through control of surface chemistry and texture. Combining infrared (IR) thermometry and high-speed photography, we observe that the reduction of water-surface contact area on superhydrophobic surfaces plays a dual role in delaying nucleation: first by reducing heat transfer and second by reducing the probability of heterogeneous nucleation at the water-substrate interface. This work also includes an analysis (based on classical nucleation theory) to estimate various homogeneous and heterogeneous nucleation rates in icing situations. The key finding is that ice nucleation delay on superhydrophobic surfaces is more prominent at moderate degrees of supercooling, while closer to the homogeneous nucleation temperature, bulk and air-water interface nucleation effects become equally important. The study presented here offers a comprehensive perspective on the efficacy of textured surfaces for nonicing applications.     

Experimental investigation of the homogeneous freezing of aqueous ammonium sulfate droplets

We have measured the light scattering intensity and homogeneous ice nucleation temperatures from water droplets containing 0-33 wt % ammonium sulfate. In these laboratory experiments, we used a free-fall freezing tube technique to determine the fraction of frozen droplets at a particular droplet temperature by measuring the depolarized light scattering intensity from the droplets in free-fall. Previously reported freezing temperatures for solution concentrations greater than 5 wt % display a larger spread than can be accounted for by the reported experimental errors. We find freezing temperatures in good agreement with the lowest temperature freezing results reported by previous experiments. Our ammonium sulfate freezing temperature data set with water activity less than 0.98 is consistent with a curve that deviates in activity shift by about 5% from the best-fit ice nucleation temperature versus water activity curve found by Koop et al. in 2000, but the significance of this deviation will only be known with further high-precision ice nucleation temperature measurements for other aqueous solutions.     

冷冻过程中胞内溶液均相成核温度的确定

为了研究冷冻过程中胞内溶液均相成核温度下降值与平衡凝固点下降值的关系, 提出了一种求解变组元系统成核温度的方法, 并联合细胞脱水方程, 进行了数值求解. 研究发现, 甘油-氯化钠-水三元系统的均相成核温度下降与平衡凝固点下降存在如下的线性关系: ⊿Th=1.17⊿Tm, 表明水溶液均相成核温度与溶质有关.     

Connection between the virial equation of state and physical clusters in a low density vapor

We carry out Monte Carlo simulations of physical Lennard-Jones and water clusters and show that the number of physical clusters in vapor is directly related to the virial equation of state. This relation holds at temperatures clearly below the critical temperatures, in other words, as long as the cluster-cluster interactions can be neglected--a typical assumption used in theories of nucleation. Above a certain threshold cluster size depending on temperature and interaction potential, the change in cluster work of formation can be calculated analytically with the recently proposed scaling law. The breakdown of the scaling law below the threshold sizes is accurately modeled with the low order virial coefficients. Our results indicate that high order virial coefficients can be analytically calculated from the lower order coefficients when the scaling law for cluster work of formation is valid. The scaling law also allows the calculation of the surface tension and equilibrium vapor density with computationally efficient simulations of physical clusters. Our calculated values are in good agreement with those obtained with other methods. We also present our results for the curvature dependent surface tension of water clusters.     

Inhibition of solute crystallisation in aqueous H(+)-NH(4)(+)-SO4(2-)-H2O droplets

Ice clouds in the Earth's upper troposphere can form via homogeneous nucleation of ice in aqueous droplets. In this study we investigate the crystallisation, or lack of crystallisation, of the solute phase and ice in aqueous (NH(4))(3)H(SO(4))(2)/H(2)O and NH(4)HSO(4)/H(2)O droplets. This is done using in situ X-ray diffraction of emulsified solution droplets mounted on a cold stage. From the diffraction patterns we are able to identify the phases of crystalline solute and ice that form after homogeneous freezing in micrometer sized droplets. An important finding from this study is that crystallisation of the solute does not always occur, even when crystallisation is strongly thermodynamically favoured. The nucleation and growth of solute phase crystals becomes inhibited since the viscosity of the aqueous brine most likely increases dramatically as the brine concentration increases and temperature decreases. If ice nucleates below a threshold freezing temperature, the brine appears to rapidly become so viscous that solute crystallisation is inhibited. This threshold temperature is 192 K and 180 K, in (NH(4))(3)H(SO(4))(2) and NH(4)HSO(4), respectively. We also speculate that the formation of cubic ice within a highly viscous brine blocks the solvent mediated cubic to hexagonal phase transformation, thus stabilising the metastable cubic ice in the most concentrated solution droplets.     

Homogeneous freezing of water starts in the subsurface

Molecular dynamics simulations of homogeneous ice nucleation in extended aqueous slabs show that freezing preferentially starts in the subsurface. The top surface layer remains disordered during the freezing process. The subsurface accommodates better than the bulk the increase of volume connected with freezing. It also experiences strong electric fields caused by oriented surface water molecules, which can enhance ice nucleation. Our computational results shed new light on the experimental controversy concerning the bulk vs surface origin of homogeneous ice nucleation in water droplets. This has important atmospheric implications for the microphysics of formation of high altitude clouds.     

Freezing of water and aqueous NaCl droplets coated by organic monolayers as a function of surfactant properties and water activity

This study presents heterogeneous ice nucleation from water and aqueous NaCl droplets coated by 1-nonadecanol and 1-nonadecanoic acid monolayers as a function of water activity (a(w)) from 0.8 to 1 accompanied by measurements of the corresponding pressure-area isotherms and equilibrium spreading pressures. For water and aqueous NaCl solutions of ~0-20 wt % in concentration, 1-nonadecanol exhibits a condensed phase, whereas the phase of 1-nonadecanoic acid changes from an expanded to a condensed state with increasing NaCl content of the aqueous subphase. 1-Nonadecanol-coated aqueous droplets exhibit the highest median freezing temperatures that can be described by a shift in a(w) of the ice melting curve by 0.098 according to the a(w)-based ice nucleation approach. This freezing curve represents a heterogeneous ice nucleation rate coefficient (J(het)) of 0.85 ± 0.30 cm(-2) s(-1). The median freezing temperatures of 1-nonadecanoic acid-coated aqueous droplets decrease less with increasing NaCl content compared to the homogeneous freezing temperatures. This trend in freezing temperature is best described by a linear function in a(w) and not by the a(w)-based ice nucleation approach most likely due to an increased ice nucleation efficiency of 1-nonadecanoic acid governed by the monolayer state. This freezing curve represents J(het) = 0.46 ± 0.16 cm(-2) s(-1). Contact angles (α) for 1-nonadecanol- and 1-nonadecanoic acid-coated aqueous droplets increase as temperature decreases for each droplet composition, but absolute values depend on employed water diffusivity and the interfacial energies of the ice embryo. A parametrization of log[J(het)(Δa(w))] is presented which allows prediction of freezing temperatures and heterogeneous ice nucleation rate coefficients for water and aqueous NaCl droplets coated by 1-nonadecanol without knowledge of the droplet's composition and α.     

On the thermodynamic equilibrium between ice and electrolyte solutions in the conditions of confined geometry

For a small volume (of about 10⁻⁶ cm³) of NaCl and other electrolyte solutions (C = 0.1 and 1 M) in thin (r = 5/10 μm) single quartz capillaries, dependencies of the column length l of frozen solutions on the temperature t were measured using comparator IZA-2 in a thermostated chamber. At temperatures range t > −4 °C (for C = 0.1 M) and t > −8 °C (for C = 1 M) the l(t) dependencies are reversible and therefore correspond to establishment of an equilibrium between ice-1 and the solution.

From the constants mass condition of the dissolved salt in a frozen column, the l(t) expression was derived, which includes thermodynamic relation between solution concentration in an equilibrium with ice, C_s, and the temperature t for bulk systems. Deviations from the data known for bulk solutions were observed in thin capillaries when temperature t decreased to −3 °C (for 0.1 M NaCl) and to −6 °C for 1 M NaCl solution.

This effect may be a result of strong adhesion of the ice column to capillary walls. In this case, some internal stresses arise in frozen solution resulting in a deviation from thermodynamic equilibrium conditions for bulk systems. When approaching the temperature of ice melting, adhesion forces decrease due to formation of a thin non-freezing water interlayer on the capillary wall. In this temperature range the experimental data are in agreement with the predictions for bulk systems. It was supposed that the observed deviation in thin capillaries may be caused by formation of an amorphous ice phase with higher density as compared with the ice-1 during rapid freezing, or by an effect of ice microlenses formation. Both effects will result in a deviation from the phase diagram corresponding to a bulk solution.     

Free energy landscapes for homogeneous nucleation of ice for a monatomic water model

We simulate the homogeneous nucleation of ice from supercooled liquid water at 220 K in the isobaric-isothermal ensemble using the MW monatomic water potential. Monte Carlo simulations using umbrella sampling are performed in order to determine the nucleation free energy barrier. We find the Gibbs energy profile to be relatively consistent with that predicted by classical nucleation theory; the free energy barrier to nucleation was determined to be ~18 k(B)T and the critical nucleus comprised ~85 ice particles. Growth from the supercooled liquid gives clusters that are predominantly cubic, whilst starting with a pre-formed subcritical nucleus of cubic or hexagonal ice results in the growth of predominantly that phase of ice only.     

Metadynamics simulations of ice nucleation and growth

The metadynamics method for accelerating rate events in molecular simulations is applied to the problem of ice freezing. We demonstrate homogeneous nucleation and growth of ice at 180 K in the isothermal-isobaric ensemble without the presence of external fields or surfaces. This result represents the first report of continuous and dynamic ice nucleation in a system of freely evolving density. Simulations are conducted using a variety of periodic simulation domains. In all cases the cubic polymorph ice I(c) is grown. The influence of boundary effects on estimates of the nucleation free energy barrier are discussed in relation to differences between this and earlier work.     

Nucleation of bulk phases in the HCl/H2O system

We report experimental results on the low-temperature uptake of HCl on H(2)O ice (ice). HCl was deposited on the surface at greater than monolayer amounts at 85 K, and the ice substrate was heated. The temperature dependence of the HCl vapor pressure from this phase was measured from 110 to 150 K, with the nucleation of a bulk hydrate phase observed at 150 K. Measurements were conducted in a closed system by simultaneous application of gas phase mass spectrometry and surface spectroscopy to characterize vapor/solid equilibrium and the nucleation of bulk hydrate phases. Combining the nucleation data reported here with data we reported previously (180 to 200 K) and data from two other laboratories (165 and 170 K), the thermodynamic boundaries for the nucleation of both the metastable bulk solution and bulk hydrate phases subsequent to monolayer adsorption of HCl have been determined. The nucleation of the metastable bulk solution phase occurs promptly at monolayer coverage at the ice/liquid coexistence boundary on the binary bulk phase diagram. The nucleation of the bulk hexahydrate occurs from this metastable solution along a locus of points defining a state of constant solution free energy. This measured free energy is -51.2 +/- 0.9 kJ/mol. Finally, the temperature dependence of the HCl vapor pressure from the low-temperature phase is reported here for the first time and is consistent with that of the metastable solution predicted by this thermodynamic model of uptake, extending the range of validity of this model of adsorption followed by bulk solution and hydrate nucleation to a lower bound in temperature of 110 K.     

Molecular dynamics simulations of ice nucleation by electric fields

Molecular dynamics simulations are used to investigate heterogeneous ice nucleation in model systems where an electric field acts on water molecules within 10-20 ? of a surface. Two different water models (the six-site and TIP4P/Ice models) are considered, and in both cases, it is shown that a surface field can serve as a very effective ice nucleation catalyst in supercooled water. Ice with a ferroelectric cubic structure nucleates near the surface, and dipole disordered cubic ice grows outward from the surface layer. We examine the influences of temperature and two important field parameters, the field strength and distance from the surface over which it acts, on the ice nucleation process. For the six-site model, the highest temperature where we observe field-induced ice nucleation is 280 K, and for TIP4P/Ice 270 K (note that the estimated normal freezing points of the six-site and TIP4P/Ice models are ～289 and ～270 K, respectively). The minimum electric field strength required to nucleate ice depends a little on how far the field extends from the surface. If it extends 20 ?, then a field strength of 1.5 × 10(9) V/m is effective for both models. If the field extent is 10 ?, then stronger fields are required (2.5 × 10(9) V/m for TIP4P/Ice and 3.5 × 10(9) V/m for the six-site model). Our results demonstrate that fields of realistic strength, that act only over a narrow surface region, can effectively nucleate ice at temperatures not far below the freezing point. This further supports the possibility that local electric fields can be a significant factor influencing heterogeneous ice nucleation in physical situations. We would expect this to be especially relevant for ice nuclei with very rough surfaces where one would expect local fields of varying strength and direction.     

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.     

On the role of surface charges for homogeneous freezing of supercooled water microdroplets

Charge induced changes in homogeneous freezing rates of water have been proposed to constitute a possible link between the global atmospheric electric circuit and cloud microphysics and thus climate. We report here on high precision measurements of the homogeneous nucleation rate of charged, electro-dynamically levitated single water droplets as a function of their surface charge. No evidence has been found that the homogeneous volume specific ice nucleation rate of supercooled microdroplets is influenced by surface charges in the range between +/-200 elementary charges per μm(2). It has also been suggested that filamentation in highly electrified liquids can induce freezing at temperatures well above the homogeneous freezing limit. We report here the observation of Coulomb instabilities of highly charged droplets that are accompanied with the formation and ejection of fine filaments from the liquid supercooled droplets. Down to temperatures of 240 K, which is close to the homogeneous freezing limit of uncharged water, no filamentation induced freezing has been detected. At even lower temperatures, the droplets froze before the instability was reached. These findings rule out that filamentation exerts an important influence on ice formation in supercooled water. Combining these findings, we conclude that the surface charges (even at their maximum possible density) have no significant effect on the homogeneous ice nucleation rate of supercooled cloud droplets.     

Mechanism of freezing of water in contact with mesoporous silicas MCM-41, SBA-15 and SBA-16: role of boundary water of pore outlets in freezing

The freezing mechanism of water contacted with mesoporous silicas with uniform pore shapes, both cylindrical and cagelike, was studied by thermodynamic and structural analyses with differential scanning calorimetry (DSC) and X-ray diffraction (XRD) together with adsorption measurements. In the DSC data extra exothermic peaks were found at around 230 K for water confined in SBA-15, in addition to that due to the freezing of pore water. These peaks are most likely to be ascribed to the freezing of water present over the micropore and/or mesopore outlets of coronas in SBA-15. Freezing of water confined in SBA-16 was systematically analysed by DSC with changing the pore size. The freezing temperature was found to be around 232 K, close to the homogeneous nucleation temperature of bulk water, independent of the pore size when the pore diameter (d) < 7.0 nm. Water confined in the cagelike pores of SBA-16 is probably surrounded by a water layer (boundary water) at the outlets of channels to interconnect the pores and of fine corona-like pores, which is similar to that present at the outlet of cylindrical pores in MCM-41 and of cylindrical channels in SBA-15. The presence of the boundary water would be a key for water in SBA-16 to freeze at the homogeneous nucleation temperature. This phenomenon is similar to those well known for water droplets in oil and water droplets of clouds in the sky. The XRD data showed that the cubic ice I(c) was formed in SBA-16 as previously found in SBA-15 when d < 8.0 nm.