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A Theory of Immersion Freezing

Immersion freezing is likely involved in the initiation of precipitation and determines to large extent the phase partitioning in convective clouds. Theoretical models commonly used to describe immersion freezing in atmospheric models are based on the classical nucleation theory which however neglects important interactions near the immersed particle that may affect nucleation rates. This work introduces a new theory of immersion freezing based on two premises. First, immersion ice nucleation is mediated by the modification of the properties of water near the particle-liquid interface, rather than by the geometry of the ice germ. Second, the same mechanism that leads to the decrease in the work of germ formation also decreases the mobility of water molecules near the immersed particle. These two premises allow establishing general thermodynamic constraints to the ice nucleation rate. Analysis of the new theory shows that active sites likely trigger ice nucleation, but they do not control the overall nucleation rate nor the probability of freezing. It also suggests that materials with different ice nucleation efficiency may exhibit similar freezing temperatures under similar conditions but differ in their sensitivity to particle surface area and cooling rate. Predicted nucleation rates show good agreement with observations for a diverse set of materials including dust, black carbon and bacterial ice nucleating particles. The application of the new theory within the NASA Global Earth System Model (GEOS-5) is also discussed.

Ice Nucleating particle

Effects of Solute Concentrations on Kinetic Pathways in Ni-Al-Cr Alloys

The kinetic pathways resulting from the formation of coherent gamma'-precipitates from the gamma-matrix are studied for two Ni-Al-Cr alloys with similar gamma'-precipitate volume fractions at 873 K. The details of the phase decompositions of Ni-7.5Al-8.5Cr at.% and Ni-5.2Al-14.2Cr at.% for aging times from 1/6 to 1024 h are investigated by atom-probe tomography, and are found to differ significantly from a mean-field description of coarsening. The morphologies of the gamma'-precipitates of the alloys are similar, though the degrees of gamma'-precipitate coagulation and coalescence differ. Quantification within the framework of classical nucleation theory reveals that differences in the chemical driving forces for phase decomposition result in differences in the nucleation behavior of the two alloys. The temporal evolution of the gamma'-precipitate average radii and the gamma-matrix supersaturations follow the predictions of classical coarsening models. The compositional trajectories of the gamma-matrix phases of the alloys are found to follow approximately the equilibrium tie-lines, while the trajectories of the gamma'-precipitates do not, resulting in significant differences in the partitioning ratios of the solute elements.

Booth-Morrison, Christopher

Ion-induced nucleation in a binary mixture

Recent ion-induced nucleation studies in a binary mixture of H2O and H2SO4 vapors indicate that conventional classical nucleation theories cannot account for the experimentally observed ion-H2O-H2SO4 microcluster spectra. An empirical-analytical, semi-molecular theory of nucleation of a binary mixture of vapors on ions has been developed. This theory includes molecular approach to ion-induced changes in dielectric properties in the immediate neighborhood of an ion core as well as the size dependence of the surface tension of the microcluster. In addition to gaseous sulfuric acid and water molecules, the effect of ion-hydrates and sulfuric acid hydrates has also been considered. This theory is further simplified by using an empirical correction factor for the electrostatic term. This correction factor has been obtained by comparing the simplified model with the molecular dynamics calculations for selected ion hydrate formation. These two theoretical models are then compared with the classical theory for a variety of experimental conditions.

Smith, A. C.

Interpreting experimental measurements of helium bubbles using stochastic cluster dynamics models of heterogeneous nucleation and growth in irradiated ferritic alloys

Among a number of other advantageous features, ferritic/martensitic steels are being considered as fusion reactor structural materials due to their low intrinsic swelling under irradiation. However, under high-energy neutron irradiation, He produced through (n, α) reactions stabilizes vacancy clusters, which then act as seeds for bubble formation and growth, negating the intrinsic swelling resistance of these alloys. Standard models of irradiation damage accumulation and microstructural evolution consider homogeneous nucleation as the basis for bubble formation and growth. However, this generally does not explain the large bubble densities and sizes observed experimentally under a number of different conditions. Here, we propose a more realistic physical model of bubble nucleation, formation, and growth designed to capture recent experimental measurements of He-bubble formation and evolution during co-implantation of He and Fe ions in model ferritic alloys. We find that experimental results are explained only when the following three features are considered simultaneously: (i) heterogeneous nucleation of He-vacancy bubbles at defect sinks (e.g., dislocations, grain boundaries, and second-phase precipitates), (ii) nucleation and growth of bubbles via the ‘trap mutation’ mechanism (i.e., spontaneous production of Frenkel pairs due to absorption of He atoms), and (iii) transition from a growth-limited, He-stabilized bubble regime to a ‘runaway’ void-type growth scenario. The model is implemented into a stochastic cluster dynamics framework that takes advantage of cluster size grouping methods to accelerate the simulations, allowing us to reach 10 dpa of simulated irradiated dose, and to capture cluster sizes in excess of 20 nm. Further, a careful extrapolation exercise conducted assuming classical nucleation theory leads to excellent agreement with the experimental measurements at 50 dpa of irradiation.

36 MATERIALS SCIENCE

Quantifying and Modeling the Impact of Phase State on the Ice Nucleation Abilities of 2-Methyltetrols as a Key Component of Secondary Organic Aerosol Derived from Isoprene Epoxydiols

Organic aerosols (OAs) may serve as ice-nucleating particles (INPs), impacting the formation and properties of cirrus clouds when their phase state and viscosity are in the semisolid to glassy range. However, there is a lack of direct parameterization between aerosol viscosity and their ice nucleation capabilities. In this study, we experimentally measured the ice nucleation rate of 2-methyltetrols (2-MT) aerosols, a key component of isoprene-epoxydiol-derived secondary organic aerosols (IEPOX-SOA), at different viscosities. These results demonstrate that the phase state has a significant impact on the ice nucleation abilities of OA under typical cirrus cloud conditions, with the ice nucleation rate increasing by 2 to 3 orders of magnitude when the phase state changes from liquid to semisolid. An innovative parametric model based on classical nucleation theory was developed to directly quantify the impact of viscosity on the heterogeneous nucleation rate. This model accurately represents our laboratory measurement and can be implemented into climate models due to its simple, equation-based form. Based on data collected from the ACRIDICON-CHUVA field campaign, our model predicts that the INP concentration from IEPOX-SOA can reach the magnitude of 1 to tens per liter in the cirrus cloud region impacted by the Amazon rainforest, consistent with recent field observations and estimations. This novel parameterization framework can also be applied in regional and global climate models to further improve representations of cirrus cloud formation and associated climate impacts.

2-methyltetrol

Thermodynamic Control of Interface Directs MnO 2 Nucleation Chemistry for Dense and Conformal Electrodeposition

Manganese dioxide (MnO 2 ) is widely recognized as a promising material for high-energy-density energy storage systems due to its broad applicability and facile electrodeposition. However, achieving uniform, thin, and high-mass-loading MnO 2 coatings on high-surface-area electrodes remains a significant challenge. Conventional electrodeposition methods typically yield nonuniform, thick layers with poor conductivity and limited material utilization, restricting their practical use. Here, we uncover a thermodynamically engineered vanadyl/pervanadyl (VO 2+ /VO 2 + ) interface that fundamentally reshapes MnO 2 electrodeposition chemistry, enabling highly uniform and dense coatings. Here, combining in situ AFM measurement, Classical Nucleation Theory, and Johnson–Mehl–Avrami–Kolmogorov modeling, we show that this interface reduces early-stage detectable MnO 2 island size by 35-fold and shifts the MnO 2 growth from diffusion-limited to reaction-limited progressive nucleation. This thermodynamically controlled interface yields highly dense and conformal MnO 2 films with record-high mass loading of 241 mg cm –2 (1607 mg cm –3 ) on 3D-printed graphene aerogels, without compromising porosity or inducing thickness gradient. As a prototype demonstration, the resulting MnO 2 electrodes deliver record-setting volumetric performance in both capacitors (106 F cm –3 ) and Zn//MnO 2 pouch cells (162 mAh cm –3 ). Beyond energy storage, our findings demonstrate the significance of thermodynamic interface control in MnO 2 nucleation chemistry for achieving dense and uniform coatings on various substrates, with implications for electrocatalysis, semiconductor processing, and advanced materials manufacturing.

Batteries

Interpreting dynamic-compression experiments to uncover the time dependence of freezing: Application to gallium

Using pulsed-power magnetic field sources to compress gallium to gigapascal pressures on nanosecond timescales, we report here experiments on shockless dynamic compression of a liquid metal. Time-resolved velocimetry data reveal signatures of rapid freezing from a metastable liquid state, and we demonstrate that the kinetics of this nonequilibrium solidification can be accurately simulated with a computational modeling framework we have developed in previous studies, where classical nucleation theory is coupled with hydrodynamics. Notably, velocity traces in some of our experiments show evidence of a phase transition, while others do not, even though other types of evidence suggest that solidification may be occurring in all of them. We explain how predictions made by our models regarding the presence or absence of these phase-transition signatures motivated additional experiments that later confirmed the theoretical predictions. Our analysis shows that due to the rapid, quasi-isentropic nature of the loading path, our experiments were able to compress liquid gallium to metastable states that are undercooled below the equilibrium melt temperature by more than 300 K and exhibit pressures that approach five times the equilibrium melt pressure. The understanding gained in this study should form the basis for future dynamic-compression experiments aimed at interrogating melt curves at high pressures.

gallium

Onset of cavitation and vapor bubble development over hydrophilic and hydrophobic surfaces

Cavitation, the formation of vapor bubbles as the liquid pressure is reduced below the saturated vapor pressure, often requires a substantial negative relative pressure in a pure liquid. Classical nucleation theory (CNT) provides an estimate for the rate of cavitation but there is often a disconnect between the predictions at the molecular scale compared to observations at the macroscale. We report on mesoscale simulations of cavitation based on many-body dissipative particle dynamics (mDPD), a coarse-grained molecular dynamics (MD), which bridges the two scales. A liquid layer is confined between smooth planar walls at a constant temperature, while the pressure is reduced slowly by expanding the wall-bounded domain. The wetting properties of the liquid are determined by the parameters of the interaction potentials. With hydrophilic walls, homogeneous nucleation is observed in the liquid bulk. As a bubble forms and grows, it creates a strong pressure pulse and oscillations that cause other bubbles that may have formed slightly later to collapse. For a nearly neutral wall with a contact angle close to 90 ° , heterogeneous nucleation occurs at the walls at a smaller negative pressure and generates weaker pressure oscillations. With hydrophobic walls or seed particles, heterogeneous nucleation readily occurs, where fluctuations and the merger of transient surface bubbles are significant.

Science & Technology - Other Topics

The importance of accounting for the Tolman correction to surface tension for nucleation and growth modeling of Fe clusters

Gibbs free energies of clusters are required for predictive modeling of cluster growth during condensation of a cooling vapor. Here, we present a straightforward method of calculating free energies of cluster formation using the data from molecular dynamics (MD) simulations. We apply this method to iron clusters having from 2 to 100 atoms. The energies obtained are verified by comparing to an MD-simulated equilibrium cluster size distribution in a sub-saturated vapor. We show that these free energies differ significantly from those obtained with a commonly used spherical cluster approximation, which relies on a surface tension coefficient of a flat surface, as it is used in the classical nucleation theory (CNT). We show that the spherical cluster approximation in CNT can be improved by using a cluster-size-dependent Tolman correction for the surface tension. The Tolman length and effective surface tension values were derived for iron clusters, and they significantly differ from the commonly used experimentally measured values. This improved approximation does not account for geometric magic number effects responsible for spikes and troughs in densities of neighbor cluster sizes. Nonetheless, it allows to more accurately model cluster formation from a cooling vapor. It better reproduces the condensation timeline, overall shape of the cluster size distribution, average cluster size, and the distribution width. In contrast, using a constant surface tension coefficient (as done in CNT) resulted in incorrect condensation dynamics and cluster size distributions. The analytical expression for cluster nucleation rate from CNT was updated to account for the size-dependence of cluster surface tension.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Multiscale Modeling Framework for Lithium Nucleation in 3D Porous Carbon Anodes

Porous carbon scaffolds offer a promising route for mitigating non-uniform lithium (Li) plating to enhance the safety and longevity of Li metal batteries. However, the influence of microstructural morphology on Li nucleation is not well understood. Here, we present a multiscale modeling framework to investigate how the porous microstructure of carbon materials affects Li nucleation behavior. Ab initio molecular dynamics simulations quantify the nucleation energy barriers of Li on graphene as a function of Li content, surface curvature, and applied potential, providing key parameters for a classical nucleation theory (CNT) model. From macroscale half-cell simulations, we obtained Li concentration and electrical potential profiles to define boundary conditions for mesoscopic simulations. At the mesoscale, three distinct synthetic 3D microstructures with different porosities and characteristic feature sizes are generated to resolve local distributions of Li flux, current density, and mechanical stress. These outputs are integrated into the CNT model to map spatial variation in nucleation rates. Our findings reveal trade-offs between suppressing nucleation rates and achieving spatial uniformity, offering design guidelines for optimizing porous carbon anodes to balance nucleation control and mechanical integrity.

Materials science

Time lag effects in the nucleation of particles in stellar atmospheres

When a system goes from a saturated state to a supersaturated one, the classical nucleation-rate formula is not instantly valid; rather, the nucleation rate relaxes exponentially (with a characteristic time - the time lag) to the value given by the steady-state formula. Under some circumstances, particularly those found in some cool stellar atmospheres, the time lag can be quite long and a decisve factor in determining the possibility of particle formation. Carbon condensation in the atmospheres of Mira variables is considered and found to be unlikely on the basis of classical nucleation theory because of the long time lags involved, unless the parameters describing the physical conditions in these atmospheres are significantly different from current estimates.

Walker, G. H.

Experimental study of cluster formation in binary mixture of H2O and H2SO4 vapors in the presence of an ionizing radiation source

Molecular clusters formed in pure nitrogen containing H2O and H2SO4 vapors and exposed to a 3 mCi Ni63 beta source were studied in the mass range 50 to 780 amu using a quadrupole mass spectrometer. Measurements were made under several combinations of relative humidity and relative acidity ranging from 0.7 to 7.5 percent and 0.00047 to 0.06333 percent, respectively. The number of H2SO4 molecules in the clusters observed ranged from 1 to 7 whereas the number of H2O molecules ranged from 1 to 16. The experimental cluster spectra differ considerably from those calculated using the classical nucleation theory. First order calculations using modified surface tension values and including the effects of multipole moments of the nucleating molecules indicate that these effects may be enough to explain the difference between the measured and the calculated spectra.

Singh, J. J.

Vibrational disequilibrium in low pressure clouds

Steady state vibrational populations of SiO and CO in several dilute blackbody radiation fields have been calculated as a function of total pressure, kinetic temperature, and chemical composition of the gas. An approximate calculation for polyatomic molecules has also been carried out. Vibrational disequilibrium becomes increasingly significant as the total pressure and radiation density decrease. Many regions of postulated grain formation are found to be far out of thermal equilibrium before the onset of condensation. The use of classical nucleation theory and equilibrium thermodynamics to predict the onset of condensation and the composition of the solids or the molecular composition of the gas phase in such regions therefore is very questionable and needs to be examined for each case.

Nuth, J. A.

Experimental and Theoretical Studies of Interstellar Grains

Steady state vibrational populations of SiO and CO in dilute black body radiation fields were calculated as a function of total pressure, kinetic temperature and chemical composition of the gas. Approximate calculations for polyatomic molecules are presented. Vibrational disequilibrium becomes increasingly significant as total pressure and radiation density decrease. Many regions of postulated grain formation are found to be far from thermal equilibrium before the onset of nucleation. Calculations based upon classical nucleation theory or equilibrium thermodynamics are expected to be of dubious value in such regions. Laboratory measurements of the extinction of small iron and magnetite grains were made from 195 nm to 830 nm and found to be consistent with predictions based upon published optical constants. This implies that small iron particles are not responsible for the 220 nm interstellar extinction features. Additional measurements are discussed.

Nuth, J. A., III

Temperature dependence of the formation of sulfate aerosols in the stratosphere

Classical nucleation theory is used in calculations of the temperature dependence of the characteristics and nucleation rates of sulfate aerosols in the binary H2SO4-H2O vapor mixture, in order to assess the influence of temperature on the formation of sulfate aerosols in the stratosphere, and to explore the possibility of new particle formation through homogeneous nucleation processes at regions where temperature is as low as -75 C, rather than the often-assumed -50 or -55 C. Calculation results indicate that the number of particles formed at a lower temperature is larger by several orders of magnitude than at higher temperatures, when water and sulfuric acid vapor concentrations are kept constant, and that large quantities of ultrafine particles which cannot be detected by conventional methods may exist at low-temperature stratospheric regions.

Yue, G. K.

A new method to measure homogeneous nucleation rates in shock tubes

The centered expansion wave of a shock tube is utilized to expand and supersaturate a condensable vapor in small concentration in an inert carrier gas. The supersaturated state, located at the rear of the expansion wave, is preserved for a controlled period and then terminated by a recompressing shock wave. During the period of supersaturation, condensation nuclei are formed homogeneously. The nucleation rate is measured as a function of supersaturation by a Mie-light scattering technique. The method is tested using water and the results are compared with classical nucleation theory.

Peters, F.

Transient nucleation in condensed systems

Using classical nucleation theory we consider transient nucleation occurring in a one-component, condensed system under isothermal conditions. We obtain an exact closed-form expression for the time dependent cluster populations. In addition, a more versatile approach is developed: a numerical simulation technique which models directly the reactions by which clusters are produced. This simulation demonstrates the evolution of cluster populations and nucleation rate in the transient regime. Results from the simulation are verified by comparison with exact analytical solutions for the steady state. Experimental methods for measuring transient nucleation are assessed, and it is demonstrated that the observed behavior depends on the method used. The effect of preexisting cluster distributions is studied. Previous analytical and numerical treatments of transient nucleation are compared to the solutions obtained from the simulation. The simple expressions of Kashchiev are shown to give good descriptions of the nucleation behavior.

Kelton, K. F.

Experimental studies of the vapor phase nucleation of refractory compounds. III - The condensation of silver

Measurements are reported of the critical supersaturation necessary to initiate the vapor phase nucleation of silver over the ambient temperature range 500-950 K at total pressures of 250 and 500 torr of hydrogen. The results are compared with the predictions of both classical nucleation theory and the theory of a physical spinodal developed by Rasmussen (1982), neither of which adequately describes the present observations. The nucleation of silver appears to be dependent on the total pressure of the system in a manner which suggests that three-body reactions are necessary in order to form the initial silver cluster (e.g., dimers) from the monoatomic vapor.

Nuth, J. A.