Molecular dynamics study of homogeneous nucleation in supercooled clusters of sodium bromide

Molecular dynamics simulations are carried out on clusters comprised of 108, 256, 500, and 864 Na⁺Br⁻ ion pairs represented by a Born–Mayer–Hugins interaction potential. Clusters with free boundaries are chosen in order to avoid the interference with nucleation caused by periodic boundary conditions. The melting point increases with increasing size of cluster as expected. The nucleation has been found to start near the surface of a NaBr cluster. The rates of nucleation in melted clusters are estimated based on classical nucleation theory. The interfacial free energies of 73.3–76.4 mJ/m² in temperature range of 400–550 K derived from kinetics of freezing are in the same order of magnitude as those predicted by Turnbull's relation and Buckle and Ubbelohde's observation. Sizes of critical nuclei are inferred from classical expressions and Voronoi polyhedra analyses.     

Molecular dynamics simulation of the kinetics of nucleation of supercooled NaCl melt clusters

Approaches to describing the structure of metastable liquids are considered. A criterion for the classification of particles in a supercooled NaCl melt is suggested. The criterion is based on the Q₆ method and structural features of salt crystals. It was applied to analyze the configurations of clusters calculated by the molecular dynamics method. The results were interpreted using classic nucleation theory and the probabilistic approach. It was shown that crystalline phase nuclei with subcritical sizes existed in a metastable liquid. The evolution of nucleus sizes follows a complex mechanism. Along with monomer attachment and detachment reactions, collective structural fluctuations play a noticeable role.     

Molecular dynamics study of phase transition and nucleation in supercooled clusters of potassium iodide

In a series of molecular dynamics (MD) runs on (KI)₁₀₈ clusters, the Born–Mayer–Huggins potential function is employed to study structural, energetic, and kinetic aspects of phase change and the homogeneous nucleation of KI clusters. Melting and freezing are reproducible when clusters are heated and cooled. The melted clusters are not spherical in shape no matter the starting cluster is cubic or spherical. Quenching a melted (KI)₁₀₈ cluster from 960 K in a bath with temperature range 200–400 K for a time period of 80 ps both nucleation and crystallization are observed. Nucleation rates exceeding 10³⁶ critical nuclei m⁻³ s⁻¹ are determined at 200, 250, 300, 350, and 400 K. Results are interpreted in terms of the classical theory of nucleation of Turnbull and Fisher and of Buckle. Interfacial free energies of the liquid–solid phase derived from the nucleation rates are 7–10 mJ m⁻². This quantity is 0.19 of the heat of transition per unit area from solid to liquid, or about two-thirds of the corresponding ratio which Turnbull proposed for freezing transition. The temperature dependence of σ_sl(T) of (KI)₁₀₈ clusters can be expressed as σ_sl(T)∝T^0.34.     

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.     

Duration of nucleation process in supercooled halide melts

We present a model allowing to estimate the so-called time lag of nucleating halide melts using electrical conductivity measurements. Due to the complex-forming nature of molten halide salts we suppose two basic types of charge carriers in the melt: complexes (playing the role of monomers-building units) and clusters of a newly forming solid phase. Within context of the nonstationary nucleation theory we determined a formula expressing the time dependency of electrical conductivity of such a system and compared this result with the experimental data obtained for the melts of PbBr2, PbCl2, and KPb2Cl5. In terms of this formula the time lag of nucleation may be estimated. This important quantity characterizing the moment from which the nucleated clusters only grow to the macroscopic sizes has been found to be approximately 75% of the total duration of the nucleation process itself.     

Non-photochemical laser-induced nucleation of supercooled glacial acetic acid

Non-photochemical laser-induced nucleation (NPLIN) of glacial acetic acid (GAA) is demonstrated. The fraction of samples nucleated depends linearly on peak laser power density at low powers (<100 MW cm(-2)) with a threshold of (9.0 ± 4.2) MW cm(-2); at higher laser powers the fraction reaches a plateau of 0.75 ± 0.24 (2σ uncertainties). A simple model based on polarizability of pre-nucleating clusters gives a value of the solid-liquid interfacial tension γ(SL) = 15.5 mJ m(-2). It is hoped that the results will stimulate new developments in experimental and theoretical studies of cluster structure and nucleation in liquids.     

A limit of stability in supercooled liquid clusters

We examine the metastable liquid phase of a supercooled gold nanocluster by studying the free energy landscape using the largest solidlike embryo as an order parameter. Just below freezing, the free energy exhibits a local minimum at small embryo sizes and a maximum at a larger critical embryo size. At T=660 K the free energy becomes a monotonically decreasing function of the order parameter as the liquid phase becomes unstable, indicating that we have reached a limit of stability. In contrast to the mean-field theory predictions for a spinodal, the size of the critical embryo remains finite as the limit of stability is approached. We also calculate the rate of nucleation, independently from our free energy calculations, and observe a rapid increase in its temperature dependence when the free energy barrier is on the order of kT. We suggest that this supports the idea that freezing becomes a barrierless process at low temperatures.     

Sequential reactions of silicon clusters with SiD4: constrained heterogeneous nucleation of deuterated silicon particles

The sequential clustering reactions of gas phase silicon cluster ions are ideally suited for studying heterogeneous nucleation of silicon particles. Stepwise reactions of silicon cluster ions with silane have been observed which lead to growth of larger deuterated silicon clusters. Extensive information is obtained about their exothermic gas phase reaction rates and product distributions as a function of cluster size and degree of hydrogenation. What is found is that each size of silicon cluster exhibits a unique pattern of growth. Furthermore, nearly all of the silicon clusters encounter chemical constraints to rapid nucleation. These constraints are a consequence of specific electronic and structural requirements in the chemical reactions. The nature of these requirements are deduced using experimental results in concert with ab initio electronic structure theoretical calculations of the energetics and structures of various species.     

Ice nucleation by particles immersed in supercooled cloud droplets

The formation of ice particles in the Earth's atmosphere strongly affects the properties of clouds and their impact on climate. Despite the importance of ice formation in determining the properties of clouds, the Intergovernmental Panel on Climate Change (IPCC, 2007) was unable to assess the impact of atmospheric ice formation in their most recent report because our basic knowledge is insufficient. Part of the problem is the paucity of quantitative information on the ability of various atmospheric aerosol species to initiate ice formation. Here we review and assess the existing quantitative knowledge of ice nucleation by particles immersed within supercooled water droplets. We introduce aerosol species which have been identified in the past as potentially important ice nuclei and address their ice-nucleating ability when immersed in a supercooled droplet. We focus on mineral dusts, biological species (pollen, bacteria, fungal spores and plankton), carbonaceous combustion products and volcanic ash. In order to make a quantitative comparison we first introduce several ways of describing ice nucleation and then summarise the existing information according to the time-independent (singular) approximation. Using this approximation in combination with typical atmospheric loadings, we estimate the importance of ice nucleation by different aerosol types. According to these estimates we find that ice nucleation below about -15 °C is dominated by soot and mineral dusts. Above this temperature the only materials known to nucleate ice are biological, with quantitative data for other materials absent from the literature. We conclude with a summary of the challenges our community faces.     

Surface area controlled heterogeneous nucleation

Heterogeneous nucleation of liquid from a gas phase on nanoparticles has been studied under various saturation ratios and nuclei size. The probability of liquid droplet nucleation, especially at a low degree of deviation from equilibrium, was measured for both atmospheric aerosol particles and engineered nanoparticles Cr(2)O(3). The concept of a critical saturation ratio and the validity of the one-to-one relationship between the nuclei number and the number of droplets were examined. A transient zone between no nucleation and established nucleation termed the surface area controlled nucleation was observed. In this zone, the probability of stable phase formation is determined by the surface area of nuclei. There are two distinctive features of the surface area controlled nucleation: the nucleation probability is much less than 1 and is proportional to the surface area of nuclei. For condensation particle counters (CPCs) counting nanoparticles, these features mean that counts measured are proportional to the surface area of nanoparticles and, therefore, the CPCs counts can be calibrated to measure the surface area.     

Nonclassical nucleation kinetics in the crystallization of a supercooled melt

A molecular dynamics simulation of homogenous nucleation of a crystal in supercooled aluminum melt is performed. Nucleation rates at a temperature of 900 K in the range of pressures from 12 to 15 GPa are calculated. Analysis of the mean first-passage times of crystalline cluster sizes is performed. A stepwise dependence of the mean first-passage time on crystal nucleus size is observed, in contrast to the sigmoidal dependence that follows from classical nucleation theory. Based on the data from atomistic simulations, it is established that the form of the free energy barrier during nucleation differs significantly from the one assumed in classical nucleation theory for a spherically symmetric nucleus. It is supposed that the observed differences are apparently due to the complex structure of the crystalline nucleus.     

H2O nucleation around Au+

First principles electronic structure calculations have been carried out to investigate the ground state geometry, electronic structure, and the binding energy of [Au(H2O)n]+ clusters containing up to 10 H2O molecules. It is shown that the first coordination shell of Au+ contains two H2O molecules forming a H2O-Au+-H2O structure with C2 symmetry. Subsequent H2O molecules bind to the previous H2O molecules forming stable and fairly rigid rings, each composed of 4 H2O molecules, and leading to a dumbbell structure at [Au(H2O)8]+. The 9th and the 10th H2O molecules occupy locations above the Au+ cation mainly bonded to one H2O from each ring, leading to structures where the side rings are partially distorted and forming structures that resemble droplet formation around the Au+ cation. The investigations highlight quantum effects in nucleation at small sizes and provide a microscopic understanding of the observed incremental binding energy deduced from collision induced dissociation that indicates that [Au(H2O)n]+ clusters with 7-10 H2O molecules have comparable binding energy. The charge on the Au+ is shown to migrate to the outside H2O molecules, suggesting an interesting screening phenomenon.     

Test of classical nucleation theory on deeply supercooled high-pressure simulated silica

We test classical nucleation theory (CNT) in the case of simulations of deeply supercooled, high density liquid silica, as modeled by the van Beest-Kramer-van Santen potential. We find that at density rho=4.38 gcm(3), spontaneous nucleation of crystalline stishovite occurs in conventional molecular dynamics simulations at temperature T=3000 K, and we evaluate the nucleation rate J directly at this T via "brute force" sampling of nucleation events in numerous independent runs. We then use parallel, constrained Monte Carlo simulations to evaluate DeltaG(n), the free energy to form a crystalline embryo containing n silicon atoms, at T=3000, 3100, 3200, and 3300 K. By comparing the form of DeltaG(n) to CNT, we test the ability of CNT to reproduce the observed behavior as we approach the regime where spontaneous nucleation occurs on simulation time scales. We find that the prediction of CNT for the n dependence of DeltaG(n) fits reasonably well to the data at all T studied. Deltamu, the chemical potential difference between bulk liquid and stishovite, is evaluated as a fit parameter in our analysis of the form of DeltaG(n). Compared to directly determined values of Deltamu extracted from previous work, the fitted values agree only at T=3300 K; at lower T the fitted values increasingly overestimate Deltamu as T decreases. We find that n(*), the size of the critical nucleus, is approximately ten silicon atoms at T=3300 K. At 3000 K, n(*) decreases to approximately 3, and at such small sizes methodological challenges arise in the evaluation of DeltaG(n) when using standard techniques; indeed even the thermodynamic stability of the supercooled liquid comes into question under these conditions. We therefore present a modified approach that permits an estimation of DeltaG(n) at 3000 K. Finally, we directly evaluate at T=3000 K the kinetic prefactors in the CNT expression for J, and find physically reasonable values; e.g., the diffusion length that Si atoms must travel in order to move from the liquid to the crystal embryo is approximately 0.2 nm. We are thereby able to compare the results for J at 3000 K obtained both directly and based on CNT, and find that they agree within an order of magnitude. In sum, our work quantifies how certain predictions of CNT (e.g., for Deltamu) break down in this deeply supercooled limit, while others [the n dependence of DeltaG(n)] are not as adversely affected.     

The molecular approach to heterogeneous nucleation

A molecular approach to heterogeneous nucleation has been developed. The expressions for the equilibrium cluster distribution, the reversible work of the cluster formation, and the nucleation rate have been derived. Two separate statements for the work of formation were formulated. If the equilibrium cluster distribution is normalized on the monomer concentration near the substrate surface, the reversible work of formation is expressed by DeltaG(het) (I) = (F(n) (het)-F(n) (hom))-(F(1) (het)-F(1) (hom)) + DeltaG(hom) where F(n) (het) and F(n) (hom) are the Helmholtz free energies of a cluster interacting with a substrate and a cluster not interacting with the substrate, respectively. If the equilibrium cluster distribution is normalized on the monomer concentration far from the substrate surface, the work of cluster formation is given by DeltaG(het) (II) = (F(n) (het)-F(n) (hom)) + DeltaG(hom). The former expression corresponds to the approach of the classical heterogeneous nucleation theory. The cluster partition function appears to be dependent on the location of a virtual plane, which separates the volume, where the interaction of the clusters with the substrate is effective from the one where interaction is negligible. Our Monte Carlo simulations have shown that the dependence is rather weak and thus the location of the plane is not very important. According to the simulations the variation of the plane position in the range from 20 to 50 Angstroms does not lead to a considerable change of the heterogeneous nucleation rate.     

Fragmentation spectroscopy of heterogeneous clusters

Photoionisation experiments were performed with heterogeneous Ar-Xe-clusters produced by supersonic expansion of argon gas with small quantities of xenon added to it. A threshold-electron photoionisation (TEPICO) technique was used to obtain time of flight cluster mass spectra. These mass spectra show particularly strong intensities for Ar₁₂Xe⁺ and Ar₁₈Xe⁺ which are attributed to the extraordinary stabilities of these cluster ions. Maxima in the ionic size distribution around Ar₇Xe⁺ are related to a particular abundance ofneutral Ar₁₂Xe which is fragmented after ionization. These stabilities are explained in terms of geometries consisting of a central Xe atom or ion surrounded by shells of Ar atoms. Filled shells exhibit particular strong bonding because these exhibit the largest number of atom-atom bonds. This conclusion is supported by simple theoretical calculations. The ionization process is discussed in terms of two direct and one indirect ionization channels the latter one proceeding via an intermediate electronic excitation of the Ar component in the neutral cluster.     

Improved quasi-unary nucleation model for binary H2SO4-H2O homogeneous nucleation

Aerosol nucleation events have been observed at a variety of locations worldwide, and may have significant climatic and health implications. Binary homogeneous nucleation (BHN) of H2SO4 and H2O is the foundation of recently proposed nucleation mechanisms involving additional species such as ammonia, ions, and organic compounds, and it may dominate atmospheric nucleation under certain conditions. We have shown in previous work that H2SO4-H2O BHN can be treated as a quasi-unary nucleation (QUN) process involving H2SO4 in equilibrium with H2O vapor, and we have developed a self-consistent kinetic model for H2SO4-H2O nucleation. Here, the QUN approach is improved, and an analytical expression yielding H2SO4-H2O QUN rates is derived. Two independent measurements related to monomer hydration are used to constrain the equilibrium constants for this process, which reduces a major source of uncertainty. It is also shown that the capillarity approximation may lead to a large error in the calculated Gibbs free energy change for the evaporation of H2SO4 molecules from small H2SO4-H2O clusters, which affects the accuracy of predicted BHN nucleation rates. The improved QUN model-taking into account the recently measured energetics of small clusters-is thermodynamically more robust. Moreover, predicted QUN nucleation rates are in better agreement with available experimental data than rates calculated using classical H2SO4-H2O BHN theory.     

Communication: crystallite nucleation in supercooled glycerol near the glass transition

Heterogeneity and solid-like structures found near the glass transition provide a key to a better understanding of supercooled liquids and of the glass transition. However, the formation of solid-like structures and its effect on spatial heterogeneity in supercooled liquids is neither well documented nor well understood. In this work, we reveal the crystalline nature of the solid-like structures in supercooled glycerol by means of neutron scattering. The results indicate that inhomogeneous nucleation happens at temperatures near T(g). Nevertheless, the thermal history of the sample is essential for crystallization. This implies such structures in supercooled liquids strongly depend on thermal history. Our work suggests that different thermal histories may lead to different structures and therefore to different length and time scales of heterogeneity near the glass transition.     

Quasi-unary homogeneous nucleation of H2SO4-H2O

We show that the binary homogeneous nucleation (BHN) of H2SO4-H2O can be treated as quasi-unary nucleation of H2SO4 in equilibrium with H2O vapor. A scheme to calculate the evaporation coefficient of H2SO4 molecules from H2SO4-H2O clusters is presented and a kinetic model to simulate the quasi-unary nucleation of H2SO4-H2O is developed. In the kinetic model, the growth and evaporation of sulfuric acid clusters of various sizes are explicitly simulated. The kinetic quasi-unary nucleation model does not have two well-recognized problems associated with the classical BHN theory (violation of the mass action law and mismatch of the cluster distribution for monomers) and is appropriate for the situations where the assumption of equilibrium cluster distribution is invalid. The nucleation rates predicted with our quasi-unary kinetic model are consistent with recent experimental nucleation experiments in all the cases studied, while the most recent version of the classical BHN model systematically overpredicts the nucleation rates. The hydration of sulfuric acid clusters, which is not considered in the classical model but is accounted for implicitly in our kinetic quasi-unary model, is likely to be one of physical mechanisms that lead to lower nucleation rates. Further investigation is needed to understand exactly what cause the difference between the kinetic quasi-unary model and the classical BHN model.     

The low frequency dynamics of supercooled LiBr, 6H2O

We present results of a series of experiments performed on LiBr, 6H(2)0 from room temperature down to 172 K ≈ 1.2T(g). These ultrasound, Brillouin and depolarized light scattering, and transient grating experiments show that, above 215 K, this solution behaves like supercooled water: its zero frequency sound velocity C(0) continuously decreases with decreasing temperature, and the reorientational dynamics of the water molecules can be directly detected at some temperatures of this domain. Conversely, below 215 K, a new regime sets in, where the apparent C(0) is practically temperature independent and where a β, Arrenhius like, relaxation process coexists with the usual, Vogel-Fulcher like, α relaxation process of the supercooled liquid. These results are similar to those recently obtained in LiCl, 6H(2)O. The onset of the new regime is possibly due to an increase of the interaction of the water molecules with a neighboring Li(+) ion when lowering the temperature. We also compare our results with published dielectric data on water solutions of glass forming polyalcohols. Some of them present a low temperature splitting of their relaxation time similar to what is found in LiBr, 6H(2)O.