Water-vapor clustering on the surface of β-AgI crystal in the field of defects with a disordered structure

The Monte Carlo method has been employed to simulate the nucleation of condensed water phase from vapor at 260 K on a crystalline silver-iodide surface containing a defect in the form of a nanoscopic spot with a random distribution of ions. The free energy and work of formation of a nucleus have been calculated in the bicanonical ensemble at the molecular level as functions of nucleus size; computer images and spatial correlation functions of molecules have been obtained. The presence of a defect with a disordered (amorphous) structure, on the one hand, entails local destructions of a monomolecular film, but, on the other hand, shifts the onset of the adsorption process toward lower vapor pressures by several orders of magnitude. Under the conditions of a growing condensate film, the defect leads to its thermodynamic stabilization and a decrease in the barrier of the formation of subsequent layers, thereby weakening the known effect of the hydrophobicity of monomolecular films on crystalline surfaces with hexagonal structures. The factors that predetermine the abnormally high efficiency of silver-iodide particles as stimulators for atmospheric-moisture nucleation at negative Celsius temperatures seem to be the presence of extended defects on the surface of aerosol particles in combination with the hexagonal structure of their crystal lattice, the optimum magnitude of direct interactions between water molecules with ions of the crystal surface layer, and the collective domain-formation effects that result from a relatively high polarizability of iodine ions.     

A kinetic model for nonisothermic homogeneous nucleation

A model for isothermal homogeneous nucleation is proposed that improves the classical model. A quasiequilibrium distribution of clusters was calculated on a basis of the Frenkel’-Lothe-Pound theory. The dependence of the free energy of clusters on their size was represented by an interpolation formula relating the free energy of dimers and large clusters to which a notion of macroscopic surface tension is applicable. The nucleation rate and the dependence of the cluster temperature on their size were calculated by balance equations describing the heating of from a cluster due to the condensation of monomers and its cooling due to collisions with an ambient gas. It is shown that the nucleation rate in excess buffer gas is higher than for the pure condensing gas by approximately two orders of magnitude. The model adequately describes the experimental data for the nucleation of methanol supersaturated vapor.     

Water vapor nucleation on an infinite substrate with complementary structure: 2. The influence of crystal defects

The simulation of the adsorption of water vapor on the infinite surface of a silver iodide crystal with regularly arranged crystal defects is performed by the Monte Carlo method. Long-range electrostatic and polarization interactions are taken into account by the Ewald method. The work of nucleus formation in the field of crystal defects is calculated by the method of bicanonical statistical ensemble. The interaction with a defect decreases the internal energy, the Gibbs energy, and the entropy of the nucleus. The rough surface of the silver iodide crystal exerts a larger stimulating effect on vapor nucleation than an ideally smooth surface. Saturation vapor pressure above the condensate layer formed on the rough surface can be several times lower than the pressure above the smooth surface. This effect is caused by the cooperative action of surface crystal defects. It may be expected that the surface with a characteristic size of rough elements of 15–20 Å is the most efficient for the formation of condensed phase nuclei. Single point crystal defects with extremely small sizes on the substrate surface do not exert a stimulating effect on the formation of the macroscopic condensed phase. Single defects with moderate sizes can lower the barrier of monomolecular film formation; however, such a route of the stimulation of ice-forming activity of the surface is less efficient than the cooperative action of the defects of rough surface.     

Argon nucleation in a cryogenic nucleation pulse chamber

Homogeneous nucleation of argon droplets has been measured with a newly designed cryogenic nucleation pulse chamber presented already in a previous paper [Fladerer and Strey, J. Chem. Phys. 124, 16 (2006)]. Here we present the first systematic nucleation onset data for argon measured in a temperature range from 42 to 58 K and for vapor pressures from 0.3 to 10 kPa. For these data we provide an analytical fit function. From the geometry of the optical detection system and the time of nucleation the experimental nucleation-rate range can be estimated. This allows a comparison of the data with the predictions of classical nucleation theory. We found 16-26 orders of magnitude difference between theory and experiment, and a too strong theoretical dependence of the nucleation rate on temperature. A comparison with the self-consistent theory of Girshick and Chiu [J. Chem. Phys. 93, 1273 (1990)] showed improved temperature dependence but still discrepancies of 11-17 orders of magnitude compared to experimental data. The thermodynamically consistent theory of Kashchiev [J. Chem. Phys. 118, 1837 (2003)] was found to agree rather well with experiment in respect to the temperature dependence and to predict rates about 5-7 orders of magnitude below the experimental ones. With the help of the Gibbs-Thomson equation we were able to evaluate the size of the critical nucleus to be 40-80 argon atoms.     

A study of nucleation in supersaturated ibuprofen vapor in a flow diffusion chamber

Isothermal nucleation of supersaturated ibuprofen racemate vapor has been experimentally studied in a flow diffusion chamber at 293.3 and 301.2 K. Nucleation rates have been measured in the range of 10⁴?10⁴ cm^?3 s^?1 as functions of supersaturation. According to the first nucleation theorem, the numbers of molecules in critical nuclei have been found and used to determine the nucleation rate and supersaturation values as depending on the sizes of critical nuclei. The comparison of the experimental data with theoretical predictions has shown that the nucleation rates measured as functions of the numbers of molecules in critical nuclei are higher than the rates predicted by the classical theory by six to seven decimal orders of magnitude but, within one order of magnitude, coincide with the rates predicted by a theory previously proposed in a work by one of the authors, in which nucleation clusters were considered to be microscopic objects.     

Homogeneous nucleation of n-nonane and n-propanol mixtures: a comparison of classical nucleation theory and experiments

The homogeneous nucleation rates for n-nonane-n-propanol vapor mixtures have been calculated as a function of vapor-phase activities at 230 K using the classical nucleation theory (CNT) with both rigorous and approximate kinetic prefactors and compared to previously reported experimental data. The predicted nucleation rates resemble qualitatively the experimental results for low n-nonane gas phase activity. On the high nonane activity side the theoretical nucleation rates are about three orders of magnitude lower than the experimental data when using the CNT with the approximate kinetics. The accurate kinetics improves the situation by reducing the difference between theory and experiments to two orders of magnitude. Besides the nucleation rate comparison and the experimental and predicted onset activities, the critical cluster composition is presented. The total number of molecules is approximated by CNT with reasonable accuracy. Overall, the classical nucleation theory with rigorous kinetic prefactor seems to perform better. The thermodynamic parameters needed to calculate the nucleation rates are revised extensively. Up-to-date estimates of liquid phase activities using universal functional activity coefficient Dortmund method are presented together with the experimental values of surface tensions obtained in the present study.     

Monte Carlo simulation study of droplet nucleation

A new rigorous Monte Carlo simulation approach is employed to study nucleation barriers for droplets in Lennard-Jones fluid. Using the gauge cell method we generate the excess isotherm of critical clusters in the size range from two to six molecular diameters. The ghost field method is employed to compute the cluster free energy and the nucleation barrier with desired precision of (1-2)kT. Based on quantitative results obtained by Monte Carlo simulations, we access the limits of applicability of the capillarity approximation of the classical nucleation theory and the Tolman equation. We show that the capillarity approximation corrected for vapor nonideality and liquid compressibility provides a reasonable assessment for the size of critical clusters in Lennard-Jones fluid; however, its accuracy is not sufficient to predict the nucleation barriers for making practical estimates of the rate of nucleation. The established dependence of the droplet surface tension on the droplet size cannot be approximated by the Tolman equation for small droplets of radius less than four molecular diameters. We confirm the conclusion of ten Wolde and Frenkel [J. Chem. Phys. 109, 9901 (1998)] that integration of the normal component of the Irving-Kirkwood pressure tensor severely underestimates the nucleation barriers for small clusters.     

Unprecedented differences in the diamond nucleation density between carbon- and silicon-faces of 4H-silicon carbides

4H-silicon carbides deposited by diamond films have wide applications in many fields such as semiconductor heterojunction, heat sink and mechanical sealing. Nucleation plays a critical role in the deposition of the diamond film on 4H-silicon carbides. Nevertheless, as a typical polar material, the fundamental mechanism of diamond nucleation on different faces of 4H-silicon carbides has not been fully understood yet. In this contribution, nucleation of diamond was performed on the carbon- and silicon-faces of 4H-silicon carbides in a direct current chemical vapor deposition device. The nucleation density on the carbon-face is higher by 2–3 orders of magnitude compared to the silicon-face. Transmission electron microscopy verifies that there are high density diamond nuclei on the interface between the carbon-face and the diamond film, which is different from columnar diamond growth structure on the silicon-face. Transition state theory calculation reveals that the unprecedented distinction of the nucleation density between the carbon-face and the silicon-face is attributed to different desorption rates of the absorbed hydrocarbon radicals. In addition, kinetic model simulations demonstrate that it is more difficult to form CH₂(s)-CH₂(s) dimers on silicon-faces than carbon-faces, resulting in much lower nucleation densities on silicon-faces.     

Crystal nucleation and the solid-liquid interfacial free energy

We present the results of molecular dynamics simulation of crystal nucleation in a supercooled Lennard-Jones liquid. Temperature and baric dependences of the nucleation rate, the Zeldovich factor, nucleus size diffusion coefficient, the radius, and the pressure in a critical crystal nucleus are defined in computer simulation. The data obtained have been used in the framework of classical nucleation theory to calculate the effective surface energy of crystal nuclei γ(e). It is shown that the value of γ(e) at T = const exceeds the value of the interfacial free energy at a flat crystal-liquid interface γ(∞) and γ(e) < γ(∞) at p = const.     

Homogeneous nucleation at high supersaturation and heterogeneous nucleation on microscopic wettable particles: A hybrid thermodynamic/density-functional theory

Homogeneous nucleation at high supersaturation of vapor and heterogeneous nucleation on microscopic wettable particles are studied on the basis of Lennard-Jones model system. A hybrid classical thermodynamics and density-functional theory (DFT) approach is undertaken to treat the nucleation problems. Local-density approximation and weighted-density approximation are employed within the framework of DFT. Special attention is given to the disjoining pressure of small liquid droplets, which is dependent on the thickness of wetting film and radius of the wettable particle. Different contributions to the disjoining pressure are examined using both analytical estimations and numerical DFT calculation. It is shown that van der Waals interaction results in negative contribution to the disjoining pressure. The presence of wettable particles results in positive contribution to the disjoining pressure, which plays the key role in the heterogeneous nucleation. Several definitions of the surface tension of liquid droplets are discussed. Curvature dependence of the surface tension of small liquid droplets is computed. The important characteristics of nucleation, including the formation free energy of the droplet and nucleation barrier height, are obtained.     

Water vapor nucleation on a crystal surface in a strong electric field

Water vapor nucleation at 260 K in a transverse electric field has been simulated by the Monte Carlo method under conditions corresponding to an internal wall of a spatially extended microcrack in a silver iodide crystal. The bicanonical statistical ensemble method has been employed to calculate, at the molecular level, the free energy of addition and the work of formation of dense phase nuclei in fields with different strengths. In a moderate field, the film mechanism of nucleation characterized by intense distortions on the film surface remains preserved. A domain structure of a film layer in contact with the surface exhibits a high stability with respect to an external field and remains preserved until the film is completely destroyed. In a strong electric field, the nucleation mechanism is fundamentally changed; i.e., the film is destroyed to yield threadlike structures. Therewith, the area of the contact with the surface drastically decreases. The orientation of nanothreads along the electric field lines overcomes a low free energy barrier. The point of equilibrium of nanothreads with vapor depends on the presence of hydrogen bonds, while their stability is determined by longer-range dipole-dipole interactions. The observed form of existence of the condensate as polarized nanothreads seems to be analogous to the superpolarized state previously revealed for water microdroplets, the transition to which has the character of the first-order phase transition.     

Hit and miss of classical nucleation theory as revealed by a molecular simulation study of crystal nucleation in supercooled sulfur hexafluoride

Classical nucleation theory pictures the homogeneous nucleation of a crystal as the formation of a spherical crystalline embryo, possessing the properties of the macroscopic crystal, inside a parent supercooled liquid. In this work we study crystal nucleation in moderately supercooled sulfur hexafluoride by umbrella sampling simulations. The nucleation free energy evolves from 5.2kBT at T=170 K to 39.1kBT at T=195 K. The corresponding critical nucleus size ranges from 40 molecules at T=170 K to 266 molecules at T=195 K. Both nucleation free energy and critical nucleus size are shown to evolve with temperature according to the equations derived from the classical nucleation theory. Inspecting the obtained nuclei we show, however, that they present quite anisotropic shapes in opposition to the spherical assumption of the theory. Moreover, even though the critical nuclei possess the structure of the stable bcc plastic phase, the only mechanically stable crystal phase for SF6 in the temperature range investigated, they are shown to be less ordered than the corresponding macroscopic crystal. Their crystalline order is nevertheless shown to increase regularly with their size. This is confirmed by a study of a nucleus growth from a critical size to a size of the order of 10(4) molecules. Similarly to the fact that it does not affect the temperature dependence of the nucleation free energy and of the critical nucleus size, the ordering of the nucleus with size does not affect the growth rate of the nucleus.     

Collective interactions in the mechanism of adhesion of condensed phase nuclei to a crystal surface. 2. Thermodynamic stability

The Monte Carlo method is used to calculate, at the molecular level, the free energy, entropy, and the work of formation at an initial stage of nucleation of a condensed phase from water vapor on the surface of a solid crystalline silver iodide substrate. The pattern of the obtained dependences confirms the pronounced layer-by-layer character of the growth of nuclei and the thermodynamic stability of a molecular film formed at the contact with the substrate. An increased hydrophilicity of the substrate surface with respect to the first monomolecular layer is enhanced by the formation of regions of spontaneous polarization in the latter. The reasons for the thermodynamic advantage of the separation of the nucleus contact layer on the substrate into domains with different types of polarization are analyzed in terms of a lattice model. Computer simulation within the framework of the lattice model demonstrates that a rise in the polarizability of the substrate is accompanied by a continuous increase in the equilibrium sizes of the domains; moreover, the model predicts their strongly nonlinear dependence on both temperature and the polarizability of the substrate.     

The Effect of Temperature on Nucleation of Condensed Water Phase on the Surface of a β-AgI Crystal. 2. Formation Work

In the condensation mechanism of heterogeneous ice formation, water crystallization occurs after a necessary amount of the liquid phase has accumulated on a substrate surface. In this way, the ice-forming activity of the surface is governed by its adsorption ability with respect to water vapor. The Monte Carlo canonical statistical ensemble method has been used to calculate the free energy, entropy, and work of nucleation of a disordered condensed water phase on the surface of crystalline silver iodide and to determine the surface tension. Comparative calculations have been performed at 260 and 320 K for the defect-free surface of a basal face of a crystal. The surface of a β-AgI crystal is completely covered with a monomolecular film even in unsaturated water vapors. The surface tension at the growing nucleus–substrate interface substantially increases due to the formation of the underlying film, and the growth of the nucleus becomes possible only in a supersaturated vapor. As the vapor density increases, the thickness of the condensed water layer grows, and, at negative Celsius temperatures, conditions are created for its crystallization. The underlying film with pronounced hydrophobic properties hinders nucleation, thereby decreasing the ice-forming activity of the surface in the condensation process. Under these conditions, the observed abnormally high ice-forming activity of silver-iodide aerosol particles may be explained by the presence of numerous crystal defects on the particle surface, with these defects representing channels that provide overcoming the hindering action of the film.     

Comparison between the classical theory predictions and molecular simulation results for heterogeneous nucleation of argon

We have performed Monte Carlo simulations of homogeneous and heterogeneous nucleations of Lennard-Jones argon clusters. The simulation results were interpreted using the major concept posing a difference between the homogeneous and heterogeneous classical nucleation theories-the contact parameter. Our results show that the multiplication concept of the classical heterogeneous nucleation theory describes the cluster-substrate interaction surprisingly well even for small molecular clusters. However, in the case of argon nucleating on a rigid monolayer of fcc(111) substrate at T=60 K, the argon-substrate atom interaction being approximately one-third as strong as the argon-argon interaction, the use of the classical theory concept results in an underestimation of the heterogeneous nucleation rate by two to three orders of magnitude even for large clusters. The main contribution to this discrepancy is induced by the failure of the classical theory of homogeneous nucleation to predict the energy involved in bringing one molecule from the vapor to the cluster for clusters containing less than approximately 15 molecules.     

Supramolecular mechanisms responsible for the high activity of aerosol stimulants of atmospheric moisture nucleation

Water vapor nucleation preceding crystal nucleation was studied by computer simulation; the role of crystal defects on the surface with a structure complementary to the structure of ice was investigated. The Gibbs energy and microdrop formation energy were calculated at the molecular level. The structure and thermodynamic stability of nuclei in the fields of crystal defects of different types were analyzed. It was found that crystal point defects could not stimulate the formation of large nuclei. Extended defects such as wedge-shaped fractures were shown to be the most effective stimulants. The stage of monomolecular film formation in fractures was preceded by the formation of three-dimensional microdrops. The conclusion was drawn that microcrystallization was favored by a relatively large surface of contact with microfracture walls, the three-dimensional structure of nuclei, and their high thermodynamic stability in the transverse microfracture field; these factors drastically accelerated the growth of nuclei and their coalescence on the surface of aerosol particles.     

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.     

Bubble nucleation in micellar solution: a density functional study

We explore the free energetics of bubble nucleation in the micellar solution subjected to a negative pressure using a density functional model of a non-ionic surfactant solution. In this two-component model, the solvent is represented by a single hard-core sphere and the surfactant is represented by two tangent hard-core spheres connected by a rigid bond. The attractive interactions between the particles are modeled by the simple 1/R(6) form. Under all conditions of pressure and interparticle interactions we studied, the free energy barrier of bubble nucleation is found to be lower in the binary surfactant solution than that in a pure solvent and to continue to decrease as the mole fraction of the surfactant in the solution increases. We analyze the free energy surface of the model system under the conditions where both the critical bubble nucleus and the stable micelle exist in equilibrium with the same metastable solution. Our study shows that at moderately low pressures, bubbles can nucleate from the stable micelle and that the resulting free energy barrier of bubble nucleation is expected to be lower than that in the absence of this mechanism. However, as the spinodal is approached at lower pressures, the mechanism of micelle-assisted bubble nucleation becomes less effective. The liquid-liquid miscibility of the model system correlates well with the mechanism of bubble nucleation from the stable micelle.     

Rethinking the application of the first nucleation theorem to particle formation

The critical cluster is the threshold size above which a cluster will be more likely to grow than to evaporate. In field and laboratory measurements of new particle formation, the number of molecules of a given species in the critical cluster is commonly taken to be the slope of the log-log plot of the formation rate versus the concentration of the species. This analysis is based on an approximate form of the first nucleation theorem, which is derived with the assumption that there are no minima in the free energy surface prior to the maximum at the critical size. However, many atmospherically relevant systems are likely to exhibit such minima, for example, ions surrounded by condensable vapour molecules or certain combinations of acids and bases. We have solved numerically the birth-death equations for both an electrically neutral one-component model system with a local minimum at pre-critical sizes and an ion-induced case. For the ion-induced case, it is verified that the log-log slope of the nucleation rate versus particle concentration plot gives accurately the difference between the cluster sizes at the free energy maximum and minimum, as is expected from the classical form of the ion-induced nucleation rate. However, the results show that applying the nucleation theorem to neutral systems with stable pre-nucleation clusters may lead to erroneous interpretations about the nature of the critical cluster.