Effect of chlorine ions on the stability of nucleation cores in condensing water vapors

The Gibbs energy and the equilibrium work of nucleation of condensed-phase nuclei in water vapors in the presence of chlorine anions are calculated at the molecular level using the Monte Carlo method at a temperature of 273 K for sizes of up to 200 molecules. It is found that the growth of a nucleus leads to the displacement of a chloride ion onto its surface, which is accompanied by a loss of the thermodynamic stability of the microdroplet. It is found that the size dependence of the work of nucleation exhibits a minimum and a maximum with an inflection point that separates the region of stable and unstable equilibrium sizes.     

Kinetic theory of heterogeneous nucleation; effect of nonuniform density in the nuclei

The heterogeneous nucleation of a liquid from a vapor in contact with a planar solid surface or a solid surface with cavities is examined on the basis of the kinetic theory of nucleation developed by Nowakowski and Ruckenstein [J. Phys. Chem. 96 (1992) 2313] which is extended to nonuniform fluid density distribution (FDD) in the nucleus. The latter is determined under the assumption that at each moment the FDD in the nucleus is provided by the density functional theory (DFT) for a nanodrop. As a result of this assumption, the theory does not require to consider that the contact angle which the nucleus makes with the solid surface and the density of the nucleus are independent parameters since they are provided by the DFT. For all considered cases, the nucleation rate is higher in the cavities than on a planar surface and increases with increasing strength of the fluid-solid interactions and decreasing cavity radius. The difference is small at high supersaturations (small critical nuclei), but becomes larger at low supersaturations when the critical nucleus has a size comparable with the size of the cavity. The nonuniformity of the FDD in the nucleus decreases the nucleation rate when compared to the uniform FDD.     

Nucleation of water vapor in microcracks on the surface of β-AgI aerosol particles: 2. Thermodynamics of nucleation

Free energy, entropy, and the work of formation of condensation nuclei at 260 K in microcracks of β-AgI crystal structure at the initial stage of nucleation preceding crystallization are calculated by the Monte Carlo method. Unlike ideal crystal surface, nuclei in microcracks are thermodynamically stable and the barrier of free energy of nucleation is absent. Conditions of microcrack are favorable for the crystallization that qualitatively changes the regime and rate of nucleation. Stable size of nuclei at the humidity corresponding to natural atmosphere is sufficient for the filling of nanoscopic microcracks and the attainment of substrate surface. The probability of nucleus formation in microcracks by the fluctuation mechanism is incomparably higher than the probability of their formation on the defect-free surface. High crystallization ability of the particles of βAgI aerosol is ensured by multiple surface microcracks acting as active sites in combination with its complementary crystal structure. The efficiency of aerosols as stimulants of the nucleation of water vapor at negative Celsius temperatures is determined by the surface density and geometry of nanoscopic cracks and fissures on the particle surface.     

Multicomponent nucleation: thermodynamically consistent description of the nucleation work

A thermodynamically consistent formula is derived for the nucleation work in multicomponent homogeneous nucleation. The derivation relies on the conservative dividing surface which defines the nucleus as having specific surface energy equal to the specific surface energy sigma0 of the interface between the macroscopically large new and old phases at coexistence. Expressions are given for the radius of the nucleus defined by the conservative dividing surface and by the surface of tension. As a side result, the curvature dependence of the surface tension sigmaT of the nucleus defined by the surface of tension is also determined. The analysis is valid for nuclei of any size, i.e., for nucleation in the whole range of conditions between the binodal and the spinodal of the metastable old phase provided the inequality sigmaT < or = sigma0 is satisfied. It is found that under the conditions of validity of the analysis the nucleation rate is higher than the nucleation rate given by the classical nucleation theory. The general results are applied to nucleation of unary liquids or solids in binary gaseous, liquid or solid mixtures.     

Experimental study of homogeneous nucleation from the bismuth supersaturated vapor: evaluation of the surface tension of critical nucleus

The homogeneous nucleation of bismuth supersaturated vapor is studied in a laminar flow quartz tube nucleation chamber. The concentration, size, and morphology of outcoming aerosol particles are analyzed by a transmission electron microscope (TEM) and an automatic diffusion battery (ADB). The wall deposit morphology is studied by scanning electron microscopy. The rate of wall deposition is measured by the light absorption technique and direct weighting of the wall deposits. The confines of the nucleation region are determined in the "supersaturation cut-off" measurements inserting a metal grid into the nucleation zone and monitoring the outlet aerosol concentration response. Using the above experimental techniques, the nucleation rate, supersaturation, and nucleation temperature are measured. The surface tension of the critical nucleus and the radius of the surface of tension are determined from the measured nucleation parameters. To this aim an analytical formula for the nucleation rate is used, derived from author's previous papers based on the Gibbs formula for the work of formation of critical nucleus and the translation-rotation correction. A more accurate approach is also applied to determine the surface tension of critical drop from the experimentally measured bismuth mass flow, temperature profiles, ADB, and TEM data solving an inverse problem by numerical simulation. The simulation of the vapor to particles conversion is carried out in the framework of the explicit finite difference scheme accounting the nucleation, vapor to particles and vapor to wall deposition, and particle to wall deposition, coagulation. The nucleation rate is determined from simulations to be in the range of 10(9)-10(11) cm(-3) s(-1) for the supersaturation of Bi(2) dimers being 10(17)-10(7) and the nucleation temperature 330-570 K, respectively. The surface tension σ(S) of the bismuth critical nucleus is found to be in the range of 455-487 mN/m for the radius of the surface of tension from 0.36 to 0.48 nm. The function σ(S) changes weakly with the radius of critical nucleus. The value of σ(S) is from 14% to 24% higher than the surface tension of a flat surface.     

Heterogeneous critical nucleation on a completely wettable substrate

Heterogeneous nucleation of a new bulk phase on a flat substrate can be associated with the surface phase transition called wetting transition. When this bulk heterogeneous nucleation occurs on a completely wettable flat substrate with a zero contact angle, the classical nucleation theory predicts that the free-energy barrier of nucleation vanishes. In fact, there always exists a critical nucleus and a free-energy barrier as the first-order prewetting transition will occur even when the contact angle is zero. Furthermore, the critical nucleus changes its character from the critical nucleus of surface phase transition below bulk coexistence (undersaturation) to the critical nucleus of bulk heterogeneous nucleation above the coexistence (oversaturation) when it crosses the coexistence. Recently, Sear [J. Chem. Phys. 129, 164510 (2008)] has shown, by a direct numerical calculation of nucleation rate, that the nucleus does not notice this change when it crosses the coexistence. In our work, the morphology and the work of formation of critical nucleus on a completely wettable substrate are re-examined across the coexistence using the interface-displacement model. Indeed, the morphology and the work of formation changes continuously at the coexistence. Our results support the prediction of Sear and will rekindle the interest on heterogeneous nucleation on a completely wettable substrate.     

The effect of temperature on the development of nanosized nucleus iron-oxygen structures in Fe<Superscript>0</Superscript>-H<Superscript>2</Superscript>O-O<Superscript>2</Superscript> Systems

The formation of nucleus iron-oxygen structures in Fe⁰-H₂O-O₂ systems has been investigated. It has been shown that temperature affects the rate of iron(II) oxidation and, accordingly, the composition of components involved in phase formation. At 10°C, only nucleus structures of protolepidocrocites are formed on the surface; at 20–40°C, structures of protolepidocrocites and ferrihydrite; and at 50–70°C, structures of magnetite and FeO. The analysis of thermodynamic functions has revealed the most probable formation reactions of nucleus iron-oxygen structures and the optimal conditions for the structure formation in morphological series.     

氩蒸气在球形固体颗粒上异质核化的分子动力学模拟

异质核化在大气中广泛存在, 但是其微观核化机理鲜为人知, 本文应用分子动力学方法模拟过热氩蒸气在纳米球形固体颗粒物上异质核化的动态特性, 讨论不同的冷却率对核化过程中系综温度、团簇分布、团簇大小以及核化速率的影响. 结果显示, 系综内蒸气的核化温度随着冷却率的增加而降低, 预先存在的球形固体颗粒在团簇的形成阶段起着重要的作用, 而且存在一个临界冷却率1.80×10^-9J·s^-1. 在该冷却率下, 在异质核化系综内均质核化出现, 并与异质核化共存, 但是异质核化在整个核化过程中仍然占主导地位.     

Universal Asymptotics of the Thermodynamic Characteristics of the Nucleation on Small Macroscopic Nuclei of Soluble Surfactants

Asymptotic behavior of thermodynamic characteristics of nucleation on small macroscopic nuclei of soluble surfactants at their complete dissolution in a nucleating droplet is studied. It is taken into account that, in the region of small sizes of nuclei and corresponding small sizes of critical nuclei of liquid phase, the chemical potential of condensate and the work of droplet formation are affected by the presence of dense surfactant adsorption monolayer on the droplet surface. It is shown that, as the limiting surface area per surfactant molecule in adsorption monolayer increases, the behavior of thermodynamic characteristics of nucleation in the region of small nucleus sizes is characterized by the transition from asymptotics at the adsorption of almost all substance comprising nucleus in a monolayer to the asymptotics at constant adsorption. The study performed is not limited by the selection of specific adsorption isotherms; therefore, the obtained asymptotic dependences of thermodynamic characteristics on the nucleus size can be considered as universal for the heterogeneous nucleation on the nuclei of soluble surfactants.     

Evaluation of surface tension and Tolman length as a function of droplet radius from experimental nucleation rate and supersaturation ratio: metal vapor homogeneous nucleation

Zinc and silver vapor homogeneous nucleations are studied experimentally at the temperature from 600 to 725 and 870 K, respectively, in a laminar flow diffusion chamber with Ar as a carrier gas at atmospheric pressure. The size, shape, and concentration of aerosol particles outcoming the diffusion chamber are analyzed by a transmission electron microscope and an automatic diffusion battery. The wall deposit is studied by a scanning electron microscope (SEM). Using SEM data the nucleation rate for both Zn and Ag is estimated as 10(10) cm(-3) s(-1). The dependence of critical supersaturation on temperature for Zn and Ag measured in this paper as well as Li, Na, Cs, Ag, Mg, and Hg measured elsewhere is analyzed. To this aim the classical nucleation theory is extended by the dependence of surface tension on the nucleus radius. The preexponent in the formula for the vapor nucleation rate is derived using the formula for the work of formation of noncritical embryo [obtained by Nishioka and Kusaka [J. Chem. Phys. 96, 5370 (1992)] and later by Debenedetti and Reiss [J. Chem. Phys. 108, 5498 (1998)]] and Reiss replacement factor. Using this preexponent and the Gibbs formula for the work of formation of critical nucleus the dependence of surface tension on the radius R(S) of the surface of tension is evaluated from the nucleation data for above-mentioned metals. For the alkali metals and Ag the surface tension was determined to be a strong function of R(S). For the bivalent metals (Zn, Hg, and Mg) the surface tension was independent of radius in the experimental range. A new formula for the Tolman length delta as a function of surface tension and radius R(S) is derived by integration of Gibbs-Tolman-Koenig equation assuming that delta is a monotonic function of radius. The formula derived is more correct than the Tolman formula and convenient for the elaboration of experimental data. Using this formula the values of delta are determined as a function of R(S) from the experimental nucleation data. It is determined that all the metals considered are characterized by strong dependence of delta on radius; for the bivalent metals delta changes sign.     

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.     

Water vapor nucleation on an infinite substrate with complementary structure: 1. The mechanism of nucleation

The nucleation of water vapor on the infinite surface of a silver iodide crystal at 260 K is simulated. Long-range electrostatic and polarization interactions are taken into account by the Ewald method. The free energy and work of equilibrium formation of nuclei are calculated at the molecular level by the method of bicanonical statistical ensemble. It is shown that, at the initial stage, the substrate is completely covered with a water monolayer. The substrate tends to decrease by two orders of magnitude the vapor pressure required to form the critical nucleus of a monomolecular film with a size of 10² molecules, the nucleation rate being increased by tens of orders of magnitude as compared to homogeneous nucleation. The saturation pressure above the adsorbed monomolecular film is 12 times lower than that above the flat ice surface. The free energy at the edges of “spots” per unit length is 1.4 × 10^?11 J/m. The critical size of the spot increases with a decrease in vapor pressure as the inverse second power of the logarithm of pressure.     

Kinetic model of electrochemical nucleation

The process of electrochemical nucleation is analyzed in terms of stochastic formation of clusters of different size over the electrode surface. It is shown that the ground equation of the atomistic theory of nucleation can be derived without resort to the thermodynamic approach, in particular, the concept of the nucleus energy and its dependence on the nucleus size.     

Time-space evolution of the cloud of ion-electron pairs formed by Auger electrons around Mossbauer ion <Superscript>57</Superscript>Fe<Superscript><Emphasis Type="Italic">n</Emphasis>+</Superscript>

It is shown that the emission of energetic Auger electrons during formation of the Mossbauer nucleus ⁵⁷Fe leads not only to the formation of multicharged ion ⁵⁷Fe ⁿ⁺, but also to the formation of a cloud of several hundred (200–300) ion-electron pairs (H₂O⁺, e ^?) around the Fe ion. This cloud is called an Auger blob. Its size (radius) is approximately ～100 Å. Fast radiation-chemical reactions in an Auger blob determine the experimentally observable ratio of yields of final chemically stable states (Fe³⁺ and Fe²⁺) of the Mossbauer ion. Knowledge of this ratio is important for an adequate interpretation of the results of Mossbauer emission spectroscopy. Although our assessments relate to iron nuclei in frozen aqueous solutions, they can be easily adjusted for media of other chemical composition.     

Computer Simulation of the Initial Stage of the Nucleation of Water Vapors on the Silver Iodide Crystal Surface: 2. Thermodynamics

The formation work of the condensed phase nucleus from the vapor on the surface of silver iodide at 273 K is calculated by the method of bicanonical statistical ensemble. The energy barrier of the formation of a nucleus of a monolayer on the surface is located in the region of extremely small sizes and its height does not exceed the energy of thermal motion k _B T. Such a barrier cannot markedly decelerate the nucleation. A point crystal defect in the form of an extra ion on the surface qualitatively changes the pattern of the formation work curve: the minimum with a depth of about 100k _B T corresponding to a thermodynamically stable nucleus appears on this curve. As the vapor pressure increases, “spots” of water molecules are formed and grow on the substrate surface around point crystal defects. These spots tend to coalesce and cover the entire surface as a monolayer; however, the high free energy barrier prevents the formation of further layers.__________Translated from Kolloidnyi Zhurnal, Vol. 67, No. 4, 2005, pp. 561–572.Original Russian Text Copyright © 2005 by Shevkunov.     

Kinetics of nucleation in highly polar substances in the presence of ions

Based on of a previously proposed model for describing the effect of the electric field of the ion on the vapor-liquid phase transition, expressions for the work of formation of the critical nucleus in highly polar substances were derived. Analytical expressions for the nucleation frequency were obtained and used to calculate the heterogeneous nucleation frequency in a supersaturated water vapor.     

Miniemulsion polymerization of styrene costabilized with polyurethane via <Superscript>60</Superscript>Co γ-ray radiation initiation

Polyurethane (PU) was successfully synthesized and used as costabilizer in the miniemulsion polymerization of styrene (St) initiated by ⁶⁰Co γ-ray radiation at room temperature. Only 2 wt% PU based on the monomer was enough to prepare a stable miniemulsion with a shelf life of more than 12 months. Preservation of original particle size and distribution throughout the polymerization observed from dynamic light scattering measurements indicates the predominance of monomer droplet nucleation. Kinetic analysis shows that there is no constant rate stage, which also suggests a droplet nucleation mechanism. Polystyrene (PS) nanoparticles with relatively small diameters (40–70 nm) and narrow size distribution could be easily prepared. The effects of surfactant, costabilizer, and absorbed dose rate on the miniemulsion polymerization were discussed.     

Accounting for fluctuations in cluster parameters upon the description of nucleation in supersaturated vapor

A theory is proposed for stationary homogeneous nucleation in supersaturated vapor in which a modified expression for the rate of cluster evaporation was used to calculate the equilibrium distribution over the nucleus sizes and the rates of their formation. This rate was determined by the extrapolation to the region of small sizes of the corresponding expression for the macroscopic droplet derived according to thermodynamic notions that take fluctuations into account. Modified dependences of the size of critical nucleus and the rate of nucleation on the supersaturation and the temperature are determined and compared with the data of the classical theory of nucleation and experimental results.     

Atomistic theory of amyloid fibril nucleation

We consider the nucleation of amyloid fibrils at the molecular level when the process takes place by a direct polymerization of peptides or protein segments into β-sheets. Employing the atomistic nucleation theory (ANT), we derive a general expression for the work to form a nanosized amyloid fibril (protofilament) composed of successively layered β-sheets. The application of this expression to a recently studied peptide system allows us to determine the size of the fibril nucleus, the fibril nucleation work, and the fibril nucleation rate as functions of the supersaturation of the protein solution. Our analysis illustrates the unique feature of ANT that the size of the fibril nucleus is a constant integer in a given supersaturation range. We obtain the ANT nucleation rate and compare it with the rates determined previously in the scope of the classical nucleation theory (CNT) and the corrected classical nucleation theory (CCNT). We find that while the CNT nucleation rate is orders of magnitude greater than the ANT one, the CCNT and ANT nucleation rates are in very good quantitative agreement. The results obtained are applicable to homogeneous nucleation, which occurs when the protein solution is sufficiently pure and/or strongly supersaturated.     

显影液中银的成核过程

本文用受阻显影技术和电镜研究方法研究了显影剂量对显影液中银成核速度和核分散度的影响。随着显影液中显影剂量的减小,卤化银颗粒上银的成核速度明显减慢,单个颗粒上显影中心的数目明显增加。实验结果表明显影液中银的成核过程和曝光后的潜影形成过程在机理上是有差别的。文章讨论了显影过程中的一些基本问题:可显性、临界尺寸和显影选择性等等。