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.     

Experimental studies of the vapor phase nucleation of refractory compounds. VI. The condensation of sodium

In this paper we discuss the condensation of sodium vapor and the formation of a sodium aerosol as it occurs in a gas evaporation condensation chamber. A one-dimensional model describing the vapor transport to the vapor/aerosol interface was employed to determine the onset supersaturation, in which we assume the observed location of the interface is coincident with a nucleation rate maximum. We then present and discuss the resulting nucleation onset supersaturation data within the context of nucleation theory based on the liquid droplet model. Nucleation results appear to be consistent with a cesium vapor-to-liquid nucleation study performed in a thermal diffusion cloud chamber.     

Sampling and analysis of nanoparticles with cold fibre SPME device

A new approach is described to capture nano‐size aerosols on internally‐cooled micro tubing of the solid‐phase microextraction (SPME) device followed by convenient introduction of the collected analytes into analytical instrument. Particles were generated using an aerosol formation by homogeneous nucleation of an organic vapor, and subsequent growth to nano‐size particles by coagulation of decanedioic acid, bis[2‐ethylhexyl] ester (DEHS). The approach was validated by using carbon dioxide‐cooled micro tubing to collect the nanosize DEHS particles followed by analyses on GC‐flame ionization detector (FID). Particle size ranged from 150 to 590 nm. Temperature difference between the SPME device and DEHS particles mixture created a temperature gradient and resulted in thermophoretic effect that was determining the extraction rate. SPME device was cooled to as low as –75°C, while the DEHS remained close to room temperature. Several aspects of nanoparticle sampling were tested to demonstrate the principle of the sampling approach. These included the effects of thermal gradient, sample flow rate, sampling time, CO₂ delivery mode (constant coolant delivery vs. constant temperature), and particle size. Results were normalized to measure particulate concentrations using direct sampling with PTFE filters. Nanoparticle extractions of DEHS mass were proportional to sampling time. Normalized mass of DEHS extracted increased with increase in temperature gradient and with increase of the cross flow velocity. Preliminary results indicate that the variation of heat transfer boundary layer caused by the variation in the cross flow velocity produce self‐compensating effect at constant coolant delivery, indicating that this approach could be used for field determinations including the time‐weighted average sampling of nanoparticles. Thus, it may be possible to develop simple device based on this concept for field applications.     

Kinetics of supersaturated vapor nucleation on molecular condensation nuclei

The kinetics of nucleation is calculated for a supersaturated vapor containing molecular condensation nuclei, that is, foreign molecules able to induce the formation of viable nuclei of a condensed phase by themselves. In contrast to the previous calculation, the possibility of the escape of molecular condensation nuclei from very small clusters containing a few condensed vapor molecules is taken into account. More exact equations are derived for the rate of steady-state nucleation and the concentration of aerosol particles in a quasisteady-state regime of nucleation. The calculation demonstrates that, at a high probability of the escape of a molecular condensation nucleus, the predominating mechanism of cluster formation is the attachment of a molecular condensation nucleus to a cluster formed from vapor molecules rather than their condensation on the nucleus. At the same time, allowances for the possible escape of molecular condensation nuclei from clusters slightly affect the rate of nucleation and the concentration of aerosol particles being formed.     

On the use of the Knudsen number and aerosol Knudsen number in the kinetics of Brownian coagulation of aerosols

We consider, on the basis of dimensional analysis, the use of the Knudsen number and aerosol Knudsen number in the kinetics of Brownian coagulation of aerosols. The aerosol Knudsen numberKn _p emerges naturally when one assumes that the aerosol particle motion can be described in terms of Brownian motion. Examples of dimensionless coagulation constants consistent with the use ofKn _p are also discussed.     

Effect of spatial inhomogeneities on the rate of homogeneous nucleation in systems with aerosol particles

The presence of growing particles in a system leads to spatial inhomogencities in the vapor concentration. The effect of these spatial variations on the rate of formation of new particles by homogeneous nucleation is examined theoretically using a cell model. Results indicate that the presence of these inhomogeneities in systems both with and without initial aerosol has generally little effect on the final number concentration of particles following a nucleation “event.”     

Phase-controlled growth of metastable Fe5Si3 nanowires by a vapor transport method

We report the synthesis of single-crystalline nanowires (NWs) of metastable Fe5Si3 phase via an iodide vapor transport method. Free-standing Fe5Si3 NWs are grown on a sapphire substrate placed on a Si wafer without the use of any catalyst. The typical size of the Fe5Si3 nanowires is 5-15 microm in length and 100-300 nm in diameter. Synthesis of the metastable phase is induced by composition-dependent nucleation from the gas-phase reaction. Depending on the concentration ratio of FeI2(g) to SiI4(g), different phases of iron silicides are formed. The growth of nanowires is facilitated by the initial nucleation of silicide particles on the substrate and further self-seeded growth of the NWs. The present work not only provides a method for the synthesis of metastable Fe5Si3 nanowires but also suggests that the phase controlled synthesis can be further optimized to produce other metal-rich silicide nanostructures for future spintronic devices.     

Microporous polyethersulfone membranes prepared under the combined precipitation conditions with non‐solvent additives

Using diethylene glycol (DegOH) as non‐solvent additive (NSA) and N, N‐dimethylacetamide (DMAc) as solvent (S), polyethersulfone (PES) flat sheet membranes were prepared via immersion precipitation combined with the vapor induced phase separation (VIPS) process. Light transmittance was used to follow the precipitation rate during the immersion process as well as during the VIPS stage. As the addition of the NSA, the viscosity of casting solutions increased, which led to a slow precipitation rate. Though the precipitation rate decreased, the instantaneous demixing type was maintained. High flux membranes were obtained only at a high mass ratio of NSA/S; producing membranes had cellular pores on the top surface and sponge‐like structure on cross section. The VIPS process prior to immersion precipitation was important for the formation of cellular pore on the surface. With the increase in exposure time, the liquid–liquid phase separation took place on the surface of casting solution; nucleation and growth induced the formation of cellular pore on the top surface. Coagulation bath temperature also had large effect on the precipitation rate; high temperature on coagulation bath mainly accelerated the transfer of solvent and non‐solvent. Higher flux membrane with a porous skin layer could be obtained at a high coagulation bath temperature, but at the same time the mechanism properties were weakened. Copyright © 2007 John Wiley & Sons, Ltd.     

A study of sulfur homogeneous nucleation from supersaturated vapor. Determination of surface tension of sulfur nanoparticles

Homogeneous nucleation in sulfur vapor is studied in a laminar-flow chamber. Concentration and size distribution of resulting aerosol particles are measured with a diffusion spectrometer of aerosols and a PK.GTA-0,3-002 photoelectric particle counter. The crystal structure of the formed particles is studied by X-ray diffraction analysis. The rate of sulfur evaporation from a boat and the profile of a deposit on the chamber wall along the axial coordinate are determined by gravimetry. Axial and radial temperature profiles are measured using a chromel-alumel thermocouple. The vapor concentration distribution in the chamber is found and the supersaturation is calculated from the solution of the mass-transfer problem. An experimental low-laborious method is developed for the supersaturation cutoff. This method enables one to rapidly deter-mine the position of the zone in which the nucleation proceeds at the highest rate. The position of the zone of nucleation found by this method is in good agreement with the results of calculations based on experimental data and theoretical calculation of the rate of nucleation by an exact formula that has been recently derived based on the works by Kusaka and Reiss, as well as the Frenkel liquid kinetics theory. The surface tension of critical sulfur nuclei resulting from the nucleation is calculated based on this formula and experimental data on the nucleation. It is established that, in a temperature range of 312–319 K, the critical nuclei have tension surface radius R _s ～ 10.6 Å and surface tension σ = 72.5 ± 1.1 dyn/cm. The surface tension of critical sulfur nuclei in this temperature range is constant and approximately 5% higher than that of a planar surface.     

An algorithm for semi-empirical design of nucleation rate surface

During the last half of century, Classical Nucleation Theory (CNT) has been developed and there have been advances in the molecular theory of nucleation. Most of these efforts have been directed towards small molecule system modeling using intermolecular potentials. Summarizing the nucleation theory, it can be concluded that the current theory is far from complete. Agreement is generally not obtained between experimental and theoretical results. In practical applications, parametric theories can be used for the systems of interest. However, experimental measurements are still the best source of information on nucleation. Experiments are labor intensive and costly, and thus, it is useful to extend the value of limited experimental measurements to a broader range of nucleation conditions. The available nucleation parameters represent only small regions of possible nucleation conditions over the range from the critical temperature to absolute zero. Thus, it is useful to develop better tools to use the data to estimate semi-empirical nucleation rate surfaces. Following our published approach, the nucleation rate surface for any system can be constructed over its phase diagram. This concept involves using the phase equilibrium diagram to establish lines of zero nucleation rates. Nucleation rate surfaces arise from equilibrium lines and their extensions that are representing unstable equilibria. Only limited experimental data is available for use in normalizing the slopes of the linearized nucleation rate surfaces. The nucleation rate surface is described in terms of steady-state nucleation rates. To design the surfaces of nucleation rates, several assumptions are presented. In the present study, an algorithm for the semi-empirical design of nucleation rate surfaces is introduced. The topology of the nucleation rate surface for a unary system using the example of water vapor nucleation is created semi-empirically. The nucleation of two concurrent (stable and unstable) phase states of critical embryos is considered in the context of multi-surface nucleation rates. Only one phase transition (melting) in the condensed state of water is considered for simplicity. The nucleation rate surface is constructed numerically using the available experimental results for vapor nucleation and phase diagram for water. The nucleation rate for water vapor is developed for the full temperature interval, i.e. from critical point to absolute zero. The results help to suggest a new direction for experimental nucleation research.     

Particle formation and coagulation in the seeded semibatch emulsion polymerization of butyl acrylate

Particle formation and coagulation in the seeded semibatch emulsion polymerization of butyl acrylate were studied under monomer‐starved conditions. To investigate the importance of the kinetics of the water phase in the nucleation process, the monomer feed rate was used as a variable to alter the monomer concentration in the aqueous phase. The emulsifier concentration in the feed was employed to alter the particle stability. Particle formation and coagulation were discussed in terms of critical surface coverage ratios. Particle coagulation occurred if the particle surface coverage dropped below θ_cr1 = 0.25 ± 0.05. The secondary nucleation occurred above a critical surface coverage of θ_cr2 = 0.55 ± 0.05. The number of particles remained approximately constant if the particle surface coverage was within θ_cr1 = 0.25 < θ < θ_cr2 = 0.55. This surface coverage band is equivalent to the surface tension band of 42.50 ± 5.0 dyne/cm that is required to avoid particle formation and coagulation in the course of polymerization. The kinetics of the water phase was shown to play an important role during homogeneous and micellar nucleations. For any fixed emulsifier concentration in the feed and above θ_cr2, the number of secondary particles increased with monomer concentration in the aqueous phase. Moreover, the presence of micelles in the reaction vessel is not the only perquisite for micellar nucleation to occur, a sufficient amount of monomer should be present in the aqueous phase to enhance the radical capture by partially monomer‐swollen micelles. The rate of polymerization increased with the surfactant concentration in the aqueous phase. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3612–3630, 2000     

Molecular nuclei of condensation. Conditions for observance and physicochemical features

The formation of aerosol particles on molecular nuclei of condensation (MoNC) is considered. An interpretation of this phenomenon, consistent with the physicochemical features of MoNC and with the observed regularities, is proposed. The nucleation is induced by the addition of two or several vapor molecules of a developing agent to MoNC to give clusters that are more stable than spontaneous heterogeneous fluctuations. The physical properties of the supersaturated vapors of empirically selected developing agents conform to the condition of low concentrations of heterogeneous fluctuations, which is needed to observe MoNC. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 208–213, February, 1998.     

A stochastic simulation of nonisothermal nucleation

The results of stochastic simulations of growth and evaporation of small clusters in vapor are reported. Energy dependent growth rates are determined from the monomer-cluster collision rate and decay rates are found from a detailed balance, with the equilibrium size and energy distribution of clusters calculated using the capillarity approximation and the equilibrium vapor pressure. These rates are used in simulations of two-dimensional random walks in size and energy space to determine the fraction of clusters in supersaturated vapor of size (i(min)+1) that reach a size i(max). By assuming that clusters of size i(min) are in equilibrium, this fraction can be related to the nonisothermal nucleation rate. The simulated rates show good agreement with the previously published analytical results. In the absence of an inert carrier gas, the nonisothermal nucleation rates are typically between 1% and 5% of the isothermal rates.     

Nucleation from supersaturated water vapors onn-dodecane substrate: A reverse Wilson chamber (RWC) method study

The reverse Wilson chamber method (RWC), developed for heterogencous nucleation investigation is applied to critical supersaturation measurements and determination of the surface concentration of nuclei (droplets) vs. supersaturation dependence in the case of nucleation from supersaturated water vapors onn-dodecane substrate. The experimental results obtained are interpreted in terms of the classical (Volmer) theory of heterogeneous nucleation as well as in the framework of the theory of barrierless nucleation. The several times lower critical supersaturations measured at four different temperatures, covering the range between 20° and 35° C, are explained by taking into account the effect of the negative line tension of three-phase contact. The temperature dependence of line tension for the three-phase systemn-dodecane/water/water vapor is extracted from the data to fir the theory. The results obtained are in complete disagreement with those ones obtained by Wu and Maa for the same system using jet-tensimeter technique, however, in another temperature interval. This discrepancy is discussed in detail in the text.     

Complete thermodynamically consistent kinetic model of particle nucleation and growth: numerical study of the applicability of the classical theory of homogeneous nucleation

A complete thermodynamically consistent elementary reaction kinetic model of particle nucleation and growth from supersaturated vapor was developed and numerically evaluated to determine the conditions for the steady-state regime. The model treats all processes recognized in the aerosol science (such as nucleation, condensation, evaporation, agglomerationcoagulation, etc.) as reversible elementary reactions. It includes all possible forward reactions (i.e., of monomers, dimers, trimers, etc.) together with the thermodynamically consistent reverse processes. The model is built based on the Kelvin approximation, and has two dimensionless parameters: S0-the initial supersaturation and Theta-the dimensionless surface tension. The time evolution of the size distribution function was obtained over the ranges of parameters S0 and Theta. At low initial supersaturations, S0, the steady state is established after a delay, and the steady-state distribution function corresponds to the predictions of the classical nucleation theory. At high initial supersaturations, the depletion of monomers due to condensation on large clusters starts before the establishing of the steady state. The steady state is never reached, and the classical nucleation theory is not applicable. The boundary that separates these two regimes in the two dimensionless parameter space, S0 and Theta, was determined. The model was applied to several experiments on water nucleation in an expansion chamber [J. Wolk and R. Strey, J. Phys. Chem. B 105, 11683 (2001)] and in Laval nozzle [Y. J. Kim et al., J. Phys. Chem. A 108, 4365 (2004)]. The conditions of the experiments performed using Laval nozzle (S0=40-120) were found to be close to the boundary of the non-steady-state regime. Additional calculations have shown that in the non-steady-state regime the nucleation rate is sensitive to the rate constants of the initial steps of the nucleation process, such as the monomer-monomer, monomer-dimer, etc., reactions. This conclusion is particularly important for nucleation from supersaturated water vapor, since these processes for water molecules at and below the atmospheric pressure are in the low pressure limit, and the rate constants can be several orders of magnitude lower than the gas kinetic. In addition, the impact of the thermodynamic inconsistency of the previously developed partially reversible kinetic numerical models was assessed. At typical experimental conditions for water nucleation, S0=10 and Theta=10 (T=250 K), the error in the particle nucleation rate introduced by the thermodynamic inconsistency exceeds one order of magnitude.     

Computer simulation of the kinetic behaviour of surface reactions driven by a linear potential sweep: Part III. Monolayer formation by a nucleation and growth mechanism

The kinetic behaviour of a surface process involving the deposition of a two-dimensional surface film by a nucleation and growth mechanism is treated for the case of linear potential sweep control. Features which distinguish nucleation and growth in monolayer formation from random electrodeposition (Langmuir case) treated in previous papers are emphasized. Two main mechanisms are considered: one where the growth occurs from a fixed surface density of nuclei and the other where growth occurs from a potential-dependent density of nuclei. Computer simulations and some analytical derivations of the kinetic behaviour for these two cases are made and the characteristic kinetic features of the process are deduced, enabling the latter to be distinguished in terms of experimentally accessible criteria. The extent of reversibility of the processes can be usefully expressed in terms of a limiting sweep-rate parameter, s₀, which is related to the rate constant for nucleation or the surface density of nuclei and the rate constant for growth.     

Data evaluation of laminar flow diffusion chamber nucleation experiments with different computational methods

In order to evaluate the experimental data from laminar flow diffusion chamber (LFDC) experiments on homogeneous nucleation, an extensive postmeasurement computational analysis is required. The present work investigates the influence of the used computational methodology on the derived nucleation curves. To this end a reanalysis is made of previous LFDC experiments of 1-butanol nucleation in helium [D. Brus et al., J. Chem. Phys. 122, 214506 (2005)] using two different methods. The first method is based on single fluid heat and vapor transport in the carrier gas ignoring the aerosol processes, as commonly made in LFDC data evaluations. The second method is more comprehensive as is based on multidimensional computational fluid-particle dynamics. The calculations are made under the usual simplification of one-way coupling between fluid flow and particles, which is a valid approximation in most practical aerosols, while full aerosol dynamical effects are accommodated. Similar results were produced by the two methods. This finding corroborates the usual practice of omitting aerosol calculations in LFDC experimental data evaluation.     

Influence of surface activation by plasma and nanoparticle adsorption on the morphology, thermal stability and combustion behavior of PET fabrics

Plasma surface activation at different process parameters (namely, power and etching time) has been combined with nanoparticle adsorption (i.e., a natural montmorillonite) in order to improve the thermal stability and flame retardancy of PET fabrics. Scanning electron microscopy coupled to elemental analysis has put in evidence a direct relationship between the distribution of nanoparticles on fibers and process parameters. The presence of the above nanoparticles affects the thermal stability of fabrics in air, as assessed by thermogravimetric analysis: a delay of the mass loss process has been observed for the treated samples.Combustion behavior has been investigated by cone calorimetry: plasma activated fabrics have shown a remarkable improvement in terms of time to ignition (up to 104%) and a slight reduction of the heat release rate (ca. 10%) as compared to neat PET.     

Determination of evaporation rates and vapor pressures of very low volatility compounds: a study of the C4-C10 and C12 dicarboxylic acids

A method for the measurement of evaporation rates and vapor pressures of low volatility compounds was developed and applied to the homologous series of C4-C10 and C12 dicarboxylic acids. Proton-transfer chemical ionization mass spectrometry was used to follow directly the temperature-dependent evaporation rates of aerosol samples collected on a cold plate that could be heated at a known rate. The vapor pressures of the deposited compounds were derived from observed evaporation rates through application of the Hertz-Knudsen equation. Temperature programmed desorption allowed for quantification of the enthalpy (DeltaHsub) and entropy (DeltaSsub) of sublimation of the diacids and is described. A strong odd-even dependence with respect to the total carbon number was observed in the derived diacid vapor pressures, consistent with previous measurements. However, the vapor pressures from this method were systematically lower than previous measurements. Though seen in the vapor pressure, no odd-even carbon chain length dependence was readily discernible in the measured values of DeltaHsub and DeltaSsub. Perhaps most importantly, these experimental results also suggest that residual solvent molecules (from the aerosol generation process) trapped in the diacid samples can have a considerable influence on the measured thermodynamic parameters and, if not properly accounted for, may give erroneous results.     

Hybrid monte carlo method for simulation of two-component aerosol coagulation and phase segregation

The paper presents the development of a hybrid Monte Carlo (MC) method for the simulation of the simultaneous coagulation and phase segregation of an immiscible two-component binary aerosol. The model is intended to qualitatively model our prior studies of the synthesis of mixed metal oxides for which phase-segregated domains have been observed in molten nanodroplets. In our previous works (J. Aerosol Sci.32, 1479 (2001); Chem. Eng. Sci.56, 5763 (2001); submitted for publication) we developed sectional and monodisperse models where the internal state of the aerosol particles was described. These methods have certain limitations and it is difficult to include additional physical effects into the framework. Our new approach combines both constant volume and constant number Monte Carlo methods. Similar to our previous models, we assume that the phase segregation is kinetically controlled. The MC approach allows us to compute the mean number of enclosures (minor phase) per droplet, average enclosure volume, and the width of the enclosure size distribution. The results show that asymptotic behavior of enclosure distribution exists that is independent of initial conditions, which is very close to the continuum self-preserving distribution. Temperature is a key parameter because it allows for a significant change in the internal transport rate within each droplet. In particular, increasing the temperature significantly enhances the Brownian coagulation rate and lowers the number of enclosures per droplet. As a result, the MC results indicate that the growth of the minor phase can be moderated quite dramatically by small changes in system temperature. These results serve to illustrate the utility of this synthesis approach to the controlled growth of nanoparticles through the use of a majority matrix to slow down the encounter frequency of the minor phase and therefore its particle size.