Homogeneous nucleation of particles from the vapor phase in thermal plasma synthesis

Particle nucleation and growth are simulated for iron vapor in a thermal plasma reactor with an assumed one-dimensional flow field and decoupled chemistry and aerosol dynamics. Including both evaporation and coagulation terms in the set of cluster-balance rate equations, a sharply defined homogeneous nucleation event is calculated. Following nucleation the vapor phase is rapidly depleted by condensation, and thereafter particle growth occurs purely by Browntan coagulation. The size and number of nucleated particles are found to be affected strongly by the cooling rate and by the initial monomer concentration. An explanation is presented in terms of the response time of the aerosol to changing thermodynamic conditions.This work appears in abbreviated from in the proceedings of the International Symposium on Combustion and Plasma Synthesis of High Temperature Materials, San Francisco, Oct. 24–26, 1988, to be published asCombustion and Plasma Synthesis of Hig Temperature Materials, Z. A. Munir and J. B. Holt (eds.), VCH, New York (in press).     

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.     

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.     

Monte Carlo simulations of critical cluster sizes and nucleation rates of water

We have calculated the critical cluster sizes and homogeneous nucleation rates of water at temperatures and vapor densities corresponding to experiments by Wolk and Strey [J. Phys. Chem B 105, 11683 (2001)]. The calculations have been done with an expanded version of a Monte Carlo method originally developed by Vehkamaki and Ford [J. Chem. Phys. 112, 4193 (2000)]. Their method calculates the statistical growth and decay probabilities of molecular clusters. We have derived a connection between these probabilities and kinetic condensation and evaporation rates, and introduce a new way for the calculation of the work of formation of clusters. Three different interaction potential models of water have been used in the simulations. These include the unpolarizable SPC/E [J. Phys. Chem. 91, 6269 (1987)] and TIP4P [J. Chem. Phys. 79, 926 (1983)] models and a polarizable model by Guillot and Guissani [J. Chem. Phys. 114, 6720 (2001)]. We show that TIP4P produces critical cluster sizes and a temperature and vapor density dependence for the nucleation rate that agree well with the experimental data, although the magnitude of nucleation rate is constantly overestimated by a factor of 2 x 10(4). Guissani and Guillot's model is somewhat less successful, but both the TIP4P and Guillot and Guissani models are able to reproduce a much better experimental temperature dependency of the nucleation rate than the classical nucleation theory. Using SPC/E results in dramatically too small critical clusters and high nucleation rates. The water models give different average binding energies for clusters. We show that stronger binding between cluster molecules suppresses the decay probability of a cluster, while the growth probability is not affected. This explains the differences in results from different water models.     

Mesoscopic dispersion of colloidal agglomerate in a complex fluid modelled by a hybrid fluid-particle model

The dispersion of the agglomerating fluid process involving colloids has been investigated at the mesoscale level by a discrete particle approach--the hybrid fluid-particle model (FPM). Dynamical processes occurring in the granulation of colloidal agglomerate in solvents are severely influenced by coupling between the dispersed microstructures and the global flow. On the mesoscale this coupling is further exacerbated by thermal fluctuations, particle-particle interactions between colloidal beds, and hydrodynamic interactions between colloidal beds and the solvent. Using the method of FPM, we have tackled the problem of dispersion of a colloidal slab being accelerated in a long box filled with a fluid. Our results show that the average size of the agglomerated fragments decreases with increasing shearing rate gamma, according to the power law A x gamma(k), where k is around 2. For larger values of gamma, the mean size of the agglomerate S(avg) increases slowly with gamma from the collisions between the aggregates and the longitudinal stretching induced by the flow. The proportionality constant A increases exponentially with the scaling factor of the attractive forces acting between the colloidal particles. The value of A shows a rather weak dependence on the solvent viscosity. But A increases proportionally with the scaling factor of the colloid-solvent dissipative interactions. Similar type of dependence can be found for the mixing induced by Rayleigh-Taylor instabilities involving the colloidal agglomerate and the solvent. Three types of fragmentation structures can be identified, which are called rupture, erosion, and shatter. They generate very complex structures with multiresolution character. The aggregation of colloidal beds is formed by the collisions between aggregates, which are influenced by the flow or by the cohesive forces for small dispersion energies. These results may be applied to enhance our understanding concerning the nonlinear complex interaction occurring in mesoscopic flows such as blood flow in small vessels.     

Homogeneous nucleation rate measurements of 1-butanol in helium: a comparative study of a thermal diffusion cloud chamber and a laminar flow diffusion chamber

Isothermal homogeneous nucleation rates of 1-butanol were measured both in a thermal diffusion cloud chamber and in a laminar flow diffusion chamber built recently at the Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, Prague, Czech Republic. The chosen system 1-butanol-helium can be studied reasonably well in both devices, in the overlapping range of temperatures. The results were compared with those found in the literature and those measured by Lihavainen in a laminar flow diffusion chamber of a similar design. The same isotherms measured with the thermal diffusion cloud chamber occur at highest saturation ratios of the three devices. Isotherms measured with the two laminar flow diffusion chambers are reasonably close together; the measurements by Lihavainen occur at lowest saturation ratios. The temperature dependences observed were similar in all three devices. The molecular content of critical clusters was calculated using the nucleation theorem and compared with the Kelvin equation. Both laminar flow diffusion chambers provided very similar sizes slightly above the Kelvin equation, whereas the thermal diffusion cloud chamber suggests critical cluster sizes significantly smaller. The results found elsewhere in the literature were in reasonable agreement with our results.     

Observation of a transition in the water-nanoparticle formation process at 167 K

Rapid-scan Fourier transform infrared spectroscopy of the vapor/solid formation process of water nanoparticles in the 180-140 K temperature range at thermal-equilibrium conditions is reported. At 167 K a transition in the formation process was observed: the particle volume quintuples and the particle formation time triples within a temperature interval of +/-0.4 K caused by the temperature control. The authors interpret this behavior by an abrupt change in the nucleation rate of the H2O monomers in He buffer gas kept at 167 K and 200 mbar. A size and shape analysis of the particles during the formation process was carried out by application of the discrete dipole approximation method which delivers excellent accordance between experimental and calculated mid-IR spectra. Compared to other compact shapes (cube, prolate ellipsoid, and hexagonal prism) the ideal spherical shape fits the experimental spectra best. A distinct change in shape by particle conversion or agglomeration could be excluded to be involved in the formation process. As a possible explanation of the observed phenomenon, a transition from vapor/liquid/solid to vapor/solid nucleation with decreasing temperature is considered which was recently theoretically predicted by van Dongen and co-workers [J. Chem. Phys. 117, 5647 (2002); private communication; J. Chem. Phys. 120, 6314 (2004)].     

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.     

Evidence for the role of ions in aerosol nucleation

Aerosol nucleation has been studied experimentally in purified, atmospheric air, containing trace amounts of water vapor, ozone, and sulfur dioxide. The results are compared with model calculations. It is found that an increase in ionization by a factor of 10 increases the production rate of stable clusters by a factor of approximately 3, probably due to ion-induced nucleation.     

Effects of charge and size on condensation of supersaturated water vapor on nanoparticles of SiO2

The effects of size and charge on the condensation of a supersaturated water vapor on monodisperse nanoparticles of SiO(2) were investigated in a flow cloud chamber. The dependences of the critical supersaturation S(cr) on particle size at diameters of 10, 12, and 15 nm as well as on charge and charge polarity are determined experimentally. A novel electrospray aerosol generator was developed to generate a high concentration of SiO(2) nanoparticles of less than 10 nm by electrospraying silicon tetraethoxide (STE) ethanol solution followed by the thermal decomposition of STE. The effects of liquid flow rate, liquid concentration, flow rate of carrier gas, and liquid conductivity on the particle size distribution and concentration were examined. For charged particles, the nucleation occurs at a critical supersaturation S(cr) lower than that on neutral particles, and the charge effect fades away as particle size increases. The charge effect is stronger than the theoretical predictions. In addition, a sign preference is detected, i.e., water vapor condenses more readily on negatively charged particle, a trend consistent with those observed on ions. However, both effects of charge and charge polarity on S(cr) are stronger than that predicted by Volmer's theory for ion-induced nucleation.     

Analytical investigation of simultaneous effects of convergent section heating of Laval nozzle,steam inlet condition,and nozzle geometry on condensation shock

Rapid expansion and supercooling of dry vapor in low-pressure steam turbines trigger nucleation phenomenon. Subsequently, following the occurrence of vapor condensation, a vapor–liquid two-phase flow is established. Entropy generation mainly by condensation shock, blade erosion, and ultimately, destruction of equipment and efficiency reduction are among adverse effects of vapor condensation, which should be either attenuated or controlled. In the present research, which is a continuation to the research performed by original authors, a one-dimensional analytical Eulerian–Lagrangian model is used to apply convergent section heating to different supersonic nozzles under various inlet conditions. The results indicate that the flow response to the heating is well dependent on the intensity of condensation shock or inlet conditions. In order to compensate for the mass flow rate resulted from the convergent section heating, effects of simultaneous reduction of inlet stagnation temperature and convergent section heating were investigated. Finally, it was found that, maintaining constant mass flow rate, simultaneous reduction of inlet stagnation temperature and convergent section heating cannot attenuate the condensation shock significantly. Therefore, the best approach to compensate for the reduction in the mass flow rate due to convergent section heating is to simultaneously increase inlet stagnation pressure.     

Strukturviskosität von verdünnten Lösungen von Biopolymeren

The importance of the rheological behaviour of solutions of macromolecules is briefly evaluated. The viscosity of the solutions depends on concentration, shear rate and time of shear, this relation being determined by the structure of the dissolved molecules. In dilute solutions shear dependence of viscosity is very frequently caused by the preferential orientation of anisotropic molecules. In such a case the particle dimensions can be calculated from the true limiting viscosity number, an anisotropy factor, the rotational diffusion constant and the effective particle density. These numbers can be derived from the flow curve, which has been extrapolated to zero concentration. It is necessary to measure the flow curve at shear gradients, which are sufficiently low to allow for an extrapolation to vanishing shear rate. By comparing the experimental flow curve with a choice of theoretical ones, the rotational diffusion constant and the anisotropy factor (axial ratio) can be found. From the limiting viscosity number and the axial ratio, the particle density can be calculated.     

Homogeneous nucleation of n-propanol, n-butanol, and n-pentanol in a supersonic nozzle

We have measured the nucleation conditions of n-propanol, n-butanol, and n-pentanol in a supersonic Laval nozzle, and estimated that the maximum nucleation rate J is 5 x 10(16) cm(-3) s(-1) with an uncertainty factor of 2. Plotting the vapor pressures p(J(max) ) and temperatures T(J(max) ) corresponding to the maximum nucleation rate as ln(p) versus 1T, produces a series of well separated straight lines. When these values are scaled by their respective critical parameters, p(c) and T(c), the data lie close to a single straight line. Comparing the experimental data to the predictions of classical nucleation theory reveals much higher experimental rates, and the deviation increases with increasing alcohol chain length and decreasing temperature. A scaling analysis in terms of Hale's scaled nucleation model [Phys. Rev. A 33, 4156 (1986); Metall. Trans. A 23, 1863 (1992)], clearly shows that our data are consistent with experimental nucleation rates measured using other devices that have characteristic rates many orders of magnitude lower.     

The mechanisms of latex particle formation and growth in the emulsion polymerization of styrene using the surfactant sodium dodecyl sulfate

A new method is presented that provides experimental information which is qualitatively and quantitatively sensitive to assumptions made as to the mechanisms of free radical entry and of latex particle formation in emulsion polymerization systems. The method consists of (1) obtaining (by electron microscopy) the full particle-size distributions (PSDs) at several different times soon after the cessation of latex particle nucleation, (2) using these PSDs to determine the volume dependences of the various rate coefficients governing particle growth by fitting the data to the appropriate evolution equations, and (3) employing these empirical rate coefficients to find that time dependence of the nucleation rate which fits the early-time PSD (again using the evolution equations). This method is quite sensitive to mechanistic assumptions: for example, one is able to determine whether or not the nucleation rate is an increasing or decreasing function of time. The technique is applied to a styrene nucleation system employing sodium dodecyl sulfate as surfactant at well above the critical micelle conventration. The data cannot be fitted even qualitatively by a simple one-step nucleation mechanis, whether it involes micellar entry or homogeneous nucleation. It is found, on the other hand, that the results can be accurately fitted by assuming that coagulation events between primary colloidal particles, perhaps formed by homogeneous nucleation, dominate both the nucleation process and the entry of free radicals into mature latex particles. In addition, the data indicate that the rate of free radical entry into the latex particles decreases with increasing particle size, at least for particles of unswollen radius less than ca. 40 nm.     

Emulsion polymerization of styrene using irreversible addition–fragmentation chain transfer agents: effect on the course of the polymerization and molecular weight

The emulsion polymerization of styrene with three different chain transfer agents (CTAs) based on irreversible addition–fragmentation chain transfer (AFCT) mechanism was first reported in this work. The influences of these irreversible AFCT agents on the rate of polymerization, particle size, and molecular weight were investigated. It was found that the intrinsic activity and desorption behaviors of the CTAs determined the efficiency for molecular weight control, rate of polymerization, and particle size in the emulsion polymerization. It has been demonstrated that the rate of polymerization and particle size decreased dramatically in the presence of the irreversible AFCT agents with high chain transfer constant (ethyl α-p-toluenesulfonyl-methacrylate), meanwhile, the molecular weight of the polystyrene could not be controlled well, whereas the irreversible AFCT agents with low chain transfer constant (butyl(2-phenylallyl)sulfane and 2,3-dichloropropene) had a slight effect on the polymerization rate, particle size, and were fairly well for molecular weight control over the whole conversion range in the emulsion polymerization of styrene. The average number of radicals per particle and the number-average molecular weight were calculated by classical radical emulsion polymerization theory, and the experimental results were in good agreement with the results of model calculations, when the irreversible AFCT agents were used as CTAs. The effect of chain transfer agents on the kinetics and nucleation in the emulsion polymerization of styrene can be attributed to desorption of chain-transferred radicals from the polymer particles. The results of this work show that butyl(2-phenylallyl)sulfane as CTA in emulsion polymerization of styrene provides the best balance between the rate of polymerization and the efficiency for molecular weight control conflicting tendencies.     

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.     

Mean-field kinetic nucleation theory

A new semiphenomenological model of homogeneous vapor-liquid nucleation is proposed in which the cluster kinetics follows the "kinetic approach to nucleation" and the thermodynamic part is based on the revised Fisher droplet model with the mean-field argument for the cluster configuration integral. The theory is nonperturbative in a cluster size and as such is valid for all clusters down to monomers. It contains two surface tensions: macroscopic (planar) and microscopic. The latter is a temperature dependent quantity related to the vapor compressibility factor at saturation. For Lennard-Jones fluids the microscopic surface tension possesses a universal behavior with the parameters found from the mean-field density functional calculations. The theory is verified against nucleation experiments for argon, nitrogen, water, and mercury, demonstrating very good agreement with experimental data. Classical nucleation theory fails to predict experimental results when a critical cluster becomes small.     

Heterogeneous Nucleation of n-Butanol Vapor on Submicrometer Charged and Neutral Particles of Lactose and Monosodium Glutamate

Condensation of a supersaturated vapor of n-butanol on monodisperse submicrometer particles of lactose and monosodium glutamate is investigated in a flow cloud chamber (FCC). The dependence of critical supersaturation S(cr) on the particle size in the range 30 to 90 nm is experimentally examined. The results show that the size dependence of S(cr) qualitatively agrees with that predicted by the Fletcher version of the Volmer theory of heterogeneous nucleation, but to a lesser degree. The experimental S(cr) is smaller than the theoretical prediction even with the line tension and surface diffusion taken into account, and they induce heterogeneous nucleation better than perfectly wetted particles. The discrepancy can not be fully accounted for by the effects of line tension and surface diffusion and the existing theory concerning the curvature-dependent surface tension. The condensation on single positive-charged particles of diameter 30, 60, and 90 nm is also examined. A lowering of S(cr) at an efficiency much larger than the prediction by Volmer's theory for ion-induced nucleation is observed, and the charge effect fades away as particle size increases. Copyright 2000 Academic Press.     

Effects of polymer adsorption on the effective viscosity in microchannel flows: phenomenological slip layer model from molecular simulations

Molecular simulations (Dissipative Particle Dynamics - DPD) were used to quantify the effect of polymer adsorption on the effective shear viscosity of a semi-dilute polymer solution in microchannel Poseuille flow. It is well known that polymer depletion layers develop adjacent to solid walls due to hydrodynamic forces, causing an apparent wall slip and reduced effective viscosity (increased total flow rate). We found that depletion layers also developed in the presence of hydrodynamically rough adsorbed layers on the wall. Polymer-polymer (steric) repulsion between flowing and adsorbed polymer expanded the depletion layer compared to no-adsorption cases, and the effective viscosity was reduced further. Desorption occurred for higher shear rates, reducing the repulsion effect and shrinking the depletion layers. A phenomenological algebraic model for the depletion layer thickness, including a shear modified adsorption isotherm, was developed based on the simulation data. The depletion layer model can be used together with the effective viscosity model we developed earlier.