Experimental Nucleation Rates Research Articles

A molecular model for homogeneous nucleation

This work concerns the theory of vapor phase homogeneous nucleation. A microscopic model for homogeneous nucleation has been extended to large clusters so it can be employed where classical theory is currently used. Attempts have been made to obtain all results in closed analytical form which are easy to compare with experimental data. The results of this model are compared with the experimental nucleation rates of ethanol, methanol and nonane. This model is very consistent with recent experimental data.

Homogeneous nucleation rates for water

We have investigated homogeneous nucleation of water droplets in the vapor phase. Nucleation in water vapor has been previously studied a number of times using various experimental techniques. The nucleation pulse technique used here allows accurate measurements of homogeneous nucleation rates J vs supersaturation S in the range from 105 to 109 cm−3 s−1. The advance reported here consists of the fact that the J–S curves are measured at a selectable constant temperature. We determined the nucleation rates in supersaturated water vapor mixed with various carrier gases as functions of supersaturation and temperature (217<T/K<259). Nucleation is found to be nondependent of the nature of the carrier gas. Data analysis was carried out in four steps. First, we observed quantitative agreement in the range of overlap with experimental results by Miller et al. [J. Chem. Phys. 78, 3204 (1983)]. Second, experimental nucleation rates were compared with the predictions of classical nucleation theory. Systematic deviations from that theory were observed as in the case of other systems (e.g., alcohols, nonane) studied previously. Third, comparison with a new version of Fisher’s droplet model reveals remarkable agreement between experiment and theory. Finally, we implemented a model-independent determination of the average nucleus size directly from the slopes of the isothermal J–S curves.

Measurement of the molecular content of binary nuclei. Use of the nucleation rate surface for ethanol–hexanol

We measured the homogeneous nucleation rates J of mixed droplets in supersaturated ethanol–hexanol vapor mixtures in argon as functions of the vapor phase activities a1 and a2 of ethanol and hexanol, respectively. Measurements ranged from pure ethanol to pure hexanol at T=260 K. The experimental nucleation rate curves shape a nucleation rate surface in the three-dimensional J−a1−a2 space. We develop a theory for obtaining the average size and composition of a nucleus from this surface determined experimentally. Following this procedure experimental nucleus compositions are determined. This theory is then combined with our measurements in order to determine the makeup of the binary ethanol–hexanol nuclei. Results are compared with the predictions of classical binary nucleation theory. Qualitatively similar trends are observed for the nearly ideal ethanol–hexanol system studied.

Comparison of theoretical and experimental expansion cloud chamber nucleation rates of n-nonane

We have applied an extension of a microscopic model to account for the nucleation of n-nonane. We have compared the nucleation rates obtained using the extended model with those of two experimental investigations. The results of the two experimental investigations are consistent. The nucleation rates predicted by the classical theory are inconsistent with experimental data and can vary by as much as 14 orders of magnitude. The extended model yields nucleation rates which are in close agreement with the two experimental works.

Binary nucleation in acid–water systems. I. Methanesulfonic acid–water

Experimental measurements of binary nucleation between methanesulfonic acid and water vapor were carried out for relative acidities (Ra), 0.05<Ra<0.65, and relative humidities (Rh), 0.06<Rh<0.65, using a continuous flow mixing-type device. The number concentration of particles leaving the nucleation and growth tube was measured as a function of the initial relative humidity and the relative acidity in the temperature range from 20 to 30 °C. Particle size distributions were also measured and found to vary with the amount of water and acid present. The system was simulated to predict the total number of particles and the total mass of acid in the aerosol phase using a simple integral model and classical binary nucleation theory allowing for the formation of acid–water hydrates in the gas phase. At low particle concentrations, condensation rates did not significantly change the saturation levels and the nucleation rates were estimated from the total number concentration data as functions of Ra, Rh, and temperature. The values of experimental and theoretical nucleation rates differed significantly, with Jexpt/Jtheor changing as a function of temperature from 10−8 to 10−4 as temperature varied from 20 to 30 °C. This work represents the first systematic experimental study of the temperature dependence of binary nucleation.

Propensity rule in homogeneous nucleation processes

A linear relation is discovered between 1n J and 1/ T (where J is the nucleation rate at temperature T in K) for homogeneous nucleation from the analysis of experimental data and is explained for water nucleation on the basis of classical nucleation theory. Nucleation theory is then combined with experimental homogeneous nucleation rate data to yield a temperature-dependent sticking coefficient, β( T), for water. It is found from this study that there exists a strong linear relationship between 1n β( T) and T.

ChemInform Abstract: Homogeneous Nucleation Rates for n‐Alcohol Vapors Measured in a Two‐Piston Expansion Chamber

Homogeneous nucleation rates J in supersaturated n‐alcohol vapors (methanol through n‐hexanol) were measured in a two‐piston expansion chamber as functions of supersaturation S and temperature T. The measured nucleation rates were compared with the classical nucleation theory. We found that the slopes of the J–S curves are in good agreement with the theoretical prediction. However, the actual values of experimental and theoretical rates were generally found to differ significantly, Jexptl/Jtheor ranging from about 10−10 (methanol, 273 K) to 107 (n‐hexanol, 257 K). In particular, the experimental nucleation rates show a significantly weaker temperature dependence as compared to the classical nucleation theory, the difference being more pronounced for the higher alcohols. Thus, a temperature dependent correction to the classical nucleation theory is needed. For the lower alcohols, in particular methanol, we found that the change of the cluster distribution during the expansion strongly influences the nucleation process. The heat released during the formation of oligomers causes a significant temperature increase in the system and thus alters the nucleation conditions dramatically. For methanol vapor under the considered experimental conditions this effect leads to a reduction of the theoretically predicted nucleation rates by factors up to about 108. Since oligomer formation is prerequisite to nucleation, this effect has to be taken into account generally for nucleation experiments in adiabatically closed systems.

Homogeneous nucleation rates for n-alcohol vapors measured in a two-piston expansion chamber

Homogeneous nucleation rates J in supersaturated n-alcohol vapors (methanol through n-hexanol) were measured in a two-piston expansion chamber as functions of supersaturation S and temperature T. The measured nucleation rates were compared with the classical nucleation theory. We found that the slopes of the J–S curves are in good agreement with the theoretical prediction. However, the actual values of experimental and theoretical rates were generally found to differ significantly, Jexptl/Jtheor ranging from about 10−10 (methanol, 273 K) to 107 (n-hexanol, 257 K). In particular, the experimental nucleation rates show a significantly weaker temperature dependence as compared to the classical nucleation theory, the difference being more pronounced for the higher alcohols. Thus, a temperature dependent correction to the classical nucleation theory is needed. For the lower alcohols, in particular methanol, we found that the change of the cluster distribution during the expansion strongly influences the nucleation process. The heat released during the formation of oligomers causes a significant temperature increase in the system and thus alters the nucleation conditions dramatically. For methanol vapor under the considered experimental conditions this effect leads to a reduction of the theoretically predicted nucleation rates by factors up to about 108. Since oligomer formation is prerequisite to nucleation, this effect has to be taken into account generally for nucleation experiments in adiabatically closed systems.

Experimental nucleation rates of the n-alcohols in comparison with theory

Experimental nucleation rates of the n-alcohols in comparison with theory

Measurements of homogeneous nucleation rates for n-nonane vapor using a two-piston expansion chamber

The homogeneous nucleation rate J in supersaturated n-nonane vapor was measured as a function of supersaturation S and temperature T using a newly developed expansion chamber. Homogeneous nucleation is observed only during a short supercritical nucleation pulse so that nucleation and droplet growth are decoupled under the considered experimental conditions. Reproducible nucleation pulses with a duration of about 1 ms are achieved by means of two spring-operated pistons moving in a well-defined time sequence. The number concentration of the droplets growing in the expansion chamber is determined immediately after the end of the nucleation pulse by means of constant angle Mie scattering. Taking into account the duration of the nucleation pulse we measured homogeneous nucleation rates ranging from about 5×105 to 5×109 cm−3 s−1. Homogeneous nucleation in n-nonane vapor was observed in the temperature range from 199 to 241 K. Argon was used as the carrier gas. The measured nucleation rates were compared with the classical theory of nucleation. The slopes of the J–S curves were found to be in good agreement and thus for n-nonane the dependence of the nucleation rate on the supersaturation appears to be correctly described by the classical nucleation theory. However, the actual values of the experimental nucleation rates were found to be several orders of magnitude higher than the theoretical prediction and show a significantly different temperature dependence. A qualitative explanation of the obtained experimental results can probably be given by means of Burton’s recent microscopic calculations of the cluster free energy.

A comparison of measured nucleation rates with the predictions of several theories of homogeneous nucleation

An expansion cloud chamber with extensive instrumentation is used to test the success of several prominent nucleation theories in describing the nucleation rate of water vapor in the presence of argon. The instrumentation of the cloud chamber permits the time-resolved measurement of pressure, temperature, supersaturation ratio and, during the later stages of condensation, the droplet size and number concentration. These observations are used directly to examine the variation of the maximum supersaturation ratio and the droplet number concentration as the initial temperature and the expansion rate are varied. When used with an algebraic form appropriate to any specific nucleation theory, these observations additionally allow the experimental determination of the pre-exponential and exponential rate constants that may be compared with the respective theoretical values. In this way, a comparison of theoretical and experimental nucleation rates is possible. The classical and Reiss nucleation theories give essentially identical results and they show the closer agreement with the measured nucleation rates.

Homogeneous nucleation of cyclohexane: A double-diaphragm shock tube study

The double-diaphragm shock tube technique was applied to the study of homogeneous nucleation for the first time. The condensation of 1% cyclohexane vapor in argon carrier gas was observed by light scattering. The measured “end of condensation” point was shown to yield information similar to that for the “onset of condensation” point observed in nozzle and shock tube driver expansion experiments. The data were fitted to a classical-type nucleation equation by means of an adjustable preexponential factor K. Definitive analysis is not possible at this stage as the surface free energy of small cyclohexane clusters is uncertain under our conditions (temperatures of about 160°K). Experimental nucleation rates were therefore determined for a range of surface free energy values.

Crystal nucleation and growth in a Na 2O.2CaO.3SiO 2 glass

The kinetics of crystal nucleation and growth were studied in a glass close to the Na 20.2CaO.3SiO 2 (NC 2S 3) composition. The experimental nucleation rates were analysed in terms of homogenous nucleation theory using the measured viscosity of the glass as a function of temperature and heat of fusion and specific heat data determined by DTA and DSC. A value of 180 erg cm −2 was deduced for the crystal-liquid interfacial free energy. The effect of small changes in the glass composition on nucleation rates were also considered and the formation of glass ceramics based on the NC 2S 3 crystal phase briefly discussed.

Nucleation and growth kinetics for the crystallization of ice from dextrose solutions in a continuous stirred tank crystallizer with supercooled feed

AbstractThe crystallization of ice in aqueous dextrose solutions is studied in an adiabatic continuous stirred tank crystallizer with a supercooled feed stream. The effective diameter of the ice crystals was determined for various values of mean crystal residence time, feed supercooling, magma density, stirring rate, and dextrose concentration. For all process conditions the supercooling was measured at 9‐12 different locations in the crystallizer. These local supercoolings were averaged algebraically to yield the bulksupercooling.From the experimental results growth and nucleation rates have been calculated. By comparing the experimental growth rates to growth rates calculated by means of a mathematical model kinetics for the inbuilding of water molecules into the ice lattice have been determined. The growth rate appears to be directly proportional to the interface supercooling. The rate constant decreases exponentially with increasing weight percentage of dextrose in the solution.The nucleation rate was found to be directly proportional to total crystal surface per unit volume of suspension and proportional to the bulksupercooling to the power 2.1. Nucleation is believed to occur by breakage of dendrites from the surface of parent crystals.

Nucleation kinetics of the potassium sulfate‐water system

AbstractSecondary nucleation in the potassium sulfate‐water system occurs by micro‐attrition processes over the entire 1.3‐26 μ size range of this study. Experimental nucleation rates were correlated with power‐law kinetics expressions in terms of supersaturation, the fourth moment of the parent seed‐crystal distribution, and stirring rate. Such kinetics expressions are similar to those used to correlate MSMPR data; however, the secondary nucleation rates of this paper are two orders of magnitude greater than those reported in previous MSMPR studies of the same system. An upper bound on growth rate of these nuclei was calculated based on a population balance analysis; maximum growth rates of these nuclei was markedly size‐dependent in the 1.3‐26 micron size range of measurement, decreasing with decreasing size. The apparent descrepancy between these nucleation rates and MSMPR values can be explained by nuclei washout during the low growth rate period. Anomalous MSMPR kinetics (low or even negative supersaturation power‐law dependence) can be explained by this growth phenomenon.

Experimental nucleation rates of silver on evaporated silicon oxide

Experimental nucleation rates of silver on evaporated silicon oxide

Analysis of In Situ Electron Microscopy Studies of Heterogeneous Nucleation

Discrepancies with theory revealed by recent nucleation experiments have been examined. It is suggested that a minor deviation between experimental nucleation rate and the atomistic theoretical model, may be ascribed to a value between 1 and 5×1011 sec−1 (instead of 1013 sec−1) for the desorption rate pre-exponential. The much larger deviation with the spherical cap classical model is shown to be due to inability of the model to adequately evaluate the Gibb's free energy of formation from the monomer, ΔGn′, for nuclei in the range n = 1–3 atoms, which is the actual critical size in these experiments. If, for Bi on C, the surface energy term is chosen to give the observed values of n*, then evaluating ΔGn′ for n = 1 gives ΔG1′ = −20 kcal/mole, whereas it should be zero. If the surface energy is chosen to make ΔG1′ = 0, then the calculated values of n* and the nucleation rate do not agree with experiments. A modified form of the monolayer disc classical model gives good agreement between theory and experiment but is less satisfactory than the atomistic model. The experimental temperature variation of the maximum number density of nuclei disagrees with that expected as a result of depletion of single atoms. The results can be explained by depletion of mobile nuclei by mutual capture.