Heterogeneous Nucleation of n-Butanol Vapor on Submicrometer Particles of SiO2 and TiO2

Condensation of a supersaturated vapor of n-butanol on monodisperse submicrometer particles is investigated in a flow cloud chamber (FCC). The size dependence of critical supersaturation in the range of 20 to 90 nm is experimentally determined. Two types of aerosol, SiO2 and TiO2, are tested. The results show that both aerosols induce heterogeneous nucleation better than perfectly wetted particles. The experimental critical supersaturation is smaller than that predicted by the Fletcher version of Volmer theory of heterogeneous nucleation even with the line tension and surface diffusion taken into account and has a size dependence in qualitative agreement with that theoretically predicted but to a lesser degree. 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 physical properties. The law of corresponding states was extended to the heterogeneous nucleation, and a simple correlation was observed. We conclude that the macroscopic theory of heterogeneous nucleation leads to a prediction of critical supersaturation higher than that experimentally measured. Copyright 1999 Academic Press.     

Heterogeneous multicomponent nucleation theorems for the analysis of nanoclusters

In this paper we present a new form of the nucleation theorems applicable to heterogeneous nucleation. These heterogeneous nucleation theorems allow, for the first time, direct determination of properties of nanoclusters formed on pre-existing particles from measured heterogeneous nucleation probabilities. The theorems can be used to analyze the size (first theorem) and the energetics (second theorem) of heterogeneous clusters independent of any specific nucleation model. We apply the first theorem to the study of small water and n-propanol clusters formed at the surface of 8 nm silver particles. According to the experiments the size of the two-component critical clusters is found to be below 90 molecules, and only less than 20 molecules for pure water, less than 300 molecules for pure n-propanol. These values are drastically smaller than the ones predicted by the classical nucleation theory, which clearly indicates that the nucleating clusters are too small to be quantitatively described using a macroscopic theory.     

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.     

Thermodynamics of epitaxial calcite nucleation on self-assembled monolayers

Classical heterogeneous nucleation theory is used to describe the epitaxial nucleation of calcite on self-assembled monolayers (SAMs). Both spherical and faceted clusters are considered. The use of faceted clusters reveals a useful relation between the shape of very small crystals and the ratio of the heterogeneous and homogeneous nucleation barriers. The experimental approach of this paper concerns the measurement of the threshold driving forces for both homogeneous and heterogeneous nucleation of calcite. This is accomplished by preparing solutions with well-defined driving forces and by measuring the resulting types of nucleation that are observed after a fixed experimental time. The results of the experiments and the theoretical shape analysis are compared, and it is shown that in the experiments no homogeneous nucleation of calcite occurs for driving forces up to at least Deltamu/k(B)T approximately equal to 6.0. A calculation of the critical cluster size for heterogeneous nucleation results in a range of 2-28 growth units and faceted critical clusters from 3-28 growth units, depending on the value of the surface free energy of calcite. These sizes are 50-100 times smaller than the crystalline domain sizes of SAMs and therefore small enough to explain the promoting effect of the substrate.     

Molecular dynamics analysis of the crystallization of an overcooled aluminum melt

The homogeneous nucleation of a crystal in an overcooled aluminum melt was modeled by the molecular dynamics (MD) method. The MD simulation used the embedded-atom potential. The crystallization delay times were determined from MD simulation data. In a set of systems at the same temperature and pressure, the lifetimes were distributed exponentially. Nucleation frequencies at different temperatures and pressures were determined. The resulting nucleation frequencies were compared with the ones predicted by classical nucleation theory.     

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

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

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.     

Efflorescence relative humidity for ammonium sulfate particles

The classical homogeneous nucleation theory was employed to calculate the efflorescence relative humidity (ERH) of airborne ammonium sulfate particles with a wide size range (8 nm to 17 microm) at room temperature. The theoretical predictions are in good agreement with the experimentally measured values. When the ammonium sulfate particle is decreased in size, the ERH first decreases, reaches a minimum around 30% for particle diameter equal to about 30 nm, and then increases. It is for the first time that the Kelvin effect is theoretically verified to substantially affect the ERH of ammonium sulfate particles smaller than 30 nm, while the aerosol size is the dominant factor affecting the efflorescent behavior of ammonium sulfate particles larger than 50 nm.     

Condensation of supersaturated n-butanol vapor on charged/neutral nanoparticles of D-mannose and L-rhamnose

The effects of size, charge, and solubility on the condensation of supersaturated n-butanol vapor on monodisperse nanoparticles of D-mannose and L-rhamnose are investigated in a flow cloud chamber. The dependence of the critical supersaturation S(cr) on particle size in the range from 30 to 90 nm is determined experimentally. The results show that the experimental S(cr) decreases with increasing particle size and solubility, qualitatively in agreement with the prediction by the Volmer theory of nucleation on soluble particles and by the Kohler theory, but quantitatively smaller than both theoretical predictions. The condensation of supersaturated vapor on singly positive/negative charged particles with diameters of 30, 60, and 90 nm is examined, and no obvious charge effect and sign preference are observed.     

Homogeneous ice nucleation from aqueous inorganic/organic particles representative of biomass burning: water activity, freezing temperatures, nucleation rates

Homogeneous ice nucleation plays an important role in the formation of cirrus clouds with subsequent effects on the global radiative budget. Here we report on homogeneous ice nucleation temperatures and corresponding nucleation rate coefficients of aqueous droplets serving as surrogates of biomass burning aerosol. Micrometer-sized (NH(4))(2)SO(4)/levoglucosan droplets with mass ratios of 10:1, 1:1, 1:5, and 1:10 and aqueous multicomponent organic droplets with and without (NH(4))(2)SO(4) under typical tropospheric temperatures and relative humidities are investigated experimentally using a droplet conditioning and ice nucleation apparatus coupled to an optical microscope with image analysis. Homogeneous freezing was determined as a function of temperature and water activity, a(w), which was set at droplet preparation conditions. The ice nucleation data indicate that minor addition of (NH(4))(2)SO(4) to the aqueous organic droplets renders the temperature dependency of water activity negligible in contrast to the case of aqueous organic solution droplets. The mean homogeneous ice nucleation rate coefficient derived from 8 different aqueous droplet compositions with average diameters of ～60 μm for temperatures as low as 195 K and a(w) of 0.82-1 is 2.18 × 10(6) cm(-3) s(-1). The experimentally derived freezing temperatures and homogeneous ice nucleation rate coefficients are in agreement with predictions of the water activity-based homogeneous ice nucleation theory when taking predictive uncertainties into account. However, the presented ice nucleation data indicate that the water activity-based homogeneous ice nucleation theory overpredicts the freezing temperatures by up to 3 K and corresponding ice nucleation rate coefficients by up to ～2 orders of magnitude. A shift of 0.01 in a(w), which is well within the uncertainty of typical field and laboratory relative humidity measurements, brings experimental and predicted freezing temperatures and homogeneous ice nucleation rate coefficients into agreement. The experimentally derived ice nucleation data are applied to constrain the water activity-based homogeneous ice nucleation theory to smaller than ±1 order of magnitude compared to the predictive uncertainty of larger than ±6 orders of magnitude. The atmospheric implications of these findings are discussed.     

Heterogeneous and homogeneous nucleation of strontium sulphate

Heterogeneous and homogeneous nucleation processes of strontium sulphate have been studied, using a homogeneous precipitation technique together with electronic particle counting. Four different heterogeneous nucleation processes were observed in solutions purified by conventional filtration. In solutions purified by continued circulation through a fibre-glass filter mat, homogeneous nucleation was observed at supersaturations about 10.75. The rate of homogeneous nucleation was found to depend on the 27th power of the sulphate concentration, indicating that the nucleus contains 52 ions. The results support the theory of homogeneous nucleation presented by Nielson.     

Transcrystallization of PTFE fiber/PP composites (I) crystallization kinetics and morphology

Transcrystallization of polypropylene (PP) on the polytetrafluoroethylene (PTFE) fiber was investigated. Both nucleation rate and crystal growth rate were determined by a polarized optical microscope. Based on the theory of heterogeneous nucleation, it has been found that the induction time can correlate well with the nucleation rate in determining the interfacial free energy difference function Δσ. The ratio of Δσ in the bulk matrix to that at the interface is 1.63 which implies the transcrystalline growth is favorable from a thermodynamic point of view. No difference in crystal growth rate of PP has been found in either spherulites or transcrystalline layers. On the basis of regime theory, a transition between regimes II and III was observed at ΔT = 48K. From the morphology studies, it has been found that the thickness of the transcrystalline layer increases with crystallization temperature, from 30 to 120 μm in the temperature range of 110–140°C. The growth of transcrystalline layer is hindered by the spherulites nucleated in the bulk. Moreover, the radius of spherulites adjacent to the transcrystalline layer is much smaller than that distant to the fiber. No significant increase in nucleation density at fiber ends is observed. Effect of internal stresses of fibers on the fiber's nucleating ability is not pronounced. © 1996 John Wiley & Sons, Inc.     

Small-angle x-ray scattering and crystallization kinetics of poly(ethylene terephthalate) crystallized in a liquid environment

By small-angle x-ray scattering, a systematic investigation was performed of the long spacing of poly(ethylene terephthalate) (PET) crystallized in a liquid environment. The results indicated that the measured long spacings were temperature dependent and apparently relatively insensitive to liquid type under the conditions studied. The kinetic nucleation model of polymer crystallization was found to adequately explain this dependence. The differences in the long spacings between thermal and liquid-induced crystallization were in part rationalized in terms of the suspected supercoolings involved in the respective processes. Calculation of the spherulite growth rates for liquid-induced crystallization was made on the basis of the kinetic nucleation model and the classic theory of polymer–diluent crystallization. The results were shown to agree with inferential experimental observations of these growth rates and to elucidate the physics underlying liquid–induced crystallization. Finally, use of this growth rate theory in conjunction with a previous model for overall crystallization kinetics was shown to adequately describe and predict the diffusion-limited kinetics observed experimentally for most liquid-induced crystallization situations.     

Fractionated crystallization of α‐ and β‐nucleated polypropylene droplets

A layer multiplying coextrusion process was used to produce multilayered polypropylene/polystyrene (PP/PS) films with various nucleating agents. When heated into the melt, the thin PP layers broke up into submicron PP droplets that exhibited fractionated crystallization. If the initial PP layers were 20 nm or less, the resulting droplets exhibited exclusively homogeneous nucleation. If a nucleating agent was added, the systematic departure from homogeneous nucleation provided insight into the nature of the heterogeneous nucleation. In this study, we used thermal analysis, atomic force microscopy (AFM), and wide angle X‐Ray scattering (WAXS) to examine the effect of two nucleating agents. We confirmed with WAXS and AFM that a soluble sorbitol nucleating agent for the PP α‐form operates in three concentration regimes as proposed in a previous study. Morphologically, homogeneous nucleation of the submicron droplets produced a granular texture. The correlation length from small‐angle X‐Ray scattering (SAXS) suggested that the grains contained 1–3 mesophase domains. Drawing on classical nucleation theory, the critical size nucleus of an individual mesophase domain was estimated to be about 2 nm³, which was considerably smaller than the mesophase domain. This pointed to mesophase crystallization that included the processes of nucleation and growth. Additional experiments were performed with nucleating agents for the PP β‐form. However, they were not effective in nucleating crystallization of the droplets, presumably because they were essentially insoluble in PP and the nucleating particles were too large to be accommodated in the PP droplets. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Argon nucleation in a cryogenic nucleation pulse chamber

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

Condensation of supersaturated water vapor on charged/neutral nanoparticles of glucose and monosodium glutamate

The effects of size, charge, dissolution, and dissociation on the condensation of supersaturated water vapor on monodisperse nanoparticles of glucose and monosodium glutamate (MSG) were investigated in a flow cloud chamber (FCC). The dependence of the critical supersaturation, S(cr), on particle size in the range of 30 to 90 nm and on temperature in the range of 10 to 50 degrees C were determined experimentally. The results show that the experimental S(cr) decreases with increasing particle size at a rate in reasonable agreement with the predictions of the Kohler and Volmer theories of nucleation for soluble particles, but decreases with increasing temperature at a rate higher than the prediction of the Volmer theory. The dissociation of MSG into ions lowers the experimental S(cr) to a value smaller than that for the more soluble glucose, agreeing with predictions. The experimental S(cr) is smaller than the predictions of both theories, and the discrepancy cannot be fully explained by the reductions in surface tension due to the dissolution of particles and curvature dependence. The condensation of supersaturated vapor on singly positively charged particles with diameters of 30, 60, and 90 nm was also examined, and no obvious charge effect on S(cr) was observed.     

Heterogeneous and homogeneous nucleation compared: rapid nucleation on microscopic impurities

We use computer simulation to calculate the rates of both homogeneous nucleation and heterogeneous nucleation on microscopic impurities. We do so in perhaps the simplest model of fluids and magnets: the two-dimensional Ising model. We expect our results to be qualitatively applicable to many simple and complex fluids. We find that heterogeneous nucleation on an impurity that is not only microscopic but also as small as possible, that is, a single fixed spin, is more than four orders of magnitude faster than homogeneous nucleation. The rate of heterogeneous nucleation then increases by a factor of approximately five for each additional fixed spin in the impurity. These results suggest that impurities as small as single molecules can result in homogeneous nucleation being irrelevant due to heterogeneous nucleation on these microscopic impurities being much faster.     

Two-component heterogeneous nucleation kinetics and an application to Mars

We develop a two-component heterogeneous nucleation model that includes exact calculation of the Stauffer-type [D. Stauffer, J. Aerosol Sci. 7, 319 (1976)] steady-state kinetic prefactor using the correct heterogeneous Zeldovich factor for a heterogeneous two-component system. The model, and a simplified version of it, is tested by comparing its predictions to experimental data for water-n-propanol nucleating on silver particles. The model is then applied to water-carbon dioxide system in Martian conditions, which has not been modeled before. Using the ideal mixture assumption, the model shows theoretical possibilities for two-component nucleation adjacent to the initial stages of one-component water nucleation, especially with small water vapor amounts. The numbers of carbon dioxide molecules in the critical cluster are small in the case of large water amounts (up to 300 ppm) in the gas phase, but larger when there is very little water vapor (1 ppm).