Overview: Homogeneous nucleation from the vapor phase-The experimental science.

Homogeneous nucleation from the vapor phase has been a well-defined area of research for ∼120 yr. In this paper, we present an overview of the key experimental and theoretical developments that have made it possible to address some of the fundamental questions first delineated and investigated in C. T. R. Wilson's pioneering paper of 1897 [C. T. R. Wilson, Philos. Trans. R. Soc., A 189, 265-307 (1897)]. We review the principles behind the standard experimental techniques currently used to measure isothermal nucleation rates, and discuss the molecular level information that can be extracted from these measurements. We then highlight recent approaches that interrogate the vapor and intermediate clusters leading to particle formation, more directly.

Homogenous nucleation rates of n-propanol measured in the Laminar Flow Diffusion Chamber at different total pressures.

Nucleation rates of n-propanol were investigated in the Laminar Flow Diffusion Chamber. Nucleation temperatures between 270 and 300 K and rates between 10(0) and 10(6) cm(-3) s(-1) were achieved. Since earlier measurements of n-butanol and n­pentanol suggest a dependence of nucleation rates on carrier gas pressure, similar conditions were adjusted for these measurements. The obtained data fit well to results available from literature. A small positive pressure effect was found which strengthen the assumption that this effect is attributed to the carbon chain length of the n-alcohol [D. Brus, A. P. Hyvärinen, J. Wedekind, Y. Viisanen, M. Kulmala, V. Zdímal, J. Smolík, and H. Lihavainen, J. Chem. Phys. 128, 134312 (2008)] and might be less intensive for substances in the homologous series with higher equilibrium vapor pressure. A comparison with the theoretical approach by Wedekind et al. [Phys. Rev. Lett. 101, 12 (2008)] shows that the effect goes in the same direction but that the intensity is much stronger in experiments than in theory.

Co-condensation of nonane and D2O in a supersonic nozzle.

We study the unary and binary nucleation and growth of nonane-D2O nanodroplets in a supersonic nozzle. Fourier Transform Infrared spectroscopy measurements provide the overall composition of the droplets and Small Angle X-ray Scattering experiments measure the size and number density of the droplets. The unary nucleation rates Jmax of nonane, 9.4 × 10(15) < Jmax /cm(-3) s(-1) < 2.0 × 10(16), and those of D2O, 2.4 × 10(17) < Jmax /cm(-3) s(-1) < 4.1 × 10(17), measured here agree well with previous results. In most of the binary condensation experiments new particle formation is dominated by D2O, but the observed nucleation rates are decreased by up to a factor of 6 relative to the rates measured for pure D2O, an effect that can be partly explained by non-isothermal nucleation theory. The subsequent condensation of D2O is inhibited both by the increased temperature of the binary droplets relative to the pure D2O droplets, and because the binary droplet surface is expected to be comprised largely of nonane. For the one case where nonane appears to initiate condensation, we find that the nucleation rate is about 50% higher than that observed for pure nonane at comparable pv0, consistent with significant particle formation driven by D2O.

Nucleation of ethanol, propanol, butanol, and pentanol: a systematic experimental study along the homologous series.

We present homogeneous vapor-liquid nucleation rates of the 1-alcohols (C(n)H(2n+1)OH, n = 2-4) measured in the well-established two-valve nucleation pulse chamber as well as in a novel one-piston nucleation pulse chamber at temperatures between 235 and 265 K. The nucleation rates and critical cluster sizes show a very systematic behavior with respect to the hydrocarbon chain length of the alcohol, just as their thermo-physical parameters such as surface tension, vapor pressure, and density would suggest. For all alcohols, except ethanol, predictions of classical nucleation theory lie several orders of magnitude below the experimental results and show a strong temperature-dependence typically found in nucleation experiments. The more recent Reguera-Reiss theory [J. Phys. Chem. B 108(51), 19831 (2004)] achieves reasonably good predictions for 1-propanol, 1-butanol, and 1-pentanol, and independent of the temperature. Ethanol, however, clearly shows the influence of strong association between molecules even in the vapor phase. We also scaled all experimental results with classic nucleation theory to compare our data with other data from the literature. We find the same overall temperature trend for all measurement series together but inverted and inconsistent temperature trends for individual 1-propanol and 1-butanol measurements in other devices. Overall, our data establishe a comprehensive and reliable data set that forms an ideal basis for comparison with nucleation theory.

Freezing water in no-man's land.

We report homogeneous ice nucleation rates between 202 K and 215 K, thereby reducing the measurement gap that previously existed between 203 K and 228 K. These temperatures are significantly below the homogenous freezing limit, T(H)≈ 235 K for bulk water, and well within no-man's land. The ice nucleation rates are determined by characterizing nanodroplets with radii between 3.2 and 5.8 nm produced in a supersonic nozzle using three techniques: (1) pressure trace measurements to determine the properties of the flow as well as the temperature and velocity of the droplets, (2) small angle X-ray scattering (SAXS) to measure the size and number density of the droplets, and (3) Fourier Transform Infrared (FTIR) spectroscopy to follow the liquid to solid phase transition. Assuming that nucleation occurs throughout the droplet volume, the measured ice nucleation rates J(ice,V) are on the order of 10(23) cm(-3) s(-1), and agree well with published values near 203 K.

Homogeneous water nucleation in a laminar flow diffusion chamber.

Homogeneous nucleation rates of water at temperatures between 240 and 270 K were measured in a laminar flow diffusion chamber at ambient pressure and helium as carrier gas. Being in the range of 10(2)-10(6) cm(-3) s(-1), the experimental results extend the nucleation rate data from literature consistently and fill a pre-existing gap. Using the macroscopic vapor pressure, density, and surface tension for water we calculate the nucleation rates predicted by classic nucleation theory (CNT) and by the empirical correction function of CNT by Wolk and Strey [J. Phys. Chem. B 105, 11683 (2001)]. As in the case of other systems (e.g., alcohols), CNT predicts a stronger temperature dependence than experimentally observed, whereas the agreement with the empirical correction function is good for all data sets. Furthermore, the isothermal nucleation rate curves allow us to determine the experimental critical cluster sizes by use of the nucleation theorem. A comparison with the critical cluster sizes calculated by use of the Gibbs-Thomson equation is remarkably good for small cluster sizes, for bigger ones the Gibbs-Thomson equation overestimates the cluster sizes.

Argon nucleation in a cryogenic supersonic nozzle.

We have measured pressures p and temperatures T corresponding to the maximum nucleation rate of argon in a cryogenic supersonic nozzle apparatus where the estimated nucleation rates are J=10(17+/-1) cm(-3) s(-1). As T increases from 34 to 53 K, p increases from 0.47 to 8 kPa. Under these conditions, classical nucleation theory predicts nucleation rates of 11-13 orders of magnitude lower than the observed rates while mean field kinetic nucleation theory predicts the observed rates within 1 order of magnitude. The current data set appears consistent with the measurements of Iland et al. [J. Chem. Phys. 127, 154506 (2007)] in the cryogenic nucleation pulse chamber. Combining the two data sets suggests that classical nucleation theory fails because it overestimates both the critical cluster size and the excess internal energy of the critical clusters.

Homogeneous nucleation of a homologous series of n-alkanes (C(i)H(2i+2), i=7-10) in a supersonic nozzle.

Homogeneous nucleation rates of the n-alkanes (C(i)H(2i+2); i=7-10) were determined by combining information from pressure trace measurements and small angle x-ray scattering (SAXS) experiments in a supersonic Laval nozzle. The condensible vapor pressure p(J max), the temperature T(J max), the characteristic time Deltat(J max), and supersaturation S(J max) corresponding to the peak nucleation rate J(max) were determined during the pressure trace measurements. These measurements also served as the basis for the subsequent SAXS experiments. Fitting the radially averaged SAXS spectrum yielded the mean droplet radius r, 5

Crossover from nucleation to spinodal decomposition in a condensing vapor.

The mechanism controlling the initial step of a phase transition has a tremendous influence on the emerging phase. We study the crossover from a purely nucleation-controlled transition toward spinodal decomposition in a condensing Lennard-Jones vapor using molecular dynamics simulations. We analyze both the kinetics and at the same time the thermodynamics by directly reconstructing the free energy of cluster formation. We estimate the location of the spinodal, which lies at much deeper supersaturations than expected. Moreover, the nucleation barriers we find differ only by a constant from the classical nucleation theory predictions and are in very good agreement with semiempirical scaling relations. In the regime from very small barriers to the spinodal, growth controls the rate of the transition but not its nature because the activation barrier has not yet vanished. Finally, we discuss in detail the influence of the chosen reaction coordinate on the interpretation of such simulation results.

Homogeneous nucleation of nitrogen.

We investigated the homogeneous nucleation of nitrogen in a cryogenic expansion chamber [A. Fladerer and R. Strey, J. Chem. Phys. 124, 164710 (2006)]. Gas mixtures of nitrogen and helium as carrier gas were adiabatically expanded and cooled down from an initial temperature of 83 K until nucleation occurred. This onset was detected by constant angle light scattering at nitrogen vapor pressures of 1.3-14.2 kPa and temperatures of 42-54 K. An analytical fit function well describes the experimental onset pressures with an error of +/-15%. We estimate the size of the critical nucleus with the Gibbs-Thomson equation yielding critical sizes of about 50 molecules at the lowest and 70 molecules at the highest temperature. In addition, we estimate the nucleation rate and compare it with nucleation theories. The predictions of classical nucleation theory (CNT) are 9 to 19 orders of magnitude below the experimental results and show a stronger temperature dependence. The Reguera-Reiss theory [Phys. Rev. Lett. 93, 165701 (2004)] predicts the correct temperature dependence at low temperatures and decreases the absolute deviation to 7-13 orders of magnitude. We present an empirical correction function to CNT describing our experimental results. These correction parameters are remarkably close to the ones of argon [Iland et al., J. Chem. Phys. 127, 154506 (2007)] and even those of water [J. Wolk and R. Strey, J. Phys. Chem. B 105, 11683 (2001)].

Evaluating nucleation rates in direct simulations.

We compare different methods for obtaining nucleation rates from molecular dynamics simulations of nucleation, using the condensation of Lennard-Jones argon as an example. All methods yield the same nucleation rate at the conditions where they can be applied correctly, with discrepancies smaller than a factor of 2. We critically examine the different approaches and highlight their respective strengths and possible limitations.

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.

Nucleation rate isotherms of argon from molecular dynamics simulations.

We report six nucleation rate isotherms of vapor-liquid nucleation of Lennard-Jones argon from molecular dynamics simulations. The isotherms span three orders of magnitude in nucleation rates, 10(23)

Homogeneous nucleation rates of 1-pentanol.

We have measured isothermal homogeneous nucleation rates J for 1-pentanol vapor in two different carrier-gases, argon, and helium, using a two-valve nucleation pulse chamber. The nucleation rates cover a range of 10(5)