Judith Wölk

Empirical function for homogeneous water nucleation rates

Very recently, Wolk and Strey [J. Phys. Chem. B 105, 11683 (2001)] presented empirical temperature correction functions for calculating homogeneous nucleation rates J of H2O and D2O (1<J/cm−3 s−1<1020) from classical nucleation theory over an extended range of temperature T (200<T/K<310) and supersaturations S (5<S<200). Here, we critically test the correction functions to the Becker–Doring nucleation rate equation JBD against an extensive set of experimental data, and find that the equations distinctly improve the agreement between theory and experiment for very little extra work. The success of the corrected nucleation rate functions is surprising, given that they were developed based on experimental nucleation rates measured in a nucleation pulse chamber over a limited nucleation rate range 105<J/cm−3 s−1<1010, supersaturation range 6<S<22, and temperature range 220<T/K<260.

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.

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)<J/cm(-3) s(-1)<10(26), in a temperature range of 45-70 K below the triple point. The rates are very accurately determined using the concept of mean first-passage times, which also allows a determination of the critical cluster size directly from the kinetics. The results deviate from classical nucleation theory (CNT) by two to seven orders of magnitude, which nevertheless is much smaller than the more than 20 orders of magnitude encountered in recent experiments in a similar temperature range. The extended modified liquid drop-dynamical nucleation theory (EMLD-DNT) shows excellent agreement with the simulation results with deviations of less than one order of magnitude over the entire studied temperature range. Both simulation and experiment confirm the same incorrect temperature trend of CNT, which seems to be corrected in the EMLD-DNT model. However, the predictions of CNT for the critical cluster sizes agree well with the results obtained from the simulations using the nucleation theorem, supporting the notion that CNT successfully estimates the location of the transition state but severely fails to predict its height.

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.

Argon nucleation: bringing together theory, simulations, and experiment.

We present an overview of the current status of experimental, theoretical, molecular dynamics (MD), and density functional theory (DFT) studies of argon vapor-to-liquid nucleation. Since the experimental temperature-supersaturation domain does not overlap with the corresponding MD and DFT domains, separate comparisons have been made: theory versus experiment and theory versus MD and DFT. Three general theoretical models are discussed: Classical nucleation theory (CNT), mean-field kinetic nucleation theory (MKNT), and extended modified liquid drop model-dynamical nucleation theory (EMLD-DNT). The comparisons are carried out for the area below the MKNT pseudospinodal line. The agreement for the nucleation rate between the nonclassical models and the MD simulations is very good--within 1-2 orders of magnitude--while the CNT deviates from simulations by about 3-5 orders of magnitude. Perfect agreement is demonstrated between DFT results and predictions of MKNT (within one order of magnitude), whereas CNT and EMLD-DNT show approximately the same deviation of about 3-5 orders of magnitude. At the same time the agreement between all theoretical models and experiment remains poor--4-8 orders of magnitude for MKNT, 12-14 orders for EMLD-DNT, and up to 26 orders for CNT. We discuss possible reasons for this discrepancy and the ways to carry out experiment and simulations within the common temperature-supersaturation domain in order to produce a unified picture of argon nucleation.

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 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)<J/cm(-3) s(-1)<10(9) at temperatures between 235<T/K<265. We observed no influence of the carrier gas on location and slope of the nucleation rate isotherms. These measurements are part of an international effort to examine 1-pentanol using various experimental techniques, which was initiated in Prague in 1995. In the present paper nucleation rate data obtained by several groups are compared to each other and to the classical nucleation theory. As expected, the classical theory is not able to quantitatively predict the experimental results. Nevertheless, relating the experimental data to the classical theory provides a suitable way to compare data of widely differing nucleation rates obtained by different experimental techniques. This comparison helps judging mutual support of the data and, at the same time, provides a rather interesting insight into the accuracy of the individual experimental techniques.

Small angle neutron scattering from D2O–H2O nanodroplets and binary nucleation rates in a supersonic nozzle

Small angle neutron scattering (SANS) experiments were used to characterize binary nanodroplets composed of D2O and H2O. The droplets were formed by expanding dilute mixtures of condensible vapor in a N2 carrier gas through a supersonic nozzle, while maintaining the onset of condensation at a fixed position in the nozzle. It is remarkable, given the small coherent scattering length density of light water, that even the pure H2O aerosol gave a scattering signal above background. The scattering spectra were analyzed assuming a log-normal distribution of droplets. On average, the geometric radius of the nanodroplets rg was rg=13 (±1) nm, the polydispersity ln σr was ln σr=0.19 (±0.07), and the number density N was N=(2±0.2)⋅1011 cm−3. The aerosol volume fractions derived from the SANS measurements are consistent with those derived from the pressure trace experiments, suggesting that the composition of the droplets was close to that of the initial condensible mixture. A quantitative analysis of the scattering spectra as a function of the isotopic composition gave further evidence that the binary droplets exhibit ideal mixing behavior. Because both the stagnation temperature T0 and the location of onset were fixed, the temperature corresponding to the maximum nucleation rate was constant at TJ max=229 (±1) K. Thus, the experiments let us estimate the isothermal peak nucleation rates as a function of the isotopic composition. The nucleation rates were found to be essentially constant with Jmax equal to (3.6±0.5)⋅1016 cm−3 s−1 at a mean supersaturation of 44 (±3).Small angle neutron scattering (SANS) experiments were used to characterize binary nanodroplets composed of D2O and H2O. The droplets were formed by expanding dilute mixtures of condensible vapor in a N2 carrier gas through a supersonic nozzle, while maintaining the onset of condensation at a fixed position in the nozzle. It is remarkable, given the small coherent scattering length density of light water, that even the pure H2O aerosol gave a scattering signal above background. The scattering spectra were analyzed assuming a log-normal distribution of droplets. On average, the geometric radius of the nanodroplets rg was rg=13 (±1) nm, the polydispersity ln σr was ln σr=0.19 (±0.07), and the number density N was N=(2±0.2)⋅1011 cm−3. The aerosol volume fractions derived from the SANS measurements are consistent with those derived from the pressure trace experiments, suggesting that the composition of the droplets was close to that of the initial condensible mixture. A quantitative analysis of the scattering...

H2O–D2O condensation in a supersonic nozzle

We examined the condensation of H2O, D2O, and four intermediate mixtures (20, 40, 60, and 80 mol % D2O) in a supersonic nozzle. Because the physical and chemical properties of protonated and deuterated water are so similar, this system is ideal for studying the change in condensation behavior as a function of condensible composition. In our experiments dilute mixtures of condensible vapor in N2 are expanded from three different stagnation temperatures resulting in a broad range of onset temperatures (190–238 K) and pressures (27–787 kPa). For a fixed stagnation temperature, the partial pressure required to maintain the onset of condensation at a given location or temperature in the nozzle is consistently higher for H2O than for D2O. In contrast, the supersaturation at fixed onset temperature is usually higher for D2O than for H2O and this difference increases toward lower temperature. The partial pressure at onset for the intermediate mixtures varied linearly between the values observed for the pure compo...

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.