No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
New Measurements of Argon and Nitrogen Nucleation in the Cryogenic Nucleation Pulse Chamber
Abstract
New measurements of homogeneous nucleation onset data for argon and
nitrogen from the cryogenic nucleation pulse chamber have been
performed. By reducing the amount of carrier gas in the gas mixture,
higher onset pressures and temperatures could be reached. The new
results are consistent with older data from the same apparatus and
literature data. Carrier gas-free experiments with nitrogen show no
associative effects. Interestingly, the classical nucleation theory
predicts the onset results of nitrogen more accurately than those of
argon, despite argon being the more ideal substance of the two.
... Deviations between experimental results and CNT predictions at high saturation have been reported for various systems. [2][3][4][5][6] ...
We report on molecular-level studies of the condensation of propane gas and propane/ethane gas mixtures in the uniform (constant pressure and temperature) postnozzle flow of Laval expansions using soft single-photon ionization by vacuum ultraviolet light and mass spectrometric detection. The whole process, from the nucleation to the growth to molecular aggregates of sizes of several nanometers (∼5 nm), can be monitored at the molecular level with high time-resolution (∼3 μs) for a broad range of pressures and temperatures. For each time, pressure, and temperature, a whole mass spectrum is recorded, which allows one to determine the critical cluster size range for nucleation as well as the kinetics and mechanisms of cluster-size specific growth. The detailed information about the size, composition, and population of individual molecular clusters upon condensation provides unique experimental data for comparison with future molecular-level simulations.
... Deviations in estimated and measured nucleation rate densities of up to 35 orders of magnitude occur for melt crystallization of metals as well as for vapour condensation and also in colloidal HS systems [35,62,[153][154][155]. Also other measured quantities deviate strongly from predictions [156]. This has been blamed on a number of issues, both conceptually and practically. ...
The interfacial free energy is a central quantity in crystallization from the
meta-stable melt. In suspensions of charged colloidal spheres, nucleation and
growth kinetics can be accurately measured from optical experiments. In
previous work, from this data effective non-equilibrium values for the
interfacial free energy between the emerging bcc-nuclei and the adjacent melt
in dependence on the chemical potential difference between melt phase and
crystal phase were derived using classical nucleation theory. A strictly linear
increase of the interfacial free energy was observed as a function of increased
meta-stability. Here, we further analyze this data for five aqueous suspensions
of charged spheres and one binary mixture. We utilize a simple extrapolation
scheme and interpret our findings in view of Turnbull's empirical rule. Our
first estimates for the reduced interfacial free energy, $\sigma_{0,bcc}$,
between coexisting equilibrium uid and bcc-crystal phases are on the order of a
few $k_BT$. Their values are not correlated to any of the electrostatic
interaction parameters but rather show a systematic decrease with increasing
size polydispersity and a lower value for the mixture as compared to the pure
components. At the same time, $\sigma_0$ also shows an approximately linear
correlation to the entropy of freezing. The equilibrium interfacial free energy
of strictly monodisperse charged spheres may therefore be still greater.
... Deviations in estimated and measured nucleation rate densities of up to 35 orders of magnitude occur for melt crystallization of metals as well as for vapor condensation and also in colloidal HS systems [36,63,[151][152][153]. Also other measured quantities deviate strongly from predictions [154]. This has been blamed on a number of issues, both conceptually and practically. ...
We extend previous analysis of data for the melt-nucleus interfacial free
energy, $\gamma$, gained from optical experiments on suspensions of charged
colloidal spheres, which crystallize with body centred cubic (bcc) crystal
structures. Compiling data from five pure species with different
polydispersities and one binary mixture, we find the equilibrium melt-crystal
interfacial energy to be considerably larger than the hard sphere reference
value. Both this quantity and the entropy of freezing decrease with increasing
polydispersity. Moreover, we give a first experimental determination of the
Turnbull coefficient for a bcc crystallizing material. The observed value
$C_{T, bcc} \approx 0.3$ agrees well with theoretical expectations for bcc
systems with short to medium ranged interactions.
We investigate homogeneous gas-phase nucleation of CO2 and C3H8 in the uniform postnozzle flow of Laval expansions for the temperature range of 31.2K to 62.9K and 32.0K to 42.1K, respectively. Time-dependent cluster size distributions are recorded with a mass spectrometry after single-photon ionization with vacuum ultraviolet light. Net monomer-cluster forward rate constants and experimental nucleation rates J are retrieved from the time-dependent cluster size distributions. The comparison of experimental enhancement factors derived from these net forward rates with calculated enhancement factors provides an indication for the transitions from barrier-limited to barrierless nucleation. Our data suggests such a transition for CO2, but not for C3H8. The values of J lie in the range from 9x10¹⁴cm⁻³s⁻¹ to 6x10¹⁵cm⁻³s⁻¹. For CO2, the comparison of J with a modeled nucleation rate JQM based on quantum chemical calculations of the free energy barrier also hints at a transition from barrierless condensation to barrier-limited nucleation. Further, we address the influence of the carrier gas pressure on the nucleation rate.
Toluene cluster formation has been investigated in the postnozzle flows of Laval expansions at flow temperatures between ~ 48 and 73 K, toluene number concentrations between ~10^13 - 10^15 cm^-3, and for growth times of up to ~170 µs. The clusters were detected by soft ionization mass spectrometry to ensure minimum cluster fragmentation upon ionization. The optimum conditions were achieved with single-photon ionization using vacuum ultraviolet (VUV) photons of 13.3 eV energy and low fluences. The nature of the onset of toluene cluster formation hints at barrierless nucleation, which seems a likely scenario for the high supersaturations (>10^19) of the present experiments. This contrasts with the onset behavior observed for propane in earlier studies, which suggested nucleation in the presence of a barrier. Subsequent cluster growth has been studied as a function of the growth time for various toluene partial pressures. Size-resolved growth data have been recorded for all cluster sizes from the dimer to aggregates composed of ~2400 monomers (~4.4 nm in size), revealing general trends in the growth behavior. The current experiments provide systematic size- and time-resolved data on cluster formation at high supersaturations as a possible benchmark for the understanding of cluster formation under such conditions.
We report on a new instrument that allows for the investigation of weakly-bound molecular aggregates under equilibrium conditions (constant temperature and pressure). The aggregates are formed in a Laval nozzle and probed with mass spectrometry in the uniform postnozzle flow; i. e. in the equilibrium region of the flow. Aggregates over a very broad size range from the monomer to particle sizes of 10-20 nm can be generated and studied with this setup. Soft ionization of the aggregates is performed with single photons from a homemade vacuum ultraviolet laser. The mass spectrometric detection provides molecular-level information on the size and chemical composition of the aggregates. This new instrument is useful for a broad range of cluster studies that require well-defined conditions.
The problems of (i) replacement free energy, (ii) 1/S, and (iii) internal consistency in the classical theory of nucleation, based on the capillarity approximation, are resolved by the proper evaluation of mixing entropy.
Homogeneous nucleation of argon has been measured with a cryogenic nucleation pulse chamber. Due to the very fast growth of the argon droplets nucleation and growth could not be decoupled. However, we can present a systematic set of onset data for argon measured in a temperature range from 42 to 58K and for vapor pressures from 0.3 to 10 kPa. Using the most recent expressions for temperature-dependent vapor pressures, surface tensions and densities predictions by the classical Becker-Döring nucleation theory are calculated. A rather high deviation of up to 26 orders of magnitude between theory and experiment is found. As in the case of other systems (e.g., water, alcohols, and alkanes) classical theory shows a stronger temperature dependence than experimentally observed.
Keywords Homogeneous nucleation, onset measurements
Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
Cryogenic shock tubes immersed in liquid nitrogen were used to study condensation onset in argon diluted in helium carrier gas. The condensation in the shock tube expansion fans was detected by light scattering; the pressure was measured and used to calculate temperature, assuming isentropic flow. Previous studies employing supersonic nozzles at higher initial temperatures produced substantial supersaturation at the onset of condensation and agreed well with theory. In contrast, the shock tube experiments showed condensation at states close to equilibrium saturation, having temperatures from 47 to 76 K and pressures from 1 to 166 torr. Possible explanations of the discrepancy require consideration of differences between the two methods in cooling rates and initial temperatures in conjunction with the theory of homogeneous nucleation.
In the past century, the homogeneous nucleation of light water (H2O) has repeatedly been studied using various experimental techniques. Generally, the onset of nucleation was recorded, while less frequently, the actual nucleation rates were determined. In contrast, the nucleation of heavy water (D2O) has been examined only in a single instance with no nucleation rates measured. Here, we report the first nucleation rate study of D2O along with nucleation rate measurements for H2O, which we repeated for comparison under identical conditions. We find that the nucleation rates for H2O and D2O differ by a factor of 2500, if compared at the same respective vapor pressure pv and temperature T, whereas the comparison at the same supersaturation S shows an agreement within experimental scatter. Also, the numbers of molecules in the critical clusters, which are determined from the slopes of the ln J versus ln S curves, are nearly the same for both isotopic waters. A satisfactory agreement with previous nucleation rate measurements of H2O made by Viisanen et al. (Viisanen, Y.; Strey, R.; Reiss, H. J. Chem. Phys. 1993, 99, 4680; 2000, 112, 8205) is observed, if the onset supersaturations S0 at nucleation rates of J0 = 107 cm-3 s-1 are compared. Using the most recent expressions for temperature-dependent vapor pressures, we calculated surface tensions and densities predictions by the classical Becker−Döring nucleation theory. Around T = 240 K, the predictions quantitatively agree with the experimental data. However, as in the case of other systems (e.g., alcohols and alkanes), classical theory shows a stronger temperature dependence than experimentally observed. A temperature-dependent correction of the classical theory is developed which permits analytical calculation of nucleation rates as function of supersaturation and temperature over extended ranges.
The formation of argon clusters by homogeneous nucleation of pure argon diluted in helium was investigated in the supersonic outflow of a shock tube, where the clusters were detected by laser light scattering from the particles in supersaturated states. The thermodynamic states for the onset of homogeneous nucleation varied between 48 and 85 K with corresponding argon partial pressures in the range 2–850 Torr. Values of adiabatic supercooling with respect to the argon phase equilibrium ranged between 3 and 10 K. The experiments are in agreement with previous investigations in subsonic shock tube and supersonic Ludwieg tube expansions but disagree with previous investigations in steady supersonic nozzle expansions. It is possible to explain qualitatively the observed differences in argon nucleation behavior on the basis of a thermodynamic and kinetic concept independent of the basic assumptions of existing nucleation theories. © 1995 American Institute of Physics.
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.
The vapor nucleation of argon was investigated in shock tube expansions starting from room temperature. The cooling from the superheated initial state to nucleation onset was attained in unsteady flow fields at high Mach numbers M = 5. Thermodynamic states for homogeneous nucleation were observed between 30 and 180 Torr at corresponding temperatures in the range of 50–70 K. The high starting temperatures do not affect the nucleation onset states compared to previous experiments on the subject, where the expansions started from much lower temperatures. The slight differences in the onset states to previous experiments employing cryogenic shock and Ludwieg tubes may be attributed to the higher cooling rates and to nonisentropic expansion effects. © 1999 American Institute of Physics.
The ‘‘kinetic theory’’ of homogeneous nucleation developed by Katz and Wiedersich is extended to derive a new expression for the rate of nucleation from an ideal supersaturated vapor. Compared to the classical expression for the nucleation rate, the new expression has a slightly different dependence on supersaturation, and a substantially different dependence on temperature. A comparison of the new expression with experimental data on nucleation rates of several organic liquids indicates that in some but not all cases the new expression gives much closer agreement with the data than does the classical expression. Discrepancies between the theory and the data are ascribed mainly to the physical assumptions of the theory presented, which are the same as in the classical theory—particularly, that the physical properties of microscopic clusters are the same as those of the bulk liquid.
Experiments on homogeneous condensation of nitrogen in helium were
performed. Various mole fractions of nitrogen in helium were expanded
from the precooled driver section of a shock tube. The cooling from the
superheated initial state of 197 K to the nucleation onset was attained
in the unsteady supersonic flow field. The nucleation onset was
determined by light scattering of the condensed particles in the
temperature range from 38 to 56 K, and the nitrogen pressure range from
2.9 to 80 Torr. Supercooling between 6 and 10 K was measured. No carrier
gas influence could be detected.
We present a new phenomenological approach to nucleation, based on the combination of the “extended modified liquid drop” (EMLD) model and dynamical nucleation theory (DNT). The new model proposes a new cluster definition, which properly includes the effect of fluctuations, and it is consistent both thermodynamically and kinetically. The model is able to predict successfully the free energy of formation of the critical nucleus, using only macroscopic thermodynamic properties. The nucleation barrier predicted by the model vanishes at a finite value of the supersaturation, thus accounting for the spinodal, and provides excellent agreement with the results of recent simulations. Of fundamental importance is the fact that the cluster definition is based on cluster volume as well as molecular content, and that a nonarbitrary specification of volume is supplied by variational transition state theory. In this connection, the importance of allowing the “process” to define the cluster is demonstrated. This nexus between chemical dynamics and nucleation should lead to a collaboration of nucleation theorists and chemical dynamicists that will form a whole that is greater than the sum of its parts.
Condensation of nitrogen carried in helium was studied in expansion waves of a cryogenic shock tube operated at 77.4 K. Condensation onset was detected by laser light scattering in conjunction with piezoelectric pressure measurements. In contrast to most of the previous studies employing supersonic nozzles or free jet expansions, the shock tube experiments showed condensation at supersaturated states close to phase equilibrium having temperatures from 66 K to 57 K and nitrogen partial pressures from 230 torr to 45 torr. The differences in condensation onset presumably caused by the different experimental conditions such as carrier gas concentrations, cooling rates and supply temperatures cannot be explained on the basis of conventional nucleation theories. It is instead possible to relate these differences qualitatively to the molecular kinetics of nitrogen microcluster formation.
A small, stainless steel, two‐dimensional source flow nozzle supplied with bottled nitrogen was used for the condensation investigation. It was found that the nitrogen supersaturates approximately 15°K or 1.2 Mach numbers when expanded from stagnation conditions of 70°F and pressures of 8.21 and 16.15 atmos. A numerical method for solving the equations of motion with the aid of the experimental data allows the computation of the fluid temperature during the condensation process. The addition of small amounts of carbon dioxide reduced the degree of supersaturation obtainable with bottled nitrogen.
Tests in a small hypersonic wind tunnel have determined critical temperature and pressure conditions for the condensation of pure dry nitrogen and have indicated that in the range of pressure (0.5–2.8 mm Hg) and temperature (52°–64°R) obtained in the tests, there is a supersaturation of about 30 Fahrenheit degrees.
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)].