A study of homogeneous nucleation of ibuprofen in a flow chamber. Determination of the surface tension of critical nuclei

Homogeneous nucleation of ibuprofen vapor is studied in a nucleation flow chamber, a horizontal quartz tube equipped with an external heater. The area of the chamber where the nucleation proceeds most efficiently is determined, and the volume of this area is estimated. The temperature and supersaturation are determined and the homogeneous nucleation rate is calculated for this area. Saturation vapor pressure over liquid ibuprofen is measured in a temperature range of 353–383 K. Using an exact formula that has recently been derived for the nucleation rate based on the works by Kusaka, Reiss, as well as the Frenkel liquid-kinetics theory, surface tension and the radius of surface of tension of a critical nucleus σ= 25.9 mN/m and R _s = 1.6 nm, respectively, are calculated at 318 K. The measurement of the surface tension of an ibuprofen planar surface shows that, at 318 K, σ_∞ = 24.38 mN/m; i.e., σ is higher than σ_∞ by 6%. A critical nucleus is established as containing nearly 36 ibuprofen molecules.     

Homogeneous nucleation of droplets from supersaturated vapor in a closed system

Kinetic equations describing homogeneous nucleation kinetics within standard model are solved numerically under the condition of a constant number of molecules in the considered system. It has consequences to decrease the supersaturation of the supersaturated vapor during the process of the formation of small droplets of a new phase. The decrease of supersaturation occurs in a short time and reaches some value which remains unchanged for a relatively long time (quasistationary regime), especially at lower initial supersaturations. This time interval decreases with increasing value of the initial supersaturation. In the quasistationary regime the nucleation rate reaches its stationary value. At higher initial supersaturation, the rate of formation of nuclei goes to some maximum value corresponding to the stationary nucleation rate and then decreases with time due to the decrease of supersaturation.     

Homogeneous nucleation rate measurements of 1-butanol in helium: a comparative study of a thermal diffusion cloud chamber and a laminar flow diffusion chamber

Isothermal homogeneous nucleation rates of 1-butanol were measured both in a thermal diffusion cloud chamber and in a laminar flow diffusion chamber built recently at the Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, Prague, Czech Republic. The chosen system 1-butanol-helium can be studied reasonably well in both devices, in the overlapping range of temperatures. The results were compared with those found in the literature and those measured by Lihavainen in a laminar flow diffusion chamber of a similar design. The same isotherms measured with the thermal diffusion cloud chamber occur at highest saturation ratios of the three devices. Isotherms measured with the two laminar flow diffusion chambers are reasonably close together; the measurements by Lihavainen occur at lowest saturation ratios. The temperature dependences observed were similar in all three devices. The molecular content of critical clusters was calculated using the nucleation theorem and compared with the Kelvin equation. Both laminar flow diffusion chambers provided very similar sizes slightly above the Kelvin equation, whereas the thermal diffusion cloud chamber suggests critical cluster sizes significantly smaller. The results found elsewhere in the literature were in reasonable agreement with our results.     

Homogeneous nucleation rates of higher n-alcohols measured in a laminar flow diffusion chamber

Nucleation rate isotherms of n-butanol, n-pentanol, n-hexanol, n-heptanol, and n-octanol were measured in a laminar flow diffusion chamber using helium as carrier gas. The measurements were made at 250-310 K, corresponding to reduced temperatures of 0.43-0.50, and at atmospheric pressure. Experimental nucleation rate range was from 10(3) to 10(7) cm(-3) s(-1). The expression and accuracy of thermodynamic parameters, in particular equilibrium vapor pressure, were found to have a significant effect on calculated nucleation rates. The results were compared to the classical nucleation theory (CNT), the self-consistency corrected classical theory (SCC) and the Hale's scaled model of the CNT. The average ratio between the experimental and theoretical nucleation rates for all alcohols used was 1.5x10(3) when the CNT was used, and 0.2x10(-1) when the SCC was used and 0.7x10(-1) when the Hale's scaled theory was used. The average values represent all the alcohols used at the same reduced temperatures. The average ratio was about the same throughout the temperature range, although J(exp)/J(the) calculated with the Hale's scaled theory increased slightly with increasing temperature. The saturation ratio dependency was predicted closest to experiment with the classical nucleation theory. The nucleation rates were compared to those found in the literature. The measurements were in reasonable agreement with each other. The molecular content of critical alcohol clusters was between 35 and 80 molecules. At a fixed reduced temperature, the number of molecules in a critical cluster decreased as a function of alcohol carbon chain length. The number of molecules in critical clusters was compared to those predicted by the Kelvin equation. The theory predicted the critical cluster sizes well.     

Kinetics of supersaturated vapor nucleation on molecular condensation nuclei

The kinetics of nucleation is calculated for a supersaturated vapor containing molecular condensation nuclei, that is, foreign molecules able to induce the formation of viable nuclei of a condensed phase by themselves. In contrast to the previous calculation, the possibility of the escape of molecular condensation nuclei from very small clusters containing a few condensed vapor molecules is taken into account. More exact equations are derived for the rate of steady-state nucleation and the concentration of aerosol particles in a quasisteady-state regime of nucleation. The calculation demonstrates that, at a high probability of the escape of a molecular condensation nucleus, the predominating mechanism of cluster formation is the attachment of a molecular condensation nucleus to a cluster formed from vapor molecules rather than their condensation on the nucleus. At the same time, allowances for the possible escape of molecular condensation nuclei from clusters slightly affect the rate of nucleation and the concentration of aerosol particles being formed.     

Role of nearest-neighbor drops in the kinetics of homogeneous nucleation in a supersaturated vapor

A theory of simultaneous nucleation and drop growth in a supersaturated vapor is developed. The theory makes use of the concept of "nearest-neighbor" drops. The effect of vapor heterogeneity caused by vapor diffusion to a growing drop, formed previously, is accounted for by considering the nucleation of the nearest-neighbor drop. The diffusional boundary value problem is solved through the application of a recent theory that maintains material balance between the vapor and the drop, even though the drop boundary is a moving one. This is fundamental to the use of the proper time and space dependent vapor supersaturation in the application of nucleation theory. The conditions are formulated under which the mean distance to the nearest-neighbor drop and the mean time to its appearance can be determined reliably. Under these conditions, the mean time provides an estimate of the duration of the nucleation stage, while the mean distance provides an estimate of the number of drops formed per unit volume during the nucleation stage. It turns out, surprisingly, that these estimates agree fairly well with the predictions of the simpler and more standard approach based on the approximation that the density of the vapor phase remains uniform during the nucleation stage. Thus, as a practical matter, in many situations, the use of the simpler and less rigorous method is justified by the predictions of the more rigorous, but more complicated theory.     

A study of sulfur homogeneous nucleation from supersaturated vapor. Determination of surface tension of sulfur nanoparticles

Homogeneous nucleation in sulfur vapor is studied in a laminar-flow chamber. Concentration and size distribution of resulting aerosol particles are measured with a diffusion spectrometer of aerosols and a PK.GTA-0,3-002 photoelectric particle counter. The crystal structure of the formed particles is studied by X-ray diffraction analysis. The rate of sulfur evaporation from a boat and the profile of a deposit on the chamber wall along the axial coordinate are determined by gravimetry. Axial and radial temperature profiles are measured using a chromel-alumel thermocouple. The vapor concentration distribution in the chamber is found and the supersaturation is calculated from the solution of the mass-transfer problem. An experimental low-laborious method is developed for the supersaturation cutoff. This method enables one to rapidly deter-mine the position of the zone in which the nucleation proceeds at the highest rate. The position of the zone of nucleation found by this method is in good agreement with the results of calculations based on experimental data and theoretical calculation of the rate of nucleation by an exact formula that has been recently derived based on the works by Kusaka and Reiss, as well as the Frenkel liquid kinetics theory. The surface tension of critical sulfur nuclei resulting from the nucleation is calculated based on this formula and experimental data on the nucleation. It is established that, in a temperature range of 312–319 K, the critical nuclei have tension surface radius R _s ～ 10.6 Å and surface tension σ = 72.5 ± 1.1 dyn/cm. The surface tension of critical sulfur nuclei in this temperature range is constant and approximately 5% higher than that of a planar surface.     

Molecular-dynamics simulation of argon nucleation from supersaturated vapor in the NVE ensemble

The possibility to conduct simulations of homogeneous nucleation of argon from a supersaturated vapor phase using a microcanonical or NVE ensemble is evaluated (NVE: number of particles N, volume V, and energy E are constant). In order to initiate a phase separation kinetic energy is removed from the system in one step which transfers the system into a supersaturated state. After this temperature jump the simulation is continued in a NVE ensemble. The simulations are performed for different initial-state points and different temperature jumps. The cluster formation and growth over the course of the adiabatic simulations are analyzed. The progression of the temperature being related to the cluster size in NVE systems is traced. Also the influence of the size of the simulation system is investigated. For a certain range of low supersaturation a dynamic coexistence between two states has been found. Furthermore, the obtained nucleation rates are correlated with two simple functions. By applying the nucleation theorems to these functions the size and excess energy of the critical cluster are estimated. The results are consistent with other theoretical data and experimental data available in the literature.     

Data evaluation of laminar flow diffusion chamber nucleation experiments with different computational methods

In order to evaluate the experimental data from laminar flow diffusion chamber (LFDC) experiments on homogeneous nucleation, an extensive postmeasurement computational analysis is required. The present work investigates the influence of the used computational methodology on the derived nucleation curves. To this end a reanalysis is made of previous LFDC experiments of 1-butanol nucleation in helium [D. Brus et al., J. Chem. Phys. 122, 214506 (2005)] using two different methods. The first method is based on single fluid heat and vapor transport in the carrier gas ignoring the aerosol processes, as commonly made in LFDC data evaluations. The second method is more comprehensive as is based on multidimensional computational fluid-particle dynamics. The calculations are made under the usual simplification of one-way coupling between fluid flow and particles, which is a valid approximation in most practical aerosols, while full aerosol dynamical effects are accommodated. Similar results were produced by the two methods. This finding corroborates the usual practice of omitting aerosol calculations in LFDC experimental data evaluation.     

On the mechanism of photoinduced nucleation in a diffusion cloud chamber

Photoinduced nucleation of NO₂ in supersaturated nonane has been studied in a diffusion cloud chamber. The photonucleation spectrum is found to correlate with the yield spectrum for the production of reactive radical species (O + NO) and not with the absorption spectrum of the nucleation inducing agent. A mechanism is proposed in which hydrogen abstraction by O from the nonane produces radicals which then react with each other or with NO₂ to produce species of low volatility that lead to nucleation. Studies of photoinduced nucleation by several alkyl iodides (known to produce radicals upon UV absorption) further support the proposed radical mechanism for photoinduced nucleation.     

Homogeneous nucleation and growth in supersaturated zinc vapor investigated by molecular dynamics simulation

Homogeneous nucleation and growth of zinc from supersaturated vapor are investigated by nonequilibrium molecular dynamics simulations in the temperature range from 400 to 800 K and for a supersaturation ranging from log S=2 to 11. Argon is added to the vapor phase as carrier gas to remove the latent heat from the forming zinc clusters. A new parametrization of the embedded atom method for zinc is employed for the interaction potential model. The simulation data are analyzed with respect to the nucleation rates and the critical cluster sizes by two different methods, namely, the threshold method of Yasuoka and Matsumoto [J. Chem. Phys. 109, 8451 (1998)] and the mean first passage time method for nucleation by Wedekind et al. [J. Chem. Phys. 126, 134103 (2007)]. The nucleation rates obtained by these methods differ approximately by one order of magnitude. Classical nucleation theory fails to describe the simulation data as well as the experimental data. The size of the critical cluster obtained by the mean first passage time method is significantly larger than that obtained from the nucleation theorem.     

The carrier gas pressure effect in a laminar flow diffusion chamber, homogeneous nucleation of n-butanol in helium

Homogeneous nucleation rate isotherms of n-butanol+helium were measured in a laminar flow diffusion chamber at total pressures ranging from 50 to 210 kPa to investigate the effect of carrier gas pressure on nucleation. Nucleation temperatures ranged from 265 to 280 K and the measured nucleation rates were between 10(2) and 10(6) cm(-3) s(-1). The measured nucleation rates decreased as a function of increasing pressure. The pressure effect was strongest at pressures below 100 kPa. This negative carrier gas effect was also temperature dependent. At nucleation temperature of 280 K and at the same saturation ratio, the maximum deviation between nucleation rates measured at 50 and 210 kPa was about three orders of magnitude. At nucleation temperature of 265 K, the effect was negligible. Qualitatively the results resemble those measured in a thermal diffusion cloud chamber. Also the slopes of the isothermal nucleation rates as a function of saturation ratio were different as a function of total pressure, 50 kPa isotherms yielded the steepest slopes, and 210 kPa isotherms the shallowest slopes. Several sources of inaccuracies were considered in the interpretation of the results: uncertainties in the transport properties, nonideal behavior of the vapor-carrier gas mixture, and shortcomings of the used mathematical model. Operation characteristics of the laminar flow diffusion chamber at both under-and over-pressure were determined to verify a correct and stable operation of the device. We conclude that a negative carrier gas pressure effect is seen in the laminar flow diffusion chamber and it cannot be totally explained with the aforementioned reasons.     

Accounting for fluctuations in cluster parameters upon the description of nucleation in supersaturated vapor

A theory is proposed for stationary homogeneous nucleation in supersaturated vapor in which a modified expression for the rate of cluster evaporation was used to calculate the equilibrium distribution over the nucleus sizes and the rates of their formation. This rate was determined by the extrapolation to the region of small sizes of the corresponding expression for the macroscopic droplet derived according to thermodynamic notions that take fluctuations into account. Modified dependences of the size of critical nucleus and the rate of nucleation on the supersaturation and the temperature are determined and compared with the data of the classical theory of nucleation and experimental results.     

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.     

Experimental study of homogeneous nucleation from the bismuth supersaturated vapor: evaluation of the surface tension of critical nucleus

The homogeneous nucleation of bismuth supersaturated vapor is studied in a laminar flow quartz tube nucleation chamber. The concentration, size, and morphology of outcoming aerosol particles are analyzed by a transmission electron microscope (TEM) and an automatic diffusion battery (ADB). The wall deposit morphology is studied by scanning electron microscopy. The rate of wall deposition is measured by the light absorption technique and direct weighting of the wall deposits. The confines of the nucleation region are determined in the "supersaturation cut-off" measurements inserting a metal grid into the nucleation zone and monitoring the outlet aerosol concentration response. Using the above experimental techniques, the nucleation rate, supersaturation, and nucleation temperature are measured. The surface tension of the critical nucleus and the radius of the surface of tension are determined from the measured nucleation parameters. To this aim an analytical formula for the nucleation rate is used, derived from author's previous papers based on the Gibbs formula for the work of formation of critical nucleus and the translation-rotation correction. A more accurate approach is also applied to determine the surface tension of critical drop from the experimentally measured bismuth mass flow, temperature profiles, ADB, and TEM data solving an inverse problem by numerical simulation. The simulation of the vapor to particles conversion is carried out in the framework of the explicit finite difference scheme accounting the nucleation, vapor to particles and vapor to wall deposition, and particle to wall deposition, coagulation. The nucleation rate is determined from simulations to be in the range of 10(9)-10(11) cm(-3) s(-1) for the supersaturation of Bi(2) dimers being 10(17)-10(7) and the nucleation temperature 330-570 K, respectively. The surface tension σ(S) of the bismuth critical nucleus is found to be in the range of 455-487 mN/m for the radius of the surface of tension from 0.36 to 0.48 nm. The function σ(S) changes weakly with the radius of critical nucleus. The value of σ(S) is from 14% to 24% higher than the surface tension of a flat surface.     

The homogeneous nucleation of 1-pentanol in a laminar flow diffusion chamber: the effect of pressure and kind of carrier gas

The influence of total pressure and kind of carrier gas on homogeneous nucleation rates of 1-pentanol was investigated using experimental method of laminar flow diffusion chamber in this study. Two different carrier gases (helium and argon) were used in the total pressure range from 50 to 400 kPa. Nucleation temperatures ranged from 265 to 290 K for 1-pentanol-helium and from 265 to 285 K for 1-pentanol-argon. Nucleation rates varied between 10(1) and 10(6) cm(-3) s(-1) for 1-pentanol-helium and between 10(2) and 10(5) cm(-3) s(-1) for 1-pentanol-argon. Both positive and slight negative pressure effects were observed depending on temperature and carrier gas. The trend of pressure effect was found similar for both carrier gases. Error analysis on thermodynamic properties was conducted, and the lowering of surface tension due to adsorption of argon on nucleated droplets was estimated. A quantitative overview of pressure effect is provided.