Nonisothermal homogeneous nucleation

Classical homogeneous nucleation theory is extended to nonisothermal conditions through simultaneous cluster mass and energy balances. The transient nucleation of water vapor following a sudden increase in saturation ratio is studied by numerically solving the coupled mass and energy balance equations. The ultimate steady state nucleation rate, considering nonisothermal effects, is found to be lower than the corresponding isothermal rate, with the discrepancy increasing as the pressure of the background gas decreases. After the decay of the initial temperature transients, subcritical clusters in the vicinity of the critical cluster are found to have temperatures elevated with respect to that of the background gas

Binary nucleation in acid–water systems. I. Methanesulfonic acid–water

Experimental measurements of binary nucleation between methanesulfonic acid and water vapor were carried out for relative acidities (Ra), 0.05<Ra<0.65, and relative humidities (Rh), 0.06<Rh<0.65, using a continuous flow mixing-type device. The number concentration of particles leaving the nucleation and growth tube was measured as a function of the initial relative humidity and the relative acidity in the temperature range from 20 to 30 °C. Particle size distributions were also measured and found to vary with the amount of water and acid present. The system was simulated to predict the total number of particles and the total mass of acid in the aerosol phase using a simple integral model and classical binary nucleation theory allowing for the formation of acid–water hydrates in the gas phase. At low particle concentrations, condensation rates did not significantly change the saturation levels and the nucleation rates were estimated from the total number concentration data as functions of Ra, Rh, and temperature. The values of experimental and theoretical nucleation rates differed significantly, with Jexpt/Jtheor changing as a function of temperature from 10^–8 to 10^–4 as temperature varied from 20 to 30 °C. This work represents the first systematic experimental study of the temperature dependence of binary nucleation

Binary nucleation in acid–water systems. II. Sulfuric acid–water and a comparison with methanesulfonic acid–water

This work presents a systematic investigation of binary nucleation rates for sulfuric acid and water and the effect of temperature on these rates at isothermal, subsaturated conditions. The results from nucleation rate measurements for the sulfuric acid (H2SO4)–water system are discussed and compared to those previously presented for methanesulfonic acid (MSA)–water [B. E. Wyslouzil, J. H. Seinfeld, R. C. Flagan, and K. Okuyama, J. Chem. Phys. (submitted)]. Experiments were conducted at relative humidities (Rh) ranging from 0.006<Rh<0.65, relative acidities (Ra) in the range of 0.04<Ra<0.46, and at three temperatures, T=20, 25, and 30 °C, in the continuous flow mixing-type apparatus described in Paper I. Particles were formed by binary nucleation and grew by condensation as the mixed stream flowed through an isothermal glass tube. Number concentrations observed at the exit of the nucleation and growth tube as a function of Rh and Ra are extremely sensitive to the binary nucleation rate, and from these data the nucleation rate was estimated as a function of saturation level and temperature. Particle size distributions were also measured using a specially constructed differential mobility analyzer. As anticipated, the H2SO4 particles formed by nucleation and growth are much smaller than those formed in the MSA–water experiments, but particle size distribution measurements confirm that most of the particles formed are being observed. The ratio of experimental to theoretical nucleation rates, Jexpt/Jtheor, was found to be a strong function of the predicted number of acid molecules in the critical nucleus for both the H2SO4–water and MSA–water systems

Binary Nucleation Kinetics. II. Numerical Solution of the Birth-Death Equations

We numerically solve the complete set of coupled differential equations describing transient binary nucleation kinetics for vapor-to-liquid phase transitions. We investigate binary systems displaying both positive and negative deviations from ideality in the liquid phase and obtain numerical solutions over a wide range of relative rates of monomer impingement. We emphasize systems and conditions that either have been or can be investigated experimentally. In almost every case, we find behavior consistent with Stauffer\u27s idea that the major particle flux passes through the saddle point with an orientation angle that depends on the rates of monomer impingement. When this is true, the exact numerical steady state nucleation rates are within 10%-20% of the predictions of Stauffer\u27s analytical theory. The predictions of Reiss\u27 saddle point theory also agree with the numerical results over a wide range of relative monomer impingement rates as long as the equilibrium vapor pressures of the two pure components are similar, but Stauffer\u27s theory is more generally valid. For systems with strong positive deviations from ideality, we find that the saddle point approximation can occasionally fail for vapor compositions that put the system on the verge of partial liquid phase miscibility. When this situation occurs for comparable monomer impingement rates, we show that the saddle point approximation can be rescued by evaluating an appropriately modified nucleation rate expression. When the two impingement rates differ significantly, however, the major particle flux may bypass the saddle point and cross a low ridge on the free energy surface. Even in these rare cases, the analytical saddle point result underpredicts the numerical result by less than a factor of 10. Finally, we study the transition from binary to unary nucleation by progressively lowering the vapor concentration of one component. Both Reiss\u27 and Stauffer\u27s rate expressions fail under these conditions, but our modified rate prescription remains within 10%-20% of the exact numerical rate

Binary Nucleation Kinetics. III. Transient Behavior and Time Lags

Transient binary nucleation is more complex than unary because of the bidimensionality of the cluster formation kinetics. To investigate this problem qualitatively and quantitatively, we numerically solved the birth-death equations for vapor-to-liquid phase transitions. Our previous work [J. Chem. Phys 103, 1137 (1995)] showed that the customary saddle point and growth path approximations are almost always valid in steady state gas phase nucleation and only fail if the nucleated solution phase is significantly nonideal. The current work demonstrates that in its early transient stages, binary nucleation rarely, if ever, occurs via the saddle point. This affects not only the number of particles forming but their composition and may be important for nucleation in glasses and other condensed mixtures for which time scales are very long. Before reaching the state of saddle point nucleation, most binary systems pass through a temporary stage in which the region of maximum flux extends over a ridge on the free energy surface. When ridge crossing nucleation is the steady state solution, it thus arises quite naturally as an arrested intermediate state that normally occurs in the development of saddle point nucleation. While the time dependent and steady state distributions of the fluxes and concentrations for each binary system are strongly influenced by the gas composition and species impingement rates, the ratio of nonequilibrium to equilibrium concentrations has a quasiuniversal behavior that is determined primarily by the thermodynamic properties of the liquid mixture. To test our quantitive understanding of the transient behavior, we directly calculated the time lag for the saddle point flux and compared it with the available analytical predictions. Although the analytical results overestimate the time lag by factors of 1.2-5, they should be adequate for purposes of planning experiments. We also found that the behavior of the saddle point time lag can indicate when steady state ridge crossing nucleation will occur

Binary Nucleation Kinetics. I. Self-Consistent Size Distribution

Using the principle of detailed balance, we derive a new self-consistency requirement, termed the kinetic product rule, relating the evaporation coefficients and equilibrium cluster distribution for a binary system. We use this result to demonstrate and resolve an inconsistency for an idealized Kelvin model of nucleation in a simple binary mixture. We next examine several common forms for the equilibrium distribution of binary clusters based on the capillarity approximation and ideal vapor behavior. We point out fundamental deficiencies for each expression. We also show that each distribution yields evaporation coefficients that formally satisfy the new kinetic product rule but are physically unsatisfactory because they depend on the monomer vapor concentrations. We then propose a new form of the binary distribution function that is free of the deficiencies of the previous functions except for its reliance on the capillarity approximation. This new self-consistent classical (SCC) size distribution for binary clusters has the following properties: It satisfies the law of mass action; it reduces to an SCC unary distribution for clusters of a single component; and it produces physically acceptable evaporation rate coefficients that also satisfy the new kinetic product rule. Since it is possible to construct other examples of similarly well-behaved distributions, our result is not unique in this respect, but it does give reasonable predictions. As an illustrative example, we calculate binary nucleation rates and vapor activities for the ethanol-hexanol system at 260 K using the new SCC distribution and compare them to experimental results. The theoretical rates are uniformly higher than the experimental values over the entire vapor composition range. Although the predicted activities are lower, we find good agreement between the measured and theoretical slope of the critical vapor activity curve at a constant nucleation rate of 107 cm-3 s-2

Transient behavior and time lags in binary nucleation

To investigate transient binary nucleation, both qualitatively and quantitatively, we numerically solved the birth-death equations for vapor-to-liquid phase transitions. We found that in its early transient stages, binary nucleation rarely, if ever, occurs via the saddle point. Instead most binary systems pass through a temporary stage in which the region of maximum flux extends over a ridge on the free energy surface before reaching the state of saddle point nucleation. Both the number of particles formed and their composition may be affected, and this could be very important for nucleation in glasses and other condensed mixtures for which timescales are very long. In order to plan experiments, accurate estimates of the time lag are important. We therefore directly calculated the time lag for the saddle point flux using our numerical results and compared it with the available analytical predictions. Although the analytical results over-estimate the time lag by factors of 2-6, the numerical results followed the predicted analytical trends quite closely under most conditions

CH₃CH₂OD/D₂O Binary Condensation in a Supersonic Laval Nozzle: Presence of Small Clusters Inferred from a Macroscopic Energy Balance

We determined the heat released in the condensing flow of a CH3 CH2 OD/ D2 O /carrier gas mixture (EtOD/ D2 O for brevity) through a supersonic Laval nozzle by integrating the equations for supersonic flow with condensation, using the static pressure, temperature, and mole fractions of EtOD and D2 O monomers [S. Tanimura, B. E. Wyslouzil, M. S. Zahniser, J. Chem. Phys. 127, 034305 (2007)] as inputs. by considering the depletion of the monomer species, the deviation of the pressure from the isentropic value, and the heat released, we estimated that ∼10% of the EtOD molecules are present as pure clusters (dimer to tetramer) upstream of the onset point of condensation. In contrast, clustering was not detected when only pure EtOD was present under the same conditions (temperature and the partial pressure of EtOD) for which clustering was observed in the EtOD/ D 2 O flow. This suggests that the formation of EtOD clusters is facilitated by D2 O in the EtOD/ D2 O flow. A comparison of the heat released to the flow and the expected heat of dissociation of the EtOD/ D2 O droplets suggests that small EtOD clusters persist downstream of the onset point. Both upstream and downstream of the onset point of condensation, the concentration of these clusters in the nozzle is higher than that expected at equilibrium. A possible mechanism for the overabundance of pure EtOD clusters is that they form in the mixed EtOD/ D2 O particles (droplets or clusters) and evaporate from them

Controlling Nucleation and Growth of Nanodroplets in Supersonic Nozzles

We present the first results for a new supersonic nozzle that decouples nucleation and droplet growth, and closely controls the supersaturation and temperature during nucleation. We characterize the expansions using pressure trace measurements, and the aerosol properties using light scattering and small angle neutron scattering. We show that when nucleation and droplet growth are separated, the aerosol number density decreases, the average particle size increases, and the aerosol can be more monodisperse than that formed in a conventional nozzle. Under these conditions, we can estimate the nucleation rate J as a function of supersaturation S and temperature T directly from the experimental data. For D2O we find that the nucleation rate is 4.3×1015⩽J/cm−3 s−⩽6.0×1015 at 230.1⩽T/K⩽230.4 and 29.2⩽S⩽32.4

The structure of D₂O-nonane nanodroplets

We study the internal structure of nanometer-sized D2O-nonane aerosol droplets formed in supersonic nozzle expansions using a variety of experimental techniques including small angle X-ray scattering (SAXS). By fitting the SAXS spectra to a wide range of droplet structure models, we find that the experimental results are inconsistent with mixed droplets that form aqueous core-organic shell structures, but are quite consistent with spherically asymmetric lens-on-sphere structures. The structure that agrees best with the SAXS data and Fourier transform infra-red spectroscopy measurements is that of a nonane lens on a sphere of D2O with a contact angle in the range of 40°-120°