liquid nucleation experiments: A review of the challenges

Aerosol Science 40 (2009) 733 -- 746

Contents lists available at ScienceDirect

Aerosol Science journal homepage: w w w . e l s e v i e r . c o m / l o c a t e / j a e r o s c i

Review

Vapor–gas/liquid nucleation experiments: A review of the challenges Michael P. Anisimova, ∗ , Elena G. Fominykha , Sergey V. Akimova , Philip K. Hopkeb a b

Institute of Chemical Kinetics and Combustion, SB RAS, 3 Institutskaja Avenue, 630090 Novosibirsk, Russia Center for Air Resources Engineering and Sciences, Clarkson University, Potsdam, NY 13699-5708, USA

A R T I C L E

I N F O

Article history: Received 25 January 2009 Received in revised form 2 June 2009 Accepted 3 June 2009 Keywords: Nucleation Liquid–vapor Critical supersaturation Measurements

A B S T R A C T

The formation of new phase embryos is described by nucleation theory. However, nucleation is not yet fully understood. The goal of this review is to summarize measurement methods and recent experimental results for vapor/liquid nucleation. Substantial inconsistencies have been reported among experimental data that may originate from the use of different experimental approaches. These inconsistencies lead to the hypothesis that typical vapor/liquid nucleation rate measurements include an uncontrolled parameter. One such parameter might be the carrier gas that can be considered as an independent nucleation component for vapor–gas/liquid systems. Mass-spectrometry measurements suggest this possibility. The most commonly applied theories suggest a variety of responses of nucleation rates to nature and pressure of the carrier gas. Some approaches to interpret vapor–gas/liquid nucleation experiments consider nuclei formation from the vapor–gas system as a binary process. This approach can be considered in terms of converting the line that originates from isothermal nucleation of a single component system to a surface representing the isothermal nucleation of a binary system. In the binary approximation, adjusted nucleation conditions (i.e. consistent trajectories for nucleation parameters) are needed to obtain consistent data for nucleation rates across the nucleation rate surface. This framework provides an opportunity to resolve the data inconsistencies. Recommendations for future vapor–gas/liquid nucleation research can then be formulated. Experimental detection of singularities in the nucleation rate surface and phase transitions in a condensed phase are reviewed. The assumptions needed for the interpretation of the empirical parameters are analyzed. The experimental data inconsistencies make it currently impossible to suggest a standard system that would permit testing the performance of measuring systems for vapor–gas/liquid nucleation. © 2009 Elsevier Ltd. All rights reserved.

Contents 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adiabatic expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diffusion chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Turbulent mixing of vapor with gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental detection of the nucleation rate surface singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Total pressure and carrier gas nature effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The experimental nucleation rate data inconsistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reference system for nucleation rate measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Recommendations for vapor–gas nucleation research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

∗ Corresponding author. Tel.: +7 383 3333348; fax: +7 383 3307350. E-mail address: [email protected] (M.P. Anisimov). 0021-8502/$ - see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jaerosci.2009.06.002

734 734 735 737 737 740 742 743 744 744

734

M.P. Anisimov et al. / Aerosol Science 40 (2009) 733 -- 746

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745

1. Introduction The first nucleation experiment can be considered to be associated with measurements of liquid and crystals supercooling done by Fahrenheit (Ostwald, 1896–1903). The nucleation of bubbles in gas saturated solutions was observed and the concept of critical embryos of a new phase was introduced in nucleation science during the second half of 19th century (Volmer, 1939). The quality of vapor/liquid nucleation rate results has improved substantially beginning in 1970s because of the development of new measurement systems. For example, the first prototype flow diffusion chamber for vapor nucleation rate measurements was developed by Anisimov, Costrovskii, and Shtein (1978), Anisimov and Cherevko (1982). Currently, the most significant problem in nucleation is the correspondence between experimental data and theoretical predictions of nucleation rate values. As a rule, theoretical and experimental data on nucleation rate are not in good agreement over a range of temperatures and/or pressures. It appears that there may be problems in both the experiments and theory and deficiencies can be identified in all versions of nucleation theories and practically all of the reported experimental results. Current theories correspond to various modifications of Classical Nucleation Theory that was completed in the 1940s (Frenkel, 1975). The theoretical results look quite reasonable for sufficiently low vapor nucleation rates where the droplet approximation is applicable (Anisimov, 2003). However, these approaches have problems at the nanometer scale when the critical embryos contain of the order of 200 or less molecules (atoms). It appears that this quantity of molecules is near the threshold for the droplet critical embryo approximation, at least for organic vapors. Some researchers (Baydakov, 1995; Protsenko, Baydakov, Zhdanov, & Teterin, 2006) have expressed unreasonable optimism that nucleation theory and experiment were in agreement for the case of bubble generation from the superheated liquids. At the present time, vapor–gas nucleation theory can produce values that deviate from the experimental results by up to several orders of magnitude (Brus, Hyvarinen, Zdimal, & Lihavainen, 2005; Fladerer & Strey, 2006). However, nucleation experiments using different devises also show significant inconsistencies in the measured rates (for example, see Brus et al., 2005). Both problems produce difficulties in establishing one or more standard vapor/liquid nucleation systems that could be used to test vapor–gas nucleation rate measurement systems. The problem of the nucleation rate standard is more complex than simply using the n-pentanol–helium system as was suggested by the International Workshop on Nucleation in the Czech Republic, Prague in 1995 as a candidate for a nucleation standard. The n-pentanol–helium system has unfortunately not produced sufficiently consistent data to date. The advantages and current problems of the vapor–gas nucleation experiments are discussed below and a view of the future studies is presented based on the assessment of vapor–gas/liquid nucleation experimental results. 2. Adiabatic expansion Initial measurements of nucleation were made by Aitken (1888) and Coulier (1875a, 1875b) using the rapid expansion of air saturated with water vapor to provide the necessary supersaturation. They initiated nucleation by adiabatic expansion of water vapor in air. Allen and Kassner (1969) modified the experimental procedure by using an expansion/compression cycle in a Wilsontype chamber where compression is introduced after the adiabatic expansion of a vapor–gas mixture. The compression stops the nucleation and initiates growth of the generated clusters to optically detectable sizes in an atmosphere of low supersaturation vapor. This key idea has been the basis for quantitative optical measurements of nucleation rate up to the present time. This expansion/compression cycle of Allen and Kassner (1969) is applied in the two-piston expansion chamber such as that described by Strey, Wagner, and Schmeling (1986). A schematic illustration of this measurement scheme is shown in Fig. 1. The expansion chamber is filled with a vapor–gas mixture at pressure, po , and temperature, To . The mixture is then expanded adiabatically. The pressure drops to pexp resulting in a temperature drop to Texp . On the right side of Fig. 1, the distribution, Nn , of the number of molecules, n, in the clusters is depicted schematically. The temperature drop causes supersaturation, S, of the vapor that drives the formation of critical embryos, n∗ , of new phase at temperature Texp . The compression of the mixture raises the temperature and reduces the vapor supersaturation such that further new particle formation is negligible. However, the resulting vapor supersaturation permits the growth of the nucleated clusters to optically detectable sizes. Nucleation pulse experiments yield the number density of droplets, Nd , that can be measured using the first Mie maximum of scattered laser light. The nucleation rate, J, is described by the ratio J = Nd / texp , where texp is the duration of the vapor–gas expansion (Strey, Wagner, & Viisanen, 1994). Precise determination of the vapor/carrier gas ratio is important for accurate measurements of the nucleation rate. These studies employ high purity materials and clean systems that are created using vacuum cleaning technologies. The pressure change, intensity of transmitted/scattered laser light, and other parameters are recorded. Temperatures are measured with uncertainties of the order of several tenths of a degree Kelvin. The shock tube as a version of the expansion technique has recently shown considerable improvements in the quality of nucleation rate data (for example, Peters & Paikert, 1989). A shock tube (or wave tube) is a tube that is initially divided by diaphragm with one side at a much higher pressure than the other. An adiabatic expansion occurs when a diaphragm is broken and the vapor–gas mixture becomes supersaturated. Nucleation then occurs. It has been thought that wave tube measurements are less accurate “because pressure pulses cannot always be accurately reproduced” in comparison with two-piston chamber

M.P. Anisimov et al. / Aerosol Science 40 (2009) 733 -- 746

735

Fig. 1. Schematic illustration of two-piston expansion chamber.

Fig. 2. Schematic presentation of a static diffusion chamber and distribution of parameters along a SDC height. Grey stripe illustrates schematically a nucleation zone.

(Holten, Labetski, & van Dongen, 2005). Supersonic jets have recently been used to produce the same adiabatic expansion scheme where cluster generation and growth are decoupled (Kim, Wislouzil, Wilemski, Wolk, & Strey, 2004). The shock tube and supersonic jets provide the opportunity to measure high nucleation rates with values up to 1017 cm−3 s−1 even if it may not yet provide as high accuracy as other measurement systems. The nucleation temperature for adiabatic expansion techniques ranges from 30 to 370 K. Nucleation rates can be measured over an interval of up to five orders of magnitude in one system. The expansion techniques cover a total nucleation rate interval from 103 up to 1017 cm−3 s−1 . The total nucleation pressures involve interval from approximately 100 kPa to 7 MPa. 3. Diffusion chambers Langsdorf (1939) created the first static diffusion chamber (SDC). The SDC is described in detail by Katz (1970), Kacker and Heist (1985), etc. The static diffusion chamber consists of two wet plates maintained at different temperatures. Fig. 2 schematically illustrates the distribution of parameters along the SDC height, where T, P, S, J are temperature, partial vapor pressure, vapor supersaturation, and nucleation rate, respectively. The subscript eq refers to vapor equilibrium with the liquid. Vapor diffusion and temperature gradient produce vapor supersaturation and nucleation in the space between the plates such that clusters of the new phase are formed. They then grow to measurable size. Particles can move toward the cold plate direction by temperature and vapor concentration gradients. A particle drops when its mass gets sufficiently large. A special SDC design was used for vapor–gas nucleation measurements at elevated pressures up to 4.0 MPa (Heist, Bertelsmann, Martinez, & Chan, 2003). The temperature and mole fraction distributions need to be calculated using a transport process model. The effect of the chamber wall is ignored except the case of heater wires using to clear wall of vapor condensate. The interaction between the wall and the central part of chamber is known to exist. Heist and coworkers have reported results of careful analysis of the SDC heat-mass transfer problem (Heist et al., 2003). They concluded that the diameter-to-height ratio and configuration of wall heater wires need to be optimized for a given set of measurements. The key problem is to achieve operational stability of the vapor–gas mixture in SDC with respect to convective flows. Important conditions such as “the total pressure must remain below a limiting value that depends on temperature, condensable vapor, and background gas” needs to be recognized (Heist et al., 2003). A mathematical approximation for the a priori calculation of the limiting total pressure values has been provided. Total nucleation

736

M.P. Anisimov et al. / Aerosol Science 40 (2009) 733 -- 746

Fig. 3. Schematic presentation of a flow diffusion chamber (top), a turbulent mixing system (bottom), and the axis's distributions of parameters along.

temperatures for SDC range from 240 to 370 K so that nucleation rates can be measured over four orders of magnitude in one system. The total nucleation rates span the range of 10−2 up to 102 cm−3 s−1 . The total nucleation pressures span the interval from near 30 kPa to 4 MPa. Another system is the flow diffusion chamber (FDC). Initial versions of the FDC were described by Anisimov et al. (1978). The current generation FDC schemes is described by Hyvarinen et al. (2006). The FDC scheme uses a hot laminar vapor–gas flow within cold boundary conditions. A simplified FDC scheme is presented in Fig. 3(top). Hot vapor–gas flow enters the chilled tube (condenser). The vapor–gas velocity distribution at the beginning of the tube is shown schematically by the parabolic line. The distributions of temperature, T, vapor supersaturation ratio, S, and nucleation rate, J, along the tube axis are presented schematically in the top figures of Fig. 3. Embryos form in the nucleation volume and subsequently grow in the supersaturated vapor. It can be seen that there is a geometrical separation of nucleation volume and the downstream zone for cluster growth. Filtered carrier gas is saturated with a volatile substance by passing the carrier gas flow through a vapor saturator. A flow laminator is used to produce fully developed laminar flow. Parameters of that flow are used as boundary conditions for the stationary heat-mass transfer problem. It is assumed that the boundary vapor pressure near the tube wall is at equilibrium at the wall temperature. The vapor concentration at the beginning of tube is defined by vapor saturator design. Solution of the heat-mass transfer problem can be achieved in the approximation of a long channel. Nucleation occurs in the condenser. The particle concentration and size distribution are measured with an aerosol counter that is placed before pressure controller to avoid the nucleation in the controller resulting from a decrease in the exhaust pressure. An algorithm for estimation of the average nucleation rate over FDC nucleation volume was suggested by Anisimov, Costrovskii, Shtein, and Mikheev (1980). The maximum experimental value of the nucleation rate, Jmax , in diffusion chambers can be measured using an obvious relation Jtheor /Ntheor = Jmax /Nexp , where Jtheor is maximum theoretical nucleation rate; Ntheor and Nexp are the theoretical and experimental FDC particle concentrations, respectively (Hyvarinen et al., 2006; Wagner & Anisimov, 1993). That relationship can also be used for Jmax measurements using a supersonic nozzle (Streletzky, Zvinevich, Wyslouzil, & Strey, 2002). The current FDC scheme has been used for vapor nucleation rate measurements at total pressures from 0.03 to 0.50 MPa. The FDC data span over six orders of magnitude in nucleation rate that can be measured in a single experimental system. Nucleation temperatures from 230 to 1000 K can be obtained in these systems now. Versions of FDC have built in Finland (Anisimov, Hameri, Kulmala, & Ovchinnikova, 1993; Lihavainen & Viisanen, 1998), the USA (Mikheev, Irving, Laulainen, Barlow, & Pervukhin, 2002), the Czech Republic (Brus et al., 2005), etc. Brock and co-authors built laminar flow systems to study single (Brock, Kuhn, & Zenavi, 1986) and multicomponent (Brock, Kuhn, & Zenavi, 1988) nucleation kinetics and properties of condensational aerosols. Several groups have used rapid turbulent mixing to measure nucleation rates of the single and binary vapors (Higuchi & O'Konski, 1960; Kogan & Burnasheva, 1960; Okuyama, Kousaka, Kreidenweis, Flagan, & Seinfeld, 1988; Sutugin & Fuchs, 1970; Wyslouzil, Seinfeld, Flagan, & Ocuyama, 1991, etc). Most studies have only measured the critical supersaturation for

M.P. Anisimov et al. / Aerosol Science 40 (2009) 733 -- 746

737

two-component vapor systems. Nguyen et al. (1987) have studied homogeneous and heterogeneous nucleation of a single vapor in a laminar flow aerosol generator. The Thomson equation was considered empirically for small clusters using an FDC (Kodenev, Baldin, & Vaganov, 1987). The nucleation theorem (Anisimov & Cherevko, 1982; Anisimov et al., 1980; Anisimov, Vershinin, Aksenov, Sgonnov, & Semin, 1987; Kashchiev, 1982) is the theoretical relationship between the nucleation rates and the number of molecules in the critical embryos of condensate for vapor–gas measurements. It has been suggested that single condensable vapor nucleation be considered as binary systems because of clear influence of carrier gas (CO2 , SF6 ) on critical embryo phase transitions (Anisimov, Koropchak, Nasibulin, & Timoshina, 1998, 2000). 4. Turbulent mixing of vapor with gas Turbulent mixing of a hot vapor–gas stream with a chilled gas can be used for particle generation. Amelin (1948) developed a system for the first nucleation rate measurements of a single vapor in the turbulent regime. Using turbulent flow (Okuyama et al., 1988; Wyslouzil et al., 1991), isothermal nucleation rates can be measured for binary systems over several orders of magnitude. Fig. 3(bottom) illustrates the turbulent mixing system schematically. Filtered carrier gas is saturated with a volatile substance by passing the carrier gas flow through a vapor saturator. Hot vapor–gas flow enters condenser with a chilled gas jointly in a turbulent regime. The distributions of temperature, T, vapor supersaturation ratio, S, and nucleation rate, J, along the tube axis are presented schematically in Fig. 3 (bottom). Embryos form in the nucleation volume and grow in the subsequent supersaturated vapor. To a first approximation, it is assumed that nucleation temperature, vapor supersaturation and total pressure are uniform within a nucleation volume. A geometrical separation of nucleation volume and the downstream zone for cluster growth take place. The nucleation volume can be measured, for example, by a direct test of a vapor–gas flow by a heat conducting mesh (Kogan & Burnasheva, 1960). Volume which is sensitive to the mesh position is associated with the nucleation zone. Mesh sensitivity appears as a result of reduction in the vapor concentration when the vapor condenses on the mesh. Parameters like temperature and vapor supersaturation are calculated using a simple averaging of the initial temperatures and vapor content of each flow. Nucleation occurs in the condenser. The particle concentration and size distribution can be measured with an aerosol counter. In the most cases, nucleation experiments with turbulent flows are conducted at atmospheric pressure. An interval of less than four orders of magnitude in nucleation rates is available for current turbulent systems. The average nucleation rate can be estimated as ratio of the particle concentration over the time interval it takes for the vapor–gas volume to pass through the nucleation zone. The problem of a turbulent mixing scheme is associated with wide spectrum of nucleation conditions that cannot be associated with particular ensembles of particles generated within the nucleation zone. To simplify the problem, one can require that nucleation starts when the system achieves homogeneous temperature and uniform vapor distributions. However, these conditions cannot be fully controlled and problems of system inhomogeneity and different nucleation conditions arise in any turbulent mixing experiments. To a first approximation, the conditions for such systems are that h >n , where n is the average time for generation of new phase embryos and h is time interval when system become homogeneous. Fluctuations of vapor supersaturation and temperature can be large enough in the pre-nucleation zone (Fig. 3b) to generate some pre-particles before system achieves homogeneity. These pre-particles initiate heterogeneous nucleation producing a problem in separating the extent of heterogeneous and homogeneous nucleation in the system. Thus, turbulent flow systems are rarely used for homogeneous nucleation measurements. However, they have proved useful for heterogeneous (Lee, Hopke, Rasmussen, Wang, & Mavliev, 2003; Mavliev, Hopke, Wang, & Lee, 2004) and ion-induced (Gamero-Castano & Fernández de la Mora, 2002; Seto, Okuyama, de Juan, & Fernández de la Mora, 1997) nucleation measurements. 5. Experimental detection of the nucleation rate surface singularities Another aspect of nucleation experiments appears when the probability exists for change in phase of the forming critical embryo. Such transitions can exist in the vicinity of the triple point. There could be a change in the dominant form of the forming embryo phase from one phase type to another such a liquid to a solid. The initial phase state of the critical embryo can exist over entire time of nucleation and embryo growth as was observed in the example of glycerin vapor nucleation and condensation (Anisimova, Hopke, & Terry, 2001). They suggested that there was a difference in accommodation of molecules on surface of the two different phase states of the condensing clusters. This difference in accommodation probability led to unequal growth rates of clusters for the different phases. Particle size measurements could then be used to detect the two separate phases. A clearly bimodal particle size distribution was found in the vicinity of glycerin triple point (Anisimova et al., 2001). This result suggests two different embryo phases for the glycerin critical embryos. If there were phase transitions in the growing clusters, the bimodal size distribution would have been smoothed into a continuum of sizes which is not what was observed in the experimental results (Anisimova et al., 2001). The Gibbs free energy of the critical embryos governs the nucleation rate. It is easy to show that first derivative of nucleation rate surface needs to split when nucleation occurs in the vicinity of phase transition of the first order in a condensed phase. In such circumstances, the conditions of continuity and monotony of the nucleation rate surface are simultaneously violated. These kinds of discontinuities have been found experimentally (Anisimov, Koropchak et al., 1998, 2000). The topology of nucleation rate surfaces near a triple point is illustrated in Fig. 4 (Anisimov, Hopke, Rasmussen, Shandakov, & Pinaev, 1998). The nucleation rate surface is hypothesized to arise from the PT phase equilibria. Two lines for phase

738

M.P. Anisimov et al. / Aerosol Science 40 (2009) 733 -- 746

Fig. 4. Nucleation rate surface topology in the vicinity of the triple point: (a) vapor–solid (light grey) and vapor–liquid (dark grey) nucleation separately; (b) resulting nucleation rate surface for both phase generation. Line, st, illustrates the equality conditions for nucleation rates of solid and liquid embryos. Lines, gt and vt, represent the boundaries of a single phase generation. Areas, stg, illustrates solid phase generation prevail and, sfvt, the most formation of droplets.

equilibria with vapor exist in the triple point vicinity. The top figure (Fig. 4a) shows only the surfaces for the formation of the liquid and solid phases, grey for solid and dark grey for liquid embryos. Line, et, shows the equal nucleation rates for both phases. The bottom figure (Fig. 4b) shows the complete nucleation surface including the simultaneous formation of both liquid and solid nuclei. Line et corresponds to line st in Fig. 4b. Line st illustrates the equality conditions for nucleation rates of solid and liquid embryo generation. That line represents dynamic equilibria where a first derivative of a nucleation rate surface is broken. Lines gt and vt show the boundaries of single, i.e. solid or liquid phase embryo generation, respectively. Area stg illustrates nucleation rates when solid embryos prevail over droplet generation. Area sfvt is characterized by the higher rate of droplet formation. Fig. 5 illustrates the experimental data for vapor activity on nucleation temperature at two constant values of nucleation rates for glycerin-carbon dioxide system (Anisimov, Nasibulin, & Shandakov, 2000). Clear discontinuities in the slopes of these curves can be seen for each data set. One discontinuity can be attributed to melting of glycerin–carbon dioxide binary system. The melting temperature (Tmelt ) clearly increases with a rise in carbon dioxide pressure from 0.1 to 0.3 MPa. Presumably the carbon dioxide concentration in solution increases proportional to the total pressure. The other disturbance is explained by an unknown phase transition in critical embryos that appears near the critical line of the glycerine–carbon dioxide binary system (Anisimov, Koropchak et al., 1998). In Fig. 5, Tcr is the critical temperature for CO2 . The experimental data in Fig. 5 illustrate the presence of discontinuities in slope for this system's nucleation rate surface. The origin of a nucleation rate surface discontinuity near critical conditions is not fully understood at this time because this type of phase transition has only been detected for the first time.

M.P. Anisimov et al. / Aerosol Science 40 (2009) 733 -- 746

739

Fig. 5. Glycerine vapor activity (a) on nucleation temperature (T) for glycerine–carbon dioxide system (Anisimov, Koropchak et al., 1998).

Fig. 6 illustrates the example of experimental nucleation rate data with a gap in a nucleation temperature trend for a glycerine–carbon dioxide system. Three sets of isotherms can be seen, i.e. groups from 283 to 292 K; from 294 to 297 K, and from 298 to 304 K. Three isotherms in nucleation temperature interval from 294 to 297 K represent the transition from one data set to another. The gap is initiated by condensed matter melting (Anisimov, Koropchak et al., 1998). A conceptual problem in vapor–gas to liquid (or solid) nucleation is its treatment of the nucleation as a single component problem instead as a two component system. The impact of a critical embryo phase change on the nucleation rate surface topology has been reported by (Anisimov, Koropchak et al., 1998, 2000; Anisimov, Hopke, Shandakov, & Shvets, 2000). A similar problem was found by Peeters, Gielis, and van Dongen (2002). However, the observed jump in the water vapor nucleation rates was not reproduced in the next report from that group (Holten et al., 2005). It may be that there is sufficient experimental variation in the nucleation rate measurements to prevent the detection of this kind of nucleation event. A major problem in detection of the nucleation rate surface singularities is the random error inherent in any experimental data. This problem exists even one has experimental results of relatively high accuracy. Anisimov, Hopke et al. (2000) have suggested using continuity and monotonic behavior in the data analysis to find the anomalies in the nucleation rate surfaces. This approach can be illustrated by defining the nucleation rate surface by the function, F(x1 , x2 , . . . , xn ), where x1 , x2 , . . . , xn are independent variables such as pressure or temperature. When function F has continuous partial derivatives, the surface described by the function F(x1 , x2 , . . . , xn ), is continuous and monotonic. For condition F = constant, the function, F(x1 , . . . , xn ) has n−1 independent variables. For one independent variable and a continuous and monotonic surface, the full derivative of F with respect to x1 at F = constant and n = 2 can be written as         *F *F *x2 dF = + = 0. (1) dx1 x2 *x1 *x2 *x1 x2

x1

F

Subscripts show the constant values of variables as the conditions at which the derivative is evaluated. According to Anisimov, Hopke et al. (2000), Eq. (1) can be rewritten as

740

M.P. Anisimov et al. / Aerosol Science 40 (2009) 733 -- 746

Fig. 6. Glycerine–carbon dioxide system nucleation rates (J) on glycerin vapor activity (a) and nucleation temperatures (T) at pressure P = 0.20 MPa (Anisimov, Koropchak et al., 1998).

 A=

*F *x1



 + x2

*F *x2

  x1

*x2 *x1

 ,

(2)

F

where A serves as a criterion for continuity and monotonic behavior. This criterion has nonzero values at any singular points in the surface F(x1 , x2 ). The more general case for n variables is considered by Anisimov, Hopke et al. (2000). The nucleation rate with two variables, such as temperature, T, and vapor supersaturation, S, and constant values of all other parameters (P1 . . . Pn ) can be considered. It is customary to present the nucleation rate experimental results with the A-criterion. A simple relation can be obtained along the surface section where J(T, S) = constant:       * ln J * ln J * ln S + = A. (3) *T S,P1 ...Pn * ln S T,P1 ...Pn *T J,P1 ...Pn The criterion value, A, will be equal to zero if the vapor nucleation rate surface J = J(T,S) has no singularities. Because of experimental noise, the calculated values of A will include nonzero values that can be characterized by a non-dimensional standard deviation. The deviation of the A values from zero can characterize the quality of experimental results (if set of experimental values for J should represent a continuous and monotonous surface). A singularity in the nucleation rate surface (or surface for any other set of experimental results) breaks the local condition for surface continuity and monotony. Fig. 7 presents the application of the A criterion for glycerin-carbon dioxide system (Anisimov, Koropchak et al., 1998). It can be seen that the A-criterion provides a sensitive tool for the detection of singularities in nucleation rate surfaces. Anisimov, Nasibulin et al. (2000) applied the A-criterion (Fig. 8a) to data from Strey, Viisanen, and Wagner (1995). The nucleation rate surface for pentanol-water vapor from Strey et al. (1995) is presented in Fig. 8b. Fig. 8a shows the A-criterion application with clear evidence of a nucleation rate surface singularity (see J0 level in Fig. 8b). This result is in contradiction to the conclusion that no effects on the nucleation rate appeared for components with only partial solubility (Strey et al., 1995). 6. Total pressure and carrier gas nature effects During the past two decades, several research groups have examined the effects of pressure and carrier gas composition on homogeneous nucleation to better understand the experimental data describing vapor to condensed phase nucleation. Classical nucleation theory assumes that the only role of the carrier gas is to maintain the temperature equilibrium of the clusters with the ambient media. Frank and Hertz (1956) made the first observations of a gas-pressure effect. They found that the nucleation rate decreased as the total system pressure increased. That effect is now called a negative gas-pressure effect. The result was reproduced in several other measurements (Brus, Zdimal, & Stratmann, 2006; Katz, Hung, & Krasnopoler, 1988). Katz et al. (1988) found experimental variation from negative to positive gas-pressure effects. Nevertheless these authors concluded that the effect

M.P. Anisimov et al. / Aerosol Science 40 (2009) 733 -- 746

741

Fig. 7. Distribution of average value of A and standard deviation,  on glycerine vapor nucleation in the vicinity of critical temperature of carbon dioxide such as A = 0.01,  = 0.46 and A = 0.04,  = 0.16 at total pressure Ptot = 0.1 MPa for log J = 3 with singularity, taken into account, and without it consequently (Anisimov, Nasibulin et al., 2000).

Fig. 8. A-criterion application for published (Strey et al., 1995) data (a) an average value of A and standard deviation,  on n-pentanol mole fraction, x, such as A = −0.68,  = 1.96 and A = 0.01,  = 0.09 for log J = 6.0 with singularity and without it consequently; (b) original view of nucleation rate surface for pentanol-water vapour (Strey et al., 1995).

is not significantly larger than the changes in nucleation rate that occur due to other uncertainties such as in thermal conductivity of the mixture. Katz et al. (1988) suggested that the parameters for the heat and mass transfer calculations (diffusion coefficients, thermal conductivities, viscosities, etc.) are not sufficiently well defined and the variations of these parameters in terms of the error bars on the calculated nucleation rate values can dramatically change the gas-pressure effects. Clear gas-pressure effects are discussed in several other publications. Anisimov and Vershinin (1988, 1990) experimentally found a positive gas-pressure effect and a gas-composition effect at gas pressures from 0.10 to 0.30 MPa. They concluded on the basis of the ideal solution approximation (known now as the nucleation theorem) that carrier gas molecules were involved in the critical embryos. Heist, Ahmed, and Janujua (1994, 1995) have reported effects of pressure and carrier gas composition on the nucleation rates for a series of short-chain alcohols. These measurements have been made using a static diffusion cloud chamber at pressures up to 4.0 MPa with H2 , He, N2 , and Ar as the carrier gases. Other experimental results have supported a dependence of the nucleation rate on the nature and total pressure of the carrier gas (Anisimov, Koropchak et al., 2000; Luijten & van-Dongen, 1999; Luijten, Peeters, & van-Dongen, 1999; Lihavainen & Viisanen, 2001). Gas-pressure effects were detected by van Remoortere, Heath, Wagner, and Strey (1996) although most of the measurements from this research group (i.e., Viisanen, Strey, & Reiss, 1993; Viisanen & Strey, 1994) did not observe carrier gas influences on nucleation rate. The sensitivity of the flow diffusion chamber is sufficient to detect nucleation rate surface singularities that are associated with phase variations in critical embryos (Anisimov, Hopke et al., 1998, 2000; Anisimov, Nasibulin, 2000; Anisimov and Hopke, 2001). Phase transitions are used as markers of the gas-pressure effects. The opposite temperature trends (as a result of a carrier gas and condensed phase (glycerin) solubility) were revealed for these phase transitions (Fig. 5). The critical temperature of

742

M.P. Anisimov et al. / Aerosol Science 40 (2009) 733 -- 746

Fig. 9. A comparative presentation of n-hexanol results from expansion measurements by Strey et al. (1986) and laminar flow techniques (Hyvarinen et al., 2004). The ratios of the experimental and theoretical (CNT) nucleation rates are presented as a function of the reduced temperature, T/Tc .

the vapor–gas solution decreases i.e. moves closer to the gas critical condition (Tcr ) with a gas pressure increase. The glycerine melting temperature (Tmelt ) is raised because of a rise of the dissolved gas content. It is reasonable to think that existing heatmass transfer uncertainties produce a directional temperature trend for both of the two phase transformations. A direct mass spectrometric measurements showed the presence of the carrier gas in the critical cluster under some nucleation conditions for a monosilane–argon system (Sharafutdinov, Zarvin, Korobeyshchikov, Madirbaev, & Khmel, 1999). It follows then that the presence of carrier gas molecules in the critical embryo needs to be included in the estimation of the free energy of formation for the critical cluster. Fladerer and Strey (2006) did attempt to measure supersaturated argon nucleation using a cryogenic nucleation pulse chamber. They concluded that growth rate of the nucleated argon droplets was too high to make permit decoupled nucleation and embryo growth. Nevertheless the onset of nucleation corresponding to a nucleation rate of J = 107(+/−2) cm−3 s−1 at temperatures 52 < T(K) < 59 and argon vapor supersaturation value near 10 was estimated. Classical theory predicts nucleation rates of the order of 10−28 –10−13 cm−3 s−1 for these conditions. Fladerer and Strey (2006) suggested that calculations based on density functional theory can only partially explain the discrepancy of 20 orders of magnitude between the experimental and theoretical nucleation rates. Wedekind, Hyvarinen, Brus, and Reguera (2008) take in to account the efficiency of thermalization and the additional work that a cluster has to spend for growing. These contributions produce the opposite trends in nucleation rates. Unfortunately, a scale of these effects is located within two orders in nucleation rates when discrepancy of theoretical and experimental results is over 20 orders. Wedekind et al. (2008) consider their own result as qualitative because “we (Wedekind et al., 2008) cannot discard the influence of other factors on the observed pressure effect.” These experiments can be provided by molecular dynamics simulations as well or/and density functional theory calculations using a Lennard-Jones potential. Unfortunately, these simulations and calculations usually fail for complex substances such as alcohols, water, etc. Experimental results of different experimental schemes used for nucleation rate measurements at cryogenic temperatures are still inconsistent (Fladerer and Strey, 2006) because of low accuracy of the experimental data. 7. The experimental nucleation rate data inconsistency Several research groups have made comparative measurements of nucleation rates (Anisimov, Hameri, Kulmala, & Ovchinnikova, 1993; Anisimov, Hameri, & Kulmala, 1994; Brus et al., 2005; Wilck, Hameri, Stratmann, & Kulmala, 1998, etc.). Fig. 9 presents results for the nucleation of n-butanol in helium using both an FDC (Hyvarinen, Lihavainen, Viisanen, & Kulmala, 2004) and an expansion chamber (Strey et al., 1986). It can be seen that the data from the different systems cross each other (Fig. 9). However, the slopes of the nucleation rate isotherms for the two measurement systems are nearly the same. The results of Brus et al. (2005) further illustrate the inconsistency between the static diffusion chamber and an FDC for identical conditions of the same chemical system. The FDC values are higher than those from the static diffusion chamber results by three to four orders of magnitude (Fig. 10). These examples illustrate the internal inconsistence of the experimental results that originate from different experimental systems. These inconsistencies generate the assumption that the typical nucleation vapor–gas experiments have an unrecognized and uncontrolled parameter. The origin of these data discrepancies can be better understood through the consideration of nucleation rate surfaces (Anisimov, Hopke et al., 1998; Anisimov, Nasibulin, 2000). Surfaces can be constructed over a pressure-composition phase diagram. At some constant nucleation temperature, the nucleation rate surface over oval shape in the P–X plane is presented in Fig. 11a. The equilibrium condition at which the nucleation rate is zero is shown by line nfm. Spinodal nucleation rates are

M.P. Anisimov et al. / Aerosol Science 40 (2009) 733 -- 746

743

Fig. 10. n-butanol vapor nucleation rate results measured by flow diffusion and static diffusion chambers (Brus et al., 2005).

Fig. 11. Nucleation rate surface for constant nucleation temperature (a) cigar-like diagram; (b) droplet-like diagram.

represented schematically by line deh. The nucleation rate surface is drawn schematically on the boundary lines. Line fe is associated with nucleation at a constant initial composition Xo . The nucleation rate which is presented schematically for concentration interval of X1 Xo by line, fy, is clearly higher with respect to an nucleation rate (line fe) for composition Xo . This variation in the nucleation rates in relation to a PX-plane trajectory which is illustrating a trend of experimental conditions is shown in Fig. 11a. One can see that nucleation rate can increase or decrease with compositional variations for nucleating system. In most events, the vapor–gas nucleation temperature is higher than the critical temperature of gas. In that case, nucleation rate surface extends over a drop-shaped region as it is shown in Fig. 11b (Anisimov, Hopke et al., 1998). The upper nucleation rate limiting line, cZeh, is beginning in critical point, c, where nucleation rate is zero. It can be easily seen that isobaric conditions produces a nucleation trajectory like, ZS. Fig. 11b illustrates qualitatively the relative view of the expansion chamber data, where vapor–gas ratio is constant (line fe) and FDC data where the composition is variable under constant total pressure (line ZS). The surfaces in Fig. 11 qualitatively reflect the behavior of the experimental nucleation rates reported, for example, by Anisimov et al. (1994). In the most cases, the gas is treated as an inert media to absorb the heat released from the phase transitions. Inconsistencies among the experimentally measured values from the different experimental schemes are a major problem for current vapor–gas nucleation experiments. Consideration of vapor–gas nucleation as a binary system is a reasonable way to resolve the data inconsistencies. It is plausible to think that different experimental systems have the inconsistent trajectories along the nucleation rate surface when the vapor–gas system is treated as binary system. Several results, for example, Anisimov, Koropchak et al. (1998) and Anisimova et al. (2001) illustrate that high pressure measuring techniques need to be designed to study multi-channel nucleation. 8. Reference system for nucleation rate measurements In order to test the accuracy of an experimental system, it is important to have a standard system that can be measured over a range of nucleation conditions. The n-pentanol–helium system was proposed in Prague, 1995 for such measurements. The available results from several research groups were collected and compared (Anisimov, Hopke et al., 2000). They proposed

744

M.P. Anisimov et al. / Aerosol Science 40 (2009) 733 -- 746

a reference equation for nucleation rates of n-pentanol–helium as a practical test of any experimental measurement system for total pressures from 0.10 to 0.30 MPa. Although the equation does not reproduce all of the results, the approximation is useful in its present form to provide a relative view of the different results up to time when a more accurate approximation can be generated. The problem of a nucleation standard can only be solved when consistent results have been obtained by independent groups that use the different experimental schemes. It is believed that the vapor–gas nucleation rates should be represented by a surface instead of the single line that is used for most current presentations of the isothermal nucleation rate data in vapor–gas systems. 9. Recommendations for vapor–gas nucleation research The current recommendations for vapor–gas nucleation rate measurements can be summarized such as: • Vapor nucleation and cluster growth volumes should be decoupled to allow the embryos to grow before light scattering detection. Because only dozens of molecules are involved in critical embryos formation for typical experimental conditions, the amount of vapor used to form the embryo is negligible compared to the total number of vapor-phase molecules and any vapor depletion problems within the nucleation volume are avoided. • Decomposition of embryos should be evaluated when an adiabatic recompression (Allen & Kassner, 1969) is applied to interrupt nucleation. • Theory independent algorithms are needed to estimate experimental nucleation rates based on FDC and others flow systems experimental data. Homogeneous nucleation rates should be measured for sufficiently high supersaturation values to produce heterogeneous nucleation such that all of the existing contaminant seeds are activated (Anisimov & Cherevko, 1985). Seeds will have no impact on the measured nucleation rates when the heterogeneous nucleation channel is fully saturated. Then the nucleation rate is only governed by homogeneously generated embryos. • Impurities in the vapor substance must not exceed 0.2% for the present time. This level of impurities shifts the nucleation rate values within one order of magnitude as shown by Anisimov et al. (1987) and Strey et al. (1995). This value is roughly the relative accuracy of modern nucleation rate measurements. Carrier gas purity of 99.995% and higher is sufficient and available everywhere. • Aerosol size distribution measurements are strongly recommended to identify the possibility of two and more channels for homogeneous and heterogeneous nucleation. • Continuity and monotony criteria should be applied for the detection of nucleation rate surface singularities and data quality characterization. • Vapor–gas systems are strongly recommended to be considered as binary nucleation systems. • Vapor–gas nucleation rate standards need to be developed to provide an absolute accuracy evaluation of experimental data. The problem of experimental data inconsistencies should be resolved to create a nucleation standard. • Nucleation rate measurements of any single component systems such as noble gases or any other single vapor in a gas-free atmosphere are very attractive for research as examples of true single component systems. • The critical embryo parameters such as number of molecules of each species, enthalpy of embryo formation, excess energy, etc can be estimated using experimental data for the nucleation rates (Anisimov and Cherevko, 1985; Anisimov et al., 1987; Anisimov and Taylakov, 1989).

10. Conclusions In this review, results and problems related to aerosol generation experiments are discussed. Adiabatic expansion and gasjet techniques, diffusion chambers, turbulent mixing apparatus were considered. It can be concluded that the development of accurate experimental techniques for vapor–gas nucleation research are still in progress. Measurable nucleation rates for the available experimental techniques span up to 19 orders of magnitude ranging from 10−2 cm−3 s−1 up to 1017 cm−3 s−1 and nucleation temperatures from cryogenic around 30 K to near 1300 K. Pressures in vapor–gas systems have been achieved within the interval from 30 kPa to 10 MPa. The detection of the critical vapor supersaturation for a given nucleation rate tends to be replaced by nucleation rate determinations that can vary by several orders of magnitude. Important semiempirical information is obtained when the critical embryo parameters are derived from experimental nucleation rate data. These relationships were called “nucleation theorems.” Kashchiev (2006) recently provided a theoretical review devoted to nucleation theorems. More easily used equations to interpret experimental results have been given in several articles (Anisimov & Cherevko, 1985; Anisimov et al., 1987; Anisimov & Taylakov, 1989). Because of the inconsistencies in the experimental data, these relationship and the results derived from them should be considered as preliminary. It can be concluded now that the differences between theory and experimental data are too large to permit reconciliation of the theoretical predictions and experimental nucleation rates. Nevertheless, some of the results and ideas reviewed above provide a reasonable basis for further development of the experimental vapor–gas nucleation research techniques. It can be hoped that the uncontrolled parameter(s) will be identified in the near future and permit consistent nucleation rate data to be derived from different research methods. The introduction of one or several nucleation standard(s) is a major

M.P. Anisimov et al. / Aerosol Science 40 (2009) 733 -- 746

745

current problem. Success in the nucleation standard development and its introduction in nucleation research practice is a key issue for current nucleation experiments. The deeper understanding of the carrier-gas effects may clarify the nature of the different experimental set data inconsistencies. High pressure measurement systems need to be designed to permit the study of multi-channel nucleation at near critical and spinodal conditions where the nucleation rate surface topology needs to be clarified. While developing new experimental systems, the existing techniques can be used to study nucleation to explore the effects of the carrier gas and multiphase phenomena that need to be further explored. Acknowledgements The scientific community that is providing vapor–gas nucleation studies is acknowledged. The present study was conducted under Basic Research Russian Foundation support through grant numbers of 07-08-13529-ofi and 07-03-00587-a. References Aitken, J. (1888). On the number of dust particles in the atmosphere. Transactions of the Royal Society of Edinburgh, 35, 1–9. Allen, L. B., & Kassner, J. L., Jr. (1969). The nucleation of water vapor in the absence of particulate matter and ions. Journal of Colloid and Interface Science, 30, 81–93. Amelin, A. G. (1948). A supersaturated vapor and aerosol generation by mixing of the different temperature vapor–gas flows. Colloidniy Journal (Russian), 10, 169–176. Anisimov, M. P. (2003). Nucleation: theory and experiment. Russian Chemical Reviews, 72, 591–628. Anisimov, M. P., & Cherevko, A. G. (1982). The experimental measurement of critical embryo size in the first order phase transition presence and an entropy for a metastable to stable state transition. Izvestia Akademy Nauk USSR. Seriya. Khimiya, 4(2), 15–19. Anisimov, M. P., & Cherevko, A. G. (1985). Gas-flow diffusion chamber for vapor nucleation studies. Relations between nucleation rate, critical nucleus size and entropy of transition from a metastable into stable state. Journal of Aerosol Science, 16, 97–107. Anisimov, M. P., Costrovskii, V. G., & Shtein, M. S. (1978). A dibutilphtalate vapor and aerosol generation at the different temperature flow mixing by molecular diffusion. Colloidniy Journal (Russian), 40(1), 116–121. Anisimov, M. P., Costrovskii, V. G., Shtein, M. S., & Mikheev, V. B. (1980). A vapor spontaneous nucleation. Colloidniy Journal (Russian), 42, 941–945. Anisimov, M. P., Hameri, K., & Kulmala, M. (1994). Construction and test of a laminar flow diffusion chamber: Homogeneous nucleation of DFB and n-Hexanol. Journal of Aerosol Science, 25(1), 23–32. Anisimov, M. P., Hameri, K., Kulmala, M., & Ovchinnikova, T. E. (1993). Homogeneous nucleation of DBF and n-Hexanol in a laminar flow diffusion chamber. Report Series in Aerosol Science, 23, 19–24. Anisimov, M. P., & Hopke, P. K. (2001). Nucleation rate surface topologies for binary system. Journal of Physical Chemistry, 105, 11817–11822. Anisimov, M. P., Hopke, P. K., Rasmussen, D. H., Shandakov, S. D., & Pinaev, V. A. (1998). Relation of phase state diagrams and surfaces of new phase nucleation rates. Journal of Chemical Physics, 109, 1435–1444. Anisimov, M. P., Hopke, P. K., Shandakov, S. D., & Shvets, I. (2000). n-Pentanol-helium homogeneous nucleation rates. Journal of Chemical Physics, 113, 1971–1975. Anisimov, M. P., Koropchak, J. A., Nasibulin, A. G., & Timoshina, L. V. (1998). Critical embryo phase transitions in the nucleated binary glycerin–carbon dioxide system. Journal of Chemical Physics, 109, 10004–10010. Anisimov, M. P., Koropchak, J. A., Nasibulin, A. G., & Timoshina, L. V. (2000). 1-2 Propanediol and 1-3 Propanediol homogeneous nucleation rates and phase transition in new phase critical embryos. Journal of Chemical Physics, 112, 9917–9928. Anisimov, M. P., Nasibulin, A. G., & Shandakov, S. D. (2000). Experimental detection of nucleation rate surface singularity. Journal of Chemical Physics, 112, 2348–2354. Anisimov, M. P., & Taylakov, A. V. (1989). Interface energy of critical embryos. Journal of Aerosol Science, 20, 1063–1066. Anisimov, M. P., & Vershinin, S. N. (1988). Spontaneous nucleation rate, size and composition of critical embryos in many component supersaturated vapor. In Lecture notes in physics (Vol. 309, pp. 393–396). Anisimov, M. P., & Vershinin, S. N. (1990). Dibutylphtalate nucleation rate at carbon dioxide different pressures. Journal of Aerosol Science, 21(1), 11–14. Anisimov, M. P., Vershinin, S. N., Aksenov, A. A., Sgonnov, A. M., & Semin, G. L. (1987). Experimental measurement of the spontaneous nucleation rates, size and a critical embryo composition in a supersaturated multicomponent vapor. Colloidniy Journal (Russian), 49, 842–846. Anisimova, L., Hopke, P. K., & Terry, J. (2001). Two channel vapor nucleation in the vicinity of the triple point. Journal of Chemical Physics, 114, 9852–9855. Baydakov, V. G. (1995). Superheating of cryogenics liquids, Ural Branch RAS, Ekaterinburg. Brock, J. R., Kuhn, P. J., & Zenavi, D. (1986). Condensation aerosol formation and growth in a laminar coaxial jet: Experimental. Journal of Aerosol Science, 17, 11–22. Brock, J. R., Kuhn, P. J., & Zenavi, D. (1988). Formation and growth of binary aerosol in a laminar coaxial jet. Journal of Aerosol Science, 19, 413–424. Brus, D., Hyvarinen, A., Zdimal, V., & Lihavainen, H. (2005). Homogeneous nucleation rate measurements of 1-butanol in helium: A comparative study of a thermal diffusion cloud chamber and a laminar flow diffusion chamber. Journal of Chemical Physics, 122, 214506–221514. Brus, D., Zdimal, V., & Stratmann, F. (2006). Homogeneous nucleation rate measurements of 1-propanol in helium: The effect of carrier gas pressure. Journal of Chemical Physics, 124, 164306–1634310. Coulier, P. J. (1875). Note sur une nouvelle propriete de l'air. J. de Pharmacie et de Chimie, Paris, Ser., 4(22), 165–173. Coulier, P. J. (1875). Note sur un nouvelle propriete de l'air. J. de Pharmacie et de Chimie, Paris, Ser., 4(22), 254–255. Fladerer, A., & Strey, R. (2006). Homogeneous nucleation and droplet growth in supersaturated argon vapor: The cryogenic nucleation pulse chamber. Journal of Chemical Physics, 124, 164710–164715. Frank, J., & Hertz, H. (1956). Messung der kritischen Ubersattigung von Dampfen mit der Diffusionsnebelkammer. Zeitschrift fur physik, 143, 559–590. Frenkel, Ja. I. (1975)). Kinetic theory of liquids. Leningrad: Nauka. Gamero-Castano, M., & Fernández de la Mora, J. (2002). Ion-induced nucleation: Measurement of the effect of embryo's size and charge state on the critical supersaturation. Journal of Chemical Physics, 117, 3345–3353. Heist, R. H., Ahmed, J., & Janujua, M. (1994). Effects of background gases on the homogeneous nucleation of vapors. 1. Journal of Physical Chemistry, 98, 4443–4453. Heist, R. H., Ahmed, J., & Janujua, M. (1995). Effects of background gases on the homogeneous nucleation of vapors. 2. Journal of Physical Chemistry, 99, 375–383. Heist, R. H., Bertelsmann, A., Martinez, D., & Chan, Y. F. (2003). Thermal diffusion cloud chamber: new criteria for proper operation. Atmospheric Research, 65, 189–209. Higuchi, W. J., & O'Konski, C. T. (1960). A test of Becker–Doring theory of nucleation kinetics. Journal of Colloid Science, 15, 14–49. Holten, V., Labetski, D., & van Dongen, M. E. (2005). Homogeneous nucleation of water between 200 and 240 K: New wave tube data and estimation of the Tolman length. Journal of Chemical Physics, 123, 104505–104509. Hyvarinen, A.-P., Brus, D., Zdimal, V., Smolik, J., Kulmala, M., Viisanen, Y. et al. (2006). The carrier gas pressure effect in a laminar flow diffusion chamber, homogeneous nucleation of n-butanol in helium. Journal of Chemical Physics, 124, 224304–224311. Hyvarinen, A.-P., Lihavainen, H., Viisanen, Y., & Kulmala, M. (2004). Homogeneous nucleation rates of higher n-alcohols measured in a laminar flow diffusion chamber. Journal of Chemical Physics, 120, 11621–11633. Kacker, A., & Heist, R. H. (1985). Homogeneous nucleation rate measurements. I. Ethanol, n-propanol, i-propanol. Journal of Chemical Physics, 82, 2734–2744.

746

M.P. Anisimov et al. / Aerosol Science 40 (2009) 733 -- 746

Kashchiev, D. (1982). On the relation between nucleation work, nucleus size, and nucleation rate. Journal of Chemical Physics, 76, 5098–5102. Kashchiev, D. (2006). Forms and applications of the nucleation theorem. Journal of Chemical Physics, 125, 014502. Katz, J. L. (1970). Condensation of a supersaturated vapor. I. The homogeneous nucleation of the n-alkanes. Journal of Chemical Physics, 52, 4733–4748. Katz, J. L., Hung, C. H., & Krasnopoler, M. (1988). The homogeneous nucleation of norare. In Proceedings of the 12th ICNAA, Vienna (Vol. 309 pp. 356–359). Lecture notes in physics. Springer-Verlag, Berlin. Kim, Y. J., Wislouzil, B. E., Wilemski, G., Wolk, J., & Strey, R. (2004). Isothermal nucleation rates in supersonic nozzles and the properties of small water clusters. Journal of Physical Chemistry, 108(A), 4365–4377. Kodenev, G. G., Baldin, M. N., & Vaganov, V. S. (1987). The Tompson's equation applicability for small clusters. In A. A. Vostrikiv , & A. K. Rebrov (Eds.) Clusters physics. (pp. 110–115). ITP Novosibirsk. Kogan, Ja. I., & Burnasheva, Z. A. (1960). The enlargement and measurement of condensation seeds in a continuous flow. Journal of Physical Chemistry (Russian), 34, 2630–2639. Langsdorf, A. (1939). A continuously sensitive diffusion cloud chamber. Review of Scientific Instruments, 10, 91–103. Lee, D.-W., Hopke, P. K., Rasmussen, D. H., Wang, H.-C., & Mavliev, R. (2003). Comparison of experimental and theoretical heterogeneous nucleation on ultrafine carbon particles. Journal of Physical Chemistry B, 107, 13813–13822. Lihavainen, H., & Viisanen, Y., (1998). Laminar flow diffusion chamber for nucleation rate measurements. In Hienola, J., & Hameri, K (Eds.), Report series in aerosol science No. 41, (pp. 381–382). Helsinki. Lihavainen, H., & Viisanen, Y. (2001). A laminar flow diffusion chamber for homogeneous nucleation studies. Journal of Physical Chemistry, 105, 11619–11629. Luijten, C. C. M., Peeters, P., & van-Dongen, M. E. H. (1999). Nucleation at high pressure. II. Wave tube data and analysis. Journal of Chemical Physics, 111, 8535–8544. Luijten, C. C. M., & van-Dongen, M. E. H. (1999). Nucleation at high pressure. I. Theoretical considerations. Journal of Physical Chemistry, 111, 8524–8534. Mavliev, R., Hopke, P. K., Wang, H.-C., & Lee, D.-W. (2004). Experimental studies of heterogeneous nucleation in the turbulent mixing condensation nuclei counter. Journal of Physical Chemistry B, 108, 4558–4564. Mikheev, V., Irving, P., Laulainen, N. S., Barlow, S. E., & Pervukhin, V. (2002). Laboratory measurement of water nucleation using a laminar flow tube reactor. Journal of Chemical Physics, 116, 10772–10786. Nguyen, H. V., Okuyama, K., Mimura, T., Kousaka, Y., Flagan, R. C., & Seinfeld, J. H. (1987). Homogeneous and heterogeneous nucleation in a laminar flow aerosol generator. Journal of Colloid and Interface Science, 119, 491–504. Okuyama, K., Kousaka, Y., Kreidenweis, S., Flagan, R. C., & Seinfeld, J. H. (1988). Studies in binary nucleation: The dibutylphthalate/dioctylphthalate system. Journal of Chemical Physics, 89, 6442–6453. Ostwald, W. (1896–1903). Lehrbuch der Allgemeinen Chemie. W. Engelmann: Leipzig. Peeters, P., Gielis, J. J., & van Dongen, M. E. (2002). The nucleation behavior of supercooled water vapor in helium. Journal of Chemical Physics, 117, 5253–5647. Peters, F., & Paikert, B. (1989). Experimental results on the rate of nucleation in supersaturated n-propanol, ethanol, and methanol vapor. Journal of Chemical Physics, 91, 5672–5678. Protsenko, S. P., Baydakov, V. G., Zhdanov, E. D., & Teterin, A. S. (2006). Nucleation in superheated liquids. In Metastable states and phase transitions. (Vol. 8, pp. 171–202). Ural Branch RAS, Ekaterinburg. Seto, T., Okuyama, K., de Juan, L., & Fernández de la Mora, J. (1997). Condensation of supersaturated vapors on monovalent and divalent ions of varying size. Journal of Chemical Physics, 107, 1576–1585. Sharafutdinov, R. G., Zarvin, A. E., Korobeyshchikov, N. G., Madirbaev, V. Zh., & Khmel, S. Ja. (1999). Clusters in a pulsed free jet of a monosilane–argon mixture. Technical Physics Letters, 25(21), 47–51. Streletzky, K. A., Zvinevich, Y., Wyslouzil, & Strey, R. (2002). Controlling nucleation and growth of nanodroplets in supersonic nozzles. Journal of Chemical Physics, 116, 4058–4070. Strey, R., Viisanen, Y., & Wagner, P. E. (1995). Measurement of the molecular content of binary nuclei. III. Use of the nucleation rate surfaces for the water-n-alcohol series. Journal of Chemical Physics, 103, 4333–4345. Strey, R., Wagner, P. E., & Schmeling, T. (1986). Homogeneous nucleation rates for n-alcohol vapors measured in a two-piston expansion chamber. Journal of Chemical Physics, 84(4), 2325–2335. Strey, R., Wagner, P., & Viisanen, Y. (1994). The problem of measuring homogeneous nucleation rates and the molecular contents of nuclei: progress in the form of nucleation pulse measurements. Journal of Physical Chemistry, 98, 7748–7758. Sutugin, A. G., & Fuchs, N. A. (1970). Aerosol generation at the rapidly changing external conditions. Colloidniy Journal (Russian), 32, 255–260. van Remoortere, P., Heath, C., Wagner, P., Strey, R. (1996). Effect of supersaturation, temperature and total pressure on the homogeneous nucleation of n-pentanol. In M. Kulmala, P. Wagner (Eds.), Proceedings of the 14th ICNAA, Helsinki (pp. 256–259). Pergamon: Oxford. Viisanen, Y., & Strey, R. (1994). Homogeneous nucleation rates for n-butanol. Journal of Chemical Physics, 101, 7835–7843. Viisanen, Y., Strey, R., & Reiss, H. (1993). Homogeneous nucleation rates for water. Journal of Chemical Physics, 99, 4680–4692. Volmer, M. (1939). Kinetik der Phasenbildung. Dresden-Leipzig: T. Steinkopf. Wagner, P. E., & Anisimov, M. P. (1993). Evaluation of nucleation rates from gas flow diffusion chamber experiments. Journal of Aerosol Science, 24(1), 103–104. Wedekind, J., Hyvarinen, A. P., Brus, D., & Reguera, D. (2008). Unraveling the “Pressure Effect” in nucleation. Physical Review Letters, 101, Article Number: 125703. Wilck, M., Hameri, K., Stratmann, F., & Kulmala, M. (1998). Determination of homogeneous nucleation rates from laminar-flow diffusion chamber data. Journal of Aerosol Science, 29, 899–911. Wyslouzil, B. E., Seinfeld, J. H., Flagan, R. C., & Ocuyama, K. (1991). Binary nucleation in acid–water systems I. Methanesulfonic acid–water. Journal of Chemical Physics, 94, 6827–6841.