A Laminar Flow Diffusion Chamber for Homogeneous Nucleation

J. Phys. Chem. B 2001, 105, 11619-11629

11619

A Laminar Flow Diffusion Chamber for Homogeneous Nucleation Studies† Heikki Lihavainen and Yrjo1 Viisanen* Finnish Meteorological Institute, Sahaajankatu 20 E, FIN-00810 Helsinki, Finland ReceiVed: March 29, 2001; In Final Form: September 5, 2001

A new version of laminar flow diffusion chamber was developed for unary homogeneous nucleation from vapor to liquid studies. The developed laminar flow diffusion chamber can quantitatively measure nucleation rates as a function of saturation ratio and temperature. A numerical model was developed for calculations of temperature and saturation ratio profiles inside the laminar flow diffusion chamber. Several experiments were made to ensure the proper and reliable operation of the device and the numerical model. Nucleation rates of n-hexanol were measured using helium as a carrier gas from 265.0 to 295.0 K. The measured nucleation rate range was from 103 to 107 cm-3 s-1. Temperature and saturation ratio dependencies were compared to the classical nucleation theory. The saturation ratio dependency was well predicted by the theory. Results were compared to the measurements made by others. They were in reasonable agreement at the lower end of the temperature range of this study. The carrier gas effect was also investigated using argon as another carrier gas. The nucleation was stronger when argon was used as a carrier gas.

Introduction The formation of a liquid droplet from vapor is referred to as nucleation. This first-order phase transition has many forms. Homogeneous nucleation is the formation of liquid phase from pure vapor. It can be further divided into unary, binary, ternary, etc. homogeneous nucleation, depending on how many substances take part in the nucleation process. Heterogeneous nucleation is referred to when nucleation occurs on foreign substances or surfaces. Nucleation always needs supersaturated conditions in order to occur. Even though nucleation has been studied over 100 years, the phenomenon is still poorly understood. To gain more understanding on nucleation phenomena, more experimental data with different kinds of devices are needed. There exist over twenty different kinds of devices to study nucleation.1 Most of these devices are variations of only a few methods. To date, experimental homogeneous nucleation rate studies have been done usually with an expansion cloud chamber and with a static diffusion chamber. The nucleation rate range of these devices does not overlap. The static diffusion chamber is applicable to measure low nucleation rates, and the expansion cloud chamber is used to measure quite high nucleation rates. The nucleation rate range of the laminar flow diffusion chamber fills this gap between these two devices. The laminar flow diffusion chamber (from now on referred to as LFDC) has been applied to homogeneous nucleation studies with variable success. The laminar flow diffusion chamber for generating fine particles is based on a method utilized at the end 1970s by Anisimov et al.2 Anisimov and Cherevko3 studied the nucleation of dibutyl phthalate in a gas flow diffusion chamber very similar to LFDC. Nguyen et al.4 named their device a laminar flow aerosol generator. The operational principle of it is the same as in the LFDC. They studied both homogeneous and heterogeneous nucleation of dibutyl phthalate in nitrogen and air. They investigated carefully the operational characteristics and the effects of different †

Part of the special issue “Howard Reiss Festschrift”.

experimental parameters. They proposed that the laminar flow aerosol generator is better suited for heterogeneous nucleation studies than for homogeneous nucleation studies because of large loss of the vapor onto the walls. This is not the case in a mixing type of instrument they developed.5 Anisimov et al.6 studied homogeneous nucleation rates of dibutyl phthalate and n-hexanol in nitrogen. They concluded that the LFDC works well with less volatile substances and when the nucleation temperature is above the room temperature. They measured nucleation rates between 102 and 108 cm-3 s-1. Vohra and Heist7 presented a version of a LFDC they built and studied its operational characteristics. They measured critical saturation ratios for 1-propanol in four different carrier gases: helium, argon, nitrogen, and hydrogen. They concluded that their device is capable of quantitative investigations of vapor nucleation, although nucleation rate measurements would be desirable. Ha¨meri et al.8 studied the operational characteristics of the LFDC and the ability of the model they used to describe the actual events inside the condenser. They used dibutyl phthalate as the nucleating vapor and both nitrogen and helium as carrier gas. They found out that the equations they presented were in reasonable agreement with the experiments. Ha¨meri and Kulmala9 measured homogeneous nucleation rates from 10 to 4.5 × 107 cm-3 s-1 over a temperature range from 246 to 317 K. They used nitrogen as the carrier gas and dibutyl phthalate as the nucleating vapor. They also studied the effects of different carrier gases on the nucleation. They concluded that the LFDC is well suited for measuring nucleation rates of substances of low volatility. The main aim of this study was to develop a version of a laminar flow diffusion chamber that can reliably measure homogeneous nucleation rate isotherms. Nucleation rates of n-hexanol in helium and argon were measured over a temperature range from 265 to 295 K and over a nucleation rate range from 103 to 107 cm-3 s-1 and compared with the results with the classical nucleation theory and also to measurements made by others.

10.1021/jp011189j CCC: $20.00 © 2001 American Chemical Society Published on Web 11/06/2001

11620 J. Phys. Chem. B, Vol. 105, No. 47, 2001

Lihavainen and Viisanen

Theory The dominating theory of unary homogeneous nucleation has been for over 70 years the classical nucleation theory. It has been developed over a period of time by Volmer and Weber,10 Volmer,11,12 Becker and Do¨ring,13 Zeldovich,14 and Frenkel.15 The classical nucleation theory predicts the nucleation rate as a function of both temperature and saturation ratio. In this theory the properties of a liquid droplet are assumed to be the same as the bulk liquid properties. This enables the use of the bulk liquid density and macroscopic flat film surface tension in the calculations. This is generally called capillary approximation. The classical nucleation theory is still widely used even though it predicts nucleation rates that differ from experimental results by orders of magnitudes. It is still useful for qualitative understanding of nucleation. A number of different theoretical alternatives have been proposed. None of these has been capable of explaining experimental results any better than the classical nucleation theory. Nucleation rate predicted by the classical nucleation theory can be written in a form

J ) C*ZNen*

(1)

where C* is the rate of arrival of monomer molecules at the critical cluster,

C* )

4πr/d p

(2)

(2πmkBT)1/2

where r/d is the size of the critical radius of the cluster, p is the vapor pressure, m is the mass of the molecule, kB is the Boltzmann constant, and T is the temperature. Z is the so-called Zeldovich nonequilibrium factor,

Z)

σ1/2Vliq

(3)

1/2 2πr/2 d (kBT)

where σ is the surface tension and Vliq is the volume occupied by a liquid molecule. It is the correction factor for the difference between the equilibrium cluster concentration Nen* and the pseudo-steady-state cluster concentration

[

Nen* ) N1 exp -

16πσ3Vl2

]

3(kBT)3(ln S)2

(4)

where N1 is the number of monomers and S is the saturation ratio. The size of the critical cluster, r/d, is determined by socalled Gibbs-Thompson or Kelvin equation

r/d )

2σVliq kBT ln S

(5)

Experimental Section Principle of Operation. The used experimental setup is presented in Figure 1. It consists of three main parts; the saturator, the preheater, and the condenser. A steady and filtered flow of carrier gas is introduced into the saturator. In the saturator the carrier gas is fully saturated with the nucleating substance by evaporation from the liquid phase. The saturator is a horizontally placed round tube. The nucleating substance is as a liquid pool at the bottom of the saturator. The amount of the vapor in the carrier gas is controlled with the temperature inside the saturator. After the saturator, mixture is led into the

Figure 1. Experimental setup used in the n-hexanol studies.

preheater. The preheater, as well as condenser, is also a round, temperature controlled tube. The preheater and condenser have the same inner diameter. They are placed vertically downward. The preheater is always at a higher temperature than the saturator. In the preaheter a laminar flow profile is achieved. From the preheater the gas stream enters into the condenser, which is at a lower temperature than the preheater and the saturator. The stream is rapidly cooled by heat exchange with the wall of the condenser. Supersaturation is achieved because equilibrium vapor pressure is a rather strong, rising exponential function of temperature. If this supersaturation is high enough, nucleation occurs. Formed droplets are counted after the condenser by light scattering. Because the boundary conditions in the device are wellknown, a mathematical model can be used to calculate the velocity, temperature, vapor pressure, and saturation ratio profiles inside the condenser. The temperatures of the preheater and the condenser are kept constant during a measurement of one nucleation rate isotherm. This means that the boundary conditions are constant and the nucleation temperature is almost constant over one nucleation rate isotherm measurement. The flow is kept laminar in the preheater and condenser to ensure that the mixing characteristics are well characterized. Typical Reynols numbers in the measurements were around 100. Experimental Setup. n-Hexanol (Acros, purity 98%) was used without further purification as the nucleating substance. Helium (AGA, purity 99.9999%) and argon (AGA, purity 99.9999%) were used as the carrier gases. Lines from the carrier gas container to the saturator are made from Teflon and stainless steel to avoid any desorption problems. The carrier gas is run trough a HEPA-filter before it enters into the saturator. The flow rate was measured with a mini-BUCK M-5 soap bubble flow calibrator, from two places; before the gas enters into the saturator and after it comes out from the condenser. The saturator is a 1.0 m long horizontal tube with an inner diameter of 0.035 m. The inner surface of the saturator tube is made from Teflon. Constant temperature over the saturator is achieved by circulating temperature-controlled circulating liquid through a jacket surrounding the inner tube. The temperature of the circulating liquid is controlled with a LAUDA RK 20 circulation liquid bath. The temperature of the nucleating vapor and carrier gas mixture is measured with a (HERAEUS QUAT 100/200) temperature sensor. It is situated on the surface of the liquid pool near the end of the saturator next to the preheater. The place of the temperature sensor was chosen so that the temperature change of the liquid surface caused by the heat of evaporation is negligible. The residence time of the carrier gas in the saturator was roughly 20 s.

Laminar Flow Diffusion Chamber for Homogeneous Nucleation

Figure 2. Schematic cross section of the connection between preheater and the condenser.

Both the preheater and the condenser are about 0.3 m long tubes. Inner diameters of the preheater and the condenser are 4.0 mm. The inner tubes, where the gas flows, are made from stainless steel and the heating and the cooling jackets are made from brass. The temperatures of the tubes were controlled by circulating temperature-controlled (preheater: LAUDA RC6 CS, condenser: LAUDA RK20 KS) circulating liquid through the jackets surrounding the tubes. The temperature drop at the wall of the tubes between the preheater and the condenser has to be as steep as possible. This is achieved with the following features; see Figure 2. In the connection between the preheater and the condenser, the inner tubes are about 1 mm longer than the cooling jackets. The preheater and the condenser are separated thermally with a Teflon insulator. The Teflon insulator is about 1 mm thick between the inner tubes and about 3 mm thick in other parts. Because the heat conductivity of stainless steel is about 100 times higher than the heat conductivity of Teflon, it is assumed that the shoulder from the preheater is at the same temperature as the preheater and the shoulder from the condenser is at the temperature of condenser. Special construction at the ends of the preheater’s heating and the condenser’s cooling jackets allows the circulating liquid to flow uniformly and close to the connection; see Figure 2. Special care was taken that the inner surface at the connection between the preheater and the condenser is as smooth as possible, so that the flow profile was not affected. The temperatures of the preheater and the condenser are measured from the circulating liquid. Temperature sensors (HERAEUS QUAT 100/200) are located at the inlets of the circulating liquid into the heating or the cooling jacket, which in turn were located about 4 cm from the end of the preheater or from the beginning the condenser; see Figure 2. Both the preheater and the condenser are thermally insulated from the environment. The preheater and the condenser are vertically placed so that the settling of the particles due to gravitation does not take place. The direction of the flow is vertically downward so that the condensed liquid from the condenser does not fall back into the preheater and interfere with the boundary conditions. After the condenser, the liquid condensed onto the wall of the condenser is separated from the gas stream. This is done in

J. Phys. Chem. B, Vol. 105, No. 47, 2001 11621 a so-called T-crossing section. The stream of gas mixture including the formed particles is forced to make a slightly over 90° turn into the optical head where the particles are counted. The liquid cannot make this turn and so it falls into the liquid drainage. The T-crossing section is made from aluminum. The T-crossing section was separately cooled with a cooling bath (LAUDA RC6 CS). It was kept at the same or colder temperature than the condenser to avoid evaporation of the formed droplets. The formed droplets are counted with a TSI 3010 Condensation Particle Counter’s (CPC) optical head. The optical head was separated from rest of the CPC and connected into the developed LFDC. Inside the CPC’s optical head the flow is taken through a laser beam. The droplets scatter laser light as they pass through the beam. These scattered laser light pulses are counted. The counts were continuously recorded with a PC. Pressure inside the LFDC was measured from the T-crossing section with the MKS barometer connected into the MKS Type 270 D signal conditioner. The temperature of the laboratory was measured with a HERAEUS QUAT 100/200 temperature sensor. Mathematical Model. Measuring temperature, vapor pressure, and flow profiles reliably from a laminar flow is an impracticable task. They have to be calculated. This means solving five coupled partial differential equations: equations for heat and mass transfer, equations of motion (both axial and radial direction), and an equation of continuity. Several assumptions were made to simplify these equations. The equations can be solved in a steady state. In all the equations, the effect of radial velocity was assumed to be negligible and it was set to zero. In calculations of the velocity profile, the flow was assumed to be incompressible. These assumptions reduced the equations of motion to a quite simple problem that has been analytically solved,16 resulting in parabolic velocity profile. The assumptions mentioned above reduce the amount of coupled partial differential equations to only two. Because of the axial symmetry, two-dimensional equations for heat and mass transfer are solved in cylindrical coordinates, giving

∂ 1 ∂ ∂T ∂ ∂T (uFcpT) ) kr + k ∂z r ∂r ∂r ∂z ∂z

[ ]

(6)

∂ 1 ∂ ∂ω ∂ ∂ω 1 d (uFω) ) × rFD + FD + ∂z r ∂r ∂r ∂z ∂z r ∂r ∂ ln T ∂ ∂ ln T rRDFω + RDFω (7) ∂r ∂z ∂z

[

] [

[

F)

MPtot RT

] } [

]

(8)

where F is the density of the carrier gas and vapor mixture, u is the velocity in axial direction, cp is the specific heat of the mixture, k is the thermal conductivity of the mixture, ω is mass fraction of nucleating vapor, D is binary diffusion coefficient, R is thermal diffusion factor, M is the molecular weight of the vapor carrier gas mixture, Ptot is the total pressure, and R is the general gas constant. In the temperature profile calculations, convective heat transfer in the axial direction and heat transfer by conduction in the axial and radial direction were taken into account. In the mass fraction profile calculation convective mass transfer in the axial direction, mass transfer by diffusion, and thermal diffusion in the axial and radial directions were taken into account.


Lihavainen and Viisanen Data Interpretation of Experimental Nucleation Rate. The LFDC experiments yield the total number of particles nucleated per unit time in the chamber. However, rates of nucleation are usually expressed in units of cm-3 s-1. The results yielded from the LFDC were converted to conventional nucleation rate units using the similar method that is used to convert static diffusion cloud chamber data.18 Wagner and Anisimov19 suggested that this method be used in LFDC. The maximum experimental nucleation rate Jmax exp can be calculated from the relationship

Jmax Jmax exp theor ) Jexp dV Jtheor dV Figure 3. Temperature, T, equilibrium vapor pressure, Peq, vapor pressure, P, saturation ratio, S, and nucleation rate, J, profiles as a function of the length of the condenser, z. The flow rate is 17 cm3/s.

Equations 6-8 are coupled with temperature and concentration. Equations are solved with the following boundary conditions,

T(r, z ) z0) ) TS2 T(R0, z0 < z e 0) ) TS2 T(R0, z > 0) ) TC

(9)

ω(r, z ) z0) ) ωeq(TS1) ω(R0, z0 < z e 0) ) ωeq(TS1) ω(R0, z > 0) ) ωeq(TC)

(10)

where TS2 is the temperature of the preheater, TC is the temperature of the condenser, TS1 is the temperature of the saturator, ωeq(Ti) is the mass fraction defined by equilibrium vapor pressure at the temperature Ti, z ) 0 is the boundary between the preheater and the condenser, z0 is a chosen starting point of calculations in the preheater (z0 is negative or zero), and R0 is the radius of the tube. The starting point of the calculations was set in the preheater, because calculations revealed that at slower flow rates the temperature started to vary already inside the preheater. The boundary conditions for mass fraction were calculated using ω ) Fvap/(Fcar + Fvap) and the ideal gas law, where subscript “vap” refers to “vapor” and subscript “car” refers to “carrier gas”. Equations 6-10 were solved using finite element method, e.g. 17. In Figure 3 calculated profiles of temperature, equilibrium vapor pressure, vapor pressure, saturation ratio, and nucleation rate (according to the classical nucleation theory) at the center of the tube with boundary conditions typical in measurements of this study are presented. It can be seen that the temperature and therefore also the equilibrium vapor pressure drop much faster than the actual vapor pressure toward the boundary values resulting supersaturation. The behavior of the profiles in the radial direction is similar than in axial direction resulting in the nucleation zone being at the center of the tube. In the axial direction the nucleation rate maximum is located slightly before the saturation ratio maximum because nucleation is a function of both temperature and saturation ratio. The size of the nucleation peak is quite small. In the volume where about 90% of the particles are formed, the temperature drops about 1.5 K and the saturation ratio changes about 3%. After the nucleation zone, the vapor is still clearly supersaturated. This enables the nucleated particles to grow to a size in which they are optically detectable.

(11)

where the integrals are over the volume of the condenser tube and Jmax theor is the theoretical nucleation rate maximum. Jexp dV is the measured particle concentration multiplied by the flow rate. The relationship (11) results from the fact that the experimental and the theoretical nucleation rates have usually the same slope even though there is a difference in the absolute values.18 It has been found that the use of different theories changes the calculated experimental results no more than 10-50%.8 In this study the classical nucleation theory was used. The experimental nucleation temperature and saturation ratio are those at the theoretical nucleation rate maximum. Thermodynamic Data. To be able to calculate nucleation rates in the LFDC, molecular weights, thermal conductivities, binary diffusion coefficients, equilibrium vapor pressures, densities, viscosities, specific heats, thermal diffusion factors, and surface tensions of the substances as functions of temperature are needed. They are presented in Table 1. The densities of the substances in a gas phase were calculated using the ideal gas law. The available experimental values for the binary diffusion coefficient20 were determined at much higher temperatures than the measurements in this study were performed, therefore simple curve fitting was out of the question. It was decided to use the method of Fuller et al. described in Reid et al.21 It describes quite well the experimental data. The viscosity and thermal conductivity of the gaseous n-hexanol were calculated using formulas based on theory.21 Verification of the Operation of the Laminar Flow Diffusion Chamber. To make reliable homogeneous nucleation measurements, the following experimental features should be fulfilled:30,31 (1) Nucleation agents should be eliminated. They can be, e.g., ions or preexisting particles. Nucleation on these surfaces needs lower saturation ratios for its occurrence than in homogeneous nucleation. (2) The supersaturation of the vapor should be achieved by a well-defined and reproducible process. (3) Droplet growth should have a negligible influence on the saturation ratio. (4) The nucleation rate should be measured as a function of the saturation ratio over a sufficiently large range so that the slope of the nucleation rate as a function of saturation ratio can be determined. (5) To have sensitive evaluation of nucleation theories both the temperature and the saturation ratio dependencies of the nucleation rate have to be determined. Several experiments were made to ensure the proper operation of LFDC. These experiments made it also possible to compare results from LFDC to results from model calculations. Figure 4 shows a typical measured particle concentration isotherm as a function of the temperature of the saturator. At the low end of the range it can clearly be seen that nucleation agents exist. The vapor condenses on them at lower saturation ratios than needed for homogeneous nucleation to occur. The concentration of nucleation agents was less than 0.1 cm-3. At


J. Phys. Chem. B, Vol. 105, No. 47, 2001 11623

TABLE 1: Thermodynamic Properties for Helium, Argon, and n-Hexanola Helium M ) 0.004003 kg/mol k ) 418.68 × (-5.85430 × 10-5 + 2.686056 × 10-6T - 0.700113 × 10-9T2 + 1.07396 × 10-11T3 -6.01768 × 10-15T4) W/mK η ) 1.4083 × 10-6T1.5/(T + 70.22) Ns/m2 cp ) 5200 J/(kg K) M ) 0.039948 kg/mol k ) exp(-8.7978 + 0.83517 ln T) W/mK η ) exp(-15.712 + 0.88153 ln T) Ns/m2 cp ) 520 J/(kg K)

b b

Argon c c

N-Hexanol M ) 0.102177 kg/mol peq ) 133.322 × exp[135.4577 - (12092.97/T) - 16.7 ln T] Pa σ ) 10-3 × (27.84 - 0.08381 × (T - 273.15)) N/m ηvap ) 0.0269[(MT)1/2/ωLΩ], where σL is the hard-sphere diameter and Ω is the collision integral and it is calculated from empirical equation Ω ) 1.16145T*-0.14874 + 0.52487 exp(-0.77320T*) + 2.16178 exp(-2.43787T*), where T* ) kBT/ and is the characteristic energy kvap ) 2.63 × 10-23[(T/M)1/2/σ2Ω] W/mK Fliq ) 1000 × (0.8269 - 5.1191 × 10-4((T - 273.15)) kg/m3 D ) 1.12189 × 10-4(T1.75/P) m2/s, in helium D ) 3.22780 × 10-5(T1.75/P) m2/s, in argon cp ) (4.811 + 5.981 × 10-1T - 3.010 × 10-4T2 + 5.4261 × 10-8T3)/0.102177 J/(kg K) (1/R) ) [-0.62264 + [T/(-23.4305 + 0.30537)]](y - 0.1548) + 0.0964, in helium where y is mole fraction (1/R) ) [25.4071 - [T/(-297.6230 + 1.33707)]](y - 2.7573) + 70.0550, in argon Mixed Properties n k ) ∑i)1 (yiki/yjAij), where Aij ) [1 + (ktri/ktrj)1/2(Mi/Mj)1/4]/[8(1 + Mi/Mj)]1/2 and ktri/ktrj ) (ηi/ηj)(Mj/Mi) n yicp,i cp ) ∑i)1

d e f f g h h f i i f f

a The parameters listed are: M molar mass, k thermal conductivity, D binary diffusion coefficient, peq equilibrium vapor pressure, F density, η viscosity, cp the specific heat of the substance in a vapor phase, R thermal diffusion factor, σ surface tension. Subscript “liq” refers to “liquid phase” and “vap” to “vapor phase”. The letters at the end of each property refer to the list of references at the end of the table. b Reference 18. c Reference 22. d Reference 23. e Reference 24. f Reference 21. g Fitted to data from refd 25, 26, and 27. h Method by Fuller et al. described in ref 21. i Estimated using the method described by Mason28 and Vasakova and Smolı´k.29

Figure 5. Particle concentration, N, as a function of time. Nucleation temperature is 270 K. Figure 4. Measured particle concentration, N, as a function of temperature of the saturator, TS1. Nucleation temperature is 280 K.

the high end of the range the effects of the depletion of vapor and the heat released by condensation on the nucleated particles can be seen. These effects were negligible at concentrations below 103 cm-3. The particle concentration range was also limited by the optical head, the optical head was not able to count all the particles in particle concentrations higher than 104 cm-3 because of the coincidence effect. The experimental temperature range with n-hexanol and helium as a carrier gas spans from 265 to 295 K. The upper temperature limit is set by the clear effect of depletion of vapor and heat released by condensation. The lower temperature limit is set by the counting efficiency of the optical head. At low temperatures the particles reaching the optical head are probably smaller and are not entirely counted by the optical head. The stability of the developed LFDC is good. Figure 5 shows the output particle concentration of n-hexanol in argon as a function of time. All the temperatures and the flow rate were kept constant during the measurement. The nucleation rate is

quite constant over a time range of 21 h. The standard deviation from the average value is l3%. Temperatures of the saturator, preheater, and the condenser were constant within the accuracy of the temperature sensors ((0.05 K) during this time. The temperature of the laboratory varied about (2 K. Reproducibility was tested by measuring the rate of particle formation at same temperatures and flow rate in 10 different days. The average deviation of particle formation was about (10%. Most of this deviation is due to the fact that the temperature of the saturator was not actually the same in the 10 different measurements. The temperature of the saturator varied about 0.1 K. To ensure the proper operation of the saturator, two different kinds of experiments were made. First the temperatures of the preheater and the condenser and the flow rate were kept constant while the temperature of the saturator was increased by small steps. When the temperature of the saturator was raised above the temperature of the preheater, the particle formation rate did not increase anymore. Even though the temperature of the saturator was raised, the amount of the vapor entering the condenser was constant. It corresponded to the equilibrium vapor


Figure 6. Nucleation rate, J, as a function of particle concentration, N, as a function volume flow rate, Q. The circles are measured concentrations and the solid line is theoretical concentration multiplied by a factor of 2 × 105.

pressure at the temperature of the preheater. The temperature of the saturator, at which the particle formation rate stopped increasing, was the same as the temperature of the preheater. The second method was to shorten the residence time of the carrier gas in the saturator by increasing the flow rate. Because the nucleation rate is a strong function of the saturation ratio, the nucleation rate will drop drastically if the residence time in the saturator is too short for full saturation. This did not happen, as can be seen from Figure 6. As a comparison, the theoretical nucleation rates predicted by the classical nucleation theory multiplied by a factor of 2 × 105 are presented. Figure 6 is also a test between the operation of the experimental device and the used mathematical model. The experimental nucleation rates as a function of flow rate does not change much at flow rates higher than 10 cm3/s. This is also the case with the theoretical nucleation rate. The nucleation rate measurements were made at about 16.7 cm3/s when helium was used as a carrier gas. The experimental nucleation rate drops toward zero at a higher flow rate than predicted by the scaled theoretical nucleation rate. This is probably due to two reasons. When the flow rate is slower, the particles grow bigger and are partly lost in the T-crossing section because of gravitation. At lower flow rates the effect of the vapor depletion is also higher because of the longer residence time in the nucleation zone. As was mentioned above, the mathematical model does not take into account the aerosol dynamics. The saturation ratio increases, according to the model, as a function of the flow rate because the effect of the axial heat conduction becomes negligible as the flow rate increases. At low flow rates the effect of axial heat conduction becomes more significant and therefore the temperature of the stream reaches the temperatures of the condenser slower than in the case where the axial conduction is not taken into account. Thus the axial heat conduction raises the equilibrium vapor pressure and lowers the saturation ratio in the nucleation zone. The axial diffusion of molecules is much slower than the axial heat conduction. Therefore the effect of axial diffusion is negligible. At flow rates higher than 10 cm3/s with helium as a carrier gas, the temperature and the saturation ratio at the theoretical nucleation rate maximum are constant. It can be concluded that the experimental device operates as expected. The mathematical model describes well the actual events inside the LFDC. The conditions for making reliable nucleation measurements described in the beginning of this chapter are fulfilled. Experimental Procedure. For one nucleation rate isotherm, the temperatures of the preheater and the condenser were kept constant. Only the temperature of the saturator was changed. The temperatures of the saturator, preheater, and the condenser were first set to their initial temperatures. These temperatures


Figure 7. Typical measurement event. Particle concentration N as a function of measuring time.

were determined with the mathematical model. When the temperatures were stabilized, a flow of carrier gas was introduced into the system. The volume flow rate was set to about 16.7 cm3/s with helium and 5 cm3/s with argon as a carrier gas. After a steady nucleation rate was achieved, the PC was set to record particle concentration. The volume flow rate, temperatures, and the pressure were recorded at the same time. The particle concentration for every different saturation ratio was recorded for at least 15 min after the nucleation rate was stabilized. In Figure 7 a typical measurement event is presented. When the saturation ratio (the temperature of the saturator) was changed, the volume flow rate, temperatures, and the pressure were recorded. Isotherms were measured using 5 K steps in nucleation temperature. The temperature difference between preheater and condenser was the same with each isotherm. After the nucleation rate isotherm measurement, the liquid drainage was emptied and it was checked that the temperature sensor in the saturator was on the surface of the pool. If not, liquid was added into the saturator. Usually one nucleation rate isotherm was measured during different days, sometimes raising the temperature of the saturator and sometimes lowering it. Results and Discussion The experimental data, the calculated experimental nucleation rate maxima, the saturation ratios, and temperatures at the theoretical nucleation rate maxima are listed in Table 2. The experimental temperature range was from 265.0 to 295.0 K with helium as a carrier gas and from 268.9 to 289.7 K with argon as a carrier gas. The measurements were made at ambient atmospheric pressure. The experimental particle concentration range, where the effects of nucleation agents, vapor depletion and heat released by condensation were negligible, was roughly from 10-1 to 103 cm-3 with helium as a carrier gas and from 100 to 102 cm-3 with argon as a carrier gas. There are two exceptions to these limits. With helium as a carrier gas at 265.0 K the lower concentrations are not valid probably because part the particles are too small to be counted, and at 295.0 K the upper limit is reduced by the vapor depletion and heat released by this. Data outside these ranges are left out from all the figures and tables in this section. Comparison with the Classical Nucleation Theory. The classical nucleation theory was chosen because it predicts the nucleation rate as a function of saturation ratio and temperature, it is widely used, and it uses macroscopic measurable quantities. In Figure 8 experimental results of n-hexanol in helium are plotted as a function of theoretical predictions by the classical nucleation theory. Experimental particle concentrations are about 5 orders of magnitude higher at 265.0 K than predicted by the



TABLE 2: Homogeneous Nucleation Rates of n-Hexanol Measured in the LFDCa n-Hexanol-Helium, 15-02-2000 TS2 ) 296.52 K, TC ) 263.69 K, P ) 99900 Pa, Q ) 16.76 cm3/s, Tlab ) 294.15 K TS1

N

Tnuc

Snuc

Jexp

293.48 293.92 294.36 294.72 294.50 294.19 293.70 293.25

17.36 93.92 471.01 1502.18 715.38 291.60 46.32 9.97

265.04 265.04 265.06 265.07 265.06 265.05 265.04 265.02

12.81 13.28 13.76 14.16 13.92 13.57 13.05 12.58

1.59E5 6.22E5 2.50E6 7.55E6 4.08E6 1.73E6 2.91E5 6.64E4

n-Hexanol-Helium, 07-02-2000 TS2 ) 301.59 K, TC ) 268.70 K, P ) 99900 Pa, Q ) 16.81 cm3/s, Tlab ) 294.16 K TS1

N

Tnuc

Snuc

Jexp

297.11 297.54 297.84 298.28

0.29 1.05 3.74 16.34

270.07 270.08 270.08 270.10

10.11 10.45 10.73 11.06

2.42E3 8.34E3 2.84E4 1.18E5


N

Tnuc

Snuc

Jexp

298.27 298.68 299.14 299.51 299.29 298.90 298.51 298.09 297.70 297.30

15.42 83.66 377.38 1371.47 600.63 153.92 37.64 7.98 1.64 0.38

270.09 270.11 270.13 270.13 270.13 270.11 270.11 270.09 270.09 270.07

11.06 11.42 11.83 12.17 11.96 11.61 11.27 10.91 10.58 10.26

1.13E5 5.83E5 2.48E6 8.63E6 3.88E6 1.04E6 2.68E5 5.99E4 1.29E4 3.14E3


N

Tnuc

Snuc

Jexp

297.30

0.39

270.08

10.26

3.26E3


N

Tnuc

Snuc

Jexp

301.68 302.11 302.50 302.83

0.14 0.74 2.98 16.82

274.86 274.87 274.89 274.90

8.92 9.21 9.48 9.71

1.28E3 6.32E3 2.42E4 1.31E5


N

Tnuc

Snuc

Jexp

304.4

922.86

274.93

10.62

6.32E6


N

Tnuc

Snuc

Jexp

303.89 303.48 303.08 302.72 303.11 302.37 301.89

512.54 131.14 29.28 6.29 32.92 1.77 0.30

274.93 274.93 274.92 274.91 274.91 274.90 274.88

10.48 10.17 9.88 9.62 9.90 9.37 9.05

3.62E6 9.74E5 2.29E5 5.13E4 2.56E5 1.51E4 2.91E3


N

Tnuc

Snuc

Jexp

306.75 307.09 307.48 307.91 308.28 308.71

0.23 0.77 3.12 17.88 63.01 284.00

279.99 279.99 280.01 280.02 280.04 280.04

7.99 8.18 8.41 8.67 8.89 9.16

2.31E3 7.41E3 2.86E4 1.55E5 5.21E5 2.23E6



TABLE 2 (Continued) n-Hexanol-Helium, 01-03-2000 TS2 ) 311.56 K, TC ) 278.49 K, P ) 99900 Pa, Q ) 16.63 cm3/s, Tlab ) 295.15 K TS1

N

Tnuc

Snuc

Jexp

308.73 309.12 308.95

318.68 1193.76 696.81

280.05 280.06 280.06

9.17 9.42 9.31

2.52E6 9.00E6 5.36E6


N

Tnuc

Snuc

Jexp

308.93 308.52 308.11 307.70 307.31 306.96 306.53

632.50 139.50 39.43 7.16 1.60 0.49 0.11

280.06 280.04 280.03 280.01 279.97 279.96 279.96

9.30 9.04 8.79 8.54 8.32 8.11 7.87

4.88E6 1.13E6 3.36E5 6.43E4 1.51E4 4.83E3 1.12E3


N

Tnuc

Snuc

Jexp

311.54 311.86 312.27 312.65 313.10 313.46 313.85

0.15 0.54 2.35 10.24 45.28 195.30 758.23

285.03 285.04 285.05 285.07 285.08 285.11 285.12

7.07 7.22 7.42 7.60 7.83 8.02 8.22

1.72E3 5.80E3 2.39E4 9.93E4 4.15E5 1.71E6 6.35E6


N

Tnuc

Snuc

Jexp

313.65 313.29 312.85 312.46 312.12 311.67

438.39 118.99 24.50 5.70 1.15 0.23

285.12 285.09 285.08 285.06 285.05 285.03

8.12 7.93 7.70 7.51 7.34 7.13

3.78E6 1.07E6 2.34E5 5.68E4 1.19E4 2.55E3


N

Tnuc

Snuc

Jexp

312.46 313.23 314.00

6.30 91.86 1271.93

285.06 285.09 285.13

7.51 7.90 8.31

6.21E4 8.24E5 1.04E7


N

Tnuc

Snuc

Jexp

316.49 316.87 317.32 317.61 318.08 318.44

0.25 1.02 5.81 21.09 111.48 406.85

289.93 289.94 289.97 289.98 290.00 290.01

6.44 6.60 6.78 6.91 7.11 7.27

3.03E3 1.16E4 6.23E4 2.18E5 1.09E6 3.81E6


N

Tnuc

Snuc

Jexp

318.44 318.67 318.27 317.91

361.65 908.97 247.86 64.42

289.98 289.99 289.97 289.96

7.28 7.38 7.20 7.04

3.41E6 8.33E6 2.38E6 6.47E5


N

Tnuc

Snuc

Jexp

317.91 317.46 317.06 316.68 316.27 316.08

53.43 11.28 2.33 0.63 0.15 0.09

289.99 289.97 289.96 289.93 289.92 289.91

7.04 6.85 6.68 6.52 6.36 6.28

5.35E5 1.19E5 2.59E4 7.32E3 1.81E3 1.14E3



TABLE 2 (Continued) n-Hexanol-Helium, 19-04-2000 TS2 ) 326.40 K, TC ) 293.1 K, P ) 101400 Pa, Q ) 16.96 cm3/s, Tlab ) 296.15 K TS1

N

Tnuc

Snuc

Jexp

321.23 321.70 322.07 322.50 322.893

0.19 1.09 5.02 26.00 89.81

294.92 294.94 294.96 294.98 295.00

5.77 5.93 6.06 6.21 6.33

2.57E3 1.38E4 6.08E4 2.99E5 9.93E5


N

Tnuc

Snuc

Jexp

322.26 321.84 321.44 321.10

10.66 2.23 0.51 0.14

294.97 294.95 294.94 294.92

6.14 5.99 5.85 5.73

1.20E5 2.64E4 6.34E3 1.82E3

n-Hexanol-Argon, 15-06-2000 TS2 ) 304.66 K, TC ) 265.11 K, P ) 100000 Pa, Q ) 5.07 cm3/s, Tlab ) 295.65 K TS1

N

Tnuc

Snuc

Jexp

300.32 300.10 299.93 299.73 299.53 299.36 299.14

403.09 199.72 103.51 52.94 26.31 15.01 8.72

268.91 268.88 268.88 268.85 268.85 268.78 268.78

10.68 10.51 10.38 10.23 10.07 9.96 9.79

5.49E5 2.80E5 1.48E5 7.77E4 3.96E4 2.31E4 1.38E4


N

Tnuc

Snuc

Jexp

310.49 310.92 311.35 311.67

10.31 38.29 172.97 502.25

280.25 280.28 280.31 280.34

7.65 7.88 8.11 8.28

1.92E4 6.75E4 2.89E5 8.06E5


N

Tnuc

Snuc

Jexp

311.48 311.16 310.71 310.32

327.14 103.86 21.96 6.64

280.31 280.28 280.26 280.23

8.18 8.01 7.77 7.57

5.40E5 1.79E5 4.00E4 1.27E4


N

Tnuc

Snuc

Jexp

320.78 321.21 321.65 321.65 321.43 321.00 320.60 320.22

47.29 211.12 821.92 831.11 430.06 115.86 27.57 8.42

290.01 290.02 290.05 290.05 290.05 290.01 289.98 290.94

6.53 6.70 6.88 6.88 6.79 6.62 6.46 6.31

9.55E4 4.04E5 1.49E6 1.51E6 8.01E5 2.28E5 5.70E4 1.82E4

a

The temperature of the preheater TS2 (K), the temperature of the condenser TC (K), total pressure P (Pa), the average flow rate Q (cm3/s), the temperature of the laboratory Tlab (K), the temperature of the saturator TS1 (K), particle concentration N (cm-3), the calculated temperature at the nucleation maximum Tnuc (K), saturation ratio at the nucleation maximum Snuc, experimental nucleation rate Jexp (cm-3 s-1). Temperatures of the preheater, condenser, and laboratory as well as pressure and flow rate are averages over one measurement session of an isotherm.

theory. The difference is slightly rising as a function of temperature, being about 6 orders of magnitude higher than theoretical predictions at 295.0 K. Isotherms plotted this way form a straight line. Straight curve, log Nexp ) intercept + slope × log Ntheor, was fitted to each isotherm. If the theory predicts correctly the experimental results, the intercepts should be 0 and slopes should be 1.18 Slopes and intercepts as a function of temperature at the nucleation maximum are presented in Figure 9. The average of the slopes is 0.98 with the statistical average error of 0.02. This implies that the saturation ratio dependency is well predicted by classical nucleation theory. It is also seen

that slopes have a clear tendency to get slightly smaller as a function of temperature. Values of the intercepts are almost constant, all values are between 5 and 6. Intercepts have a very slight tendency to get bigger as the temperature rises, which would imply a slightly stronger temperature dependency than theory predicts. Relationship (11) was applied to convert the experimental results from this study into conventionally used nucleation rate units. The results are shown in Figure 10. It is seen that the nucleation rates as a function of saturation ratio form almost a straight line. This can be used in determining the number of



Figure 8. Experimental particle concentration, Nexp, of n-hexanol as a function of theoretical predictions, Ntheor. Mean temperatures at the theoretical nucleation rate maxima are presented in the figure. The solid lines are fitted curves.

Figure 9. Intercepts and slopes from curve fitting to isotherms in Figure 8 as a function of the temperature, T, at the theoretical nucleation maximum. The white squares are the intercepts, and the black circles are the slopes.

Figure 10. Homogeneous nucleation rate, J, of n-hexanol as a function of saturation ratio, S. Experimental results are presented with black symbols. The mean nucleation temperatures corresponding to the series A-G are 265.0 (A), 270.1 (B), 274.9 (C), 280.0 (D), 285.1 (E), 290.0 (F), and 295.0 (G). Predictions of the classical nucleation theory are shown as dotted lines and symbols with primes corresponding to experimental temperature. The solid black lines are regression lines.

molecules in the critical cluster. The molecular content of the critical cluster was calculated by using a so-called nucleation theorem. It was first derived by Kashchiev32 and later in more general ways by Viisanen et al.33 and Oxtoby and Kashchiev.34 The nucleation theorem states

|

∂ ln J ≈n* ∂ ln S T

(12)

Equation 12 means that the size of the critical cluster at a constant temperature can be determined from the experimental results by calculating the slopes of the nucleation rates as a function of the saturation ratio.

Figure 11. Molecular content of the critical cluster, n*, of n-hexanol as a function of the critical saturation ratio, Scri, at 105 cm-3 s-1. The black circles are the experimental results calculated from eq 12. The solid line is a theoretical prediction from the Gibbs-Thompson equation.

Figure 12. Experimental nucleation rates, J, as a function of saturation ratio, S. Temperatures when helium is as a carrier gas (the black symbols) from right to left: 270.1, 280.0, and 290.0 K. Temperatures when argon is as a carrier gas (the white symbols) from right to left: 268.9, 280.3, 290.0 K.

In Figure 11 the number of molecules in the critical cluster is presented as a function of saturation ratio. The saturation ratio that is used is the experimental critical saturation ratio, at a nucleation rate of 105 cm-3 s-1. The theoretical predictions were calculated by using the Gibbs-Thompson equation (5) at the experimental critical saturation ratios. The number of molecules in the critical cluster determined from experimental results decreases as the saturation ratio rises, varying from 41 at 265 K to 64 at 295 K. The experimentally determined size of the critical cluster is well predicted by theory. This is quite surprising because in Gibbs-Thompson equation the bulk liquid properties are used. Comparison with Other Measurements. The results of the nucleation rates of n-hexanol from this study were compared to data published by Strey et al.35 They used a device where the supersaturation is achieved by adiabatic expansion. Strey et al.35 measured nucleation rates of series of a alcohols including n-hexanol in argon at temperatures around 258, 267, 277, 286, and 295 K in the two piston expansion chamber. The nucleation rate range is from about 106 to 109 cm-3 s-1. The temperature dependency is clearly different: Strey et al.35 report a weaker temperature dependency than predicted by the classical nucleation theory. In this study the temperature dependency is slightly stronger than the theory predicts. At the lower temperature range of this study the results are similar with Strey et al.,35 but the difference increases with temperature. Results from this study are about 5 orders of magnitude higher than results by Strey et al.35 at 295 K. Carrier Gas Effect. In Figure 12 the nucleation rates as a function of saturation ratio using both helium and argon as a carrier gas are presented. It is seen that nucleation rates in argon

Laminar Flow Diffusion Chamber for Homogeneous Nucleation are higher. The difference is reduced though at higher temperatures. A similar kind of behavior has been reported also by others. Vohra and Heist7 studied the critical saturation ratio of n-propanol in various carrier gases including helium and argon. The critical saturation ratios in helium were about 10% higher than in argon. Ha¨meri and Kulmala9 studied nucleation rates of dibutyl phthalate in helium, argon, and nitrogen. They also reported that nucleation in argon was stronger than in helium. The carrier gas effect has not been found in expansion type devices.33 This effect needs to be further studied. Accuracy of Experimental Results. The experimental results may be inaccurate for many different reasons. Most critical, considering the accuracy of the results, are the temperatures of the saturator and the condenser. Other possible sources of error in experiments are the flow rate, the total pressure, and the temperatures of the preheater and the laboratory. The temperature measurements were accurate within (0.05 K (according to the manufacturer). Calibration of the temperature sensors was done by the manufacturer. Temperature sensors were tested against each other in a heating bath. The results were within the accuracy given by the manufacturer. The temperature variation of the saturator, preheater, and condenser were within the accuracy of the temperature sensors during the measurements. Temperature variation in the laboratory during the measurements was typically about (2 K, and pressure variation was about (1%. Variation of the flow rate was less than (5%. The accuracy of the flow calibrator is (0.5% (according to the manufacturer). All these combined caused a change of about (70% to the calculated theoretical total particle output in the worst case. Converted into nucleation rate units this means that the experimental nucleation rate maximum changed about (1%, the saturation ratio at the nucleation rate maximum changed about (1%, and the temperature at the nucleation rate maximum changed less than (0.1%. The maximum deviation in particle concentration from the average value was less than (50%, which was determined from tests of repeatability and steadystate measurements. This deviation can be explained by the inaccuracy of the experimental parameters. As can be seen above, the inaccuracy of the parameters caused (70% change in the theoretical particle concentration. The variation in measured particle concentration caused the same amount of variation to the calculated experimental nucleation rate. Error in the calculated saturation ratio depends mainly on the accuracy of the binary diffusion coefficient. The deviation between the calculated and the measured binary diffusion coefficient is less than 3%. This causes less than a 2% error into the calculated saturation ratio. The total inaccuracy in the calculated saturation ratio was less than (3%. The accuracy of the critical saturation ratio consists of statistical error from line fitting, experimental error, and error from model calculations. The inaccuracy of the critical saturation ratio is less than 10%. The inaccuracy of the molecular contents of critical cluster was approximated to be less than 4%. This is the statistical error in a calculation of the slope of the log(S) - log(J) curve. Summary and Conclusions A laminar flow diffusion cloud chamber was developed for unary homogeneous nucleation rate studies. The main goal of this study was to build a device for producing reliable homogeneous nucleation rate data. Several experiments were made to verify and understand the operation of the device. These experiments showed that the different parts of the device work as was expected. It was shown that the developed mathematical model describes well the events inside the laminar flow diffusion chamber.

J. Phys. Chem. B, Vol. 105, No. 47, 2001 11629 Homogeneous nucleation rates of n-hexanol were measured. The results were compared to the classical nucleation theory. The saturation ratio dependency of the experiments is in good agreement with the theory. Experimental nucleation rates have a slightly stronger temperature dependency than the classical nucleation theory predicts. The molecular content of the critical cluster was well predicted by the Gibbs-Thompson equation. Homogeneous nucleation rates were compared to results by Strey et al.35 At lower temperatures the data agree quite well. However, the temperature dependency is different: This study shows a slightly stronger temperature dependency than the classical nucleation theory predicts. In contrast, the temperature dependency measured by Strey et al. is weaker than the theory predicts. In this study the carrier gas effect was found. The nucleation rates in argon were orders of magnitude higher than in helium. A similar behavior has been found also by others in a laminar flow diffusion chamber.7,9 References and Notes (1) Heist, R. H.; He, H. J. Phys. Chem. Ref. Data 1994, 23, 781. (2) Anisimov, M. P.; Kostrovskii, V. G.; Shtein, M. S. Colloid J. USSR 1978, 40, 90. (3) Anisomov, M. P.; Cherevko, A. G. J. Aerosol Sci. 1985, 16, 97. (4) Nguyen, H. V.; Okuyama, K.; Mimura, T.; Kousaka, Y.; Flagan, R. C.; Seinfeld, J. H. J. Colloid Interface Sci. 1987, 119, 491. (5) Okuyama, K.; Kousaka, Y.; Warren, D. R.; Flagan, R. C.; Seinfeld, J. Aerosol Sci. Technol. 1987, 6, 15. (6) Anisimov, M. P.; Ha¨meri, K.; Kulmala, M. J. Aerosol Sci. 1994, 1, 23. (7) Vohra, V.; Heist, R. H. J. Chem. Phys. 1996, 104, 382. (8) Ha¨meri, K.; Kulmala, M.; Krissinel, E.; Kodenyov, G. J. Chem. Phys. 1996, 105, 7683. (9) Ha¨meri, K.; Kulmala, M. J. Chem. Phys. 1996, 105, 7696. (10) Volmer, M.; Weber, A. Z. Phys. Chem. 1926, 62, 277. (11) Volmer, M. Z. Elektrochem. 1929, 35, 555. (12) Volmer, M.; Flood, H. Z. Phys. Chem., A 1934, 170, 273. (13) Becker, R.; Do¨ring, W. Ann. Phys. (Leipzig), 1935, 24, 719. (14) Zeldovich, B. Zh. Exp. Teor. Ph. (USSR), 1942, 12, 525. (15) Frenkel, J. Kinetic Theory of Liquids; Dover: New York, 1955. (16) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; John Wiley & Sons: New York, 1960. (17) Henwood, D.; Bonet, J. Finite Elements, A Gentle Introduction; MacMillan Press: London, 1996. (18) Hung, C.-H.; Krasnopoler, M. J.; Katz, J. L. J. Chem. Phys. 1989, 90, 1856. (19) Wagner, P. E.; Anisimov, M. P. J. Aerosol Sci. 1993, 24, s103. (20) Seager, S. L.; Geertson, L. R.; Giddings, J. C. J. Chem. Eng. Data 1963, 8, 168. (21) Reid, R. C.; Prausnitz, J. M.; Boling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. (22) Ha¨meri, K. Homogeneous Nucleation in a Laminar Flow Diffusion Chamber. Ph.D. Thesis, Department of Physics, University of Helsinki, Helsinki, 1995. (23) Schmelling, T.; Strey, R. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 871. (24) Strey, R.; Schmeling, T. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 324. (25) Handbook of Chemistry and Physics, 79th ed.; CRC Press: New York, 1998. (26) Landolt-Bo¨ rnstein, Zahlenwerte und Funktionen aus Physik Chemie - Astronimie - Geophysik - Technik; Springer: Berlin, 1960. (27) Timmermans, J. Physico Chemical Constant of Pure Organic Compounds; Elsevier: New Yord, 1950; Vol. I. (28) Mason, E. A. J. Chem. Phys. 1957, 27, 75. (29) Vasakova, J.; Smolik, J. Rep. Ser. Aerosol Sci. 1994, 25, 1. (30) Wagner, P. E.; Strey, R. J. Chem. Phys. 1984, 80, 5266. (31) Strey, R.; Wagner, P. E.; Viisanen, Y. J. Phys. Chem. 1994, 98, 7748. (32) Kashchiev, D. J. Chem. Phys. 1982, 76, 5098. (33) Viisanen, Y.; Strey, R.; Reiss, H. J. Chem. Phys. 1993, 99, 4680. (34) Oxtoby, D. W.; Kashchiev, D. J. Chem. Phys. 1994, 100, 7665. (35) Strey, R.; Wagner, P. E.; Schmeling, T. J. Chem. Phys. 1986, 84, 2325.

A Laminar Flow Diffusion Chamber for Homogeneous Nucleation

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