Critical embryo phase transitions in the nucleated binary glycerin–carbon dioxide system

JOURNAL OF CHEMICAL PHYSICS VOLUME 109, NUMBER 22 8 DECEMBER 1998

Critical embryo phase transitions in the nucleated binary glycerin–carbondioxide system

M. P. Anisimov and J. A. KoropchakChemistry and Biochemistry Department, Southern Illinois University, Carbondale, Illinois 62901-4409

A. G. Nasibulin and L. V. TimoshinaGeneral Physics Department, Kemerovo State University, Krasnaya Str.6, 650043 Kemerovo, Russia

~Received 6 July 1998; accepted 3 September 1998!

In order to develop a consistent nucleation theory, the main assumptions of the theory should berevised. One of the questionable problems is the role of the carrier gas in nucleation and the surfacetension for the critical embryo as a function of cluster size. Using a flow diffusion chamber, thevapor nucleation rates were measured with high precision and phase transitions in critical embryoscontaining two and more dozen molecules were detected. Phase transitions in critical embryos wereused as markers to detect that the new phase critical embryos contain two components. Phasetransitions of the first order related with critical point second-order phase transitions in the pure CO2

carrier-gas were used as markers to demonstrate the presence of CO2 in critical embryos ofcondensate. Results of this research, in our opinion, very clearly demonstrate that vapor nucleationin a gaseous atmosphere is a binary process and must be interpreted from the point of view ofnucleation theory within a binary system. ‘‘Supercritical’’ nucleation is a virtual term born byinterpretation of binary vapor–gas nucleation by using the nucleation model of a single component.A critical condition for the binary system could be a higher level for the single component criticalpressure and/or temperature, which can produce the illusion of supercritical nucleation. Onecomponent interpretation can be used far from the critical condition. On the other hand, the Laplacepressure practically always is able to approach the nucleation condition to the critical pressure. Thislevel of detail is a problem for future studies. The traditional application of classical nucleationtheory for vapor–gas nucleation should be modified to consider the nucleation conditions inpressure-temperature-composition space. ©1998 American Institute of Physics.@S0021-9606~98!52146-0#

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I. INTRODUCTION

Studies of vapor nucleation are of significant interestthis is a fundamentally important problem of the first-ordphase formation kinetics description. Such informationnecessary to create computational engineering methwhich can be applied to modeling industrial new phase fmation processes. The current technical level of researchthe study of aerosol formation is of fairly high quality, bthere is no theory that is suitable for quantitative predictof experimental results.

The history of nucleation theory began about a hundyears ago. As a result of its rapid development, the classtheory of nucleation was created1,2 in the 1940’s. However, itmay hardly be considered as universal theory, because ocoincidence with experimental results within only a narrorange of temperatures and supersaturations for only ssubstances. In the common case, the theory of phase trtions cannot predict the phase transition pressure andperature nowadays, and includes a number of assumptiodescribe small clusters. Further, when the size dependenof the surface tension and density of nuclei were takenaccount3,4 and the inherent degrees of freedom were conered in the statistical sum for a nascent cluster,5 agreementbetween theoretical predictions and experimental resultsworse.

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In order to develop a consistent theory, the mainsumptions of the theory should be reconsidered. One ofquestionable problems is the role of the carrier gas in nuation and the surface tension behavior of the critical embas a function of cluster size. From the standpoint of classnucleation theory, a carrier gas does not participate information of critical embryos, but only serves as a mediuthat maintains an isothermal condition for the nucleation pcesses. Users of classical theory employ the bulk liquid sface tension to calculate the nucleation rates.

II. EXPERIMENT

A. Basis for an experimental research

To create a more accurate theory and gain a betterderstanding of the aerosol formation processes, new quative experimental results are required. In 1989 the potentity of the experimental detection of phase transitions insthe embryos of new phase was shown on the basis of criembryo size measurements.6 It is well known that the equi-librium freezing–melting temperature in the bulk condensphase is stable for a single component system. Withcooling, one can detect supercooled liquid and a freezpoint which is lower than the equilibrium temperature trasition from the liquid to crystal state. Small pressures~up to

4 © 1998 American Institute of Physics

IP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp

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10005J. Chem. Phys., Vol. 109, No. 22, 8 December 1998 Anisimov et al.

1 MPa! do not influence the freezing temperature, i.e.,liquid–solid line of an interphase equilibrium is practicalvertical in the pressure-temperature axes for all compouThe dT/dP values7 are around or less than 1.1 K/MPa~ure-thane!. In the case of a binary system, the second componcan shift the melting point more effectively. This means ththe temperature of the phase transition in the condensedcould be used as a marker to identify that a system is binA system with a phase transition in the condensed state cbe used to study the role of a carrier gas for vapor nucleain a gaseous atmosphere.

It is well known that the chemical potential of a codensed phase has a singularity at the first-order phase trtion temperature. The Gibbs’ free energy of a critical embof a condensed phase, and therefore, the vapor nuclerate, must respond to the nonmonotone temperature behof the chemical potential near the phase transition. Thaone can use the nonmonotone temperature nucleationbehavior of the nucleation rate to detect the phase transin a condensate.

Using this point, it is attractive to study glycerin vapnucleation, because of the phase transition~freezing–melting! of glycerin, which occurs at a temperatureTmelt

5292.4 K. If carbon dioxide is used as the carrier gas aenters a glycerin critical embryo, one should detect incondensate the phase transition related to the cadioxide–glycerin critical line. Carbon dioxide (CO2) has alow critical temperatureTcr5304.2 K and critical pressurePcr57.39 MPa, where a second-order phase transitioncurs. A simplest estimation of the Laplace pressure, obtafrom the bulk surface tension for the glycerin critical embryos, gives a pressure of more than 40 MPa. This presis supercritical for CO2, as well as~shown below! for thebinary system of glycerin–carbon dioxide. One could fithe phase transition, related with the critical line of thenary system, if the system under investigation is bin~components have at least partial solubility!. Any glycerinphase transitions~except transition at critical point! higherthan the glycerin melting point are unknown. Detection ophase transition at a temperature higher than the glycmelting point in condensate should guarantee that the cagas (CO2) molecules enter into the critical embryos antherefore, indicate that the nucleation of the carbon dioxidglycerin system is a binary nucleation. If the carbdioxide–glycerin system is a binary phenomenon, the sface tension for critical embryos should be analyzed asurface tension of the binary system.

In the present work, nucleation of a carbon dioxidglycerin system in the vicinity of the glycerin melting poinand CO2 critical temperatures is studied. It is necessarynote that the applied pressure interval 0.10–0.30 MPa forsystem under investigation is much less than the critical psures of the gas-carrierPcr57.39 MPa. However, if theLaplace pressure is taken into account, the embryo ofnew phase formation conditions should be near, butthan, the system critical pressure.


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B. Experimental scheme

Aerosol formation was experimentally studied in a flodiffusion chamber, which is suitable to measure the depdence of the nucleation rate on the glycerin vapor activitydifferent pressures of the carrier gas.

The experimental setup~Fig. 1! contains an aerosol generator~1!, which consists of hot~A,B! and cold thermostats~C!. A high-pressure cylinder provided the inert carrier g~with purity 99.99 vol. % or higher! which maintained theflow, via a pressure gas reducer, filter, flow meter, and psure regulator, to the hot thermostat. Then, gas pasthrough a chromatographic carrier, alumina,~A! where vaporsaturation of the substance under investigation occurredside the second thermostat~B!, a steady-state laminar flowwas established. The vapor–gas mixture becomes superrated in the cooler~C!, because of molecular diffusion anheat transfer. Aerosol particles are produced in the vicinitythe highest vapor supersaturation. The volume rate offlow was controlled to the level of 6.10 cm3/s, which guar-anteed laminar flow inside the aerosol particle generaTemperature was measured with copper-constantan thecouples, which were calibrated in the appropriate tempeture range by using mercury thermometers with an accurof 0.1 °C.

The aerosol concentration was measured by a lasertoelectric aerosol counter~2!. Computer control of the aerosol concentration allowed the achievement of sufficient stistical data in the complete range of the experimenaerosol nucleation rates achievable in these experiments.relative error in an aerosol concentration did not exceedin these experiments. The sensor’s signals were digitizedstored in buffer memory and then passed to a personal cputer ~3! for further processing.

C. A vapor nucleation rate evaluation

The vapor activity of the substance under investigatwas evaluated by computer solution of heat and mass trfer equations for steady-state laminar axisymmetrical viscvapor–gas flow. This steady-state vapor–gas flow maydescribed by a set of Navier–Stokes equations; in the cydrical coordinate system, they can be representedfollows:8

P5rR0T/m, ~1!

FIG. 1. Experimental setup scheme. 1-aerosol generator, containingthermostat with vapor saturation volume,A, laminator,B, and cooler,C;2-laser aerosol counter; 3-system for computer collection of experimeparameters.


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10006 J. Chem. Phys., Vol. 109, No. 22, 8 December 1998 Anisimov et al.

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Here,x is the coordinate along the axis of a cylindrical tubr is the coordinate along its radius,u is the velocity of thegas;T is the temperature;P is the pressure;r is the density ofthe gas;h andl are its viscosity and heat conductivity, respectively;Cp is the heat capacity of the gas;Ro is the uni-versal gas constant;m is the molecular weight of the gas;Ris the radius of the tube; andQ is the mass flow rate of thegas.

The carrier gas flow was described by Eqs.~1!–~4! withthe following boundary conditions:

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u~R,x!50, T~R,x!5Tc~x!, ~5!

T~r ,0!5To~r !, u~r ,0!5uo~r !,

whereu(R,x) andTc(x) are the given gas flow velocity antemperature at the tube wall; andTo(r ) and uo(r ) are theinitial gas flow uniform temperature and velocity distributioat the inlet of the tube, respectively. The effect of mingaseous admixtures~vapor of the substance under investigtion! on the density, heat capacity, viscosity, and head cductivity of the carrier gas was neglected. The velocity atemperature space distribution for the carrier gas were foby numerical solution of the Navier–Stokes Eqs.~1!–~4!with the boundary conditions~5! by the finite-differencemethod.

Vapor diffusion in a steady-state laminar flow of a vicous gas within a cylindrical tube was described for the stem under investigation by the molecular diffusion equatiin the cylindrical coordinate system, it assumes the form

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Here,C is the mass concentration of the vapor of substaunder investigation;D is the molecular diffusion coefficientC0(P,Tc) is the concentration of saturated vapor at the tuwall ~the walls of the tube are assumed to be covered wthe glycerin film!; andC* (r ) is the initial uniform concen-tration profile for vapor at the inlet of the tube. The flovelocity distribution in the tube inlet cross section wassumed to be a Poiseuille’s profile. The viscosity of carb


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dioxide h (Pa3s) was calculated using an approximatioequation, obtained on the basis of handbook data7

h525.03733102715.68731028T21.729310211T2.

The activity of glycerin vaporsa(r ,x) was evaluated byusing the temperatureT(r ,x) and concentrationC(r ,x) dis-tribution as

a~r ,x!5C~r ,x!

C0~r ,x!,

whereC0(r ,x) is the equilibrium concentration of saturateglycerin vapor at the temperatureT(r ,x).

The pressure of saturated glycerin vapors,9 P ~mm Hg!,was approximated by the Clapeyron equation log(P)5A2B/T, whereA511.44 andB54532 for conditions of theseexperiments.

The diffusion coefficientD ~cm2/s! was calculated forthe glycerin–carbon dioxide binary gas system by usingempirical correlation by Fuller, Schettler, and Giddings10~a!

D53.3979•1026T1.75

P,

where P is expressed in bar. The heat conductivityl~J m21 s21 K21! of carbon dioxide was approximated by aequation

l5T1.75~P3e1k!1~P23 l 1Pm1n!,

based on the published data,11 wheree524.419 9531029,k55.749831027, l 59.547731027, m51.551031024, n54.069331023, P is expressed in physical atmosphereThe maximum rate of aerosol particle formation was callated by using the algorithm developed for the flow diffusichamber by Wagner and Anisimov12

Jexpmax5

Nexp Jtheormax

*Jtheordv,

whereNexp and*Jtheordv are the experimental and theorecal numbers of particles produced by the aerosol generper unit time, respectively;Jtheor

max is the maximum of the the-oretical nucleation rate in the experimental device. The toretical nucleation rate was calculated by using the classnucleation theory13

Jtheor5V

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wheres is the surface tension;m, V are molecular mass anvolume, andlnS is the vapor supersaturation~or vapor activ-ity!.

The relative error for vapor activitya and nucleationtemperatureT did not exceed 2% to 3%. By determining thnucleation rate with high relative accuracy, it is possibledetect the critical embryo phase transitions with confidenThe absolute error was some percents larger than the relerror due to inaccuracy of thermophysical constants. Thetal relative error for the nucleation rateJ was about 25% or0.1 decimal order.


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III. EXPERIMENTAL RESULTS AND DISCUSSION

Isothermal nucleation of supersaturated glycerin vapin the carbon dioxide atmosphere was studied in the tempture interval of 283.2–331.4 K at the total pressuresP50.10, 0.20, and 0.30 MPa. Figures 2–4 display the expmental nucleation rates, logJ, versus activity of glycerin va-pors, loga, at different nucleation temperatures and topressures.

The experimental glycerin vapor activity on nucleatitemperature at fixed nucleation rates (logJ52.0;4.0) isshown in Figs. 5~a!–5~c!. The singularity temperature behaior for vapor activity allows identification of two-phase trasitions in the condensate. One of them is two degrees cegrade higher than the equilibrium bulk glycerin meltingfreezing temperature in CO2 atmosphere at the total pressuof 0.10 MPa. We suggest that this singularity identifiesphase transition with glycerin embryos freezing–meltinThe narrow temperature interval~2–6 °C! of phase transi-

FIG. 2. ~a! and ~b! Glycerin nucleation rate,J, on the vapor activity,a, attotal pressureP50.10 MPa.


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tions, shown by the shaded strips in Figs. 5~a!–5~c!, illustratethe low ability of condensate embryos to be in metastaliquid and crystal states. By application of the equation14

S ] ln J

] ln aDT,P

5n12,

the number of glycerin molecules (n* ) in critical embryoswas evaluated. Results are presented at the same Figs.~a!–5~c! by diamond-shaped signs. It can be seen that invicinities of the phase-transition temperatures, thereanomalous jumps in the embryo sizes.

As mentioned above, a glycerin first-order phastransition higher than the glycerin melting point is unknowPhase transitions were found at temperatures higher thanglycerin melting point. The temperature of this second trasition comes nearer to the carbon dioxide critical temperawhen the carbon dioxide partial pressure is higher. For thtwo reasons, the second break on the loga(T) curve should



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be identified as the phase transition related with the critpoint of carbon dioxide. This result indicates that carbdioxide is incorporated inside the critical embryos of tsystem under investigation. Because the experiment shthat carbon dioxide exists inside embryos of the new phasystems such as carbon dioxide–glycerin should be conered as being binary systems.

As shown in Figs. 5~a! and 5~b!, the phase-transitiontemperatures for single CO2 and glycerin phase transitionand the experimental values for the system under investtion increase to 7° when the CO2 atmosphere pressure increased up to 0.30 MPa. The break related with the melpoint shifts to higher temperatures when the total pressincreases~at the system pressureP50.10 MPa: 293.8–295.9K; at the pressureP50.20 MPa: 295.9–298.0 K; underP50.30 MPa: 298.0–300.1 K!. The temperature interval othe next phase transition has the opposite trend: Withcreasing pressure, the phase-transition temperature is



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ered~at the system pressureP50.10 MPa: 315.9–319.0 Kat the pressureP50.20 MPa: 314.8–316.9 K; and atP50.30 MPa: 310.7–314.8 K!.

The supercooled vapor could produce supercooled liqglycerin. This should reduce the temperature for freezingglycerin as in the case, for example, of freezing of C6F5OH15

and other compounds. The experimental results show theposite trend for the glycerin–carbon dioxide system. Tphase-transition latent heat cannot initiate the trend in thexperiments. This heat is insufficient to increase the clutemperature, because the CO2 and glycerin partial pressurdiffer by four orders of magnitude. The correspondinghigher CO2 collision frequency with growing clusters avoidsuperheating of the new phase embryos.

At critical conditions~critical point or critical line, forbinary system!, phase transitions of the second order taplace. At the critical condition, the surface tension and nucation rate drop to zero, because phase transitions of theond order have no different phases nor any interfacefaces. Nonzero nucleation rates correlated with the critline of the carbon dioxide–glycerin system were measure

FIG. 5. ~a!–~c! The experimental glycerol vapor activities,a, on nucleationtemperatures,T, at fixed nucleation rate$lgJ52.0 ~j!; 4.0 ~d!% and totalpressuresP50.10, 0.20, 0.30 MPa. The number of glycerin molecules,n*~l!, in critical embryos vs the nucleation temperature,T, at lgJ53.0.


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the given research. This means that the nucleation conditfor this phase transition are under critical. It is also obviothat the detected phase transition is of the first order, becthe smallest deviation to lower temperature from a vapliquid critical condition temperature leads to phase trantions of the first order.

Critical points for single components in the case obinary system produce the critical line from one to anotcritical point. The method offered by Li, Kreglewski, anKay10~b! was used to evaluate the critical line temperatuand pressures for the system under investigation. The critemperatures and pressures for the system glycerin–cadioxide versus composition are presented in Fig. 6. Onesee that the system critical pressures do not exceed 25 Mwhich is much less than an our estimation of critical embpressure, 40 MPa, in a droplet approximation with a surftension of bulk glycerin. This means that the surface tensof critical embryos is smaller than the bulk glycerin surfatension. In approximation of the bulk liquid density, the crical embryo surface tension is smaller by 38% than the bglycerin surface tension.

As mentioned above, the Laplace pressure in critical ebryos of glycerin is high enough to establish conditionscritical embryo formation near the critical pressure. Lowing of the second phase-transition temperature with increing mole fraction of the carrier gas was observed. It can

FIG. 6. ~a! Carbon dioxide–glycerin system critical pressure,P, and ~b!temperature,T, on glycerin mole fraction.


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seen from Figs. 5 and 6 that lowering the phase-transitemperatures has good correlation with lowering of the crcal line temperature with increasing gas-carrier pressure~ormole fraction!. We should note here that phase-transititemperature can only have correlation with the critical teperature of the system under investigation. We have insucient knowledge about the pressure and composition of nphase embryos for more careful analysis. On the other hthe relationship of the second phase transition with the ccal line of the glycerin–carbon dioxide system is very cleashown in our experiments. Such system behavior has gqualitative agreement with the calculated trend for critictemperature of a binary system@Fig. 6~b!#. This conclusion isin agreement with preliminary results of the glycerin–sulfhexafluoride system,16,17 where a phase transition of criticaembryos was detected too.

During the last decade, there has been discussion ofrole of the carrier or background gas and the effect ofpressure. For example, Katzet al.18,19 have observed a gapressure effect on vapor critical supersaturation. With resgiven here, the validity of interpretation of glycerin vapnucleation in helium, argon, and nitrogen atmospheres inapproximation of binary ideal solutions20 increases. Heistet al.21 have reported strong effects of pressure and theture of the carrier gas on vapor nucleation rates at pressup to 40 bar. On the other hand, good quality measuremwith expansion chambers have shown no effects of theture of the background gas on nucleation rates.22,23 Wagneret al.22 conclude that there is no influence of the carrier gon the vapor nucleation. All of the carrier gas effectsnucleation can to be explained by the thermal effectsnucleation and the kinetic properties of a nucleated vapormixture. To test this point a special analysis of heat-mtransfer in a cloud diffusion chamber was done.24

Seemingly, the results of our research contain enoevidence for the point of view that vapor nucleation in a gatmosphere is binary nucleation. In a common casevapor–gas nucleation, the presence of the critical line fobinary vapor–gas system should be found. Ideas of thepology of the equilibrium interface surfaces for binary~ormulticomponent! phase state diagrams described, for eample, by Prausnitzet al.10~c! should be involved for inter-pretation of a vapor–gas nucleation rate surfaces.

In Fig. 7 is shown comparison of the experimental nucation rates with classical nucleation theory at four nucleattemperatures and a total pressure 0.10 MPa. It can bethat experimental curves at 327 and 304 K could be theorcally described by fitting the theory parameters. For eample, surface tension variations of 0.1%–0.3% can chathe theoretical nucleation rate by some orders of magnituThe next two experimental curves could be fit only wiconsiderable change in the number of molecules in the nphase embryos. Using the surface tension of bulk liqcould lead to considerable contradictions of classical thewith experimental results on nucleation rates, when the ccal line for the vapor–gas system limits the critical embrynucleation conditions. The surface tension for critical ebryos should be used in the approximation of a binary s


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tem. This will lead to considerable progress in classitheory application.

IV. CONCLUSION

Using a flow diffusion chamber, one can measure vanucleation rates with high precision and detect phase trations in critical embryos containing two and more dozmolecules. Related with the glycerin–CO2 critical line, aphase transition can be used as a marker to demonstrateCO2 exists in critical embryos of condensate. In our opinioresults of this research very clearly demonstrate that vanucleation in a gas atmosphere is binary nucleation and mbe interpreted by using formalism of a binary system. Supcritical nucleation is a virtual term born by interpretationbinary vapor–gas nucleation in the approximation of a sincomponent. It is well known that nucleation can take plaonly under the critical condition, because a supercritical flhas no ability to be heterogeneous. The critical conditionthe binary system could be higher than the single componcritical pressure or/and temperature. This can produceillusion of supercritical nucleation. One component interptation for a vapor–gas nucleation could be used if oneevidence that a carrier gas influence on nucleation is smenough to use the one component nucleation theory fordescription of experimental results. On the other hand,Laplace pressure is practically always able to produce ncritical pressure. This level of detail is a problem for futustudies. The traditional application of classical nucleattheory for the vapor–gas nucleation will be modified by cosideration of nucleation conditions in the pressutemperature-composition space.25

FIG. 7. Comparison of experimental nucleation rates,J, vs glycerin vaporactivity, a, of carbon dioxide–glycerin system with classical nucleatitheory ~Ref. 13! at total pressureP50.1 MPa.


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ACKNOWLEDGMENTS

The authors acknowledge John M. Prausnitz, whose 7birthday is being celebrated by the scientific communnow, for the main idea of this research. The work at SouthIllinois University was partially supported by funds from thNational Science Foundation and U.S. Army Research Of~ARO 125-94! through Grant No. CHE-9311427. Grant NRFBR 97-03-33586 to Kemerovo State University is aknowledged for the partial support of the work there.

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21R. H. Heist, M. Janjua, and J. Ahmed, J. Phys. Chem.98, 4443~1994!.22P. E. Wagner, R. Strey, and Y. Viisanen,Nucleation and Atmospheric

Aerosols, Edited by N. Fukuta and P. E. Wagner~Deepak, Hampton,Virginia, 1992!, pp. 27–29.

23Y. Viisanen, R. Strey, and H. Reiss, J. Chem. Phys.99, 4680~1993!.24A. Bertelsmann and R. H. Heist, J. Chem. Phys.106, 610 ~1997!.25Experimental values of saturation temperatures, aerosol concentratio

the cold thermostat wall temperatures, and total vapor–gas press~more than 3000 points! are available on request.


Documents

Critical embryo phase transitions in the nucleated binary glycerin–carbon dioxide system