J. Phys. Chem. 1995,99, 16792-16799
16792
Homogeneous Nucleation of Vapors: Critical Supersaturation Measurements for Methanol, Ethanol, 1-Propanol, and 2-Propanol Richard H. Heist Department of Chemical Engineering, University of Rochester, Rochester, New York 14627-0166 Received: March 14, 1995; In Final Form: August 22, 1 9 9 9
We report data describing the temperature dependence of the critical supersaturation for methanol, ethanol, 1-propanol, and 2-propanol. The data obtained in this investigation came from two different thermal diffusion cloud chambers. A few data points were also included for comparison purposes from a literature report involving a third thermal diffusion cloud chamber (ref 22). Together, these data span temperature ranges of 150- 160 K. The critical supersaturation data were obtained using either helium or hydrogen as the background gas. On the basis of our observations for the temperature ranges and the total pressure (1.013 bar) employed in this investigation, we find that the critical supersaturations for all of these alcohols when hydrogen is used as a background gas are either equal to or greater than those obtained when helium is used as the background gas. This behavior is consistent with observations reported in refs 18 and 23 resulting from studies in which the dependence of the critical supersaturation of these alcohols on the background gas was investigated and in which the critical supersaturation was found to depend on both the kind of background gas as well as the total pressure.
Introduction Critical supersaturation measurements have, for many years, been the primary focus of homogeneous nucleation investigations. The strong dependence of nucleation rate on supersaturation made the concept of an “onset of nucleation” a reasonable measure of a critical supersaturation. However, this same strong dependence of rate on supersaturation made it difficult to obtain quantitative measurements of nucleation rate, which helps to explain the relative paucity of nucleation rate data prior to the early 1980s. During the last decade or so, because of significant improvements in diffusion and expansion cloud chamber technology, accurate nucleation rate measurements have become feasible, and this development has resulted in quantitative measurement of rates for a variety of substances as a function of supersaturation at various temperatures.’ A serious drawback of nucleation rate measurements that still exists, however, is the difficulty of obtaining nucleation data over wide ranges of temperature and pressure. This is directly related to the operational characteristics of the devices typically used for nucleation investigations and indirectly related to the strong dependence of nucleation rate on supersaturation. Ranges of temperature employed in recent nucleation rate investigations are typically somewhat limited (Le. usually 30-40 K and, occasionally, up to 80 K; see, for example, refs 2-5), and while much information concerning the relationship of rate to supersaturation and temperature and (recently) the size and composition of the critical n u ~ l e u sis~ obtained - ~ ~ ~ from these investigations, it is desirable (and, ultimately, necessary) to have nucleation data available over much wider ranges of temperatures. In addition to extending the range of nucleation measurements, another important issue of recent concern is the effect of background gases on the nucleation process itself. It has long been assumed that the presence of a noncondensable background (or carrier) gas during vapor to liquid homogeneous nucleation acts primarily to maintain the thermal environment and has little, if any, effect on the nucleation process itself. The ~~
@
Abstract published in Aduance ACS Abstracts, October 1, 1995.
0022-3654/95/2099- 16792$09.Oo/O
conventional models of nucleation (e.g. Becker-DoeringZeldovitch theory) do not, in general, account explicitly for the presence of a background gas. Until recently nearly all experimental nucleation data have been obtained at (relatively) low total pressures and have appeared to suggest no (significant) effect of background gas on the nucleation process. Moreover, most experimental devices used in nucleation research do not permit operation at elevated pressures or over large variations in total pressure, thus making it difficult to observe possible total pressure effects, if indeed any exist. Recent literature reports based on a variety of homogeneous nucleation experimental investigations have produced conflicting claims regarding the role of the background gas in the nucleation process. Nucleation rate data for the 1-hexanoYargon system,* the butanohrgon and methanoYargon system^,^ and the water/ (helium, neon, argon, krypton, and xenon) systems3 obtained using a modified version of the expansion cloud chamber, as well as nucleation onset data for the watednitrogen and ethanol/ nitrogen systems’O obtained using a supersonic nozzle, suggest no definitive effect of the background gas on nucleation. However, nucleation rate data for the water/(helium, argon) systems’’ obtained using an expansion cloud chamber indicate an increase in rate when using argon as opposed to helium, nucleation rate data for the nonanehelium s y ~ t e m ~obtained q’~ using a diffusion cloud chamber indicate a decrease in rate with increasing total pressure, critical supersaturation data for the stearic acidhelium systemI3 obtained using a diffusion cloud chamber indicate an increasing rate with increasing total pressure, and nucleation rate data for the dibutyl phthalate/ (carbon dioxide, helium) system^'^,'^ obtained using a flow diffusion cloud chamber suggest that the nucleation rate increases with increasing total pressure. Furthermore, recent model calculationsI6 which examine the dependence of the equilibrium distribution of precritical embryos on the system pressure suggest that there is a total pressure effect on the vapor to liquid nucleation rate and that this effect will depend upon the kind of background gas in use. Sample calculations for the n-nonane/(helium,hydrogen, argon) systems predicted that the nucleation rate would decrease as the total 0 1995 American Chemical Society
Homogeneous Nucleation of Vapors pressure increased and that this dependence would be small for helium and hydrogen but large for argon.16 These predictions agreed qualitatively with experimental trends although the predicted magnitude of the total pressure effects was considerably smaller than that observed. In addition, experimental results (at least until recently) show little or no background gas effect when argon is used whereas the model predicts the maximum dependence for this case. Also, the model calculations indicate that data obtained using expansion cloud chambers should exhibit larger total pressure effects than data obtained using diffusion cloud chambers, whereas exactly the opposite has been observed experimentally. It is certainly possible that the effect of total pressure on nucleation has not been widely noticed because most nucleation experiments are routinely performed at relatively low pressure and over small ranges of total pressure, e.g. 0.5 to 2 bar. It may be that larger variations in background pressure and operating temperature ranges are required to manifest the role of the background gas in the nucleation process. It may also be that background gas effects become small at lower pressures and that different substances exhibit different degrees of dependence on the presence of a background gas. While nucleation rate data often provides a more sensitive measure of nucleation effects, critical supersaturation data, carefully taken, should also allow observation of such effects provided appropriate temperature and pressure conditions are employed. What is clear, however, is that there exist considerable confusion and conflicting observations in the nucleation literature regarding the role of the background gas in nucleation. In this investigation we address the (relatively narrow) range of temperature currently available for most nucleation measurements, and we also examine the effect of background gases on vapor to liquid homogeneous nucleation in the range of relatively low total pressures to moderate pressures. Concerning the former, we present data (obtained using two different diffusion cloud chambers in this laboratory and supplemented with selected data from the literature) from measurements of the temperature dependence of the critical supersaturation for vapors of methanol, ethanol, 1-propanol, and 2-propanol. The temperatures employed in these studies range approximately from 230 to 410 K. The objective of these measurements is to investigate the homogeneous nucleation of vapors over wide ranges of temperature and thereby provide a rigorous basis of comparison for nucleation model descriptions. Regarding the latter, we present data obtained from critical supersaturation measurements as a function of temperature employing helium and hydrogen as background gases. The objective of these measurements is to ascertain a dependence of the critical supersaturation versus temperature data of methanol, ethanol, 1-propanol, and 2-propanol vapors on the kind of background gas used in the investigation.
Experiment Description and Procedure Two diffusion cloud chambers were used in this investigation. The first, the low-pressure diffusion cloud chamber (LPCC), was designed to be used at total pressures of 2 bar or less and lower plate temperaturesup to approximately 425 K. It consists of two aluminum plates of cylindrical geometry, 0.203 m in diameter and 0.02 m thick. These plates are separated by a Pyrex ring, 0.0254 m high with an inside diameter of 0.14 m. Viton gaskets were used to separate the Pyrex ring and the aluminum plates. The temperature of each plate was controlled to within 0.1 K by Haake constant temperature circulator baths attached to baths in direct thermal contact with each plate. The surface temperature of the working fluid pool on the lower plate was measured using a thermocouple inserted through the bottom
J. Phys. Chem., Vol. 99,No. 45, 1995 16793
plate, with the junction dimpling the surface of the pool. The top plate thermocouple was mounted in the plate with the junction located just above the surface interior to the chamber. During observation of the nucleation, a 150 V/cm dc electric field was connected across the two chamber plates. A more detailed description of the LPCC along with the associated gas handling system and the temperature- and pressure-measuring instrumentation is available elsewhere,*,I7so in the interest of space it need not be repeated here. The second chamber, the high-pressure diffusion cloud chamber (HPCC), is a specially designed high-pressure, hightemperature diffusion cloud chamber capable of operation at pressures up to 100 bar and lower plate temperatures up to approximately 525 K. The HPCC consists of two metal plates and a cylindrical quartz ring. Each metal plate is grooved for an O-ring which is used to provide a seal between the metal plate and the quartz ring. Silicon O-rings were used for methanol experiments,and Viton O-rings were used for ethanol, I-propanol, and 2-propanol experiments. The upper metal plate was machined from an OFHC, pure (99%+) copper blank. The lower metal plate was machined from a Cupronickel CDA 706 blank (10% nickel, 88.35% copper, 1.25% iron, 0.4% manganese). Both metal plates were finished to a diameter of 0.2032 m and a thickness of 0.0244 m. The interior surfaces of both plates have been polished to smooth, mirror-like finishes. Two holes have been drilled through the lower plate to accommodate thermocouples used to measure the temperature of the liquid pool, and two holes have been drilled part way into the upper plate to permit mounting of two thermocouples used to measure the upper plate temperature. Quartz was chosen for the cloud chamber ring because of the high tensile strength and low coefficient of thermal expansion of fused silica and because it permitted unobstructed viewing of the chamber interior. After the quartz was machined and polished, the outside diameter of the ring measured 0.1581 m, the inside diameter measured 0.1038 m, the wall thickness measured 0.0272 m, and the ring height measured 0.0152 m. The quartz ring was designed to withstand an internal pressure of 1.01 x lo7 Pa with a safety factor of 3 at ambient conditions. The inside diameter to height ratio of the quartz ring is 6.8 (approximately 7.5 when the depth of the liquid pool is included). During operation, the upper and lower plates are electrically insulated from each other allowing a 200 V/cm dc electric field to be applied across the plates during operation of the chamber. A more detailed description of the HPCC, the associated highpressure gas-handling system, and the temperature- and pressuremeasuring instrumentation is available e l ~ e w h e r e , 'so ~ ~in' ~the interest of space it will not be repeated here. The methanol, ethanol, 1-propanol, and 2-propanol reagents used as working fluids in this investigation were Baker Analyzed Reagent Grade purity and were used without further purification. The helium and hydrogen used as carrier gases were obtained from Air Products and were Ultra-Pure Carrier Grade, 99.999% purity. Chamber assembly and preparation procedures for this investigation are similar to those described elsewhere.*J8 In a typical critical supersaturation experiment involving either cloud chamber, the total pressure is first set to (approximately) the desired value. Next, the upper and lower plate temperatures are brought to their desired values with Haake constant temperature circulators. When the measured plate temperatures are steady and the total pressure is at the desired setting and the nucleation rate is steady at a rate of approximately 1-3 drops cm-3 s-l (with an applied dc electric field), the temperature of the working fluid pool surface on the
16794 J. Phys. Chem., Vol. 99, No. 45, 1995
Heist
lower plate, the temperature of the upper chamber plate surface, and the total pressure are measured and recorded. These data are used to determine the temperature and supersaturation profiles between the lower and upper chamber plates by solving the coupled energy and mass transport equations utilizing an appropriate equation of state for the system under investigation (see below). The temperature of each plate is then raised (lowered) to increase (decrease) the nucleation temperature and obtain a steady rate of 1-3 drops cm-3 s-I at these new conditions. In all cases the total pressure is maintained between two to three times the vapor pressure of the liquid pool on the lower plate (see the discussion section below).
4'5
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Temperature and Supersaturation Profile Calculation
where L is the scaled molar flux of diffusing material equal to Ih where 1 is the molar flux of diffusing material and h is the height of the diffusion cloud chamber, usually measured from the surface of the pool of working fluid to the upper plate at one-half the radius of the cloud chamber ring, c is the total molar density, 0 1 2 is the binary diffusion coefficient (assumed to be independent of composition), y is the mole fraction of the diffusing material, Tis the absolute temperature, z is the reduced chamber height defined by Z h where Z varies from 0 to h, aT is the thermal diffusion ratio defined by kd[y(1 - y ) ] where k~ is the thermal diffusion factor, Q is the scaled energy flux equal to qh where q is the energy flux, A is the mixture thermal conductivity, H i s the vapor enthalpy, and R is the gas constant. In writing eqs 1 and 2, we have assumed no external forces, no net pressure gradient, no chemical reaction, and one dimensional transport. We also recognized that one of the two components is stagnant. In applying eqs 1 and 2, we further assume they are valid over the pressure range of our experiments (e.g. Pro,I28 bar). In order to solve eqs 1 and 2 and obtain the necessary supersaturation and temperature profiles in the cloud chambers, we also require an equation of state. In this investigation we use the Peng-Robinson equation of state2OS2la 4T)
V(V+ b)
+ b(V- b)
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The general equations describing the mass and energy transport for lo? to medium total pressures in the diffusion cloud chamber for a two-component system areI8
p = - - RT ( V - b)
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where a(T) and b are material specific parameters, Vis the molar volume, and the other symbols are as defined above. In this investigation it is necessary to consider the effects of both the temperature and the total pressure on the various hydrodynamic and thermodynamic properties used in eqs 1 and 2 and on the boundary conditions necessary for the solutions eqsl and 2. All of the hydrodynamic and thermodynamic properties used in this investigation which are applicable at low total pressures have already been given elsewhere2,'* and need not be repeated here. Adjustments to those low-pressure expressions to account for increasing total pressure and elevated temperatures are discussed in detail elsewhereI8 and will not be repeated here. It should be mentioned, however, that in the
Figure 1. Experimentally determined variation of the critical supersaturation of methanol with temperature. The solid, convex curves correspond to experiments in which helium was used as the background gas, and the dashed, convex curves correspond to experiments in which hydrogen was used as the background gas. The solid curve labeled BDZ is the predicted variation of the critical supersaturation based upon the Becker-Doering-Zeldovitch theory. The numbers refer to the Data Set numbers in Table 1. 4.5
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Figure 2. Experimentally determined variation of the critical supersaturation of ethanol with temperature. The solid, convex curves correspond to experiments in which helium was used as the background gas, and the dashed, convex curves correspond to experiments in which hydrogen was used as the background gas. The solid curve labeled BDZ is the predicted variation of the critical supersaturation based upon the Becker-Doering-Zeldovitch theory. The numbers refer to the data set numbers in Table 2. total pressure range employed in this investigation, the effects of increasing total pressure on the various hydrodynamic and thermodynamic properties are minimal. In the determinination of the supersaturation and temperature profiles in the cloud chambers, eqs 1 and 2 are solved numerically subject to the assumption that the mole fraction of the diffusing vapor at the lower and upper liquid surfaces is given by the equilibrium mole fraction at the temperature of each surface. The measured upper plate temperature is corrected for the presence of the liquid film on the interior side of the plate. In the determinination of the equilibrium mole fractions, the Poynting equation2Ibis used to correct the equilibrium vapor fugacity for the presence of the carrier gas. In this investigation, the carrier gas was assumed insoluble in the working fluid, and the liquid was taken as compressible. Once the mole fraction and temperature profiles were obtained, eq 3 was used to obtain the corresponding fugacity profile. The supersaturation, S, is then
(4)
Homogeneous Nucleation of Vapors 4.5
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J. Phys. Chem., Vol. 99,No. 45, 1995 16795
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Figure 3. Experimentally determined variation of the critical supersaturation of 1-propanol with temperature. The solid, convex curves correspond to experiments in which helium was used as the background gas, and the dashed, convex curves correspond to experiments in which hydrogen was used as the background gas. The solid curve labeled BDZ is the predicted variation of the critical supersaturationbased upon the Becker-Doering-Zeldovitch theory. The numbers refer to the data set numbers in Table 3.
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Figure 4. Experimentally determined variation of the critical supersaturation of 2-propanol with temperature. The solid, convex curves correspond to experiments in which helium was used as the background gas, and the dashed, convex curves correspond to experiments in which hydrogen was used as the background gas. The solid curve labeled BDZ is the predicted variation of the critical supersaturationbased upon the Becker-Doering-Zeldovitch theory. The numbers refer to the data set numbers in Table 4. wherefis the vapor fugacity andfol is the equilibrium vapor fugacity of the diffusing material. The remaining symbols have already been defined. The result of one of the critical supersaturation experiments is a pair of (calculated) working fluid vapor supersaturation and temperature profiles between the two chamber plates. At the particular location in the chamber (typically 65-80% of the height between the lower plate pool and the upper plate surface) where the 1-3 drops cm-3 s-' rate of nucleation was observed to occur under the existing total pressure and plate temperature conditions, the supersaturation is the critical supersaturation, and the temperature is the nucleation temperature. The portion of the supersaturationprofile adjacent to this point when plotted as a function of the temperature profile adjacent to the nucleation temperature gives rise to a curve similar to those shown in Figures 1-4. Thus, each curve in these Figures represents one critical superFaturation experiment and the envelope of all the curves in each of the Figures 1-4 is the experimentally determined variation of the critical supersaturation with temperature for each of the working fluid vapors.
TABLE 1: Methanol Critical SupersaturationData background cloud data set TL (K) TU(K) PI,, (bar) gas chamber 1 268.2 231.2 0.3492 Hz 3 2 274.0 236.4 0.6744 Hz 3 3 284.1 246.3 0.8929 Hz 3 4 292.3 255.1 0.7318 Hz 3 5 296.0 257.0 1.6661 He 2 6 306.2 267.5 1.6261 He 2 7 308.5 270.7 0.8825 Hz 3 8 313.3 274.7 1.6261 He 2 9 318.6 280.0 0.8601 Hz 3 10 320.2 280.9 1.7594 He 2 11 324.5 284.4 1.7461 He 2 12 353.8 303.7 8.0100 Hz 1 13 366.1 315.8 5.7200 He 1 14 366.2 316.2 5.7200 Hz 1 15 378.8 326.7 11.650 He 1 16 391.8 339.5 19.000 He 1 17 403.5 350.9 19.580 He 1 18 417.4 361.7 27.580 He 1 TABLE 2: Ethanol Critical Supersaturation background data set TL (K) TU(K) PI,, (bar) gas 1 269.5 228.8 0.6656 Hz 2 276.0 235.8 0.6964 Hz 3 283.2 243.2 0.5070 Hz 4 288.9 248.8 0.5066 HZ 5 291.3 250.2 1.3995 He 6 300.3 258.5 1.0127 Hz 7 301.3 259.4 1.4529 He 309.1 268.6 8 0.5064 Hz 9 318.4 277.3 0.6731 HZ 328.8 287.1 10 1.0167 HZ 11 349.0 299.9 1.5800 He 12 355.7 306.1 2.4900 He 13 362.8 310.9 3.oooo He 14 371.1 319.0 HZ 3.9800 15 381.5 327.1 6.1600 Hz 16 390.6 335.6 8.0500 Hz 17 10.770 400.7 345.0 Hz 410.5 354.0 13.620 18 Hz 420.4 360.8 17.930 19 He 420.7 363.0 20 18.550 HZ TABLE 3: 1-Propanol Critical Supersaturation background data set TL(K) TU(K) Plot(bar) gas 1 294.9 248.3 1.3995 He 2 302.0 255.1 1.3329 He 3 304.7 259.1 1.3329 He 4 311.2 265.7 1.2796 He 5 315.6 269.7 1.2929 He 6 324.6 278.9 1.1996 He 7 336.1 288.8 1.5995 He 8 341.1 293.0 1.7328 He 9 367.8 313.0 2.2500 He 10 382.0 323.6 3.0300 He 11 393.7 333.3 5.1900 He 12 405.7 341.1 9.1900 Hz 13 He 417.8 354.3 10.100 14 437.9 370.9 He 17.170
cloud chamber 3 3 3 3 2 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 cloud chamber 2 2 2 2 2 2 2 2 1 1 1 1 1 1
Experimental Results In Tables 1-4 we list data set numbers for each experiment, the measured values of the (lower plate) working fluid pool surface temperature, TL,the upper plate temperature, TU,the total pressure, Ptot,the background gas used in the experiment, and the cloud chamber used to obtain the data for the working fluids, methanol, ethanol, 1-propanol, and 2-propanol, respectively. In these tables, cloud chamber 1 refers to the HPCC
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16796 J. Phys. Chem., Vol. 99,No. 45,1995 TABLE 4: 2-Propanol Critical Supersaturation background data set TL(K) TU (K) PtOt (bar) gas He 253.8 1.5995 1 298.0 He 1.4662 2 258.0 302.0 He 264.1 1.5595 3 309.3 He 1.4662 4 316.1 271.1 He 1.5995 5 280.8 325.8 He 287.5 1.7328 6 332.6 He 1.7194 7 294.0 339.6 He 2.6800 8 308.0 364.2 308.4 3.1300 9 366.0 H2 He 319.2 4.6000 376,l 10 He 7.5000 11 335.0 395.1 12 342.6 3.100 405.8 H2 He 13 344.1 0.020 406.6 He 4.500 14 356.2 420.5 15 H7 359.5 0.980 424.2 16 435.2 369.6 20.920 Hi 17 446.2 380.5 26.820 He
cloud chamber 2 2 2 2 2 2 2 1
1 1 1 1 1
1 1 1 1
described briefly above and used in this investigation, cloud chamber 2 refers to the LPCC described briefly above and used in this and earlier investigations,2 and cloud chamber 3 refers to the thermal diffusion cloud chamber used in an earlier (independent) investigation described in the literature.22 As explained above, each set of temperatures and total pressure corresponds to one experiment in which the nucleation rate was constant and observed to be in the range of 1-3 drops cm-3 s-’. Each of these sets of data was used to calculate the supersaturation and temperature profiles between the chamber plates corresponding to the observed nucleation rate. All the thermodynamic and hydrodynamic data for each of the four working fluids and each of the two background gases have been listed elsewhere and will not be repeated here.’8,23 These supersaturation profiles are plotted versus the corresponding temperature profiles in Figures 1-4 for methanol, ethanol, 1-propanol, and 2-propanol, respectively. Only the portions of the profiles adjacent to the region where nucleation was observed to occur have been plotted in the interest of clarity. The envelope of each set of these curves for each of the working fluids represents the experimentally determined variation of the critical supersaturation with t e m p e r a t ~ r e . ~ , The ~ ~ - ~actual ~ envelope has not been included in these figures for the sake of clarity. As a point of reference, the Becker-Doering-Zeldovitch (BDZ) nucleation theory prediction of the variation of the critical supersaturation with temperature is shown for each of the working fluid vapors as the solid, continuous curve spanning the entire range of temperature. The solid, convex curves represent critical supersaturation data obtained using helium as the background gas; the dashed, convex curves represent critical supersaturation data obtained using hydrogen as the background gas. The numbers labeling each of the individual curves correspond to the data set numbers listed in Tables 1-4, respectively.
Discussion and Conclusions Alcohols are one of the most widely studied substances in nucleation research.’ There are reliable nucleation rate data and critical supersaturation data (over limited ranges of temperature and pressure) available in the literature for alcohols.’ Furthermore, it has recently been decided to focus on one particular alcohol (I-pentanol) in an attempt to provide the nucleation research community and others with the most comprehensive set of nucleation rate and critical supersaturation data obtained from a variety of experimental devices ever ~ollected.~’It is important that we examine the nucleation of alcohols over as
wide a range of temperature and pressure as possible-this is one of the objectives of this investigation. Alcohols are known to undergo molecular association to various degrees depending upon temperature, pressure, and molecular weight. While association is more pronounced for the first few members of this particular homologous series, the actual effect is relatively small-compared, say, to the carboxylic acids-and diminishes with increasing temperature. Molecular association, in general, has been examined in considerable detail with regard to both diffusion cloud chambers and expansion cloud chambers. For example, the homogeneous nucleation of carboxylic acids and the effect of association on determining temperature and supersaturation conditions in a diffusion cloud chamber have been examined by the present a ~ t h o r . ~ ~ It - ~isO interesting to note that the alcohols that are expected to associate the most (Le. methanol and ethanol) appear to have the least dependence upon the kind and amount of background g a ~ . ’ ~ , ~ ~ It is also interesting to note that irregularities or “breaks” observed in the general shape of the critical supersaturation versus temperature curve have been suggested to be related in some way to associative effects exhibited by the alcohols.2There are, in fact, similar breaks in the shapes of the curves shown in Figures 1-4 in this paper. There is now evidence that this behavior is, in fact, due to the dependence of the nucleation on the background gas pressure and not on molecular as~ociation.~’ We might also note that similar background gas effects involving alkanes where molecular association is not an issue have also been observed in our laboratory. Several features exhibited by the plots in Figures 1-4 warrant additional comment: (1) The temperature range spanned by this data is 150- 160 K. This larger range of temperatures will make possible more extensive comparison of model calculations and experimental data. It is interesting to note in this regard that in each case the overall trend and (approximate) magnitude of the critical supersaturation dependence are similar to the BDZ prediction. (2) The critical supersaturation versus temperature profiles in ref 22 were originally calculated with the Wassiljewa coefficients in the mixture thermal conductivity expression set equal to unity. We have recalculated these profiles using the Lindsay-Bromley formalism for these coefficients. This is why the critical supersaturation data from ref 22 shown in Figures 1 and 2 appear different than those shown in the original reference. Details of this calculation are given elsewhere.2 (3) There are additional ethanol critical supersaturation versus temperature data available for somewhat lower temperatures than those shown in Figure 2.32 These data are plotted in ref 2 in comparison with other data shown there. These data depart significantly from the trend exhibited in Figure 2 in this paper. For this reason and because we choose to focus on similar ranges of temperature for the four alcohols examined in this investigation, we elect not to include these data in Figure 2. Generally speaking, the critical supersaturation data shown in all these plots obtained using hydrogen as the background gas is greater than or approximately equal to that obtained using helium as the background gas. In this regard, it will be helpful to compare a number of the observations from this investigation (evident in Figures 1-4) with results from our earlier studies of the total pressure dependence of the critical supersaturation of these same four alcohols. In what follows we shall refer to this previous workI8 involving 1-propanol as I and the previous workz3 involving methanol, ethanol, and 2-propanol as 11. Methanol. The curves for data sets 13 and 14 shown in Figure 1 suggest a small (but reproducible) difference in the critical supersaturation of methanol when using hydrogen or
Homogeneous Nucleation of Vapors helium as the background gas. In this temperature range, the value of H2SCI, the critical supersaturation measured with hydrogen as the background gas, generally exceeds the value , the critical supersaturation measured with helium as of the background gas. This behavior is consistent with our reported observations in 11. In that investigation, we reported that, at a temperature of approximately 333 K and total pressures in the range of 5 to 10 bar, H2SCr would exceed (by a small amount). We also observed in I1 that the values of H2SCr and He& for methanol would differ little over the 350-390 K (and presumably higher) temperature range and the range of total pressures used in our critical supersaturationversus temperature investigations. The curves for data sets 4 through 11 in Figure 1 indicate that H2Sc,is somewhat larger than over the temperature range 270-300 K. Unfortunately, the total pressure data reported in our earlier investigation do not extend to these lower temperatures. However, if those reported observations are extrapolated to lower temperatures and total pressures, we anticipate a somewhat larger difference between H2Sc,and with the former still being larger than the latter. This conjecture remains to be verified, however. Finally, we note that the curves for data sets 4 and 5 in Figure 1 suggest that H2Sc, is also larger than in the range of 270-280 K but that the difference appears small. As will be described below, this is a general observation we have made, and it is consistent with the results of a number of the reported investigations of background gas effects on homogeneous nucleation. At the lower temperatures and pressures used by a number of nucleation research groups, little, if any, background gas effect has been observed for a variety of substances and background gases. Ethanol. The curves for data sets 19 and 20 in Figure 2 over the temperature range 380-390 K indicate that the measured value of H2SCris slightly (but reproducibly) greater than the value of This behavior is consistent with reported observations in 11. In that investigation, it was reported that, at a temperature of approximately 383 K and total pressures in would exceed (by a small the range of 20 bar, H2SCr amount). As is evident in Figure 2, there are no overlapping helium and hydrogen background gas data in the temperature range 310-380 K. However, comparing the critical supersaturation versus total pressure data obtained in I1 in the range of 330-380 K and covering the same range of total pressures employed in this investigation with the data shown in Figure 2, we anticipate the values of H2Sc,and to be nearly the same over this range of temperature and total pressure. This behavior is, in fact, suggested by a comparison of the trend exhibited by the curves for data sets 11 through 13 and the curves for data sets 14 through 18 shown in Figure 2. The curves for data sets 4 through 7 shown in Figure 2 suggest that values for H2Scrare slightly larger than those for in this lower temperature range, e.g. 260-280 K. While data for this range of temperatures are not available in the results from our earlier investigation, if we extrapolate the trends exhibited by the data reported to lower temperatures and total pressures, the results we obtain appear to be consistent with the observation that H2SCr is larger than 1-Propanol. Our critical supersaturationdata for 1 -propanol with hydrogen as the background gas is limited. The curves for data sets 11, 12, and 13 in Figure 3 span the temperature range of 350-380 K and correspond to similar total pressures. For these data, the value of H2SCr is somewhat larger than that of This observation is consistent with results from I in which the value of H2SCr was also found to be somewhat greater than the value of at a temperature of 363 K and at total
J. Phys. Chem., Vol. 99, No. 45, 1995 16797 pressures ranging from 5 to 10 bar. If the trends observed in the total pressure dependence of the critical supersaturation data described in I are extrapolated to 350 K and to 380 K over corresponding ranges of total pressure, we also find behavior similar to the results shown in Figure 3. 2-Propanol. The curves for data sets 12, 13, 14, and 15 shown in Figure 4 suggest values for H2SCr over this range of temperatures and total pressures that are greater than values for . This observation is consistent with results from I1 in at 364 K and total pressures in the range which values for H2Scr 10-13 bar were found to exceed values for HeSc,,and, similarly, values for H2Sc,at 381 K and total pressures in the range 1420 bar were found to be greater than values for In addition, the curves for data sets 8 and 9 shown in Figure 4 indicate a larger value for H2SCr than for for a temperature range of approximately 330 K and a total pressure range of 2-3 bar. This is also consistent with results from I1 in which we found the value for H2Scrto be larger than that for at 332 K over a similar range of total pressures. To review briefly these results, we conclude, for the temperature and total pressure ranges employed in this investigation, that the measured critical supersaturations for methanol, ethanol, 1-propanol, and 2-propanol when hydrogen is used as a background gas are either larger or approximately the same as those obtained when helium is used as the background gas. Interestingly, the results presented in I and I1 indicate that as the total pressure is increased (at the same temperature) the measured value for eventually will become larger than the value for H2SCr(significantly larger in some cases). During critical supersaturation measurements, however, the temperature and total pressure conditions used for diffusion cloud chamber operation generally are not consistent with those necessary to that are larger than values for H2Sc,. produce values for The role of total pressure on the operation of the diffusion cloud chamber and the effect of total pressure on the nucleation data obtained using the chamber are becoming increasingly important issues. On the basis of the results of the investigations described in I and 11, increasing the total pressure of helium or hydrogen (as background gases) results in increasingly larger values of the measured critical supersaturation for methanol, ethanol, 1-propanol, and 2-propanol. We note here that similar results using the HPCC have been obtained using argon and nitrogen as background gases and using 1-butanoland n-hexane as working Increasing total pressure during diffusion cloud chamber operation cannot be done without limits, however. Stable (no convection) operation of the diffusion cloud chamber is essential in order to obtain reliable and reproducible results. One requirement for this stable operation is a continuously decreasing total density gradient from the surface of the liquid pool on the lower plate to the surface of the condensate film on the upper If the total pressure becomes too great, the mole fraction of background gas becomes so large in the upper (cooler) region of the cloud chamber that buoyancy-driven convection can result. Using the HPCC we are, in fact, able to easily observe this behavior. When a portion of the density gradient does reverse, what one often observes is copious nucleation brought about by increased mass transport due to the convection. We examined this behavior during measurements of the critical supersaturation of 1-propanol using helium as the background gas at approximately 270 K. We found that if we maintained the total pressure at or less than approximately 2.4 bar, the cloud chamber functioned normally. If, however, we increased the total pressure, copious nucleation was observed. Examining the calculated density profiles, we
16798 J. Phys. Chem., Vol. 99,No. 45,1995 found that above approximately 2.4 bar a portion of the density profile in the upper part of the cloud chamber reversed. Interestingly, decreasing the total pressure also has significant limitations. When the diffusion cloud chamber is used to obtain critical supersaturation data like that shown in Figures 1-4, it is usual to maintain the total pressure at least two to three times greater than the equilibrium vapor pressure (corrected for total pressure) of the working fluid at the‘temperature of the surface of the liquid pool on the lower plate. This ratio is routinely called the pressure ratio, PI. This is an empirical rule based on observations (from a number of laboratories) that diffusion cloud chamber operation and the quality of the resulting data appear to suffer as the total pressure falls below this range. What is often observed for small values of P, (less than 2, for example) is a decreasing value of the critical supersaturation. While this behavior seems to be consistent with the observed dependence of the critical supersaturation on total pressure at higher pressures, it appears to occur at low values of P, for a different reason. In I, we provided a simple, qualitative analysis of diffusion cloud chamber operation with the objective of examining the effect of P, on the mass and energy fluxes through the diffusion cloud chamber to illustrate why this ratio of total pressure to equilibrium vapor pressure at the lower pool surface temperature should, in fact, remain well above 2. According to that simple analysis, when the value of P, falls below the 2 to 3 range, the vapor flux through the cloud chamber increases significantly. Experimentally, this means we need to reduce the temperature difference between the upper and lower surfaces to maintain a nucleation rate of 1-3 drops cm-3 s-I. This results in a smaller value of the calculated critical supersaturation. Interestingly, this analysis also indicates that as PI is increased much above 3, there is little predicted effect upon the overall flux and, hence, the calculated critical supersaturation. This behavior is consistent with our observations (and those of other investigators) at lower temperatures but not at higher temperatures (see, for example, I and II). During measurements of the critical supersaturation of 1-propanol at approximately 270 K (see above), we varied the value of P, from 7 to 55 and observed no general trend in the value of the critical super~aturation.~~ At values of PI less than 2, however, the critical supersaturation decreases significantly. Clearly, by itself, the pressure ratio is of limited utility. These investigations suggest that to obtain with a diffusion cloud chamber critical supersaturation (and nucleation rate) data that may be compared with similar data obtained using other devices (i.e. expansion cloud chambers), it is necessary to keep the value of the total pressure large enough so as to avoid having a P, value that is too small, thus artificially lowering the value of the critical supersaturation, but not so large as to induce buoyancy-driven convective effects or to increase the value of the critical supersaturation due to the total pressure effects described in I and 11. The useful range of total pressures intermediate to these two extremes becomes increasingly smaller as the temperature is increased. During the course of this investigation, we maintained the total pressure at least two to thret times the vapor pressure of the working fluid (corrected for total pressure) at the temperature of the pool surface for all the critical supersaturation measurements involving the HPCC and LPCC illustrated in Figures 1-4. One of the concerns regarding the reliability of experimental data obtained using the HPCC and LPCC is the effect of the uncertainty in the values of the thermal diffusion ratio, the binary diffusion coefficient, and the mixture thermal conductivity (particularly with regard to the pressure and temperature dependence of these quantities) on the calculated supersaturation
Heist and temperature profiles obtained from solving eqs 1-4. We have examined this issue at some length in I and 11 and will not repeat the discussion here. It is also noted that the variation of total pressure used in this investigation is significantly smaller than that used in I and I1 with most of the results reported here corresponding to values of the total pressure less than 21 bar. A brief discussion concerning the general reproducibility of the critical supersaturation data shown in Figures 1-4 is appropriate. During this investigation (and the earlier investigations, I and 11,as well), we routinely would repeat data points to determine a measure of the degree of reproducibility. As discussed in I and II,when a critical supersaturation experiment was repeated and the observed rate was identical (within a factor of 2, to the eye), the supersaturation vs temperature profiles (shown in Figures 1-4) were nearly coincident. Agreement was generally as good as or better than the differences shown between the curves for helium data set 13 and hydrogen data set 14 in Figure 1 and between the curves for helium data set 19 and hydrogen data set 20 in Figure 2. When there was a small difference between two different supersaturation profiles, such as 13 and 14 in Figure 1 and 19 and 20 in Figure 2, several measurements were done to convince us of the reproducibility of the data. Finally, we present a comment conceming critical supersaturation versus nucleation rate measurements. Nucleation rate measurements are clearly important and useful, particularly when nucleation models are compared or when extreme sensitivity is appropriate (e.g. photoinduced nucleation, etc.). The author, in fact, was an early proponent of nucleation rate measurements. The author also believes that it is important to remember that critical supersaturation measurements have not been made obsolete and rendered useless because of the “state of the art” techniques that currently exist for nucleation rate measurements. When large ranges of temperature or pressure are accessible, the extreme sensitivity of nucleation rate measurements makes data gathering difficult (but not unimportant!) over these large ranges. It is convenient, certainly in the initial stages of an investigation, to utilize carefully obtained critical supersaturation measurements. It is useful to maintain the nucleation rate constant and examine the roles played by the temperature, supersaturation, and total pressure, just as it is useful to maintain the temperature constant and examine the roles played by the rate, supersaturation, and total pressure or to maintain the total pressure constant and examine the roles played by the temperature, supersaturation, and rate. We have adopted the former approach during our high-pressure and hightemperature nucleation studies to date, and that approach is reflected in the data presented in this paper. Nucleation rate measurements are part of our overall agenda.
Acknowledgment. The research described in this paper was supported in part by National Science Foundation Grant No. CTS 8919847. References and Notes (1) Heist, R. H.; He, H. J. Phys. Chem. Re$ Data 1994, 23, 781. (2) Kacker, A.; Heist, R. H. J. Chem. Phys. 1985, 82, 2734. (3) Viisanen, Y.;Strey, R.; Reiss, H. J. Chem. Phys. 1993, 99, 4680. (4) Katz, J. L.; Hung, C. H.; Krasnopoler, M. J. In Atmospheric Aerosols and Nucleation; Wagner, P. E., Vali, G. Eds.; Springer: Berlin,
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