271
J. Phys. Chem. 1993, 97, 271-278
Condensation Flux Estimates Derived via a Kinetic-Molecular Model S. H.Bauer' and C. F. Wilcox, Jr. Baker Luboratory of Chemistry, Cornel1 University, Ithaca, New York 14853- 1301 Received: July 7, 1992; In Final Form: October 15, 1992
The readily calculable format of our previously published kinetic-molecular model for condensation rates was tested on 14 diverse systems. A single adjustable parameter (SP) that represents the collisional efficiency for removal of the heat of condensation (and thus stabilizes the nascent clusters) permits estimation of flux values to well within the experimental error limits. The deduced range of excursions of SP is 0.2-1 -0; it increases with declining temperature. This trend parallels the temperature dependence observed for other direct association reactions and for deexcitation cross-sections of energized molecules undergoing unimolecular dissociations. Regrettably, there are no reliable data for condensation rates from supersaturated vapors of metals, metal oxides, or other refractory materials upon which our model can be tested.
Introduction
During the past year we undertook an extended reanalysis of
-
S(T;J) functions, i.e. of critical levels of supersaturation for the onset of condensation (vapor droplets) at selected temperatures and observed fluxes. The published data were interpreted in terms of a self-consistent kinetic-molecular model that we initially proposed in 1977.' This approach was recently amplified and reduced to a computer code-for a PC.* Here we report on the successful resolution of J(S;T)values for 14 systems, representativeof a widevariety of molecular species. We achieved several objectives: (i) While the model incorporates many molecular parameters, the prescription for assigning values to all but one was fixed for all systems, based on known molecular properties. (ii) The two most sensitive model parameters have been identified; however, we found it expedient to fix the magnitude of one of these and use the other (which has an obvious kinetic-molecular interpretation) as an overall fitting parameter. (iii) The magnitudes of this parameter (designated SP) range from 0.2 to 1.0, and its variation with temperature is consistent with that found for other types of association reactions. It is our hope that the derived magnitudes for classes of compounds are typical, so that this model will provide a means for predicting S(T;J) functions to a useful level of reliability. Section I is a brief review of the basic kinetic relations to establish the nomenclature for the subsequentdiscussion. Section I1 is devoted to comments on the status of the available experimental data and to a justification of the procedure we followed to extract values of Jexp(T;Scxp) for comparison with correspondingcomputedvalues. Section I11 is devoted to sections of a table, with explanatory comments on each of the 14 systems that wereanalyzed. Mentionismadeofthreemetalvaporsystems, for which fragmentary data havebeen reported, that defy complete analysis. This report concludes with Section IV-a discussion of the kinetic-molecular significance of the S P parameter.
all species present in the ensemble that can serve as stabilizing collision partners. The species X consist principally of AI and any added "inert" gas. To a sufficient approximation:
[All + X[RgI (3) In this formulation K , , ~ ( K - ~ ~are ) deexcitation (excitation) rate constants for collisions with X; X (-0.10-0.05) takes into account the lower efficiency for energy transfer via R,. Theproduction rate of A, is [XI,,=
(4)
Upon imposing the steady-state approximation for the shortlived C, (present in relatively low concentrations), one arrives at
The production rate is controlled by the small difference between the two large numbers within the [ ] brackets. The partial derivative dN,/dt], is independent of u during the steady-state period; it is identified with Jcxp,the number of visually observed droplets that appear per cubic centimeter per second, and approaches zero when the system drifts toward equilibrium. The latter condition is constrained by thermodynamics. Thus, for the overall conversion u A + A,
Section I
The kinetic model is based on the sequence of reactions Mu0 -
X-"
A,-, + A , =, C ,
(1)
XY
C, is a nascent u-mer that has not yet been stabilized. The heat of condensation is removed from the cluster by
+ X =, A , + X* K-Y,
C,
(2)
XY.
The * designatesthe kinetic energy carried by X,which represents 0022-3654/58/2097-0271$04.00/0
K,_,,U(C)= RTexp[-
RT
(7) The enthalpy and entropy increments refer to conversions under standard state conditions. The K'S can be expressed in terms of molecular parameters and fundamental constants. The ratio ( K , / K - " ) is an equilibrium constant for particles interacting pairwise via a Lennard-Jones 0 1993 American Chemical Society
Bauer and Wilcox
272 The Journal of Physical Chemistry, Vol. 97, No. 1, 1993
potential (modeled after the theory for atom/atom recombination38) :
The K,'S are collisional rate constants between monomers and (u-1)-mers, each at unit concentration, interacting along an attractive L-J potential with a hard repulsive core:3b
(programmed on a PC).
wherein u = (I + 1). We introduced two major assumptions, which were justified empirically: -Muo = u Q ( T ) [ 1 - Au-']
K,D,-' = 0.7937(kbT/h);
is the reciprocal of the mean duration of the interaction between A,,-! and AI and is dependent on T only. The stabilization constant K , , ~ is the binary collision rate constant between the transient C, and X (also controlled by a hard sphere +r6 attractive potential) but is modulated by a relative efficiency factor for energy transfer that depends primarily on the temperature, and slightly on u. The encounter frequency is3b K-,
K - ~
(15)
where Q( T) is the standard heat of vaporization at T and A = 0.85 and B = 'u
(;){SlM,'l
- kbTj
(16)
where S)AHUol= IAHUoI- IAH,-I'I. e, is the depth parameter in the Lennard-Jones potential between colliding u-mers and monomers; it appears in the evaluation of w ( ...). Section I1
Then
= W(c,;x)sP (11) The stabilization parameter corresponds to the conventional 'sticking coefficient". K-,,, expresses the activation step for evaporation, similar to that for a unimolecular decomposition. Based on RRK formalism for unimolecular dissociation K,,
L,. Then &-I,,, = D,L,, which relates Let the ratio [ K , ~ / K - , , ] the thermochemical terms to the kinetic terms:
PAS,'
A M , ' + R In L , + R l n - DU AS,' - ASU-1' = RT T
(13) where
AM,,'
AH,' - AHu-lo
It follows that, given magnitudes for the rate constants (all the the time-dependent concentrations of clusters of all sizes can be calculated. The onset of essentially unidirectional cluster growth (determined by eq 5) becomes evident from inspection of the computed rates. The conceptual advantages of this model, in contrast to the well-known flaws intrinsic to the classical nucleation theory werediscussed in our previous report.2 Therein, coupled sets of simultaneous rate equations [ ( l ) and (2)] were solved for n-nonane, covering the temperature range 315-203 K and various levels of supersaturation. Good agreement with experimental values of J(S;T) were obtained. We also developed an approximate 'short cut" procedure for computing condensation fluxes. On combining eqs 6 and 7, one may calculate the cluster size distribution attained, at the constrained equilibrium, i.e. the long time kinetic limit. In practice, one must insert an upper bound (m)to compute summation (6). For any specified m, the calculated values N,q(m) pass through a minimum. However, there always is some low value of m (found by successive approximations) such that the location of the minimum (I) is independent of m. We found that using a revised expression (5) an adequate approximation for the flux can be rapidly computed K's),
For several decades ingenious experimental configurations were developed to measure J(S;T). In the published reports the experimenters took particular pains to analyze sources of errors and to minimize difficulties arising from artifactsa4v5 They, and others whoareconcerned withcomparing thereported magnitudes with predictions based on classical nucleation theory or its manyfold modifications, encountered a variety of problems. Most striking is the recognition that neither the supersaturation pressure nor the temperature at which condensation occurs is directly measured but must be calculated from the experimental conditions. In the published tabulations S and Tvalues are cited, but p@)(Le. the actual pressure of the condensing gas) is not. Since the dependence of the nucleation flux on supersaturation is very steep (example, n-propanol at 298 K: J = 10-l drops cm-3s-l at S = 2.50 vs J = lo3drops cm-3 s-l a t S = 2.71), determination of the pressure at criticality, as well as the equilibrium vapor pressurep(e) at T, is crucial. In all but a few cases condensation takes place at temperatures much lower than the range over which equilibrium data are available. Thus, much depends on the method used for extrapolatingthe measured vapor pressure values. Strange as it seems, some investigators do not report the equilibrium vapor pressure relations they use for their quoted S(T);those that do appear to believe that three or four parameter equations that besr represent an extendedrange of experimentally determined values (and hence is useful for interpolation) should also serve for extending the data to temperatures well below the range of observation. With this we disagree. After many trials, using various proposed vapor pressure functions and a multitude of calculations, we evolved the following uniform, self-consistent p r d u r e for all the cases discussed below. CRC tables list temperatures at which equilibrium vapor pressures of most substances of interest have magnitudes 1.0, 10.0, and 40.0 Torr. These are smoothed values, subject to minimal experimental fluctuations. The three pairs of quantities as listed in the CRC tables were then fitted to an Antoine relation and used to calculate logIopcl(c)(Torr) = A - B/(T- C). Then Q(T) = 4.5761B(T/(T- C))2. Inthismannerweminimizedthelength of the extrapolated region. To check, we also evaluated In pe2(C) (Torr) = JT,,.,TQ(T)/RFdT, where T,fwaschosenfortabulated equilibrium pressures between 1.0 and 10.0 Torr. Then
Q(7') = Q(T,,r) + JT:er [Cp(u)- c&Old T
(17)
When the temperature range over which S(T;J) was measured
The Journal of Physical Chemistry, Vol. 97, No. I, 1993 273
Condensation Flux Estimates
expansion technique (in the driver section) and attained the low temperatures 210-255 K, for Jvalues of approximately 108drops ~ ms-I. - ~Perhaps the lackof agreement between these techniques is an example of the old a d d a g e w h e n probing nature, the answer one gets depends on how the question is posed.
- t 5
section I11
1.20
L')
" I.00t
*.
0.8OL
I
I
2.20
2.00
I
2.40
I
I
I
I
2.60
2.80
IO~IT-~/Z
Figure 1. Correlation plot [In &,it vs 104/T3/*]for CzH50H. Data by Peters and Paikert:lo ( 0 )J = 1E8 drops cm-3 s-I. Data by Kacker and s-I. Data by Schmitt et a L 7 (V)J = Heist? (*) J = 1E3 drops 1E3 drops cm-3 s-I, (A) I = 1E5 drops ~ m s-I- (set ~ A). Data by Strey et (0)J = 1E5 drops ~ m s-l, - ~( X ) J = 1E8 drops ~ m s-I - (set ~ B). 0.70
0.60 Y m
e
I-
0.50
-
-
-
TiC14 I
I
I
I
I
I
I
I
was not far below the 1-Torr level, these two methods for estimating p(C) checked well. To compare literature values of S(T;J) with those derived from our kinetic model, the listed critical supersaturations were then corrected according to
[Stabin most cases were read from enlarged graphs of S(T), as presented in the original reports. Thus we used smoothed values that were relatively free of individual experimental fluctuations.] To provide the reader with a measure of internal consistency (or lack of it) among four groups of workers who used four different techniques for measuring critical supersaturations for ethyl alcohol, refer to Figure 1. Here In S(T ) was plotted vs 104T3/2.6 The data from each technique do show the expected Jdependence, but overall agreement is considerably less than desired. The disagreement for the other alcohols is somewhat less dramatic. Schmitt et ala7used an expansion cloud chamber to cover the temperature range 252 I T I 272 K, for values of J between lo2 and 105. Kacker and Heist* used a thermal diffusion cloud chamber and covered the temperature interval 261-298 K, with J values from 10-2 to lo3 drops cm-3 s-1; Strey et al.9 used a two piston expansion chamber and obtained Jvalues from lo6to lo9 drops ~ m s-I- over ~ the temperature range 240-280 K. More recently, Peters and Paikertlodeveloped a shock-tube gas dynamic
As stated above, with cluster population distributions calculated under the constrained equilibrium condition and our computer code, one may readily evaluate Jthfor any specified S(T). As anticipated, these magnitudes depend on various molecular parameters and the assumed relations (15) and (16) and most sensitively on the value of SP (eq 11) and the values off and g in eq (12). To minimize overall ambiguities, we set f = 1 and g = 3; we also assumed w(C,;X) = w(A,;X), whereas our model suggests that the former is larger than the latter. Thus we collapsed all parameter variations into the SP parameter. The value of g is the most sensitive parameter in this model because it controls the activation energy for evaporation. Were the evaporating clusters in thermal equilibrium with the ambient gas, we would have assigned g = 5 , the inverse of the coefficient (1/5) in eq 16. However, it has been demonstrated experimentally," and argued theoretically, that the nascent but stabilized clusters are considerably hotter than the ambient gas, due to incomplete removal of the heat of condensation. Hence we selected a lower value to adjust for the lower activation energy required to initiate vaporization. We found that the dependence of SP on temperature (and slightly on J) has an attractive molecular interpretation. The compilation of values listed in the tables and illustrated in the accompanying graphs show how well Jthcan be matched to Jcxpfor S,( T). The derived SP values scale with 0 ( ( T c- T ) / T c ) ;T, is the critical temperature. 0 is a rational, dimensionless scaling factor that vanishes when T = T,. For T > T , a phase change due to droplet formation cannot occur. Tetrahhral Structures [CCb TiC4, SnCb] (DM = 0). (Concern with the dipole moment is justified below.) Katz et al.12 investigated the homogeneous condensation of CC14and of three freons, in an upward thermal diffusion cloud chamber, where they observed 2 < J < 3 drops cm-3 s-I; the range in condensation temperatures was 220 < T < 290 K; H2 or He was the carrier gas. For C C 4our refitted equilibrium vapor pressure parameters are: A = 7.441 53, B = 1493.21, and C = 21.79. Reference to Table Ia shows that SP rises slightly with increasing temperature (0.367 at 0 = 0.476; 0.333 at 0 = 0.533). El-Shall,13 using a similar apparatus, measured critical supersaturation levels for - ~H e was the carrier gas for 248 TiCI4 and SnC14 ( J = 1 ~ m s-I); < T < 304 K. Our refitted Antoine parameters are, for the Ti and Sn compounds, respectively A = 7.3494 and 7.3226, B = 1642.60 and 1513.95, and C = 35.75 and 43.7. Sections b a n d c of Table I show that also for these species SP declines with decreasing temperature and at a rate greater than for CCI,. Note also the significant difference between the equilibrium vapor pressure values proposed by the author and our recalculated magnitudes, particularly from those given in his Figures 1 and 2. Fe(C0)s (DM = 0.63 D). Since we anticipated that SP would follow an upward trend with increasing 0,we analyze condensation data for iron penta~arbony1.I~ Over the temperature range 250 < T < 300 K, 1 < J < 3 droplets cm-3 s-I were observed in a diffusion cloud chamber, with helium as the carrier gas (Table Id). Our Antoine parameters are A = 7.637 42, B = 1710.00, and C = 20.15. Here also the SP parameter declines with increasing 0 . HCCI3 and HFCN (DM (respectively) = 1.870 and 3.92 D). Reference 12 includes condensation data on chloroform. We did not attempt to reproduce the author's vapor pressure values. Following our set strategy we used the information provided in
274
Bauer and Wilcox
The Journal of Phtsical Chemistry, Vol. 97, No. I, 1993
TABLE I a
b
C
d
e
f
g
h
j
k
1
m
n
p
CC14 (556.25)
290 285 275 265 260 304 Tic14 (530 est) 288 280 272 264 256 SnC14 (591.9) 304 288 272 256 248 288 Fe(C0)s (550 est) 280 272 264 256 265 CHC13 (536.2) 250 240 230 220 H3CCN (547.84) 297.8 283.3 268.1 254.3 246.2 239.6 1,1,2,2-C2H2C14(569 est) 330 310 285 260 240 o-xylene (642.2) 340 330 310 290 270 n-butylbenzene (653.0) 360 340 300 260 240 220 n-nonane (Katz's data) (594.2) 314.4 3 14.4 284.6 285.1 257.9 258.0 238.5 238.1 n-nonane (Schmitt's data) 266.8 265.8 249.8 248.1 229.4 226.6 218.2 216.0 n-nonane (Strey and Wagner) 240.73 234.14 222.05 215.68 205.98 202.23 H20 (647.3) 320 310 300 290 285 HzO(647.3) 287
86.69 61.99 37.1 1 21.19 15.70 16.01 6.81 4.28 2.62 1.56 0.895 39.25 18.21 7.72 2.94 1.73 17.78 11.36 7.06 4.27 2.50
87.47 43.15 18.95 8.24 4.84 3.06 30.97 10.84 2.22 0.302 0.0403 55.26 35.32 12.97 4.00 0.99 32.25 12.60 1.17 0.040 0.0040 0.00022
74.85 58.67 35.03 20.04 14.90 16.83 6.88 4.21 2.49 I .42 0.779 32.09 13.35 4.91 1.55 0.8 17 17.92 11.40 7.04 4.22 2.44 37.65 15.41 7.82 3.67 1.56 89.86 44.99 19.77 8.44 4.86 2.99 33.26 12.27 2.87 0.497 0.0923 55.51 35.29 12.93 4.06 I .04 31.33 12.50 1.31 0.061 0.0084 0.00075 11.400 1.777 0.212 0.0307 0.457 0.0991 0.0107 0.00250 0.0391 0.00421 0.00175 0.000214 78.81 46.55 26.43 14.35 10.38 11.83
4.92 5.095 6.36 7.91 8.63 6.67 1 1.62 15.06 19.76 25.42 3 1.05 4.61 8.18 13.83 23.12 33.72 6.04 7.69 9.79 12.59 16.03 5.65 7.755 9.77 12.47 15.94 2.72 3.36 4.31 5.26 6.29 7.15 5.33 7.34 11.55 19.74 3 1.82 4.16 4.78 6.72 9.62 14.94 4.49 5.94 11.62 27.32 50.21 104.9 5.384 6.192 9.069 10.84 16.67 19.29 29.06 38.95 19.62 21.50 27.98 32.65 6 1.02 82.81 110.76 145.6 63.02 120.4 138.5 300.4 257.5 444.9 2.804 3.13 3.43 3.77 3.98 4.70 3.98 I
2--3 2--3 2--3 2--3 2--3 1-3 1-3 1-3 1-3 1-3 1-3 1-3 1-3 1-3 1-3 1-3 1-3 1-3 1-3 1-3 1-3 2--3 2--3 2--3 2--3 2--3 1-3 1-3 1-3 1-3 1-3 1-3 2--3 2--3 2--3 2--3 2--3 -1 -1 -1 -1 -1
2-3 2-3 2-3 2-3 2-3 2-3 1.43 (-4) 3.17 (0) 1.73 (-4) 3.40 (0) 2.28 (-4) 2.56 (-1) 3.02 (-4) 5.80 (0) 2.00 (3) 7.74 (3) 2.7 (2) 8.70 (3) 6.75 (2) 9.37 (4) l.805 (3) 1.08 (5) 3.30 (6) 2.80 (9) 2.40 (6) 2.50 (9) 1.20 (6) 4.60 (8) 1-3 1-3 1-3 1-3 1-3 3.4 (4) 2.25 (2)
2.86 3.05 2.81 2.61 2.00 1.25 2.44 2.42 1.32 1.34 2.96 2.32 1.39 1.24 2.57 1.78 1.93 1.19 1.50 1.73 1.57 2.695 3.15 2.11 2.17 2.27 2.03 1.44 2.19 1.80 1.84 2.06 2.63 2.09 2.66 2.19 2.36 1.04 0.82 0.87 1.08 0.97 2.02 1.93 2.40 1.91 2.20 2.25 1.40 (4) 3.23 (0) 1.85 (-4) 3.45 (0) 2.63 (-4) 2.64 (-1) 3.97 (-4) 5.91 (0) 1.71 (3) 7.56 (3) 2.79 (2) 8.04 (3) 6.29 (2) 9.52 (4) 1.71 (3) 1.03 (5) 3.28 (6) 2.84 (9) 2.32 (6) 2.63 (9) 1.52 (6) 4.89 (8) 1.75 2.24 2.33 1.34 1.97 3.45 (4) 2.31 (2)
0.367 0.377 0.350 0.333 0.333 0.520 0.410 0.349 0.340 0.375 0.336 0.520 0.373 0.300 0.265 0.224 0.515 0.460 0.415 0.375 0.343 0.380 0.375 0.380 0.400 0.445 0.480 0.520 0.580 0.690 0.740 0.815 0.523 0.539 0.588 0.670 0.810 0.275 0.280 0.285 0.305 0.326 0.400 0.420 0.505 0.780 1.05 [1.67] 0.277 0.283 0.296 0.294 0.340 0.340 0.416 0.404 0.308 0.303 0.367 0.372 0.427 0.437 0.462 0.476 0.319 0.306 0.385 0.380 0.640 0.700 0.257 0.282 0.320 0.365 0.396 0.3846 0.408
0.479 0.488 0.506 0.524 0.533 0.426 0.457 0.472 0.487 0.502 0.517 0.486 0.513 0.540 0.567 0.581 0.476 0.491 0.505 0.520 0.534 0.506 0.534 0.552 0.571 0.590 0.456 0.483 0.511 0.536 0.551 0.563 0.420 0.455 0.499 0.543 0.578 0.462 0.478 0.510 0.541 0.573 0.449 0.479 0.541 0.602 0.632 0.663 0.471 0.471 0.521 0.520 0.566 0.566 0.599 0.599 0.551 0.553 0.580 0.582 0.614 0.619 0.633 0.636 0.595 0.606 0.626 0.637 0.653 0.660 0.506 0.521 0.536 0.552 0.560 0.557
The Journal of Physical Chemistry, Vol. 97, No. 1, 1993 215
Condensation Flux Estimates TABLE I (Continued) section
p
cpd (TCritial K) H20(647.3)
q
C2HsOH (516) (set A)
r
C2HsOH (516) (set B)
s
n-CjH70H (536.8)
t
Hg(1735)
Texp,K 268.3
p(e)rCpr Torr p(e)rccalc, Torr 3.18
245.7
0.484
232.5
0.133
(292.2) 272.0 262 252 245.3 (292.2) 272 262 252 (245.3) 279.18 260.92 241.11 277.35 259.94 239.81 298 298 276 276 26 1 26 1 293.4 256.4 236.0 300 275.5 257.5
40.12 10.84 5.24 2.386 1.355 40.12 10.84 5.24 2.386 1.345 17.66 4.83 0.936 15.63 4.481 0.8318 21.036
19.643
4.345
4.252
1.229
1.278 14.554 0.858 0.119 0.001 70 1.536 (-4) 1.850 (-5)
their Table I and our “best fit” Antoine parameters: A = 6.509 9 1, B = 1015.09, and C = 59.27. Table Ie shows that for this compound, for 220 < T < 265 K, there is a small but steady increase of SP with 8. A much steeper SP/8 dependence was found for methyl cyanideI5 (Table If), again in a diffusion cloud chamber, for 1 < J < 3 drops ~ m s-I, - for ~ the temperature range 240 < T < 298 K. Tabulated equilibrium vapor pressure data were refitted: A = 6.8730, B = 1239.2,and C = 45.9. Corrections to the quoted vapor pressure values proved minimal. 1,1,2,2-C2H2CL (DM = 1.32 D). We reanalyzed data for another freon;l2 refer to Table Ig. For the range 240 < T < 330 K and 2 < J < 3 drops cm-3 s-1, SP rises appreciably with 8.In this case our refitted equilibrium vapor pressure relation led to a considerably higher value at 240 K than that proposed by the authors, and thus reduced their listed magnitudes of S at low temperatures. A = 7.8910, B = 2001.09, and C = 15.81. Alkylated BenzeneP (DM = 0.62 D for *Xylene). This paper summarizes some of the early studies using a thermal diffusion cloud chamber. Our reanalysis shows that we agreed well with the author’s equilibrium vapor pressure equation for o-xylene, but for n-butylbenzene at low temperature there are significant differences in the extrapolated equilibrium vapor pressures between those used by the authors and our refitted equation. For o-xylene the temperature range covered is 270 < T < 340 K, while for the latter a wider range was tested: 220 < T < 360 K. Foro-xylene (Table Ih),A = 7.5886,B = 1794.93,and C = 32.7. For n-butylbenzene (Table Ij), A = 7.538 39, B = 1951.84,and C = 36.98. The rapid increase in SP at low temepratures (0.60 I8 I 0.66) is somewhat disconcerting. That SP rises above unity could be due to the fact that for a rigid Cg unit with a long dangling chain, the assumption w(C,;X) w(A,;X) does not apply. Were one to increase w(C,;X), the magnitudeof S P would decrease. At any rate there are serious questions regarding which vapor pressure relation should be used. mNonane (Table Ik,l,m) (DM 0). This system has been assigned benchmark status with respect to tests of classical
-
-
Sad,
6.00 4.98 8.98 1.49 11.99 10.02 2.316 2.423 2.521 2.790 3.802 2.451 2.575 2.666 2.840 3.109 2.61 2.957 3.73 2.88 3.17 4.174 2.717 2.84 3.12 3.28 3.93 4.05 3.43 5.18 7.81 2663 21983 55049
Jexp, drops
cm-) s-I
5.6 (4) 2.8 (2) 9.7 (4) 4.8 (2) 3.5 (4) 7.95 (2) 1E3 1E3 1E3 1E3 1E3 1E5 1E5 1E5 1E5 1E5 8E5 4E5 3.8E5 l.lE8 2.OE8 l.lE8 0.5 200 0.5 100 0.5 100 1.5E8 1.9E8 2.6E8 -1 -1 -1
Jcalc,drops 6111-3 s-I
SP
5.67 (4) 2.73 (2) 9.63 (4) 4.89 (2) 3.53 (4) 7.97 (2) 1.17 (3) 9.65 (2) 1.06 (3) 9.93 (2) 1.97 (3) 1.01 (5) 1.06 (5) 1.08 (5) 1.28 (5) 1.48 (5) 8.46E5 3.45E5 2.48E5 1.72E8 1.63E8 1.09E8 0.45 214 0.48 106 0.49 102 1.47E8 2.02E8 2.61E8 1.22 0.954 1.16
0.528 0.559 0.808 0.837 1.048 1.1205 0.255 0.428 0.570 0.734 0.876 0.265 0.450 0.605 0.820 0.980 0.380 0.592 1.000 0.420 0.688 1.16 0.206 0.223 0.319 0.342 0.401 0.443 0.295 0.656 1.056 1.12 0.504 0.70
0 0.586 0.620 0.641 0.434 0.473 0.492 0.512 0.525 0.434 0.473 0.492 0.512 0.525 0.459 0.494 0.533 0.4625 0.496 0.535 0.449 0.486 0.514 0.453 0.522 0.560 0.827 0.841 0.852
nucleation theory.” The authors reviewed careful measurements of J ( $ n by three independent methods (upward diffusion cloud chamber, expansion cloud chamber, and double piston technique). We pointed out in our preceeding report2 that these three sets of data are not entirely consistent, as was indicated by Professor Katz. He sent us a set of tables to facilitate our analysis, for which we express sincere thanks. We accepted the equilibrium vapor pressure magnitudes derived from his four-parameter equation but refitted the values a t 310, 295, and 280 K to an Antoine expression (A = 7.2992, B = 1624.89, and C = 54.1). Both equations predict p(e)(at 274.55 K) = 0.85 Torr, whereas C R C No. 71 lists the vapor pressure a t that temperature to be 1 .O Torr. For all three sets, SP increases with 8. Overall, while SP rises from 0.277 to 0.700, 8 increases from 0.471 to 0.660. H 2 0 (DM = 1.87 D). We reduced two sets of data. For 285 < T < 320 K,18 J values were derived from a diffusion cloud chamber; for 232 < T < 287 K,I9 S(T) was obtained in an expansion cloud chamber. A third report,*Obased on double piston expansion measurements did not present sufficient details to permit analysis. S(T;J)values were read from an enlarged Figure 3-18 For 285 < T < 320 K, with 1 < J < 3 drops cm-3 s-I, SP values ranged from 0.257 to 0.396, increasing with 8 (Table In). Our Antoine parameters are A = 8.166 28, B = 1782.23,and C = 35.74. For the lower temperature range typical values were selected from an enlarged Figure 719 and tables submitted by Professor Hagen, excerpted from Miller’s dissertation. Here we note (Table Ip), 0.385 < S P < 1.120. The small extension above unity may be due to the approximation w(C,;X) = o(A,;X). CzHsOH and m C & O H (DM = 1.69 and 1.61) D). In the analysis of S(T$) for alcohols we encountered the problem of disparity in the data to which attention was called in Figure 1 . Ultimately, we selected what appear to us as concensus values: for low J experiments (set A; Table Ig), cover the range 245.3 < T
