J . Phys. Chem. 1989, 93, 6201-6205 gregates. Experiments to investigate this mixed aggregate system are currently in progress in our laboratory.
Acknowledgment. This work has been supported by the Robert A. Welch Foundation and the Research Corporation. We thank
6201
Professor G. Wilse Robinson for letting us use the equipment and facilities at the Picosecond and Quantum Radiation Laboratory at Texas Tech University. Registry No. Pseudoisocyanine, 977-96-8; silica, 763 1-86-9.
Phases and Phase Changes of Molecular Clusters Generated in Supersonic Flow Lawrence S. Bartell,* Laszlo Harsanyi, and Edward J. Valentet Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109 (Received: February 14, 1989; In Final Form: April 17, 1989)
Molecular clusters of a wide variety of substances have been generated by homogeneous nucleation in nozzle flow and studied by electron diffraction. Clusters were the order of 100 8, in diameter. The majority of the clusters were found to be liquidlike. Two examples could be produced as either liquid or crystalline clusters by adjusting flow conditions. Several others could be induced to organize into two or more different crystalline packings by controllingmole fraction, carrier gas, and/or stagnation pressure. Substances exhibiting large ranges of liquid existence in the bulk gave liquid clusters while those with small or null ranges gave solid aggregates. In intermediate cases the entropy of fusion, representing a measure of difficulty of molecular reorientation, helped to sharpen the diagnostic rule of thumb regarding cluster form. Approximate computations of the temperatures of clusters growing in their supersaturated vapor during nozzle flow indicate that the condensing clusters are appreciably warmer than the gaseous medium and much warmer than the grown clusters exiting the nozzle. In a number of cases, the clusters appear to have undergone phase changes in the course of some microseconds of cooling in adiabatic flow after they were fully grown.
Introduction The phenomenon of homogeneous nucleation has been a recurrently studied,lS2if contr~versial,~ subject for many years, partly because of its implications in important natural and technological processes and partly because of its challenging theoretical diffic ~ l t i e s .A~ subclass ~ of this phenomenon that has been scrutinized searchingly is the condensation of supersaturated vapor. Experimental research in this area includes condensation in cloud c h a m b e d and in supersonic flow.2 Cooling by supersonic expansion in nozzle or free jet flow is of special interest because of the directness with which the structure of the condensation products can be probed by electron diffraction immediately after they are formed.'-IO Molecular aggregates of widely varied internal arrangement have been examined by this method over the past few years. Since only a fraction of the results have been reported in the standard literature, it seems worthwhile to outline what has been observed. Systematic observations of the structural chemistry of clusters generated in supersonic flow are useful in characterizing the course of events occurring during condensation. How such information may be put into context is sketched below. Just as the nucleation process itself is imperfectly understood, so also is the subsequent growth of the nuclei in supersaturated vapor. Because it is the latter process which governs the nature of the condensate, it is important to learn how to delineate it. None of the existing techniques are ideally suited to the investigation of all aspects of condensation. Conditions of the medium during nucleation can be monitored more directly in cloud chambers6 and during flow through large nozzles" than in the micronozzles so far used in the electron diffraction studies to be described. Hence, the former are especially satisfactory for studying the onset of nucleation. On the other hand, the great advantage of the latter approach is that it makes possible a determination of the structure and, in favorable cases, the temperature and size of the molecular clusters produced. These properties of the grown clusters are, at best, marginally related to the properties of the nuclei at onset of nucleation. Condensation nuclei themselves, being clusters comprised of but a handful of molecules (perhaps a half-dozen) 'Present address: Department of Chemistry, Mississippi College, Clinton, MS 39058.
0022-365418912093-6201$01SO10
are too small to be committed to any final structural form.I2 Since the melting points of crystals decrease as crystals become the minuscule embryonic clusters first nucleated are almost certainly liquidlike, even though they may transform into solids as they accrete matter. Diffraction studies can substantially augment accounts of the aggregation process. This is particularly true when any of two or more different structural forms (phases) can be induced to grow, depending upon flow conditions. Important clues may be provided in such cases about cluster temperatures as the growing molecular aggregates pass through the stage in which their structure is finally established. Cluster temperatures during condensation can be far out of equilibrium with the surrounding thermal bath because of the latent heat evolved. No technology exists for the direct determination of such information inside micronozzles. Cluster temperatures during growth can also be much higher than they are after clusters leave the nozzle. Therefore, when several forms can exist, the form actually produced is sometimes more indicative of temperature during growth than is the exit temperature. As will be seen below, however, the kinetics of phase change can be important, too. ( I ) Early papers identifying crucial factors were by Gibbs and Einstein: Gibbs, J. W. Trans. Conn. Acad. IIZ 1875, 108; 1877, 343. Einstein, A. Ann. Phys. 1910, 33, 1275. (2) For excellent reviews, see: Wegener, P. P. In Nonequilibrium Flows; Wegener, P. P., Ed.; Marcel Decker: New York, 1969. Wegener, P. P.; Wu, B. J. C. Adu. Colloid Interface Sci. 1977, 7 , 325. (3) Lothe, J.; Pound, G. M. J . Chem. Phys. 1%2,36,2080 1968.48, 1849. Feder, J.; Russell, K. C.; Lothe, J.; Pound, G. M. Adu. Phys. 1966, 15, 11 I . (4) Reiss, H.; Katz, J. L. J . Chem. Phys. 1967, 46, 2469. Reiss, H.; Katz, J. L.; Cohen, E. R. Ibid. 1968, 48, 5553. (5) Ruth, V.;Hirth, J. P.; Pound, G. M. J . Chem. Phys. 1988, 88, 7079. Reiss, H. In Advances in Chemical Reaction Dynamics; Rentzepis, P. M., Capellos, C., Eds.; D. Reidel: New York, 1986. (6) See, for example: Schmitt, J. L.; Adams, G. W.; Zalabsky, R. A. J . Chem. Phys. 1982, 77, 2089; 1983, 79, 4496. (7) Raoult, B.; Farges, J. Reo. Sci. fnstrum. 1973, 44, 430. (8) Farges, F.; de Feraudy, M. F.; Raoult, B.; Torchet, G. J . Chem. Phys. 1986, 84, 3491. (9) Stein, G. D. Phys. Teach. 1979, 17, 503. (IO) Bartell, L. S. Chem. Rev. 1986, 86, 491. ( 1 1 ) Moses, C. A,; Stein, G. D. J . Fluids Eng. 1978, 100, 311. (12) Bartell, L. S. Comments Chem. Phys., in press. (13) Thomson, J . J. Applications of Chemical Dynamics; London, 1888. (14) Buffat, P.; Borel, J.-P. Phys. Reu. A 1976, 13, 2287. (15) Reiss, H.; Whetten, R. L. Preprint, 1988.
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Some success has been achieved in accounting theoretically for details of condensation in nozzle flow in the presence of carrier gas under conditions of comparatively low pressure and mole fraction of subject ~ a p o r . ~ ~At~higher ' ~ ~ 'pressures ~ and mole fractions the complex behavior observed is not satisfactorily understood.'* Even though a truly definitive modeling has yet to be devised, existing approaches can yield helpful clues, as will be shown. Meanwhile, as improved computational routines are developed, experimental observations of cluster form, size, and temperature will provide demanding targets for theoretical treatments of nozzle flow to reproduce Experimental Section Electron diffraction patterns of clusters issuing from a small Laval nozzle (glass, no. 6)16 were recorded on photographic plates and measured as described elsewhere.'* Some aspects of the experimental conditions that have not been discussed adequately in prior reports deserve mention. They concern the transmission of the cluster beam through the skimmer separating the nozzle chamber from the diffraction chamber. A standard Beam Dynamics conical skimmer 23 mm long with an entrance orifice 1 mm in diameter was placed approximately 7 mm from the tip of the 30-mm-long nozzle. Let D be the 0.115-mm nozzle throat diameter and X,be the distance between the nozzle throar and the skimmer. The ratio X , / D used in our experiments, then, was about 320, a very large value compared with ratios commonly used in free jet expansions. Nevertheless, it was far too small to get clean skimming of the jets emerging from the Laval nozzle, because the gas flow was much more directed than in free jets. The severe skimmer interaction encountered seemed to influence the cluster pattern under some conditions, and it certainly strongly scattered the uncondensed g a s i g In partial compensation for this complication associated with the Laval nozzle, the clusters generated tended to be far larger than those produced in free jet expansions at comparable initial conditions of flow. The large clusters were able to plow through the shock wave near the skimmer entrance with much smaller changes than those reported when small clusters were deliberately passed through a shock wave.20 Clusters described in the present paper have been subjected to the skimmer interaction which, in most cases, is not expected to have a strong effect on results. Current investigations2' have pointed the way to eliminating skimmer interaction, however, and future studies may be free from uncertainties ascribable to this effect. Sources of the compounds and a complete list of experimental conditions are summarized in the supplementary material. (See paragraph at end of paper regarding supplementary material.) Simulations of Cluster Growth Computations of homogeneous nucleation and the growth of clusters in nozzle flow were carried out for diagnostic purposes to be described later. Because the focus of the present paper is not on the simulations themselves, a detailed presentation will not be given here. In rough outline procedures followed several published ~ c c o u ~ ~based s ~ on ~ the * ~work ~ - of~ Ostwatitsch. ~ Except for the growth law of clusters adopted, they were as described in an earlier paper of this series." The growth law, described in more detail elsewhere,12 is believed to be more realistic than the alternative laws incorporated in earlier work which either disre(16) Valente, E. J.; Bartell, L. S. J . Chem. Phys. 1983, 79, 2683. (17) Valente, E. J.; Bartell, L. S. J . Chem. Phys. 1984, 80, 1451. ( I 8) See, for example: Harsanyi, L.; Bartell, L. S.;Valente, E. J. J . Phys. Chem. 1988, 92, 451 I . (19) French, R. J.; Bartell, L. S. Unpublished research. (20) Torchet, G.; Schwartz, J. G.;de Feraudy, M. F.; Raoult, B. J . Chem. Phys. 1983, 79,6196. Torchet, G.; Farges. J.; de Feraudy, M. F.; Raoult, B. Z . Phys. D in press. (21) Bartell. L. S.; French, R. J. 2. Phys. D,in press; Reu. Sci. Insfrum., in press. (22) Ostwatitsch, K. Z . Angew. Murh. Mech. 1942, 23. I . (23) Wu. B. J. C. NTIS Report AD-7755, 1974. (24) Sherman, P. M.; McBride, D. D.; Chmielewski, T.; Pierce, T. H.; Oktay, E. Aerospace Research Laboratories Report ARL 69-0089, 1969. (25) Chmielewski, T.; Sherman, P. M. AIAA J . 1970, 8, 789. (26) Abraham, 0.:Kim, S. S.;Stein, G. D. J . Chem. Phys. 1981, 75,402.
Bartell et al. TABLE I: Some Substances That Yield Liquid Clusters and Pertinent
Phvsical Prowrties" substance BC13 BBr,
cs,
A&" I .5 1.6
3.28 4.31 5.05 4.05 4.66 2.18
CHF3 CHCl, CH*Ci2 CH,Br2 CHIOH
0.94 1.19 3.81 3.84 4.5 4.7 3.39 4.05
CC14' C2HSOH oxirane cyclopropane C3F8 acetone n-butane methyloxirane ethyloxirane cyclopentane C,H, " "
sidI4
0.41 4.24 5.01 0.4 0.66 0.93 4.57
GeC14 SnCI,
4.59
C6F6
2.2-dimethvlbutane 2,3-dimeth;lbutane PF,'
(Tb
- T,)/Tb ( T , - T , J / T , 0.42 0.38 0.49 0.41 0.37 0.43 0.40 0.48 0.52 0.39 0.29 0.55 0.43 0.39 0.62 0.46 0.51 0.47 0.42 0.44 0.21 0.21 0.46 0.56 0.29 0.38 0.37 0.38
(0.35) (0.23) 0.01 0.15 0.19 0.10 0 06 -0.16 -0.06 0.15 0.30 -0.40 0.06 0.20 -0.28 -0.04 0.01 0.03 0.02 0.11 0.36 0.30 -0.02 -0.22 0.30 0.14 (0.24) (0.20)
R,b 0.43 0.39 0.56 0.54 0.55 0.55 0.55 0.51 (0.66) 0.40 0.30 0.65 0.54 0.53 0.77 0.54 0.62 >0.47 >0.42 0.44 0.34 0.39 0.46 0.56 0 31 0.53 (0.52) 0.53
"Entropies of fusion, melting and boiling points T , and Tb, and hypothetical temperatures of evaporatively cooled clusters T,, as discussed in text. Thermodynamic information from ref 32-37. Entries involving estimated quantities in parentheses. In this table CCll and PF, are treated as liquid clusters. *Index of tendency to form liquid clusters; eq 2. (Can also be generated as solid clusters at lower mole fractions.
TABLE 11: Some Substances" That Yield Solid Clusters and Pertinent Physical Properties* substance Ned Ard Krd Xed HCI HBr NO N2O
co2
C2H2(2)' H2O NH3 PF3(2?)/ CH4d CMe4 CCld SiF, C2F6 C4Fd3)' cyclohexane
SF,(2)' SeF6( 2)' TeF,( 2)'
u m / R 1.64 i .69 1.69 1.71 1.51 1.57 2.52 4.3 1 4 63 2.4 2.64 3.47 0.93 1.25 1.53 1.19 4.64 1.86 I .43 1.12 2.72 3.59 3.63
-
(Tb - T m ) / T b
(Tm - T c J / T m
R,'
0.10 0.04 0.04 0.03 0.16 0.10 0.10 0.01 -0.1 I -0.02 0.27 0.18 0.29 0.16 0.09 0.29 0.02 0.1 1 0.13 0.21 -0.08 -0.05 -0.00
0.58 0.56 0.54 0.54 0.37 0.41 0.21 0.34 0.55 0.35 0.32 0.39 0.27 0.48 0.49 0.26 0.35 0.44 0.39 0.37 0.48 0.50 0.53
0.12 0.06 0.06 0.05 0.17 0.1 1 0.11 0.14 -0.02 0.0 0.32 0.26 0.30 0.17 0.1 1 0.30 0.17 0.13 0.14 0.22 -0.03 0.04 0.09
'All substances except C 0 2 (ref 30), H 2 0 (ref 31), and C H I (ref 29j were investigated at the University of Michigan. Additional information on rare gases was taken from ref 8 and 28. *Thermodynamic information from ref 32-37. Entropies of fusion, melting and boiling points, and hypothetical temperatures of evaporatively cooled clusters as discussed in text. Index of tendency to form solid clusters; eq 2. dObserved as polyicosahedral solids when clusters small and fcc when large; ref 8, 28, 29. eClusters seen in two or three different solid phases as indicated in parentheses, depending on expansion conditions. 'Seen as either liquid or solid clusters, depending on conditions. Treated here as solid in calculating Tc,.
garded the difference in temperature between clusters and surrounding gas or equated the cluster vapor pressure to the surrounding partial pressure of the (cooler) vapor. Instead, the
Molecular Clusters Generated in Supersonic Flow I
The Journal of Physical Chemistry, Vol. 93, No. 16, 1989 6203
I
1
2
3
S,i-‘
4
Figure 1. Diffraction patterns of several crystalline clusters: top pattern, HCI; middle pattern, SiF,; bottom pattern, neopentane.
Figure 3. Diffraction patterns of clusters of PF, generated at stagnation pressures of approximately 5.1 bar but different mole fractions in neon. Top curve: X = 0.12, liquid clusters. Second curve: X = 0.076, crystal features emerging. Bottom two curves: X = 0.048 and 0.034 with crystal lines sharpening at small angles, blurring at intermediate angles (due to a dense, more complex pattern of rings?).
A
to govern the phase of the clusters produced are discussed in the next section.
Figure 2. Diffraction patterns of several liquid clusters: top pattern, BCI,; middle pattern, cyclopropane (for a more complete pattern, see ref 45); bottom pattern, CS2.
present computations explicitly take into account the rates of transfer of heat and matter between the growing clusters and the surrounding vapor via the kinetic theory of gases and Baule’s classical thermal accommodation ~oefficient.~’
Results Results of electron diffraction studies of clusters are summarized in Tables I and I1 along with experimental properties that serve as useful indexes for interpreting results. Most entries are of compounds examined at the University of Michigan, but a few from Orsay28-31have been included for purposes of comparison. Of principal concern in the present investigation is the physical state of the clusters generated in supersonic expansions, usually but not always carried out with a rare gas carrier. Liquid clusters were observed more often than solid, but in two cases condensation could be controlled to yield clusters in either state. Illustrating the distinctly different aspects of liquid and crystal diffraction patterns are the “leveled” intensity plots for fairly large clusters ( 100-8, diameter) shown in Figures 1-3. A number of the substances forming solid clusters could be induced to aggregate in two or three different packing arrangements. Factors tending N
(27) Baule, B. Ann. Phys. 1914, 44, 145. (28) Farges, J.; de Feraudy, M. F.;Raoult, B.; Torchet, G. Surf. Sci. 1981, 106, 95. (29) Farges, J.; de Feraudy, M . F.; Raoult, B.; Torchet, G. Ber. BunsenGes. Phys. Chem. 1984,88, 211. (30) Torchet, G.; Bouchier, H.; Farges, J.; de Feraudy, M. F.; Raoult, B. J . Chem. Phys. 1984, 81, 2137. (31) Torchet, G.; Schwartz, P.; Farges, J.; de Feraudy, M. F.; Raoult. B. J . Chem. Phys. 1983, 79, 6196.
Discussion The most conspicuous correlation between cluster type and properties of the bulk ~ n a t e r i a l ~ is ~ -a~natural ’ one. The greater the range of liquid existence, the more likely clusters are to be liquid. In Tables I and I1 the range for each substance is expressed in reduced form as ( Tb- T,)/ Tb where Tb is the normal boiling point (inferred via the Clapeyron equation for materials that sublime) and T, is the normal melting point (triple point for materials that sublime). Substances with small or null liquid ranges invariably give solid clusters. In a preliminary report38 another strong correlation was advanced that introduced the reduced difference ( T , - T c l ) / T ,between melting point and hypothetical cluster temperatures, TcI. Here, TcIwas not an observed quantity but was inferred from the expression T,, = 0.04AEc,,d/R (1) proposed to represent the temperature reached by a cluster undergoing “evaporative c ~ o l i n g ’ ’ . ~If~T, ~ ~-~ TcIis large, it is natural to expect clusters to be solid, and if it is negative, clusters are unlikely to be unmolten. This index is approximately as successful as that of the liquid range and is included in Tables I and 11, but it is less fundamental for two reasons. First, it has been shown the actual cluster temperature can be decreased appreciably below Tclby heat exchange with an expanding carrier gas.I6tZ1Second, if Trouton’s rule is obeyed, more or less, by the material, the condensation energy AEcond at TcIcan be deduced quite well from the normal boiling point. Hence, ( T , - Tcl)/T , is so strongly correlated with (Tb - T,)/Tb that it cannot be considered to be a truly independent index. Molecular shapes and characteristics play a reasonably understandable role in influencing cluster structure. Spherical and many quasispherical molecules (e.g., rare gases, methane, tetra(32) Yaws, G. L. Physical Properties, A Guide; McGraw-Hill: New York, 1977. (33) Stull, D. R.; Westrum, E. F.; Sinke, G. C. The Chemical Thermodynamics of Organic Compounds; Wiley: New York, 1969. (34) Ubbelohde, A. R. The Molten State of Matter; Wiley-Interscience: Chichester, 1978. (35) Parsonage, N. G.;Staveley, L. A. K. Disorder in Crystals; Clarendon: Oxford, 1978. (36) CRC Handbook of Chemistry and Physics; Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1982. (37) Gmelin Handbuch der Anorganischen Chemie; Springer-Verlag: Berlin; Beilsteins Handbuch der Organischen Chemie; Springer-Verlag: Berlin. (38) Bartell, L. S.; Harsanyi, L.; Valente, E. F. NATO AS1 Ser., Ser. B 1987, 158, 31.
(39) Gspann, J. In Physics of Electronic and Atomic Collisions; Datz, S., Ed.; Hemisphere: Washington, DC, 1976. (40) Klots, C. J. Phys. Chem. 1988, 92, 5864.
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Bartell et al.
TABLE 111: Selected Properties“of Some Substances Yielding Clusters in Nozzle Flow substance
R,b -0.03
C(CH3)4 PF3
0.1 1 0.30
transition melting bcc-monoclinic melting melting
CCI4
0.30
melting
250.2
185
100-80 145-140 205-180 155-125 165-125 270-250
C6H6
0.34
melting
278.7
179
250-225
F6
Ttranse
Tcld 120
222.5 94 256.6 121.9
130 89
T*Clc
comments‘ X = 0.02, Po = 5; clusters bcc + monoclinic X = 0.06, Po = 5; clusters bcc a t low Po,monoclinic a t 5 bar X = 0.1, Po = 3.3; clusters solidg a t all Po,X tried X = 0.076, Po = 4-6; clusters solid” X = 0.12, Po = 4-6; clusters liquid X = 0.038, Po = 3.4; clusters solid’ a t higher Po,lower X and clusters liquid at lower Po,higher X X = 0.04, Po = 2.7; clusters liquid a t all Po,X tried
“Temperatures in kelvin. Thermodynamic information from ref 32-37. bIndex of tendency for clusters to be liquid. See text and eq 2. Temperature of indicated transition in the bulk material. dCalculated temperature of cluster attained in “evaporative cooling”; eq 1. e Calculated temperatures of growing clusters as fraction of vapor condensed increases from 0.1 to 0.7 under expansion conditions specified under “comments”. fX is the mole fraction of subject gas in the carrier gas, and Po is the stagnation pressure in bar of carrier plus subject gas. Conditions before the semicolon pertain to the calculation of Tgcl.Comments afterward pertain to experimental findings. Carrier gas was Ar for SF6 and benzene, Ne for the others. gfcc, a 3 8.8, A. *Warmer solid phase appears to be cubic, a ii 6.70 A. ‘Rhombohedral plastic crystal.
and hexahalides) do not encounter large barriers to orientational redistribution and can quite readily organize into crystalline aggregates. Accordingly, such molecules commonly form solid clusters in supersonic flow. The characteristic behavior of these molecules, however, is not entirely independent of the above index involving range of liquid existence. Ease of molecular reorientation, of course, underlies the phenomenon of orientational disorder in plastic crystals. For such materials, a substantial fraction of the entropy change between cold, ordered phases and the melt has already been accumulated before melting is reached. Therefore, the entropy of fusion tends to be small and, in order for the free energy of fusion to vanish, the temperature must be comparatively high (and the range of liquid existence comparatively small). As Tables I and I1 show, however, neither do all tetrahalides have low entropies of fusion nor does CF4, the one with the lowest, form solid clusters. The entropy of fusion correlated only roughly with range of liquid existence and is a much weaker predictor of the state of the cluster produced. The simple polar molecules so far studied include HCI, HBr, H 2 0 , NH,, and PF3. All of these examples give solid clusters under mild expansion conditions. Phosphorus trifluoride, however, has the largest value of (Tb - T,,,)/Tb and can be induced to generate liquid clusters if expansion conditions are adjusted to make clusters warmer (by increasing the concentration of PF3 in the carrier). The trifluoride is also of interest because it undergoes two solid-solid phase transitions, the first one occurring only 11 K below the melting point.41 A systematic trend in the diffraction pattern of clusters of PF3 as the concentration in carrier is decreased (Figure 3) suggests that varying proportions of two (or more) crystalline phases may be present. The linear molecules COz, N 2 0 , and C2Hzall give solid, cubic clusters closely related to each other in structure. Acetylene, however, exhibits an additional phase in a temperature range that is easily accessible in supersonic expansions. As discussed in detail flow conditions can readily be adjusted to yield clusters of this second solid phase. Not all qualitatively similar linear molecules give solid clusters. Carbon disulfide clusters are liquid as might be expected from its comparatively large range of liquid existence. Most substances condensing into liquid clusters have reduced liquid ranges greater than (Tb - T,,,)/Tb = 0.3. Benzene and perfluorobenzene, alone among the two dozen compounds observed to aggregate into liquid microdrops, have reduced ranges as low as 0.2 1. Simulations of the nucleation and growth of clusters of these two similar materials indicate that the growing clusters are kept warm enough by the heat of condensation to be naturally liquid as long as they accrete material. When condensation is complete, they quickly cool in the expanding medium by evaporation and by heat exchange with the much colder carrier gas until, some dozens of microseconds later when they are probed by an electron beam, they are supercooled by as much as 100 K. Their disklike constituent molecules, unlike the quasispherical molecules
of plastically crystalline molecules, are unable to overcome reorientational barriers to crystallization in the time available. To some extent it is plausible to associate the barrier to molecular reorientation with entropy of fusion, as explained above. It is reasonable to suggest that a somewhat better criterion for the production of liquid clusters can be devised than that based solely on the reduced liquid range. If the frustration of molecular motion is taken into account, a plausible empirical index might be such that, in the case of substances with R , exceeding 0.32 for the bulk, clusters are likely to be liquid. If R, is close to 0.32, as it is for CCI4 and PF3 for example, clusters may be liquid or solid depending upon expansion conditions. Low values of R, imply solid clusters. At the University of Michigan, new techniques are making it possible to vary expansion conditions over considerably wider ranges than was previously possible.z1 Whether this will blur or render obsolete the above criterion is not yet known. The new procedures, however, are demonstrating the production of solid phases not previously seen. Simulations of the growth of clusters in the supersaturated medium complement the experimental investigation and shed additional light on the condensation process. This digital modeling of the kinetics of transfer of heat and matter computes, among other things, the temperatures of both the clusters and the gaseous medium during the course of the flow. Although the approach is marred by its failure to take fully into account details of boundary layer flow in micronozzles and also by our ignorance of physical properties of small clusters, there are several compensating aspects in the treatment. As explained elsewhere,12these compensations make the quantity of greatest interest, the temperature of growing clusters, fairly insensitive to the above sources of uncertainty. It is not the purpose of the present paper to give a detailed documentation or account of the simulations. Nevertheless, it is worthwhile to present a few results as suggestive, if somewhat speculative, clues about processes taking place during the formation of clusters. For this purpose, calculated temperatures Tgclof growing clusters are listed in Table 111 for some of the more interesting cases studied. Typical flow conditions were used in computations. Also listed are the indexes R, for type of cluster formed, the hypothetical final temperature T,, of evaporatively cooled clusters, and temperatures of certain bulk-phase transitions. Substances are tabulated in Table I11 in order of increasing index Rc corresponding to an increasing tendency for the clusters generated to be liquid after exiting the nozzle. Sulfur hexafluoride, with a very low index, is never seen as a liquid, and its growing clusters appear to be far colder than the bulk melting (or sublimation) temperature. At low mole fraction in argon carrier Tgcl is lower than ”TC1” and can even fall below the 94 K temperature for transition from body-centered cubic to the low-temperature monoclinic phase of bulk SF6.43 At higher mole fractions (e.g.,
(41) Pace, E. L.; Petrella, R. V. J . Chem. Phys. 1962, 36, 2991
(42) Bartell, L. S.; Harsanyi, L. To be published.
(43) Eucken, J.; Schroder, E. Z . Phys. Chem. 1938,841, 307
J . Phys. Chem. 1989, 93, 6205-621 1
6205
~ 0 . 0 6 the ) growing clusters are calculated to be substantially warmer than 94 K, particularly at pressures higher than, say, 5 bar. Yet in experiments under such expansion conditions monoclinic clusters are efficiently produced. This observation suggests that the fully grown clusters undergo a solid-solid phase transition as they cool for many microseconds in the cold adiabatic expansion. Molecular dynamics simulations of Fuchs and Pawley support such an argument by indicating that this phase transition can take place in microclusters in nanoseconds or less.44 N e ~ p e n t a n e ,although ~ ~ * ~ ~ similar in molecular shape, size, and melting point to CC14 (which can be condensed into liquid clusters), has yielded only crystalline clusters under all conditions so far tried.& This behavior is consistent with the compound's low value of R, and with the calculated cluster formation temperature, TKcl, which is well below the bulk freezing point. In the tabulated examples the increasing empirical index R, agrees with experience in implying a greater tendency for clusters to be liquid. This accords with experiment even though the tabulated cluster temperatures TKclfall below the bulk melting point for the last case, benzene, which has so far always been seen as liquid. While it cannot be ruled out that the model temperatures TKclmay be lower than the true cluster temperatures during condensation, 50-100-A clusters only 10% cooler than the bulk freezing point would surely fail to freeze, anyway, if the typical freezing point depression with drop size is a p p l i ~ a b l e . ' ~ .The '~ activation barrier to reorganization, as mentioned before, must
inhibit freezing as the clusters cool rapidly after condensation ends. Growing clusters of PF, and CCI,, on the other hand, appear to be appreciably warmer than the bulk freezing point, even under conditions that yield crystalline clusters. The fact that liquid clusters are seen at higher mole fractions, which give warmer expansions, seems straightforward. The fact that solid clusters are seen in higher concentrations of carrier gas suggests that freezing takes place during the chilling expansion after condensation is complete. From the handful of examples presented it is clear that not enough is yet understood to predict with assurance the outcome of experiments on new substances. Nevertheless, rough guidelines have been formulated. Auguring well for progress in the field are concurrent developments of both experimental*I and computational treatments4' of cluster formation. As discussed in the foregoing, experimental evidence afforded by diffraction studies is more valuable when supplemented with results of computer modeling of condensation. The combined information provides a plausible means to reconstruct the processes taking place during the production of clusters in nozzle flow.
(44) Fuchs, A. H.; Pawley, G. S. J . Phys. (Les Ulis, Fr.) 1988, 49, 41. (45) Bartell, L. S.; Barshad, Y . 2. J . Phys. Chem. 1987, 91, 2890. (46) In earlier r e p ~ r t s , ' ~neopentane ~ ~ ~ * ~ ' was claimed to yield liquid clusters under certain conditions. This incorrect claim was based on seriously flawed measurements of the diffraction intensities that resulted in considerable blurring of the diffraction features. The original diffraction plates themselves display conspicuous Debye-Scherrer rings clearly showing that the neopentane clusters were crystalline.
Supplementary Material Available: Sources of the compounds studied and a complete list of electron diffraction plates taken, including a documentation of experimental conditions (1 3 pages). Ordering information is given on any current masthead page.
Acknowledgment. This research was supported by a grant from the National Science Foundation. We express our appreciation to Messrs. Paul Lennon and Theodore Dibble and to Miss Kathleen Nolta for their considerable assistance in electron diffraction experiments and the processing of data. We gratefully acknowledge a generous allocation of computing time from the Michigan Computing Center.
(47) Machonkin, R.; Bartell, L. S. Unpublished research.
Vibrational Coupling Effects for Cyanide and Aromatic Adsorbates at Gold Electrodes: A Comparative Study Using Surface Raman and Infrared Spectroscopies Ping Gao and Michael J. Weaver* Department of Chemistry, Purdue University, West Lafayette. Indiana 47907 (Received: February 21, 1989)
Corresponding surface-enhancedRaman (SER) and infrared spectra in the C-N stretching frequency, vCN, region are reported for various 1ZCN-/13CN-mixtures at constant cyanide coverage on gold electrodes in order to compare the manner and extent to which adsorbate dipole-dipole coupling, or "vibrational coupling", is sensed by these two techniques. Although the extent of coupling, as manifested in the dependence of vcN upon both the isotopic composition and intensity transfer to the high-frequency band partner, is only moderate, essentially identical results are obtained from the Raman and infrared spectra. This indicates that the adsorbate geometry and environment as sensed by the SER probe are unlikely to differ significantly from those of the preponderant adsorbate that is presumably probed by the infrared technique. Protiated/deuterated mixed-isotope layers of benzene, toluene, nitrobenzene, and pyridine at gold electrodes were also examined with SERS to explore vibrationak coupling for a wider class of adsorbates and to ascertain whether such effects can be utilized to gain information on the adsorbate binding geometry. For benzene and toluene, which are known to adsorb in a flat orientation, the vI ring mode displays vibrational coupling; the ~ 1 vibration 3 for the latter adsorbate is also coupled, but surprisingly the u I2mode is not. The coupling is attributed to the dynamic dipole normal to the surface involving aromatic a electrons. In contrast, the ring modes for adsorbed nitrobenzene display no detectable vibrational coupling, consistent with surface binding via the nitro substituent and the resulting pendant configuration of the aromatic ring. Adsorbed pyridine also displays no discernible vibrational coupling on gold, suggesting that adsorbate-surface a overlap is relatively unimportant. Surprisingly, this study appears to be the first examination of adsorbate vibrational coupling by surface Raman spectroscopy.
A strategy commonly utilized to unravel vibrational coupling effects between adsorbate molecules at metal interfaces in ultra0022-3654/89/2093-6205$01.50/0
high vacuum (uhv) involves the measurement of surface infrared spectra for isotopic mixtures.] A primary application of such 0 1989 American Chemical Society
