2944
J. Phys. Chem. 1991, 95, 2944-2946 0.7
.
4
0.6 0.5
0.4
0.3 0.2
I
I
-1
0 CO.
1
e
probabilities of different orientations of a water molecule near Ne (curves for other inert gases are similar). 0 is the Ne-0-H angle. The probabilities for cos 8 = A1 are not very accurate because of a crude configurational grid employed in the computations Figure 1. Relative
(see the text).
0.15 A). The evaluation of expressions 1 and 2 was performed with two schemes, one of them underestimating and the other overestimating their values. We assumed that the converged values equal to the mean of the corresponding results obtained with the two schemes, after checking that they converge toward each other at similar rates. The estimated error due to numerical inaccuracies is less than 0.3 kcal/mol. Some details of the results obtained with our method are given in Figure 1 that shows relative probabilities of different orientations of water molecules near the solute. The shape of the curve in Figure 1 is very similar to that of the corresponding curves from the molecular s i m ~ l a t i o n . ~ , ~The ~ * 'ratio ~ of the maximum to minimum probablities in the middle of our curve is similar to the corresponding ratio obtained in the simulation36 with the same water model, but is about half that obtained in the other simul a t i ~ n . * This * ~ ~ means that the corresponding difference in energies for different orientations of a water molecule near a nonpolar solute is about 0.4 kcal/mol larger in molecular simulationssJ3 than in our computations and in ref 36. It may reflect the difference in water models used in the computations or the contribution of orientational correlations that are neglected in this study and will be analyzed elsewhere. The interplay of different factors contributing to hydration entropy is rather complex, and the magnitude of the spread in energies of different configurations of hydration water is a major factor. It may be worth noting that
the only attempt to calculate hydration entropy (for methane) with the semiempirical molecular theory3' led to an absolute value of the computed hydration entropy 1.5 kcal/mol too large. An attempt to reproduce the temperature dependence of hydration free energies of inert gases with full molecular simulation32led to rather inconclusive results (see ref 10 for a discussion). Large uncertainties in the water-water interaction energies around nonpolar solutes obtained in molecular simulation,22along with significant discrepancies in changes of these energies and their -~**~~ interpretations found in different molecular s t ~ d i e s , ~ preclude a definite interpretation of relatively small differences between our results and those of molecular theories a t this time. Thus our results, which correctly reproduce experimentally observed decrease in entropies upon a dissolution of inert gases, suggest that it can be quantitatively explained by a larger (than in the bulk water) spread of configurational energies of water molecules around nonpolar solutes. This is determined by the loss of hydration enthalpy by water molecules in some configurations around a nonpolar solute. This loss of the hydration enthalpy, and not an "enhanced hydrogen b ~ n d i n g " ~(or~ ,"structure ~~ making") already disputed in the literature,22constitutes the basis of the hydrophobic effect according to our results. Of course, the existence of any preferred configurations can be interpreted as formation of a structure, but this is quite different from the meaning usually assigned to the structure making. The importance of the hydrophobic effect and rapidly increasing popularity of the continuum a p p r ~ a c h " ~in~ our ~ - ~opinion, ~ an exposure of the new possibilities of its application presented here. Further development and analysis of our approach are, of course, desirable, and they are under way. They may lead to a progress in our understanding of the thermodynamics of hydration, as well as of the limits of applicability of the continuum approach. Acknowledgment. We thank R . M. Fine, B. K. Lee, and H. Meirovich for productive and illuminating discussions and P. J. Rossky and J. Malinsky for helpful suggestions. This work has been supported by NIH grant GM-38144. (30)Jorgensen, W.L.;Chadrasekhar, J.; Madura, J. D. J. Chem. Phys. 1983, 79, 926. (31) Pratt, L. R.; Chandler, D. J. Chem. Phys. 1977,67, 3683. (32)Swope, W.C.; Andersen, H. C. J. Phys. Chem. 1984, 88, 6548. (33)Zichi, D.A.; Rossky, P . J. J . Chem. Phys. 1985, 83, 797. (34)Sharp, K. A.; Honig, B. Annu. Rev. Eiophys. Eiophys. Chem. 1990, 19, 301. (35)Davis, M. E.;McCammon, J. A. Chem. Reo. 1990,90, 509. (36)Postma, J. P. M.; Berendsen, H. J. C.; Haak, J. R. Faraday Symp. Chem. SOC.1982, 17, 55.
Heats of Sublimation from a Polycrystalline Mixture of Cg0and C,o C. Pan, M. P. Sampson, Y. Chai, R. H. Hauge,* and J. L. Margrave* Department of Chemistry and Rice Quantum Institute, Rice Unioersity. Houston, Texas 77251 (Received: January 14, 1991)
Knudsen effusion mass spectrometric measurements of vapors in equilibrium with a polycrystalline mixture of C , and C ~ O were carried out over the temperature range 640-800 K. From the second-law method, average values obtained for the heats of sublimation of Cm and C70from a polycrystalline C , matrix were found to be respectively 40.1 1.3 and 43.0 2.2 kcal mol-', at the average temperatures 707 and 739 K. It was also noted that it was necessary to heat treat the samples at temperatures of at least 170 O C for greater than 12 h to achieve stable vaporization. This was consistent with the sample becoming more crystalline.
*
Introduction Cb0 has been of interest since smalley and co-workersl sueceeded in producing a remarkably stable C , cluster ion by laser
vaporization of graphite in a high-pressure supersonic nozzle in 1985. However, it was not practical to investigate traditional thermodynamic properties until Kratschmer, Huffman, and coworkers2 recently reported a procedure that for the first time
H. W.;Heath, J. R.; O'Brien, S. C.; Curl, R. F.; Smalley, R.
(2)Kriitschmer, W.; Lamb, L. D.; Fostiropoulos, K.; Huffman, D . R. Nature 1990, 347, 354.
( I ) Kroto,
E.Nature 1985, 318, 162.
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0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 2945
Letters allowed the preparation of macroscopic quantities of solid C,. Graphite electrodes were vaporized to form a soot that contained a small amount of material that was soluble in nonpolar solvents. This soluble portion, separated either by sublimation or extraction, was found to consist primarily of solid C, and C70. Literature reports of the relative amounts of Cm and CT0in graphitic soot have varied. Kratschmer et aI.* initially reported C7o:C, ratios of 0.1 and 0.02 for two different samples based on mass spectrometric determinations. Whetten et al.' analyzed two different samples by HPLC,mass spectrometry and 13CN M R spectroscopy, and determined a C7O:C, ratio 6f 0.18. These authors also noted a temperature dependence for the vapor-phase ratio of C7o:C,9 Kroto et a1.5 have most recently reported a C7o:C, ratio of 0.2. This paper describes the determination of the heats of vaporization of C, and C70. Two factors that contribute to the vapor-phase temperature dependence of the C7o:CW ratio are also observed: (1) the change in degree of crystallinity of c 6 0 with heat treatment and (2) the differences in heats of vaporization of c60 and C70.
Experimental Section A single sample was used for the six vaporization runs. The sample was prepared by the contact-arc procedure recently described by Smalley et al? Contact-arc vaporization of a graphite rod in 100 Torr of helium yielded a graphitic mot that was scraped from the walls of the collection cylinder. The soot was subsequently extracted with toluene, and the toluene solution of C60 filtered through a fine-fritted Buchner funnel. The solvent was then removed in a rotary evaporator. We also found it necessary to condition the sample by heating under vacuum at 170 OC for 1 day in order to fully crystallize the sample. Powder X-ray data exhibited weak peaks for material that was obtained immediately after solvent removal. X-ray scattering due to an ordered Csosolid was seen to increase by 4-S-fold when the sample was conditioned at temperatures as low as 170 OC for times as short as 12 h. Longer heating periods or elevated heating temperatures did not appreciably change the intensities of its X-ray powder diffraction pattern. Under a microscope, both needles and plates were found to be dominant in the conditioned Cm which is in agreement with that reported by Kratschmer and Huffmad and K r ~ t o .We ~ conclude that heating the initially amorphous C, causes it to become a largely crystalline form of c60. A quadrupole mass spectrometer with pulse-counting detection electronics was used in the investigation of vapor species. The molecular beam source was a copper Knudsen effusion cell (i.d. = 6.35 mm, height = 35.56 mm, wall thickness = 1.59 mm). The molecular beam issued from the cell through an orifice of 1-mm diameter. The cell was filled about three-quarters full with the sample and was held in a resistively heated furnace. The sample was allowed to sit at each temperature for 1-2 h to ensure that equilibrium was reached. Most experimental runs, except for the first run where the ion current of C70++was measured only in the cooling process, were performed in a heating and cooling cycle. Ion intensities for the doubly charged Cs0++and C70++ were obtained for at least six different temperatures in the temperature range 640-800 K. Previous reports have noted that both the singly and doubly charged Csoand C70 ions dominate the mass spectrum. We chose to use the doubly charged ions because they were more conveniently monitored. The ion currents of the doubly charged $ detected as the quadrupole scanned species, Ca++ and c70++were the ranges 355-365 and 41 5-425 amu. Temperature was measured with a tungsten-6% rhenium vs tungsten-26% rhenium thermocouple. The tip of the thermocouple was firmly attached
-
-
(3) Ajie, H.; Alvarez, M. M.; Anz, S. J.; Beck, R. K.; Diederich, F.; Fostiropoulos. K.;Huffman, D. R.; Krfitschmer. W.; Rubin, Y.; Schriver, K. E.; Sensharma, D.; Whetten, R. L. J . Phys. Chem. 1990, 94, 8630. (4) Haufler, R. E.; Chai, Y.; Chibante, L. P. F.; Conceicao. J.; Jin, C.; Wang, L. S.;Maruyama, S.; Smalley, R. E. Symposium on Clusters and Cluster Assembled Materials Special Session on Buckmiwterfullerene; Boston, MA, Nov 29, 1990 [Mater. Res. Soc. Symp. Proc., in press]. ( 5 ) Taylor, R.; Hare, J. P.;AWul-Sada, A. K.;Kroto, H.W. J . Chem. Soc.. Chem. Commun. 1990, 1423.
12.3
13.3
12.8
13.8 10000/T(Kl
14.0
14.3
15.3
Figure 1. Temperature dependence of In (IT) for CW++in run 4.
12.5
13
14
13.5 10000/TIKl
1
5
Figure 2. Temperature dependence of In (IT) for C7,,++ in run 4.
TABLE I: Second-Law H a t s of Sublimation for C,
and Cm from
the P O l y C ~ S t r l l C i ~, MaMx
run
T, K
6 mean value
706 712 734 731 706 698 707
I 2 3 4
5
C24H 12
C3ZHI4
469 600
Cm++ AHo(vap, T), kcal mol-' 39.1 i 0.7 39.4 i 1.3 42.3 i 0.9 41.3 i 0.8 39.1 f 0.7 39.5 f 1.3 40.1 f 1.3'
Go++ T,K 760 735 145 744 734 722 739
W(vap,T), kcal mol-' 45.3 4 1.0 43.4 f 2.1 47.0 f 2.2 42.2 f 1.0 41.6 i 0.8 41.7 i 4.1 43.0 i 2.2O
AHo(vap,T) = 14.1 kcal mol-] (ref 7) AHo(vap,T) = 21.9 kcal mol-' (ref 7)
95% confidence.
to the rear of the Knudsen cell. Seventy-electronvolt electrons were used to ionize the molecular beam. At each equilibrium temperature, three or four mass spectra were taken consecutively. The intensities of Ca++ and C70++ ions at each temperature were calculated by integrating all peaks in the respective isotopic patterns. These intensities were then averaged to give a mean value, I, of the intensity of Ca++ or C70++ions. From the well-known van't Hoff equation, the slope of the least-squares curve fit of a In ( I T ) versus 1/T plot yielded the average heat of sublimation for the species of interest for the measured temperature range?
Results and Discussion Six experimental runs were carried out. Figures 1 and 2 show the temperature dependencies of In (IT) of Cso++and CTO++, respectively, in run 4. The second-law heats of sublimation of Csoand C70 obtained from the polycrystalline C, matrix in each experimental run are shown in Table I. For comparison the heats of vaporization for two large aromatic molecules, coronene ( 6 ) Grimley, R. T. The Characterization of High-Temperature Vapors; Margrave, J. L., Ed.; Wiley: New York, 1967; Chapter 8, pp 222-225. (7) Stephenson, R. M.; Malanowski, S.Handbook of the Thermodynamics of Organic Compounds; Elsevier: New York, 1987.
J. Phys. Chem. 1991, 95, 2946-2948
2946
The ion intensities read from the plots were converted to relative partial pressures by assuming that the ionization cross sections were directly proportional to the number of carbon atoms in the ions. Thus
TABLE II: Ratio of Partid Pmsurea of Cmover C,
1 2 3
4 5 6 ref 3
3.1 5.6 5.3 5.0 4.3 4.2 12.8 (613 K)
8.1 9.2 9.5 5.6 5.9 5.5
#Corrected for ionization cross sections: P(C,o)/P(C,) 601(C70++)/7O1(C,++)
(CZ4Hl2)and ovalene (Cj2HI4).have been included. The temperature, T,represents the mean temperature of each run. The lower value for the heat of sublimation of C60reported in the previous publication should be considered as that of an amorphous Cm, where the sample was undergoing a change during the experiment! The more scattered values of the heats of sublimation of C70 may have resulted from the low intensities of the C70++ ion. However, it is clear that in a polycrystalline Cm matrix, C70 has a slightly higher heat of sublimation than Ca. Table I1 lists the ratio of CT0to C60 calculated at two temperatures by using the second-law plots for each of the six runs. (8) Haufler, R. E.; Conccicao, J.; Chibante, L. P. F.; Chi, Y.; Byme, N. E.; Flanagan,.S.; Haley, M. M.; OBrien, S.C.; Pan, C.; Xiao, Z.; Billups, W. E.; Ciufolini, M. A.; Hauge, R. H.; Margrave, J. L.; Wilson, L. J.; Curl, R. F.; Smalley, R. E. J. Phys. Chem. 1990, 96, 8634-6.
p(c70) -p(cm)
- 601(c70") 701(C60++)
As expected from the difference in heats of vaporization, the amount of C70 in the vapor phase relative to Cm increased with increasing temperature. The heats of vaporization measured for C70 for runs 4 - 6 differ slightly from those measured for the first three runs, but the Cm heats of vaporization do not show this anomaly. In addition, the calculated C7& , ratio for runs 1-3 differs from that determined for runs 4-6. We do not know the reason for these observations, although we note that the sample was allowed to sit at room temperature in air for 2 weeks between runs 3 and 4. Selective oxidation of C70, leading to lesser amounts of this species, could account for the observed difference in the C70:Cm The data may also suggest that at higher concentrations of C70 the increased probability of interactions between adjacent C70 molecules in a Cs0 matrix leads to a higher heat of vaporization for C70. Acknowledgment. We thank the laboratory of Prof. R. E. Smalley for providing the graphitic soot and Dr. S.J. Hwu and his students Y. C. Hung, S.M. Wang, and J. D. Carpenter for their help with the X-ray diffraction. We also acknowledge the financial support of the Robert A. Welch Foundation and MSNW, Inc.
Femtosecond Laser Study of the Alignment of Reactant and Products in the Photolsomerization Reactions of ck-Stlibene Roseanne J. Sension, Stephen T. Repinec, and Robin M. Hochstrasser* Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (Received: February 4, 1991) Polarized femtosecond laser studies of the products of the photoisomerization of cis-stilbene demonstrate an unexpectedly high degree of alignment between the cis reactant and trans product transition dipoles and an unexpectedly low degree of alignment between the cis reactant and dihydrophenanthrene (DHP) product transition dipoles. These results are consistent with the reaction toward both trans and DHP involving a significant angular displacement of the ethylene bond. Some possible reasons for this displacement are discussed. Time-resolved spectroscopic studies of the photoisomerization of cis-stilbene have yielded a great deal of information on this simple reaction.'+ The isomerization of electronically excited cis-stilbene (cis*) occurs in 1-2 ps even in high-friction envir o n m e n t ~ . ~As. ~this is much faster than the rotational diffusion, the intramolecular rearrangement occurs while the molecule is essentially fixed in space. In this situation the alignment of the reactant and product molecules can be measured with polarized light pulses and hence the reaction coordinate can be determined. We have performed such a study of the photoisomerization of cis-stilbene. ( I ) Sumitani, M.; Nakashima, N.; Yoshihara, K. Chem. Phys. Lett. 1979, 68, 255-257. (2) Yoshihara, K.; Namiki, A.; Sumitani, M.; Nakashima, N . J . Chem. P h p . 1979, 71, 2892-2895. (3) Greene, 9. 1.; Farrow, R. C. J . Chem. Phys. 1983, 78, 3336-3338. (4) Doany, F. E.; Hochstrasser, R. M.; Greene, B. I.; Millard, R. R. Chem. P h p . Lett. 1985, 118, 1-5. (5) Abrash, S. A.; Repinec, S. T.; Hochstrasser, R. M. J . Chem. Phys. 1990, 93, 1041-1053. (6) Todd, D. C.; Jean, J. M.; Rosenthal, S.J.; Ruggerio, A. J.; Yang, D.; Fleming, G. R. J . Chem. Phys. 1990, 93, 8658-8668.
The femtosecond transient absorption spectrometer used for these experiments has been described previou~ly.~The pump wavelength was 312 nm. A flowing sample of cis-stilbene (less than 0.1% trans-stilbene) in hexadecane was used for all measurements. cis-Stilbene excited at 312 nm forms trans-stilbene and dihydrophenanthrene (DHP) with quantum yields of 0.35 and 0.10, re~pectively.~The remaining cis* molecules return to the ground electronic state on the same time scale as DHP and trans formation. The time-resolved absorption of cis-stilbene probed between 540 and 420 nm exhibits a transient which decays in 1.4 ps due to the excited state of cis-stilbene, and a persistent increase which rises in 11.7 ps. The time-resolved absorption obtained by using a 480-nmprobe is shown in Figure 1. The persistent spectrum found between 540 and 420 nm is consistent with the known spectrum of ground electronic state DHP (Amx = 450 nm*). A persistent absorption signal is also observed by using probe (7) Wismonski-Knittel, T.; Fischer, G.; Fischer, E. J . Chem. Soc., Perkin Trcms. 2 1974, 1930-1940. (8) Muszkat, K. A.; Fischer, E. J . Chem. Soc. ( B ) 1967,662678.
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