J . Phys. Chem. 1991, 95, 8941-8944 reorient by 60°, fluorines of one molecule then fit nicely into hollows of a neighbor, leading to a nominally hexagonal closest packing of fluorines when the lattice readjusts to the monoclinic form. Although this more compact structure has a lower energy than the bcc, the bcc has a higher entropy (accounting for its greater stability at higher temperatures). Especially to be noted, then, is the close similarity of the monoclinic structure to that of the bcc. If s F 6 (or TeF,) molecules were somehow to transform smoothly into spheres, the monoclinic structure would transform smoothly to body-centered cubic. If, on the other hand, molecules in the orthorhombic structure were gradually to become spherical, the lattice would smoothly transform to hexagonal closest packed. Because the coordination in this structure is markedly different from that in bcc, it can be seen that a transition from bcc or monoclinic to orthorhombic requires a major reorganization, and one which would be expected to be comparatively slow. The present MD computations are entirely consistent with this picture. They indicate that throughout the range of temperatures over which the monoclinic TeF, clusters were encountered they were metastable with respect to the orthorhombic. That they were seen at all, then, is due to the kinetics of the transition, not to the thermodynamics. It is no longer strange that the lower symmetry monoclinic form is seen at a higher temperature than the orthorhombic form. Neither is it surprising that the monoclinic clusters of TeF, were seen even though the monoclinic phase had never been found for bulk TeF6 or for the transition-metal hexafluorides whose molecules so closely match TeF, in size and shape. Observations of monoclinic clusters were made only microseconds after rather warm microcrystals had condensed from the vapor in a cooling flow. Orthorhombic clusters seem to be generated only if they are grown in flow that is already very cold. That TeF6 is closer in its crystal chemistry to the metal hexafluorides than to its smaller homologues SF6and SeF, is indicated
8941
by the lack of a thermodynamically stable monoclinic phase of TeF6. These and the above considerations prompted us to propose a study of clusters of the metal hexafluorides. Removing all doubts about the close kinship between the hexafluorides of tellurium and the transition metals was the outcome of the suggested investigation. Clusters of WF6 produced in supersonic flow were found to behave almost identically with those of TeF6.'* When nucleated in very cold flow, they displayed orthorhombic diffraction patterns. When formed in warmer flow conditions, however, their diffraction patterns were unmistakably those of monoclinic crystals. Certain details remain to be settled before the hexafluoride story is complete. Whether an elusive trigonal form of SF6 reported to exist at temperatures between those of bcc and monoclinic4J9 is stable or metastable and whether it can occur in the heavier hexafluorides is uncertain. It is a t least a likely intermediate in the transition from bcc to monoclinic. Neither is it entirely substantiated that the lighter hexafluorides cannot exist as orthorhombic crystals at sufficiently low temperatures. Nevertheless, the present research appreciably clarifies the relationship between the chalcogen and metal hexafluorides.
Acknowledgment. This research was supported by a grant from the National Science Foundation. We thank Messrs. T. S.Dibble, J. W. Hovick, and P. J. Lennon for permission to cite their unpublished results for clusters of tungsten hexafluoride. We are indebted to Mr. F. Dulles for considerable help in computations and to Dr. W. Smith of the Daresbury Laboratory for the program MDMPOL. Registry No. TeF6, 7783-80-4. (18) Bartell, L. S.;Hovick, J. W.; Dibble, T. S.;Lennon, P. J. Unpublished research. (19) Bartell, L. S.;French, R. J. Rev. Sd. Instrum. 1989,60, 1223.
Calculated Equillbrlum Yields of Csofrom Hydrocarbon Pyrolysis and Combustion J. Thomas McKinnon TDA Research, Inc., Wheat Ridge, Colorado 80033 (Received: January 22, 1991; In Final Form: May 17, 1991)
The equilibrium yield of Buckminsterfullerene, Cso, has been computed for the pyrolysis and oxidation of a hydrocarbon source using a free-energy-minimization computer code as a function of temperature, pressure, and element ratios. High Cm yields are favored by low pressure and high C/H ratios and low oxygen concentrations. A temperature window exists in which fullerene yields are favored between 2200 and 2600 K. The computed yields are extremely sensitive to the value used for the Cso heat of formation and are fairly sensitive to the vibrational frequencies of the molecule.
Gerhardt et al. reported in 1987 that microscopic quantities
Introduction
In 1985, Kroto et a1.l proposed the existence of a class of
of Cm and C70 were produced in sooting benzene and acetylene flame^.^ Our recent discovery that macroscopic quantities of
closed-cage carbon molecules with aromatic structure. The most abundant of these molecules, c60, was speculated to have a structure resembling a soccer ball and was given the name Buckminsterfullerene in honor of Buckminster Fuller's work on geodesic domes. The other molecules in this class, such as C,,,. have come to be known as fullerenes. Interest in this area has increased greatly with the discovery by Kratschmer et a1.2 of a simple method to produce large quantities (ca. 100 mg) of fullerenes. In the Krsitschmer et al. process, fullerenes are formed by vaporizing carbon rods in an electric arc.
fullerenes could be extracted from combustion soot4 led us to conduct an investigation on the thermodynamic limits to fullerene production. We have shown that Cm and C70can be extracted from combustion soot produced in a premixed benzene/oxygen/ argon flame a t a C/O ratio of 0.96 and a pressure of 40 Torr. The yield of fullerenes from the soot is about 1% (grams of Cso + C70 per gram of soot) and the yield of soot from fuel carbon is about 3%. The overall yield of fullerenes from fuel carbon, 0.0396,is quite low compared to the yields of fullerenes from
(I)Kroto, H. W.;Heath, J. R.;OBrien, S. C.; Curl, R. F.;Smalley, R. E. Nature 1985,318, 162-163. (2)Kratschmer, W.;Lamb, L. D.; Fostiropulos, K.;Huffman, D. R.
137, 306-3 10. (4) McKinnon, J. T.; Bell, W. L.; Barkley, R . M. Combusr. Flame, sub-
Nature 1990. 347, 354-358.
(3)Gerhardt, Ph.; Loffler, S.;Homann, K. H. Chem. Phys. Lerr. 1987, mitted for publication.
0022-3654/91/2095-8941%02.50/0 0 1991 American Chemical Society
8942 The Journal of Physical Chemistry, Vol. 95, No. 22, 1991
McKinnon
TABLE I: Thermodynamic Properties of BF and Other Mdecuka Important in the Equilibrium Calcllhtion AHd298),
species CJ+, C;H; Alp
S(2981, cal/(mol K) 48.02 64.37 136.86 122.4
kcal/(mol K)
BF
54.20 19.8 1 99.10 870.0
300 K 10.6 19.9 134.8 108.4
500 K 13.0 33.3 166.2 190.7
C, cal/(mol K) 1500 K 18.3 58.3 240.9 321.8
2000 K 19.5 63.0 252.1 335.6
lo00 K 16.3 51.1 216.6 290.5
2500 K 20.3 65.7 258.0 342.6
O A l O = CJ2HI4.10 aromatic rings.
carbon rods in the electric arc method. We conducted an equilibrium analysis to investigate the effects of the experimental parameters on fullerene yield. Reported below are the computed yields of Buckminsterfullerene (BF) as a function of temperature, pressure, oxygen concentration, and C / H ratio. The equilibrium concentration represents the point of minimum free energy of the mixture. Calculation of equilibrium concentrations implicitly ignores any kinetic limitations to growth, so the results are more an indication of direction than a prediction of absolute concentrations. Nonetheless, in the absence of reliable kinetic data on the growth rates of fullerenes, equilibrium calculations are a valuable starting point.
BF Thermodynamic Properties Before making any calculations on the equilibrium yield of BF, we needed to estimate its thermodynamic properties: AHf,S298, and Cp(T). There are several methods of estimating the thermodynamics of a molecule for which no data exist. Group additivityS is a simple, robust method for "normal" molecules, but it cannot account for the strain energy introduced by the curvature of the BF sphere. (Possibly a better way to state this is that no group has been developed for the strain of a 60-member sphere.) Fortunately, the enthalpy of formation has been previously computed for BF using the MNDO (minimum neglect of differential overlap) method,6 and the vibrational frequencies have been determined based on the MNDO bond strength^.^ The geometry of the molecule and the vibrational frequencies are sufficient information to calculate the entropy and heat capacity from statistical mechanics. The contributions to entropy and heat capacity are the sum of the components from translation, rotation, and vibration (1) s298 = slrans + Srot + S v i b cP = + cu3trans + cv,rot + Cu.vib (2) where R is the gas constant. The formulas for these quantities are tabulated in several SOU^^.^^^ The translational and rotational partition functions are fully in the classical limit for the temperature region of interest, but the vibrational partition function is not. The translational components of s 2 9 8 and C, are given by Stran, = 3 7 . 0 + 3R In 2
(g)+
In
(&)+
R In (n)
(3)
where M is the molecular mass in daltons, R is the gas constant in cal/(mol K), Tis the temperature in K, and n is the number of optical isomers. The rotational components are
where I,,, is the moment of inertia in amu A2 and u, is the external ( 5 ) Benson,
S.W. Thermochemical Kinerics; Wiley: New York, 1976. (6) Newton, M. D.; Stanton, R. E. J . Am. Chem. Soc. 1986, 108, 2469-2470. (7) Stanton, R. E.; Newton, M. D. J . Phys. Chem. 1988, 92, 2141-2145. (8) McQuarrie, D. A. Statistical Mechanics; Harper and Row: New York, 1976; p 135.
Moo
1500
2500
Temperature (K)
3ooo
-
Figure 1. Equilibrium of BF for the reaction 30C2H2 a function of temperature at 1 atm.
Cm
+ 30H2 as
symmetry number. The moment of inertia was determined to be 5844 amu A2 by making the assumption that the mass of BF was uniformly distributed in a thin, spherical shell of diameter 7 . 0 A and numerically integrating over the shell. The external symmetry number is the number of indistinguishable ways the molecule can be oriented. BF has been determined to be of the icosahedral point group, Ih6. From the point group, the symmetry number can be computed by summing the pure rotation symmetry operations8 from the I, character table^;^ this yields a value of u = 60 (it is coincidental that the symmetry number is the same as the number of atoms in the molecule). The vibrational components of the entropy and heat capacity are given by
n= I
- In (1 - exp(-x,)) Cv.vib
+
174 x,Z exp(x,) =RE n=l(exp(x,) -
x, = 1.44un/T
(9)
where u, is the vibration frequency in cm-' of the nth mode and the summation is over all the vibration modes of BF (3N - 6 = 174 for a three-dimensional molecule where N is the number of atoms). The vibrational frequencies have been determined from the MNDO force constants.' Table I shows the thermodynamic properties of BF, which represents the sum of the individual contributions. Also shown on Table I are the thermodynamic properties of several other species which are important in the equilibrium calculation. The reported accuracy of MNDO is to within =1 kcal/mol per C for hydrocarbons with five and sixmembered rings! The sensitivity to uncertainties in this quantity is explored below.
Constrained Equilibrium Calculation The thermodynamic properties computed above have been used to compute the equilibrium concentration of BF for the chemical reaction 30C2H2
c m + 30H2
(10)
(9) Cotton, F. A. Chemical Applications of Group Theory; Wiley: New York, 1990; p 436.
The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 8943
Equilibrium Yields of Cm
1
0.70 r
0.60
1-
0,oI
I
0.00 -
2200
I
0.80
Y
\
-w 2"
1
2600
2800
3Ooo
0.00
t
1800
Temperature (K)
Temperature (K)
Figure 2. Computed global equilibrium yield of BF as a function of temperature at I atm for C/H = 1.0 (circles), 1.25 (squares), and 2.0 (triangles).
Figure 3. Computed global equilibrium yield of BF as a function of temperature at a C/H ratio of unity for P = 0.01, 0.10.0.50, 1.00, and 2.00 atm.
This reaction has a AHB8 of -756.0 kcal/mol and AS298of -38 1.8 cal/(mol K). Thus, it is enthalpically favored but entropically disfavored. Consistent with reactions of this type, the equilibrium is shifted to the right at low temperatures but becomes more balanced as the endothermicity becomes less important relative to entropy at high temperatures. Figure 1 shows the equilibrium conversion for this reaction.
Global Equilibrium Calculation The above equilibrium calculation is interesting in that it shows the direction which is favored with changing temperature, but it is unrealistic in that it is constrained to only three types of molecules, A real physical system can shift to form any thermodynamically allowed molecule. We have thus computed the global equilibrium of the BF in equilibrium with 88 other species, both hydrocarbons and oxygenates. The list includes saturated and unsaturated aliphatics and substituted and unsubstituted polycyclic aromatics up to IO aromatic rings. The thermodynamic properties for these compounds were assembled from available datal0 and from group additivity methods." We have excluded solid graphite from our list of species on the basis of observations in sooting flames. If graphite were included in the list, the equilibrium would predict that all the carbon would go to this state. However, observations of rich combustion systems show that PAH are formed rather than soot (which is similar to graphite) under conditions where equilibrium would predict only graphite. In a sense,we are implicitly applying a kinetic constraint to the equilibrium calculation. The experimental observation of fullerenes in flames is further justification for this kinetic constraint. The base-case computations have been based on the pyrolysis of a mixture with a 1:l elemental carbon-to-hydrogen ratio, such as would be achieved in the pyrolysis of acetylene or benzene at a pressure of 1 atm. The calculations were repeated at a number of temperatures. The calculations are for a gas-phase mixture and the relative concentrations are determined through the minimization of the free energy using the STANJAN equilibrium solver.12 The results of this calculation, shown in Figure 2, are quite striking. They show that BF is favored thermodynamically in the temperature range of 2200-2600 K, to the point that over 8% of the carbon is converted to the carbon cluster at the maximum conversion levels (at 2350 K). BF falls into a window of thermodynamic stability between PAH and acetylenes. At temper(IO) Kee, R. F.;Rupley, F. M.; Miller, J. A. "The CHEMKIN Thermodynamic Data Base"; Sandia National Laboratories Report SAND87-8215, 1987. ( I I ) Stein, S. E.; Fahr, A. J . Phys. Chem. 1985,89, 3714-3725. ( I 2) Reynolds, W. R. 'Implementation of the Interactive Program STANJAN"; Stanford University, Department of Mechanical Engineering Report, 1986.
0.00
m
22K)
2 m
2350
2"
2450
2500
Temperature (K) Figure 4. Computed global equilibrium yield of BF as a function of temperature for various element ratios, C/H/O = l:l:z, where z = 0.00, 0.05,0.10, 0.15,0.20. atures cooler than 2200 K, PAHs are the dominant equilibrium product, while at temperatures hotter than 2600 K, acetylene and polyacetylenes become the most stable molecules. The effect of carbon-to-hydrogen ratio is also shown in Figure 2. As might be expected, increasing the carbon loading of the system increases the fullerene yield. The pyrolysis of a material with a C / H ratio of 1.25 (such as naphthalene) results in a predicted maximum yield of 23.2%, also at 2350 K. When the C / H ratio is 2.0 (such as with diacetylene), the maximum yield is 49.5%. The effect of pressure is shown in Figure 3. These calculations were done using a C / H ratio of unity and are shown as a function of temperature. At the high-temperature end of the BF envelope there is very little effect of pressure. At the low-temperature end, however, there is a pronounced pressure effect, primarily due to a shift in stability away from PAH and to BF. The maximum yield of fullerenes increases monotonically with decreasing pressure. The lowest pressure used, 0.01 atm, shows a peak BF yield of 63.7%. The temperature a t which the maximum yield occurs also decreases monotonically as pressure decreases. The effect of oxygen is shown in Figure 4, using a C / H ratio of unity and a pressure of 1 atm. In general, oxygen has the effect of reducing the BF yield because of the low-enthalpy carbon monoxide channel provided by the addition of oxygen. The peak fullerene yield drops steadily as oxygen is added, as does the temperature of the peak. It is interesting to note that, a t low temperatures, systems which contain oxygen show larger fullerene yields than the pyrolytic base case. For example, at 2250 K,the pyrolytic system has a predicted BF mass fraction of 4.84 X 10-4, while a system with 9% atom fraction oxygen (C/H/O = 1:1:0.2) has a BF mass fraction of almost 5 times that. The equilibrium calculation predicts a zero concentration of BF under the experimental conditions in which we have shown fullerene production, that is, using a pressure of 0.053 atm, a
8944
J . Phys. Chem. 1991, 93, 8944-8947
temperature of 2100 K, and a C / H / O ratio of 1:1:0.96. We did a calculation in which the oxygen concentration was reduced until the predicted BF yield matched the experimental BF yield. This condition occurred at an elemental ratio of C/H/O of 1 :I :0.52. In other words, experimental flames produce fullerenes under conditions much leaner than is predicted by an equilibrium analysis. It is interesting to compare this result to oxygen levels for soot inception. Equilibrium predicts that soot would not form until the C/O ratio exceeds unity. However, for benzene, the fuel used in our experiments, the soot inception level is at C/O = 0.76. Thus, flames produce both soot and fullerenes at oxygen concentrations much higher than is predicted by equilibrium. We have by no means experimentally mapped the fullerene production parameter space, but all other soot samples we have tested, which were from flames at higher pressures and lower temperatures, did not produce fullerenes. These results are extremely sensitive to the Nffvalue used. As stated above, the accuracy limits on the MNDO calculation for these types of molecules is f l kcal/mol per carbon atom. Decreasing the AHI by this amount increases the maximum equilibrium weight fraction for the base case system (C/H of unity, 1 atm) from 8.18 at 2350 K to 26.6% at 2250 K. Increasing the AH, by 1 kcal/mol per carbon atom drops the maximum equilibrium weight fraction of the base case to 5.0 X lod. The results are also sensitive to the vibrational frequencies used to compute the entropy and heat capacity. We have done these calculations using the frequency set of Wu et alef3 This data set came from a parameter fit of the Newton and Stanton frequencies. The geometric mean frequency is 870 cm-' as opposed to 914 cm-' for the Newton and Stanton set. The result for the base case (13) Wu,Z. C.; Jelski, D. A.;George, T. F. Chem. Phys. Lerr. 1987, 137, 291-21 94.
system was an increase in yield from 8.1% to 23.6% at 2350 K. The only fullerene included in these calculations was BF. Newton and Stantod have computed that C70 has a heat of formation 1 kcal/mol per carbon atom lower than Cm so it would be expected that C70 would be produced in larger quantities than Cb0. All experimental results to date have shown the opposite, so there may be a kinetic limitation to the larger fullerene. The vibrational frequencies were not available for C70 so its entropy and heat capacity could not be calculated.
Conclusions Equilibrium calculations using the available thermodynamic properties for Buckminsterfullerene indicate that, possibly, relatively large quantities of the carbon cluster can be produced by pyrolysis of a hydrocarbon or from the rich combustion of a hydrocarbon. The limited experimental data available are in very good agreement with the equilibrium calculations. That is, fullerenes are produced in flames at a very high temperature (2100 K), a low pressure (0.053 atm), and a low oxygen concentration (C/O = 0.96). The experiments show that flames produce fullerenes at leaner conditions than predicted by the equilibrium model, but this result is in very good agreement with the trends seen in C / O ratio of soot inception. Buckminsterfullerene falls into a temperature window of thermodynamic stability between PAHs on the low-temperature side and acetylenes on the high-temperature side. Computed Buckminsterfullerene yields are favored by high carbon-to-hydrogen ratios, low oxygen concentrations, and low pressures.
Acknowledgment. This project was partially supported by the Department of Energy, under the Small Business Innovative Research Program, contract no. DE-FG03-90ER80999.000. Registry No. Car 99685-96-8; C2H2,74-86-2; CsH,, 71-43-2; 0, 7782-44-7;C, 7440-44-0; H, 1333-74-0.
Thermochemical Properties of the Osmium Oxides Lyn R. Watson, Terry Thiem, Rainer A. Dressler, Richard H. Salter, and Edmond Mucad* Phillips Laboratory, WSSI, Hanscom Air Force Base, Massachusetts 01 731 -5000 (Received: March 27, 1991)
The enthalpy, AH', for the gaseous equilibrium OsO,(g) s Os03(g) + '/202(g) was measured by using high-temperature mass spectrometry. Over the temperature range 1139-1471 K, a second-law heat of reaction AHollO5(II)= 161 f 14 kJ mol-' was obtained, which yields the standard enthalpy AH0298(II) = 164 f 14 kJ mol-', and a third-law heat of reaction AH0298(III)= 189 f 7 kJ mol-' was calculated by using the known and estimated molecular constants for OsO,(g) and and OsO3(g), respectively. Because of uncertainties in molecular constants, an average standard enthalpy of AHo298(II) AH0298(IlI),176 f 29 kJ mol-', is reported for the equilibrium. From this heat of reaction the heat of formation for gaseous Os03, ArHo298(0s03) = -163 f 29 kJ mol-', is obtained, leading to a bond energy for O-Os03 of 423 f 29 kJ mol-'. The ionization potentials for Os03 and Os04were found to be 11.4 f 0.2 and 12.3 f 0.2 eV, respectively. A small signal of OsOl was observed, and an upper limit of 12.2 f 0.4 eV for its ionization potential was obtained. It is concluded that osmium films which disappear when exposed to the low earth orbit environment probably do so by forming OsO,(g).
I. Introduction Osmium thin films, used as optical coatings in spectrometers because of their high reflectivity in the vacuum ultraviolet, are found to disappear quickly on space-borne instruments.' It is surmised that the disappearance is related to chemistry initiated by the collisions of high-velocity 0 atoms (-7.8 km/s) with surfaces. Possible causes for the mass loss include the following: the formation of volatile oxides of osmium; the distribution of the excess reaction energy to the material lattice, resulting in subsequent vaporization of reaction products or unreacted material;
or chipping of surface materials, particularly thin films. To determine which process causes the mass loss and develop a predictive understanding of the interaction between the highvelocity atmospheric oxygen atoms and the surfaces of materials, it is necessary (among other things) to determine the thermochemical properties of gaseous oxides of the materials.* For osmium, Os04(g) is a well-known gaseous oxidizing agent which is used for many applications, including as a biological fixative. The high vapor pressure of Os04(g) at room temperature has facilitated its study, and infrared,*5 ultraviolet: and photoelectron (2) Murad, E. J. Spacecr. Rockers 1989, 26, 145.
This article not subject to U.S.Copyright. Published 1991 by the American Chemical Society
