J . Phys. Chem. 1992,96, 5 146-5 151
5146
Free-Radlcal Reactions in Supercritical Ethane: A Probe of Supercrltlcal Fluid Structure Theodore W. Randolph* and Claude Carlier Department of Chemical Engineering, Yale University, New Haven, Connecticut 06520 (Received: December 16, 1991; In Final Form: February 20, 1992)
Bimolecular rate constants for the Heisenberg spin-exchange reaction between nitroxide free radicals are reported in nearcritical and supercritical ethane. Rate constants are independent of radical concentration over the range investigated. Measured activation volumes for the diffusioncontrolled reaction are as large as 7.5 L mol-' and are well-predicted from Stokes-Emtein hydrodynamics. Reaction probabilities, however, show the effect of local density augmentation of solvent molecules around the radicals, particularly in the immediate vicinity of the critical point. Local density augmentation increases the length of time that the radicals are in contact with one another, thus increasing the probability of reaction per collision. The disparate time scales for diffusion, cluster lifetime, and collision lifetime are used to explain the effects of local density augmentation on the reaction rate constants.
Introduction Supercritical fluids offer a unique environment for both extraction and reaction processes, especially in the immediate vicinity of the critical point, where the fluid's solvent properties are strongly influenced by pressure. To date, the use of supercritical fluids for extraction has received the most attention. (See, for example, Randal1,l Paulaitis et a1.,* Brunner and Peter,3 McHugh and Krukonis? Eckert et al.,5 and Randolph.6) Many of the same pressuretunable properties that make supercriticalfluids attractive for extraction also provide advantages for carrying out reactions. This work examines the effects of the unique physical properties of supercritical fluids on very fast free-radical reactions. The data on solvent effects on reactions in supercritical fluids are sparse, though several measurements of rate constants in the supercritical fluid region have been reported. Johnston and Haynes' reported that the reaction rate constant for the unimolecular decomposition reaction of a-chlorobenzyl methyl ether in 1,ldifluoroethane could be varied over 2 orders of magnitude by adjusting the pressure. Activation volumes were as low as do00 cm3/mol. Peck et aL8 reported that the equilibrium constant for the unimolecular tautomerization reaction between 2-hydroxypyridine and 2-pyridone could be varied 4-fold in supercritical 1,l-difluoroethane. A study by Flarsheim et al.9 on the redox potential of the I&- couple in supercritical water gave activation volumes of -1000 cm3/mol. Rate constants for bimolecular reactions in supercritical fluids have been reported by Chateauneuf et aI.'O Rate constants for the reaction of the benzophenone triplet with 2-propanol in supercritical carbon dioxide at 33 OC decreased from about 8.8 X lo6 to about 2.8 X lo6 mol L-l s-I as pressure increased from 7.1 to 11.0 MPa. Paulaitis and Alexander" reported that bimolecular rate constants for a Diels-Alder reaction in carbon dioxide increased with increasing pressure. A bimolecular rate constant that decreased with pressure was observed by Penninger and Kolmschate,I2 while Brennecke et al.I3 reported trends toward higher bimolecular rate constants with increasing pressure. The analysis of pressure effects on the reaction systems described in the aforementioned studies is generally complicated by several factors. Uncertainty about the properties (critical temperature, critical pressure, dipole moment, etc.) of the transition state, difficulties in analysis of the concentrations of reactants and products, and side reactions are among the most common. We have chosen to examine Heisenberg spin exchange between stable free radicals, a system which avoids some of these difficulties and which allows us to probe the nature of solvent structure near the critical point. The Heisenberg spin-exchange reaction between free radicals is an extremely fast reaction in which the collision of radicals with antiparallel spin states results in an exchange of spin states. The *To whom correspondence should be addressed. 0022-365419212096-5146$03.00/0
reaction rate may be measured in a noninvasive fashion using electron paramagnetic resonance (EPR) spectroscopy. Because the nitroxide free radicals that we use are chemically stable, the yproducts" of the reaction are chemically identical to the reactants, so that concentrations do not change with time. An additional advantage of EPR spectroscopy is its high sensitivity, which allows reaction measurements to be made at conditions approaching infinite dilution. The reaction may be schematically represented as follows:
A
B
A
B
We may represent the rate of reaction as
= kCIAl
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fB1
(la)
In our system the two paramagnetic molecules which are exchanging spin are identical, and we may write the reaction as rexcbange
= k[CI*
(1b)
where [C] is the concentration of nitroxide free radicals. For small, nearly spherical particles (as will be used here), the spin-exchange rate constant k, may be represented as the product of a binary collision rate constant kD multiplied by the average reaction probability for one collision, p :
kc = PkD (2) The reaction probability p for nitroxide free radicals may be written as (3) where the exchange integral J is a molecular property of the nitroxide free radical and T, is the collision time. For a fluid with hydrodynamics described by the Stokes-Einstein relation, the collision time rCscales as T,
0:
7p-2/3/T
(4)
where r) is the solvent viscoSity, p is the molar volume, and kD may be calculated as kD = 4wRD (5) where R = RA + RB is the sum of the van der Waals radii of colliding particles A and B, and 33 is the sum of diffusion coefficients, each of which may be calculated from the Stokes-Einstein relationship:
33= ~ kT/6*sR~ 0 1992 American Chemical Society
(6)
The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 5147
Free-Radical Reactions in Supercritical Ethane ThermoStatted Bath
To Vac Figure 1. Experimental apparatus: (A) manual syringe pump, (B) high-pressure injection valve, and (C) high-pressure recirculation pump.
If, as in this case, the two exchanging particles are chemically identical, the diffusional collision rate constant may then be calculated as kD = 8kT/31
(7)
If accurate values of solvent viscosity are available, deviations of measured Heisenberg spin-exchange rate constants from those predicted from Stokes-Einstein considerations may be used to probe the degree of solvent structure. The type of collision which is monitored is the same as that which would lead to product formation in a general free-radical reaction. Thus, information gained concerning SCF effects on spin-exchange rate constants will be equally applicable to general free-radical reaction rate constants (scaled, of course, by specific reaction probabilities and steric factors14). Also, because the reaction probabilities are so well-characterized for the exchange reaction, we can obtain a great deal of information regarding the supercritical fluid solvent structure. The work reported here deals with reactions which take place at near S i t e dilution (mole fractions ranging from lod to IO4) so as to gain an understanding of pressuredependent solvent effects in pure supercritical fluids. Because the reaction is diffusion limited, it serves to probe the microhydrodynamicsof the fluid near the critical point and thus may be of general application in understanding reactions in supercritical fluids. The free radical that we have chosen to study is di-tert-butyl nimxide (DTBN). It is a liquid at room temperature and is stable at the temperatures used in this work. While experimental critical parameters are not available for DTBN, the critical temperature of DTBN estimated by the group contribution method of Ambrose15J6is 598 K. DTBN is quite soluble in near-critical and supercritical ethane; at 308 K millimolar amounts easily dissolve even at pressures as low as 3.8 MPa. Rate constants for the spin-exchange reaction of DTBN have been measured in a wide variety of liquid sol~ents.'~In liquid hexane in the temperature range 0-60 "C,spin-exchange rate constants may be predicted to within a few percent using simple Stokes-Einstein hydrodynamic theory (results not shown).
Materials and Metbods Heisenberg spin-exchange frequencies were measured in a Bruker ESP300 EPR spectrometer. A high-pressure EPR cell was constructed from fiberglass tubing donated by NVF Co. Temperatures in the cell were measured with a thermocouple, and the cell was thermostated to f0.1 OC using a liquid nitrogen boil-off and a Eurotherm temperature controller. The EPR cell was attached via insulated 1/16-in. stainless steel tubing to a pressure vessel (see Figure 1). The total volume of the pressure vessel, tubing, and EPR cell was 99.8 f 0.2mL. The pressure vessel was kept in a thermostated air bath. Pressure was controlled with a hand-operated syringe pump (High Pressure Equipment) and measured with a digital pressure transducer (Omega). Several times prior to each run the pressure vessel and EPR cell were alternately attached to a vacuum line and then filled with ethane to 3.8 MPa. Ethane (Air Products) passed through
-50 -40 -30 -20 -10
0
10 20
H - Ho (Gauss)
30 40
50
F m 2. Experimental (solid lines) and simulated (dashed lines) EPR spectra at (a) 4.5 MPa, 313 K and (b) 11.0 MPa, 313 K. a scrubber to remove traces of oxygen. Ethane was liquified inside the syringe pump by cooling the pump with liquid nitrogen. DTBN (Sigma, used as received) weighed to *O. 1 mg inside a 1OO-pL injection loop. The DTBN was added to the system via a high-pressure injection valve (Rheodyne). To ensure adequate mixing, a high-pressure recirculating pump (Micropump) was used to circulate the ethane/nitroxide mixture through the EPR cell and the pressure vessel. The flow rate of the pump was approximately 100 mL/min. Care was taken to check that the solution was in the single-phase region at all times. X-band EPR spectra were recorded using a modulation amplitude of 1 G, a 100-kHz modulation frequency, a time constant of 0.04 ms, and microwave power of 10 mW. The center field was set at 3450 G. Each recorded spectrum was the average of two &s, 100-G scans. To ensure that the system had equilibrated after each change in pressure, spectra were recorded until no difference between subsequent spectra could be discerned by computer subtraction of the two spectra. Measurements were made using one of two methods, either at constant DTBN concentration or at constant DTBN mole fraction. In the first, the system was pressurized to approximately 3.8 MPa with deoxygenated ethane and a measured amount of DTBN was injected. After allowing the system to stabilize, an EPR spectrum was recorded. Then the pressure was increased by adding fresh ethane from the syringe pump (keeping the DTBN concentration constant), and the process was repeated. In the second, the system was first pressurized to ca. 15.0 MPa with deoxygenated ethane before the DTBN was injected. After the system was allowed to stabilize, an EPR spectrum was recorded. A new pressure was then set by opening a micrometering valve to allow both ethane and DTBN to be vented, thus maintaining constant mole fractions. Both methods gave equivalent results. Digitized spectra were transferred to a VAX 6800 computer. Simulated EPR spectra were fit to experimental spectra using modified programs based on the EPR simulation programs of Schneider and Freed.18 In the fitting of simulated spectra to experimental spectra, only the spin-exchangerate per molecule and the nitrogen hyperfine coupling constant A N were varied. Line-width corrections for spin-rotation interacti~nsl'-~~ as a function of T/swere made by measuring the line width in the absence of spin exchange at a maximum mole fraction of 1 X IO+. Figure 2 shows typical experimental and fitted spectra. Agreement between the two was excellent at all pressures and temperatures; the simulations of the two spectra presented here are representative of fits obtained at both high and low rates of spin exchange.
Results and Discussion As expected for a reaction whose rate approaches the diffusion limit, the observed bimolecular rate constants for Heisenberg spin exchange decreased with increasing pressure, especially very near
A' '
5148 The Journal of Physical Chemistry, Vol. 96, No. 12, 1992
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sum of the stoichiometric coefficients of the reactants and the transition state (here equal to 0). The activation volume is the difference in partial molar volumes between the transition state and the reactants, Vb - vA, and kT is the isothermal compressibility. For a diffusion-controlled reaction in a fluid obeying the Stokes-Einstein relation, the activation volume for reaction may be predicted from collision frequencies using
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Concentration (mM) Figure 4. Spin-exchangerate per molecule versus DTBN concentration in ethane at 308 K, 4.31 MPa (circles), 4.92 MPa (squares.),and 15.07 MPa (triangles).
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P r e s s u r e (MPa) Figure 3. Bimolecular rate constants (L mol-' s-I) for Heisenberg spin exchange in ethane. Temperatures are (a) 308, (b) 313,and (c) 331 K. Different symbols represent various nitroxide concentrations.
the critical point, where viscosity increases sharply. Figure 3 shows the observed spin-exchange rate constants as a function of pressure for several nitroxide concentrations. Rate constants are higher, and their decrease with increasing pressure is less steep at higher temperatures. Over the range of DTBN concentrations investigated, the rate constants were constant with concentration. Plots of the spinexchange rate per molecule versus nitroxide concentration gave linear plots at all temperatures and pressures. Scatter in the plots increased at lower pressures due to the high sensitivity of the reaction rate to small variations in pressure and temperature, but in no case was the least-squares correlation factor 9 less than 0.95. Typical plots of spin-exchange rates per molecule versus DTBN concentration are given in Figure 4. The effect of pressure on reaction rate constants may be analyzed by transition-statetheoryB to give
where A v ~ , is, the activation volume for the reaction (in this case representative of the activation volume for diffusion) and Y is the
Viscosities required to compute kD were calculated using the method of Jossi et al.21with a calculated low-pressure gas viscosity22and a 32-parameter modified Benedict-Rubin-Webb equation of state23to give accurate density values for ethane. Density values are reported to be accurate to within 596 near the critical point and to within 0.2% away from the critical point, while viscosities are accurate to within 5% and 2%, respectively. Observed activation volumes and those predicted from Stokes-Einstein theory are plotted versus pressure in Figure 5. The agreement between the observed and predicted values is excellent. No adjustable parameters are used to obtain the agreement. The observed maximum in the activation volume at 308 K is more than 7500 cm3mol-'. This may be compared with activation volumes in which are typically in the range of f50 om3 mol-l. Maxima in activation volumes decrease and occur at higher pressures as the temperature increases. Such behavior is consistent with the behavior of the isothermal compressibility, which also exhibits maxima whose sharpness and magnitude decrease and occur at higher pressures as temperature increases. It is apparent that the bulk of the effect of pressure on activation volumes for this reaction can be predicted using only the simple Stokes-Einstein representation of collision frequencies combined with accurate equations for ethane density and viscosity. This agreement between a mean-field theory and experiment suggests that translational diffusion, and hence collision frequencies, for nitroxides in supercritical ethane is largely unaffected by any critical density fluctuations. Solvent Clustering
The importance of clustering of supercritical solvent molecules about a dilute solute has been the subject of some recent Evidence exists for local density augmentation, or clustering, of solvent molecules about solute^.^^*^* Spectroscopic evidence includes solvatochromicshift measurements in supercritical carbon dioxide which indicate that local concentrations of cosolvents such as methanol are higher than bulk values, especially near the critical point.29 Other solvatochromic measurements in supercritical ethane provide evidence of the formation of solvent clusters about 4-(dimethylamino)bem0nitrile.~~ in addition, fluorescence measurements in C02,ethane, and CF3H show indications of
The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 5149
Free-Radical Reactions in Supercritical Ethane
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Pressure (MPa) Figure 6. Observed values of bimolecular spin-exchange rate constant and value predicted from the Stokes-Einstein relationship. Data points are the slopes found from a linear regression on spin-exchangerates per molecule versus nitroxide concentration for six different concentrations. Temperatures are (a) 308, (b) 313, and (c) 331 K.
cluster f ~ r m a t i o n , ~as' , ~do~ molecular simulation studies." While the largest part of the pressure effect on the diffusional activation volume can be explained with models such as the Stokes-Einstein relationship that assume a "structureless" fluid, it is instructive to look also at the magnitudes of the reaction rate constants that can be predicted from such a model and compare them with experimental values. Solvent clustering, if it exists, should cause a deviation in rate constants from those predicted by structureless models. In Figure 6, both the experimentally measured rate constants and those predicted from the StokesEinstein relationship are plotted against pressure. To construct
this plot, one parameter (JT,(P = 15.0 MPa,T = 308 K)) was adjusted to force agreement between the Stokes-Einstein predictions and the experimental data at 308 K and 15.0 MPa. This same parameter, scaled according to eq 4, was used to compute rate constants for all the other pressure and temperature points. K) was found to be 0.87. The value of J ~ ~ ( P l 1 5MPa,T=308 .0 The value of J14is about 1014rad/s,giving a reasonable collision s. For comparison, T~ values in liquids are lifetime of ca. about 3 orders of magnitude larger.14 While the Stokes-Einstein relationship gives accurate predictions of the rate constant at high pressures, deviations are seen closer to the critical point. When
5150 The Journal of Physical Chemistry, Vol. 96, No. 12, 1992
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Pressure (MPa) Figure 7. Ratio of observed bimolecular rate constant for spin exchange in ethane to the rate constant predicted from the Stokes-Einstein relationship as a function of pressure. Temperatures are 308 K (circles), 3 13 K (diamonds), and 331 K (squares). 3.5
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Randolph and Carlier is about 10-100 ns, 6 orders of magnitude longer. If the characteristic lifetime of a solventsolute cluster lies between these two time scales, then it would be expected that translational events could be predicted from mean-field theories such as the StokesEinstein model, while the duration of individual collisions would be sensitive to fluctuations in solvent density. Such an explanation is supported by the results of molecular dynamics simulations by Debenedetti et al.,34who found that solvent clusters had lifetimes of approximately 0.1-1 ps. A supporting piece of evidence for solvent clustering is the lack of dependence of the rate constants on solute concentration. If the observed enhancements in rate constants with respect to predicted values were due to solute-solute clustering, a strong dependence on solute concentration would be expected. No such dependence is observed. In addition, plots of spin-exchangerates per molecule vs concentration yield zero intercepts, which would also not be expected if significant solute-solute clustering were present. It should be noted that systems in which solute-solute clustering has been observed have used more asymmetric solute solvent pairs such as ~holesterol-CO~,~~ cyclohexenoneethane,36 and ~ y r e n e - C O ~ . ~Estimated ' Lennard-Jones pair interaction energies t l l / k and t12/kfor DTBN-DTBN and DTBN-ethane interactions are 435 and 291 K, respectively. For comparison, q l / k and t12 k for the pyrene-CO, pair are 662.8 and 386.4 K, respectively."' Clustering behavior in supercritical fluids has been shown tu be dependent on the asymmetry of the system, and mixtures become more attractive as the ratio of the solute-solute interaction energy to the solventsolvent interaction energy increase~.~~
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Pressure (MPa) Figure 8. Ratio of the observed reaction collision time T~ to T : ~ , the cobion time predicted from the Stokes-Einstein relation. Temperatures are 308 K (circles), 313 K (diamonds), and 331 K (squares). the ratio of experimental-to-predicted rate constants is plotted in Figure 7,it can be seen that the deviations go through maxima, with the sharpest maxima at temperatures nearest to the critical temperature. A possible explanation of observed rate constants higher than those which are predicted from Stokes-Einstein theory is solvent cage effects or clustering. Radical-radical collisions in a fluid exhibiting solventsolute clustering would undergo a longer collision time T~ than those in an unstructured fluid. In a lowviscosity fluid like ethane where Pr: c 1, an increased collision time results in stronger spin exchange and a higher rate of reaction. Figure 8 shows a plot of the ratio of observed collision time to the predicted Stokes-Einstein collision time. Again, as in Figure 7, one fitted parameter is used to force the experimental and predicted values of T~ to be equal at 308 K and 15.0 MPa. The ratio of observed-to-predicted collision times increases as the pressure is decreased from high pressures toward the critical pressure. The effect is most apparent at temperatures near the critical temperature and decreases as temperature increases. Collision lifetimes and hence reaction probabilities are higher than those predicted by Stokes-Einstein theory, yet the activation volumes (which largely reflect collision frequencies) are wellpredicted from this mean-field theory. This effect can be understood upon examination of the relative time scales for nitroxide collision, translational diffusion, and the time scale for solvent clustering. The characteristic time for the duration of a single collision is on the order of 0.01 ps, while the characteristic time for diffusion (i.e., the average time between nitroxide collisions)
Conclusions Heisenberg spin exchange provides a sensitive tool to examine pressure-dependent solvent effects in supercritical fluids. The bimolecular rate constant for spin exchange can be manipulated by almost 10-fold by small changes in pressure near the critical point of ethane. No dependence of the rate constants on solute concentration was observed, indicating that any effects of solute-solute clustering were not apparent, perhaps because of the small energy differences between solvent and solute. The activation volume of the reaction, which is quite large in magnitude compared with typical liquid-phase activation volumes, can be predicted with good accuracy using bulk property measurements. However, careful examination of predicted and observed rate constants in the vicinity of the critical point show that rate constants are larger than those predicted by models based on the Stokes-Einstein relationship. Evidence for solvent clustering about dilute solute molecules includes an average reaction contact time T~ that is about 3 times larger than the Stokes-Einstein prediction. Because the lifetime of solvent clusters is short compared to diffusional time scales but long compared with the duration of a solute-solute collision, solvent clustering affects only the reaction probability and not the collision frequency.
Acknowledgment is made to the donors of the Petroleum R e search Fund, administered by the American Chemical Society, for partial support of this work. Further achowledgment is made to the National Science Foundation for their support (Grant BCS-9014119 and a Presidential Young Investigator Award). Registry No. DTBN,2406-25-9; ethane, 74-84-0. References and Notes (1) Randall, L. G. Sep. Sci. Technol. 1982, 17, 1. (2) Paulaitis, M. E.; Krukonis, R. T.;Reid, R. C. Rev. Chem. Eng. 1982,
_.(3) Brunner, G.; Peter, S.Chem.-1ng.-Tech. 1981, 53, 529. 1. 179.
(4) McHugh, M. A.; Krukonis, V. J. Supercriticul Fluid Extrucrion: Principles and Practice; Butterworths: Boston, 1986. ( 5 ) Eckert, C . A.; Van Alsten, J. G.; Stoicos, T.Enuiron. Sci. Technol. 1986, 20, 319. (6) Randolph, T.W. Trends Biotechnol. 1990,8, 78. (7) Johnston, K. P.;Haynes, C. AIChE J . 1987, 33 (12), 2017. (8) Peck, D. G.; Mehta, A. J.; Johnston, K.P. J . Phys. Chem. 1989, 93, 4297. (9) Flarsheim, W.M.;Bard, A. J.; Johnston, K. P. J. Phys. Chem. 1989, 93, 4234.
J. Phys. Chem. 1992,96, 5151-5156 (10)Chateauneuf, J. E.; Roberts, C. B.; Brennecke, J. F. ACS Symp. Ser., in press. (1 1) Paulaitis, M. E.; Alexander, G. C. Pure Appl. Chem. 1987,59 (l), 61. (12) Penninger, J. M. L.; Kolmschate, J. M. M. In Supercritical Fluid Science and Technology; Johnston, K. P., Penninger, M. L., Eds.; ACS Symposium Series No. 406;American Chemical Society: Washington, DC, 1989;p 242. (1 3) Brennecke, J. F.;Tomasko, D. L.; Eckert, C. A. J. Phys. Chem. 1990, 94, 7692. (14) Molin, Yu. N.;Salikhov, K. M.; Zamaraev, K. I. Spin Exchange: Principles and Applications in Chemistry and Biology; Springer-Verlag: Berlin, 1980. (15) Ambrose, D. NPL Rep. Chem. 1978, 92. (16) Ambrose. D. NPL Rep. Chem. 1979,98. (17) Plachy, W.; Kivelson, D. J. Chem. Phys. 1967, 47, 9,3312. (18)Schneider. D. J.; Freed, J. H.1n.Biological Magnefic Resonance; Berliner, L. J., Reubens, J., Eds.; Plenum Press: New York, 1989;Vol. 8, p 1. (19)Atkins, P. W.; Kivelson, D. J . Chem. Phys. 1966, 44, 169. (20) Hamman, S.D. In High Pressure Physics and Chemistry; Bradley, R. S.,Ed.; Academic Press: New York, 1963;Vol. 2, p 163. (21) Jossi, J. A.; Stiel, L. I.; Thodos, G. AIChE J . 1962,8, 59. (22) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; John Wiley and Sons: New York, 1960; p 22. (23) Younglove, B.A.; Ely, J. F. J. Phys. Chem. Ref. Data 1987,16 (4), 577. (24) Kohnstam, G.The Kinetic Effects of Pressure. In Progress in Reaction Kinetics; Pergamon Press: Oxford, 1970; p 335.
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(25)Economou, I. G.;Donohue, M. D. AIChE J. 1990, 36 (12), 1920. (26) Brennecke, J. F.;Debenedetti, P. G.; Eckert, C. A.; Johnston, K. P. AIChE J . 1990, 36 (12), 1927. (27) Johnston, K. P.; Kim, S.;Combes, J. ACS Symp. Ser. 1989, No. 406, 52. (28) Debenedetti, P. G.;Chialvo, A.; Knutson. B.; Eckert, C.; Tomasko, D. Local Density Enhancements in Dilute SupercriticalMixtures: Camprison Between Theory and Experiment. Abstract from paper 204e, 1991 Annual Meeting of the AIChE, Los Angeles. (29)Kim, S.;Johnston, K. P. AIChE J. 1987, 33 (IO), 1603. (30) Morita, A.; Kajimoto, 0. J . Phys. Chem. 1990, 94, 6420. (31) Betts, T. A.; Zagrobelny, J.; Bright, F. V. J. Supercrit. Fluids, in press. (32) Brennecke, J. F.;Eckert, C. A. Supercritical Fluid Science and Technology; Johnston, K. P., Penninger, J. M. L., Eds.; ACS Symposium Series No. 406;American Chemical Society: Washington, DC, 1989;p 14. (33) Petsche, I. B.; Debenedetti, P. G. J . Chem. Phys. 1989,91 (Il), 7075. (34) Debenedetti, P. G.;Petsche, I. B.; Mohamed, R. S. Fluid Phase Equilib. 1989, 52, 347. (35)Randolph, T. W.; Clark, D. S.;Blanch, H. W.; Prausnitz, J. M. Science 1988, 239, 387. (36)C o m b , J. R.; Johnston, K. P.; OShea, K. E.; Fox,M. A. In Recent Advances in Supercritical Fluid Technology: Applications and Fundamental Studies, in press. (37)Brennecke, J. F.;Tomasko, D. L.; Eckert, C. A. J. Phys. Chem. 1990, 94, 7692. (38)Chialvo, A. A.; Debenedetti, P. G. Ind. Eng. Chem. Res., in press. (39) Petsche, I. B.; Debenedetti, P. G. J . Phys. Chem. 1991, 95, 386.
Thermodynamic Characterlzatlon of C60by Differential Scanning Calorimetry7 Yimin Jin, Jinlong Cheng, Manika Varma-Nair, Guanghe Liang, Yigang Fu, Bernhard Wuaderlich,* Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 -61 97, and Department of Chemistry, The University of Tennessee, Knoxville, Tennessee 37996- 1600
Xiao-Dong Xiang, Roman Mostovoy, and Alex K. Zettl Materials Science Division, Lawrence Berkeley National Laboratory and Department of Physics, The University of California, Berkeley, California 94720 (Received: December 23, 1991; In Final Form: February 18, 1992)
Heat capacity measurements on Csowere carried out by differential scanning calorimetry from 120 to 560 K. This heat capacity was linked based on existing normal-mode and lattice calculation, to the vibrational heat capacities. In this way the thermodynamic functions are available from absolute zero of temperature. The phase transition at 256 K could be identified as a crystal-to-plastic crystal transition with an increase in entropy of 27.3 J/(K mol). A broad beginning of this transition at 190 K is linked to the change from a jumplike rotation that is starting already at about 100 K without increase in entropy to the rotational motion that ultimately causes the disordering transition. This classification is based on reinterpretation of the solid-state NMR results with calorimetry data. No melting temperature could be detected up to 950 K, the temperature limit of our calorimeter.
I. Iatroductioa Besides diamond and graphite, the two well-known crystalline allotropes of carbon, a totally new form of crystalline carbon has been discovered a few years ag0.I It consists of ball-shaped Cso molecules (buckminsterfullerene) and has become well-known because of its special structure? Before 1990 most research on Cso was limited to theoretical studies3-I2because of insufficient material to undertake large-scale experimental studies. In 1990, Kriitschmer et al. first reported a method to synthesize C6,, in macroscopic quantity.I3J4 Since then, the study of this new class of compounds and their derivatives is receiving more a t t e n t i ~ n . ' ~ -For ' ~ example, there has been a characterization of the molecular structure using mass s p e c t r ~ s c o p y ' * ~ * and " ~ J ~X-ray , ~ ~ diffractionI4as well as UV-vis light,7.I3,17.18 IR 13,14,I7-19 Raman,20 NMR, 17.1 821-23 and BRIT spectroscopies and high-pressure liquid chromatography (HPLC).17 tR*lcnted at the American Physical Society Meeting, March 16-20, 1992.
Initial information about a phase transition below room temperature became available recently through differential thermal analysis.2e26 Coupled with X-ray data, orientational ordering was suggested to occur on cooling. In this paper measurements and computations of heat capacity will be reported. The computations are based on vibrational spectra. These new data permit a quantitative interpretation of the transition and, in addition, allow the generation of complete thermodynamic functions, of enthalpy (H), entropy (S), and Gibbs function (G). The heat capacity of Cso was measured from 120 to 560 K by using a single-run differential scanning calorimetry (DSC) te~hnique~ which ~ - ~ needs ~ only 20-30-mg samples to produce quality data. The heat capacity contribution from vibrations was calculated next, based on existing normal-mode and lattice vibration frequen~ies,"~*~~q~~ and then compared with the experimental data. It will be shown that the phase transition that occurs at 256 K is a crystal-to-plastic crystal transition with an entropy of 27.3 J/(K mol), typical for such transitions involving orientational disordering. A broad beginning of this transition can be
0022-365419212096-5151%03.00/0 0 1992 American Chemical Society
