J . Phys. Chem. 1992, 96, 421-425 Species A seems to be bound to Al,,-pillars (site A in Figure 9) as is demonstrated by the observation of distinct 27Almodulation in the ESE of this species recorded on samples activated at 250 OC. In proposing a site for the location of species A l , the observation of distinct 'Li modulation in the ESE signal recorded for this species must be accounted for. There are two possible sites at which Pd3+ could be located that would result in 7Li modulation. These are pseudohexagonal cavities (site A1 in Figure 9) near a Li site and at the edges of the Laponite crystallites (site A2) with proximal Li. Species A2, which like species B gives no modulation of the ESE signal, must be bound to the Laponite layers and cannot be
421
proximal to Li sites. Possible binding sites of species A2 and B are within pseudohexagonal cavities that are not proximal to Li sites, edge sites not proximal to Li sites, or the three basal oxygen atoms of S i 0 4tetrahedra which also are not proximal to Li sites.
Acknowledgment. We thank Dr. A. Ghosh for his initial contributions to this study. We thank Dr. D. Marton for recording XPS spectra and Laporte Industries for providing the Laponite. This research was supported by the Robert A. Welch Foundation, the National Science Foundation, and the Texas Advanced Research Program. Registry No. Pd2+,16065-88-6.
Orientational Disorder in Solid Cubane: A Thermodynamic and 13C NMR Study Mary Anne White,* Roderick E. Wasylishen, Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 453
Philip E. Eaton, Yusbeng Xiong, Kakumanu Pramod, and Nereo Nodari Department of Chemistry, University of Chicago, Chicago, Illinois 60637 (Received: May 31, 1991; In Final Form: July I I , 1991)
Through a combination of adiabatic calorimetry, differentialscanning calorimetry, and I3CNMR spectroscopy,cubane (CBH8, pentacyclo[4.2.0.~~503~8.0"~7]octane) has been found to exhibit rapid rmrientational motion in the solid state at room temperature. The molecules rotate more rapidly as the temperature is increased, and this motion culminates in a transition (Ttr= 394.02 f 0.04 K, A,,H = 5940 20 J mol-I, AJ = (1.849 f 0.006)R) to an orientationally disordered solid phase that exists for a short temperature range, 11 K, prior to melting at 405 K. The entropy change at the melting point (Af,,$ = (2.7 f 0.1)R) is typical for a solid composed of globular-shaped molecules with "plastic crystalline" characteristics.
*
Introduction Polymorphism in polycyclic hydrocarbons has been known for many years.' It can arise due to the presence of an orientationally disordered phase that freezes out on cooling; one example of considerable current interest should be the fullerenes. Certainly, their known rotational disorder in the solid state2-, makes them candidates for polymorphism. For many years, there has been speculation of an orientationally disordered solid state in the cagelike hydrocarbon with the smallest number of atoms and highest symmetry: cubane (C8Hs,pentacyclo[4.2.0.02~5.03~8.04~7]octane). Indications that orientational disorder is possible are the nearly spherical molecular shape, the high vapor pressure (ca. 1 Torr at room temperature4), the low calculated barriers to single-particle re~rientation,~ and the apparent absence of welldefined shoulders in the 13CNMR spectrum of a static powder sample above T = 20 K.6 Although the room-temperature structure of cubane had_been determined by X-ray diffraction7 (trigonal, space group R3, 1 molecule per unit cell), the final disagreement factor (residual of 7.3%) was higher than one might expect for such a highly symmetric molecule if it were static. (1) For example: Parsonage, N. G.; Staveley, L. A. K. Disorder in Crystals; Clarendon Press: Oxford, U.K., 1978. (2) Yannoni, C. S.;Johnson, R. D.; Meijer, G.; Bethune, D. S.; Salem, J. R. J. Phys. Chem. 1991, 95, 9. (3) Tycko, R.; Haddon, R. C.; Dabbagh, G.; Glarum, S. H.; Douglas, D. C.; Mujsce, A. M. J. Phys. Chem. 1991, 95, 518. (4) Kybett, B. D.; Carroll, S.; Natalis, P.; Bonnell, D. W.; Margrave, J. L.; Franklin, J. L. J. Am. Chem. Soc. 1966, 88, 626. (5) Fyfe, C. A.; Harold-Smith, D. J. Chem. Soc.,Faraday Trans. 2 1975, 71, 967. (6) Facelli, J. C.; Orendt, A. M.; Solum, M. S.; Depke, G.; Grant, D. M.; Michl, J. J. Am. Chem. SOC.1986, 108, 4268. (7) Fleischer, E. B. J. Am. Chem. SOC.1964, 86, 3889.
A recent report8 of a Raman spectroscopic investigation of cubane provides evidence for a high-temperature solid-solid phase transformation. In this paper we address the question: Is there polymorphism in cubane? We present thermodynamic evidence for a transition to a high-temperature orientationally disordered phase of cubane and solid-state dynamical information based on variable-temperature I3C N M R relaxation studies.
Experimental Section The cubane sample used in these determinations was prepared at Chicago from cubane-1,4-dicarboxylicacid9using Barton methodology,1° viz. radical decarboxylation via photodecomposition/thermaldecomposition of the bis(thiohydr0xamic acid ester) in the presence of 2methyl-1-propanethiol as a hydrogen donor. The hydrocarbon was carefully purified by crystallizations from benzene and methanol, dried by transfer under vacuum through 4-A molecular sieves, and then finally sublimed at reduced pressure. Cubane is a colorless, crystalline solid at room temperature: the previously reported mp is 130 O C 9 It is stable at room temperature to oxygen, moisture, and light. The heat capacity of 0.949 g of cubane was measured by adiabatic heat pulse calorimetry for the temperature range 30 K 5 T I400 K. The calorimeter is described in detail elsewhere;" for these experiments, the upper temperature range of the calorimeter was extended 20 K beyond that of the earlier report. Due to the volatile nature of this sample, the calorimeter was filled and sealed at an ambient temperature of 5 O C , where, from thermodynamic data: we estimated the vapor pressure to be lowered to 0.09 Torr. Differential scanning calorimetry (DSC) was carried out with a Perkin-Elmer DSC-7 calorimeter, on samples of mass about 5 mg (known (8) Dalterio, R. A.; Owens, F. J. Solid State Commun. 1988, 67, 673. (9) Eaton, P. E.; Cole, T. W., Jr. J. Am. Chem. SOC.1964, 86, 962. (10) Barton, D. H. R.; Crich, D.; Motherwell. W. B. J. Chem. SIX., Chem. Commun. 1983, 939. (1 1 ) Van Oort, M. J. M.; White, M. A. Rev. Sci. Imtrum. 1987,58, 1239.
0022-365419212096-42~%03.00/0 Q 1992 American Chemical Societv
422 The Journal of Physical Chemistry, Vol. 96, No. I, 1992
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1
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I
T/K Figure 1. The molar heat capacity of cubane as a function of temperature. The open circles represent the experimental values determined under the saturated vapor pressure, Cmt,m.The solid line represents the smoothed experimental values, corrected to the molar isobaric heat capacity, Cp,m,as described in the text. The dotted line represents the calculated contribution of the optic modes to the heat capacity. The dashed line represents the baseline heat capacity in the region of the phase transition, as described in the text.
Hz Figure 3. A typical I3C NMR spectrum of cubane at 293 K.
T/ K
I
420
380 I
I
I
I
1
I
I
3-
I
n
-
w
-
e
-C
0 -
3.0
3.5
3 -1 4 10 T / K Figure 4. The spin-lattice relaxation times for cubane, as determined from the I3CNMR experiments, as a function of reciprocal temperature.
Figure 2. A typical heatingxooling differential scanning calorimetric trace for cubane. I represents solid I, I1 represents solid 11, and L represents the liquid phase. The arrows indicate the direction of the run. to four significant figures). The samples were in aluminum pans, sealed in air. Heating and cooling rates were 1 or 2 K m i d . Temperature and enthalpy calibrations were carried out with use of the melting points of indium (at 156.61 "C) and NBS standard 1,2-diphenylbenzene (at 58 "C). For the I3C NMR experiments, a sample of cubane (ca. 0.6 g) was sealed under vacuum in a IO-mm 0.d. thick-walled NMR tube. Natural-abundance variable-temperature 13C(1H) NMR T I measurements on a were carried out using the inversion-recovery pulse ~equencel*.'~ Nicolet NT-360 NB spectrometer at 8.48 T (vc of 90.78 MHz), in the temperature range from 273 to 353 K. At higher temperatures, the sample sublimed out of the BI radio frequency coil to the cooler region of the NMR tube before Ti's could be determined. The NMR sample (12) Farrar, T. C.; Becker, E . D. Pulse and Fourier Transform NMR; Academic: New York, 1971. (1 3) Wasylishen, R. E. In NMR Spectroscopy Techniques;Dybowski, C., Lichter, R. L., Eds., Marcel Decker Inc.: New York, 1987; Chapter 2.
temperatures were calibrated using observed 'H NMR chemical shift differences for pure ethylene glycol or methanol samples,Icl6 and are believed to be accurate to *2 K. Typically, inversion-recovery spectra were obtained for 12-15 variable delays using T and ~ / p2 k of 60 and 30 ps duration, respectively. Spin-lattice relaxation times were calculated using a three-parameter fitting available on the Nicolet software. Errors in TIare estimated to be less than 10%; however, the precision was much tetter (5%). The 'H decoupliig field, yE2/(2x),was determined, using standard procedures,18 to be 8 kHz.
Results
In the adiabatic calorimetry experiment, the molar heat capacity of cubane was measured from 30 to 400 K. The results are illustrated in Figure 1. In the region of the solid-solid phase transition, the sample contributed more than 90% to the total heat capacity; at lower temperatures, the sample contributed about 1052 to the total heat capacity. On the basis of the accuracy of the (14) Kaplan,
1703.
M.L.; Bovcy, F. A.; Cheng, H. N. Anal. Chem. 1975, 47,
( I S ) Piccini-Leopardi, C.; Fabre, 0.;Reisse, J. Org. Mum.Reson. 1976, 8, 233. (16) Van Geet. A. L. AMI. Chem. 1968, 40, 2227; 1975,42,679. (17) Levy, G. C.; Peat, I. R. J . Magn. Reson. 1975, 18, 500. (18) Martin, M. L.; Dclpuech, J.-J.; Martin, G. J. Prucricul N M R Specfroscopy; Heydon and Sons Ltd.: London, 1980; p 215.
The Journal of Physical Chemistry, Vol. 96, No. 1, 1992 423
Orientational Disorder in Solid Cubane determination of the heat capacity of Calorimetry Conference benzoic acid in this calorimeter,” we estimate the accuracy of the present results to be within 2%. The results were reproducible through seven series of measurements and showed no signs of thermal history effects. A typical heating/cooling DSC trace is shown in Figure 2. Two phase transitions were observed; the one at the lower temperature is the solidsolid transition observed in the adiabatic calorimetry experiment, and the one at higher temperature is the melting of cubane (vide infra). From the I3C NMR experiment, it was found that the approximately Lorentzian line (see Figure 3 for a typical spectrum) narrowed as the temperature increased and broadened as the temperature decreased. For example, v l p was 250 f 30 Hz at 294 K, 225 f 30 Hz at 350 K, and 850 f 100 Hz at 272 K. At temperatures much below 270 K, the signal was not observable because of the long I3C TI values and the relatively low power available for ‘H decoupling using the standard Nicolet highresolution NMR probes (yB2/(27r) < 10 kHz). Spin-lattice relaxation times were determined as a function of temperature; the results are shown in Figure 4.
Discussion Immediately apparent from Figure 1 is the large heat capacity anomaly associated with a solidsolid phase transition in cubane. The adiabatic calorimetry experiments measured the molar heat capacities for cubane in a sealed vessel under its own saturated vapor pressure, C,,,. In order to calculate the thermodynamic properties for the transition, it is imperative to have C ,, the molar isobaric heat capacity. C,,,, and C,,, are related by19
where P is the vapor pressure, Tis the temperature, and H is the enthalpy. It is more practical here to consider, for a given experimental determination of the heat capacity, the relationship between the true enthalpy increment during the heat pulse (AH), the input energy (q), the increase in the product of the vapor pressure, and the free volume in the container (A(PV)) and a further term for the sublimation of the sample, as given byZo
AH = q + A(PV) - A[(V- mu)L/(u’-
u)]
(2)
where m is the sample mass, u and d a r e the volume per unit mass of the solid and vapor, respectively, L is the enthalpy of sublimation, and A refers to the final temperature of the heat capacity point relative to the initial temperature. The use of eq 2 to derive C,, from the measured values of, ,C requires the vapor pressure as a function of temperature for cubane; although this has been measured from 239 to 262 K$ it is not appropriate to extrapolate this data to the temperature range of the solidsolid phase transition, as that overestimates the high-temperature vapor pressure, as evidenced by a calculated boiling point some 25 K before the observed melting point. From comparison with other polycyclic hydrocarbons with melting and boiling points similar to those of cubane,21we have chosen to use A and B of 2200 K and 8, respectively, where A and B are the parameters in the Clausius-Clapeyron equation: log (P/Torr) = -A/T
+B
(3)
The resultant calculation of C,,, from smoothed CSat,,values is given by the solid line in Figure 1. The C,,, and C,,, values are indistinguishable below 300 K but differ by as much as 5% at the highest temperatures examined. In order to assess the contribution of the solidsolid phase transition to the heat capacity in excess of that associated with (19) Aston, J. G.; Fritze, J. J. Thermodynamics and Statistical Thermodyanmics; Wiley: New York, 1959. (20) Douglas, T. B.; King, E. G. In Experimental Thermodynamics; McCullough, J. P., Scott, D. W., Eds.;IUPAC: London, 1968; Vol. 1, p 324. (21) Landolr-Bornsrein 1950, 2 (2a), 89.
the lattice, the heat capacity contribution of the optic (internal molecular vibrational) modes was calculated from existing vibrational assignments for c~bane.83*~-~~ This contribution is shown by the dotted curve in Figure 1. The only other (nontransitional) contributor to the heat capacity should be the acoustic modes of the lattice, and this contribution should approach a constant value (3R, where R is the gas constant) in the region of the solidsolid phase transition. The nontransitional (“baseline”) heat capacity through the temperature region of the solidsolid transition therefore has been chosen to parallel the contribution of the optic modes; the baseline heat capacity is shown by the dashed line in Figure 1. From Figure 1, it is apparent that the additional degrees of freedom due to the solidsolid phase transition (as judged by the anomalous contribution to the heat capacity) start in at about 285 K. From the maximum in the heat capacity, we find the transition temperature to be 394.02 f 0.04 K. The very high values of C,, in the transition region make determination of the transition enthalpy (area between the measured and baseline heat capacity curves) uncertain from direct integration, and therefore we determined the enthalpy over the peak of the transition by direct “long-heat” m e a ~ u r e m e n t . ~The ~ result is that the transition enthalpy is 5940 f 20 J mol-’. The transition entropy, determined from the excess (C,,,,T/) from the adiabatic calorimetry results, integrated over the transition region, is 15.37 f 0.05 J K-I mol-I (=(1.849 f 0.006)R). From the DSC results (Figure 2), both the solidsolid transition and the fusion of cubane can be observed. Although the two look well separated in the DSC experiment, the adiabatic calorimetric results show that melting begins immediately on completion of the solidsolid transition (Figure 1 near 400 K). This apparent contradiction is not unusual and is due to the inability to see the more gradual anomalous components of the heat capacity in the DSC experiment because it is a scanning measurement not an equilibrium measurement.26 From the DSC experiments, we found the enthalpy of the solid-solid phase transformation in cubane to be 2600 f 200 J mol-’ at a heating rate of 2 K min-I. This is considerably lower than our value from the more accurate adiabatic calorimetry experiment, again since the DSC is unable to detect the large gradual component of the transition enthalpy. This is not unprecedented in DSC and again is due to the scanning nature of the experiment.26 Furthermore, the DSC results show increased transitional enthalpy with increased DSC scan rate, as has been observed elsewhere for similar gradual phase transitions.26 Therefore, the (equilibrium) adiabatic calorimetric results for the solid-solid transition enthalpy and entropy are to be favored. One major advantage of the DSC experiment over adiabatic calorimetry is that in DSC the sample also can be scanned in the cooling mode. (Again, however, the DSC solid-solid transition enthalpy results are unreliable due to the reasons cited above.) The solidsolid transition (onset) temperature in DSC is 394 K on heating and 391 K on cooling, showing slight hysteresis for this transition, consistent with a first-order phase transition. If the transition were entirely first-order, this would make A$ (=A,,H/T,, for a first-order transition) equal to 1.815R (from the adiabatic calorimetric values of AtrHand T,,),which is very close to the observed (adiabatic calorimetric) value of 1.849R. Therefore, although the solidsolid phase transition in cubane at 394 K has a gradual component trailing back to about 285 K, the transition is predominantly first-order. Against the backdrop of possible loss of sample due to decomposition, measurement of the melting point of cubane by adiabatic (22) Della, E. W.; McCoy, E. F.; Patney, H. K.; Jones, G.L.; Miller, F. L. J . Am. Chem. SOC.1979, 101, 7441. (23) Cole, T. W., Jr.; Perkins, J.; Putnam, S.;Pakes, P. W.; Straws, H. L. J . Phys. Chem. 1981,85, 2185. (24) Pine, A. S.;Maki, A. G.; Robiette, A . G.; Krohn, B. J.; Watson, J. K. G.; Urbanek, Th. J . Am. Chem. SOC.1984, 106, 891. (25) Van Oort, M. J . M.; White, M. A. J . Chem. SOC.,Faraday Trans. I 1985, 81, 3059. (26) White, M. A. Thermochim. Acta 1984, 74, 5 5 .
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extreme narrowing condition applies. Under such conditions, one does not observe a TI minimum and only E, can be obtained directly (from the linear dependence of In TI on the reciprocal of the temperature), although T , can be obtained if one assumes a reasonable value for rCH. From Figure 4,the TI minimum (0.17s) is observed in cubane at 355 K (7,= 1.4ns). From the value of T I at its minimum, one can determine the value of the C-H bond length. (Of course, the analysis is more complicated if the spin-lattice relaxation is affected by more than one IH contributing to the relaxation. Although each C in cubane has only one nearest ‘H, it does have three equidistant next-nearest protons bonded to adjacent C atoms; however, the rCHddependence of eq 4 means that in cubane more than 95% of the relaxation is from the ’H bonded directly to the 13Catom.) Equations 4-6 have been combined, and rCH,E,, and T , have been optimized to fit the experimental TI data using a downhill simplex method.38 The continuous line in Figure 4 was calculated from the optimized values: rCH= 1.109 A; E, = 57.98 kJ mol-I; T , = 4.841 X s. Extrapolation of this data to 394 K,the temperature of the solid IIsolid I phase transition, gives a mean single-particle jump time at the transition of 2 X s. Extrapolation to low temperatures gives a mean jump time of about lo3 s at 150 K and lo5 years at 100 K. In light of these findings, we conclude that the reorientationai motion cannot be responsible for the observed6 broadening of the cubane I3CNMR signal at 20 K. The activation energy for the reorientation process in solid cubane, as determined from the I3C NMR experiment, is 58 f 6 kJ mol-’. (The error is not known from the fit, but 10% is reasonable.) This compares favorably with the value of 47 kJ mol-’ determined from the variable-temperature Raman sepctroscopic study of cubane,8 especially considering the rather large uncertainty in the determination of the line width from which the Raman value was derived. The activation energy for reorientation where of cubane is somewhat on the high side for an orientationally disordered molecular solid. For example, E, for adamantane is ~ ( w , T J = ~,{l/(l ( w H - W C ) ~ T : ) + 3/(1 + w C 2 r c 2 )+ 27.2 kJ mol-’ in the comparable phase (solid II).37 The higher 6/(l + (wH + w C ) 2 7 c 2 ) ) ( 5 ) activation energy in cubane correlates with the higher temperature of its solidsolid phase transformation and the greater energy and RIDD is the rate of relaxation, N is the number of protons required to move or rotate a cube relative to a more spherical bonded to the I3C, yHand yc are the magnetogyric ratios of IH and I3C,respectively, rCHis the C-H bond length, wH and wc are molecule. the Larmor frequencies in rad s-I for IH and I3C, respectively, From the I3C N M R results, it is apparent that the cubane and 7,is the rotational (jump) correlation time. Generally, it is molecules are moving rapidly even at room temperature, where the mean jump time is lo-’s. This is much below the temperature found that the temperature dependence of T , can be described by of the solidsolid phase transition, but this finding is consistent an Arrhenius expression:36 with the adiabatic calorimetric results which show that the T , = T , exp(E,/RT) (6) transformation actually begins at about 285 K (the minimum temperature of the deviation of the experimental and baseline heat where E, is the activation energy for reorientation. capacities, see Figure l), although it does not reach fruition until With vH = 361.0 MHz and vc = 90.78 MHz, the function 394 K. That the room-temperature structure of cubane has been f l w , ~ , ) is a maximum for 7, = 1.39 X s. That is, the rate solved by X-ray diffraction techniques strongly suggests that the of spin-lattice relaxation is a maximum (TI is a minimum) when rapid motion of the cubane molecule in the solid state is about T , N 1.4 ns. With the combination of eqs 4-6,it is apparent that one of its symmetry axes; i.e. it “jumps” into itself, into its same the temperature dependence of T , can be described completely orientation in the lattice, not into another orientation. The rapid by T,, E,, and rCH.Unfortunately, it is necessary to observe the jump rates are undoubtedly responsible for the large residual in TI minimum in order to determine rCH. In the high-temperature phase of most plastic crystals, (wH + wC)’rc2
