J. Phys. Chem. 1995,99, 14052-14057
14052
Vapor Pressure of
c60
Buckminsterfullerene
V. Piacente,” G. Gigli, P. Scardala, and A. Giustini Dipartimento di Chimica, Universita’ di Roma “La Sapienza”, Piauale A. Mor0 5, 00185 Roma, Italy
D. Ferro CNR, Centro per la Termodinamica Chimica alle Alte Temperature, c/o Dipartimento di Chimica, Universita’ di Roma “La Sapienza”, Piauale A. Mor0 5, 00185 Roma, Italy Received: January 4, 1995; In Final Form: June 9, 1995@
The equilibrium pressures over CWwere measured over a large temperature range, 730-990 K, by the torsion effusion and Knudsen effusion methods. The data obtained are well represented by the following selected linear equation: log@/kPa) = (8.28 f 0.20) - (9154 f 150)/T. Considering the vapor phase constituted by only C W ( ~the ) , sublimation standard enthalpy of this compound, AS,JY0(298) = 181 f 2 kJ mol-’, as derived by second- and third-law elaboration of the experimental data, is proposed. Considerations on free energy functions of the solid Cm are also reported.
TABLE 1: Instrument Constants of the Used Torsion Cells
Introduction
Among the large number of investigations in the physical and chemical properties of the fullerenes, the thermodynamic studies are relatively few. In particular the sublimation enthalpy of pure Buckminsterfullerene, Cm, was estimated’ or experimentally determined from oxidation2 and desorption kinetics3 and from the temperature dependence of its vapor The available AsubHo(7‘) values range from 138.5 kJ mol-’ reported by Tokmakoff3 to 181.4 kJ mol-’ as determined by Mathews et al.,5 discarding the first and underestimated value proposed by Hauffler et al.’ Recently, Korobov and Sidorov6 published a review of the thermodynamic properties of Cm where three unpublished vapor pressure values determined mass spectrometrically in their laboratory are also reported. Interesting thermodynamic data above c&70 mixtures are also reported in the literat~re.~-’* The aim of the present study is to provide a contribution to the assessment of the vapor pressure data of Cm together with its sublimation enthlpy as determined from the temperature dependence of the vapor pressure itself. The experimental method mainly employed was torsion effusion, a method which is both direct and independent with respect to those used in previous investigations. Some pressure values were also determined by the Knudsen effusion method in which a knowledge of the molecular weight of the effusing vapor is required in the pressure evaluation, so that the comparison of the results obtained with the two methods might be very useful. Experimental Section
The torsion effusion assembly used in this work is described in detail e1~ewhere.l~ Briefly, the vaporization was studied by loading with the c 6 0 a particular cell, with two housings having effusion holes on the opposite side walls, suspended under vacuum from a torsion wire into the isothermal zone of the furnace. On heating the sample, the equilibrium vapor effusing from the cell in the vacuum produces a torque (a)of the torsion wire so that its vapor pressure @) can be calculated through the simple relation p = aK‘ where in the constant K‘ are collected the torsion constant, the length of the torsion wire, the areas, the distances from the rotation axis, and the geo@Abstractpublished in Aduunce ACS Absrructs, August 1, 1995.
0022-365419512099-14052$09.0010
cell
symbol
graphite graphite graphite graphite graphite copper copper pyrophyllite
A B C D E F G H
nominal diameter/” 2 1 1 0.5 0.2 1 1.5 0.3
F k P a rad-’ 4.15 x 2.39 1.94 7.55 x 1.94 x 1.62 x 6.73 x 2.44
10-5 10-4 10-4 10-4 10-3
10-4 10-5 10-3
metrical factors of both the effusion holes of the used cell. The value of K‘ was determined by vaporizing reference substances (pure cadmium and lead) having an accurately known vapor pres~ure.’~ To evaluate possible variation of the accommodation coefficient of C ~ Q )eight , torsion cells, different in materials and in the effusion hole diameters, were used in the measurements. The constants of these cells are reported in Table 1. The torsion apparatus is appropriately suspended from a Chan 1000 automatic vacuum electrobalance so that, at one fixed temperature T, by measuring the weight loss rate of the sample (dgldt), its vapor pressure can be also determined by the Knudsen effusion method, simultaneously with the value obtained from the torsion effusion one, employing the r e l a t i ~ n ’ ~ p = (dgldt)K”(Tli14)”2, where M is the molecular weight of the effusing vapor and KO a constant depending also on the effusion holes of the cell. The constant KO was determined simultaneously with the torsion constant by measuring, during the vaporization of the pure standards, the weight loss rate in isothermal conditions. In the sublimation studies of Cm, the purity of the used sample is of foremost importance. The three C60 samples used in the present work were supplied by “TERM Ltd.”, and as certified, the purity checked by chromatographic analysis was 99.98%, the impurities being constituted mainly by C ~ (about O 0.01 %). In addition, the parameters of the phase transition T,, = 261 K and AtrH= 8.75 Jig were also certified. X-ray analysis of the samples compared with that reported by Kratschmer et a1.I6 shows them constituted by a hexagonal close-packed lattice. Results and Discussion
The sublimation process of Cm, studied in the approximate temperature range 730-990 K, was characterized by two steps. 0 1995 American Chemical Society
Vapor Pressure of Cm Buckminsterfullerene -1
J. Phys. Chem., Vol. 99, No. 38, 1995 14053
,
I
\
first step:
log(p/kPa) = (8.28 f 0.20) - (9154 f 150)/T (1)
second step:
log(plkPa) = (8.73 f 0.25) - (9668 f 200)/T (2)
'< I
-5
10
11
13
12
14
1o ~ / ( T / K )
Figure 1. Vapor pressure of C a during the sublimation process. The lines a and b represent eqs 1 and 2, respectively. TABLE 2: Temperature Dependence of Vapor Pressures Measured in the First Step of the Sublimation of CSO log@/kPa)= A - B / ( T / K ) cell no. of runs no. of points ATK A" B" A 1 5 729-839.5 7.91 f 0.17 8 8 3 0 f 136 B 2 15 764-879.5 8.36 f 0.1 1 9098 f 89 C 7 751-876 8.07 f 0.12 8955 f 99 39 D 2 10 842-946.5 8.38 f 0.09 9209 f 80 E 1 5 827-930 8.06 f 0.26 8934 5 236 F 1 11 798-910.5 8.10 f 0.14 8956 f 118 24 756-871.5 8.20 f 0.18 9106 f 150 G 3 H 4 25 857-991 8.84 f 0.23 9717 f 209 a
The errors are standard deviations.
TABLE 3: Temperature Dependence of Vapor Pressures Measured in the Second Step of the Sublimation of Ca log@/kPa)= A - B / ( T / K ) cell no. of runs no. of points A T / K A" B" B 2 20 773-896 9.16 f 0.18 10018 f 150 C 7 34 751-876 8.38 f 0.20 9359 f 161 9 835-952 8.36 0.21 9382 f 194 E 1 F 1 9 818-920 9.49 f 0.17 10346 f 144
*
" The errors are standard deviations, During the first step the vapor pressures were found to lie on a log p vs 1/T line, and their values were well reproducible on ascending and descending the temperatures. Unexpectedly, going on with the sublimation of the sample, the vapor pressure values decreased by a factor of about 1.2-1.4 with respect to the values determined in the f i s t sublimation step at the same temperatures lying on a new log p vs 1/T line. These values also were well reproducible on ascending and descending the temperatures. This sublimation behavior of Cm was observed, practically, in all our experiments. The vapor pressures measured in a typical vaporization run (cell C) are reported in Figure 1. In this work we have prevalently measured and taken into consideration the vapor pressures in the f i s t step which we have hypothesized to be more representative of the sublimation of pure CW. The log p vs UT equations determined by a least-squares treatment of all the data obtained using a same cell are reported in Table 2. Some equations referring to vapor pressures measured during the second sublimation step, and calculated in the same way, are reported in Table 3. By weighting the constants A and B of the equations reported in Tables 2 and 3 in a way proportional to the numbers of points, the following equations, representative of the first and the second step of the sublimation of Cm, were selected:
where the associated overall errors are estimated. Equation 1 is drawn in Figure 2 for comparison with the literature data. It is interesting to note that also Abrefah et al.5 seem to have observed a behavior similar to that observed by us. Indeed, they report that "the first runs for each sample showed higher vapor pressures and lower heats of sublimation than subsequent runs, presumably because of the presence of impurities" so that the data measured in the f m t runs were rejected. Unfortunately, in their work is not clearly stated neither the amount of substance vaporized in the first runs nor how much the vapor pressures were higher and the A,,@(T) lower than the values obtained in the other runs. However, it seems questionable to attribute to impurities a behavior which should have implied, to be able to derive a meaningful second law As&, the vaporization of a substantial amount of substance. At present we are not able to predict when the vapor pressure shows the small pressure decrease and to understand its sublimation behavior, but some observations were made: (i) By stopping some sublimation runs of Cm, often, on the upper part of the sample, a thin layer of brown crystals was observed. As verified in separate and appropriate vaporization and recondensation experiments of Cm, these thin crystals also originated from recondensation of the vapor. By carefully separating these crystals, it was found that when submitted to vaporization they present vapor pressures practically equal to those measured in the first stage above pure Cm. The presence of this layer, therefore, cannot be considered responsible for the pressure decrease observed during the vaporization. (ii) The comparison of the X-ray analyses of pure C a and of the residues of sublimations, interrupted when their vapor pressures fitted the log p vs 1/T equation representative of the second stage (eq 2), exhibited similar diffraction patterns (hexagonal close-packed lattice) even if the diffraction lines of the residues are less intense than those of pure Cm. (iii) A scanning electron microscopic investigation of these residues showed that the surfaces of the crystals present a coverage of soft, fluffy material (see Figure 3) not well identified. At the end of each experiment a final residue of about 0.1-0.3% of the original weight of the sample was observed having a vapor pressure not measurable up to about 1000 "C and an amorphous structure (as deduced from X-ray analysis). The presence of these final residues segregated and observed at the end of all the sublimation experiments of Cm can be interpreted as due to either the impurities of the sample or as product of a general transformation occurring during the heating andor the sublimation of the sample. The reproducibility of the pressure values measured in the second step and the very small amount of the final residues lead us to believe that their presence over the sample cannot be the cause of the pressure decrease observed during the vaporization of Cm. (iv) The reproducibility of the pressure data in both steps and the large amounts (about 30-40% of the original one) of the sample vaporized in the various runs when the pressure starts to decrease, evidence, in our opinion, that also the possible presence in the sample of the solvent employed in its recrystallization could hardly be responsible for the pressure decreasing. Simultaneously, during the measurements of the vapor pressure by the torsion method, also some measurements of the weight loss rate of the sample were made in order to determine some vapor pressure values by the Knudsen method. In Table
Piacente et al.
14054 J. Phys. Chem., Vol. 99, No. 38, 1995
TABLE 4: Comparison of the Vapor Pressures of Cm Measured by the Knudsen Method (PK)with Those Measured by the Torsion One (Pa)and Those Last Calculated in the First and Second Step from the Selected Eqs 1 and 2, Respectively cell
10
12
14
16
18
20
IO~/(T/K)
Figure 2. Comparison of the vapor pressure of Cm: 1, this work: ref 4; 3, ref 5; 4, ref 3; 0, ref 6; A, ref 7.
T/K
A 769 806 840 B 862 894.5 800 860.5 868.5 876 897.5 C 882 D 917.5 912.5 946.5 E 898 941.5 952 F 882 894 901.5 910.5 920 G 828.5 858
sublimation sublimation rate step (104 g min-l) first first first first first second second second second second second first first first second second second first first first first second first first
1.03 3.09 8.25 2.3 1 4.45 0.23 1.33 1.69 2.03 3.86 3.31 3.25 2.54 6.46 0.53 1.60 2.00 5.69 7.42 9.30 11.63 11.00 3.08 7.25
p&F’a 2.69 x 10-4 8.13 x 10-4 2.24 x 10-3 5.01 x 10-3 9.77 x 10-3 4.79 x 10-4 2.88 x 10-3 3.72 x 10-3 4.47 x 10-3 8.51 x 10-3 7.24 x 10-3 2.00 x 10-2 1.55 x 3.98 x 8.13 x 10-3 2.57 x 3.24 x 8.51 x 10-3 1.12 x 10-2 1.41 x 1.78 x 1.68 x 1.62 x 10-3 3.89 x 10-3
p&Pa 2.40 x 10-4 8.32 x 10-4 2.40 x 10-3 4.57 x 10-3 1.10 x 10-2 4.47 x 10-4 3.09 x 10-3 3.98 x 10-3 4.90 x 10-3 9.12 x 10-3 5.87 x 10-3 2.00 x 1.78 x 4.07 x 9.12 x 10-3 2.88 x 3.72 x 7.94 x 10-3 1.10 x 10-2 1.35 x 1.70 x 1.66 x 1.70 x 10-3 3.89 x 10-3
TABLE 5: Differences between the Vapor Pressures of Cm Step Calculated in the First and Second Sublimation (4’) from Eqs 1 and 2 and Those Measured by the Differential Torsion Cell (Ap) TK ~ p 1 y0 3 ~ a )AP( 103ma) T/K A ~ O ( 1 0 3 ~ 4~ p103ma) (
Figure 3. SEM analysis of Cm, residue of a sublimation experiment. It is evident that a very aeriform substance exists on the crystals.
4 are reported the data obtained considering Ca(g) the only
gaseous species in the vapor. The good agreement of the pressure values obtained by both methods showed that the sublimation of c60 is congruent in both sublimation steps and that the instrument constants used in the vapor pressure calculations are reliable. To ascertain, at a some experimental temperature, the reliable difference of the vapor pressures of Cm in the two vaporization steps, torsion effusion measurements were also made employing a “differential cell”, i.e., a conventional effusion cell having both the effusion holes of the housings on the same side. In this way, by filling one housing with pure C a and the other with sample residue of a vaporization run stopped when the torsion angle lie definitely on the second line, the measured torsion angles of the assembly provided a direct evaluation of the difference between the vapor pressures of pure C a and of the residue. Some preliminary experiments in which only one single housings was filled with a reference substance (cadmium) were carried out to evaluate the two instrument constants of each housings. In other experiments, in which both housings were filled, the possible differences of these constants were also determined. The measurements showed that the instrument constants of both housings are practically equal (27.5 x lo3 and 26.3 x lo3 Wa rad-’) so that the value 27 x lo3 Wa rad-’ was used to calculate the vapor pressure differences from the torsion angles measured by the differential cell. The obtained results, reported in Table 5, agree with those calculated, at the same temperatures, utilizing the pressure values derived from eqs 1 and 2, confirming also
863.5 875 910
1.40 1.82 3.71
1.32 -1.6f0.2 3.09
944 951.5
7.12 8.56
6.82 9.02
the real difference of the vapor pressures of Ca in the first and in the second step of its vaporization. Considering that the sublimation of C a occurs according to the reaction C ~ O ( ~ c60(g), ) from the slope of the selected eq 1 the second law sublimation enthalpy at the midpoint temperature, Asu#(860) = 175 f 3 kJ mol-’ was calculated. This sublimation enthalpy was reduced to 298 K, Asu@(298) = 182 f 3 kJ mol-’, by using the heat contents reported in the Appendix. The same heat contents were employed to calculate from the literature data the standard sublimation enthalpies reported in Table 6. The vapor pressures represented by eq 1 were also used to derive the third-law standard sublimation enthalpy values. The free energy functions necessary for these calculations are reported in the Appendix. In Table 7 are reported the values obtained at 50 K intervals across the temperature range covered in our experiments. As is apparent, the Asud;r”(298)values show a temperature trend. The average third-law value, Asu#(298) = 171.6 kJ mol-’, together with the literature values recalculated by using the new thermodynamic functions reported in the Appendix, and the corresponding third-law trends are reported in Table 6. On looking at these third-law trends and the differences between second- and thirdlaw values, it must be pointed out, preliminarily, that, with the exception of the results of Abrefah4 and T~kmakoff,~ all the others appear to be within the usual range for the experimental techniques used. In particular, the data reported by Mathews et al.5 and those of Schonherr7 exhibit differences between second- and third-law enthalpies, and their trends are about a factor of 2 smaller than our own results. However, it is
-
J. Phys. Chem., Vol. 99, No. 38, 1995 14055
Vapor Pressure of Cm Buckminsterfullerene
TABLE 6: Comparison of the Vapor Pressures (kPa) and the Sublimation Enthalpies (kJ mol-') of Cm Available in the Literature log(plkf)a)= A - B/(T/K) second law third law method T/K A B &,bHo(T) AS,bHo(298Y AS,8(298) trend/J mol-' K-' oxidation rates2 788 '167 p ( T ) = (2~cmkT)%"exp(-A,,a/RT)b desorption rates) 510-590 142.9 173.5 $35.7 138.5 f 3.8 Knudsen4' 673-873 6.587 f 0.108 8281 f 873 163.8 181.0 $22.3 158.9 f 4.2 mass ~pectrom~~600-800 9475 f 80 185.6 180.7 -6.8 8.185 f 0.032 181.4 f 2.3 mass spectrom6 725-820 181 Knudsen" 8865 f 328 169.7 f 1.4 176.0 173.0 -5.2 774-953 7.86 f 0.39 UV-visible absS 819-995 180 f 10 mass spectromZ6 680-790 158.3 f 2.3 7.49 f 0.14 8267 f 120 162.8 167.4 $5.8 729-991 8.28 f 0.20 175 f 3 this work 9154 f 150 182 f 3 171.6 -12.7 ~
a
Calculated by using the heat contents reported in the Appendix. Where m is the molecular mass, k and R are the Boltzmann and gas constants,
8 is the zeroth-order preexponential, and A,,Jf is the sublimation enthalpy value. The results were calculated using the vapor pressure data
reported in the original work.4dEven if Mathews et aL5 report as final equation log@/Pa) = 11.582 f 0.126 - (9777 f 138)/T obtained by "pooling all the individual points", the constants here reported were obtained as the average of those experimentally determined by the authors in four runs (11.279, 11.157, 11.149, 11.155 as intercepts and 9587, 9573, 9370, 9370 as slopes). In the calculation of their selected second-law ASufl(T)(181.4 f 23 kJ mol-') the authors used the slope reported in this table. e The results were calculated by us utilizing eight vapor pressure values measured by the authors.' TABLE 7: Third Law A&P(298) of Cm and [Go(T)H0(298)]/T of the Solid Phase Recalculated from Our Vapor Pressure Data -[(Go(T) - Ho(298))]/T/
T/K 700 750 800 850 900 950 1000
-R In pl J mol-' K-' 130 113 99 86 74.5 64 55
J mol-' K-' a
A,,bHo(298)1
Ab
C@(S)C
kT mol-'
117.5 117.1 116.6 116.2 115.7 115.1 114.5
614.8 649.9 686.2 721.8 757.5 792.7 828.1
173.3 172.9 172.4 171.8 171.2 170.4 169.7
a Calculated from eq 1. Calculated from the data reported in the Appendix. Calculated by third law using the selected value A,@(298) = 181 kT mol-' (see text).
interesting to note that the aforementioned data of Mathews5 and Schonherr' are somewhat in disagreement. On the other hand, a critical analysis of the reliability of the third-law results leads one to conclude that the used thermodynamic functions of gaseous Cm should be considered fairly reliable being based on, by now, well-established experimental molecular parameters. In particular, the very recent vibrational frequencies here adopted (see Appendix) are more reliable than those used by Korobov and Sidorov.6 As a consequence, the vibrational contribution to the entropy of the gaseous Cm is greater with respect to that used by Korobov and Sidorov6 (29.3 J K-' mol-' at 700 K) and accounts for almost all the differences between our and their estimated thermodynamic functions. On the contrary, in the evaluation of the free energy functions of the solid phase, for which the estimates made by Korobov and Sidorov6 were here adopted, some uncertainties seem to be still present considering both the discussion made by Korobov and Sidorov6 and some peculiar behaviors or anomalies observed in the measured heat capacities as emerge from recent work^.'^-'^ An evaluation of the residual entropy at 0 K was also recently published.20 However, these different findings, which mainly pertain to the temperature range 0-298 K, and as far as it matters here, may affect, mainly, the entropy values and, hence, both the derived free energy functions and the third-law enthalpy values. For this reason we believe, on the other hand, that the heat content functions needed to reduce to 298 K the secondlaw enthalpies will not be remarkably modified so that the second A,,JP(298) values are to be considered more reliable than the third-law values. Even if our A,,@(298) is based on
a large number of experimental points and either our and Schonherr's results came from a direct experimental method, on selecting among the various second-law enthalpies reported in Table 6 , we preferred to average Mathews's, Schonherr's, and our values to take full account of the three different methods employed. Therefore, we propose for the A,,@(298) of Cm the value of 181 kJ mol-' with an uncertainty that should not exceed 2 kJ mol-'. Employing this selected value together with the vapor pressures calculated by eq 1 and the free energy functions of Cm(g) reported in the Appendix, the free energy functions of the solid phase were derived by the third-law procedure. The obtained values reported in the same Table 7 are lower by about 11 J mol-' K-' than those evaluated from calorimetric data.6 While the evaluation of free energy functions lies outside the scope of the present work, nevertheless, our experimental vapor pressure data and the hsubH0298 selected here seem to favor, and we propose, a new set of free energy functions of the solid phase of Cm. As concerns the vapor pressures measured in the second vaporization step (eq 2), their elaboration by the second- and third-law treatment gives the following results: AsubH0(850)= 185 f 4 kJ mol-' and A,,@(298) = 192 f 4 kJ mol-' from the second-law calculation, and A,,@(298) = 177 and 171 kJ mol-' at 700 and 1000 K, respectively, from the third-law procedure. It is interesting to note that with these vapor pressures the third-law A,,@(298) values exhibit a temperature trend more evident and their average value, As,@(298) = 174 kJ mol-', a larger difference with the second law (192 kJ mol-'). This fact could be taken as a further indication that the fiist step is the most representative of the overall vaporization process of c60. It is of interest here to mention a recent work by Li et al.2' on the formation, at the experimental temperatures covered in this work, of a nonevaporable skin on Cm crystals exposed to illumination. These skins have been shown to be composed of photopolymerized Cm and an amorphous material which comes from the decomposed Cm during illumination or the subsequent heat treatment. It is attractive to hypothesize that some relation may exist between these findings and our observation of the second step in the vaporization and/or the thin amount of a nonevaporable residue. Finally, by using the recentz2heat of formation of C ~ Odata (~) AfOrHO(298)= 2327 f 17 kJ mol-', we derive as the standard heat of formation of Cwg)the value AfOrW(298)= 2508 f 20 kJ mol-' corresponding to Af0,H0(298) = 41.8 f 0.3 kJ per C atom.
14056 J. Phys. Chem., Vol. 99,No. 38, 1995
Piacente et al.
TABLE 8: Standard Molar Thermodynamic Functions of
log(plPa) = 10.49 f 0.14 - 8276.4 f 1204WT)
C60k)ll
298 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
543.890 286.844 392.666 546.987 720.365 896.342 1066.663 1227.709 1378.354 1518.690 1649.350 1771.155 1884.956 1991.559 209 1.695 2186.018 2275.104 2359.457 2439.522 2515.689 2588.301
58.437 4.105 20.523 59.363 120.120 199.287 292.896 397.492 510.388 629.590 753.640 881.465 1012.273 1145.469 1280.602 1417.325 1555.366 1694.511 1834.592 1975.469 2 117.034
347.891 245.794 290.050 349.109 420.066 497.767 578.502 659.864 740.369 819.146 895.710 969.823 1041.396 1110.429 1176.979 1241.135 1303.000 1362.686 1420.305 1475.969 1529.784
a The vibrational wavenumbers adopted for Cw were the following (degeneracies within brackets): Ag(1) 491, 1458; Hg(5) 266,429,710,
768, 1095, 1254, 1437; TI,(^) 565, 850, 1289; T2.&3) 535, 764, 805, 1334; G&4) 484, 570, 738, 1135, 1314, 1515; A”(1) 973; TI,@) 527, 578, 1184, 1439; Tzu(3)355, 714, 1040, 1187, 1565; H,(5) 403, 486, 669, 740, 1211, 1342, 1530; G,(4) 344, 760, 771, 967, 1321, 1415.
Appendix
The heat capacity and the thermodynamic functions of solid were taken from Korobov and Sidorov6 where a critical reevaluation of the experimental heat capacities reported in the literature has been made. As concerns the thermodynamic functions of gaseous Cm, reported in Table 8, they were calculated by the methods of statistical thermodynamics, in the harmonic oscillator rigid rotator approximation. The electronic levels calculated by Negri et al.23,24were taken into account; however, as the fundamental state is of the type ‘A, and the first excited states, even if with fairly large degenerancies, are found more than 2 eV above, no electronic contribution to the thermodynamic functions does appear up to 3000 K. The necessary 174 frequencies were taken from S ~ h e t t i n owhere ~ ~ a complete vibrational assignment has been performed using, together with a recent density functional perturbation calculation, the infrared, Raman, and inelastic neutron scattering spectra. The wavenumbers here employed, an average of the observed values reported in Schettino, are collected in a footnote to Table 8. As for the rotational contribution, while the symmetry number u = 60 comes out from the I h symmetry of the Cm molecule itself, the principal moments of inertia, by taking full account of the atomic coordinates, were evaluated to be IA = 113 = IC = 9.82 x kg m2.
which yields a second-law sublimation enthalpy of 158 f 3 kJ mol-’. The pressure values are slightly higher than ours and the literature ones. During their other experiments, in which Cm samples containing organic solvent were used, the vapor pressures of Cm decreased rapidly, when heated above a certain temperature (700-740 K), lying on a log p vs 1/T line similar to that found in the literature by refs 4, 5 , and 6. The authors report “the material transformed to a lower pressure form was rapidly scanned by an high resolution TEM’ and found it was “partially decomposed in a not volatile amorphous carbon”. The authors demonstrate in their work that the partial decomposition of Cm in carbon soot was due to the presence of solvent in the original material and conclude that when the fullerene is solvent-free, it does not decompose on heating. This behavior can be considered similar to that found by us. The small pressure decrease observed in our measurements can be probably due, contrary to that hypothesized in the first part of this text (see observation iv), to the presence of a very small amount of solvent in the original samples which can produce the formation of a carbon soot, responsible for the decrease. It is very interesting to note that the results reported by authors refer to the evaporation of redistilled material showing fcc structure. The vapor pressures measured above this structure are practically equal to those measured, by the same authors, above the original sample containing solvent and having an hcp form.
c60
Acknowledgment. We are deeply indebted to Prof. E. Schonherr for providing us with his Knudsen effusion unpublished original data. The critical reading of the manuscript by Prof. G. Balducci is gratefully acknowledged. Note Added in Proof. During the submission of this paper, Popovic et al. have published an interesting work.26 The authors measured by a mass spectrometer the vapor pressures of pure, resublimed Cm obtaining as their temperature dependence expressed by the equation
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