J . Phys. Chem. 1992, 96, 3566-3568
3566
Vaporlzation Studies on Buckminsterfullerene C.K. Mathews,* M. Sai Baba, T. S.Lakshmi Narasimhan, R. Balasubramanian, N. Sivaraman, T. G. Srinivasan, and P. R. Vasudeva Rao Radiochemistry Programme, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamil Nadu, India (Received: December 30, 1991)
A Knudsen cell mass spectrometric study of pure Ca was carried out in the temperature range 600-800 K to obtain the vapor pressure and enthalpy of sublimation. The measured appearance potential for Ca+(8.1 f 0.5 V) is in good agreement with the recommended value (7.6 0.2 V) for the ionization potential of Ca. The enthalpy of sublimation was found to be 181.4 f 2.3 kJ/mol at 700 K by the second law method. The vapor pressure of c 6 0 is given as a function of temperature by the equation log @/Pa) = -9777 138/T (K) + 11.582 0.126.
*
*
Introduction A simple method for the preparation of bulk quantities of fullerenes, first reported by Kratschmer et al.' a year ago, has opened up an exciting area of research on the physical and chemical properties of these fascinating molecules. The international interest is reflected in the large number of reports on the spectroscopic (IR, UV-vis, Raman, and NMR), electrochemical, and structural (XRD) properties of Cm as well as on their derivatives and compounds. However, very limited attention has been given to thermodynamic properties. There have been two measurements on heats of s~blimation,~.~ but both of them were made on mixtures of fullerenes. Further, no vapor pressure data have been reported. In this paper we report for the first time the vapor pressure of pure Ca as a function of temperature as well as its heat of sublimation. The principal technique used in this study is Knudsen cell mass spectrometry, which has earlier been employed in our laboratory in our studies on selenium and tellurium clusters4and on the vaporization thermodynamics of metal tellurides.5-9
Experimental Section The procedure used for the preparation of C60was similar to the contact arc method described by Haufler et a1.I0 The arc was struck between two graphite electrodes in a helium atmosphere of 200 Torr, and the graphite soot collected was subjected to Soxhlet extraction by using toluene or carbon tetrachloride as the solvent. The extract was evaporated using a rotary evaporator to obtain solid samples consisting mainly of Ca and C70. This mixture was separated by column chromatography by using a neutral alumina column, and Cm was eluted with hexane. The samples were characterized by HPLC, UV-vis as well as IR spectroscopy, and XRD. The details of characterization are given (1) Krastchmer, W.; Lamb, L. D.; Forstiropoulos, K.; Hauffman, D. R. Nature 1990, 354, 347. (2) Pan, C.; Sampson, M. P.; Chai, Y.; Hauge, R. H.; Margrave, J. L. J . Phys. Chem. 1991, 95, 2944. (3) Mathews, C. K.;Vasudeva Rao, P. R.; Srinivasan, T. G.; Ganesan, V.; Sivaraman, N.; Lakshmi Narasimhan, T. S.; Kaliappan, I.; Chandran, K.; Dhamcdaran, R. Curr. Sci., in press. (4) Viswanathan, R.; Sai Baba, M.;Darwin Albert Raj, D.; Balasubramanian, R.; Mathews, C. K. In Advances in Mass Spectrometry; Todd, J. F. J., Ed.; John Wiley & Sons: New York, 1985; Vol. 10, p 1087. ( 5 ) Saha, B.; Viswanathan, R.; Sai Baba, M.; Darwin Albert Raj, D.; Balasubramanian, R.; Karunasagar, D.; Mathews, C. K.J . Nucl. Mater. 1985, 130, 316. (6) Sai Baba, M.; Viswanathan, R.; Darwin Albert Raj, D.; Balasubramanian, R.; Saha, B.; Mathews, C. K. J. Chem. Thermodyn. 1988,20, 1157. (7) Viswanathan, R.; Sai Baba, M.; Darwin Albert Raj, D.; Balasubramanian, R.; Saha. B.; Mathews, C. K. J. Nucl. Mater. 1987, 149, 302. (8) Viswanathan, R.; Sai Baba, M.;Darwin Albert Raj, D.; Balasubramanian, R.; Saha, B.; Mathews, C. K. J . Nucl. Mater. 1989, 167, 94. (9) Viswanathan, R.; Balasubramanian, R.; Mathews, C. K. J . Chem. Thermodyn. 1989, 21, 1183. (10) Haufler, R. E.; Conceicao, J.; Chibante, L. P. F.; Chai, Y.; Byrne, N. E.; Flanagan, S.;Haley, M. M.; OBrien, S. C.; Pan, C.; Xiao, Z.; Billups, W. E.; Caufolini, M. A.; Hauge, R. H.; Margrave, J. L.; Wilson, L. J.; Curl, R. F.; Smalley, R. E. J . Phys. Chem. 1990, 94, 8634.
*
else~here.~ The purity of the substance was also checked by mass spectrometry. A VG Micromass 30BK mass spectrometer (electron impact ion source, single focusing, 90° sector magnetic analyzer) was used for vapor pressure measurements. The molecular beam effusing out of the Knudsen cell was ionized by electrons of 38-eV energy. The ions were accelerated to 3 kV and measured by a secondary electron multiplier. For determining the appearance potential, ionization efficiency curves were obtained by measuring the ion intensities as a function of electron energy at constant temperature. The electron impact energy scale was calibrated against the first ionization potentials of Ag, In, Hg, Ar, and He.' The relevant data were acquired and processed by an IBM compatible PC. Alumina Knudsen cells (i.d. = 7.5 mm, 0.d. = 10.0 mm, height = 10.0 mm, and orifice diameter = 0.5 1 mm) were used to contain the samples. The Kundsen cell with the sample (normally half to three-fourths of the cell) was kept inside a molybdenum cup which was heated by electron bombardment. Temperatures were measured by a chromel-alumel thermocouple touching the base of the Knudsen cell. The thermocouple was calibrated against the melting point of silver. Two samples from independent preparations were used in these experiments. Sample 1 was annealed at 500 K for about 12 h while sample 2 was preheated at 800 K for about 3 h. In each experiment the ion intensities were measured as a function of time from those temperatures where a detectable signal was obtained, and the sample was taken to the next temperature (either higher or lower) only after ensuring equilibrium conditions for a reasonable period of time (normally 3 W min). Such stable reading at each temperature was chosen for obtaining the temperature dependence of the ion intensities. The samples were weighed (along with the Knudsen cell) in a Mettler microbalance (sensitivity 10 pg) before and after the experiment to obtain the weight loss during the experiment. Experiments were carried out with samples of different initial weights and for different durations. Prior to each experiment with C, an experiment with silver (NBS standard) was carried out. Results and Discussion In the mass spectrum of the equilibrium vapor, major peaks were observed in the mass ranges 720-722 and 360-361. The peaks in the mass range 720-722 were attributed to Ca+ on the basis isotopic abundance. The peaks in the mass range 360-361 may be due to fragmentation of Ca molecules or doubly positive ions of c60. No other peak with significant ion intensity was detected up to a mass of 1020. Particular care was taken to detect any C70 present. The ratio of Ia+fI,,-,+ at the highest temperature (800 K) was around 4000. Such a large value for the ratio indicates the purity of Ca and the effectivenessof the separation procedure. An appearance potential of 8.1 f 0.5 eV obtained for the ion Ca+ is in good agreement with the ionization energy value of 7.61 f 0.2 eV given in the assessment of Kroto et a1.l' (11) Kroto, H. W.;Allaf, 4. W.; Balm,S. P. Chem. Rev. 1991, 91, 1213.
0022-3654/92/2096-3566$03.00/00 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 9, 1992 3567
Letters TABLE I: Details of Weight Loss Experiments with Silver and Cso sample initial no. expt no. weight, mg
c 6 0
73.44 59.17 6.62 4.03 10.82
1 2 1 26 3
At3 14
24
weight loss, mg
QX
6.79 6.43 2.59 0.51 4.13
lo6
k'x
6.370 7.198 1.277 1.167 1.176
lo2
a c x 10'
1.36 1.60 0.108 0.099 0.099
1.71 1.65 1.68 1.68 1.68
4Samples 1 and 2 belong to two different preparation lots. bSample 1 was reweighed after experiment 1 and used for experiment 2. TABLE 11: Vapor P r w u r e of C&)
over Pure Cso
sample
no.
expt no.
run no.
1
1
2
2 3
1 2 3 4 U
log @/Pa) = - A / T (K)
temp range, K
690-800 600-800 650-800 650-800 600-800
+B
P, Pa
Ab
Bb
9587 i 94 9573 i 52 9370 i 95 9370 i 12 9777 i 138
11.279 f 0.024 11.157 i 0.032 11.149 i 0.038 11.155 i 0.033 11.582 i 0.126
700 K 3.83 x 10-3 3.03 x 10-3 5.80 x 10-3 5.88 X 10-3 4.12 X lo-'
800 K 0.197 0.155 0.273 0.277 0.229
4Recommended equation is obtained by pooling all the individual points. bThe errors are standard deviations.
The ion intensity measured at any temperature can be related to pressure by the equationI2
2.0 1.5 -
(1)
1.0 -
In eq 1 k' = (klush), where k is the instrument calibration constant, u the ionization cross section, s the detector response, and h the isotopic abundance. The conventional procedure of obtaining k12 by using a standard substance (like silver whose vapor pressure is well-known) may not be applicable in the present case on account of the nonavailability of a reliable ionization crosssection value for Cm Hence, the following procedure was adopted to obtain the vapor pressure of Cm. The weight loss w due to Knudsen effusion for time t is given by the equationsI2
0.5 -
p = k'ZT
w = QJ ZT1t2dt Q = k'(aC)(hf/Z~R)~/~
-
0.0 -0.5
-
5c -1.0v
01
O -1.5-
-2.0 -2.5 -
(I2?
1
-3.0 0 -3.5
(3)
where a is the orifice area, C the Clausing factor, M the average molecular weight, T the temperature, and R the universal gas constant. The constant Q was calculated from eq 2 by using the weight loss during the experiment and area under the curve ZT1I2 vs time. Since experiments with silver yield k' (using measured Z(Ag+) and known p(Ag)13), this can be substituted in eq 3 to obtain aC, the product of the orifice area and the Clausing factor. This, being independent of the sample, can now be used in eq 3 to calculate k' for Cm and hence its partial pressure via eq 1. Figure 1 gives a typical plot of log (ZT1l2)vs time. As can be seen from the plot, the reproducibility of ion intensities at each temperature is reasonably good. A similar trend was observed in other experiments. Table I summarizesthe details of the weight loss experiments and the constants derived from them. Table I1 gives the results of least-squares-fitted log p vs 1/ T plots. The agreement between the pressures obtained in various runs is reasonably good. The recommended pressure equation for c 6 0 was obtained by a least-squares fitting of all the points obtained in all the experimental runs. Figure 2 gives a typical plot of log (IT) vs 1 / T for two temperature dependence runs obtained in a particular experiment. Second law12 enthalpy of sublimation was obtained from the slope of the least-squares-fitted log ( I T ) vs 1/ T data and are given in Table 111. The recommended value (181.4i 2.3 kJ/mol) is t h e average of all the runs. This is slightly higher than the value obtained by us earlier3 over a mixture of c60 and C70(176 f 2 (12) Drowart, J. In Proceedings of the International School on Mass Spectrometry, Ljubljana, 1969; Marsel, J., Ed.; Stefan Institute: Ljubljana, 1971; p 187. (13) Paule, R. C.; Mandel, J. Analysis of Interlaboratory Measurements on the Vapour Pressures of Cadmium and Silver. National Bureau of Standards Special Publication 260-21, 1971.
0
4
12
16
Time ( Ho urs)
Figure 1. Plot of log (IT1/2) vs time (weight loss experiment for Cm: sample 2). 6.0
oRun 3
5.0
ORun 4
4.0
--t?
3.0
h
c
2.0
1 .o
0.0
-1.0 -
I
I
-2.0
1
1
1
1
2
2 3
2 3 4 u
I
690-800 600-800 650-800
650-800 600-800
745 700 125 725 700
183.6 f 1.8 183.3 h 1.0 179.4i 1.8 179.4i 1.4 181.4 f 2.3
Recommended value is the average of the individual runs, and the error is the standard deviation of the mean. *The errors are standard deviations.
3568
J. Phys. Chem. 1992,96, 3568-3570
kJ/mol). Pan et a1.2 report a somewhat lower (167.8 f 5.4 kJ/mol) value, but their measurements were also on a mixture of Ca and C7* The present measurements were carried out with pure Cso, and the agreement between different samples and runs suggests that our value is reliable. The trend toward a lower enthalpy of sublimation in mixtures of Ca and C70 and the small magnitude of the difference are consistent with the picture of a
solid solution held together by van der Waals forces. Acknowledgment. We thank Mr. R. Viswanathan and Dr. D. Darwin Albert Raj for their assistance in the mass spectrometric measurements and useful discussions. We also thank Mr. I. Kaliappan and Mr. R. Dhamodaran for their help in the preparation and purification of c 6 0 samples.
Nonstatlstical Energy Flow Dynamics in Slllcon Clusters as a Result of Bond Directionality Thomas A. Holme* and William J. Leei Department of Chemistry, University of South Dakota, Vermillion, South Dakota 57069 (Received: January 21, 1992)
Energy flow dynamics for two model clusters containing 39 silicon atoms are reported. When nondirectionalpairwise interactions are assumed between silicon atom, energy placed in one region is rapidly shared among all atoms of the cluster, the statistical expectation. By contrast, when directionality is introduced such that silicon prefers to bond with tetrahedral bond angles, energy flow from a locally excited region to the remainder of the cluster is quite slow. This nonstatistical tendency could have implications for several observed characteristics of silicon microclusters.
Silicon microcluster chemistry has been the subject of signficant experimental'-I0 and investigation. While other elemental microclusters have also been studied, silicon attracts special attention, due at least in part to its covalent bonding nature. This very nature also imparts the constraint of directional bonding, preferably along tetrahedral bond angles. In this report, we will note that this constraint appears to have important dynamical consequences whose ramifications in the study of silicon microclusters may in turn prove to be crucial. Two distinct issues within silicon microcluster chemistry may be impacted by the findings presented here. Silicon clusters have been observed to have unusual fragmentation patterns,I-j with fragmentation favoring six atom pieces, as opposed to the sequential individual atom fragmentation observed for other microclusters." The silicon fragmentation pattern changes to favor 5-1 1 atom fragments after the cluster size exceeds 30 silicon atoms.3 This observation may be connected to evidence that clusters above this range are structurally distinct from the smaller cluster^.^ Considerable theoretical effort has been put forth to help elucidate the nature of magic numbers," including those implied by the fragmentation behavior. In addition to the structural probes of silicon microclusters, their chemical reactivity patterns have also been in~estigated.~-~ Reaction rates were observed to vary dramatically between clusters differing by only one atom,5 though the extent of the variation has been found to depend on the experimental condition^.^^^ Annealing long after cluster formation has also been shown to effect the outcome of silicon microcluster chemistry.s Among the reagents used to attack silicon microclusters, oxygen has provided some of the most enticing observations. For clusters below some threshold value, roughly SiM,oxygen repeatedly etches the cluster leading to only dimers of Si0 or Si? At largers sizes, greater than Si3s, adduct formation becomes the dominant product channel. JarroldlO has suggested that dynamical factors contribute to this observation; small clusters are unable to accommodate the exothermicity of the reaction and break apart within the proposed scenario. The calculations reported in this work were undertaken to help determine the nature of the energy flow dynamics suggested by Jarrold's explanation. 'Present address: School of Medicine, University of Iowa, Iowa City, IA 52245.
The theoretical study of cluster dynamics is not new. There have been numerous investigations of Ar clusters,I* helping to elucidate such fundamental issues as the origins of melting. There have also been some investigations using molecular dynamics calculations with silicon clusters.12-16 Early calculations were concerned primarily with describing stable structures using simulated annealing,l* and subsequent investigations have assessed the effects of finite temperatures on structure^.'^ Vibrational spectra have been calculated,14 and a b initio molecular dynamics methods have been used to investigate cluster melting a t tem(1) Bloomfield, L. A,; Freeman, R. R.; Brown, W. L. Phys. Rev. Lerr. 1985, 54, 2246. (2) Zhana. O.-L.: Liu. Y.; Curl. R. F.; Tittel, F. K.; Smalley, R. E. J . Chem. Physr1988,88, 1670. (3) Jarrold, M. F.; Honea, E. C. J. Phys. Chem. 1991, 95, 9181. (4) Jarrold, M. F.; Constant, V. A . Phys. Rev. Lerr. 1991, 67, 2994. (5) Elkind, J. L.; Alford, J. M.; Weiss, F. D.; Laaksonen, R. T.; Smalley, R. E. J . Chem. Phys. 1981,87, 2397. ( 6 ) Jarrold, M. F.; Power, J. E.; Creegan, K. M. J. Chem. Phys. 1989,90, 3615. (7) Creegan, K. M.; Jarrold, J. F. J . Am. Chem. SOC.1986, 112, 3678.
Alford, J . M.; Laaksonen, R. T.; Smalley, R. E. J . Chem. Phys. 1991, 94, 2618. (8) Maruyama, S.;Anderson,&. R.; Smalley, R. E. J . Chem. Phys. 1990, 93, 5349. Anderson, L. R.; Mamyama, S.;Smalley, R. E. Chem. Phys. L e r r . 1991, 176, 348. (9) Jarrold, M. F.; Ray, U.; Creegan, K. M. J . Chem. Phys. 1990,93,224. (10) Jarrold, M. F. Science 1991, 252, 1085. (11) Phillips, J. C. J . Chem. Phys. 1988,88,2090. Jelski, D. A,; Wu, 2. C.; George, T. F. Chem. Phys. Lett. 1988,150,447. Kaxiras, E. Phys. Rev. Drr. 1990,64, 551. Patterson, C. H.; Messmer, R. P. Phys. Reu. B 1990,42, 7530. Jelski, D. A.; Swift, B. L.; Rantala, T. T.; Xia, X.; George, T. F. J . Chem. Phys. 1991, 95, 8552. (12) Blaisten-Barojas, E.; Levesque, D. Phys. Rev. B 1986, 34, 3910. (13) Feuston, B. P.; Kalia, R. K.; Vashishta, P. Phys. Rev. B 1987, 35, 6222. (14) Sankey, 0. F.; Miklewski, D. J.; Drabold, D. A.; Dow, J. D. Phys. Reo. B 1990, 41, 12750. (15) Ballone, P.; Andremi, W.; Car, R.; Parrinello, M. Phys. Reu. LeU. 1988, 60, 271. (16) Mistirotis, A. D.; Flytzanis, N.; Farantos, S.C. Phys. Reu. B 1989, 39, 1212. Chelikowsky, J. R.; Glassford, K. M. Phys. Reu. B 1990, 41, 12750. Phillips, J. C. Phys. Reu. B 1991, 44, 1538. (17) See: Barnett, R. N.; Landman, U.; Rajagopal, G. Phys. Rev. L e f f . 1991, 67, 3058 and references therein. (18) Wales, D. J.; Berry, R. S. J . Chem. Phys. 1990, 92, 4283. Adams, J. E.; Stratt, R. M. J . Chem. Phys. 1990,93, 1332. Stillinger, F. H.; Stillinger, D. K. J . Chem. Phys. 1990, 93, 6013. Rick, S . W.; Leitner, D. C.; Doll, J. D.; Freeman, D. L.; Frantz, D. D. J . Chem. Phys. 1991, 95, 6658.
0022-365419212096-3568%03.00/0 0 1992 American Chemical Society
