O2(a1Δg) production and oxygen diffusion in C60 films

O2(a1Δg) production and oxygen diffusion in C60 films

Synthetic Metals, 62 (1994) 1-7 1 O2(alAg) production and oxygen diffusion in S.C. Howells*, G. Black** C60 films and L.A. Schlie Laser and Ima...

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Synthetic Metals, 62 (1994) 1-7

1

O2(alAg) production and oxygen diffusion in S.C. Howells*,

G. Black**

C60

films

and L.A. Schlie

Laser and Imaging Directorate (PL/LIDD), Phillips Laboratory, Kirtland AFB, NM 87117 (USA)

(Received June 29, 1993; accepted July 4, 1993)

Abstract Photoexcitation of C6o thin films by either 532 nm pulsed or 514.5 nm c.w. radiation in the presence of oxygen yielded O2(alAg) luminescence. The O2(alAg) emission peak at 77 K was centered at 1281___1 nm and slightly red shifted to 1283 + 1 nm at 250 K. The emission decay time ranged from approximately 10 ms at 80 K to about 1 ms at 280 K and the steady state emission intensity dropped by an order of magnitude as the temperature was raised from 80 to 280 K. Comparison between O2(alAg) luminescence in solutions of C6o dissolved in CC14 and in C6o films resulted in a quantum yield estimate for O2(alAg) production in the film of 0.15 and an O2(aaAg) concentration estimate in the film of 0.18% relative to the C6o concentration. This set a lower limit for the oxygen concentration in the films. The low oxygen concentration relative to C6o concentration in the films led to saturation of the O2(alAg) emission intensity under 532 nm pulsed laser irradiation. Also, the O2(alAg) luminescence intensity was measured as a function of film thickness, from which an oxygen penetration distance of approximately 2500 /~ in the C6o films was inferred. Finally, the O2(a1Ag) emission was used to monitor the diffusion of oxygen out of C6o films. From the variation of the diffusion rate with temperature, the energy required to remove an oxygen molecule from the film was determined to be approximately 7 kcal/mol.

1. Introduction Since the discovery of a straightforward method for producing fullerenes in large quantities, an explosion of experimental research probing the physical properties of fullerenes and exploring their potential applications has occurred. One area of recent research emphasis is studying the photophysical properties of fullerenes, including whether C6o and C7o can be used to produce singlet oxygen [1-4], O2(a~Ag), like many polycyclic hydrocarbons. In fact, C6o dissolved in benzene has been shown to be an extremely efficient generator of singlet oxygen with a quantum yield approaching unity [1]. Because of the importance of Oz(a~Ag) in a number of applications, including its use as an energy transfer species in the chemically driven iodine laser [5-7] and also in some medical therapies, the possibility of using photoexcited C6o as the basis for a compact O2(a~Ag) generator has excited interest. There are a variety of methods currently used to produce O2(a~Ag), but they all suffer from drawbacks. While the well-known basic hypochlorite/peroxide solution technique for producing O2(a1Ag) is efficient, it is a biologically hazardous process that is both bulky and heavy. O t h e r methods, such as

photolysis of 03 and an electric discharge in an oxygen atmosphere, produce Oz(alAg) in a safer and more straightforward manner, but they tend to be less efficient and produce other species, e.g. free oxygen atoms. For these reasons, the possibility of using photoexcited solid C60 films as the basis for an O2(aIAg) generator has been studied. This p a p e r reports on the O2(aaA~) emission seen in C60 thin films and the effects of t e m p e r a t u r e and laser fluence on the O2(aaAg) luminescence. Also, by comparing the O2(alAg) emission from oxygen in C60/ CC14 solution to similar emission from C6o thin films under identical illumination conditions, the quantum yield of O2(alAg) in thin films is estimated. Furthermore, the O2(a~Ag) emission is measured as a function of film thickness in order to determine whether the O2(a~Ag) is at the film surface of in the bulk of the sample. Finally, by measuring the diffusion rate of oxygen out of the films as a function of temperature, the energy required to remove an oxygen molecule from its binding site in C6o films is determined. These results show that oxygen can incorporate itself into C6o films rather easily, contrary to some earlier reports.

2. Experimental details *Also affiliated with Department of Physics, University of New Mexico, Albuquerque, NM 87131, USA. **NRC Senior Research Associate.

0379-6779/94/$07.00 © 1994 Elsevier Sequoia. All rights reserved

The starting fullerene material was purchased from the Texas Fullerene Corp. (Houston, TX) and had a

C6opurity of 99.9%. The film growth process was initiated by placing the C6o powder in an alumina crucible inside a diffusion-pumped vacuum system with a base pressure of = 2 × 1 0 -8 Torr. After heating the crucible to 200 °C for at least 12 h and at 300 °C for 1 h to liberate any residual solvents that were incorporated in the C6o powder, the shutter obscuring the crucible from the 1 inch diameter quartz substrates, mounted 10 cm above the effusion cell, was removed and samples of various thicknesses were deposited. No special cleaning procedures were performed on the polycrystalline quartz substrates and they were maintained at approximately room temperature during deposition. The crucible temperature during deposition was held between 300 and 400 °C depending on the thickness of the film grown. The film thickness was monitored with a quartz crystal microbalance (Leybold Inficon, Inc.) and later checked using a stylus profilometer. These techniques agreed to within 15%. Films ranging in thickness from 50 to 5000/~ were deposited and tested. Polycrystalline films grown in a nearly identical manner on single crystal quartz substrates were reported [8] to have a crystal coherence length of about 60 /~, approximately four unit cells. No special treatments, such as annealing, were done on the films and they were stored under ambient conditions until used. Luminescence studies of singlet oxygen were performed using a c.w. Ar + laser as well as a frequencydoubled, 10 ns Nd:YAG laser (Quanta Ray, DCR-2A). The samples were mounted in a four-window, liquid nitrogen cryostat (Janis Research Co.) and were placed at 45 ° with respect to the incident radiation. The emitted luminescence was directed into a spectrometer placed near a second quartz window of the cryostat such that the angle between the incident radiation and emitted luminescence was 90°. The 0.3 m, f/5.6 spectrometer (McPherson) with a 300 1/mm grating, blazed at 1/zm, provided a bandwidth of 10.3 nm/mm slit width. Typically, the slits were set at 2 mm to maximize the luminescence signal, though any spectral measurements of the O2(a1A~) emission were also done at smaller widths. To remove any residual long wavelength radiation (> 1 /zm) from the lasers entering the spectrometer, several IR suppressor filters (Corion, FR400, Acu,.ofr--800 nm, trans.=0 for A>800 nm) and narrow bandpass filters, centered around the incident wavelength, were placed in the laser beam path. A liquid nitrogen-cooled intrinsic germanium detector (Applied Detector Corp., No. 403NS), with a bandwidth of ~ 100 kHz and a peak spectral response at approximately 1300 nm, was used in conjunction with a lock-in amplifier (SR530, Stanford Research Systems) or a boxcar averager (SR250, Stanford Research Systems) to detect the emitted radiation. In all measurements of O2(alAg) emission intensity, the samples were

placed in the cryostat and then exposed to the desired pressure of oxygen for approximately 1 h at room temperature or higher (320 K) to allow the amount of oxygen in the film to equilibrate.

3. Results

The absorption spectra of an 1100,8, thick C60 film taken using a Cary-5E spectrophotometer is shown in Fig. 1. It has the characteristic C6o band centered at 345 nm and the broad tail that approaches zero near 700 nm. While the shape of the absorption is in agreement with previous measurements on films [8, 9], quantitative values for the absorption are difficult to obtain using the spectrophotometer due to beam attenuation by scattering. The absorption coefficients were measured previously as 0.45 and 0.32 per /~m at 514.5 and 532 nm, respectively [9], using a technique that minimizes the effect of scattering. Initially, experiments emphasized measuring the peak and full-width half-maximum (FWHM) of the O2(alAg) emission as a function of temperature. Figure 2 shows the O2(alAg) luminescence at 77 K. The emission peak is centered at 1281 __1 nm, significantly longer than that reported [3] for C6o in CCI4, and has a FWHM of 19+_1 nm. After warming the sample up to room temperature, evacuating the cell to a pressure of 1 mTorr for at least 1 h and then recooling the sample to 77 K, the signal disappeared. Furthermore, the signal only reappeared when oxygen was readmitted into the cryostat. The signal was therefore attributed to O2(alAg) emission. Additional spectra taken from the same sample at 150, 200, 250 and 298 K revealed that the peak wavelength slightly red shifted and the signal broadened with increasing temperature to the extent that, at 250 K, the peak wavelength was 1283 _+1 nm and the FWHM was 26_+ 3 nm. The spectrum at 298 K was too weak to obtain accurate measurements. Furthermore, the

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500 (nm)

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Fig. 1. A b s o r b a n c e of a 1100 ~ thick C ~ film on a quartz substrate from 300 to 700 nm.

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spectra appeared symmetric at all temperatures. This is in contrast to studies [10] where no shift in the peak was reported but asymmetric internal structure in the peak, attributed to Stokes and anti-Stokes transitions in the peak, was seen. Even with a slit width as small as 0.3 mm, corresponding to a bandpass of 3 nm, these features were not seen. We believe this is due to the much smaller crystallite size (approximately 60 /~) in our films which causes a smearing out of the electronic transition. Measurements of the O 2 ( a l A g ) lifetime as a function of temperature are shown in Fig. 3(a). At room temperature the lifetime is less than 1 ms and rises to 10 ms at 80 K with a sharp increase near 270 K. The lifetime was found to be independent of laser power up to 6 m J/pulse. Shown in Fig. 3(b) is the steady state O2(alAg) emission intensity using c.w. 514.5 nm excitation. In this case, the emission drops more uniformly with increasing temperature. At 80 K the O2(alAg) intensity is approximately 10 times the emission intensity at 280 K. From these two curves, a relative production rate of O2(a~Ag) can be derived by simply taking the steady state intensity values and dividing by the lifetime. Figure 4 shows the O2(alAg) emission intensity at 200 K as a function of the Y A G laser fluence over approximately 5 cm 2. At low power the signal grows linearly, then appears to saturate at = 2 mJ/pulse ( = 1.1 × 10 ~5 photons/cm2). Figure 4 also shows similar behavior at 1/3 of the initial oxygen concentration. Both sets of data were taken after exposing the sample to the given pressure of oxygen for at least 1 h at room temperature and then cooling the sample to 200 K. Similar saturation results were obtained with samples held at room temperature, although, as expected, the emission intensity was much lower at saturation due to increased non-radiative losses. Due to the large quantum yield of O2(alAs) in solid films, which will be discussed later in this paper, the

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Fig. 3. (a) O2(aZAg) lifetime vs. temperature measured using a 5000 /~ thick C6o film. The 532 nm Nd:YAG laser fluence was approximately 1.2 m J / c m 2. T h e uncertainty grows slightly with increasing temperature. (b) Steady state O2(a~As) emission intensity measured using a 5000 ,~ thick C6o film. T h e 514.5 nm laser intensity was 2.5 W / c m 2. The uncertainty is approximately the same for all of the data points. 0.8 T = 200 K

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Fig. 4. O2(atAg) emission intensity from a 5000 ,~ thick film as a function of Nd:YAG laser fluence at 532 nm.

O2(alAg) emission was measured quite easily, even in 50 ,~ thick films. Figure 5 shows the emission intensity, upon irradiation with c.w. Ar ÷ laser excitation, as a function of temperature for a number of films with thicknesses ranging over two decades. The samples, which were stored under ambient conditions, were

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Fig. 5. Steady state O2(al~g) emission intensity vs. temperature for C60 films of thicknesses ranging from 50 to 5000/~. The 514.5 nm laser intensity was 2.5 W/cm 2. The uncertainty of each measurement is approximately 5:15%.

placed in the cryostat and immediately cooled down to 200 K, then evacuated and cooled further to 77 K. The reason for this two-step process was that evacuation of the cryostat at temperatures above 250 K caused oxygen to diffuse out of the films at an unacceptable rate, while oxygen left in the cryostat at 77 K caused condensation. Due to the very slow diffusion of oxygen out of the films below 200 K, the O2(alAg) emission intensity was stable over the time it took to perform the measurements. Upon reaching 77 K, the sample was irradiated with approximately 2.5 W/cm2 of 514.5 nm light and the temperature raised to 240 K over the period of 1 h while the emission was monitored. Figure 5 shows that, within experimental error, the signal rises linearly with thickness up to 2500/~,, where it saturates. Obviously, even exposure to air allows oxygen to diffuse far into the bulk of polycrystalline C6o films. The O 2 ( a l A g ) emission intensity at a fixed illumination intensity and temperature measures the relative amount of oxygen in the films. Figure 6 shows the time for half attenuation of the O2(a~Ag) signal, after evacuating the cryostat, as a function of temperature for two different films. A concern of this method was that, because of the steady state concentration of O2(alAg), it could have affected the measured rate of oxygen removal from the film as compared to a film containing only ground state 02. However, by blocking the c.w. Ar ÷ laser beam for at least 80% of the time, it was verified that the excitation of O2(alAg) in the film did not affect the measured rate. Another concern was that illumination of the film in the presence of oxygen might cause photo-oxidation [11]. However, by verifying that the O2(alAg) emission intensity did not change under constant laser illumination and oxygen pressure, this possibility was rejected. The decay of O2(alAg) emission after evacuating the cryostat could not be accurately fitted by a simple

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1/Temperature (K-t) Fig. 6. Time for half attenuation of the O2(a~As) signal after evacuation of the cryostat for two different thickness C60 films as a function of temperature. The Ar + laser intensity was approximately 2.5 W/cm 2. The temperature of the sample was maintained within 1 K of the specified temperature and all data points were taken under constant illumination.

exponential. Initially, the signal dropped off relatively quickly, presumably as oxygen was removed from nearsurface sites, but, following this, the O2(alAg) emission decreased at a much slower rate. Therefore, it was not possible to assign a single exponential decay rate to any of the diffusion curves. Instead, the time to decay to one half of the initial signal intensity was used as the parameter for the y-axis in Fig. 6. This description of the data worked well. From the slopes of the lines in Fig. 6, the energy needed to remove an oxygen molecule from the film, Eb, can be calculated from the expression (decay time)50~-l=A exp(-Eb/RT). For 5000 and 200/k thick films, Eb is found to be 6.7 and 7.4 kcal/mol, respectively.

4. D i s c u s s i o n

It is interesting to compare the steady state O2(alAg) luminescence in the solid phase with the luminescence in the liquid phase and calculate both the quantum efficiency of O2(alAg) production and the excited state oxygen concentration in the C6o films. Using a 1 cm thick cuvette filled with a 1.5 x 10 -4 M solution of C6o in CC14placed in a 514.5 nm c.w. laser beam of intensity 0.72 W/cm2, it was found that the total O2(alAg) emission in solution was 83 times larger than the O2(alAg) signal of a 5000 /~ thick film exposed to air under identical illumination. From this comparison, one can estimate the quantum yield of O2(alAg) production in the C60 films. Using a measured molar absorbance in solution at 514.5 nm of 850 M-1 cm-1 [3] and an absorption coefficient in the solid phase of 0.45 per /zm [9] at 514.5 nm leads to nearly 1.6 times more absorption in the film than in the solution. Then, correcting the ratio

of emission intensities for both the lifetime of the O2(alAg) at room temperature (7"~olution/~'film=20)and the absorption leads to a relative quantum efficiency of ~)(O2(alAg))film/t~O2(alAg))solution = 0.15. It should be mentioned that implicit in this calculation is the assumption t h a t the radiative lifetimes of O2(alAg) in CC14 and in the films are equal. If they are not equal then the relative quantum efficiency must be multiplied by 7radfilm/'rr, a solution" Bearing in mind all of the uncertainties in the measurement and assumptions, it is certainly possible that the quantum yield in the solid film is just as high as in solution. Furthermore, from the O2(a~Ag) emission ratio between the solution and the film, the O2(alAg) concentration in the film can be estimated. Correcting for the thickness difference in the samples leads to a relative singlet oxygen concentration, [02(a1Ag)]film/ [O2(alAg)]solutio, = 240. Based on the absorption of C6o in CC14, the intensity of the Ar + laser and the lifetime of singlet oxygen in a 1.5×10 -4 M solution of C6o in CCL (22 ms) [3], the concentration of O2(a~Ag) in solution is calculated to be 1.7×10 -5 M. Using this value leads to a singlet oxygen concentration in the thin film of 4.2× 10 -3 M, or about 0.18% of the C6o concentration. Of course, the total oxygen concentration will be higher since not all of the oxygen molecules are excited at any time. In fact, it has been estimated [12] that, under ambient conditions, C6o contains on the order of 1% oxygen (relative to C6o) in interstitial sites. If this applies to our films then, even under weak Ar ÷ laser irradiation at room temperature, a large fraction of the oxygen exists as O2(alAg). Figure 3(a) shows very similar behavior to that reported previously [10], with the lifetime dropping steadily in the range 80-250 K, followed by a much faster drop in lifetime above 250 K. However, ref. 10 reported lifetimes approximately a factor of four greater than shown in Fig. 3(a). This may be due to the small crystallite size used in this work compared to the previous study or to possible contamination during the evaporation process. In light of the above large fractional conversion of oxygen t o O2(alAg) under c.w. Ar ÷ laser irradiation, it is not surprising that oxygen availability limits the signal obtainable under the higher powers possible with the Nd:YAG laser. This behavior is shown in Fig. 4 for two oxygen pressures. The ratio of the plateau intensities does indeed approximate the ratio of the oxygen pressures and the lower pressure curve saturates at a lower laser power. Other explanations of the behavior shown in Fig. 4 are less reasonable. First, optical saturation of the C6o can be eliminated since only = 1% of the C6o is excited during a laser pulse (3 mJ over approximately 5 cm2). Secondly, increasing non-radiative quenching of the O2(a~Ag) with increasing

laser power does not occur, the O2(alAg) lifetime was independent of laser fluence. Finally, possible competition between triplet C6o transfer to 02 and triplet-triplet annihilation can be eliminated since it would give non-plateau behavior and the downward curvature would be more pronounced at the lower 02 pressures. A recent report [13] suggested various del~ths of oxygen penetration in C6o, from less than 200 A when the film was not illuminated in the presence of oxygen to very significant penetration (stoichiometry--- C6o02.6) after exposure to visible light. Another study [14] of O2(alAg) emission in C6o films stated that 02 diffused into the surface layer but no quantitative estimates were given. As shown by the family of curves in Fi~. 5, the O2(alAg) emission from films less than 2500 A is roughly proportional to the thickness of the film. This is evidence that 02 diffuses into the bulk of sublimed C60 films under ambient conditions. It was found that for films thicker than 2500/~, specifically the 5000/~ film, the O2(alA~) emission did not increase further, suggesting that under ambient conditions oxygen diffuses approximately 2500/~ into C6o films. This was checked several times and at no temperature was the O2(alAg) emission from the 5000/~ film appreciably larger than the O2(alAg) emission from the 2500/~ film. Also, there does not appear to be a large amount of O2(alAg) emitting at the surface because, if there were, the thinnest films would show larger than expected emission. It may be that there are many monolayers of oxygen present at the surface, but that it has a much lower excitation cross section. It is also possible that the environment of the film surface results in a much longer O2(alAg) radiative lifetime, which would lower the rate of emission of excited oxygen at the surface. Oxygen diffusion studies out of two separate films (Fig. 6) show an average of 7.1 kcal/mol needed to remove an oxygen molecule from the film. As stated previously, the diffusion out of the films does not appear to be single exponential and therefore fitting to different parts of the signal decay curve leads to different decay rates. However, using different fitting criteria, e.g. fitting the first quarter of the decay, leads to only small changes in the oxygen removal energy, i.e. the slope of the curve in Fig. 6. This is evidence that describing the decay by the time for the O2(alAg) emission intensity to drop to one half of its initial intensity is valid, at least for determining the oxygen removal energy. The fact that the oxygen removal energy is so large implies that the oxygen is not simply physisorbed to the surface of the polycrystallites that comprise the film, as it is expected that physisorption would be much weaker than 7.1 kcal/mol. More probably, the oxygen molecules are diffusing into the film and being trapped in the octahedral sites of the face-centered-cubic lattice, as suggested by high resolution ~3C NMR studies [12].

The octahedral interstices are about 4.1/~, in diameter, based on the 10.04 /~ van der Waals radius of C6o molecules in an f.c.c, lattice [15], easily large enough to accommodate an oxygen molecule with a van der Waals radius of 1.4 /~ [16]. The energy needed to remove an oxygen from the film calculated from the measured diffusion times is then the amount of energy needed to remove the oxygen from the octahedral site. Due to favorable van der Waals interaction, the binding energy of oxygen in such a site has been estimated [12] as 7 kcal/mol. The agreement with our measured energy is fortuitous since our measurement also includes the energy barrier to removing oxygen from the octahedral site (in addition to its binding to that site). This energy barrier can be a considerable fraction of our measured 7 kcal/mol as the following simple argument will show. The energy, E, required to dilate a cylindrical hole of depth w from radius ra to r is given by [17]

E = TrGw(r- ra)2

(1)

where G is the shear modulus of the medium. McElfresh and Howitt [18] take w to be half of the average jump distance traveled by the diffusing species. In C6o, w equals 7.1/~ (half of the lattice constant). From measured values [19, 20] of the bulk modulus, assuming a Poisson's ratio of 1/3, the shear modulus G can be calculated [17]. A value of = 6 GPa is obtained. Assuming rd = 1 /~ and r= 1.4 /~, a value of E = 3 kcal/ tool is obtained from eqn. (1). Hence a large fraction of the measured 7 kcal/mol can be the energy barrier for removal. The diffusion time for oxygen out of the C6o films is several orders of magnitude shorter than the diffusion out of C6o powder [12]. Presumably this is due to a much smaller crystallite size for our films compared to the C6o powder. Powder that was ground up to reduce the grain size allowed for much faster diffusion [12], although still about 100 times slower than the typical diffusion rates shown here at room temperature. Still, one expects that, even after grinding, the crystallite size of the powder is significantly larger than the approximately 60 /~ crystallite size of the films used in this study. Furthermore, referring to Fig. 6, the diffusion time out of the films is greater for the thicker film, suggesting that diffusion of oxygen is a multi-step process of oxygen moving from one octahedral site to another. Typical diffusion times for films held at room temperature ranged from seconds to several minutes, much shorter than the hours measured for pure C6o powder [12] after exposure to high 02 pressures (100-1000 atm). Again, this probably relates primarily to the larger crystallites that constitute the powder. A second contribution may come from the much lower oxygen pres-

sures used in this study, since greater 02 pressures appear to lead to slower diffusion out of C6o [12].

5. Conclusions

By monitoring the O2(alAg) emission, the diffusion rate of oxygen out of polycrystalline C6o films was measured. Our findings showed that oxygen readily diffused into the bulk of the film. Comparisons of the O2(alAg) emission from films ranging between 50 and 5000/~ thick revealed that the O2(alAg) emission was proportional to the thickness of the film up to 2500 /~, suggesting that oxygen diffused uniformly into the bulk of the films. Diffusion of oxygen out of the C6o films was a sensitive function of temperature, taking approximately 400 times longer at 200 than at 298 K. From the diffusion curves (Fig. 6), the energy needed to remove an oxygen from the film was calculated to be 7.1 kcal/mol with a significant part of this due to the lattice distortion energy. Furthermore, thicker films displayed slower diffusion rates suggesting that diffusion was a multi-step process in these films. Finally, comparing the O2(alAg) luminescence of the solid thin films with O2(alAg) emission in solution indicated that, under low power Ar ÷ laser irradiation, O2(a~Ag) concentration in the film was =0.0042 M, or about 0.18% of the C6o concentration. With pulsed Nd:YAG irradiation, oxygen availability limited the concentration of O2(a~Ag) that could be obtained. Since the quantum efficiency for O2(alAg) production could be unity, solid C6o films may provide the basis for a simple, compact, O2(a1Ag) generator. However, before this becomes possible, several other issues must be addressed. One of these is that the generated O2(a~Ag) be liberated from the films. In the diffusion experiments, the effect of having the Ar ÷ laser on continuously versus intermittently was measured. No effect on the diffusion time was seen. Since it seems likely that = 10% of the oxygen can be excited with the Ar ÷ laser, diffusion of O2(a~Ag) cannot be much faster than O2(X3Eg-) or an effect would have been seen. If the measured 7.1 kcal/mol also applies to O2(alAs) then, in order to remove the O2(alAg) before it decays to the ground state, either the generator will have to be operated at elevated temperatures or the C6o films deposited in sufficiently thin layers so that oxygen does not get trapped in the interstitial sites. Other issues to be addressed are whether, and to what extent, C6o molecules in thin film quench the O2(a~Ag). This process was studied in solution where a very low quenching rate coefficient was measured [3].

Acknowledgement This work was supported by the Chemistry Division of the Air Force Office of Scientific Research (AFOSR/ NC). The loan of the Nd:YAG laser by Chris Clayton is gratefully acknowledged.

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