4374
J . Phys. Chem. 1991, 95,4374-4318
Fluorescence and Photochemical Yields of Sulfur (S,) in Methanol upon 266-nm
Anthony C. Bevilacqua and Jonathan E. Kenny* Department of Chemistry, Tufts University, Medford, Massachusetts 02155 (Received: August 8, 1990; In Final Form: December 4, 1990)
We report the upper limit of the fluorescencequantum yield, cPf, and the photochemical yield of disappearance, a d , for solutions of & dissolved in methanol and irradiated with pulsed 266-nm light. In an effort to measure fluorescence from the &-methanol solutions, we used a laser source whose wavelength corresponds to the peak of the first electronic absorption band. Despite the significant photon flux and the excitation into the first electronic absorption band, the s g samples were not observed to fluoresce, nor did the photochemical products fluoresce. An attempt to slow down the photochemical and the other nonradiative deactivation pathways of electronically excited s8 by complexation with #?-cyclodextrin was made, but still no fluorescence was observed. The limit of detection of cPf for s8 was determined from the observed emission spectrum and known spectroscopic quantities of naphthalene. We report the upper limit for +f of sulfur to be 1.O X lo-'. Measurements of sample transmittance as a function of irradiation time at various laser pulse energies and repetition rates and sg concentrations resulted in a value of 0.043 f 0.006 for a d (molecules of Sa lost/photon absorbed). The application of a simple kinetic model, one which predicts only photoproducts that are transparent at 266 nm, yields systematic differences between the observed and predicted transmittances. The addition of a term to the kinetic model which accounts for nontransparent transient photoproducts markedly reduces these differences.
Introduction The optical properties of solid, liquid, and gaseous sulfur have been the subject of numerous studies.'+ However, the existence of large numbers of allotropic forms of the element and the prediction of large numbers of low-lying excited electronic states for the dominant species, s8, among other problems, have prevented detailed analysis of the spectroscopy, photophysics, and photochemistry of these systems. Recently, there has been renewed interest in experimental measurements of the properties of the allotropes of sulfur.'J This interest is partly due to their importance in improving the parametrizations of semiempirical MO programs which are now widely used!.' In addition, the sulfur allotropes provide a useful benchmark for evaluating more sophisticated parameter-free techniques for calculating the properties of systems with large numbers of electrons, e.g., density functional methods! Furthermore, elemental sulfur vapor has been detected in the clouds of Venus? and it is believed that the excitation and decay processes of S, and its photoproducts contribute significantly to the radiation budget of the planet. Similarly, the presence of sulfur vapor in the early earth atmosphere from volcanic activity may have provided our planet with an ultraviolet shield prior to the existence of the ozone layer. Recently, several studies of photoinduced processes in s8 under varying conditions have appeared. Elbanowski and Wojtczak'* reported that SBdoes not fluoresce upon 254-nm irradiation in methanol and that it quenches the fluorescence of benzene, naphthalene, and pyrene. Elbanowski" reported a quantum yield of 0.39 f 0.04 for the photodecomposition of at 254 nm in methanol. Casal and Scaiano12studied the photolysis of s8 in cyclopentane using a pulsed laser at 308 or 337 nm; they obtained evidence for S3and S4photoproducts from transient absorption spectra but reported no information on photophysical or photo(1) Bass, A. M. J . Chem. Phys. 1953, 21, 80.
(2) Cook, B. E.; Spear. W. E. J . Phys. Chem. Solids 1969, 30, 1125. (3) Meyer, B.; Gouterman, M.; Jensen, D.; Oommen, T. V.; Spitzer, K.; Stroyer-Hansen, T. Adv. Chem. Ser. 1972, 110, 53. (4) Steudel, R.; Jensen, D.; Gbbel, P.; Hugo, P. Ber Bunsen-Ges Phys. Chem. 1988,92, 118. (5) Lenain, P.; Piquenard, E.: Corset, J.; Jensen, D.; Steudel, R. Ber Bunsen-Ges Phys. Chem. 1988, 92, 859. (6) Dewar, M. J. S.;Reynolds, C. H. J . Compur. Chem. 1986, 7 , 140. (7) Jug, K.;Iffert, R. J . Compur. Chem. 1987, 8, 1004. (8) Hohl. D.; Jones, R. 0.;Car, R.; Pattinello, M. J . Chem. Phys. 1988, 89. 6823. (9) Krasnopolsky, V. A. Ado. Spuce Res. 1987, 7 , 25. (IO) Elbanowski, M.; Wojtczak, J. Phosphorus Sulfur 1978,5, 107. (1 1) Elbanowski, M. Phosphorus Sulfur 1978.5, 1 1 1. (12) Casal, H . L.; Scaiano, J. C. J . Phorochem. 1985, 30, 253.
0022-3654/91/2095-4374$02.50/0
chemical yields. Most recently, Strauss and SteudeP have reported the results of HPLC product analysis of the results of broad-band (200-600 nm) irradiation of various sulfur species, including S8,in carbon disulfide. They found mixtures of sulfur homocycles S,, n L 5 ; relative amounts of each species as a function of irradiation time were reported, but no quantum yields were given. We became interested in exploring the photophysics of elemental sulfur and were intrigued by a number of unanswered questions. For example, the reported lack of fluorescence was not expressed quantitatively. Perhaps a very weak but detectable emission could be excited by using an intense laser; such emission would facilitate a number of spectroscopic and dynamical studies. In this work, we report the results of our attempts to observe fluorescence from s8 in methanol upon irradiation with pulsed light of wavelength 266 nm, very near the absorbance maximum of the lowest energy electronic transition. We also attempted to enhance the probability of radiative decay in s8 by forming the inclusion complex with p-cyclodextrin. Cyclodextrins have been shown to form inclusion complexes with nonpolar molecules in polar s01vents.l~ The hydrophobic cavity of the cyclodextrin traps the molecule, while the polar exterior wall allows solubility in the methanol. Cyclodextrins can change the photophysical properties of included molecules and protect them from quenching interactions with other species. The choice of p-cyclcdextrin was made based on the cavity size and the dimensions of s g . While no fluorescence was observed in either case, an upper bouhd for the fluorescence quantum yield based on our instrument's detection limits was determined. Naphthalene was chosen to determine the detection limit of our apparatus because of its strong fluorescence and its known fluorescence spectrum and quantum yield. Also, both and naphthalene have their lowest lying UV absorptions -270 nm, and their emission would normally be expected to appear in approximately the same spectral region. In the course of the work, we observed that the solution being irradiated, initially strongly absorbing a t the laser wavelength, gradually became transparent. We quantified this effect and obtained a value of the quantum yield of photochemical decomposition of sg. We also modeled the formation of photoproducts and qualitatively determined their subsequent decay rate and its dependence on the photon intensity. We discuss the photophysics and photochemistry of sg in the light of our results and other available information. (13) Strauss, E.-M.; Steudel, R. Z . Naturforsch. 1987, 426. 682. (14) Nelson, G.:Neal, S. L.; Warner, 1. M. Spectroscopy 1988,3(8), 24.
0 1991 American Chemical Society
Photochemical Yields of Sulfur
(ss) in Methanol
Experimental Section
Sulfur (Aldrich, 99.999%), naphthalene (Fisher, ACS grade), Bcyclodextrin (Aldrich), methanol (Fisher, HPLC grade), and cyclohexane (Fisher, spectrophotometric grade) were used without further purification. The s8 solutions were prepared in methanol, while the naphthalene solutions, to be used for calibration purposes, were prepared in cyclohexane. The configuration of the fluorimeter/absorption spectrometer is as follows. A Spectra-Physics DCR-11 pulsed Nd:YAG laser (1064 nm, 10 Hz repetition rate) and two frequency-doubling crystals produced up to 2.0 mJ per 5-nspulse of 266-nm light at the sample cuvette, which corresponds to a peak flux of 5 X lo2' photons/s. The donut-shaped beam was focused by a 15 cm focal length lens through the long path of a 1 cm X 2 cm sample cuvette (NSG Precision, UV fused silica). The front face of the cuvette was placed 8.5 cm from the lens. The laser beam was 4.0 m m in diameter at the cuvette entrance and 2.5 mm at the exit. This provided a large photon density while preventing damage to the faces of the cuvette. A. Fluorescence Yield Experiment. For the fluorescence experiments, the concentration of varied from 2.62 x IO4 to 2.62 X lod M. Given the absorptivity of sulfufl (e2& = 6700 M-' cm-I), these concentrations provided optical densities of 3.5-0.035 (3 X lo4 to 0.92 transmittance). Pulse energies up to 2.0 mJ of 266-nm radiation were used. Light from the s8 samples was collected at 90° by six polished 600 pm core diameter, 1 m long fused silica optical fibers (Fiberguide Industries) placed against the outside wall of the cuvette. The collected light was delivered to a 0.156 m focal length Jarrell-Ash spectrograph fitted with an EG&G 1420 blue-sensitive 1024element diode array (controlled by an EG&G 1461 detector controller) with 700 intensified elements. The resulting band-pass was 4.0 nm. The grating was positioned so that the wavelength region from 280-650 nm could be monitored in a single scan. The cathode was cooled to -5 OC; responsivity was 1 count/.-6 photons at 300 nm. The integration time was typically set for 30 s, utilizing up to one-half of the dynamic range with background dark signal. Scans were successively added, providing total integration times of up to 30 min. The collected data were stored to disk on a Compaq 386/20 MHz personal computer. Similar experiments were carried out with the addition of up to a 10-fold molar excess of concentrated 8-cyclodextrin/H20 solutions to the dilute &/methanol solutions. Under identical conditions to the s8 fluorescence experiments (laser intensity, integration time, number of scans), the fluorescence of naphthalene solutions was recorded. Beginning with 10-4 M solutions of naphthalene in cyclohexane, the concentration was lowered until the fluorescence could be reliably recorded. At high concentrations (>IO" M) there was considerable laser beam attenuation due to naphthalene absorption. From -lo-' to lW5 M, the resultant fluorescence signal was saturating the A/D counters for the 30-s integrations. However, the fluorescence of these samples and subsequently diluted samples were determined to be linear with concentration as determined by scans with shorter integration times. B. Photochemical Depletion Experiment. In four separate experiments (trials 1-4), laser pulse energy was varied from 0.5 to 2.0 mJ/pulse. In each case, a volume of 5.00 mL of 3.9 X lWs M in methanol was used. The transmittance of the S8sample was determined by monitoring the pulse energies of the incident (Io)and transmitted (I,) beams. A Laser Precision RjP-765 silicon photovoltaic detector recorded relative Io values obtained from a partial reflection of the laser beam with a fused silica beam splitter placed before the cuvette. A fused silica neutral-density filter (OD = 2.0) was placed in front of this detector to prevent photodamage. A Laser Precision RjP-735 pyroelectric detector energy probe was placed behind the cuvette and provided absolute values of It. A Laser Precision Rj-7200 joulemeter reported the energy per pulse for Io and It at each detector, and the ratio, Il/Io, for 100 laser shot averages. The blank value, (Il/Io)b was measured prior to each experiment with only solvent in the cuvette. Measurements were made at l-min intervals until the transmittance reached 0.99. Transmittance of the sample was also checked on
The Journal of Physical Chemistry, Vol. 95, No. 11, 1991 4375 a conventional absorption spectrophotometer at the beginning and end of the irradiation period. Similar measurements of the transmittance vs time were also made for two different laser repetition rates, 10 and 14 Hz (trials 5,-6), with a constant laser pulse energy, 1.O mJ/pulse, and a fixed s 8 concentration, 3.29 X lW5 M. The transmittance was recorded every 10 s. Measurements of the transmittance vs time were also made for three different concentrations of Sa in CH,OH: 7.30 X lW5, 3.29 X and 1.05 X 10" M (trials 7-9), which provided initial transmittance readings within the response range of the detectors. These three experiments were performed at a constant laser pulse energy, 1.0 mJ/pulse, and a fixed repetition rate, 10 Hz. The measurement of Il/Zo was recorded once every minute for the most concentrated solution, and once every 10 s for the more dilute solutions. Results A . Fluorescence Yield Determination. I . s8 in Methanol. Even under the most intense excitation conditions employed, no luminescence was observed. In the event that the high photon flux resulted in immediate saturation and subsequent transparency of the solution, we attempted to measure fluorescence at lower laser powers but the result was the same. The absence of saturation effects could further be verified by the fact that the a b sorbances of the solutions were the same when measured with the laser source and with a conventional absorption spectrophotometer. Also,the solutions used in the decomposition experiments produced an initial absorbance which was equal to the product of sample path length, molar absorptivity, and s8 concentration. 2. s8 and 8-Cyclodextrin in Methanol. Even a 10-fold molar excess of j3-cyclodextrin to s8 in methanol solution did not produce detectable fluorescence. To the contrary, the weak fluorescence produced by irradiating a solution of 8-cyclodextrin was quenched by the addition of s8. 3. Limit of Detection. Since we observed no fluorescence from s8, we could only determine the upper bound on the fluorescence quantum yield. That is, given the sensitivity of our experimental apparatus as demonstrated in the detection of naphthalene fluorescence at low concentration, what quantum yield for Sa would produce an amount of fluorescence just equal to our detection limit? We determined the detection limit based on a single-point measurement, i.e., the number of detector counts registered at the maximum in the emission spectrum. We then made the reasonable assumption that naphthalene and sa,with nearly equal absorption frequencies for their lowest electronic transitions, have similar emission wavelength distributions and emission maxima near enough to each other that the detector response may be considered constant. The accepted definition of detection limitls is based on a signal that is larger than the blank by a factor of 3 standard deviations of the blank. For an integration time of 5 min, we estimated the blank standard deviation to be 200 counts, so the minimum detectable signal would be 600 counts above blank. From the linear relationship between signal and concentration determined at low naphthalene concentrations, and the literature valuesI6 for its molar absorptivity and fluorescence quantum yield [& = 5400 M-I cm-I, a; = 0.211, a detection limit for naphthalene of 5.9 X 1W" M was calculated. The quantum yield for s8 emission required to produce the same signal was calculated by using the relation (appropriate for dilute solutions) -ss=
k~~Ts&tP(L)@%&" (1) S" kl"C"l'"
[email protected](Xun) where S is the signal from the photodiode array spectrometer, k is an apparatus constant, I is the light source intensity, C is the analyte concentration, T is the integration time of the photodiode (1 5 ) A.C.S. Subcommittee on Environmental Analytical Chemistry A w l . Chem. 1980,52,2142A. (16) Berlman, I. B. Handbook of Fluorescence Spectra of Aromatic Molecules, 2nd 4.;Academic Press: New York, 1971.
Bevilacqua and Kenny
4376 The Journal of Physical Chemistry, Vol. 95, No. 11, 1991
centration of s8 is, at first glance, justified by the observation that continued irradiation of the solutions produces samples that are 199% transparent; Le., the photoproducts do not absorb appreciably at 266 nm. This assumption is discussed further below. The first derivative on the right side of eq 3 is obtained from Beer's law:
1.o 0.9
E 2
0.8 0.7
[%],=
0.6
v)
-2.303tlT
(4)
0.5
The change in concentration is obtained by multiplying the number of photons absorbed by the quantum yield for photodecomposition and dividing by the volume and Avogadro's number, NA:
0.4
0.3
i*'" 0
5
"
1
" "
'
10
15
1
"
'
2b
" " I " "
25
3b
""I
35
(5)
IRRADIATION TIME (minutes) Figure 1. Transmittance of SBsolutions, 3.9 X IO-' M in methanol, vs time for four values of laser pulse energies at 266 nm (trials 1-4). The symbols represent experimental data points (see figure for legend). The
smooth curves are the predicted transmittances for the two models described in the text. The solid bold curve, shown for trial l, is predicted from the model which assumes that the photoproducts are transparent. The remaining smooth curves, shown for trials 1-4, are predicted from the model which assumes that the photoproducts are long-lived transients that absorb 266-nm radiation. The curves are obtained using the average value for ad,0.042. array detector, and D(X,,) is the detector response as a function of emission wavelength. The superscripts s and n refer to sulfur and naphthalene, respectively. When signal levels for naphthalene a t its detection limit and for S8 under the most favorable experimental conditions (highest concentration and intensity) are equal, the ratio above may be set equal to unity and the expression solved for @!(A,,,). This procedure yields a maximum quantum yield for Sa of 1 .O X IO-'. B. Yield of Photodecomposition of S8. Using the measurements of the two energy detectors, we calculated the transmittance of the sample from
where the subscripts s and b are the sample and blank measurements. The increasing transmittance as a function of time for the four different laser pulse energies (trials 1-4) is shown in Figure I . In each case, the initial transmittance was about 0.30 and the final transmittance exceeded 0.99. The values of transmittance measured on a conventional spectrophotometer at the beginning and end of each experiment agreed with the corresponding measurements made with the laser. Similar plots of transmittance vs. time were obtained for trials 5-9. In the course of trials 1-4, the value of Io as determined by a 100-shot average measured once per minute remained nearly constant. The mean f l standard deviation for all the measured Iovalues were 1.978 f 0.063, 1.542 f 0.047, 1.101 f 0.012, and 0.529 f 0.006, all in mJ/pulse. Maximum deviations from the mean were never more than 2 standard deviations. In the analysis presented below, we use the simplifying assumption that Io was a constant, equal to its mean value, throughout each experiment. Furthermore, we switch to units of photons per second for Io by multiplying the pulse energies by the repetition rate, 10 Hz, and dividing by the energy of a photon, h c / X . Because the initial transmittances of the sample at all four pulse energies agreed with each other and with that calculated from the Beer's law absorbance, we concluded that only one-photon absorption processes were important. Under this assumption, the time-averaged incident intensity could be used to calculate an instantaneous rate of change of sample transmittance from the relation (3) The assumption that the observed T depends only on the con-
Substituting eqs 4 and 5 into eq 3 and rearranging, we obtain
Integrating eq 6 from T = To to T and t = 0 to t, one obtains (7) The slope of a plot of the left-hand side vs t can be used to obtain an initial estimate of Such plots were prepared for trials 1-4, along with the best-fit lines constrained to pass through the origin. Because the experimental error in determining 1 - T i s large for T close to unity, these fits utilized only the data points with T 5 0.95. The values of our initial estimates of ad obtained from the slopes, from high to low power, were 0.021,0.019,0.023, and 0.022, all with standard deviations of 0.001. The average value from the four determinations is 0.021 f 0.002. In each case, the plots showed systematic deviations from the straight line fits, negative at short times and positive a t long times. We rearranged eq 7 and plotted T as a function o f t using the value of 0.021 for +d for trials 1-4. The plots of the predicted and the observed T vs t curves showed the same systematic deviations in each case: the predicted transmittance was greater than the observed transmittance at short times while the contrary was true at the longest times. The fact that the deviation was similar in all four trials suggested a flaw in the model. We ascribe the deviations to transient photoproducts which absorb 266-nm radiation. Such photoproducts only need live a tenth of a second to decrease the transmittance measured with the next laser pulse; evidence for this effect has been reported.'* Yet the photoproducts must have a short enough lifetime, certainly under 10 min, to account for the complete transparency of the sample a t the end of each experiment. The presence of any photochemically produced species that absorbs 266-nm radiation would tend to lower the measured value of ad since the number of absorbed photons due to Sa would be less than the total number of absorbed photons. The suggestion was made by an anonymous referee that the value of ad is only a lower limit and a better value could be obtained by using only the long time data. Further suggestions included a "dark" decay experiment and a study of the laser repetition rate (trials 5 and 6) and sg concentration (trials 7-9) dependence on The dark decay experiment might give information on thermal processes occurring after the photochemical event. The determination of for various s8concentrations and laser repetition rates might help to quantify the extent of photochemically produced absorbers and their average transient lifetime. The dark decay experiment was performed by irradiating an S8/CH3OH solution and monitoring the transmittance as usual. However, after irradiation for 5-10 min, the laser beam was blocked for 10 min and then allowed to irradiate the s g sample again. The initial transmittance readings from the second irradiation period were lower than the last reading from the initial irradiation, albeit only -256, indicating that the absorption increased slightly as the solution relaxed in the dark. +de
The Journal of Physical Chemistry, Vol. 95, No. 11, 1991 4311
Photochemical Yields of Sulfur (Sa)in Methanol
TABLE I: Photodecomposition Yields of S, in CH30Ho trial
Od 0.0350 0.037, 0.047, 0.0481 0.042, 0.0399 0.0137 0.0416 0.0515
U
0.0020
0.000, 0.0058 0.0049 0.0046 0.007, 0.00 1’I
0.0036 0.001,
laser pulse energy, mJ/pulse 1.978 1.542 1.101 0.529 1.o 1.o 1.o 1.o 1.o
rate,
Hz IO 10
10 10 10 14 10 10 10
SBconcn lo5, M
X
3.9 3.9 3.9 3.9 3.3 3.3 7.3 3.3 1.1
0.05
Valucs of photodecomposition yield, ad,and standard deviation, u, of S8in CH30H upon 266-nm irradiation for each trial as a function of laser power and S8 concentration.
In order to determine a more accurate value of a d , the potential for interferences from any photochemically formed absorbing species must be minimized. This condition is satisfied at or near the end of each experiment when the solutions are most transmissive and producing the least amount of photoproduct. We rule out the use of data at the initial stages of the experiment because, although there is no absorbing photoproduct at t = 0, photoproducts are formed in the largest quantities when the S8 concentration is the highest. The improved value of @d for each trial was determined in the following manner: 1. @d was determined the same way as before, from the slope of the least-squares line plotted from eq 7, but not constrained to pass through the origin and using only data from T = a to 0.95, where a = 0.30. We now define a as the lower limit of the transmittance used to determine the range of data points. 2. Repeat step 1, except determine @d using only data points from T = a to 0.95 where a = 0.40, 0.50, 0.60,0.70, and 0.80. For each of the nine trials which vary laser pulse energy, repetition rate, and Sa concentration, we have a measurement of @d at several CY’S.
3. For each trial, plot @d vs a,determine the slope and intercept from the least-squares fit, and determine the value of @d by extrapolation to a = 0.95. We chose to apply a linear relationship between @d and a because of the general trends in the plots with no clear dependence on any parameter. The plots of @d vs a for each of the nine trials are shown in Figure 2. The final values of @d a t high dilution and their respective standard deviations are given in Table I. In all but one case, the value of ad increases with a,approximately doubling over the range from a = 0.30 to 0.95. The average of ad for all experiments results in a value of 0.040 f 0.01 1. The deviant value of 0.014 from trial 7 can be eliminated from the final results by a Q test a t the 95% confidence level, thereby increasing the average @d to 0.043 f 0.006 (l/uz-weighted average 0.042 f 0.002). Discussion A. Fluorescence Quantum Yield and Excited-State Lifetime.
We can obtain some useful information on the radiative and nonradiative decay rates of SBby considering the upper bound on the fluorescence quantum yield determined in this work and aspects of the lowest energy electronic absorption band studied by previous workers. In methanol solutions, the lowest energy electronic absorption band4 of S8has a maximum a t 263 nm (6263 = 6730 M-’ cm-I) and a shoulder at 276 nm ( 9 7 6 = 6415 M-’ cm-I). The slight dip in the absorption spectrum at 250 nm (czso estimated to be 6000 M-’ cm-I from figure 2 of ref 4) probably separates the lowest electronic transition from the next strong absorption band at 220 nm (eao 12000 M-I an-’).While this absorption band appears to be a separate electronic transition from the band at 263 nm, it is not known how many electronic transitions, weak or otherwise, are embedded in the UV spectrum. Calculati~ns’~J~ predict that (17) Chen, 1. Phys. Reo. B 1970, 2, 1053.
r-----,
I
1
1
1
I
I
,
1
40
50
60
70
80
90
I
0.05
30
a
11 0
Figure 2. Plots of ad vs a for each of the nine trials, including the least-squares line and extrapolation of a d to a = 0.95. See text for the description of a. (top) Trials 1-4 constants: 10 Hz,3.9 X 10” M. (1, a) 1.978 mJ/pulse: (2, A) 1.542 mJ/pulse; (3, 0) 1.101 mJ/pulse; (4, 0) 0.529 mJ/pulse. (middle) Trials 5-6 constants: 1.0 mJ/pulse, 3.3 X 10” M. ( 5 , O ) 10 Hz;(6, M) 14 Hz. (bottom) Trials 7-9 constants: 1.0 mJ/pulse, 10 Hz. (7, a) 7.3 X 10” M; (8, 0) 3.3 X 10” M; (9, A) 1.1 X
M.
-
the lowest electronic transition is ‘El ‘Al. This transition would then be allowed by symmetry ( x and y polarized); the strength of the absorption seems to validate this assignment. The addition of 0-cyclodextrin had no observable effect on the positions and intensities of the Sa absorption bands, exclusive of dilution. If this lowest band corresponds to a single electronic transition, and if the intensity of this band is intrinsic as opposed to vibronically induced, a measure of the radiative lifetime of the upper state may be obtained from the integrated absorption spectrum using the Strickler-Berg re1ati0n.l~ Carrying out this procedure yielded a radiative lifetime, T ~ of, -6 ns. The excited state lifetime, 7 , is related to T~ by 7
= soar
(8)
Applying these equations gave a minimum value for 7 of 0.6 fs. This corresponds to a homogeneous line width (full width a t half-maximum) of 8300 cm-’ in the UV absorption spectrum due to lifetime broadening. This is more than 5 times the widths of two distinct features in the long-wavelength absorption band observed3 at 77 K, whose estimated half-widths at half-maximum put a lower bound of 1-4 fs on the excited-state lifetime. The implication is that, for one or both of the abovementioned reasons, the Strickler-Berg relation does not hold for Sa. Multiple allowed electronic transitions in this region have been predicted,20 and vibronic coupling might be expected in this system because of the known sensitivity of S-Sbond properties to electronic factors.z1 Although we cannot specify the excited-state lifetime exactly, given the available information, the low value of the fluorescence quantum yield indicates it must be very short, too short for quenching by oxygen, which we did not purge from the samples. Assuming the methanol solutions were saturatedZZin oxygen a t 0.21 atm partial pressure, and using quenching rate constants appropriate to comparably sized aromatic molecules,z3we cal(18) Meycr, B.; Spitzer, K. J. Phys. Chem. 1972, 76, 2274. (19) Strickler, S. J.; Berg, R. A. J . Chem. Phys. 1962, 37, 814. (20) Richardson, N. V.; Weinberger, P. J. Electron Spectrosc. Relat. Phenom. 1975,6, 109. (21) Steudel, R. Angew. Chem., Int. Ed. Engl. 1975, 14, 655. (22) Rollie, M. E.; Patonay, G.; Warner, I. M. I d . Eng. Chem. Res. 1987, 26, 1.
4378 The Journal of Physical Chemistry, Vol. 95, No. 1I, I991
culated a maximum quenching rate of less than lo8 s-I. B. Photochemical Decomposition of s8 in Methanol. The bond scission energy for s8 has been reported" to be 148 kJ/mol. The energy of the photons used in this experiment is 37 580 cm-', or 450 kJ/mol. No evidence for multiphoton processes has been found in this or any of the previous studies"-I3 of the photodecomposition of Sa,performed with either lamp or laser illumination. The average of the eight values of ad obtained from the various experiments, 0.042, when inserted into eq 7, can be used to value is obtained by generate T vs t curves. Because this extrapolation to long times, such theoretical curves will agree with experiment only at long times. The experimental transmittance values in every trial deviate from the curves predicted by our model in a systematic way: they fall below the curves at all times, except at long times. The bold continuous curve in Figure 1 shows the predicted transmittance values for trial 1; the deviations between this curve and the experimental data are representative of all trials. The deviations are due to transient photoproducts with nonzero absorbance at 266 nm. In an attempt to further justify the extrapolation method used,we present below a model which accounts for transient absorption in an approximate way. Equations 3-7 are based on the assumption that all photoproducts are transparent. In an improved model, C and Tin that derivation should be altered to C, and T,, where the subscripts refer to the species s8 only. If we collectively include all photoproducts as one additional species, a, then the total transmittance, T, is the product of T, and T,. The problem now reduces to solving for a time-dependent expression for T,(t). There are boundary conditions for Ta(t); T,(t) must be unity at t = 0 and t = m. The expression for T,(t) must permit growth of species a as well as its eventual decay. Equation 9 describes the time dependence of the concentration of a, C,(t), by the recursion formula
C,(t,) = Ca(t,-l)e-(AJ/r*) + AC,(At)
(9)
where T, is the mean lifetime of the photoproducts, At is the time between consecutive measurements, and AC,(At) is the difference between the previous and present measurements of C,. The first term includes the previously produced photoproduct, reduced by the exponential factor, which guarantees the decay of the photochemically formed absorbers in a finite time. The second term accounts for the most recently formed photoproducts. Since the measurements were recorded every 10 or 60 s for each trial, At is a constant for each experiment. At any time t , T, is determined from eq 7 and Ta is determined from eq 9 and Beer's Law. Thus T i s dependent on T, and e,, respectively. We have attempted to calculate T vs t curves which give improved agreement with experiment by varying T, and c, within reasonable limits. A reasonable range for e, would be lo3-lo4 M-'cm-I, corresponding to the absorption strength at 266 nm for other S, species. In this approximation, we assume constancy of ca for all trials. The lifetime of the photoproducts, T,, may vary, however, depending on whether they are depleted by photon-dependent or -independent processes. An approximate determination of ea and T, was performed by trial-and-error adjustment of each variable. The predicted T vs t curves were sufficiently sensitive to ea and T, (ad was fixed at 0.042) so that the best value of each could be readily determined to within *SO0 M-' cm-l and A25 s, respectively. (23) Ware, W. R. J . Chem. Phys. 1962, 66, 455.
Bevilacqua and Kenny The improvement in the fit between the observed data and the adjusted model (thin, solid curve) is evident in Figure 1 for trial 1, compared to the original model (bold, solid curve). The same improvement is achieved for the remaining trials. In all cases, except the anomalous trial 7 results, good agreement was obtained when c, was held a t 5000 M-' cm-I. The optimum value of T, was different for different trials. For example, the solid transmittance curve shown in Figure 1 uses a lifetime of 200 s. For the three lower laser powers (trials 2,3, and 4), the optimum values of T, were approximately 300, 350, and 400 s, respectively. T vs t curves for these trials are also shown in Figure 1. For trials 5 and 6 (10 and 14 Hz), the lifetimes are -240 and 160 s, respectively. Although the laser pulse energies were identical for each experiment, the higher repetition rate resulted in shorter lived photoproducts. These results confirm our hypothesis that the decay of photoproducts includes a photochemical channel. In the fits to the data from trials 7-9, the value of c, had to be increased to 15000 M-I cm-' to achieve agreement at the highest concentration (trial 7), while the original value of 5000 M-' cm-' was still substantially better for the two trials at lower s8 concentrations. The value of T, decreased as the s 8 concentration decreased, from 400 to 300 to 160 s for trials 7, 8, and 9, respectively. These results suggest the interdependence of the chemical and photochemical reactions, elucidation of which will require more detailed experiments and models. The transparency of the photoproducts a t long times can be rationalized by appealing to the available literature. In Strauss and Steudel's photoly~is,'~ broad-band irradiation of Sa in CS2 produced substantial amounts only of S7and S6,both of which have appreciable absorbance a t 266 nm. However, it has been reported4 that, in methanol, S7decomposes to under irradiation, and s 6 decomposes to s7and s8 even without irradiation. so s6 and S7are not expected to persist under our experimental conditions, although they are likely culprits for the deviant behavior discussed above. In the dark decay experiments, the slightly decreased transparency may be attributed to the spontaneous conversion of S6to s8: the value of e for s8 at 266 nm is nearly 4 times larger4 than e for s6. Elbanowski" has demonstrated the presence of (CH3)2Sas a substantial photoproduct with 254-nm irradiation of Sa in methanol. With the 266-nm radiation, we noticed the distinct, unpleasant odor of H2S only after irradiation, and we expect the presence of (CH&S and CH3SH as well. Each of these species has very weak or no absorbance a t 266 nm. Elbanowski" reports a quantum yield of disappearance of SB with 254-nm irradiation. However, there is an inconsistency in the paper between the reported value for @d, 0.39 f 0.04, and the data provided, which seem to indicate a quantum yield approximately 100 times smaller. We do not know which reported values are in error. C, Excited-State Dynamics. An excited-state lifetime of several femtoseconds would be consistent with direct dissociation upon absorption and with all available data. However, efficient recombination would then have to be postulated to explain the small quantum yield for disapparence of s8. Alternatively, absorption could take place to a predissociative state with one or several other radiationless decay channels besides ring opening. The lack of significant emission exacerbates the experimental difficulties of fast-time experiments. However, further exploration of the cyclodextrin inclusion complexes, which should promote recombination in the former case, may provide useful information.
