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Detection of triplet—triplet absorption in microcrystalline benzophenone by diffuse-reflectance laser flash photolysis
Volume 104, number 2,3
CHEMICAL PHYSICS LETTERS
3 February 1984
DETECTION OF T R I P L E T - T R I P L E T ABSORPTION IN MICROCRYSTALLINE BENZOPHENONE BY DIFFUSE-REFLECTANCE LASER FLASH PHOTOLYSIS F. WILKINSON and C.J. WILLSHER Department of Chemistry, University of Technology, Loughborough, Leicestershire LE11 3TU, UK Received 15 November 1983; in final form 29 November 1983
An apparatus is described which can detect transient absorptions in the nanosecond-microsecond time domain in opaque scattering materials by analysing diffusely reflected monitoring light following nanosecond laser excitation. For microcrystalline benzophenone excited by a 20 ns pulse at 354 nm, a transient absorption is easily recorded, having a maximum at 540 nm. Its decay is a mixture of first- and second-order processes, with the initial and final slopes of the first-order kinetic analysis differing by a factor of 10. The second-order rate constant is estimated to be (8.5 +- 1.0) × 109 cm3 moV1 sq . Microcrystalline benzophenone emits a phosphorescence which, within experimental error, has an identical kinetic decay.
1. Introduction There is currently a good deal of interest in the photochemical and photophysical properties of materials in solid form. This research is aimed at unravelling the processes which occur at catalytic surfaces [ 1 ], at studying the fate of excited states of materials which show promise in solar energy conversion [2], and at probing the mechanism of energy dissipation in crystals [3]. The principal monitoring tool in surface photochemistry and in energy-dissipation studies is luminescence, which permits a thorough examination of excitedstate behaviour provided the sample in question does emit light. We have already demonstrated the existence of transient absorptions in zinc oxide and Cr-doped LaA10 3 [4], and in a number of organic compounds adsorbed on 7-alumina [5]. Beck and Thomas [6] have recently reported the detection of a triplet-triplet absorption of pyrene adsorbed on alumina. We are currently developing the technique of diffuse-reflectance laser flash photolysis in this laboratory, and expect it to extend the scope of photochemistry by allowing direct measurement of transient absorptions following laser excitation in opaque, light-scattering materials either in bulk form or adsorbed on some suitable substrate. We now report on the first known studies o f a transient absorption in opaque, microcrystalline benzo272
phenone by the diffuse-reflectance technique, and give details of the apparatus used to capture transient events in the nanosecond-microsecond time domain.
2. Experimental Fig. 1 is a diagram of the apparatus. The exciting light is the tripled output of a pulsed n e o d y m i u m YAG laser (J.K. Lasers Ltd.), giving a pulse of 40 mJ for 20 ns at 354 nm. The monitoring light is a pulsed 250 W xenon arc lamp (Applied Photophysics Ltd.) with a pulse width o f 0.5 ms. The detector is an R928 photomultiplier (rise time 2 ns) (Hanamatsu Ltd.) and signals are then digitized/displayed by a Tektronix 7912 AD programmable digitizer. Prior to detection, the light passes through a monochromator (Applied Photophysics Ltd.,f/3.4, grating). A Minc PDP 11/03 minicomputer (Digital Equipment Corporation Ltd.) is in overall control of the operation of the system; it fires the laser, pulses the arc lamp, operates shutters, drives the monochromator grating, sets the digitizer and reads digitized data. The digitizer is synchronously triggered from the power unit of the Pockels cell which Q-switches the laser. The sample of benzophenone is contained in a powder holder behind a fused silica window, the ma-
0 009-2614/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 104, number 2,3
CHEMICAL PHYSICS LETTERS
while the specular reflection is not. Diffusely reflected exciting light is filtered out by a solution of biphenylene in benzene at the monochromator entrance. The best arrangement is as follows: the sample is placed at 45 ° to the exciting beam and finely adjusted so that the laser specular reflection just misses the monochromator entrance. The arc lamp is then positioned normal to the sample face, and a lens placed between the sample and the monochromator to give optimum signal of diffusely reflected light from the pulsed arc lamp. Other geometries are possible, such as excitation normal to the sample and analysis at 45 °, but no improvement is obtained. Ground-state spectra were obtained with the diffuse-reflectance attachment of a P y e - U n i c a m SP 8250 spectrometer, and emission spectra were measured with a Perkin-Elmer 3000 fluorescence spectrometer. Analysis of decays is performed by the minicomputer. The analysing light before and after lasing constitutes an excelleng blank, and the difference z2ur between each point of the decay and the mean pretrigger value is then obtained. ~ r is taken to be directly proportional to the concentration of transient species produced (see section 4). For a first-order kinetic analysis, loge(Zk/) is plotted against time, followed by least-squares fitting to obtain the slope. For secondorder analysis, ( 1 / ~ / ) against time is plotted and then fitted.
YAGLaser
pulsing unit
Monochromator T Photomultiplier
Fig. 1. Schematic diagram of the apparatus. terial having been recrystallised several times from ethanol. Microscopic examination of the sample revealed a range of particle sizes, from less than 5/am in diameter to more than 30/am. For experiments with O2-free benzophenone, the sample was held in an evacuated quartz cuvette which had been left under vacuum for several days. The geometry of sample, exciting and analysing beams and monochromator enthrance is such that the areas which receive exciting and monitoring light are overlapping, but with a larger excitation area than analysing area. The maximum diffusely reflected monitoring light is then collected,
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Fig. 2. Transient absorption of benzophenone (excited at 354 nm (20 ns pulse) and monitored at 535 nm) as a function of time. (a) First-order analysis; (b) second-order analysis. 273
Volume 104, number 2,3
CHEMICAL PHYSICS LETTERS
3. Results
The ground-state diffuse-reflectance spectrum of microcrystaUine benzophenone shows an absorption edge spanning the 3 7 0 - 4 3 0 nm region. Little change is seen in this spectrum after lasing the sample, indicating no detectable damage has occurred. Fig. 2 shows the transient absorption as a function of time, monitored at 540 nm. Upon pulsed excitation at 354 nm, the diffusely reflected monitoring light signal is decreased by ~45% and then returns to the original reflection (i.e. 0% transient signal) after ~50 #s. These events are plotted in fig. 2 as percentage of monitoring light absorbed by the sample against time. Inspection of the insets of fig. 2 suggests the decay follows a predominantly second-order pathway. The first 30 s of the second-order kinetic analysis has a slope of (0.29 -+ 0.06) X 106 s -1 . The initial slope of the first-order kinetic analysis is (0.17 -+ 0.04) × 106 s -1 , and the final slope is (0.14 + 0.009) X 105 s-1 . Fig. 3 shows emission decay after excitation at 354 nm by the pulsed laser, monitored at 460 nm, and the insets show firstand second-order kinetic analyses. The behaviour is identical to that of the transient absorption within experimental error. A slope of (0.24 + 0.01) X 106 s-1 over the first 30bts of the decay is obtained for the
3 February 1984
second-order kinetic analysis. The initial slope of the first-order plot is (0.15 -+ 0.002) X 106 s-1, and the final slope is (0.14 -+ 0.009) X 105 s-1 . No significant differences in the decay of the emission or the transient absorption were noted if oxygen was excluded from the sample. Fig. 4 shows excited-state absorption spectra immediately after the laser flash and at various times during the decay.
4. Discussion To our knowledge, this is the first report of a transient absorption in microcrystalline, opaque benzophenone, which has been achieved using the technique of diffuse-reflectance laser flash photolysis. The close similarity between the decay of this absorption and that of the emission leads us to infer that a triplettriplet absorption is being observed. Furthermore, we observe that the emission spectra obtained by both laser excitation and from the Perkin-Elmer spectrometer (where the phosphorescence spectrum is recorded at much lower excitation intensities) are almost identical in shape. This suggests that no delayed fluorescence is induced by laser excitation. The similarly between the shapes of excited-state absorption spectra during
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Fig. 3. Emission of benzophenone (excited at 354 nm (20 ns pulse) and monitored at 460 nm) as a function of time. (a) First-order analysis; (b) second-order analysis.
274
Volume 104, number 2,3
CHEMICAL PHYSICS LETTERS
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Wavelength (nm) Fig. 4. Transient absorption of benzophenone (excited at 354 nm (20 ns pulse)) as a function of monitoring wavelength. (a) At maximum absorption; (b) I #s after maximum; (c) 4 #s after maximum.
the decay of the transient absorption (fig. 4) is additional proof of the existence on only one decaying species. An absorption, centered at 540 nm, has been reported by Morris and Yoshihara [7] for single-crystal benzophenone, detected by transmission laser flash photolysis. This was assigned as a triplet-triplet absorption and has a similar spectrum to the absorption shown in fig. 4. There also exists a similarity between this spectrum and the triplet-triplet absorption of benzophenone in solution [8]. Morris and Yoshihara [7] report that triplet exciton-exciton annihilation is a predominant process in the decay of both the transient absorption and the phosphorescence of a single crystal of benzophenone, and also note the evidence of non-exponential decays. By making certain assumptions, these authors give a triplet-triplet exciton annihilation rate constant of 1 X 10 -18 m 3 s -1 at 295 K (i.e. 6 X 101] cm 3 tool -1 s-l). In order to quote a second-order rate constant from the slopes of the second-order kinetic analyses of the decays of the transient absorption and emission, we need a value of the initial concentration of excited states. Certain assumptions have to be made in order to arrive at this value: (i) the density of benzophenone is 1.1 g c m -3 [9], thus giving a concentration of 6 mol
dm -3 in the sample, and that no " e m p t y spaces" exist between crystals, (ii) the depth of penetration of exciting light can be calculated from the B e e r - L a m b e r t law using an extinction coefficient of 110 £ mo1-1 cm -1 at 354 nm for a solution of benzophenone in benzene, and (iii) the triplet quantum yield is 0.05. We arrive at the last assumption by the following reasoning. Preliminary experiments to study the effect of laser intensity on the transient absorption and emission reveal a nonlinear relationship between laser intensity and the size of these signals, with near-saturation occurring for exciting energies in excess of 10 m J/pulse. For energies below 5 mJ/pulse, a linear relationship can be seen, and in this area we take the triplet quantum yield to be unity. Extrapolation of the linear portion furnishes a value of 0.05 for the 40 mJ pulse used in our experiments. (The lowering of the quantum yield at higher energies may be due to singlet-singlet interactions, producing both the ground state and the triplet when the singlet concentration is high. We will present these details in a future publication.) Based on these assumptions, we obtain a value for the second-order rate constant for the transient absorption decay of (8.5 -+ 1.0) × 109 cm 3 mo1-1 s -1 and (7.2 + 0.5) X 109 cm 3 real -1 s-1 for the emission decay. Our estimate for 275
Volume 104, number 2,3
CHEMICAL PHYSICS LETTERS
these constants has a considerable absolute uncertainty. At present we do not know the scattering coefficient at 354 nm of these microcrystals and we do not have a standard against which we can check our estimate for the quantum yield o f triplet production. The secondorder rate constant quoted by Morris and Yoshihara is larger than ours by a factor of ~80. In considering this difference it should be borne in mind that these authors have made assumptions in estimating the initial excited-state concentration within the single crystal, and they estimate that their constant has an absolute error of +50%. Another publication reports that a significant second-order contribution to the phosphorescence decay of a benzophenone crystal at 77 K is known to exist, and an equation which accounts for both first- and second-order processes can be made to fit that decay [10]. This combination of first and second effects is certainly exhibited by the decays we report here. In section 3 we cited that A / w a s taken to be directly proportional to the concentration of excited states. We have reported previously that if the change in transient reflectance following pulsed excitation is less than 10%, then this change is likely to be a linear function o f transient concentration [11 ]. This conclusion was based on a correlation between the emission decay and that of the transient absorption for weakly absorbing materials. Therefore, we might expect a deviation from this linearity for benzophenone, since an initial 45% change in reflectance is observed. Our justification in using A / i s that, firstly, the majority of the decay seen in fig. 3 has an absorption of less than I0%, with only the initial 10/as exceeding this figure and, secondly, a very good correlation between the analysis of the tran-
276
3 February 1984
sient absorption decay and that of the emission decay is obtained when using A / i n both cases throughout the entire decay. (Emission intensity is a linear function of excited-state concentration.)
Acknowledgement We thank the SERC for funding this project and for a Fellowship to CJW.
References [ 1] W.R. Ware and K.C. Wu, J. Am. Chem. Soc. 104 (1982) 4635. [2] T. Kajiwara, K. Hashimoto, T. Kawai and T. Sakata, J. Phys. Chem. 86 (1982) 4516. [3] R. Kopelman, in: Spectroscopy and excitation dynamics of condensed molecular systems, eds. V.M. Agranovich and R.M. Hochstrasser (North-Holland, Amsterdam, 1983) ch. 4, p. 139. [4] R.W. Kessler, D. Oelkrug and F. Wilkinson, Appl. Spectry. 36 (1982) 673. [5] R.W. Kessler and F. Wilkinson, J. Chem. Soc. Faraday Trans. I 77 (1981) 309. [6] G. Beck and J.K. Thomas, Chem. Phys. Letters 94 (1983) 553. [7] J.M. Morris and K. Yoshihara, Mol. Phys. 36 (1978) 993. [8] H. Tsubomura, N. Yamamoto and S. Tanaka, Chem. Phys. Letters 1 (1967) 309. [9] R.C. Weast, ed., CRC handbook of chemistry and physics (CRC Press, Cleveland 1979-80) p.C-200. [ 10] R.A. Keller, J. Chem. Phys. 42 (1965) 4050. [ 11] R.W. Kessler, G. Krabichler, S. Uhl, D. Oelkrug, W.P. Hagan, J. Hyslop and F. Wilkinson, Opt. Acta 30 (1983) 1099.
CHEMICAL PHYSICS LETTERS
3 February 1984
DETECTION OF T R I P L E T - T R I P L E T ABSORPTION IN MICROCRYSTALLINE BENZOPHENONE BY DIFFUSE-REFLECTANCE LASER FLASH PHOTOLYSIS F. WILKINSON and C.J. WILLSHER Department of Chemistry, University of Technology, Loughborough, Leicestershire LE11 3TU, UK Received 15 November 1983; in final form 29 November 1983
An apparatus is described which can detect transient absorptions in the nanosecond-microsecond time domain in opaque scattering materials by analysing diffusely reflected monitoring light following nanosecond laser excitation. For microcrystalline benzophenone excited by a 20 ns pulse at 354 nm, a transient absorption is easily recorded, having a maximum at 540 nm. Its decay is a mixture of first- and second-order processes, with the initial and final slopes of the first-order kinetic analysis differing by a factor of 10. The second-order rate constant is estimated to be (8.5 +- 1.0) × 109 cm3 moV1 sq . Microcrystalline benzophenone emits a phosphorescence which, within experimental error, has an identical kinetic decay.
1. Introduction There is currently a good deal of interest in the photochemical and photophysical properties of materials in solid form. This research is aimed at unravelling the processes which occur at catalytic surfaces [ 1 ], at studying the fate of excited states of materials which show promise in solar energy conversion [2], and at probing the mechanism of energy dissipation in crystals [3]. The principal monitoring tool in surface photochemistry and in energy-dissipation studies is luminescence, which permits a thorough examination of excitedstate behaviour provided the sample in question does emit light. We have already demonstrated the existence of transient absorptions in zinc oxide and Cr-doped LaA10 3 [4], and in a number of organic compounds adsorbed on 7-alumina [5]. Beck and Thomas [6] have recently reported the detection of a triplet-triplet absorption of pyrene adsorbed on alumina. We are currently developing the technique of diffuse-reflectance laser flash photolysis in this laboratory, and expect it to extend the scope of photochemistry by allowing direct measurement of transient absorptions following laser excitation in opaque, light-scattering materials either in bulk form or adsorbed on some suitable substrate. We now report on the first known studies o f a transient absorption in opaque, microcrystalline benzo272
phenone by the diffuse-reflectance technique, and give details of the apparatus used to capture transient events in the nanosecond-microsecond time domain.
2. Experimental Fig. 1 is a diagram of the apparatus. The exciting light is the tripled output of a pulsed n e o d y m i u m YAG laser (J.K. Lasers Ltd.), giving a pulse of 40 mJ for 20 ns at 354 nm. The monitoring light is a pulsed 250 W xenon arc lamp (Applied Photophysics Ltd.) with a pulse width o f 0.5 ms. The detector is an R928 photomultiplier (rise time 2 ns) (Hanamatsu Ltd.) and signals are then digitized/displayed by a Tektronix 7912 AD programmable digitizer. Prior to detection, the light passes through a monochromator (Applied Photophysics Ltd.,f/3.4, grating). A Minc PDP 11/03 minicomputer (Digital Equipment Corporation Ltd.) is in overall control of the operation of the system; it fires the laser, pulses the arc lamp, operates shutters, drives the monochromator grating, sets the digitizer and reads digitized data. The digitizer is synchronously triggered from the power unit of the Pockels cell which Q-switches the laser. The sample of benzophenone is contained in a powder holder behind a fused silica window, the ma-
0 009-2614/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 104, number 2,3
CHEMICAL PHYSICS LETTERS
while the specular reflection is not. Diffusely reflected exciting light is filtered out by a solution of biphenylene in benzene at the monochromator entrance. The best arrangement is as follows: the sample is placed at 45 ° to the exciting beam and finely adjusted so that the laser specular reflection just misses the monochromator entrance. The arc lamp is then positioned normal to the sample face, and a lens placed between the sample and the monochromator to give optimum signal of diffusely reflected light from the pulsed arc lamp. Other geometries are possible, such as excitation normal to the sample and analysis at 45 °, but no improvement is obtained. Ground-state spectra were obtained with the diffuse-reflectance attachment of a P y e - U n i c a m SP 8250 spectrometer, and emission spectra were measured with a Perkin-Elmer 3000 fluorescence spectrometer. Analysis of decays is performed by the minicomputer. The analysing light before and after lasing constitutes an excelleng blank, and the difference z2ur between each point of the decay and the mean pretrigger value is then obtained. ~ r is taken to be directly proportional to the concentration of transient species produced (see section 4). For a first-order kinetic analysis, loge(Zk/) is plotted against time, followed by least-squares fitting to obtain the slope. For secondorder analysis, ( 1 / ~ / ) against time is plotted and then fitted.
YAGLaser
pulsing unit
Monochromator T Photomultiplier
Fig. 1. Schematic diagram of the apparatus. terial having been recrystallised several times from ethanol. Microscopic examination of the sample revealed a range of particle sizes, from less than 5/am in diameter to more than 30/am. For experiments with O2-free benzophenone, the sample was held in an evacuated quartz cuvette which had been left under vacuum for several days. The geometry of sample, exciting and analysing beams and monochromator enthrance is such that the areas which receive exciting and monitoring light are overlapping, but with a larger excitation area than analysing area. The maximum diffusely reflected monitoring light is then collected,
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Fig. 2. Transient absorption of benzophenone (excited at 354 nm (20 ns pulse) and monitored at 535 nm) as a function of time. (a) First-order analysis; (b) second-order analysis. 273
Volume 104, number 2,3
CHEMICAL PHYSICS LETTERS
3. Results
The ground-state diffuse-reflectance spectrum of microcrystaUine benzophenone shows an absorption edge spanning the 3 7 0 - 4 3 0 nm region. Little change is seen in this spectrum after lasing the sample, indicating no detectable damage has occurred. Fig. 2 shows the transient absorption as a function of time, monitored at 540 nm. Upon pulsed excitation at 354 nm, the diffusely reflected monitoring light signal is decreased by ~45% and then returns to the original reflection (i.e. 0% transient signal) after ~50 #s. These events are plotted in fig. 2 as percentage of monitoring light absorbed by the sample against time. Inspection of the insets of fig. 2 suggests the decay follows a predominantly second-order pathway. The first 30 s of the second-order kinetic analysis has a slope of (0.29 -+ 0.06) X 106 s -1 . The initial slope of the first-order kinetic analysis is (0.17 -+ 0.04) × 106 s -1 , and the final slope is (0.14 + 0.009) X 105 s-1 . Fig. 3 shows emission decay after excitation at 354 nm by the pulsed laser, monitored at 460 nm, and the insets show firstand second-order kinetic analyses. The behaviour is identical to that of the transient absorption within experimental error. A slope of (0.24 + 0.01) X 106 s-1 over the first 30bts of the decay is obtained for the
3 February 1984
second-order kinetic analysis. The initial slope of the first-order plot is (0.15 -+ 0.002) X 106 s-1, and the final slope is (0.14 -+ 0.009) X 105 s-1 . No significant differences in the decay of the emission or the transient absorption were noted if oxygen was excluded from the sample. Fig. 4 shows excited-state absorption spectra immediately after the laser flash and at various times during the decay.
4. Discussion To our knowledge, this is the first report of a transient absorption in microcrystalline, opaque benzophenone, which has been achieved using the technique of diffuse-reflectance laser flash photolysis. The close similarity between the decay of this absorption and that of the emission leads us to infer that a triplettriplet absorption is being observed. Furthermore, we observe that the emission spectra obtained by both laser excitation and from the Perkin-Elmer spectrometer (where the phosphorescence spectrum is recorded at much lower excitation intensities) are almost identical in shape. This suggests that no delayed fluorescence is induced by laser excitation. The similarly between the shapes of excited-state absorption spectra during
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Fig. 3. Emission of benzophenone (excited at 354 nm (20 ns pulse) and monitored at 460 nm) as a function of time. (a) First-order analysis; (b) second-order analysis.
274
Volume 104, number 2,3
CHEMICAL PHYSICS LETTERS
o°°
3 February 1984
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Wavelength (nm) Fig. 4. Transient absorption of benzophenone (excited at 354 nm (20 ns pulse)) as a function of monitoring wavelength. (a) At maximum absorption; (b) I #s after maximum; (c) 4 #s after maximum.
the decay of the transient absorption (fig. 4) is additional proof of the existence on only one decaying species. An absorption, centered at 540 nm, has been reported by Morris and Yoshihara [7] for single-crystal benzophenone, detected by transmission laser flash photolysis. This was assigned as a triplet-triplet absorption and has a similar spectrum to the absorption shown in fig. 4. There also exists a similarity between this spectrum and the triplet-triplet absorption of benzophenone in solution [8]. Morris and Yoshihara [7] report that triplet exciton-exciton annihilation is a predominant process in the decay of both the transient absorption and the phosphorescence of a single crystal of benzophenone, and also note the evidence of non-exponential decays. By making certain assumptions, these authors give a triplet-triplet exciton annihilation rate constant of 1 X 10 -18 m 3 s -1 at 295 K (i.e. 6 X 101] cm 3 tool -1 s-l). In order to quote a second-order rate constant from the slopes of the second-order kinetic analyses of the decays of the transient absorption and emission, we need a value of the initial concentration of excited states. Certain assumptions have to be made in order to arrive at this value: (i) the density of benzophenone is 1.1 g c m -3 [9], thus giving a concentration of 6 mol
dm -3 in the sample, and that no " e m p t y spaces" exist between crystals, (ii) the depth of penetration of exciting light can be calculated from the B e e r - L a m b e r t law using an extinction coefficient of 110 £ mo1-1 cm -1 at 354 nm for a solution of benzophenone in benzene, and (iii) the triplet quantum yield is 0.05. We arrive at the last assumption by the following reasoning. Preliminary experiments to study the effect of laser intensity on the transient absorption and emission reveal a nonlinear relationship between laser intensity and the size of these signals, with near-saturation occurring for exciting energies in excess of 10 m J/pulse. For energies below 5 mJ/pulse, a linear relationship can be seen, and in this area we take the triplet quantum yield to be unity. Extrapolation of the linear portion furnishes a value of 0.05 for the 40 mJ pulse used in our experiments. (The lowering of the quantum yield at higher energies may be due to singlet-singlet interactions, producing both the ground state and the triplet when the singlet concentration is high. We will present these details in a future publication.) Based on these assumptions, we obtain a value for the second-order rate constant for the transient absorption decay of (8.5 -+ 1.0) × 109 cm 3 mo1-1 s -1 and (7.2 + 0.5) X 109 cm 3 real -1 s-1 for the emission decay. Our estimate for 275
Volume 104, number 2,3
CHEMICAL PHYSICS LETTERS
these constants has a considerable absolute uncertainty. At present we do not know the scattering coefficient at 354 nm of these microcrystals and we do not have a standard against which we can check our estimate for the quantum yield o f triplet production. The secondorder rate constant quoted by Morris and Yoshihara is larger than ours by a factor of ~80. In considering this difference it should be borne in mind that these authors have made assumptions in estimating the initial excited-state concentration within the single crystal, and they estimate that their constant has an absolute error of +50%. Another publication reports that a significant second-order contribution to the phosphorescence decay of a benzophenone crystal at 77 K is known to exist, and an equation which accounts for both first- and second-order processes can be made to fit that decay [10]. This combination of first and second effects is certainly exhibited by the decays we report here. In section 3 we cited that A / w a s taken to be directly proportional to the concentration of excited states. We have reported previously that if the change in transient reflectance following pulsed excitation is less than 10%, then this change is likely to be a linear function o f transient concentration [11 ]. This conclusion was based on a correlation between the emission decay and that of the transient absorption for weakly absorbing materials. Therefore, we might expect a deviation from this linearity for benzophenone, since an initial 45% change in reflectance is observed. Our justification in using A / i s that, firstly, the majority of the decay seen in fig. 3 has an absorption of less than I0%, with only the initial 10/as exceeding this figure and, secondly, a very good correlation between the analysis of the tran-
276
3 February 1984
sient absorption decay and that of the emission decay is obtained when using A / i n both cases throughout the entire decay. (Emission intensity is a linear function of excited-state concentration.)
Acknowledgement We thank the SERC for funding this project and for a Fellowship to CJW.
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