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Optical study of nanosecond spin—lattice relaxation in the triplet state of benzil near room temperature
Volume
119. number 5
CHEMICAL
OPTICAL STUDY IN THE TRIPLET
Rrceivcd 29 Aprd
OF NANOSECOND STATE OF BENZIL
PHYSICS LJZTTERS
SPIN-LATTICE NFAR ROOM
13 September 1985
RELAXATION TEMPERATURE
1965. rn fma1 form 20 June 1985
Nanosscond spin-ldtlice rclavalion (SLR) times arc measured m chv:rriplel s~rllt:of Ned benul IIL’W room ~cmperawrc The &CCI of the SLR on Ihe phosphorescence EZdewcLed by using a rimc-corrclsred single-phoron-counllng lechniyue from 150 LO X8 K. The rhermal dcacuxalion of zhe rrap is also invesIigated The chnmcxnstic ensrgws dcvan~ 10 the SLR and Lhe dszxwntron or rhe wrap are 1.3 x lo3 and 3 7 x 10’ cm- ‘_ rrrpeci~vely.
1. Introduction During the past two decades much work has been done with regard to the strucLure and dynamics of the lowest triplet state of organic molecules. The technique of optically detected magnetic resonance (ODMR) [l] has been extensively used with great success. Spinlattice relaxation (SLR) times were measured for various molecules at liquid helium temperatures. However, at high temperatures where the SLR time is very short, m~asuremcnt of the SLR time becomes very difficult_ GiIIies et al_ [2] improved the technique of ODMR and reported an observation of SLR times of about 100 ns But, to our knowledge, no measurement has been reported on SLR times less than 100 ns *. Knowledge of SLR at high temperatures is important to elucidate the role of the excited triplet state in chemical reactions.. In this paper we report OR a purely optical measurement of SLR runes less than 100 ns in the triplet state of a neat benzil crystal near room temperature from lS0 to 288 K. The sample was irradiated w1t.h a short optlcal pulse and the SLR tunes were measured frcm the fast change (decay) of the phosphorescence intensity after the excitation pulse. The SLR affects the
* Recently Tak&
[3] observed nanosecond relaxations of optically induced magnetization at room temperature in aromatic hydrocarbons
438
phosphorescence because the intersystem-crossing populating rates and the rates of radiative decay vary greatIy among the Three sublevels of the triplet state_ Fast SLR times can be detected if the followmg conditlons are satisfied: (1) the optlcal excitation pulse is much shorter than the SLR times, (2) intersystem crossing occurs much faster than the SLR and (3) the fast phosphorescence change can be detected. In our experimental conditions (1) and (2) are satisfied, and the shortest SLR time which can be measured is determined by condition (3). As WJII be described below, the existence of strong fluorescence just after the optical excitation pulse inhibited the direct observation of the fast phosphorescence decay. Therefore we performed an experiment at low light intensities using a time-correlated single-photon-counting technique and succeeded in measuring SLR times of the order of 10 11s. The thermal deactivation of the trap was also examined. Benzil molecules undergo large geometrical changes when they are optlcaiIy excited to the trJplet state [4]. Therefore the trap is very deep. Photoexcited benzil molecules can be considered as impunties in a host crystal of unexcited moIecules. The study of emission from a very deep trap is particularly interesting as it provides informatlon about both the SLR and the thermal deactivation of the trap at high temperatures.
0 009-26 14/8S/S 03.30 0 Elsevier Science Publishers ~o~-Ho~~d Physics Publishing Division)
B-V.
Volume 119. number5
CHEMICAL
PHYSICS
2. Experimental The experimental apparatus is shown in fig. 1_ A single crystal of benzil is irradiated with short (0.2 ns width) optical excitation pulses at 430 nm from a dye laser pumped by a rutrogen laser (PRA LN103). The light beam is loosely focused on the sample and the pulses are repeated at 30 Hz. The phosphorescence at 520 nm is detected by a photomultiplier (RlOGUH) after passing through a monochromatorThe direct observation of the fast phosphorescence decay was difficult because of the existence of a strong fluorescence from the smglet state that saturates the photomultiplier. Although the lifetime of the fluorescence is less than 1 ns, its intensity is about lo3 times larger than that of the phosphorescence (with 1 ns resolved detection) at room temperature_ The effect of the saturation persists for more than 50 ns. In order to avoid this experimental d~~culty, we introduced a tme-correlated singe-photon~ounting technique_ We attenuated the excitation pulses such that at most one phosphorescence photon was detected in the time region of the measurement for each laser shot. The delay time between the excitation of the sample (start) and the detection of the phosphorescence photon (stop) was measured by a tune-to-pulse-height converter (TPHC, Ortec 467). The fluorescence photons were also detected just after the excitation pulse, but the stop-mhibit mode of the TPHC was used for preventing the fluorescence photons from being counted. Thus the dead time could be reduced to less than 10 ns. The output of the TPHC was accumulated by a multichannel analyzer (LeGroy NIM model 3001).
LElTERS
13 September
The overall time resolution of the detection system was about 1 I-IS. The lifetime of the phosphorescence, which is much longer than the SLR times, was measured directly on the oscilloscope- When the sample was excited by nitrogen laser pulses (337 nm, 200 kW, 0.2 ns and 30 Hz), we observed a decrease of the lifetime of the phosphorescence probably due to a thermal effect or an interaction among the excited molecules_ The temperature of the sample was changed between 150 and 360 K by a flow of cold nitrogen gas and hot air. A thermocouple attached to the sample was used to measure the temperature of the sampI=. AU data were taken at zero magnetic field.
3. Results and discussion The SLR times among the sublevels in the triplet state are much shorter than the lifetime of the triplet state in our temperature region [21- The depopuiation of the triplet state occurs long after the SLR is completed_ Therefore the phosphorescence decay becomes very simple. Actually we observed decay curves of a biexponential form I(f) = 1:
exp(-kl
Laser 4c DY= Laser
Fig. 1. Block diagram of the experimental
apparatus
t) + 1: exp(-k2t)
,
(1)
with the first term representing the SLR and the second term representing the depopulation of the triplet state (kl Z+kz). Generally the decay due to SLR may be the sum of two or three exponentials, but we observed single-exponential decay curves within experimental errors. The initial intensity I,-, (=I! + 1:) of the phosphorescence can be expressed as fo=K(k;Px
N2
1985
+k;P,,
+k;P,)N,
(2)
P,, and k: (u =x, y, z) are the relative popuIation and radiative decay rates of the sublevel u (P, + Pv + Pz = 1, kg + kJ + k: = l), respectively, ?v’ is the initial population pumped to the triplet state, and K is a constant_ After the SLR is completed, the population of each sublevel is equalized in our high-temperature experiment, and the intensity of the phosphorescence is reduced to be 1, (=I!) = 4 KiV. The reduction factor R = IelI is given by where
R = [3(a$P,
+ k;,P,, + kfP=)]-1
_
(3) 439
Volume
CHEMICAL
119. number S
PHYSICS
According to the data obtained by Chan and Nelson [5], R is expected to be 0.39 at liquid helium temperatures. Fig. 2 shows the change (decay) of the phosphorescence intensrty due to SLR observed from 10 to 100 ns after the excitation pulse at 248,232 and 219
(a)
I
0
20
40
60
a0
loo
WEec)
(hlsd
(b)
I
0
I
0
20
LO
60
80
100
20
40
60
80
loo
(nsed
Fig 2. Change of the phosphorescence intensity after the excitation pulse observed at (a) 248 K, @) 232 K and (c) 219 K. The SLR times obtained are 14 f 2.25 5 f 2.5 and 36.5 f 4 ns for (a), (b) and (c), respectively, and the solid lines show the theoretical curves.
440
LETTERS
13 September
1985
K. Similar curves were obtained between 150 and 288 K. The SLR times are equal to the time constants of these decay curves. The (effective) SLR times obtamed from curves (a), (b) and (c) are 14 -C2, 25.5 22.5 and 36 5 + 4 ns, respectively- As the temperature increases the SLR time decreases to about 5 ns at 288 K, l/200 of the value at 150 K. In the derivation of SLR times at higher temperatures, we used the reduction factor R of O-39, expecting that the rate constants PU and tiU inR (eq. (3)) are not sensitive to the temperature. From the decay curves below about 200 K where the SLR time was longer than 100 ns. we obtamed the value of R nearly equal to O-39- The same value of R was obtained also at higher temperatures, although the accuracy became poorer with increasing temperature. The fact that the observed value of R is nearly equal to 0.39, the value at liquid helium temperatures, suggests that the phosphorescence we observed originates from a single emitting species, i.e. one of the two X traps which Chan and Nelson observed at a liquid helium temperature [5]_ They reported that the ODMR signal from the other emittmg species IS weak and quickly loses intensity upon warming up from the boihng point of helium. This 1s possibly due to a decrease of the SLR time or of the total population of their weak-signal species. If we detect the phosphorescence from both emitting species, the observed reduction factor must be larger than 0.39 because their weak-signal species is expected to have an SLR time shorter than the time resolution of our apparatus at high temperatures and to give an apparent reduction factor of unity. We also observed the effect of a magnetic field on the phosphorescence intensity and ODMR signals at 400 MHz near the levelcrossing point at 77 K. The direction and magnitude of the appIied magnetic field for these observations could be reasonably interpreted by taking their strong-signal species [6]. The temperature dependence of the measured SLR rate constant kI(T) is shown in fig. 3a. The data obtained by Gillies et al. [2] m the lower-temperature region by an ODMR method is also plotted for comparison. The solid line was calculated with the functional form kl(T)
= AT+B
whereA=l.gX
exp(-AEl/kT), 103s-l
K-l,B=9X
(4) 101os-l,
Volume
119. number 5
CHEMICAL
PHYSICS
AE1 = 13 X 103 cm-l and k is the Boltzmann constant. The first and second terms in eq_ (4) are dominant at lower and higher temperatures, respectively_ In the temperature region where the results of Gullies et al. [2] are available, our results are in good agreement with theirs. But our results deviate from the extrapolation of their results at higher temperaturesTo examine the possibility that AE, represents the deactivation energy of the triplet state, we also measured the lifetime of the phosphorescence. Fig. 3b shows the temperature dependence of the depopulation rate constant kz(T) of the triplet state in the temperature range from 170 to 360 K. The lifetime is independent of the temperature up to 200 K and decreases as the temperature is increased. The lifetime is 3.5 ms at 170 K and becomes 5 ps just below the melting point of benzil(363 K)_ The solid line was calculated with the functional form kZ(T) = C + D exp(-AE,/kT) whereC=2_9X
,
~O*S-~,D=~X
(3 1Ol1 s-landAE2
( 5-I)
(s-‘)
lo6 F-----l”’
2
4
6 0 IO'/ T (K-l)
10
12 -
Fig. 3. Temperature dependences of (a) the SLR rate constants (fffled circles) and (b) the depopulation rate constants (triangles). The SLR rate constants obtained by an ODMR method (reF_ [2]) are also platted (open circles). The solid lines were calculated as described III the text.
13 September
LETTERS
1985
= 3.7 X IO3 cm-l. The solid line fits very well to the experimental results. The deactivation energy A&? of the triplet state thus obtained is not equal to AE,. NOW we have two different characteristic energies AE1 and AE2 representing the slopes of curves (a) and (b) in fig. 3, respectively. We suggest that AE2 represents the depth of the trap. The value of AE, may seem too large as the trap depth. but it is probable from the fact that the benzil molecules undergo large geometrical changes when they are excited to the triplet state from the ground state [4]. Also the excitation spectrum measwed at 77 K [7] suggests rhe existence of such a large deacrivation energy. As an attempt to interpret the temperature dependence of the SLR rate given by eq. (4), we consider the Orbach process [S], which gives an SLR rate proportional to [exp(AE/kT)
-
11-1 ,
(6)
where AE is the energy separation between the relaxing levels and a third level. When AE < kT and AE 3 kT, function (6) approximates to (k/AE)T and exp(-AE/kT), respectively. The former and the latter have the same functional forms as rhe first and second terms of eq. (4), respectively_ Therefore, if there are two sets of third levels whose energy separations AEare such that (1) AE < kTand (2) AE = AE, (SkT), the temperature dependence of thz SLR given by eq. (4) can be attributed to the Orbach process. Any energy level above the triplet state may act as the third level in the Orbach process. In organic molecular crystals external-vibration (local phonon) and internal-vibration levels may be the candidates for the third level. Data on infrared absorption [9] and Raman scattering [ 10,l l] show that the energy of the external modes is less than 100 cm-l and that of the internal modes is 100-3300 cm-l in the ground state or benzil. Although the energies of vibrational modes in the triplet state may differ from those in the ground state, we consider that the differences, especially difference with respect to the internal-vibration modes. are not large. Thus the first term of eq. (4) can be explained by the Orbach process due to the local phonon modes [ 121 because the energies of these modes are smaii and most of them satisfy the condition AE
Volume
119, number 5
CHEMICAL
PHYSICS
nal-vibration modes which effect the SLR are localized around A&‘, . Although there are many mtemal-vrbration modes, only some of them effect the SLR. It is expected that a strong spin-orbit coupling is present between nx* and mien*states in the close vicinity of the carbonyl(s) in molecules such as benzil, and mtersystern crossing causes an anisotropy with respect to the orientation of the spin angular momentum that depends on the local symmetry of electron distribution around the carbonyl(s). Therefore the vrbratronal modes to which the carbonyls contnbute may effect the SLR For example, the vibrational energy of C=O stretchmg mode is 1671 cm-l in the ground state 19, IO]. Our experimental results suggest that this mode and some others around 1300 cm-l have dominant contribution to the SLR In conclusion, we have measured nanosecond SLR times m the triplet state of neat benzil near room temperature. The temperature dependences of the SLR rate and of the depopulation rate are obtained. The former can be attributed to the Orbach process involving two types of molecular vibrations and the latter to the deactivation of the trap Characteristic energres for the SLR and the depth of the trap were estimated_
442
Ll3TERS
13 September
1985
Acknowledgement We would like to thank Dr_ S. Yamauchi, Professor N. Hirota, Dr_ Y_ Takagi and Dr. K. Kan-no for many helpful discussions.
References
[ll [21 131 (41
ISI
R H- Clarke, Triplet state ODMR spectrompy wiey, New York, 1982). R. Gfies, W-U. Spendel and A.M. Ponte Goncalves, Chem. Phys Letters 66 (1979) 121. Y. Takagj_ private communicatioh 1-Y. Ghan and B.A Heath, J. Chem. Phys 71 (1979) 1070. 1 Y_ Chan and B-N. Nelson, 3. Chem. Phys 62 (1975)
4080_
VI 1-Y Chan and B A. Heath, Chem. Phys Letters 46
(1977) 164. Bera. R hiukhejee and M. Chowdhury, J. Chem. Phys Sl(l969) 754. 181 R Orbach and HJ. Stapleton, in: Electron paramagnetlc resonance, ed S. Geschwind (Plenum Press, New York, 1972) p_ 158. PI J Mann and H-W. Thompson, Proc. Roy. Sot. 211A (1951) 168. [lOI S A. Sobn and A-K. Ramdas, Phys. Rev. 174 (1968) 1069. t111 D.R Moore, V-l. Tekippe, AK. Ramdas and J.C. Toledano, Phys. Rev B27 (1983) 7676 t121 P.J.F. Verbeek, AI-M. Dicker and J. Schrrudt. Chem. Phys. Letters 56 (1978) 585
[71 SC
119. number 5
CHEMICAL
OPTICAL STUDY IN THE TRIPLET
Rrceivcd 29 Aprd
OF NANOSECOND STATE OF BENZIL
PHYSICS LJZTTERS
SPIN-LATTICE NFAR ROOM
13 September 1985
RELAXATION TEMPERATURE
1965. rn fma1 form 20 June 1985
Nanosscond spin-ldtlice rclavalion (SLR) times arc measured m chv:rriplel s~rllt:of Ned benul IIL’W room ~cmperawrc The &CCI of the SLR on Ihe phosphorescence EZdewcLed by using a rimc-corrclsred single-phoron-counllng lechniyue from 150 LO X8 K. The rhermal dcacuxalion of zhe rrap is also invesIigated The chnmcxnstic ensrgws dcvan~ 10 the SLR and Lhe dszxwntron or rhe wrap are 1.3 x lo3 and 3 7 x 10’ cm- ‘_ rrrpeci~vely.
1. Introduction During the past two decades much work has been done with regard to the strucLure and dynamics of the lowest triplet state of organic molecules. The technique of optically detected magnetic resonance (ODMR) [l] has been extensively used with great success. Spinlattice relaxation (SLR) times were measured for various molecules at liquid helium temperatures. However, at high temperatures where the SLR time is very short, m~asuremcnt of the SLR time becomes very difficult_ GiIIies et al_ [2] improved the technique of ODMR and reported an observation of SLR times of about 100 ns But, to our knowledge, no measurement has been reported on SLR times less than 100 ns *. Knowledge of SLR at high temperatures is important to elucidate the role of the excited triplet state in chemical reactions.. In this paper we report OR a purely optical measurement of SLR runes less than 100 ns in the triplet state of a neat benzil crystal near room temperature from lS0 to 288 K. The sample was irradiated w1t.h a short optlcal pulse and the SLR tunes were measured frcm the fast change (decay) of the phosphorescence intensity after the excitation pulse. The SLR affects the
* Recently Tak&
[3] observed nanosecond relaxations of optically induced magnetization at room temperature in aromatic hydrocarbons
438
phosphorescence because the intersystem-crossing populating rates and the rates of radiative decay vary greatIy among the Three sublevels of the triplet state_ Fast SLR times can be detected if the followmg conditlons are satisfied: (1) the optlcal excitation pulse is much shorter than the SLR times, (2) intersystem crossing occurs much faster than the SLR and (3) the fast phosphorescence change can be detected. In our experimental conditions (1) and (2) are satisfied, and the shortest SLR time which can be measured is determined by condition (3). As WJII be described below, the existence of strong fluorescence just after the optical excitation pulse inhibited the direct observation of the fast phosphorescence decay. Therefore we performed an experiment at low light intensities using a time-correlated single-photon-counting technique and succeeded in measuring SLR times of the order of 10 11s. The thermal deactivation of the trap was also examined. Benzil molecules undergo large geometrical changes when they are optlcaiIy excited to the trJplet state [4]. Therefore the trap is very deep. Photoexcited benzil molecules can be considered as impunties in a host crystal of unexcited moIecules. The study of emission from a very deep trap is particularly interesting as it provides informatlon about both the SLR and the thermal deactivation of the trap at high temperatures.
0 009-26 14/8S/S 03.30 0 Elsevier Science Publishers ~o~-Ho~~d Physics Publishing Division)
B-V.
Volume 119. number5
CHEMICAL
PHYSICS
2. Experimental The experimental apparatus is shown in fig. 1_ A single crystal of benzil is irradiated with short (0.2 ns width) optical excitation pulses at 430 nm from a dye laser pumped by a rutrogen laser (PRA LN103). The light beam is loosely focused on the sample and the pulses are repeated at 30 Hz. The phosphorescence at 520 nm is detected by a photomultiplier (RlOGUH) after passing through a monochromatorThe direct observation of the fast phosphorescence decay was difficult because of the existence of a strong fluorescence from the smglet state that saturates the photomultiplier. Although the lifetime of the fluorescence is less than 1 ns, its intensity is about lo3 times larger than that of the phosphorescence (with 1 ns resolved detection) at room temperature_ The effect of the saturation persists for more than 50 ns. In order to avoid this experimental d~~culty, we introduced a tme-correlated singe-photon~ounting technique_ We attenuated the excitation pulses such that at most one phosphorescence photon was detected in the time region of the measurement for each laser shot. The delay time between the excitation of the sample (start) and the detection of the phosphorescence photon (stop) was measured by a tune-to-pulse-height converter (TPHC, Ortec 467). The fluorescence photons were also detected just after the excitation pulse, but the stop-mhibit mode of the TPHC was used for preventing the fluorescence photons from being counted. Thus the dead time could be reduced to less than 10 ns. The output of the TPHC was accumulated by a multichannel analyzer (LeGroy NIM model 3001).
LElTERS
13 September
The overall time resolution of the detection system was about 1 I-IS. The lifetime of the phosphorescence, which is much longer than the SLR times, was measured directly on the oscilloscope- When the sample was excited by nitrogen laser pulses (337 nm, 200 kW, 0.2 ns and 30 Hz), we observed a decrease of the lifetime of the phosphorescence probably due to a thermal effect or an interaction among the excited molecules_ The temperature of the sample was changed between 150 and 360 K by a flow of cold nitrogen gas and hot air. A thermocouple attached to the sample was used to measure the temperature of the sampI=. AU data were taken at zero magnetic field.
3. Results and discussion The SLR times among the sublevels in the triplet state are much shorter than the lifetime of the triplet state in our temperature region [21- The depopuiation of the triplet state occurs long after the SLR is completed_ Therefore the phosphorescence decay becomes very simple. Actually we observed decay curves of a biexponential form I(f) = 1:
exp(-kl
Laser 4c DY= Laser
Fig. 1. Block diagram of the experimental
apparatus
t) + 1: exp(-k2t)
,
(1)
with the first term representing the SLR and the second term representing the depopulation of the triplet state (kl Z+kz). Generally the decay due to SLR may be the sum of two or three exponentials, but we observed single-exponential decay curves within experimental errors. The initial intensity I,-, (=I! + 1:) of the phosphorescence can be expressed as fo=K(k;Px
N2
1985
+k;P,,
+k;P,)N,
(2)
P,, and k: (u =x, y, z) are the relative popuIation and radiative decay rates of the sublevel u (P, + Pv + Pz = 1, kg + kJ + k: = l), respectively, ?v’ is the initial population pumped to the triplet state, and K is a constant_ After the SLR is completed, the population of each sublevel is equalized in our high-temperature experiment, and the intensity of the phosphorescence is reduced to be 1, (=I!) = 4 KiV. The reduction factor R = IelI is given by where
R = [3(a$P,
+ k;,P,, + kfP=)]-1
_
(3) 439
Volume
CHEMICAL
119. number S
PHYSICS
According to the data obtained by Chan and Nelson [5], R is expected to be 0.39 at liquid helium temperatures. Fig. 2 shows the change (decay) of the phosphorescence intensrty due to SLR observed from 10 to 100 ns after the excitation pulse at 248,232 and 219
(a)
I
0
20
40
60
a0
loo
WEec)
(hlsd
(b)
I
0
I
0
20
LO
60
80
100
20
40
60
80
loo
(nsed
Fig 2. Change of the phosphorescence intensity after the excitation pulse observed at (a) 248 K, @) 232 K and (c) 219 K. The SLR times obtained are 14 f 2.25 5 f 2.5 and 36.5 f 4 ns for (a), (b) and (c), respectively, and the solid lines show the theoretical curves.
440
LETTERS
13 September
1985
K. Similar curves were obtained between 150 and 288 K. The SLR times are equal to the time constants of these decay curves. The (effective) SLR times obtamed from curves (a), (b) and (c) are 14 -C2, 25.5 22.5 and 36 5 + 4 ns, respectively- As the temperature increases the SLR time decreases to about 5 ns at 288 K, l/200 of the value at 150 K. In the derivation of SLR times at higher temperatures, we used the reduction factor R of O-39, expecting that the rate constants PU and tiU inR (eq. (3)) are not sensitive to the temperature. From the decay curves below about 200 K where the SLR time was longer than 100 ns. we obtamed the value of R nearly equal to O-39- The same value of R was obtained also at higher temperatures, although the accuracy became poorer with increasing temperature. The fact that the observed value of R is nearly equal to 0.39, the value at liquid helium temperatures, suggests that the phosphorescence we observed originates from a single emitting species, i.e. one of the two X traps which Chan and Nelson observed at a liquid helium temperature [5]_ They reported that the ODMR signal from the other emittmg species IS weak and quickly loses intensity upon warming up from the boihng point of helium. This 1s possibly due to a decrease of the SLR time or of the total population of their weak-signal species. If we detect the phosphorescence from both emitting species, the observed reduction factor must be larger than 0.39 because their weak-signal species is expected to have an SLR time shorter than the time resolution of our apparatus at high temperatures and to give an apparent reduction factor of unity. We also observed the effect of a magnetic field on the phosphorescence intensity and ODMR signals at 400 MHz near the levelcrossing point at 77 K. The direction and magnitude of the appIied magnetic field for these observations could be reasonably interpreted by taking their strong-signal species [6]. The temperature dependence of the measured SLR rate constant kI(T) is shown in fig. 3a. The data obtained by Gillies et al. [2] m the lower-temperature region by an ODMR method is also plotted for comparison. The solid line was calculated with the functional form kl(T)
= AT+B
whereA=l.gX
exp(-AEl/kT), 103s-l
K-l,B=9X
(4) 101os-l,
Volume
119. number 5
CHEMICAL
PHYSICS
AE1 = 13 X 103 cm-l and k is the Boltzmann constant. The first and second terms in eq_ (4) are dominant at lower and higher temperatures, respectively_ In the temperature region where the results of Gullies et al. [2] are available, our results are in good agreement with theirs. But our results deviate from the extrapolation of their results at higher temperaturesTo examine the possibility that AE, represents the deactivation energy of the triplet state, we also measured the lifetime of the phosphorescence. Fig. 3b shows the temperature dependence of the depopulation rate constant kz(T) of the triplet state in the temperature range from 170 to 360 K. The lifetime is independent of the temperature up to 200 K and decreases as the temperature is increased. The lifetime is 3.5 ms at 170 K and becomes 5 ps just below the melting point of benzil(363 K)_ The solid line was calculated with the functional form kZ(T) = C + D exp(-AE,/kT) whereC=2_9X
,
~O*S-~,D=~X
(3 1Ol1 s-landAE2
( 5-I)
(s-‘)
lo6 F-----l”’
2
4
6 0 IO'/ T (K-l)
10
12 -
Fig. 3. Temperature dependences of (a) the SLR rate constants (fffled circles) and (b) the depopulation rate constants (triangles). The SLR rate constants obtained by an ODMR method (reF_ [2]) are also platted (open circles). The solid lines were calculated as described III the text.
13 September
LETTERS
1985
= 3.7 X IO3 cm-l. The solid line fits very well to the experimental results. The deactivation energy A&? of the triplet state thus obtained is not equal to AE,. NOW we have two different characteristic energies AE1 and AE2 representing the slopes of curves (a) and (b) in fig. 3, respectively. We suggest that AE2 represents the depth of the trap. The value of AE, may seem too large as the trap depth. but it is probable from the fact that the benzil molecules undergo large geometrical changes when they are excited to the triplet state from the ground state [4]. Also the excitation spectrum measwed at 77 K [7] suggests rhe existence of such a large deacrivation energy. As an attempt to interpret the temperature dependence of the SLR rate given by eq. (4), we consider the Orbach process [S], which gives an SLR rate proportional to [exp(AE/kT)
-
11-1 ,
(6)
where AE is the energy separation between the relaxing levels and a third level. When AE < kT and AE 3 kT, function (6) approximates to (k/AE)T and exp(-AE/kT), respectively. The former and the latter have the same functional forms as rhe first and second terms of eq. (4), respectively_ Therefore, if there are two sets of third levels whose energy separations AEare such that (1) AE < kTand (2) AE = AE, (SkT), the temperature dependence of thz SLR given by eq. (4) can be attributed to the Orbach process. Any energy level above the triplet state may act as the third level in the Orbach process. In organic molecular crystals external-vibration (local phonon) and internal-vibration levels may be the candidates for the third level. Data on infrared absorption [9] and Raman scattering [ 10,l l] show that the energy of the external modes is less than 100 cm-l and that of the internal modes is 100-3300 cm-l in the ground state or benzil. Although the energies of vibrational modes in the triplet state may differ from those in the ground state, we consider that the differences, especially difference with respect to the internal-vibration modes. are not large. Thus the first term of eq. (4) can be explained by the Orbach process due to the local phonon modes [ 121 because the energies of these modes are smaii and most of them satisfy the condition AE
Volume
119, number 5
CHEMICAL
PHYSICS
nal-vibration modes which effect the SLR are localized around A&‘, . Although there are many mtemal-vrbration modes, only some of them effect the SLR. It is expected that a strong spin-orbit coupling is present between nx* and mien*states in the close vicinity of the carbonyl(s) in molecules such as benzil, and mtersystern crossing causes an anisotropy with respect to the orientation of the spin angular momentum that depends on the local symmetry of electron distribution around the carbonyl(s). Therefore the vrbratronal modes to which the carbonyls contnbute may effect the SLR For example, the vibrational energy of C=O stretchmg mode is 1671 cm-l in the ground state 19, IO]. Our experimental results suggest that this mode and some others around 1300 cm-l have dominant contribution to the SLR In conclusion, we have measured nanosecond SLR times m the triplet state of neat benzil near room temperature. The temperature dependences of the SLR rate and of the depopulation rate are obtained. The former can be attributed to the Orbach process involving two types of molecular vibrations and the latter to the deactivation of the trap Characteristic energres for the SLR and the depth of the trap were estimated_
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13 September
1985
Acknowledgement We would like to thank Dr_ S. Yamauchi, Professor N. Hirota, Dr_ Y_ Takagi and Dr. K. Kan-no for many helpful discussions.
References
[ll [21 131 (41
ISI
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