J. Phys. Chem. 1982, 86, 507-514
507
Triplet Excitons in 4,4'-Dichlorobenzophenone S. B. Slngham and D. W. Pratt" oepamnent ot Cbmktry, Unlvmb' of Plttsbwgh, Pittsburgh, Pennsylvania 15280 (Received: June 18, 1981; In F M Form: September 2 1, 198 1)
Low-temperatureoptical and magnetic resonance experiments,both continuous-wave(CW) and time-resolved, have been performed on photoexcited single crystals of 4,4'-dichlorobenzophenone (DCBP). The CW results show the presence of both triplet excitons and several intrinsic traps in this system. A kinetic model is developed to describe excitation transport between exciton and trap states in the presence of resonant microwaves. By comparing the results of the time-resolved experiments with the predictions of the model, we conclude that the triplet exciton lifetime in DCBP is of the order of microseconds or less. This lifetime, which is much shorter than those in pseudo-one-dimensional systems, appears to be a consequence of the two-dimensional nature of the exchange interaction in the DCBP crystal.
Introduction Several spectroscopic investigations have been carried out to elucidate the nature of the intermolecular interaction forces in molecular crystals.' The energetic structure of Frenkel exciton bands2 and the dynamics of exciton migration3 in these systems are also topics of current theoretical and experimental interest. Some of the physical methods which have been used to directly probe the static and transport properties of the lowest triplet exciton band are optically detected magnetic resonance (ODMR)? spin-echo and related coherence mea~urements,~ and optical absorption and line-shape analysisS6 It has been established that ODMR transitions of a one-dimensional triplet exciton band may be analyzed to determine the intermolecular exchange interaction and the anisotropy of spin-orbit coupling in the first Brillouin 20118.~ The line shape obtained is a sensitive function of phonon and other scattering processes and may be used to determine the coherence lifetime of the k states in the band under conditions of slow exchange. Further insight into the nature of the exciton dephasing and scattering processes has been provided by recent electron spin coherence experimentaS8 Excitonic properties have also been studied indirectly by means of the optical emission of X and Y traps in neat organic crystals. Both steady-stateg and time-resolved1° trap phosphorescence intensities have been observed in these experiments, which are particularly useful in cases where the phosphorescence from the exciton band is weak. Microwave-induced perturbations of the exciton sublevel (1)For a review, see A. M. Ponte Gonqalves, Prog. Solid State Chem., 13,1 (1980). (2)For a review, see G. W. Robinson, Annu. Reu. Phys. Chem., 21,429 (1970). (3)For reviews, see: D. M. Burland and A. H. Zewail, Adu. Chem. Phys., 40,369(1980);C. B.Harris and D. A. Zwemer, Annu. Rev. Phys. Chem., 29,473 (1979). (4)A. H. Francis and C. B. Harris, Chem. Phys. Lett., 9,181, 188 (1971). (5)B. J. Botter, A. I. M. Dicker, and J. Schmidt, Mol. Phys., 36,129 (1978). (6)D. M. Burland, D. E. Cooper, M. D. Fayer, and C. R. Gochanour, Chem. Phys. Lett., 52,279 (1977). (7)C. B. Harris and M. D. Fayer, Phys. Reu. B , 10, 1784 (1974). (8)A. J. van Strien, J. F. C. van Kooten, and J. Schmidt. Chem. Phys. Lett., 76,7 (1980). (9)D. D. Dlott and M. D. Fayer, Chem. Phys. Lett., 41,305 (1976); M. D. Fayer and C. B. Harris, Phys. Rev. E, 9,748(1974). (10)D. D. Dlott, M. D. Fayer, and R. D. Wieting, J . Chem. Phys., 69, 2752 (1978);69,1996(1978);R.M. Shelby, A. H. Zewail, and C. B. Harris, ibid., 64,3192 (1976). 0022-3654/82/2086-0507$01.25/0
populations may be transmitted to these trapping sites by triplet migration in the crystal, and the line-shape function obtained gives a measure of scattering processes that occur before the trapping event." Much of the work on excitons in organic crystals, with respect to both band structure and the dynamics of excitation propagation, has centered around aromatic hydrocarbons. Two systems which have been studied extensively by magnetic resonance and other spectroscopic techniques are 1,2,4,5-tetra~hlorobenzene~-'~ and 1,4-dibromonaphthalene.13J4 The highly anisotropic exchange interactions in these crystals result in an exciton transport topology which is quasi-one-dimensional. Studies of the properties of dimers3 have confirmed the dimensionality of 1,2,4,5-tetrachlorobenzeneand 1,4-dibromonaphthalene and have provided information about the two-dimensional nature of the exchange interaction for m* states in naphthalene and phenazine. Excitons have also been detected in neat crystals of benzophenone by high-field ODMR spectroscopy.15 No strongly preferred direction for exciton transport was evident, presumably because benzophenone has a fairly complex crystal structure.16 Given the importance of excitons in energy transport processes in the condensed phase, it was considered worthwhile to search for other model systems which might exhibit this behavior. Of the possibilities, 4,4'-dichlorobenzophenone (DCBP) seemed to be a reasonable choice since it has a relatively simple crystal structure17 with probable two-dimensional topology in the bc plane. Indeed, the high-field ODMR spectrum of photoexcited DCBP shows, in addition to trap transitions, a signal with characteristics very similar to those of excitons in benzophenone.18 In this paper, we report the detection of triplet excitons in DeBP by zero-field optical and microwave experiments. A rate model for excitons and traps in this system is used to interpret the time-dependent behavior (11)A. H. Francis and C. B. Harris, J. Chem. Phys., 55,3595(1971). (12)J. Zieger and H. C. Wolf, Chem. Phys., 29,209 (1978). (13)R.Schmidberger and H. C. Wolf, Chem. Phys. Lett., 32, 18,21 (1975);25, 185 (1974);16,402 (1972). (14)R.M. Hochstrasser and J. D. Whiteman, J. Chem. Phys., 56,5945 (1972). (15)M. Sharnoff, Symp. Faraday Soc., 3,137(1969);E.B. Iturbe and M. Sharnoff, Mol. Cryst. Lip. Cryst., 67,227 (1980). (16)E. B. Fleischer, N. Sung, and S. Hawkinson, J . Phys. Chem., 72, 4311 (1968). (17)K. G.Shields and C. H. L. Kennard, J.Chem. Soc., Perkin Tram. 2,2,463 (1977). (18)J. A. Mucha, Ph.D. Thesis, University of Pittsburgh, Pittsburgh PA,1974.
0 1982 American Chemical Society
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The Journal of Physical Chemistry, Vol. 86, No. 4, 1982
4125
4135
8
Singham and Pratt
3.60
3.64
GHz
3.60
3.64
GHz
5.11
GHz
5.06
Figure 1. Portion of the phosphorescence spectrum of 4,4'dichlorobenzophenone at 1.4 K, recorded wlth the ab plane normal to the viewing axis. The arrow denotes the position of the So T, origin at 4124.6 A,'*
-
observed for the deep-trap phosphorescence intensity in the presence of a resonant microwave pulse at an exciton or trap frequency. This allows us to determine the time scale for the establishment of thermal equilibrium between delocalized band states and localized trap states at low temperatures, a time scale which is very different from those of pseudo-one-dimensional systems. Possible reasons for this are discussed.
Figure 2. Optically detected magnetic resonance (ODMR) spectra of triplet excitations in DCBP at 1.4 K. A and C were obtained by monitoring the (0,O)band of the deep-trap phosphorescence at 4135.4 A; B was obtained by monltoring the (0,O)band of the shallow-trap phosphorescenceat 4126.5 A.
-
Experimental Section 99% pure DCBP (Aldrich Chemical Co.) was purified by several recrystallizations from absolute ethanol and zone refined under an atmosphere of nitrogen. Single crystals were grown by the Bridgman technique and annealed for 2 weeks at 10-15 "C below the melting point. DCBP has a face-centered monoclinic structure (space group C&)17 with four molecules per unit cell and two molecules per primitive cell. The dimensions of the unit cell are a = 25.16 A, b = 6.128 A, c = 7.586 A, and ,d = 102.05O. Each molecule is at a site having C2 symmetry, and the C2 axis is parallel to b. The two molecules in the primitive cell have their dipole moments pointing in opposite directions. Zero-field ODMR experiments were carried out at liquid-helium temperatures by using a spectrometer of standard design. Optical excitation was usually provided by a filtered 100-W high-pressure Hg lamp. The phosphorescence was detected with a 0.75-m Spex monochromator equipped with a 1P28 photomultiplier tube. Steady-state ODMR spectra were obtained in a conventional manner with the microwave power being supplied by a Hewlett-Packard 8690B sweep oscillator and the appropriate plug-ins. Temperatures above 4.2 K were reached by permitting the liquid-helium level to drop below the sample. In time-resolved experiments, the microwave power was amplified with an Alfred 502 microwave amplifier; signal averaging was performed by a transient recorder and digital computer.
vicinity of 4124.6 A, the origin of the So TI transition.lg The spectrum is qualitatively similar to that which has been previously reported.20 The strongest emission at the lowest temperatures is from a deep trap at 4135.4 A, with a separation of 63 cm-l from the electronic origin. Weaker emission is observed from several shallow traps at around 4126.5 A, which corresponds to a trap depth of 11 cm-'. In addition, a very weak emission is detected at 4124.6 A which may be attributed to radiative decay from either the exciton band or extremely shallow traps which lie within the bandwidth of the detection system at this wavelength. The relative intensity of this band is strongly dependent on orientation, peaking with the viewing axis perpendicular to the ab (cleavage) plane. The spectrum shown in Figure 1was taken under these conditions. When the sample is warmed above 2 K, all lines except those associated with the deep trap decrease rapidly in intensity. Steady-State ODMR and PMDR Spectra. The zerofield ODMR spectra of triplet excitations in DCBP, which were obtained by monitoring both deep- and shallow-trap phosphorescence at 1.4 K, are illustrated in Figure 2. In the 3.5-3.7-GHz region, the ODMR spectrum of the deep trap shows a very strong signal at 3.66 GHz, a less intense broad band at 3.60 GHz, and weak transitions at 3.62 and 3.64 GHz (Figure 2A). The spectrum obtained for the shallow-trap emission in the same microwave region consists of a strong signal at 3.64 GHz, a weaker transition at 3.62 GHz, and a very weak broad band at around 3.60 GHz (Figure 2B). In the 5.0-5.2-GHz region, a strong transition at 5.07 GHz and a weak signal at 5.12 GHz were observed for the deep-trap phosphorescence (Figure 2C) while only one line at 5.12 GHz was observed when monitoring the shallow-trap emission. All transitions detected corresponded to decreases in the phosphorescence intensity. As an aid to the assignment of these spectra, phosphorescence-microwave double resonance (PMDR)21ex-
Results and Interpretation Phosphorescence Spectra. Figure 1shows a portion of the phosphorescence spectrum of DCBP at 1.4 K in the
(19)R. M. Hochstrasser and J. W. Michaluk, J.Mol. Spectrosc., 42, 197 (1972). (20)S.J. Sheng and M. A. El-Sayed, Chem. Phys. Lett., 45,6 (1977).
The Journal of Physical Chemlstry, Vol. 86, No. 4, 1982 509
Triplet Excitons in 4,4'-Dichiorobenzophenone
periments were performed in the 4124-4136-A wavelength region at microwave frequencies of 3.66,3.64,3.62, and 3.60 GHz. At 3.66 GHz, no change in emission was detected at 4124.6 A, a very weak band was present at 4126.5 A,and a very strong signal was observed at 4135.4 A. The 3.64and 3.62-GHz PMDR spectra exhibited strong bands at 4126.5 A, less intense signals at 4135.4 A, and no change in intensity at 4124.6 k At 3.60 GHz, a signal was detected a t the electronic origin as well as at trap wavelengths. These results, together with those of the ODMR experiments, suggest that the strong signals at 3.66 and 5.07 GHz should be assigned to the D - E (Z-Y) and D E (Z-X) transitions of the deep trap. The lines at 3.64 and 5.12 GHz are the corresponding shallow-trap frequencies. These assignments are consistent with those made by Sheng and El-Sayed" in an earlier study of DCBP. These workers did not, however, report the observation of the weak lines at 3.62 and 3.60 GHz whose origin(s) remain unexplained. It is apparent from the above that population changes in the shallow-trap sublevels, produced by resonant microwaves, cause a change in the deep-trap emission intensity. As direct trapto-trap migration is statistically improbable because of the low concentration of intrinsic defects in the pure crystal, this transfer of excitation probably takes place by detrapping into the exciton band followed by retrapping at a subsequent site. A similar transfer of excitation from the deep trap to the shallow trap would result in a change in the shallow-trap intensity on irradiation with a deep-trap microwave frequency. From the relative trap intensities observed in the PMDR spectra, it may be inferred that the shallow-trap detrapping rate is fairly large while that of the deep trap is small at 1.4 K. This is consistent with the different trap depths of two defects. The absence of shallow-trap emission at higher temperatures may be caused by phonon-assisted detrapping into the exciton band which is enhanced by the increase in temperature and competes with radiative decay to the ground state. It is important to note that no PMDR signal is observed at the electronic origin on application of 3.64-GHz microwaves, in spite of the rapid shallow-trapdetrapping rate. This suggests that the emission a t 4124.6 A originates in a state with an exceedingly short lifetime since its steady-state populations are not significantly perturbed by population changes in the shallow-trap sublevels. As the transition at 3.62 GHz shows a similar behavior, we believe it should also be assigned to one of the several intrinsic traps present in the crystal, emitting in the vicinity of 4126.5 A. However, the transition at 3.60 GHz shows a different behavior; a PMDR signal was detected at the electronic origin as well as at the trap wavelengths when irradiating with microwaves at this frequency. This suggests that the 3.60-GHz transition is probably not due to a trap. In fact, when taken together, the ODMR and PMDR results can best be explained by assuming that the weak emission at 4124.6 A is excitonic in nature, that triplet excitons in DCBP have a very short lifetime, and that the 3.60-GHz microwave transition connects the magnetic sublevels of the triplet exciton band directly, producing population changes in both the exciton and, following transfer of excitation, the trap sublevels. Temperature Dependence of the ODMR Spectra. ODMR spectra of the deep-trap phosphorescence in the 3.57-3.68-GHz region were obtained at temperatures from 1.4 to above 4.2 K. Representative results are shown in
;Ic
+
~
I
I
3.60
3.66
GHz
Figure 3. Temperature dependence of the D - E (T,-T,) ODMR spectrum obtained by monitoring the (0,O) band of the deep trap. Spectrum A was recorded wkh the sample at 4.2 K; spectra B and C were recorded at higher temperatures.
Figure 3. The gross features of the spectrum at 4.2 K are similar to those at 1.4 K. Above 4.2 K, the ODMR transitions at 3.62 and 3.64 GHz decrease in intensity and eventually disappear while the signals at 3.60 and 3.66 GHz increase in intensity. At still higher temperatures the latter two transitions are found to broaden, decrease in intensity, and ultimately disappear. An increase in the rate of phonon-assisted detrapping probably accounts for the behavior of the shallow-trap signals at 3.62 and 3.64 GHz. The lifetimes of these states decrease with an increase in temperature, and eventually their microwave transitions cannot be detected. With the increase in the rate of spin-selective shallow-trap detrapping and retrapping, an enhancement of the deep-trap ODMR signal at 3.66 GHz is expected and observed. The temperature dependence of the transition around 3.60 GHz supports the exciton assignment. Increased populating rates caused by detrapping of the shallow traps result in more intense exciton microwave transitions. The behavior of the 3.60-GHz signal could also be attributed to a nonradiative deep trap, but this assignment would be inconsistent with the PMDR results. Thus, we conclude that the weak phosphorescence at 4124.6 A is indeed excitonic in origin and that 3.60 GHz corresponds to a resonant microwave frequency of the triplet exciton band. A further feature observed in the temperature-dependent spectra is that the exciton transition narrows appreciably, with a maximum around 3.60 GHz, when the temperature is raised. This could be due to the loss of possible shallowtrap signals in the vicinity of 3.60 GHz or exchange averaging of the exciton k states:,' or both. Finally, the decrease in intensity of the exciton and trap ODMR transitions at still higher temperatures is probably caused by the onset of substantial deep-trap detrapping, spinlattice relaxation, and other nonradiative processes. Time-Resolved Experiments. Phosphorescence and MIDP. Strong MIDP22transients at 4135.4 A were ob-
~~~~
(21) D.S.Tinti, M. A. El-Sayed, A. H. Maki, and C. B. Harris,Chem. Phys. Lett., 3, 343 (1969).
(22) J. Schmidt, D.A. Antheunis, and J. H. van der Waals,Mol. Phys., 22,l(1971).
510
Singham and Pratt
The Journal of Physical Chemistry, Vol. 86, No. 4, 1982
TABLE I: Kinetic Data for t h e Triplet Sublevels of t h e Deep Trap in Neat DCBP a t 1.4 K __ -
-
--
k,, s ' 52 i 10
la
x y
43 t 9 6 5 1 : 65
z a
- -- -
--
-
k,' 0.027 t 0.005 0.035 i 0.007
1
PI
0.067 0.030 1
i f
nIo
0.013 0.005
0.8
i
0.5 1
i
0.3 0.3
Sublevel
tained at low temperatures for the D - E and D + E transitions of the deep trap following delays of the order of 10 ms. Weak MIDP signals at the same wavelength were observed at 3.64 and 5.12 GHz, the shallow-trap ODMR frequencies, but no signal was detected at 3.60 GHz. The last observation suggests that the exciton population is rapidly trapped into the shallow and deep traps. This was confirmed by time-resolved phosphorescence spectra which were obtained at various delays with respect to pulsed optical excitation with a nitrogen laser. It was found that the relative intensity of the shallow- and deep-trap phosphorescence is similar to that under steady-state conditions, and no increase in exciton emission intensity was observed, even at delays of only a few microseconds. Kinetic Parameters of the Deep Trap. The MIDP method is inappropriate for the determination of kinetic parameters of the deep trap because of the populating route provided by shallow-trap detrapping even after the exciting light is shuttered. A combination of the adiabatic fast passage23 and saturation recovery methods24 was therefore used to determine the total decay rate constants (Iti), the relative radiative rate constants to the (0,O)band ( k c ) , the relative populating rates (pi),and the relative populations (n:) of the triplet sublevels at 1.4 K. These are listed in Table I. The parameters given are qualitatively similar to those obtained for DCBP in a 4,4'-dibromodiphenyl ether host crystal.25 In the latter case, the populating rate of the z sublevel is large when compared with those of the x and y sublevels owing to selective spin-orbit coupling of the z sublevel with the singlet manifold. In the neat crystal the same disparity would hold for the populating rates of the triplet exciton sublevels. The probability of populating a particular spin state of the trap from an exciton sublevel is given by the square of the direction cosine relating the fine structure axis of the trap to that of the exciton, when the spins transfer randomly with respect to the Larmor precession.26 If it is assumed that the trap fine structure axes are only slightly distorted from the exciton axes and that the direction cosines relating the pair of axes are approximately equal for all three sublevels, the relative populating rates of the trap depend entirely on the relative populations in the exciton sublevels. Since the relative populating rates of the trap are qualitatively similar to those expected for the exciton, spin-lattice relaxation rates in the exciton sublevels must be slow relative to trapping rates at liquid-helium temperatures. Microwave Pulse Experiments. Having determined the kinetic properties of the deep-trap sublevels, and having established that spin-lattice relaxation among the exciton sublevels is slow, we can finally turn our attention to the question of the dynamics of exciton trapping in this system. Some information about this process can be derived from a comparison of the time dependence of the (deep) (23) C. J. Winscom and A. H. Maki, Chem. Phys. Lett., 12,264 (1971). (24) A. L. Shain and M. Sharnoff, J. Chem. Phys., 69, 2335 (1973). (25) G. Kothandaraman and D. W. Pratt, unpublished results. (26) H. C. Brenner, J. C. Brock, and C. B. Harris,Chem. Phys., 31,137 (1978).
!
> (k, + k,)/2, I#) should approach its new equilibrium value with two very different exponentials. When the microwave power is turned off after a time tl (tl >> T2),the intensities before and after tl are Zp(ti-)
+ k;)[n,(tJ + n,(ti)l = k:nZ(ti) + k;ny(ti)
= l/z(k,'
Zp(tl+)
(13) (14)
I t is assumed that the sublevel populations are constant while the field is turned off. If n,(tl) # n,(tl), a change in intensity results which is given by Mp'(tJ =
72(k,' - k,')[n,(ti) - n,(tJl
(15)
The populations in T, and Tysubsequently revert to their steady-state (no microwave) values with rate constants k, and k,. Implicit in this treatment of the problem is the assumption that, at times much longer than T2,the coherent Bloch equations reduce to simple fit-order rate equations for two "independent" sublevels. In fact, the sublevels are not independent, being coupled by the microwave field. The mixing of the sublevel wave functions by this field is retained in the model by using the average radiative decay constant in eq 13. The model thus predicts a change in the phosphorescence intensity on turning off the microwave pulse, given by eq 15, which is very fast compared
512
The Journal of Physical Chemistry, Voi. 86, No. 4, 1982
Singham and Pratt
4=
- kznz ny = p,(t) - kyny
P
i
I
I
I I I
l!;
I
di
I I
I I I
I 1 I I
kf
ki
-
(17)
where the populating rates of the trap sublevels are now time dependent. The populations in the exciton z and y sublevels, n," and %e, which determine p z and p,, are given by equations completely analogous to eq 4-7. In using these expressions for n,"(t) and n,"(t), we assume that the contributions to the populating rates of the z and y exciton sublevels from shallow-trap detrapping and scattering from other k states remain time independent in the presence of the microwave field. The effective exciton decay constant then becomes the mean of the individual decay constants of the z and y levels. Since spin angular momentum is conserved in triplet-triplet energy transfer30
I
Shallow
(16)
Ground
State
pAt) = %k,t[n,e(t) + n,"(t)]
+ p,"'
(18)
p,(t) = l/zk,t[n,"(t) + n,"(t)l
+ pqk
(19)
Figure 5. Schematic energy-level diagam for triplet excitons and traps in DCBP. pp is the Intersystem crossing rate, and p,' and p i are the populating rates of the shallow and deep traps, respectively. d,' and d , are the detrapping rate constants for the shallow and deep traps, respectively, and k,' and k , are the correspondlng rate constants for decay to the ground state. k,( is the exciton rate constant for decay to the ground state.
where the kit are trapping rate constants and the pf' refer to populating rates from the k states in the exciton band which are not coupled by the microwave field. Solving the differential equations 16 and 17 by using these expressions for p,(t) and p,(t) yields a change in the trap phosphorescence intensity of the form
to the decay times of the sublevels. The validity of this approach is confirmed by the fact that the experimentally observed optical transients are found to contain all features predicted by the model. Applications. The dominant rate processes for the population and decay of the exciton and trap triplet states in DCBP are summarized in Figure 5. In general, the symbols pi denote populating rates, ki the total decay constants to the ground state, and di the detrapping rates. Here, we show how the rate equations can be used to extract the exciton and trap rate parameters from the time dependence of the trap intensity in the presence of saturating microwave fields. Microwave Puke at a Deep-Trap Resonance Frequency. The equations derived for the two-level system considered above are appropriate for the z and y sublevels of the deep trap in the presence of an oscillating field at 3.66 GHz and may be used to interpret the optical transients shown in Figure 4. When the microwave pulse is turned on, the deep-trap phosphorescence intensity is expected to show damped transient nutations corresponding to the loss of coherence in the spin system, the time constant for decay being typically of the order of 10 ps.27 These nutations were observed on expanding the spectrum in Figure 4A. After the oscillations are completely damped out, the phosphorescence intensity is seen to exhibit the biexponential behavior expected from eq 8, the exponentials being clearly differentiated only under conditions of high power. In the latter case, the lifetime of the slower exponential is found to be identical with the value calculated for A, (eq 10) using the kinetic parameters of the deep trap given in Table I. When the microwave power is turned off before steady state is established, a sudden increase in intensity is observed (Figure 4A) which corresponds to AI; in eq 15. This is not observed at the end of the long microwave pulse (Figure 4B)as n, N ny at steady state, when r is very large. The negative AIp observed when steady state is reached is expected from the value calculated for C' in eq 12. Microwave Pulse a t a n Exciton Resonance Frequency. The rate equations for the deep-trap populations n, and ny in the presence of a microwave field which couples the exciton z and y sublevels of a particular k state are
AIp(t) = A" exp(-k,t)
+ Be exp(-k,t) + Ce exp(-X,"t) + De exp(-X,")
+ E" (20)
Here, Ae, Be, Ce,and De are arbitrary constants and Ee is the intensity obtained when steady state is reached. Thus, the approach of the trap phosphorescence intensity to a new equilibrium value following application of a microwave pulse at an exciton resonance frequency is characterized by four exponentials, rather than the two exponentials of the previous case. Two of the four decay constants, k, and k,, can be measured independently. By a simple extension of these arguments, it is easily shown that the return of the trap intensity to its original (no microwave) value at the end of the present experiment is also described by four exponentials, with decay constants k,", k;, It,, and ky3I A comparison of these results with those observed experimentally (Figure 4)allows us to conclude immediately that the values of k," and/or k," (and, therefore, Ale and Xze) are much larger than k, and k,. This is seen most clearly in Figure 4C,the short-pulse experiment. Here the increase in phosphorescence intensity which occurs at the end of the pulse is much faster than either k;' (= 1.5 ms) or ';k (23 ms). This gives us an upper limit of 1-2 ps for a value the exciton sublevel lifetimes (k,B)-' and/or &,")-I, which is consistent with the results of the MIDP and time-resolved phosphorescenceexperiments, as well as with the recent work of Avdeenko et We may further conclude that, since emission from the exciton band is very weak, the exciton sublevel lifetimes are determined by the rate of trapping, or by the rate of scattering to other k states, or both. In this connection, it is interesting to note that no nutations were observed on (time-scale)expansion of the initial decrease in intensity in Figure 4C, suggesting that the process responsible for the short exciton lifetime may also be contributing to a dephasing of the spins. At longer times (e.g., with millisecond time resolution, as in Figure 4D), both the rise and fall times are governed by (30)M. Sharnoff and E. Iturbe, Phys. Reo. Lett., 27,576 (1971);D. L. Dexter, J. Chem. Phys., 21,836 (1953). (31)S. B. Sinaham, Ph.D. Thesis, University of Pittsburgh, - Pittsburgh, PA, 1981.(32) A. A. Avdeenko, T. L. Dobrovolskaya, V. A. Kultchitskii, and Yu. V. Naboikin, Phys. Status Solidi B , 99, 409 (1980).
The Journal of Physical Chemlstry, Vol. 86,No. 4, 1982 513
Triplet Excitons in 4,4'-Dichlorobenzophenone
the same decay constants (k,and k,,),which explains the apparent symmetry in the transient response. Finally, the data also show that, for both exciton and trap, the microwave-induced steady-state population of the z (y) sublevel is smaller (larger) than the corresponding value in the absence of microwaves. Microwave Pulse a t a Shallow-Trap Resonance Frequency. We have also examined the behavior of the deep-trap phosphorescence intensity in the presence of a microwave field oscillating at the shallow-trap frequency. Our analysis31shows, in agreement with expectations, that the optical transient is characterized by six exponentials. The two additional parameters are d,S and d;, the shallow-trap detrapping rate constants. Therefore, at least in principle, the transient produced by a microwave pulse at a shallow-trap frequency will be different from that observed following a pulse at an exciton frequency. Comparison with Other Systems. The most striking property of triplet excitons in DCBP is their extremely short lifetime [ I1ps] at liquid-helium temperatures. In this respect, they differ markedly from triplet excitons in 1,2,4,5-tetrachlorobenzene(TCB) and 1,Cdibromonaphthalene (DBN) which have lifetimes of the order of milli~econds.'~J~ Here, we comment briefly on some possible reasons for this difference in behavior. Factors which are likely to influence the lifetime of a particular k state in the triplet exciton band are the strength of spin-orbit coupling with states in the singlet manifold, the rate and range of k k' scattering induced by phonons and impurities, and the rate of exciton trapping. Of the three, the last factor appears to be most important in DCBP. This is because the magnitudes of the total decay constants of the deep-trap sublevels in this system are not much larger than those of traps in TCB and DBN and because the free exciton quantum yield in DCBP, as measured by the relative intensity of trap and exciton emission in the phosphorescence spectrum, is much lower than in TCB, where the k k' scattering rate is very large, at least over a limited range.* The rate of exciton trapping, however, depends on other factors which might be quite different in the three systems. These include the strengths of intermolecular interactions, the concentrations of traps, and the topologies of exciton transport. The interchange splitting of the %a* exciton state in DCBP is 1.8 cm-l; l9 this places an upper limit of -0.5 cm-' on the intermolecular interaction matrix element for neighboring inequivalent molecules in this crystal. If the values for equivalent molecules are similar, this cannot be an important factor since the corresponding values for TCB and DBN are 0.34 and 7.4 cm-l, re~pectively.'~J~ The concentration of traps in DCBP may be higher, particularly because the potential surface for twisting of the rings away from their equilibrium configuration is probably quite shallow, but we think this is unlikely. This is because crystals of DCBP grown and carefully annealed by a variety of methods exhibit little or no exciton emission. Thus, we believe that the principal factor responsible for the difference in exciton lifetimes in DCBP and TCB/ DBN is the topology of exciton transport. This suggestion, not without precedent,14 is easily rati.onalized. The trapping rate constant, K, for an exciton executing a random walk in a one-dimesional lattice with regularly spaced traps is33
-
-
K(1D) = ( a 2 / 2 ~ ) F
(21)
where T is the characteristic jump time of the exciton and (33)G. W. Robinson in Brookhaven Symp. Biol., No. 19, 16 (1966).
C
Flgure 6. Stacking pattern for DCBP molecules in the bc crystallographic plane.
F
