3480
J. Phys. Chem. 1991, 95, 3480-3486
that the error is larger for the less impulsive potential (k = 3.0) but that the agreement between the exact and approximate results would be adequate for distinguishing between rotational distributions obtained from competing theoretical models, since angular momentum values derived from the approximation and the exact solutions would show fractional errors about half of those obtained for the energies. Again, the curve for k = 3.0 shows the error changes sign for reasons described in the last paragraph.
Conclusions This is a summary of what we have demonstrated in the previous sections. First, we tested the simplest form of the impulse approximation-in which the force between retreating atom A and the rotor is along the line AB-using repulsive potentials in which the interaction is a nearest-neighbor repulsion. Values of the steepness of the repulsion were chosen with reference to some recent calculations, and for these values, the approximation gives reasonable values of fractional energy conversion. Next, we used a potential that is more general in having forces directed other than between nearest neighbors, but still using exponential attractions and repulsions. When used in the way we described, the impulse approximation also works well for calculating the fragment rotation over our range of bond angles in the initial configuration. Such a calculation would enable the experimenter to make easy comparison of dynamical models with, for example, the variety of statistical models that are frequently cited. The present study will be extended to a comparison of approximate and exact computations for other sources of rotation: parent rotation and bending vibration. Finally, we tested the extended
impulse approximation applied to a potential of a widely used type involving short-range repulsion and 'bending forces" and showed that the approximation gives good results for short-range repulsion. When will the impulse approximation fail to give an adequate estimate of fragment rotation? The graphs illustate that it can be in error if the potential is not short range, that is, if k is small. But it has been found that even if the potentials in the dissociating molecule are short range, the elementary form of the approximation fails to yield acceptable results. The nearest-neighbor repulsion model does not correctly describe fragment rotation in CICNi5or in NOC12*even though the classical trajectory results obtained with a short-range potential are in good agreement with experiment. Probably the reason for this failure is that the nearest-neighbor repulsion model of the approximation uses an incorrect direction for the initial force on the fragment. The dissociation can still be impulsive, as described in this note, even though the initial force is not directed along the direction AB. It remains to be determined if the extended impulse approximation provides a good approximation to fragment rotation for ClCN. It is clear from the calculations of error given earlier that the impulse approximation gives good estimates of fragment rotation for some potentials that do not satisfy the requirements given by Schinke and his collaborators's~22for the successful application of the impulse approximation. It is evident that the impulse approximation has more usefulness than these recent criticisms suggest. (22) Schinke, R.; Nonella,M.; Suter, H.U.; Huber, J. R. J . Chem. Phys. 1990, 93, 1098.
Triplet Energy Transfer of the Intramolecular System Havlng Benzophenone and Dibenz[ b ,t]azepine at the Chain Ends: Chain Length Dependence Hideaki Katayama, Shogo Maruyama, Shinzaburo Ito, Yoshinobu Tsujii, Akira Tsuchida, and Masahide Yamamoto* Department of Polymer Chemistry, Faculty of Engineering, Kyoto University, Sakyo- ku, Kyoto 606, Japan (Received: September 28, 1990; In Final Form: January 4, 1991)
Intramolecular triplet-triplet energy transfer in a series of polymethylene chains having a benzophenone (BP) group as an energy donor and a dibenz[bflazepine (DBA) group as an energy acceptor (BP-O(CH,),CO-DBA) has been studied by phosphorescence measurement and nanosecond laser photolysis. In a rigid solution and PMMA matrix, the quantum yield of triplet-triplet energy transfer is close to unity for the chain lengths shorter than n = 5 . On the basis of the through-space mechanism of energy transfer, phosphorescencedecay curves were analyzed by Dexter's equation in which the distribution of donor-acceptor distance was calculated by the conformational energy analysis. The results of the simulation were in fairly good agreement with the experimentallyobserved decay curves. The rate constant of triplet-triplet energy transfer is strongly dependent on the chain length, Le., about one-tenth decrease per every methylene unit, and the rate is much smaller than that of singlet-singlet energy transfer.
Introduction Triplet-triplet (T-T) energy transfer is a fundamental photophysical process.' Many kinds of photochemical reactions proceed via the triplet state and are often initiated by so-called "triplet sensitizer", which transfers its excited energy to a reactant with a high efficiency.2 T-T energy transfer is forbidden by the ( I ) (a) Turro, N. J. Modern Moleculur Phorochemisrry;Benjamin: Menlo Park, CA, 1978;p 306. (b) De Schyver, F. C.; Boens, N. Ado. Phorochem. 1977,10, 359. (c) Thiery, C. Mol. Phorochem. 1970,2, I . (d) Birks, J. B. Phorophysics oJAromotic Molecules; Wiley: N e w York, 1970;p 518. (e) Wilkinson, E Q.Reu. 1966,20,403.(f) Fox, M.A. J . Phorochem.Phorobiol. 1990, 52,617. (2)(a) Galley,, W.; Stryer, L. Proc. Nurl. Acad. Sci. U.S.A. 1968,60, 108. (b) Wu, 2.;Mornson, H. Phorochem. Phorobiol. 1989.50,525. (c) Eisinger, J.; Shulman, R. G. Science 1968, 161, 1311.
0022-3654/91/2095-3480%02.50/0
dipole-dipole mechanism but is spin-allowed by the exchange mechanism? Therefore, the critical radius of T-T energy transfer, Ro, is relatively short compared with that of the singlet-singlet energy transfer and is in the range 1.0-1.5 nm.4 Owing to this factor, the rate constants are highly sensitive to the distance of separation between donor and acceptor molecules. In the case of intramolecular energy transfer, the rate will be markedly affected by the intramolecular donor-acceptor distance that is determined by the molecular structure and conformation of the molecules. Many studies on intramolecular T-T energy transfer systems Lamola et aLs studied T-T energy transfer have been (3)Dexter, D.L.J . Chem. Phys. 1953,21, 836. (4)Ermolaev, V. L. Sou. Phys. Dokl. 1962,6,600.
0 1991 American Chemical Society
Chain Length Dependence of Triplet Energy Transfer of bichromophoric compounds, with benzophenone (BP) as a donor and naphthalene as an acceptor, connected by a methylene chain where the chain length was 1-3. The quantum yields of T-T energy transfer were unity in all compounds in EPA glasses at 77 K, since the intramolecular donor-acceptor distance, R , is shorter than 1.0 nm. Keller et aL6>' also studied T-T energy transfer of systems similar to that of Lamola et al.; a phthalimide group was employed as the triplet energy donor. They also obtained a quantum yield of unity in a rigid glass at 77 K. Since the distance R between these compounds was too short, the transfer process was finished completely within a picosecond time order,* and no structural effect was observed on the transfer efficiency. Keller et ale9estimated the rate constant of T-T energy transfer for the first tAime,by using bichromophoric compounds connected with a large steroid spacer. Recently Closs et al.I4 also investigated bichromophoric compounds connected by a rigid spacer and estimated the rate constant of T-T energy transfer in benzene solution at room temperature, by using picosecond laser photolysis. They concluded the through-bond mechanism for the T-T energy-transfer process. In the present work, intramolecular T-T energy transfer is directly observed by measuring transient T-T absorption and benzophenone phosphorescence decay after an excitation with a nanosecond laser pulse. The samples used here are a series of polymethylene chains having the BP group as an energy donor, and the dibenz[bflazepine (DBA) group as an energy acceptor:15
W n= 1, 3 , 4 , 5 , 7 These compounds are denoted by DA-n ( n = 1-7), each numeral representing the number of methylene units for each polymethylene chain. In these chain lengths, the donor-acceptor distance varies from 0.9 to 1.8 nm provided that the methylene chain of each compound is extended in all-trans conformations. As mentioned later, the critical radius of T-T energy transfer for this system is ca. 1.5 nm. Then the donor-acceptor distance for a series of bichromophoric compounds varies from the inside of R,, to the outside of Ro. This means that the rate constant of T-T energy transfer, kTT,will vary distinctly with increasing methylene chain length. In the current work, we analyzed the obtained data with the through-space mechanism for which Dexter's theory was applied and determined the basic parameters of T-T energy transfer. Experimental Section Materials: A series of polymethylene compounds having the DBA group and BP group as the chain terminals were synthesized by Williamson reaction of w-bromoalkanoyl-DBA (for DA-I, -3, (5) Lamola, A. L.; Leermakers, P. A.; Byers, G. W.; Hammond, G. S. J . Am. Chem. SOC.1965,87, 2322. (6) Breen, D. A.; Keller, R. A. J . Am. Chem. SOC.1968, 90, 1935. (7) Keller, R. A. J . Am. Chem. Soc. 1968, 90, 1940. (8) Maki. A. H.; Weers, J. G.; Hilinsky, E. F.; Milton, S. V.; Rentzepis, P. M. J . Chem. Phys. 1984,80, 2288. (9) Keller, R. A.; Dolby, L. J. J . Am. Chem. SOC.1969, 91, 1293. (10)Zimmerman, H. E.; Mckelvey, R. D. J. Am. Chem. SOC.1971, 93,
3638. ( 1 I ) Amrein, W.; Schaffner, K. Helu. Chim. Acta 1975, 58, 397. (12) Gust, D.; Moore, T. A.; Bensasson, R. V.; Mathis, P.; Land, E. J.; Chachaty, C.; Moore, A. L.; Liddell. P. A.; Nemeth, G. A. J . Am. Chem. Soc. 1985, 107, 3631. (13) Ito, Y.; Uozu, Y.; Arai, H.; Matsuura, T. J . Org. Chem. 1989, 54, 506. (14) (a) Closs, G. L.; Piotruwiak, P.; Maclnnis, J. M.; Fleming, G. R. J . Am. Chem. Soc. 1988, 110,2652. (b) Closs, G. L.; Johnson, M. D.; Miller, J. R.; Piotrowiak, P. J . Am. Chem. SOC.1989, 1 1 1 , 3751. (1 5) (a) Ashikaga, K.; Ito, S.; Yamamoto, M.; Nishijima, Y. J. Am. Chem. Soc. 1989, 110, 198. (b) Ashikaga, K.; Ito, S.; Yamamoto, M.; Nishijima, Y. J . Photochem. 1987, 38, 321.
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3481
-5, -7) or 5-chloropentanoyl-DBA (for DA-4) with the potassium salt of phydroxy-BP. Bromoalkanoyl-DBA was synthesized from bromoalkanoyl chloride with DBA.IS Commercial bromoalkanoyl chloride (Aldrich Chemical Co.) was used for the reaction except 8-bromooctanoyl chloride. 8-Bromooctanoyl Chloride. 8-Bromooctanoic acid (Aldrich Chemical Co.) was dissolved in thionyl chloride, and the solution was stirred at room temperature for 0.5 h and then heated to 50 OC for a further 2 h. After the evolution of hydrogen chloride ceased, excess thionyl chloride was removed by distillation. An oily product was obtained. Potassium Salt of p-Hydroxy-BP (KOBP). p-Hydroxy-BP (Aldrich Chemical Co.) was added to a solution of equimolar potassium hydroxide in methanol. The product was obtained by evaporation of the solvent and dried in vacuo. DA-1. Bromoacetyl chloride was added dropwise to the stirred 1,2-dichloroethane solution of DBA (Aldrich Chemical Co.) a t room temperature. The product, bromoacetyl-DBA, was recrystallized from methanol. A solution of KOBP in D M F was added dropwise to the equimolar solution of bromoacetyl-DBA at room temperature and stirred for 0.5 h. The mixture was stirred for 3 h at 100 "C and then cooled and washed with water. The reaction product was extracted with dichloromethane and dried over calcium chloride, and finally evaporation of the solvent yielded a product. The product was recrystallized from methanol; IR (KBr) 1680,1600,1490,1270,1180,740, and 700 cm-l; lH NMR (CDCI3) 6 4.5 (4,oxymethylene H), 6.8-7.9 (m, Ar H). DA-3. DA-3 was synthesized and purified by the same method as used for DA-1. 4-Bromobutanoyl chloride was used instead of bromoacetyl chloride; mp 149 "C; IR (KBr) 1660, 1600, 1490, 1400, 1300, 1280,740, and 700 cm-l; IH NMR (CDCI,) 6 1.8-2.5 (m, methylene H), 4.0 (9, oxymethylene H), 6.8-7.9 (m, Ar H). DA-4. DA-4 was synthesized by the same method as DA-1. 5-Chloropentanoyl chloride was used instead of bromoacetyl chloride. The product was oily and purified by column chromatography on silica gel eluted with a mixture of ethyl acetate and hexane (4:6). IR (KBr) 2940,1670,1600,1480,1260,1170, 740, and 700 cm-I. 'H N M R (CDCI,) 6 1.6-2.4 (m, methylene H), 3.9 (t, oxymethylene H), 6.8-7.9 (m, Ar H). DA-5. DA-5 was synthesized and purified by the same method as used for DA-4. 6-Bromohexanoyl chloride was used instead of 5-chloropentanoyl chloride; IR (KBr) 2940, 1670, 1600, 1490, 1260,1170,740, and 700 cm-'; 'H N M R (CDCIJ 6 1.3-2.4 (m, methylene H), 4.0 (t, oxymethylene H), 6.8-7.9 (m, Ar H). DA-7. DA-7 was synthesized and purified by the same method as used for DA-4. 8-Bromooctanoyl chloride was used instead of 5-chloropentanoyl chloride; IR (KBr) 2930, 1670, 1600, 1490, 1260,1170,740, and 700 cm-'; 'HN M R (CDC13) 6 1.2-2.5 (m, methylene H), 4.0 (t, oxymethylene H), 6.8-7.9 (m, Ar H). The DA-n compounds were finally purified by liquid chromatography (Japan Spectroscopic Co. Ltd.) to remove any trace amount of impurities. The final product showed a single peak on the chromatogram. 4-Methoxybenzophenone (MeO-BP). Commercial 4-methoxybenzophenone (Aldrich Chemical Co.) was used after recrystallization from ligroin. Valeryl-DBA. To a stirred solution of DBA in dried 1,2-dichloroethane, a solution of valeryl chloride (Nakarai Tesque, Inc.) in 1,2-dichloroethane was added dropwise and then the solution turned from orange to light yellow. The solution was stirred at room temperature for 0.5 h and refluxed for 3-4 h at 90-100 OC. Then it was cooled to room temperature, washed with water, and dried with calcium chloride. The yellow oily product was recrystallized several times from ligroin, and the luminous component was removed by column chromatography on silica gel eluted with a mixture of dichloromethane and methanol (500:3). Sample Preparation. Spectroscopic grade sec-butyl chloride (sec-BuCI) was used for a rigid glass a t 77 K. It was dried by the use of molecular sieves. PMMA solid samples were prepared as follows: The bichromophoric compounds were dissolved in methyl methacrylate that was purified by distillation at a reduced pressure. After addition of 3 mg of azobisisobutyronitrile, the
3482 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 I \
Katayama et al.
It
Figure 1. Structural parameters of DA-n used for conformational analysis. R represents donor-acceptor distance.
solution in a Pyrex cell was degassed by several freezethaw cycles and polymerized for 12 h at 60 OC and for a further 12 h at 120 OC. The GPC analysis of the bulk polymer showed no residual monomer in the low molecular weight range. Spectroscopic Measurement. The absorption spectra were measured by a Shimadzu UV-ZOOS spectrophotometer. Phosphorescence spectra in a photostationary condition were measured with a Hitachi 850 spectrophotometer fitted with a phosphorescence attachment. The transient absorption and phosphorescence decay were obtained by use of a nanosecond laser photolysis apparatus.I6 Photoexcitation was done by a Lambda Physik EMG IOlMSC excimer laser (XeF) which emits a short pulse of approximately 20 ns in width at 351 nm. For the detection system, a photomultiplier (Hamamatsu, R928) with an oscilloscope (Iwatsu, TS-8123) was used. Measurement at low temperature was made in a Dewar at 77 K in liquid N2. Conformational Analysis. Conformational analysis was performed by an empirical potential energy c a l ~ u l a t i o n ; ~in~this -~~ calculation, the van der Waals interaction energy between nonbonded atoms, intrinsic torsional potential energy associated with the rotation about C-C and C-0 bonds, and the dipole-dipole interaction energy were taken into account.22 The van der Waals energies were calculated by a Lennard-Jones type function and given as the sum over all pairs of nonbonded atoms including the terminal chromophores. The potential energy of electronic dipole moments was calculated by consideration of the potential energy of a pair of dipole moments, and total electronic potential energy was considered as the sum of them:
where U,j is the potential energy of thejth dipole moment in the electronic field induced by the ith dipole moment. For the present compounds, three dipole moments, the carbonyl bond of BP, the ether bond attached to BP group, and the amide bond attached to DBA group, were taken into account. The values of the dipole moments were adopted from the l i t e r a t ~ r e : 3.90 ~ ~ D for the carbonyl bond of BP, 1.30 D for the ether bond, and 3.00 D for the amide bond attached to DBA groups where the dipole takes an angle of 40’ with the reference to C-N axis. Dielectric constants of 7.09 and 3.3 were used for the sec-BuCI and for PMMA, re~pectively.~~ The total potential energy was obtained as the sum of the potential energies that came from the van der Waals interaction, the dipole moments, and the potentials of intrinsic torsional deformation. (16) (a) Tsuchida, A.; Tsujii, Y.; Ohoka, M.; Yamamoto, M. Nippon Kagaku Kaishi 1989, 1285. (b) Yamamoto, M.; Tsujii, Y.; Tsuchida, A. Chem. Phys. Lett. 1989, JSI, 559. (c) Tsuchida, A.; Tsujii, Y.; Ito, S.; Yamamoto, M.; Wada, Y. J . Phys. Chem. 1989, 93, 1244. (17) (a) Ikeda, T.; Lee. B.; Kurihara, S.;Tazuke, S.;Ito, S.; Yamamoto, M. J . Am. Chem. Soc. 1988, 110,8299. (b) Ito, S.; Takami, K.; Tsujii, Y . ; Yamamoto, M. Macromolecules 1990, 23, 2666. ( I 8) Flory, P. J . Statistical Mechanics of Chain Molecules; Wiley: New York, 1969. (19) Hopfinger, A. J . Conformational Properties of Macromolecules; Academic: New York. 1973. (20) (a) Ito, S.; Yamamoto, M.; Nishijima, Y. Bull. Chem. Soc. Jpn. 1982, 55, 363. (b) Kanaya, T.; Hatano, Y . ; Yamamoto, M.; Nishijima, Y . Ibid. 1979, 52, 2079. (21) Takenaka, A.; Sasada, Y. J . Cryst. Soc. Jpn. 1980.22, 214. (22) Smyth, C. P. Dielectric Behavior and Structure; The Technology Press, MIT: Cambridge, 1948. (23) (a) McClellan, A. L. Table of Experimental Dipole Moments; New Series 11/4, Springer: Berlin, 1967. (b) Kotera, A.; Shibata, S.;Sone, K. J . Am. Chem. Soc. 1955, 77,6183. (24) Riddick, J. A.; Bunger, W. B. Techniques of Chemistry, 11, Organic Soloents; Wiley: New York, 1970.
Figure 2. Perrin plot for BP-DBA system in sec-BuC1 glass at 77 K. From the slope of the plot, Ro was determined to be 1.56 nm.
Figure 3. Phosphorescence spectra of (a) DA-7, (b) DA-3, and (c) DA-I in sec-BuCl at 77 K. The excitation wavelength is 360 nm. Concentration of chromophores is 1.6 X IO-) mol L-’.Spectra are normalized to the same intensity at the peaks. Figure 1 shows the structural parameters used in this calculation. The parameters for the BP group and the DBA group were obtained from the data of X-ray analysis on MeO-BPZS and N-acetyl-DBA crystal,26and those of skeletal alkane chain were taken from the references by Abe et al.27 N + 1 rotational angles, &, &, ..., are needed to generate a given conformation for each DA-n compound.
Results and Discussion Spectroscopy at the Photostationary Condition. The absorption spectra of DA-n compounds compond to the sum of valeryl-DBA and M G B P spectra within experimental error, and no additional absorption band was detected. This means that chromophores of DA-n compounds do not interact with each other at the ground state. The critical radius (Ro) of phosphorescence quenching between BP and DBA was determined by the Perrin’s formula, eqs 2 and 3,28where I and lo are the donor (BP) phosphorescence I o / I = exp(vN’c) (2) v = (4/3)uRO3 (25) (26) (27) 631. (28)
(3)
Norment, H. G.; Karle, J. L. Acra Crystallogr. 1962, I S , 873. Harding, M. M. Acra Crystallogr. 1983, C39, 397. A h , A.; Jernigan, R. L.;Flory, P. J. J . Am. Chem. Soc. 1966,88, Perrin, F. Comp. Rend. 1924, 178, 1978.
Chain Length Dependence of Triplet Energy Transfer
100-
0
0
0
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3483
l
/A
0
P
...
zmw
Y
U.
y60-
Y
-
HW & O
0
3
a
20
-
o
"
;
;
;
l
S
CHAIN LENGTH (n)
t
;
Figure 4. Chain length dependence of quenching efficiency of BP triplet at photostationary condition (0)in sec-BuCI and ( 0 )in PMMA at 77 K. The quenching efficiencies are calculated from the ratio of phosphorescence intensity of DA-n compounds to that of MeO-BP. intensities with and without the acceptor (DBA), respectively, N' is the Avogadro number, c is the concentration of acceptor in moles per liter: then N'c is the number of molecules dissolved in 1 cm3 of solution, u is the sphere of quenching in cm3 with a critical radius, Ro. The value of Ro was determined from the slope of the plot of In lollvs c. Figure 2 shows a plot for BP-DBA system in sec-BuC1 glass at 77 K: Ro = 1.56 nm. The quenching efficiency for the DA-n compounds was estimated at a photostationary condition both in a rigid glass and in a polymer matrix at 77 K. Relative phosphorescence intensity of DA-n compounds (IDA+) was determined in reference to that of MeO-BP (IMeBp), which was chosen as the isolated BP model compound, and the quenching efficiency was evaluated by
800
600
400
WAVELENGTHlnm
Figure 5. Transient T-T absorption spectra in sec-BuCI at 77 K: DA-I (-); MeO-BP (- - -) 50 1.1s after excitation. The excitation wavelength is 351 nm. I
0
0
4 00
600
800
WAVELENGTH/ nm
Figure 6. Transient T-T absorption spectra of DA-3 in sec-BuCI at 77 K: 0.5 ps after excitation (-), 4 ps after excitation (---). The excitation wavelength is 35 1 nm.
IDA-?IIMcO-BP*
Figure 3 shows the normalized phosphorescence spectra of DA-7 (a), DA-3 (b), and DA-1 (c). The quantum yield of BP phosphorescence is reported to be 0.9,Iaand that of DBA calculated from phosphorescence spectrum is 0.005, which is much smaller than that of BP. In the case of DA-I, the obtained spectrum is mainly of DBA emission, and the peak intensity of BP emission is only ca. 1/1000 compared with that of MeO-BP. This shows that for DA-I the energy transfer from BP to the DBA chromophore occurs completely. In the case of the DA-3 spectrum, the peak of BP is higher than that of DBA, but as mentioned above, the quantum yield of DBA is so small that the quenching efficiency is estimated to be close to unity (0.998). Figure 4 shows the chain length dependence of quenching efficiency. The energy transfer is almost completely accomplished for the samples DA-I, DA-3, DA-4, and DA-5. On the other hand, the transfer is insufficient for the compound DA-7. This means that in the chain lengths shorter than n = 5, all DBA groups exist at the inside of the critical radius of BP, but for DA-7 some parts of the DBA groups exist outside of the Re The chain length n = 5 is a critical length of perfect energy transfer. At the most extended conformation of n = 5, i.e., in the all-trans conformations of methylene chain units, the distance between the carbonyl group of BP and the C-C double bond of DBA is ca. 1.5 nm. This value is almost equal to the critical radius obtained from the Perrin plots: 1.56 nm. The quenching efficiency at the chain length n = 7 in PMMA matrix is higher than that in sec-BuC1 matrix. Laser Photolysis. Figure 5 shows the transient absorption spectra of DA-I (solid line) and MeO-BP (dotted line) in sec-BuCI at 77 K, at 50 1.1safter excitation. The peaks at 420 and 540 nm are assigned to T-T absorption of DBA triplet and BP triplet, respectively. The DA-I shows the same spectrum as that of DBA even just after the excitation, i.e., at a few tens of nanoseconds. This means that the energy transfer of DA-1 is accomplished within a nanosecond, probably in a picosecond time range. Figure 6 shows the transient absorption spectra of DA-3. The spectra shows both the BP triplet absorption band (540 nm) and the DBA triplet one (420 nm) a t the early stage after the exci-
I
I
,
,
,
,
,
SWns cc
I , 0 Figure 7. Decay curve of BP triplet and the rise curve of DBA triplet for DA-3 in sec-BuCI at 77 K. The broken line represents the time that BP is excited. The excitation wavelength is 351 nm.
,I
1
tation. With the elapse of time, the BP absorbance decreases with the increase of DBA absorbance. This indicates that the energy transfer from BP to DBA mainly occurs in a microsecond time range in the solid matrix. Figure 7 shows the decay curve of BP triplet and the rise curve of DBA triplet for DA-3; similar behavior was observed for the samples longer than n = 3. Besides the slow transfer process, prompt energy transfer also occurs immediately after excitation; that is, some of the BP triplet decays quickly after t = 0, which is indicated by the broken line in the figure. In place of BP, considerable absorption of the DBA triplet is already detected at the end of the laser pulse. This behavior indicates that a part of the energy transfer occurs at an extremely fast rate, and most of the subsequent energy transfer occurs with a slow rate. The efficiency of this rapid energy transfer was determined as the ratio of the triplet DBA concentration just after the excitation to the total concentration of DBA triplet. The triplet DBA concentration of DA-1 compound was used as a reference of the total concentration, because the triplet energy of DA-1 is completely transferred from BP to DBA by the end of the laser pulse period.
3484 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
Katayama et al.
90
0
.
-
. 8
-901
1
2
3 4 5 CHAIN LENGTH ( n )
6
L
o
7
Figure 8. Chain length dependence of the efficiency of prompt triplet energy transfer: (0)in sec-BuCI and ( 0 )in PMMA. 0
270
90
Figure 10. Conformational energy map of DA-I. Numerals on the contours are the energy values (kcal mol-') relative to the minimum energy at the position marked by X.
I
a I
I
I
1
,
b I
Figure 9. Phosphorescence decay curve of DA-n compounds (a) in secBuCl and (b) in PMMA at 77 K. The excitation wavelength is 351 nm.
Figure 8 shows the calculated efficiency of the prompt transfer. As mentioned above, the efficiency for DA-1 is unity. The value decreases with increasing chain length, but a fairly large value, 0.3,was obtained for DA-3. Considering that the total quenching efficiency of this compound is close to unity, the fraction is not so significant. This prompt quenching is probably due to the close approach or partial overlap of large aromatic rings in the frozen state. Such geometrical arrangement is likely to appear with a higher probability for the shorter chain samples. T-T Energy Transfer Rate and Computer Simulation. The wavelength ranges of the T-T absorption and phosphorescence emission overlap with each other and the decay profile of transient T-T absorption of DBA is deformed by the BP phosphorescence. Hence, the BP phosphorescence decay was measured to determine the rate of energy transfer. Figure 9 shows the BP phosphorescence decay of DA-n compounds in sec-BuC1 (a) and in PMMA (b) at 77 K. The decay of DA-I was not detected due to its fast energy-transfer rate. For the other compounds, the decay curves are nonexponential and strongly dependent on the chain lengths. Thus, the decay profile is quite sensitive to the conformational distribution of the D-A chains. Analysis of this nonexponential decay was carried out with Dexter's equation, in which the distance between BP and DBA was estimated from conformational energy calculation. The calculations were performed by the empirical potential functions described in the experimental section. Figure 10 shows the conformational energy map for DA-I. This map was drawn from the potential energies calculated at intervals of 10' for 4, and 42, which were taken as Oo at the trans conformation. The energy minima are marked by the symbol X, and the contours are drawn every 2 kcal mol-' relative to the minimum. The energy map indicates that the energy minima of the DA-1 are located at 120° and 240' of 4i angle. These values were adopted for d1 angles and for the other angles, 42-4n+i,three
Figure 11. Distribution function of R for the DA-n compounds (a) at 143 and (b) at 333 K. The ordinates show the fraction of conformers (O.l/division) at a distance increment of 0.02 nm.
rotational isomers, trans, gauche (+), gauche (-), were considered in the following potential energy calculation. On the basis of rotational isomer 3" x 2 conformations were generated, and the fraction of the ith conformation,1;., was calculated by eq 4 under the assumption that the distribution of conformations
1;. = e x p ( - E i / k T ) / C e x p ( - E i / k T ) i
(4)
obeys the Boltzmann relation, where Ei is the calculated potential energy for the ith conformation, according to the procedures described in the Experimental Section. In eq 4, T = 143 K was used for sec-BuC1 glass. This temperature is the melting point of sec-BuC1, and therefore, the conformation of DA-n compounds will be fixed at this temperature. In the same way, T = 333 K was used for the PMMA matrix. This temperature is the polymerization temperature of methyl methacrylate. For all the conformations the interchromophore distance, R, was calculated: R was defined as the distance between the carbonyl carbon atom of BP and the carbon of the amide group, as shown in Figure 1. The lowest triplet state of BP is n-r* which localizes on the
rhe Journal of Physical Chemistry, Vol. 9S, No. 9, 1991 3485
Chain Length Dependence of Triplet Energy Transfer
1
TABLE I: Averaged Interchromophore Mstances of DA-n Communds sample ~~~
( R ) in see-BuC1, nm
(R)in PMMA, nm
0.74
0.75 0.98 1.06 1.16 1.34
DA- 1 DA-3 DA-4 DA-5 DA-7
0.98 1.09 1.22 1.44
carbonyl group. On the other hand, the DBA triplet is m r * and extends over the planar aromatic rings. The amide group is found to be almost coplanar with the phenyl rings of DBA.27 Then, the adopted distance is the shortest distance between the electron orbitals that belong to the D-A chromophores. The distribution functions of R for n = 3, n = 4,n = 5 , and n = 7 at 143 and 333 K are shown in Figure 1 I , in which the distribution was calculated at every 0.02-nm increment. The ensemble-averaged interchromophore distance of each DA-n compound, (R), was calculated by eq 5 , where R, is the (R) = XRifi/uj
0
0.2
0.L
0.6
0.80
t / ms
0.2
,
I
,
0.L
0.6
0.8
t / ms
Figure 12. Phosphorescence decay simulation (a) in set-BuCI and (b) in PMMA at 77 K. The solid lines are the calculated curves. The dots are observed points. The employed parameters are 0.1 1 nm for L and 6 X lo-'* s-' for ko.
(5)
interchromophore distance of the ith conformer and J;: is the fraction of the ith conformation, given by eq 4. Table 1 shows the ( R ) values calculated. The value increases nearly 0.1 nm/methylene chain and the distribution spreads with increasing chain length. The distribution functions spread wider in the PMMA matrix than in the sec-BuCI matrix. The difference between them arises from two factors: the temperature in which molecular motion is fixed, and the dielectric constant of the media. The result obtained in this study is mainly due to the effect of temperature, and the effect of dielectric constant is rather minor on the conformation. Theoretical treatment of triplet energy transfer was performed by using the rate constant expressed by Dexter' in eq 6, where K is a constant with the dimension of
km = (2r/h)z2J~D(a) JA(~) de Z2 = ?f exp(-2R/L)
(6) (7)
energy, L is a constant called the effective average Bohr radius, is the emission spectrum of donor,fA(r) is the absorption spectrum of acceptor, and R is the donor-acceptor distance. For all the samples, the donor is BP and the acceptor is DBA; thus the Franck-Condon factor, JfD(e) fA(3) ds, is constant. Then, Dexter's equation is expressed by
fD(D)
kTT = ko exp(-2R/L)
(8)
and the energy-transfer rate for the ith conformation is expressed by eq 9, where R, is the donor-acceptor distance of the ith con-
km, = ko exp(-2Ri/L) (9) formation. Then phosphorescence decay is expressed by the sum of the decay in the ith conformation multiplied by the fraction of the conformation: I
Io exp(-t/7o)Xh exp(-km,t) i
(10)
where so is the intrinsic lifetime of B P so = 5 ms. This equation was used for BP decay simulation where the Bohr radius, L, and ko were employed as the variable parameters. The best-fit parameters were 0.1 l nm for L and 6 X 10l2s-I for ko. These values are in fairly good agreement with those of the intermolecular system, from benzophenone to naphthalene, studied by Mataga et al.:29 L = 0.1 1 nm, ko = 1.64 X lOI3 s-I. Galley et aLm studied the intermolecular energy-transfer system from carbazole to naphthalene and obtained a value of L (0.107 nm) similar to our value but their ko value (1.8 X IO" s-l) is smaller than ours. This difference may be due to the different characters of ?r* and n* in the triplet state. ~
~~~
(29) Kobashi. H.;Morita, T.;Matap,
N.Chem. fhys. Lett. 1973,20,376. (30) Strambini, G. B.; Galley, W. C. J . Chem. fhys. 1975, 63, 3467.
0.5
1
cR>/nm
1.5
Figure 13. Chain length dependence of the rate constants of the intramolecular T-T energy transfer and of the intramolecular S-S energy transfer. The rate constants of T-T energy transfer were calculated with the obtained parameters, and the rate constants for S-S energy transfer are the values reported for dinaphthylalkane~.~~~
Figure 12 shows the results of this simulation: the solid lines indicate the calculated decay curves, and the dots indicate the observed points. The simulation is fairly good except for n = 3 in sec-BuCI glass. Figure 13 shows a comparison of the chain length dependence of the rate constants for the present intramolecular T-T energy-transfer system and for the intramolecular S-S energy transfer of dinaphthylalkanes reported by Ikeda et The rate constant of T-T energy transfer is much smaller than that of S-S energy transfer at a fixed chain length and is strongly dependent on chain length, i.e., about one-tenth decrease per methylene unit. Analyses based on Dexter's theory were performed for the slower component of energy transfer observed in the time range from nano- to millisecond regions. The agreement is satisfactory, but the other rapid component, which is revealed by the T-T absorption measurement, is out of the prediction of Dexter's equation; calculation for the DA-n molecules cannot reproduce such a prompt transfer rate. At the present stage, we do not know the origin of the prompt component, but two possibilities are noted. (1) The calculation is based on the distance between two spatial points representing the shortest distance between the chromophoric units. However, the real system consists of large aromatic rings, and the A electrons are delocalized throughout the aromatic planes. The geometrical arrangement may take a partial approach, or
J , Phys. Chem. 1991, 95, 3486-3491 partial overlapping of the aromatic rings. The rate under such contact arrangement cannot be evaluated by the present calculation. This may be true for the shorter chain lengths. (2) Dexter’s theory indicates that the transfer rate constant should decrease exponentially with the distance, according to the form of eq 8. This relation is given as follows: in Slater-type 2P orbitals the decay part of electron orbitals is exponential of the form e-=#/*, and the square of the overlap of two orbitals gives the distance dependence e-p’L, where t = 2u0/Zeff(Zeff:effective nuclear charge). A lot of works on the T-T energy transfer support the validity of this approximation. However, Galley et al. found an exceptionally steep rise of the transfer rate at distances shorter than 1 n ~ n , ~ They O pointed out the possibility that for intermolecular separation of 0.4-0.5 nm the effective nuclear charge may become larger than unity and give rise to a steeper distance dependence near the van der Waals contact. It is clear that eq 8 cannot be applied to such a short-distance D-A pair. In the present system, for example, the decay data for DA-3 fairly deviate from the theoretical curve, and the prompt transfer of DA-1 is outside the scope of the theoretical prediction. That is, the average distance ( R ) of DA-1 is 0.75 nm; then we can estimate the value of kTTfrom the line for the T-T energy transfer in Figure 13 as krr = 7 X IO6 s-]. This transfer rate should be easily observed by our apparatus, but the actual process finished within a picosecond time range. Detailed analysis of this prompt energy transfer in the picosecond time range is now in progress.
equation. The result of simulation was in fairly good agreement with the experimental values. The rate of T-T energy transfer is strongly dependent on chain length, Le., about onetenth decrease per methylene unit, and is 103-106 times slower than that of S-S energy transfer. The appreciable part of the bichromophoric compounds is in an extended form in rigid solution, but it is slightly shrunken in the PMMA matrix. There is still controversy as to whether a “through space” or “through bond* mechanism governs the process of intramolecular T-T energy transfer.’ 1 ~ 1 4 * 3 1 Both mechanisms are possible, and the problem is which one is predominant for a given molecular structure. In the current study, we used a flexible single chain molecule and tried to analyze the data with the through space mechanism, since in the case of the flexible chains the average distance between D-A chromophores is relatively short compared with the systems of rigid spacer in the same number of bonds. The following points strongly suggests the validity of this mechanism: (a) The marked chain length dependence can be reproduced by this treatment. (b) The obtained two values, L and ko, are in agreement with those of intermolecular transfer systems. (c) The decay curves are affected by the molecular conformations fixed in different matrices, e.g., in sec-BuC1 and in PMMA. The present results indicate that the through space mechanism is adequate for the flexible D-A molecules.
Concluding Remarks
Acknowledgment. We thank Professor Masami Okamoto of Kyoto Institute of Technology for instructions on the laser photolysis at a low temperature.
Intramolecular T-T energy transfer of bichromophoric compounds connected with methylene chain ( n = 1-7) was directly measured by using the nanosecond laser photolysis. The donoracceptor distance was calculated by a conformational analysis, and the phosphorescence decay was simulated by using Dexter’s
(31) (a) Overing, H.; Paddon-Row, M. N.; Hepperer, M.; Oliver, A. M.; Cotsaris, E.; Verhoevcn, J. W.; Hush, N. S. J . Am. Chem. Soc. 1987. 109. 3258. (b) Oevering, H.; Verhwen, J. W.; Paddon-Row, M,N,;Cotsaris, E.; Hush, N. S. Chem. Phys. Lett. 1988,143,488. (c) Kroon, J.; Oliver, A. M.; Paddon-Row, M. N.; Verhoeven, J. W. J . Am. Chem. SOC.1990,112,4688.
A Redetermination of the ‘B2”
-
’A,, Fluorescence Quantum Yield of Benzene Vapor
David B. Johnston and Sanford Lipsky* Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455 (Received: October 16, 1990)
The fluorescencequantum yield of benzene vapor excited at 253.7 nm and at pressures from 10 to 50 Torr has been determined at 22 OC by comparison with the fluorescence from a dilute solution of benzene in cyclohexane. The value thus obtained is 0.044 f 0.006, which is significantly lower than has been reported in all previous investigations. Although the origin of the discrepancy remains unknown, a theoretical argument is presented that tends to support the lower value.
I. Introduction In 1962 Ishikawa and Noyesl reported a fluorescence quantum yield of 0.22 0.04 for benzene vapor a t 20 Torr and 29 O C excited into its first absorption system a t 253.7 nm. The value of 0.22 was obtained by comparison of the emission from benzene with that from biacetyl (excited at 435 nm), for which an absolute emission quantum yield had been earlier determined by Almy and Gillette.2 Several years later, Poole3 using basically the same technique reported a rather similar quantum yield of 0.27 (also 9 and for excitation at 253.7 nm). The a t 20 Torr and ~ 2 OC pressure dependence of the quantum yield was shown to be rather negligible as was too the effect of 80 Torr of cyclohexane.
*
(1) Ishikawa, H.; Noyes, W. A., Jr. J . Chem. Phys. 1962, 37, 583. (2) Almy, G. M.; Gillette, P. R. J . Chcm. Phys. 1943, 1 1 , 188. (3) Poole, J. A. J . Phys. Chem. 1965.69, 1343.
In 1965, Noyes, Mulac, and Harter4 attempted a direct absolute measurement of the benzene fluorescence quantum yield and obtained a value of 0.18 f 0.04 at 253.7 nm over the pressure range from 8 to 14 Torr. This value, although appreciably lower than those obtained via the comparison with biacetyl, was nevertheless considered to be within the range of estimated uncertainties in these rather difficult measurements. In 1977 another absolute value of 0.19 f 0.02 at -254 nm was reported by Rockley5 using a photoacoustic technique, and since then a variety of investigationsbg into the fluorescence of single vibronic levels (4) Noyes, W. A., Jr.; Mulac, W. A.; Harter, D. A. J . Phys. Chem. 1966, 44,2100. ( 5 ) Rockley, M. G. Chem. Phys. Leu. 1977, 50, 421. (6) Parmenter, C. S.; Schuyler, M. W. Chem. Phys. Leu. 1970. 6, 339. (7) Abramson, A. S.;Spears,K. G.; Rice, S.A. J . Chem. Phys. 1972,56, 2291.
0022-3654/91/2095-3486$02.50/00 199 1 American Chemical Society
