Nonradiative relaxation processes of the higher excited triplet states of anthracenes studied by a double excitation method

ChemicalPhysics

27 (1978) 399-407

.’

I

..‘- 0 North_Hohand Publishing Company

-: NoPi&kirvERELAXATION OF ANTHBACENES

~ROCESSESOFTHE

.. Shunsuke KOBAYASHI *, Koichi KIKUCHI

and Hiroshi

Facult); of Science, Tohoh Aramaki, Aoba, Sendai 980, Japan Department

HIG~IEREXCITEDTRIPLETSTATES

STUDIED BY A DOUBLE EXCITATION METHOD

of Chemistry,

KOKUBUN

Uttiversity,

Received 2.5 August 1977

lritersystem crossing from higher excited triplet states, Tn (n > 2), to the lowest excited sib&et state, S1, has been studied by a newly devised double excitation method. The quantum yields of Tn --f S 1 intersystem crossing of anthracene, 9methylanthracene, 9-phenylanthracene, 9,lOdichloroanthracene and 9,10-dibromoanthracene are determined to be 2.6 X 10m5.3.6. X lo*, 4,7 X lo*, 1.5 X 103 and 2.7 X IO@, respectively. The large increases in quantum yields of mesoderivatives are interpreted ia terms of level inversion of Ta and Sr with substitution at the meso-position. Internal heavy atom effects are observed in Ts + S1 intersystem crossing. In comparison with Th +St intersystem crossing the rate of Ta -t Tt internal conversion is estimated to be 10” s-r for ail compounds studied.

1. Introduction.

The investigation of the nonradiative processes of the fluorescing state in anthracene and its derivatives has received considerable attention from experimental and theoretical points of view [I 1. Their fluorescence yields depend on both temperature [2] and phase [3]. The decreases in fluorescence yields are accompanied by the increases in triplet state production. The sum of the quantum yields of fluorescence and intersystem crossing is unity within experimental error [4-7; 1, p_ 25 l] _Therefore, it is clear that intersystem crossing is responsible for the nonradiative decay of the fluorescing state. Kellogg [3] confirmed that in solution the second triplet state, T2, of anthracene is slightly below the -lowest_excited singlet state, Sl. He explained the remarkable change of the fluorescence yield in going from solution to crystal by the level inversion of S1 and TI, assuming that in crystal the dispersion force lowers ST relative to T2.-This explanation was confried by the observation of the temperature dependence of the delayed fluorescence intensity in crystal * Present.address: Electrotechnical Laboratory, Tar&hi, Tokyo 188, Japan.

[8], and also supported by the existence of the pressure effect on the fluorescence lifetime at 77 K [9] _ The fluorescence yields of meso-substituted anthracenes increase with decreasing temperature. At 77 K it becomes unity and no triplet formation can be detected [5,10,11 j. These facts are explained by the level inversion of S, and T, with substitution at meso-position. The lack of the pressure effect in 9-methylanthracene and 9,10-diphenylanthracene supports this explanation [9]. However, the T2 levels of meso-derivatives [5] have not been determined spectroscopically. An alternative explanation was cffered by Kearvell and Wilkinson ‘[12]. On the basis of the temperature dependence of the fluorescence yield, the rate of intersystem crossing can be represented in terms of an Arrhenius equation

k S+T = ki-.= +-$+= exp(-ES,TlkT)

.

(1)

The activation energy, Es_T, is regarded as the energy gap between S1 and T, (II B 2) into which intersystem crossing occurs. They proposed that in anthracene the intersystem crossing occurs mainly through Tz as a temperature independent process but in meso-derivatives the temperature dependent intersystem crossing through T, dominates and T, is less likely to contribute to the overall values of 7cS_T [12,13] _

400

S. Kabaykhi et ai./NonradiativerelaxationpmCessesin anthraceties -. :. ;

;’

.. _

:

-_j- .. .--

However, the mechanisms ofintersystem crossing of anthracenes seem to be more complicated than the above models. The nonradiative rate of low pressure anthracene vapor shows no clear variations with excitation en-rgy over the range-where T2 and T3 may be situated 114,151. On the basis of the theory of nonradiative transition, the intersystem crossing must be interpreted as crossing directly from S, to the quasicontinuum of T, with an enhanced probability due to the presence of T2 and/or T3 116,171. Sharf and Silbey [lS] predicted that the rate of intersystem crossing depends on the square of the energy gap, therefore, the intersystem crossing from S, to T2 and TX can occur if T2 and T, are situated in the vicinity of s,. The present investigation is concerned with T, +S, intersystem crossing of anthracene and its mesoderivatives, which can be regarded as the inverse process of the intersystem crossing described above and is expected to provide further information about mtersystem crossing between closely lying states. With a newly devised double excitation method we have observed S, + So fiuorescence-resulting from the excitation of S, through T, and determined the quantum yields of T, --f S, intersystem crossing. The results show clear differences between anthracene and mesoderivatives and are interpreted in terms of the level inversion model of S, and T,.

eosin (1 X 1O-5 mol &tr’j.‘I ?remo!ar extinctjon coefficients of T-T absor$ tion, eT, were determined by the experiments of the energy transfer from eosin triplet-to arrthracenes [20]. Absorbance.df Tn + T1- absorptiorrat 14400 cm-r was measured by a ToshibaV-R65 cut-off ftiter, a Narumi I@423 monochromator, an EMI 9659QB pho-tomultiplicr and 2 Tektronix 545B-lA5 oscilloscope_ An Ushio UXLJSODSS l5OW Xe-arc Iamp was used as a monitoring light source. The relative values of the two-photon absorption cross section at 2 X 14400 cm-l were determined by a transverse excitation with a IO X 10 mm2 cell containing 1 x IO-4 mol drn-3 degassed ethanol solution. The system collecting fluorescence was the same as that of &e double excitation method. Delayed fluorescence was measured by two different excitation methods; p ffash and ns laser excitation. The total energy 6f the laser was measured by a TRG balhstic therrnopile model CDC 108. Anthracene, 9-metjrlanthracene, 9-phenylanthracene, 9,10-dichloroanthracene and 9,10-dibromoanthracene were purified by repeated recrystallization from ethanol, thin layer chromatography on silica gel layer with nhexane as a developing solvent, and vacuum sublimation. Eosin was purified by repeated recrystallization from ethanol. Ethanol (99.5%; G.R. grade, Wako Junyaku) was used without further purification.

2. Experimental

3. Results and analysis

The fluorescence following T, + T, absorption was measured with the double excitation method which utilizes two excitation light pulses fired at appropriate time intervals described previously [19]. The energy transfer from eosin triplet produced by a conventional f&h photolysis was used to populate T, of anthracenes [20]. Subsequently T1 was irradiated to excite to the higher excited states with 2 cryptocyanine Q-switched ruby laser at 14400 cm-l. Fluorescence was observed with an RCA lP28 photomultiplier and a Tektronix 7904-7Al9, 7B92 oscilloscope through 2 5 cm saturated aqueous cupric sulfate sohrtion filter, a Toshiba V-V40 band path filter, and a Hitachi G-3 monochromator. Measurements were made at room temperature in a degassed ethanol solution containing arrthracenes (1 X 10d4 mol drne3> and

Fig. 1 shows the relation between the laser and the normal fluorescence intensity produced by the double excitation method. The fluorescence consists of two kinds of fluorescence; one shows a squared dependence and the other shows a linear dependence on the laser intensity. The former is a two-photon absorption tluorescence, F(T2), caused by simultaneous S, + So (m 2 1) two-photon absorption. The latter is proportional to T, concentration under the constant laser intensity.as shown in fig, 2 and is termed as a double excitation fluorescence;F(I1), because it is caused by the successive excitation-of T, and S,..In addition to the normal fluorescence, a long-lived delayed fluores.’ cence, fDF, isalso observed which is produced by : .. T1-T1 annihilation. The.time integrated normal fluorescence intensity,

’

401

S. Koboymhi et aL/Notiadiative relaxationprocesses in anthracenes

i

L

I

absorption in photons cmT3 s-l (= the number of molecules excited into S1). In the double excitation fluorescence,

and F(f& = ‘yL&=o’h$ ~~&~

Law

Intemlty

Fig. 1. Relationship between the laser and the normal fluorescence intensity of 9-methylanthracene produced by the double excitation method. F: total fluorescence intensity, F(IZ): two phaton absorption fluorescence intensity.

dt ,

‘0)

where rxLis the geometrical factor for laser excitation, u’ the apparent absorption cross section of T1 moIecules in cm2 molecuW1, NT the number of T, molecules per cm3, and I,:,(t) the excitation laser intensity in photons cmA2 s-l. In this equation, the decay of T, during laser excitation (= 30 ns) is neglected. The apparent absorption cross section consists of twoterms: (i) a direct excitation into an excited singlet state by S, + T, absorption and (ii) an excitation into a higher excited triplet state by T,, -+ T, absorption followed by intersystem crossing to singlet manifold; o’=o&

"T1)+QT+Su(T,+T1),

(4)

where u is the one-photon absorption cross section in cm2 molecule- 1 and $*_,s is the quantum yield of T, + SI intersystem crossing. in the-two-photon absorptioiI fluorescence &j,(t) = 6 No &(0 and (9 where 6 is tke two-photon absorption cross section in cm4 s photon-l molecule-l and No is the number of the ground state molecules per cm3. Since the decay of T, is neglected duripg the laser excitation, the delayed fluorescence intensity is written as follows [21]

Triplet Cmwntraiion I lW6-mol.dmJ Pi. 2. Relatkkhip between the tiplet concentration and the double excitation fluorescence intensity of 9-methylantbracene.

F, is generally described by

whkre f(t) is the fluorescence intensity, (Ya geometrical factor depending on apparatus and experimental conditions, @$ the fluorescence yield, and &b(t) the light

f~~=~&Pk~_&,

(6)

where aF is the geometrical factor of the delayed fluorescence caused by flash excitation, p the efficiency of S, formation by T,-T, annihilation and kT_T is the second order decay constant of T, in cm3 molecule-l s-l _ In a previous paper [19] we have determined u* of anthracene to be 0.91 X 1O-24 cm2 molecule-l in comparison with the two-photon absorption fluorescence. There is no satisfactory agreement among the reported values of 6 of anthracene [ 1, p. 621. To avoid

:

402

S. Kobayasli.et@/Nonradiativerelaxatiqnprocfrses-inant@acenes

--

1

dt .,

=-Y

I

I

I

I

.2

.4

.6

.8

.D (42lnml

Fig. 3. Relationship between ?he triplet concentration and the delayed fluorescence intensity of anthracene. Flash: flash excitation, SHG: Iaser excitation (347 nrn)_

this ambiguity, we have determined the value ofu’ by measuring the delayed fluorescence which has been extensively studied with an emission-absorption flash technique [20,21] _The fluorescent volume of the double excitation fluorescence is smaller than that of the delayed fluorescence, because the sample cell is partIy irradiated by laser through an iris to eliminate scattering light from ceil wall. Therefore, the geometrical factor of the double excitation fluorescence is not equal to that of the delayed fluorescence. To determine the correlation factor, 7 m (Y&Y~, we compared the delayed fluorescence caused upon excitation by the flash and the second harmonics of a ruby iaser. The former is the same geometry as the

first stage and the latter is the same geometry as the second stage of the doubIe excitation method. Fig. 3 shows the relations between _# and NT in the flash and the laser excitation. Since jPDFis proportional to NT in both cases, the ratio of the slopes gives the square root of 7. From eqs_(3) and (6) and the relaxation NT/Nk =&-(A)/~~(Xjcl, we obtain

(7). where D.$) is the tibsorbance of T=T absorption atwavelength h, d the opticalpath length of a cell, and Ni is the Avogadro number divided by l@_ The value of kT_-@i/q-@)d in eq. (7) was determined to be 2.2 X lo3 s-l at h =.421 mn from the observed.s&ond order decay constant~of Tr [21]. Puttingi =-0.077 [Z ] and y = 0.45, we determined the (I’ value of anthracene to be 5.2 X lo-” cm* molecule-r. This value is not very different from that previously obtained.091 X 10Wz4cm2 niolecule-1 which was determined by measuring the two-photon absorption fluorescence r191The double excitation fluorescence of meso-derivatives was measured relative to that of akhracene. Using a fluorescence~intena~ty ratio p 5 F($)/F(12), we get a formuIa for the relative value of u u’,/u;=fl x 6x N T,r N 0,x /fl r Sr N T,x N 0,r 2 where indices r and x represent reference and unknown, respectively. The ratio of 6 was determined by the transverse excitation by the use of a 10 X 10 mm2 rectangular cell to avoid .the.geometrical uncertainty of a cylindrical cell. The results are given in table 1. The (T’values of 9-methyianthracene and 9-phenylantbracene~are the same order of magnitude, but one order of magnitude larger than that of anthracene. Internal heavy-atom effects are obvious in 9,10-dicbloroantbracene

and 9,10-dibromoantbracene.

Fig. 4 shows the log-log plot of u’ versus ~&$, the sum of the square of atomic spin-orbit coupling Table 1

Two-photonabsorption crosssection (61,and apparent akorption crosssection (a’) %el

4eI

0.

(Cm2 molecule-t) anthracene 9-methylanthracene 9qhenylanthracene 9,lOdichloroanthracene 9,lO-dibromo-’ anthracene

0.50 0.08 * 0.01 1 1 0.94 0173* 0.03

5.2 x 10-4 6.5 x 10-23 411 x 10-23

1.0

(5.8 F 0.5) x 10

3.7 x 103’

3.6

11.0i 0.1) X.103

6.5 x.io-e

S..Kobayashi et aL/&onradiative relaxatioti processes in anthrakenes

403

cm-t), could not be determined, because the decay of the tripIet is so fast that enou& concentration of the triplet state could not be obtained. By the substitution; ET at absorption maximum of'the ‘Big +3B& transition is r.:duced but its integrated intensity is little affected. The substitution slightly affects the_ value of eT at 14400 cm-r. As to e-f at 14400 cm--1 of anthracene our value is four times smaller than that of Meyer et al. [25] in alcohol at 113 K.

4. Discussion 4.1. Direct S, + T, radiative transition probabiiity -24

4 lw

,

I

I

5

6

7

y:

Fig. 4. Plot of fogd (in cm2 molecule-L) versus log ZQj-& (ii cm-‘). The data plotted are for the following molecules: (I) anthracene; (2) 9-methylanthracene; (3) 9-phenylanthracene; (4) 9.10-dichloroanthracene; (5) 9,lOdibromoanthracene.

factors [22-241. A linear relationship between d and E& is seen in the meso-derivatives, but anthracene deviates from this relation. The molar extinction coefficients of the T-T transition of anthracenes at 14400 cm-l are shown in table 2. In the case of 9,10-dibromoantbracene, er( 14400

It is diffct.!t to evaluate the spin-forbidden radiative transition probability of aromatic molecules. For anthracene the S, + T, radiative transition probability is not known but the T1 +- SO radiative transition probability h..s been measured [26] - We will evaluate the S,,, + T, radiative transition probability in comparison with &heT, + So radiative transition. The radiative lifetime of T1, r:, of anthracene was reported to bl: 180 s [26]. The T, + S, radiative transition probability is expressed as fallows [24, p. 171;

where Fe is t!re mean wavenumber of phosphorescence spectrum. To estimate the absorption cross section of the T, + So transition, we make the approximation

Table 2 Molar extinction coefficient (ET), absorption cross section (u) and oscillator strength cfosc) of the triplet State r&(3 B; g + ’ R;u)

q (14400 cm-‘) ET(xm=)

anthraccne 9-methylanthracene 9-phenylanthracene 9, IO-dichloroanthracene 9,lOdiphenylanthracene

a) Ref. [19].

5.2 x 104 a)

(at 421 run) 4.3 x lo4 a) (at 424 run) 1.4 x 10~ 4 (at 430 mn) 4.6 X 104 (at417nm) 2.6 X lo4 (at 421 nm)

DCr, c Tt) at 14400 cm-’

(cm2 molecule-‘)

0.16

1.0 x 10-a

2.0 x 16’9

0.18

1.1 x 10-3

1.8 x 10-19

0.13

2.0 x 10-s

1.DX 10-19

-

1.4 x 10-3

2.4 X lo-”

404

.. _.

:.

S. _K&ymhi et aI.lNonradia~~~ielarnrioh processes in anthr@cen&i

If di-= 1 2 Em; @a, where ATa-is the width of T, i So abstirption band. &t&g $, = 13500 &I-~ and. .. Aa .? 6000 c.$?l [27,28], we obtain emax = 1,x 1o-5 mol-l cm-l; or u max -. (T1:+- S;) = 4 X lo-T6 cm* moiecule-1. ‘#I; en&y levels of lower excited singlet and triplet statei of anthrabene are shown in fig. 5. The O-O band.of the Sl(lB2n) +- SO(lAl& transition lies at 26600 cm-l. The second singlet sfate, S,(IB,u), is reported to be located at about 1500 cm-l above the lBzU o&in [29]. The O-O band of the Tl(3B2,) + !@A,,) transition lies at 14900 cm-l [27]. In the double excitation method the triplet molecules are excited to 29300 cm-1 above the ground state and the 1B2Uand lB3,, states may be excited. From the spinorbit coupling selection rules, the 3B,, + IA,, radiative transition is orbitally allowed [30]. The radiative transitions, lBzu -+ 3B2u and lB3” + 3B2,,, are. both orbitally forbidden. Therefore, their transition probabilities may be much smaller than that of orbitally allowed 3g2a + 1A,, radiative transition. As the value of d is two order of magnitude larger than that of @B2,, + 1Al,), the contribution of a@, + T1) to d in eq. (4) may be neglected.. Although mono-substitution to the meso-position reduces the symmetry from Dm to C2v, the absorptionspectra(S1-+SO,Sm +S, [31] andT,+T1)of 9-methylanthracene and 9-phenylanthracene are essentially similar to those of anthracene. The ItEthyl OT phenyl substitution does not significantly affect the electronic states of anthracene. Then the selection rule for orbitally forbidden transitions may not so largely be broken by the substitution and the values of o(lB, f- 3B2,) or o(!B3, +- 3B2,) of mono-substituted anthracenes may be the same as those of anthracene at least in order of magnitude. Therefore, the contributions of direct S, + T1 transitions to d may also be neglected in mono-substituted anthracenes. The same approximation is valid for 9,10-disubstituted anthracenes. On the assumption that d is equal to $T_s u(T, + Tl), we determined the value of $=+ by using the experimental value of u(T,, + Tl) at 14400 cm-l.

:

Table 3

Quarturn yield fill 2 S intersystem &ok& meanliF~&eof thS triple~tianifold (FT)

(&ii)

The energy levels of triplet states of anthracene are

and

..

anthraceni

2.6x 10s

9-metbyltithracene 9-phenylanthracene 9,lOdichloroanthracene 9,lOdiirotioanthracene

3.6x lo*

0 76 x lo-l4 0:73 x lo-‘3

4.7 x 104

ii1

x lo-‘3

1.5 x lo* 2.0 x lo-‘3 = 2.7 X lo@ a) 2.9 k lo-r3

a) The value of &f+S of 9,lOdibromoanthiacene is calculated on the assumption.that oCr, +Tl) of 9,lO&mmoanthracene is the same as that of 9,lOdichloroanthracene.

shown in fig. 5. Kellogg has observed that 3Bl, is 11200 cm-1 above 3B, and is about 500 cm-1 below lB2n [3]. The third triplet, 3B3,,, was calculated to be 14900 cm-l above 3B2U 1251. Fig. 6 shows the energy l&Is of lower singlet and triplet states of anthracene and Its derivatives. The second triplets of meso-derivatives havenot been dbs&ved. The higher triplet states (broken line), assumed to be 3B3u, are estimated from the activation energy of kS_,* [12]. Figs. 5 and 6 indicate that there are two singlet and two triplet states which may be concerned with T--f S intersystem crossing. According to the selection rule

-

02”

The results are shown in table 3. 4.1. T + S intersys tem crossing

~..

. .

‘J$ .

Fig. 5. Energy level diagram of anthracene.

: -S. Kobayafii et al.)Nonradiative relaxation processes in anthracenes

--ST_-

..: .__-.s,- -TzS,-

!iT

405

ST

____

_--St-

..

log A,, _-LlL AnfhrecCnC

-B-MdhylanthracCnC

B-PhCIIylanthrCCCnC

.Fig. 6. Energy level diagram of anthracene and its meso-

Fig. 7. Plot of log d (ii cm* mblecuIe-r ) versus log AS-T (in I’). The data plotted rire for the following molecules: (1) anthracene; (2) 9-methylanthracene; (3) I)-phenylanthracene; (4) 9,lOdichIoroanthracene; (5) 9JO-dibromoanthracene.

derivatives. of nonradiative transitions [32], 3B3,, + lBzU transition is orbitally allowed and the others are forbidden, so that 3B3n + lBZu transition is expected to be important for the intersystem crossing process. We first consider the excitation of the 3B3u state followed by intersystem crossing from 3B3u to lB2”. The rate constant of intersystem crossing, k~-+s, from the triplet manifold to the singlet manifold is related to h_,s with the equation

where ;iT is the mean Lifetime of the triplet manifold from which intersystem crossing occurs. Fig. 7 shows the relation between #T+s and A,,, which is the ire-exponential factor in eq. (1). The vahn?s of&&T were rep&ted by Kearvell and Wilkinson [ 121. The

dope of the log-log plot is approximately unity for meso-derivatives. which suggests that T + S intersystern crossirig is the inverse process of thermally activated S + T intersystem crossing. Therefore, we assume+-+? =‘+-tT * t and estimste the value of FT * Parker and Hatchard [33] qgested in the study of E-type delayed fluorescence that tie preexponential factor for thermally activated S1 + T1 intersystemcrossingis nearly equal to the rate of inverse S I* T1 intersystem crossing.

for each compounds. The results are Iisted in table 3. The mean lifetimeS of meso_derivatives are nearly the same order of magnitude with each other and seem to bs shorter than that expected from a vibrational relaxation: The mean lifetime of anthracene is one order of magnitude smaller than those of meso-derivatives. Since 3BsU and 3B,, are ciosely iying, the internal conversion between them are expected to be very rapid compared with vibrational relaxation. Therefore, the values of FT may be regarded as the electronic relaxation time between these states. It seems probable that the nonradiative relaxation occurs from the Franck-Condon excited state of 3B3u. The quantum yield of this process is given by 4-S

N-kT43B3u * 1B#IC(3B3u

+ 3Blg) 3 (9)

where k,, is the rate constant of internal conversion. The theoretical expression for the nonradiative rate constant of the orbitally allowed intersystem crossing is given by kT+

= Zni-llffk

12p, ,

where pm is the density of fmaI vibronic states and

_ 406

>. 1z’obayash.f et al.fNonradiative relaxaiioti processes in anihracenei

.

IfA is the transition matrix element governed by direct spin-orbit coupling 13x1

01) where h~~[~ is the electronic factor and Fis the Franck-Condon factor. In meso-derivatives @T+ are linearly related to CK~; as so d are. The large increases in I$=_+~of haloanthracenes are attributed to the internal heavy atom effect [I 1,22-241. The othei factors in OT+ may be appreciably unaffected by the substitution. Since IS& of anthracene is almost the same as those of 9-methylanthracene and I)-phenylanthracene [22], the rates of nonradiative transition from 3B3u of anthracene should be the same order of magnitude as those of meso-derivatives. The above consideration does not explain the differences in $T_s between anthracene and meso-derivatives. As the second mechanism we assume that either 3B3,, + 3B1g internal conversion is rapid or 3B3u is not excited, and intersystem crossing originates from the Boltzmann distribution of the vibrational levels of 3B1,. Since the energy gap for 3B + 3BZUinternal conversion is about 11000 cm-l, %$, state is expected to have a relatively long lifetime. Therefore, 2u intersystem crossing may contribute to 3Blg “B QT+,. On the basis of this mechanism, OT+ is expressed as follows,

Substitution effect on k,, has been studied by Murata et al. [34] about the S2 + S1 internal conversion of azulene derivatives which have energy gap of about 12000-14000 cm-l. They concluded that the rate of internal conversion mainly depends on energy gap between them and the electronic matrix element is practically unaffected by the substitution. The energy gaps between 3BI, and 3B2u of 9-methylanthracene and 9-phenyhutthracene seem to be only a few hundred cm-l larger than that of anthracene. If the energy gap law is valid for the 3B,, -? 3B*u internal conversion of the anthracenes, kI,[3B,, + 3B2u) of 9-methylanthracene and 9-phenylanthracene are a little smaller than that of anthracene. However, the large differences of QT+ with the substitution cannot be explained by the small decreases in krc. Since the 3B,, state of anthracene is about 500 cm- 1 below IBz,, state, lB2,, +- 3Blp intersystem crossingis necessarilythermally qctivked. On the

.

_ : ._

.-

-_

other hand, no activation energy is needed for 3Blg -, ‘. . lBau intersystem crossing of me&-derivatives, because the 3Blg state of meso-derivatives isassumed to be above the lB2,, state [5]. If thi difference of kTds between a&hracene and mesa-derivatives is astiribed to theparticipation of thermal activation process, kT,s of anthracene should be smaller than that of meso-derivatives by a factor of exp(-ET_&&“), where ET_,s is the activation energy of lBZu g 3B1, intersystem crossing. The factor is 0.1 at room temperature, which is consistent.withthe results. Therefore, T + S intersystem crossing is satisfactorily explained by this mechanism_ We must consider the possibility of the third mechanism; intersystem crossing occurs from the vibrationally excited 3B,, state in competition with vibrational relaxation to the Boitzmamt distribution. Atthough it is very difficult to evaluate the contribution of this mechanism to rjTes, the vibrational relaxation in anthracenes is supposed to be not so largely modified by the substitution. This mechanism scarcely produces the large difference in +_,,. In the above discussion, we have assumed that (I) there is no appreciable effect of methyl- or phenyisubstitution on kT_&3B3, + lBzu), krc(3F.33u+ 3B,,), ami kiCC3BI 01) kT-+s(3Brg + lBzu f~~~_$~,,-lB~u) X exp(-ET4s/kTJ and the pre-exponential fac-

tor is the same in anthracene, 9-methylanthracene and 9-phenylanthracene, and (III) the heavy-atom substitution affects on ]r~ir]~ of &J3B3u 3 ‘B,) and kT+s(3B,, + lB,,). These assumptions allow us to estimate the rate of internal conversion between excited triplet states. The observed intersystem crossmg processes are mainly due to the second mechanism, i.e. &._,s= Gds_ PuttingAT-,~(3Blg + IB,,) =ks+_T (1B2n -, 3Blg)A lo8 s-1 which is the rate of temperature-independent intersystem crossing of anthracene [35], we obtain + 3B2u) zz IO* s-l/(4 X 104) = 2 X IO11 W3B,, s-1 according to eq. (12). The rate of inter& conversion between the.eIectronic states, which have energy gap about II000 cm-l, has been reported;(a) modamine 6G, k&S2 + S,) N-5 X iOIL s-l [36] and (b) azulene derivatives, @e extrapolation of log k&Q. ? S1) versus (f&-Est), plot to about lJOO0 cni-1 gives k&S2 + S1) = 10lFs-1 [37]. The agreement between these values and the esti-

: S. Kobayashi et al./Nonradiative relaxation processes in anthracenes

mated Ayes of krC(3Blg + 3B,,) of anthracenes supports the validity of our model -of T + S intersystem.crossing which corresponds to the level inversion tiod& used to explain the nonradiative transition of the fluorescing state in anthracene and meso-derivatives.

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