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Excited singlet yield in T-T annihilation, a comparative study of naphthalene and anthracene in solution
Chemical Physics 10 (1975) 471-478 0 North-Holland Publishing Company
EXCITED SINGLET YlELD IN T-T
ANNIHILATION.
A COMPARATIVE
STUDY OF
NAPHTHALENE AND ANTHRACENE IN SOLUTION F. TFIBEL Luboraroire
and L. LINDQVIST de Phorophysiqrrc
Molc’culairc
drr C.N.R.S..
UnirersirC Paris&d,
91405
- Orsay, France
Received 7 February 1975 Revised manuscript received 4 July 1975 A method based on the study or both triplet absorptior! and delayed fluorcsccnce (DF) dccsys afccr tlssh csciwtion hz.s to dctcrmine DT: yield,. Values of the excited singlet yield in the T-T wmihilaion process have been obtained for n3phthzdenc and anrhraccnc in solution at room xmperaturc by application of this method. Trlplct extinction cocfficicnts and annihilation rate constants for thcsc compounds wcrc also detcrmincd. Exited singlet generation is the predominant annihilation channel for naphth&nc whcrcxs it is only of minor importance for anthracenc. The diiferencc in DF yields is ascribed to dlffercnccs bctwccn these nromatics with respect to the efticicncics of the anmhdation channels leading respectively to ckcitcd singlet and triplet states. The higher mtc of exited singlet formation for naphrhrdcnc is qualitatively occountcd for by considering the possibilily of radiation&s transitions from the bimolxular states formed in T-T interaction towards an upper cxcimer singlet slate. been developed
I.
Introduction
Encounters between molecules in the triplet state lead with a high efficiency to the depopulation of this state (T-T annihilation). This annihilation is in part due to population of the excited singlet state, as evidenced by the observation of a “delayed fluorescence” (DF). The intensity of the DF is determined by tic nature of the different electronic energy transfer processes invo!ved in the T-T annihilation. hleasur~menb of DF yields are therefore an important means of studying the annihilation mechanism; however, although DF has been extensively studied (for a review sec. e.g., Parker [l]) , truly quantitative data on DF yields are very scarce. We have developed an experimental technique to determine DF yields based on combined triplet absorption and DF measurements following flash excitation which eliminates many of the uncertainties involved in previous methods used. All the parameters required to evaluate the DF yield are obtained directly using this method. A similar principle has bcrn described by Kikuchi et al. [2]; their method requires however the knowledge of the intersystem crossing yield which often is not known with great accuracy. Our technique has been applied to the study of the excited singlet formation efficiency in the T-T annihilation process for naphthalene and anthracene in so-
lution at room temperature. An examination of rhe results of DF studies by Parker [ 11 shows that the DF efficiencies for these two polyacenes are very different. There seems to be no obvious connection between thcsc eliiciencies and molecular parameters which would account for this difference. In his studies, Parker set as an approximation the annihilation rate constant equal to the rate of encounters. In the present investigation, the annihilation rate constants were determined experimentally; the DF yields thus obtained are consistent with Parker’s results. The data have been used to discuss the different annihilation channels for naphthalenc and anthracene. A model is proposed for the mechanism of excited singlet generation which qualitatively accounts for the difference between the DF rates for these two compounds_
2. Principle of detemination
of the DF yield
One may define an experimental excited singet T-T annihilation process as
yield pe in the
Ys = PC4 where yS is the rate constant l
(1) of direct*
formation
of
of population of the excited sinflct state in stages subsequent to the annihilation (c.g.. rxlical recombination) is not included in pc_
The possibility
472
F. Tfibei, L. LindqvistlExcired singleI
yield in T- 7 annihilation
excited singlets* from T-T annihilation and k, is the experimentally observed rate constant of depletion of the triplet due to the annihilation. To determine pe, the triplet absorption and DF intensity decays were measured after excitation by a short duration high brightness flash. The total number of photons emitted per unit volume and unit time in the solution (fDF) at time I after the end of excitation may be expressed as IDF = *FP,k2c+
.
(2)
where eF is the fluorescence quantum yield and cT is the triplet concentration. The DF intensity was measured at selected wavelengths using a monochromator and a photomultiplier. The photomultiplier signal VDF is related to IDF by a wavelength-dependent apparatus factor p(x) as follows: V,,
= 8@) t)(A) *FPck&
(3)
where ~0) is the fraction of DF photons emitted in the experimental bandpass centered at h. A calibration procedure involving chemical actinometry and steady-state measurement of the prompt fluorescence of the compound to be studied was used to obtain
the product p(x) n@) aF which can be applied directly in eq. (3); &F thus does hot need to be known. One evaluates CT from measurements of the optical density of the triplet (DT) as a function of tune after flashing, using the relationship DT = lTdcT, where lT is the triplet extinction coefficient and d the optical path for the monitoring light. Values of k2 and E? were obtained from separate triplet absorption measurements by the use of an energetic flash photolysis apparatus described previously [3]. The value of pe was then derived using eq. (3).
3. Experimental 3.1. Apparatus for DF and triplet absorption measurements An apparatus was developed (fig. 1) to allow measurements of DF and triplet absorption time decays under identical experimental conditions. The sample l
Ihe present treatment emission will not be
is limited to monomeric
considered.
H.V. ‘CAPAC.
DF; excimer
Fig. 1. Flash apparatus used to mcasurc transient triplet absorption and DF emission. L = xenon lamp; F’ = filter; C = sample cell; F = lilter jacket; T = flash tube; hl,, h12 = mir101s:&,,bs = hws used in absorption measurcmcnts; hf = monoctuomalor; P = delection photomultiplier; A = nmplitier; 0 = osciUoscapc; km = lenses used in emission mcasuremcnts. is contained in a cylindrical silica cell (C) with plane end windows (di = 10 mm, length 29 mm). The cell is surrounded by an annular jacket(F) containing a filter solution (5 mm solution thickness). The jacket is separated from the cell by a spacing of 1 mm. A specially developed flash lamp [4] was used for excitation. In this type of lamp, the discharge is conducted through the plasma in the inner tubing and returns through the
annular space between the two concentric tubes. The lamp length is 30 mm. The lamp is connected to a 100 J, 10 kV capacitor (Hivotronic). The tube is ionized by the application of a high voltage pulse. The lamp is filled with a 1: 1 oxygen-argon mixture. The light pulse width obtained in a 100 J discharge is 1.5 ps at l/e of peak intensity and 2.5 PS at l/lO.of peak intensity. The lamp output was reproducible within 5%. The fluorescence is collected by two quartz lenses adapted to the apertures of the cell and monochromator (M) (Bausch and Lomb, f/3,6.4 nm/mm in the visible). The detection photomuftiplier signal is fed to one of the inputs of a double beam oscilloscope (Tektronix 565). The other oscilloscope input receives the
F. Tfibel. L. LindqrisrlExcired singlet yield in T-T
signal corresponding to the integrated current of a photodiode (BPY 13. Radiotechnique), viewing the fluorescence emitted by the solution during the flash. The triplet absorption is monitored across the length of the cell using a 75 W xenon arc lamp (L) (Osram Xl30 75 W/2) as light source. The intensity of the light transmitted by the solution is measured using the same detection system (M and P) as in the emission studies. An image of the lamp is focused at the entrance slit of the monochromator. The photomultiplier signal is fed to the differential comparator plugin unit (Tektronix 3A7) of the oscilloscope. The transient signal is displayed on the oscilloscope screen as a function of time after the excitation. The factor /3t)in eq. (3) converts the detector signal to the true DF emission of the compound under study per unit volume. The calibration factor is obtained by measuring the prompf fluorescence of the solution, using continuous monochromatic light to excite the fluorescence. The conditions (solute concentration, detection system, etc.) were in this calibration the same as in the DF measurements, except that the detector sensitivity was increased by a known factor (r) of 500-1000. The measured prompt tluorescencc signal VF then is equal to @qlF, where IF is the number of photons emitted per unit time and unit volume. The number of photons absorbed per unit time and unit volume (labs) in the solution in the fluorescence measurement was determined by chemical actinometry. %‘tce IF/tabs is by definition equal to GF, one obtains flr)@F from: flr@F = J’P/rla,,
.
(4)
It may be noted that p, n and aF need not be known separately since only their product appears in eq. (3). A low pressure Hg lamp (Philips 93109 E) was used as excitation light source for the calibration. The 2537 A line was isolated by a set of filters. In the actinometry study, a chemical actinometer solution was contained in the irradiation cell. The actinometer concentration was adjusted to give the same OD (G 0.05) at the excitation wavelength as that of the solution under study. Since the actinometry and the prompt fluorescence measurements could not be carried out simultaneously, an additional photomultiplier tube receiving a fraction of the excitation light was used as a secondary reference. The photomultiplier tube was calibrated with respect to the number of photons absorbed in
mnihilarion
473
the solution by recording its signal on a X-t recorder throughout the time of exposure of the actinorneter solution. This detector was then used to monitor labs in the measurements of the prompt fluorescence intensity VF. Malachite green leucocyanidc (synthesized as described by Sporer [S]) proved to be a suitabfe actinometer at the very low excitation intensities used (ca. lOI* quanta s-’ absorbed in 2.5 cm3). The quartturn yield reported by Fisher et al. [6] was used (reconfirmed in the present study). The delayed fluorescence was observed in thoroughly deoxygenated solutions. To distinguish the DF from stray emission (stray light + prompt tluorescence) during the tail of the Bash, the emission of slightly oxygenated solutions was also recorded. Under these conditions the prompt tluorescencc yield is not altered. yet the DF is completely quenched. This signal was then subtracted from that obtained with the fully deoxygenatcd solution to obtain the DF componcnt of the luminescence intensity. In the present study, actinic W light from the Bash was eliminated by filter solutions. Deoxygenated IO-’ M solutions of anthracene in ethanol and naphthalene in cyclohexane rcspectiveljr were studied. At these concentrations, the OD of the solutions across the cell diameter (1 cm) was less than 0.05 in the CXcitation wavelength range. The flash energy chosen was such (50-80 J) that the triplet state population was less than 15%. DF was monitored at one of the peaks of the fluorescence spectrum (400 nm for anthracene. 336 run for naphthalene) at a bandwidth of 12 nm at 400 mn and 6 urn at 336 run. Reabsorption of DF by molecules in the ground state was negligible (a minor correction was applied to take into account reabsorption of DF by molecules in the triplet state
in the case of the anthracene/ethanol system). The et: ror in the calibration was estimated to be less than 12%. 3.2.
Measurements
of
and triplet extinction
T-T
annihilation
mte cottstat~Is
coefficients
The measurements of the rate constants of T- T annihilation (kz) and the triplet extinction coefficients (ET) were carried out using an energetic (max. 3700 I) flash apparatus for kinetic spectrophotometry with a 20 cm analysis path [3;. Triplet absorption spectra were measured by monitoring the triplet OD ;is a function of wavelength (bandpass 1.6 nm) at constant
F. T/bet, L. Lindqvisr/Excited singlet yield in T-T annihilatiorr
474
flash energy. Solute concentrations were in these experiments 5 X 10m7 - 2 X 10m6 M. A liquid cut-off falter contained in a jacket surrounding the irradiation cell absorbed light below 240 nm (naphthalene) or 305 run (anthracene). 3.3. Solutions Anthracene (Koch and Light Scintillation grade) was recrystallized and zone refined. Naphthalene (Aldrich Golden Label) was used without further putification. 95% ethanol and cyclohexane (both hlerck Uvasol grade) were used as solvents. Thorough degassing was obtained by the freeze-pump-thaw technique with intermittent argon saturation of the solutions.
DF intens’ty and triplet absorption decays for naphthalene and anthracene in solution* were measured to determine the excited singlet yieldsp,. This evaluation also requires the determination of the trip let extinction coefficients E-,- and the annihilation rate constants k, which were obtained from separate triplet absorption measurements. 4.1. Dctem~ination
of E=
The maximum of triplet absorption in the visible was found at 419 and 414 nm respectively for anthracene in ethanol and naphibalene in cyclohexane. To determine ~7, the triplet OD was measured at the end of an energetic flash converting a high fraction of the solute molecules to the triplet state. In the case of anthracene, total conversion to the triplet state was obtained. The results gave the value: eT = 50000 * 5000 M-’ cm-’ at 419 run (bandpass =z 2 nm). In the case of naphthalene it was not possible to obtain complete conversion to the triplet state. The triplet concentration was determined in this case by an extrapolation procedure (for details see, e.g.,
Ethanol was initially selected as solvent. Ho*.vever.tbe flash determination
4.2. Tr@let state decav kinetics The triplet decay after the end of flash excitation was monitored at the maximum of the main triplet absorption band in the visible. The decay was found to follow the relationship:
4. Results
l
ref. [7]). monitoring the ground state OD after excitation at the maximum and adjacent minima of the ground state absorption band at 286 run. According to reported triplet absorption spectra [S], the triplet absorption was expected to be small at this band and without any structure. Monitoring the triplet OD, we obtained: ET = 24000 + 3000 M-L cm-t at 414 nm. This value is consistent with results of energy transfer studies in pulse radiolysis (ET = 7,450O [9], ET = 20000 + 5000 [lo]). For anthracene in ethanol, a higher ET v&e (75000 + 5000 !I-’ cm-r) has been reported by Dempster et al. [ 11); this value was extrapolated from runs at small triplet conversion.
of the naphthatene
triplet Lifetime in this sol-
vent gave a low value probably due to quenching by photoproducts. When using cyclohe.xane a.s solvent, no such effect was observed.
-d c,/dt
= k, cT + k2c; .
(5)
The values of k, obtained using our ET v~ucs are 3.0 X 10’ M-’ s-l for anthracene in ethanol and 3.3 X 10’ M-t s-l for naphthalene in cyclohexane. Values reported in the literature are 5.7 X 109 [ 121 and 7 X 10’ [ 111 for anthracene in ethanol and 3.5 X 10’ [13] and 8 X 10’ [lo] for naphthalene in cyclohexane. 4.3. Determination
of the excited
singlet yield pe
To obtain the experimental excited singlet yield PC [see eq. ( l)], 7s was determined from measurements of the triplet OD (DT) and the DF intensity (IoF) time decays after flash excitation. For both naphthalene and anthracene, plots (fig. 2) of I&!versus DT yielded straight lines passing through origin, in agreement with the expected dependence of the DF intensity on triplet concentration [see eq. (2)]. rs was evaluated from the slope of these plots. The analysis of the DF decay confirmed the values of k2 obtained from triplet absorption measurements (section 4.2.). Table 1 lists the resulting values of 7s and pc. The error on the pe values is estimated to be about 30%. It is Men that 7s and pe are several times higher for naphthalene than for anthracene. This difference is not due to a solvent effect since Parker found the
F.
Tfibel, L. LindqvistlExcited singlet yield
415
in T-Tannihilatian
same DF yield for anthracene clohexanc [ 141.
in both ethanol
and cy-
5. Discussion A discussion of the possi,ble reasons for the observcd difference in excited singlet yicid between naphthalcnc and anthracene requires a close examination of the T-T annihilation process. This process may be described by the following general scheme: (4
+/hl
‘XI* + 'hl
0)
Pok, 2
/
3bl + 3hl
P&+3hf
\PA
@)
+ ‘?.I
olhcr products
&round state. ions, etc.)
a-
.
A-
a 101
- -1. 0‘-3
_-L_Oil!-
Fig. 2. Correlation between transient DF intensity (I&?) and trIplet absorption (D-,-) mensurcmcnts. (a) Anthraccnc m clhanol (the triplet OD &-is monitored at 4 19 nm); (b) naphthticnc in cyclohexanc (DT ISmonilored at 414 nm).
(C)
in which k, is the total rate of annihilation evcnk and pC,pl,p2 are the respective probabilities(po fpl +p2 = 1) of processes (a),(b) and(c). The triplet state is partly repopulated by processes (a) (with a probability equal to the quantum yield of triplet formation QT) and (b). This gives rise to a difference between k, and the experimentally observed annihilation rate CORstant k,; thus, the experimental yield pe [evaluated with respect to k2, cf. eq. (I)] does not in fact rcprcsent the actual probability p. of excited singlet gencration. The following relationships hold between k2, k,. Pe adpC:
k2=kaf2-@‘~*~+~,)] and Table 1
Results of the determination of -ys,Pe and Pd
pok, ‘~$2
=k,[p,,(7_-rpT)+p,
+qg,l (6)
.
3
2.4 X lo* hi’ 8
1.7 x 109 M-1 s-1
Since no experimental values of k, are available, one may only give limiting values of this rate: k2/2
PC
0.08
pd
0.08 o.o@; - o.oab);
0.52 0.46
* While no value orpo has been reported for naphthAme.
Anthrnccnc
Naphthalcne
0.56=)
- O.OIC)
al Parker’s values in cthsnol [ 11; b, Parker’s value in cyclohexane [ 14); ‘1 in methylene chloride [IS].
3 value of 0.077 has been given for ylchmcene in cth~~~ot 121: this value is in fact ;I lower limit because of the assumption pz = C and should be corrected to about 0.1 to take into account the rcpopulNion of the triplet smte by process (a). This value is consistent with our lower limit of 0.08.
476
F. Tfibel. L. Lindqvisr&cired
0.74 for naphthalene (using the value aT = 0.77 [ 171): excited singlet formation is tie predominant annihilation process for naphthdene and is at leasst four times more efficient than for anthracene. For comparison with Literature. table 1 also gives the probability pd obtained by assuming that every encounter between two triplets leads to an annihilation, i.e., by setting k, = 2.k, (and ys =pdkd), where kd is the rate constant of a diffusion controlled reaction between identical species. Indeed, most of the literature reports on DF yields were derived under the above assumption, following Parker’s original treatment [I]. The yields thus obtamed actually give the probability
of excited sing-
let generation from all the encounters between two triplets, including those not producing annihilation. that is, only a lower limit to the value ofp,. In order to compare with literature reports, the vibes of pd were obtained by calculating k,. as in Parker’s treatment, from the Debye formula: 2/cd = 8RT/3000~) [ 181. Our value for anthracene in ethanol agrees quite well with Parker’s result despite the difference in the methods of determination used. As for naphthalene. there is no significant difference between Parker’s result in ethanol and ours in cyclohexane. The observed difference in excited singlet yield between the two aromatics investigated may be due to differences in the nature and efficiency of the competing processes occurring in the T-T annihilation. According to theoretical and experimental evidence [ 191, few of the possible annihilation processes are likely to compete efficiently with direct excited singlet or trip let formation. Excimen may be generated in T-T annihilation which are known to be unstable for both naphthalene and anthracene under the present experimental conditions and therefore contribute to the observed DF. The availability of an additional excimer deactivation path in the case of anthracene, namely stable dimer formation, could possibly give rise to a difference in excited singlet yield between the two aromatics. Dianthracene formation is indeed observed in our flash experiments; however, from the amount of dianthracene
formed, one may infer that this de-
activation process cannot contribute by more than a fraction of 0.06 to the annihilation process. Stable dimer formation thus does not account for the low excited singlet yield for anthracene. Another annihilation process to be considered is the generation of ionic species (especially free ions in polar solvents) from
singlet yield in T-Tannihilotion
an initial bimolecular state with strong charge transfer character; back electron transfer in (or between) these species may result in formation of excited singlets and triplets. The absence of any significant effect of solvent polarity on excited singlet formation points to a negligible contribution to the DF from this annihilation process. Moreover, if the latter were occurring, one would expect a higher value of k2 iu ethanol than in cyclohexane, contrary to the data obtained (3.5 X IO9 and 3.3 X 10’ hl-’ s-’ for naphthalene in ethan01 and cyclohexane respectively; 3 X lo9 and 3.6 X lo9 M-I s-’ for anthracene in ethanol and cyclohexnne respectively). One may also stre& that no detectable absorption due to radicalons was found and that no significant amounts of stable photoproducts were formed (the ions will not recombine in ethanol 1201). It is concluded that this annihilation process is not involved to any appreciable extent for these two are matics in the solvents used. One may then consider that generation of excited singlet and triplet states are the only important annihilation processes for anthracene (A) and naphthalene (N), which leads to PO == 0.08 for A and p. = 0.58 for N. The DF yields for A and N are thus mainly determined by the respective efficiencies of these two processes*_ Excited singlet formation in T-T annihilation has been postulated on theoretical grounds to involve a pure charge transfer state as the intermediate state (in crystals) [22]. However,experimental evidence favouring this mechanism is lacking at present. It may be noted that singlet exciton fission (Le.. the reverse of T-T annihilation) in tetracene and anthracene crystals is considered to involve more probably upper excited singlet levels 1231. We suggest an alternative model which allows a qualitative comparison between naphthalene and anthracene. In this model, it is assumed that the initial bimolecular state formed in a T-T encounter undergoes a radiationless transition to an upper excimer singlet, which is followed by dissociation or rapid relavation towards lower unstable excil
From the analysis of the &~a in terms of Merritield’s kinetic scheme [Zl], assuming mean effective interaction radii for T-T annihilation of 5.5 A for N and 7 A for A. one obtains for the rate constant of the singlet channel available to the encounter triplet pair 1.7 X 10” and 1.4 x lo”<’ I-ZSJXCtively for N and A and for the rate constant of the triplet channel 4.2 X 10” and 5.4 X 10” s-’ respectively for N and A.
E Tfibel, L. Lindqvisr/Excired Table 2 Vatucs of ti
Elcm-‘I
= E(’ Bb) - x(3La),
Hydrocvbon
E(‘Bb) (Xl@ cm+)
and pda)
ff12 b,
AE
pd
(debye’)
(X IO-”
Ro (A)
45.3
79.4
+2.7
0.56
5.3
Acenaphthcnc Pyrcne 1,2-Bcnwnthraanc Anthraccne (A) 9-Mcrhyl A 9.10-Dimethyl A 9-Phcnyl A 9,10-Diphenyt A Phcnanthrcnc
43.7 36.7 33.4 39
52.5 25.6 101.7
+1.9 +2.9 +0.4
0.31 0.27 -0.21
5.2 3.6 10.9
38.7 39.9
123.5 114.2 99.1 83 76.4 58.7
+9.4 +9.1 +9 +9.8 >9 -4.3
Fluorannlhene 3.4.Bcnzpyrcnc
34.9 34.5
16 55.4
-2.3 +5.1
-0.04 -0.03
3.8
Pcrylcne
39.6
29.7
+14.4
-0.02
2.2
38.4
39.2
NAPHTHALENE ‘q
L5.000 -
cm-’ 1
Naphthalenc
39.1
417
singlet yield in T-Tarrnihilarion
0.08 4 0.03 3.9 0.01 3.8 0.05 3.5 0.13 c3.5 0.05 -
35000.
a) AE data from rcfs. [ 27 Jand 11);Pd data from ref. [ 1) (in ethanol at room temperalure). b) Data from ref. [ 27 1or cstimated from spectra rcportcd in ref. 127).
ANTHRACENE mer singlet
states
(according
to previous
experimental
reports on direct excited singlet formation by T-T annihilation [ 1,241, this channel should be efficient at larger intermolecular distances than those required for excirner formation). The primary radiationless thannel of interest is suggested to lead to the excimcr singlet of ’ Bb parentage, denoted ’ B,E according to Birks’ notation [35]*. There are indeed some indications that the ’ B, singlet state, particularly, plays a role in the annihilation process. It is seen from table 2 that high pd values among Parker’s data [I] for aromatics in ethanol appear to be connected with low and positive w&es of the knergy gap AE = E(l BJ 2&(3 L,) (0 < hE < -3000 cm-‘). It may also be mentioned that delayed fluorescence from this excited singlet state to the ground state has been observed quite recently [26] for two of the compounds listed in table 2. A schematic model based on the potential energy curves of the initial bimolecular state and the lBbE state may be used (cf. fig. 3) to compare the probability of transition between these states (with spin conservation) and hence the excited singlet forma*
T RIA
Excimcr singlets of ’ Ba paentagc could be involved too (e.g., in the case of pyrcnc 1251) but this seems unlikely for antbra-
cene and napht+enc from both energy and oscillator strength considerations.
Fig. 3. Potcnlial energy curves diagrams for tlw singlet channel in anthracene and naphthalenc T-T annihilation respcctivel~: (3 L, + 3 b) denotes the encounter pair site with sin&t character. ’ BbE the upper excimcr single1 state of * Bb parentage. R the distance bcnvecn the two interacting triplets. The adia-
batic curves are drawn as a continuous
line.
tion rate for naphthalene and anthracene. It is assumed in this model that the ‘B,E state is mainly stabilized through dipole-dipole interaction and that the triplet pair may reorient itself rapidly into a sandwichlike configuration. The main parameters affecting the rate of excited singlet formation through the postulated radiationless channel are then m, the transition moment for the ‘A, + ‘Bb transition, and R,, the “crossing” distance for the potential energy curves. Predictions from this scheme agree with the observations that energy gaps AE have low and positive values and that R, > 4 A (except for pyrene) for the compounds with high pd values in table 2. It is clear from fig. 3 that the excited singlet formation rate should indeed be higher for naphthalene (m2 = 79.4 debye’ [27J, R. = 5.3 A] than for anthracene (m2 = 123.5 debye [27], Rt, = 4 A). If excited singlet generation, considered above, is more efficient for naphthalene, it should be noted that
478
F. Tfibel, L. Lindqrizr/lhired
a higher efficiency of triplet formation for anthracene may contribute also to the observed difference in DF yield between these two aromatics. However, the present knowledge on upper triplet states does not allow a substantiated evaluation of the role of this process.
6. Concluding remarks It is concluded from the detailed consideration of the annihilation channels that the DF yield for anthracent and naphthalenc is mainly determined by the efficiencies of the channels leading respectively to excited singlet and to triplet final states. The higher rate of DF for naphthalene is qualitatively accounted for by a model considering the possibility of radiationless transitions from the bimolecular state formed in a T-T encounter to an upper excimer singlet of I Bb parentage.
Acknowledgement
We thank Drs. A. Tramer and C. Tric, Professor H. Labhart and Professor R. Voltz for helpful discussions and suggestions. WC gratefully acknowledge the assistance of Miss E. BrCheret in carrying out the experiments.
References
[I] CA. Parker, Photolumincsccncc of solutions (Rsevicr, Amsterdam, 1968). 121 K. Kikuchi. H. Kokubun and hi. Koizumi. Bull. Chem. Sot. Jap.41 (1968) 1545. L. Lindqvist. Rev. Phys. Appl. 3 (1968) 15. F. Ttibel, Rev. Phys. Appl.. in press. A.H. Sporcr. Trans. Far. Sot. 57 (1961) 983. G.J. Fisher, J.C. Lc Blanc and H.E. Johns, Photochem. Photobiol. 6 (1967) 757. [7] SC. Hadlcy and R.A. Keller. J. Phys. Chem. 73 (1969) 4351.
(31 14 ] [S] 161
singler yield in T-Tannihilation 181 Y.H. Mcycr. R. Astier and J.M. Leclcrcq, J. Chem. Phys. 56 (1972) 801. 191 R. Bensasson and E.J. Land.Trans. Far. Sot. 67 (1971) 1904. [ 101 F. Dainton, T. Morrow, GA. Salmon and C.F. Thompson, Proc. Roy. Sot. A 328 (1972)481. [ 111 D.N. Dempstcr. T. hlorrow and M.F. Quinn, J. Photothem. 2 (1974) 329. [ 121 A. Adamayk and F. Wilkinson in: Organic scintillators and liquid scintillation counting, eds. D.L. Horrocks and C.T. Peng (Academic Press, New York, 1971) p. 223. [ 131 R. Bonneau. J. Faure and J. Joussot-Dubien, Chcm. Phys. Letters 2 (1968) 65. [ 14 1 C.A. Parker in: Advances in Photochemistry, Vol. 2. eds. W.A. Noycs. C.S. Hammond and J.N. Pitts, Jr. (Interscicncc. New York, 1964) p. 305. 1151 H. Tachikawa and A.J. Bard, Chem. Phys. Letters 26 (1974) 10. [ 161 C.A. Parker and T.A. Joyce, Chcm. Commun. (1966) 234. (171 A.R. Horrocks and F. Wilkinson, Proc. Roy. Sot. A306 0968) 257; LB. Bcrlman, Handbook of fluorescence spectra of aromaric molecules (Academic Press, New York, 1971). (181 P. Dcbyc, Trans. Elcctrochem. Sot. 82 (1942) 265. [ 191 V.G. Krishna, J. Chem. Phys.46 (1967) 1735; K.R. Naqvi.Chem. Phys. Letters 1 (1968) 561: B. Brocklchurst, Radiation Rcs. Rev. 2 (1970) 149; R.A. Keller. Chem. Phys. Lcrters 3 (1969) 27; R.P. Crofi. R.E. hlenificld and P. Avakian. Chcm. Phys. Letters 5 (1970) 168. 120) S. Ard and L.M. Dorfman, J. Chcm. Phys. 4 1 (1964) 2190. [21] R.E. Merritield, J. Chcm. Phys.48 (1968) 4318. (221 C.E. Swenberg. J. Chcm. Phys. 51 (1969) 1753. (231 G. Klein, R. Voltz and hf. Schott, Chem. Phys. Letters I? (1973) 391. 124) C. Tanaka, J. Tanaka, E. Hutton and B. Slevcns, Nature 198 (1963) 1192; B. Stevens and MI. Ban. Mol. Cryst. 4 (1968) 173; B. Stevens. Chem. Phys. Letters 3 (1969) 233. [2S] J.B. Birks. in: Progress in reaction kinetics; Vol. 5, cd. G. Porter (Pergamon press, Oxford, 1970). (261 B. Nickel, Chem. Phys. Letters 27 (1974) 84. 127) H.B. Klevens and J.R. Platt. J. Chem. Phys. 17 (1949) 470; R.S. Becker, LS. Singh and E_A. Jackson, J. Chem. Phys. 38 (1963) 2144; E. Ctar, Polycyclic hydrocarbons (Academic Press, New York, 1964).
EXCITED SINGLET YlELD IN T-T
ANNIHILATION.
A COMPARATIVE
STUDY OF
NAPHTHALENE AND ANTHRACENE IN SOLUTION F. TFIBEL Luboraroire
and L. LINDQVIST de Phorophysiqrrc
Molc’culairc
drr C.N.R.S..
UnirersirC Paris&d,
91405
- Orsay, France
Received 7 February 1975 Revised manuscript received 4 July 1975 A method based on the study or both triplet absorptior! and delayed fluorcsccnce (DF) dccsys afccr tlssh csciwtion hz.s to dctcrmine DT: yield,. Values of the excited singlet yield in the T-T wmihilaion process have been obtained for n3phthzdenc and anrhraccnc in solution at room xmperaturc by application of this method. Trlplct extinction cocfficicnts and annihilation rate constants for thcsc compounds wcrc also detcrmincd. Exited singlet generation is the predominant annihilation channel for naphth&nc whcrcxs it is only of minor importance for anthracenc. The diiferencc in DF yields is ascribed to dlffercnccs bctwccn these nromatics with respect to the efticicncics of the anmhdation channels leading respectively to ckcitcd singlet and triplet states. The higher mtc of exited singlet formation for naphrhrdcnc is qualitatively occountcd for by considering the possibilily of radiation&s transitions from the bimolxular states formed in T-T interaction towards an upper cxcimer singlet slate. been developed
I.
Introduction
Encounters between molecules in the triplet state lead with a high efficiency to the depopulation of this state (T-T annihilation). This annihilation is in part due to population of the excited singlet state, as evidenced by the observation of a “delayed fluorescence” (DF). The intensity of the DF is determined by tic nature of the different electronic energy transfer processes invo!ved in the T-T annihilation. hleasur~menb of DF yields are therefore an important means of studying the annihilation mechanism; however, although DF has been extensively studied (for a review sec. e.g., Parker [l]) , truly quantitative data on DF yields are very scarce. We have developed an experimental technique to determine DF yields based on combined triplet absorption and DF measurements following flash excitation which eliminates many of the uncertainties involved in previous methods used. All the parameters required to evaluate the DF yield are obtained directly using this method. A similar principle has bcrn described by Kikuchi et al. [2]; their method requires however the knowledge of the intersystem crossing yield which often is not known with great accuracy. Our technique has been applied to the study of the excited singlet formation efficiency in the T-T annihilation process for naphthalene and anthracene in so-
lution at room temperature. An examination of rhe results of DF studies by Parker [ 11 shows that the DF efficiencies for these two polyacenes are very different. There seems to be no obvious connection between thcsc eliiciencies and molecular parameters which would account for this difference. In his studies, Parker set as an approximation the annihilation rate constant equal to the rate of encounters. In the present investigation, the annihilation rate constants were determined experimentally; the DF yields thus obtained are consistent with Parker’s results. The data have been used to discuss the different annihilation channels for naphthalenc and anthracene. A model is proposed for the mechanism of excited singlet generation which qualitatively accounts for the difference between the DF rates for these two compounds_
2. Principle of detemination
of the DF yield
One may define an experimental excited singet T-T annihilation process as
yield pe in the
Ys = PC4 where yS is the rate constant l
(1) of direct*
formation
of
of population of the excited sinflct state in stages subsequent to the annihilation (c.g.. rxlical recombination) is not included in pc_
The possibility
472
F. Tfibei, L. LindqvistlExcired singleI
yield in T- 7 annihilation
excited singlets* from T-T annihilation and k, is the experimentally observed rate constant of depletion of the triplet due to the annihilation. To determine pe, the triplet absorption and DF intensity decays were measured after excitation by a short duration high brightness flash. The total number of photons emitted per unit volume and unit time in the solution (fDF) at time I after the end of excitation may be expressed as IDF = *FP,k2c+
.
(2)
where eF is the fluorescence quantum yield and cT is the triplet concentration. The DF intensity was measured at selected wavelengths using a monochromator and a photomultiplier. The photomultiplier signal VDF is related to IDF by a wavelength-dependent apparatus factor p(x) as follows: V,,
= 8@) t)(A) *FPck&
(3)
where ~0) is the fraction of DF photons emitted in the experimental bandpass centered at h. A calibration procedure involving chemical actinometry and steady-state measurement of the prompt fluorescence of the compound to be studied was used to obtain
the product p(x) n@) aF which can be applied directly in eq. (3); &F thus does hot need to be known. One evaluates CT from measurements of the optical density of the triplet (DT) as a function of tune after flashing, using the relationship DT = lTdcT, where lT is the triplet extinction coefficient and d the optical path for the monitoring light. Values of k2 and E? were obtained from separate triplet absorption measurements by the use of an energetic flash photolysis apparatus described previously [3]. The value of pe was then derived using eq. (3).
3. Experimental 3.1. Apparatus for DF and triplet absorption measurements An apparatus was developed (fig. 1) to allow measurements of DF and triplet absorption time decays under identical experimental conditions. The sample l
Ihe present treatment emission will not be
is limited to monomeric
considered.
H.V. ‘CAPAC.
DF; excimer
Fig. 1. Flash apparatus used to mcasurc transient triplet absorption and DF emission. L = xenon lamp; F’ = filter; C = sample cell; F = lilter jacket; T = flash tube; hl,, h12 = mir101s:&,,bs = hws used in absorption measurcmcnts; hf = monoctuomalor; P = delection photomultiplier; A = nmplitier; 0 = osciUoscapc; km = lenses used in emission mcasuremcnts. is contained in a cylindrical silica cell (C) with plane end windows (di = 10 mm, length 29 mm). The cell is surrounded by an annular jacket(F) containing a filter solution (5 mm solution thickness). The jacket is separated from the cell by a spacing of 1 mm. A specially developed flash lamp [4] was used for excitation. In this type of lamp, the discharge is conducted through the plasma in the inner tubing and returns through the
annular space between the two concentric tubes. The lamp length is 30 mm. The lamp is connected to a 100 J, 10 kV capacitor (Hivotronic). The tube is ionized by the application of a high voltage pulse. The lamp is filled with a 1: 1 oxygen-argon mixture. The light pulse width obtained in a 100 J discharge is 1.5 ps at l/e of peak intensity and 2.5 PS at l/lO.of peak intensity. The lamp output was reproducible within 5%. The fluorescence is collected by two quartz lenses adapted to the apertures of the cell and monochromator (M) (Bausch and Lomb, f/3,6.4 nm/mm in the visible). The detection photomuftiplier signal is fed to one of the inputs of a double beam oscilloscope (Tektronix 565). The other oscilloscope input receives the
F. Tfibel. L. LindqrisrlExcired singlet yield in T-T
signal corresponding to the integrated current of a photodiode (BPY 13. Radiotechnique), viewing the fluorescence emitted by the solution during the flash. The triplet absorption is monitored across the length of the cell using a 75 W xenon arc lamp (L) (Osram Xl30 75 W/2) as light source. The intensity of the light transmitted by the solution is measured using the same detection system (M and P) as in the emission studies. An image of the lamp is focused at the entrance slit of the monochromator. The photomultiplier signal is fed to the differential comparator plugin unit (Tektronix 3A7) of the oscilloscope. The transient signal is displayed on the oscilloscope screen as a function of time after the excitation. The factor /3t)in eq. (3) converts the detector signal to the true DF emission of the compound under study per unit volume. The calibration factor is obtained by measuring the prompf fluorescence of the solution, using continuous monochromatic light to excite the fluorescence. The conditions (solute concentration, detection system, etc.) were in this calibration the same as in the DF measurements, except that the detector sensitivity was increased by a known factor (r) of 500-1000. The measured prompt tluorescencc signal VF then is equal to @qlF, where IF is the number of photons emitted per unit time and unit volume. The number of photons absorbed per unit time and unit volume (labs) in the solution in the fluorescence measurement was determined by chemical actinometry. %‘tce IF/tabs is by definition equal to GF, one obtains flr)@F from: flr@F = J’P/rla,,
.
(4)
It may be noted that p, n and aF need not be known separately since only their product appears in eq. (3). A low pressure Hg lamp (Philips 93109 E) was used as excitation light source for the calibration. The 2537 A line was isolated by a set of filters. In the actinometry study, a chemical actinometer solution was contained in the irradiation cell. The actinometer concentration was adjusted to give the same OD (G 0.05) at the excitation wavelength as that of the solution under study. Since the actinometry and the prompt fluorescence measurements could not be carried out simultaneously, an additional photomultiplier tube receiving a fraction of the excitation light was used as a secondary reference. The photomultiplier tube was calibrated with respect to the number of photons absorbed in
mnihilarion
473
the solution by recording its signal on a X-t recorder throughout the time of exposure of the actinorneter solution. This detector was then used to monitor labs in the measurements of the prompt fluorescence intensity VF. Malachite green leucocyanidc (synthesized as described by Sporer [S]) proved to be a suitabfe actinometer at the very low excitation intensities used (ca. lOI* quanta s-’ absorbed in 2.5 cm3). The quartturn yield reported by Fisher et al. [6] was used (reconfirmed in the present study). The delayed fluorescence was observed in thoroughly deoxygenated solutions. To distinguish the DF from stray emission (stray light + prompt tluorescence) during the tail of the Bash, the emission of slightly oxygenated solutions was also recorded. Under these conditions the prompt tluorescencc yield is not altered. yet the DF is completely quenched. This signal was then subtracted from that obtained with the fully deoxygenatcd solution to obtain the DF componcnt of the luminescence intensity. In the present study, actinic W light from the Bash was eliminated by filter solutions. Deoxygenated IO-’ M solutions of anthracene in ethanol and naphthalene in cyclohexane rcspectiveljr were studied. At these concentrations, the OD of the solutions across the cell diameter (1 cm) was less than 0.05 in the CXcitation wavelength range. The flash energy chosen was such (50-80 J) that the triplet state population was less than 15%. DF was monitored at one of the peaks of the fluorescence spectrum (400 nm for anthracene. 336 run for naphthalene) at a bandwidth of 12 nm at 400 mn and 6 urn at 336 run. Reabsorption of DF by molecules in the ground state was negligible (a minor correction was applied to take into account reabsorption of DF by molecules in the triplet state
in the case of the anthracene/ethanol system). The et: ror in the calibration was estimated to be less than 12%. 3.2.
Measurements
of
and triplet extinction
T-T
annihilation
mte cottstat~Is
coefficients
The measurements of the rate constants of T- T annihilation (kz) and the triplet extinction coefficients (ET) were carried out using an energetic (max. 3700 I) flash apparatus for kinetic spectrophotometry with a 20 cm analysis path [3;. Triplet absorption spectra were measured by monitoring the triplet OD ;is a function of wavelength (bandpass 1.6 nm) at constant
F. T/bet, L. Lindqvisr/Excited singlet yield in T-T annihilatiorr
474
flash energy. Solute concentrations were in these experiments 5 X 10m7 - 2 X 10m6 M. A liquid cut-off falter contained in a jacket surrounding the irradiation cell absorbed light below 240 nm (naphthalene) or 305 run (anthracene). 3.3. Solutions Anthracene (Koch and Light Scintillation grade) was recrystallized and zone refined. Naphthalene (Aldrich Golden Label) was used without further putification. 95% ethanol and cyclohexane (both hlerck Uvasol grade) were used as solvents. Thorough degassing was obtained by the freeze-pump-thaw technique with intermittent argon saturation of the solutions.
DF intens’ty and triplet absorption decays for naphthalene and anthracene in solution* were measured to determine the excited singlet yieldsp,. This evaluation also requires the determination of the trip let extinction coefficients E-,- and the annihilation rate constants k, which were obtained from separate triplet absorption measurements. 4.1. Dctem~ination
of E=
The maximum of triplet absorption in the visible was found at 419 and 414 nm respectively for anthracene in ethanol and naphibalene in cyclohexane. To determine ~7, the triplet OD was measured at the end of an energetic flash converting a high fraction of the solute molecules to the triplet state. In the case of anthracene, total conversion to the triplet state was obtained. The results gave the value: eT = 50000 * 5000 M-’ cm-’ at 419 run (bandpass =z 2 nm). In the case of naphthalene it was not possible to obtain complete conversion to the triplet state. The triplet concentration was determined in this case by an extrapolation procedure (for details see, e.g.,
Ethanol was initially selected as solvent. Ho*.vever.tbe flash determination
4.2. Tr@let state decav kinetics The triplet decay after the end of flash excitation was monitored at the maximum of the main triplet absorption band in the visible. The decay was found to follow the relationship:
4. Results
l
ref. [7]). monitoring the ground state OD after excitation at the maximum and adjacent minima of the ground state absorption band at 286 run. According to reported triplet absorption spectra [S], the triplet absorption was expected to be small at this band and without any structure. Monitoring the triplet OD, we obtained: ET = 24000 + 3000 M-L cm-t at 414 nm. This value is consistent with results of energy transfer studies in pulse radiolysis (ET = 7,450O [9], ET = 20000 + 5000 [lo]). For anthracene in ethanol, a higher ET v&e (75000 + 5000 !I-’ cm-r) has been reported by Dempster et al. [ 11); this value was extrapolated from runs at small triplet conversion.
of the naphthatene
triplet Lifetime in this sol-
vent gave a low value probably due to quenching by photoproducts. When using cyclohe.xane a.s solvent, no such effect was observed.
-d c,/dt
= k, cT + k2c; .
(5)
The values of k, obtained using our ET v~ucs are 3.0 X 10’ M-’ s-l for anthracene in ethanol and 3.3 X 10’ M-t s-l for naphthalene in cyclohexane. Values reported in the literature are 5.7 X 109 [ 121 and 7 X 10’ [ 111 for anthracene in ethanol and 3.5 X 10’ [13] and 8 X 10’ [lo] for naphthalene in cyclohexane. 4.3. Determination
of the excited
singlet yield pe
To obtain the experimental excited singlet yield PC [see eq. ( l)], 7s was determined from measurements of the triplet OD (DT) and the DF intensity (IoF) time decays after flash excitation. For both naphthalene and anthracene, plots (fig. 2) of I&!versus DT yielded straight lines passing through origin, in agreement with the expected dependence of the DF intensity on triplet concentration [see eq. (2)]. rs was evaluated from the slope of these plots. The analysis of the DF decay confirmed the values of k2 obtained from triplet absorption measurements (section 4.2.). Table 1 lists the resulting values of 7s and pc. The error on the pe values is estimated to be about 30%. It is Men that 7s and pe are several times higher for naphthalene than for anthracene. This difference is not due to a solvent effect since Parker found the
F.
Tfibel, L. LindqvistlExcited singlet yield
415
in T-Tannihilatian
same DF yield for anthracene clohexanc [ 141.
in both ethanol
and cy-
5. Discussion A discussion of the possi,ble reasons for the observcd difference in excited singlet yicid between naphthalcnc and anthracene requires a close examination of the T-T annihilation process. This process may be described by the following general scheme: (4
+/hl
‘XI* + 'hl
0)
Pok, 2
/
3bl + 3hl
P&+3hf
\PA
@)
+ ‘?.I
olhcr products
&round state. ions, etc.)
a-
.
A-
a 101
- -1. 0‘-3
_-L_Oil!-
Fig. 2. Correlation between transient DF intensity (I&?) and trIplet absorption (D-,-) mensurcmcnts. (a) Anthraccnc m clhanol (the triplet OD &-is monitored at 4 19 nm); (b) naphthticnc in cyclohexanc (DT ISmonilored at 414 nm).
(C)
in which k, is the total rate of annihilation evcnk and pC,pl,p2 are the respective probabilities(po fpl +p2 = 1) of processes (a),(b) and(c). The triplet state is partly repopulated by processes (a) (with a probability equal to the quantum yield of triplet formation QT) and (b). This gives rise to a difference between k, and the experimentally observed annihilation rate CORstant k,; thus, the experimental yield pe [evaluated with respect to k2, cf. eq. (I)] does not in fact rcprcsent the actual probability p. of excited singlet gencration. The following relationships hold between k2, k,. Pe adpC:
k2=kaf2-@‘~*~+~,)] and Table 1
Results of the determination of -ys,Pe and Pd
pok, ‘~$2
=k,[p,,(7_-rpT)+p,
+qg,l (6)
.
3
2.4 X lo* hi’ 8
1.7 x 109 M-1 s-1
Since no experimental values of k, are available, one may only give limiting values of this rate: k2/2
PC
0.08
pd
0.08 o.o@; - o.oab);
0.52 0.46
* While no value orpo has been reported for naphthAme.
Anthrnccnc
Naphthalcne
0.56=)
- O.OIC)
al Parker’s values in cthsnol [ 11; b, Parker’s value in cyclohexane [ 14); ‘1 in methylene chloride [IS].
3 value of 0.077 has been given for ylchmcene in cth~~~ot 121: this value is in fact ;I lower limit because of the assumption pz = C and should be corrected to about 0.1 to take into account the rcpopulNion of the triplet smte by process (a). This value is consistent with our lower limit of 0.08.
476
F. Tfibel. L. Lindqvisr&cired
0.74 for naphthalene (using the value aT = 0.77 [ 171): excited singlet formation is tie predominant annihilation process for naphthdene and is at leasst four times more efficient than for anthracene. For comparison with Literature. table 1 also gives the probability pd obtained by assuming that every encounter between two triplets leads to an annihilation, i.e., by setting k, = 2.k, (and ys =pdkd), where kd is the rate constant of a diffusion controlled reaction between identical species. Indeed, most of the literature reports on DF yields were derived under the above assumption, following Parker’s original treatment [I]. The yields thus obtamed actually give the probability
of excited sing-
let generation from all the encounters between two triplets, including those not producing annihilation. that is, only a lower limit to the value ofp,. In order to compare with literature reports, the vibes of pd were obtained by calculating k,. as in Parker’s treatment, from the Debye formula: 2/cd = 8RT/3000~) [ 181. Our value for anthracene in ethanol agrees quite well with Parker’s result despite the difference in the methods of determination used. As for naphthalene. there is no significant difference between Parker’s result in ethanol and ours in cyclohexane. The observed difference in excited singlet yield between the two aromatics investigated may be due to differences in the nature and efficiency of the competing processes occurring in the T-T annihilation. According to theoretical and experimental evidence [ 191, few of the possible annihilation processes are likely to compete efficiently with direct excited singlet or trip let formation. Excimen may be generated in T-T annihilation which are known to be unstable for both naphthalene and anthracene under the present experimental conditions and therefore contribute to the observed DF. The availability of an additional excimer deactivation path in the case of anthracene, namely stable dimer formation, could possibly give rise to a difference in excited singlet yield between the two aromatics. Dianthracene formation is indeed observed in our flash experiments; however, from the amount of dianthracene
formed, one may infer that this de-
activation process cannot contribute by more than a fraction of 0.06 to the annihilation process. Stable dimer formation thus does not account for the low excited singlet yield for anthracene. Another annihilation process to be considered is the generation of ionic species (especially free ions in polar solvents) from
singlet yield in T-Tannihilotion
an initial bimolecular state with strong charge transfer character; back electron transfer in (or between) these species may result in formation of excited singlets and triplets. The absence of any significant effect of solvent polarity on excited singlet formation points to a negligible contribution to the DF from this annihilation process. Moreover, if the latter were occurring, one would expect a higher value of k2 iu ethanol than in cyclohexane, contrary to the data obtained (3.5 X IO9 and 3.3 X 10’ hl-’ s-’ for naphthalene in ethan01 and cyclohexane respectively; 3 X lo9 and 3.6 X lo9 M-I s-’ for anthracene in ethanol and cyclohexnne respectively). One may also stre& that no detectable absorption due to radicalons was found and that no significant amounts of stable photoproducts were formed (the ions will not recombine in ethanol 1201). It is concluded that this annihilation process is not involved to any appreciable extent for these two are matics in the solvents used. One may then consider that generation of excited singlet and triplet states are the only important annihilation processes for anthracene (A) and naphthalene (N), which leads to PO == 0.08 for A and p. = 0.58 for N. The DF yields for A and N are thus mainly determined by the respective efficiencies of these two processes*_ Excited singlet formation in T-T annihilation has been postulated on theoretical grounds to involve a pure charge transfer state as the intermediate state (in crystals) [22]. However,experimental evidence favouring this mechanism is lacking at present. It may be noted that singlet exciton fission (Le.. the reverse of T-T annihilation) in tetracene and anthracene crystals is considered to involve more probably upper excited singlet levels 1231. We suggest an alternative model which allows a qualitative comparison between naphthalene and anthracene. In this model, it is assumed that the initial bimolecular state formed in a T-T encounter undergoes a radiationless transition to an upper excimer singlet, which is followed by dissociation or rapid relavation towards lower unstable excil
From the analysis of the &~a in terms of Merritield’s kinetic scheme [Zl], assuming mean effective interaction radii for T-T annihilation of 5.5 A for N and 7 A for A. one obtains for the rate constant of the singlet channel available to the encounter triplet pair 1.7 X 10” and 1.4 x lo”<’ I-ZSJXCtively for N and A and for the rate constant of the triplet channel 4.2 X 10” and 5.4 X 10” s-’ respectively for N and A.
E Tfibel, L. Lindqvisr/Excired Table 2 Vatucs of ti
Elcm-‘I
= E(’ Bb) - x(3La),
Hydrocvbon
E(‘Bb) (Xl@ cm+)
and pda)
ff12 b,
AE
pd
(debye’)
(X IO-”
Ro (A)
45.3
79.4
+2.7
0.56
5.3
Acenaphthcnc Pyrcne 1,2-Bcnwnthraanc Anthraccne (A) 9-Mcrhyl A 9.10-Dimethyl A 9-Phcnyl A 9,10-Diphenyt A Phcnanthrcnc
43.7 36.7 33.4 39
52.5 25.6 101.7
+1.9 +2.9 +0.4
0.31 0.27 -0.21
5.2 3.6 10.9
38.7 39.9
123.5 114.2 99.1 83 76.4 58.7
+9.4 +9.1 +9 +9.8 >9 -4.3
Fluorannlhene 3.4.Bcnzpyrcnc
34.9 34.5
16 55.4
-2.3 +5.1
-0.04 -0.03
3.8
Pcrylcne
39.6
29.7
+14.4
-0.02
2.2
38.4
39.2
NAPHTHALENE ‘q
L5.000 -
cm-’ 1
Naphthalenc
39.1
417
singlet yield in T-Tarrnihilarion
0.08 4 0.03 3.9 0.01 3.8 0.05 3.5 0.13 c3.5 0.05 -
35000.
a) AE data from rcfs. [ 27 Jand 11);Pd data from ref. [ 1) (in ethanol at room temperalure). b) Data from ref. [ 27 1or cstimated from spectra rcportcd in ref. 127).
ANTHRACENE mer singlet
states
(according
to previous
experimental
reports on direct excited singlet formation by T-T annihilation [ 1,241, this channel should be efficient at larger intermolecular distances than those required for excirner formation). The primary radiationless thannel of interest is suggested to lead to the excimcr singlet of ’ Bb parentage, denoted ’ B,E according to Birks’ notation [35]*. There are indeed some indications that the ’ B, singlet state, particularly, plays a role in the annihilation process. It is seen from table 2 that high pd values among Parker’s data [I] for aromatics in ethanol appear to be connected with low and positive w&es of the knergy gap AE = E(l BJ 2&(3 L,) (0 < hE < -3000 cm-‘). It may also be mentioned that delayed fluorescence from this excited singlet state to the ground state has been observed quite recently [26] for two of the compounds listed in table 2. A schematic model based on the potential energy curves of the initial bimolecular state and the lBbE state may be used (cf. fig. 3) to compare the probability of transition between these states (with spin conservation) and hence the excited singlet forma*
T RIA
Excimcr singlets of ’ Ba paentagc could be involved too (e.g., in the case of pyrcnc 1251) but this seems unlikely for antbra-
cene and napht+enc from both energy and oscillator strength considerations.
Fig. 3. Potcnlial energy curves diagrams for tlw singlet channel in anthracene and naphthalenc T-T annihilation respcctivel~: (3 L, + 3 b) denotes the encounter pair site with sin&t character. ’ BbE the upper excimcr single1 state of * Bb parentage. R the distance bcnvecn the two interacting triplets. The adia-
batic curves are drawn as a continuous
line.
tion rate for naphthalene and anthracene. It is assumed in this model that the ‘B,E state is mainly stabilized through dipole-dipole interaction and that the triplet pair may reorient itself rapidly into a sandwichlike configuration. The main parameters affecting the rate of excited singlet formation through the postulated radiationless channel are then m, the transition moment for the ‘A, + ‘Bb transition, and R,, the “crossing” distance for the potential energy curves. Predictions from this scheme agree with the observations that energy gaps AE have low and positive values and that R, > 4 A (except for pyrene) for the compounds with high pd values in table 2. It is clear from fig. 3 that the excited singlet formation rate should indeed be higher for naphthalene (m2 = 79.4 debye’ [27J, R. = 5.3 A] than for anthracene (m2 = 123.5 debye [27], Rt, = 4 A). If excited singlet generation, considered above, is more efficient for naphthalene, it should be noted that
478
F. Tfibel, L. Lindqrizr/lhired
a higher efficiency of triplet formation for anthracene may contribute also to the observed difference in DF yield between these two aromatics. However, the present knowledge on upper triplet states does not allow a substantiated evaluation of the role of this process.
6. Concluding remarks It is concluded from the detailed consideration of the annihilation channels that the DF yield for anthracent and naphthalenc is mainly determined by the efficiencies of the channels leading respectively to excited singlet and to triplet final states. The higher rate of DF for naphthalene is qualitatively accounted for by a model considering the possibility of radiationless transitions from the bimolecular state formed in a T-T encounter to an upper excimer singlet of I Bb parentage.
Acknowledgement
We thank Drs. A. Tramer and C. Tric, Professor H. Labhart and Professor R. Voltz for helpful discussions and suggestions. WC gratefully acknowledge the assistance of Miss E. BrCheret in carrying out the experiments.
References
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