J . Phys. Chem. 1990, 94, 4377-4378 potential. Where actually the photocurrent starts with respect to the flat-band potential is determined by recombination rates and/or charge capture cross sections of recombination centers in the semiconductor. Already with a band bending of as much as a few tenths of an electronvolt the concentration of electrons at the surface (calculated by using the thermionic model) is high enough to compensate for all low light intensity induced minority carrier concentrations. Therefore, the onset potential of -1.5 V (SCE) agrees well with a flat-band potential of -1.8 V (SCE). Registry No. CdS, 1306-23-6, lnstitut fur Solarenergieforschung GmbH Sokelantstrasse 5 0-3000Hannouer I , West Germany
Dieter Meissner
Receiced: July 17, 1989
TABLE I: Relative Rate Constants of IO2Phosphorescence, kp' =
kdkdCnHn)
solvent C6H6
CHCI, cyclohexane CHjCN tetrahydrofuran 2-ethylnaphthalene C6H& iodopropane C6H51
CHjCN H2O D20 CH,OH 2-propanol 1-methylnaphthalene C6H5F
Effect of Solvent on the Phosphorescence Rate Constant of Singlet Molecular Oxygen ( 'Ag) Sir: In this Comment we intend to (1) terminate the controversy about the solvent effect on the rate constant kp of singlet oxygen (IAg, IO2) phosphorescence initiated by us and (2) present a physically reasonable explanation of that extraordinary effect. Recently, we published relative kpl values varying from kpl(CH,CN) = 0.62 to kpl(CHC1,) = 1.16 if related to k,'(C,H6) = 1.' Considering the uncertainty, we interpreted our data on six solvents as accidentally scattering values of a solvent-independent kpl. This interpretation was in agreement with earlier studies on this subject2' but in conflict with several recent papers, which report a distinct solvent effect on kpl.&' In particular, our conclusions contradicted the work of Scurlock and Ogilby, which presents data for 15 solvents and points to a correlation between kpl and the solvent p~larizability.~ A Comment on our paper by Ogilby summarizes the controversy.6 In the meantime, we have extended our studies on kpl to 27 solvents using in part three different techniques. Our results are listed in Table I. Despite the scatter and the uncertainty of the kpl data, they clearly reveal that, in contrast to our previous interpretation, kpl is actually solvent dependent. Thus, we confirm the findings of Scurlock and Ogilby. Obviously, it was the small number of investigated solvents (indicated in Table I by FP) in combination with their unfortunate selection without alcohols and water which led us to the wrong conclusion of a solvent independence of kpl. With the exception of H 2 0 , the kpl values determined by time-resolved (TR) and stationary spectral (SP) techniques agree very well. Values of kpl have been determined recently in [TPPI-dependent measurements by the FP technique,' which compares sensitizer fluorescence as internal standard with IO2 phosphorescence. ( I ) Schmidt, R.; Seikel, K.; Brauer, H.-D. J . Phys. Chem. 1989, 93,4507. (2)Long, C.; Kearns, D. R. J . Chem. Phys. 1973,59, 5729. (3)Krasnovsky, A. A., Jr. Chem. Phys. Lett. 1981, 81, 443. (4)Scurlock, R. D.; Ogilby, P. R. J . Phys. Chem. 1987, 91, 4599. (5)Gorman, A. A.; Hamblett, I.; Lambert, C.; Prescott, A. L.; Rodgers, M. A. J.; Spence, H. M. J . A m . Chem. Soc. 1987, 109, 3091. (6)Losev, A. P.; Byteva, 1. M.; Gurinovich, G. P. Chem. Phys. Lett. 1988, 143, 127. (7)Nonell, S.; Braslavsky, S.E. Private communication. (8) Ogilby, P. R. J . Phys. Chem. 1989, 93, 4691. (9)Schmidt, R.; Brauer, H.-D. J . A m . Chem. SOC.1987, 109, 6976. (10)Schmidt, R. J . A m . Chem. Soc. 1989, 1 1 1 , 6983. ( I I) Aldrich Katalog Handbuch Feinchemikalien; Aldrich-Chemie: Steinheim, 1986. ( I 2) Rossbroich, G.; Garcia, N . A.; Braslavsky, S. E. J. Photochem. 1985, 31,37. ( I 3) Bonnet, R.; McGarvey, D. J.; Harriman, A,; Land, E. J.; Truscott, T. G.; Winfield, U.-J. Photochem. Photobiol. 1988, 48,271. (14)Gandin, E.; Lion, Y . ; Van de Vorst, A. Photochem. Photobiol. 1983, 37, 27 1.
0022-3654/90/2094-4377$02.50/0
4377
C,H,CI CiD,' C6D,Br C6F6
C,F,CI C6F;Br C6F51 C6H6
CzF4Br2 C6F131
Freon 113 CCI,
cs2
TPP TPP TPP TPP TPP TPP TPP TPP TPP RB RB RB RB RB TPP
SPe f20% i25% 0.62s 1.00 0.55 0.76 0.67 0.43 0.60 0.36 0.62 0.47 0.63 1.32 0.69 1.39 0.77 0.94 0.70 1.79 0.54 0.36 0.75' 0.08, 0.75' 0.191 0.81 0.26' 0.76 0.41' 0.34 1.97
TPP TPP TPP TPP TPP TPP TPP TPP RUB RUB RUB TPP TPP TPP
0.60 0.61 0.62 0.69 0.57 0.57 0.66 0.75 0.31"' 0.31" 0.31' 0.41"' 0.54" 0.51"'
S"
0.91 1.07 0.89 1.38 0.34' 0.59' 0.83' 0.82' 1 .oo 0.93' 0.94'
kpl TRd f25% 1.00 0.70 0.49 0.31 0.55 1.38 1.56 0.99 1.88 0.31 0.19 0.18, 0.29 0.3@
FP f33% kpl 1.00h 1.00 0.82h 0.76 0.46 0.45h 0.37 0.51 1.35 1.47 0.96 1.83 0.45h 0.37 0.12' 0.2@ 0.28, 0.42j 1.97
1.501 1.466 1.426 1.344 1.407 1.598 1.559 1.504 1.620 1.344 1.333 1.330 1.328 1.377 1.616
0.91 1.07 0.89 1.38 0.34 0.59 0.83 0.82 1.00 0.93 0.94 O.9Oh 0.90 0.62h 0.62 0.67h 0.67
1.465 1.524 1.498 1.557 1.377 1.421 1.449 1.497 1.501 1.400 1.328 1.358 1.460 1.627
nd
"Sensitizers (S): 5,10,15,20-tetraphenylphorphine (TPP), rose bengal (RB), rubicene (RUB). bQuantum yields Q, of IO2 formation by S in airsaturated solutions determined photochemically. 1,3-Diphenylisobenzofuran (DPBF) was the IO2 trap if not otherwise indicated. Q, values in C6H6, CHCIj, and CH,CN are averages of new measurements with DPBF and previous experiments with mesodiphenylhelianthrene (MDH).' In stationary spectral (SP) experiments integrated IO2 emission bands XIp of sample and of standard E:lp(ST) are compared. Setup is described in ref 9. The standards consisted of the same S dissolved either in C6H6 or in CH,CN and were optically matched. Evaluation according to the following equation, with 7, the actual IO2 lifetime:
In time-resolved (TR) experiments '0, phosphorescence following laser pulse excitation (0.05 5 EL 5 1 mJ) was extrapolated to the time directly after the decay of fluorescence of S yielding I p o values. Only experiments satisfying Ipo a EL have been evaluated. Setup is described in ref 10. Evaluation is according to
--kP kp(ST)
-
n2hoQA(sT) n2(sT)Ipo(ST)QA
cThe FP technique is described in ref 1. 'Solvent refractive indexes from ref 11. guncertainty only f5%. Literature values: 0.58,ref 12, and 0.63,ref 13. hCalculated from raw data of ref 1 and Qa values of Table I. 'Reference 14. 'Mean value kpl (RB,CHjCN) = 0.37 used as standard. Therefore, the average kp' is by the factor 0.37/0.334larger than the mean of kpl(SP) and kpl(TR). 'Qa(D20) = QA(H20) assumed. 'f35%. "'Reference 1, determined with MDH. "QA(C2F4Br2)= QA(C6H6)assumed, &25%. "QA(C6FljI) = &(c&) assumed, f25%.
Correcting for the slightly changed Q A values of TPP in C6H6, CHCI,, and CH3CN (see footnote b of Table I ) , slightly smaller kpl values than reported earlier are obtained, which agree with the results of the S P and TR measurements, proving the reliability of the FP technique. Using the quantum yield QP = 4.7 X of IO2 phosphorescence in c&6" and the corresponding lifetime 7, = 31 gs, we calculate the absolute value kP(C6H6) = 1.5 s-l. Multiplying kpl data of Table I with that value, we obtain absolute rate constants ranging from 0.18 s-' in H 2 0 to 3.0 s-I in 1methylnaphthalene. (15)Schmidt, R. Chem. Phys. Lett. 1988, 151, 369.
0 1990 American Chemical Society
1.1 . I
a-
Comments
The Journal of Physical Chemistry, Vol. 94, No. 10, 1990
4318
0.9 0.8 0.7 0.6 0.5 Q.4
0.3 0.2
Here Vis the solvent molar volume, N = 6.02 X IOz3 mol-', e = cm3j2g'/2 s-' is the charge, and me = 9.1 1 X 4.80 X g is the mass of the electron, c = 3.00 X 1O'O cm S-I, i indicates the strong solvent transitions, and trD = 16980 cm-' is the wavenumber of measurement of n. Thus, the approximation =D,~ uD2 holds quite well. Because of the large density of states in the high-energy region, most transitions lead to singlet states being nearly degenerate with some triplet state 3MI. Therefore, Making use of eq 4,19 with we approximate t ; f k / u k 2 by the statistical weights g2 = 3 and g, = 2, we finally obtain eq 5 linking the rate constant kpl with a macroscopic solvent parameter, i.e., the molar refraction.
u/Q,2.
0.7 0
0
+a
20
Molar
refraction
[cm-
BO
mol-']
Figure 1. Correlation of kpl with solvent molar refraction. Different symbols indicate different measurement techniques: ( 0 )TR, SP, and FP; (+) TR and SP; ( 0 )SP; ( X ) FP. Linear least-squares fit: slope 0.031 mol intercept 0.003.
The distinct solvent dependence of the IO2 radiative rate constant is an extraordinary phenomenon. Scurlock and Ogilby found a correlation between kpl and solvent polarizability P = (n2 l)/(n2 2). The kpl data of Table I can also roughly be correlated with P. The question arises how P influences kpl. A perturbation model developed by Andrews and Hudson predicts the dependence of the radiative rate constant of a forbidden transition on P if the energy separation of this transition and the next-nearest strongly allowed transition is small and dependent on P.I6 For O2 the first allowed transition that could borrow intensity occurs at 51 300 cm",'' which is too far apart from the 'A, 32,- transition at 7840 cm-' for effective perturbation. Moreover, the energies of the lowest singlet states of O2 are practically independent of the surrounding medium2 Thus, a direct influence of P on kp' via the energetical shift of electronic states of O2 can be excluded. Long and Kearns used a different approach to explain successfully the large difference between oscillator strengths of the 32,- ]A, transition determined either in the diluted gas phase or in the liquid phase., They considered electronic transitions of short-lived collision complexes of 0, and solvent molecule M, the electronic states of which are composed of the states of the individual species. For every solvent strongly allowed transitions with oscillator strengthsfk to higher excited singlet states 'Mk will exist that are almost degenerate with triplet states 3MI. Therefore, such a 3(32,1Mk)state of the collision complex can be strongly mixed with the triplet component of the almost degenerate 1s3*5(3Zg 3MI)state. Since the singlet component of the 1.3,5(32g3M,) state can be mixed via exchange perturbation selectively with the '('AgIMo) state with matrix element flexand 3MJ state since the singlet and triplet components of the 1*3,5(3Zg can be scrambled by spin-spin and spin-orbit interactions, some of the 3(32,1Mk)state character is added indirectly to the '('Ag1MO)state. In this way intensity from the strong 'Mo 'Mk transition is introduced indirectly in the 32, 'A, transition. Equation 1 was derived for the corresponding oscillator strength fa, wherefi = 0.2fk is the strength of the 02-perturbed 'Mo )MI transition and AEk = Ek - E, is the difference of energies O f 'Mk and
+
-
-
-
-
-
-
(1) We consider that several transitions 'Mo 'Mk with different numbers k contribute to the enhancement offa, if 3M, triplet states states. As strong solvent transitions occur exist nearby the ' M k only at Vk 2 50000 cm-1 >> D~ = 7840 cm-I, pk = zk - D, holds true. Equation 2 relatesf, with solvent absorption properties in a very similar way like eq 3 does for the molar refraction R of the solvent.I8 f A
=
Pex%/
AEk2
(16) Andrews, J. R.; Hudson, B. S . J . Chem. Phys. 1978, 68, 4587. (17) Calvert, J. G.; Pitts, J. N . , J r . Phofochemistry; Wiley: New York, 1967; p 205.
fn Figure 1 our values of kpl are plotted against R. Actually, the linear correlation without intercept predicted by eq 5 is found, although the data scatter considerably. From the slope we estimate the matrix element of exchange perturbation between '(3Zg3MI) and I(IAK1Mo)to flex= 8 cm-I. Hence, a very small exchange interaction is sufficient to account for the observed increase of the phosphorescence rate constant by 3-4 orders of magnitude in going from the diluted gas phase to solution phase2 and to explain the solvent dependence of kpl. The dependence of a forbidden radiative transition on solvent molar refraction should be a general effect. However, due to the third-order nature, solvent perturbation is rather weak and can be detected only for very low oscillator strengths, Le., in the present example in the range of f,(C&) = 2.5 x Considerably stronger transitions will not be influenced by the solvent due to that mechanism. That is the reason why the correlation of the radiative rate constant of '0, with R is such an exceptional phenomenon. Surprisingly, no particular heavy atom effect on the spin-forbidden radiative transition is noted. With the exception of kpl(C6H51),which deviates from the calculated fit by +50%, the k< values measured in iodopropane, C6F51,and C6Fl,I scatter randomly in the limits of uncertainty. The missing heavy atom effect is consistent with the perturbation model. Instead of the forbidden transition of an individual molecule, the transition of a collision complex perturbed by interactions between several of its excited states is considered. The probability for the multiplicity change is increased in the perturbation model by strong mixing of the state due to singlet and triplet components of the 1,3,5(32g3M,) spin-spin and spin-orbit interactions, which are considerable in the case of oxygen.2 Obviously, in that case a further enhancement of mixing between these components cannot be effected even by iodo substituents.
Acknowledgment. Support by the Deutsche Forschungsgemeinschaft and helpful discussions with Professor Dr. H.-D. Brauer are gratefully acknowledged. Registry No. 0,. 7182-44-1. ~~~~
(18) Kauzmann, W. Quantum Chemisiry; Academic Press: New York, 1957; p 688. (19) Reference 17, p 173.
lnstitut fur Physikalische Chemie Unicersitat Frankfurt Niederurseler Hang, 0-6000 FrankfurtlMain, F.R.G.
Reinhard Schmidt* Ebrahim Afshari
Received: September 29, 1989; I n Final Form: February I , 1990
