3928
STEPHEN
w.FELDBERG
A Possible Method for Distinguishing between Triplet-Triplet Annihilation and
Direct Singlet Formation in Electrogenerated Chemiluminescence'
by Stephen W.Feldberg Brookhaven N d w n d Laboratory, Upion, New York
(Received June 84, 1966)
Several workers have suggested that the observed singlet emission in electrogenerated chemiluminescence arises from a triplet-triplet annihilation mechanism rather than from direct singlet formation by the cation radical-anion radical reaction. The cation radicalanion radical reaction yields a triplet instead of an excited singlet; two triplets then annihilate producing the excited singlet. The quantitative aspects of parallel direct singlet and triblet-triplet mechanisms are calculated and compared to previously calculated relationships for the direct singlet formation. The difference between the two mechanisms becomes moat apparent only when there is significant triplet quenching.
A recent publication2 presented the relationship of the current, time, and light emission parameters for the electrogeneration of chemiluminescence at a single electrode using a doublestep controlled-potential technique. The quantitative relationships were calculated for the following mechanism (to be referred to m mechanism a)
R
+ e- -+
R- first potential step
R-+R++eR- -+ R +
R-
+ 2e-
IR*
+ hv
+ Z -% R
+ R -% 2R
(2)
(4)
light emission
(5)
quenching
(6)
self-quenching
(7)
The calculations indicated that when the rate constant for reaction 4 was very high, one could write the following simple expression for the generation of light as a function of time log wa = -1.45(tr/tf)'/'
+ 0.71
(8)
where t i and tr are the durations of the first and second potential steps and w., the normalized rate of light generation, is defined in relationship 9 The Journal of Phgsical Chemistry
where I is the rate of singlet emission in moles of photons per second, CR is the bulk concentration of R, D is the diffusion coefficient of all species, A is the electrode area, F is the faraday, and it is the current at time tt. The quantum efficiency, (o, is defined as
(1) (3)
+ R + -% IR* + R
IR* -% R IR*
1
second potential step
(9)
where CZ is the concentration of quencher 2. If the output of a photomultiplier tube, P , is proportional to I , then a plot of log Ptr"' us. (tt/tt)'/' should have a slope of -1.45. This relationship has been verified by Lansbury, Hercules, and Roe,a who investigated the chemiluminescence of rubrene in acetonitrile and dimethylformamide. Visco4 has also obtained verification in studies of rubrene in benzonitrile. The plots he obtained, however, had slopes of -1.9, slightly more negative than the theoretical - 1.45. Virtually all workers have at one time or another (1) Research supported by the U. 8. Atomic Energy Commission. (2) S. W. Feldberg, J . Am. Chem. Soc., 88, 390 (1966).
(3) R. C. Lansbury, D. M. Hercules, and D. K. Roe, presented at the Winter Meeting of the American Chemical Society, Phoenix, Ariz., Jan 1966, Abstract No. 28. (4) R. E. Visco, Bell Telephone Laboratories, Murray Hill, N. J., private communication.
SINGLET FORMATION IN ELECTROGENERATED CHEMILUMINESCENCE
slggested the possibility that reaction 4 generates a triplet state (instead of a singlet) and that a triplettriplet annihilation produces the excited singlet. This may be written as the following sequence of parallel reactions (to be referred to as mechanism b) mechanism a (reactions 1-7)
+
R++R--%3R*+R 3R* +
3R*
(11)
k12_ lR* + R
3929
close to the theoretical value predicted by eq 8 and 9 for (p = 1, then mechanism b can be ruled out. If, however, w is found to be less than the theoretical value, this does not necessarily imply y > 0 since the lower value may also be explained by cp < 1 as well as by y > 0. When the triplet-quenching term, p, becomes significant, however, the distinction between the two mechanisms becomes more apparent. For p >> 8ywa, eq 14 reduces to (see Appendix, eq A9 and A10)
triplet-triplet annihilation (12) 3R*
+ Q -% R
triplet quenching
(13)
The objective of the calculations in this paper is to show that the slopes greater than -1.45 might be a manifestation of mechanism b and to show further what experimental conditions might be best suited for distinguishing mechanism a from b. On the basis of eq 8 and 9, it is possible to obtain a modified equation describing the behavior of mechanism b by introducing the added parameters kll, k12, k13, and CQ, the concentration of quencher, Q. The term I/cp of eq 9 is really the rate of production of excited species and thus wa may also be defined as the normalized rate of production of excited species. The details of t,he derivation are presented in the Appendix. The normalized light emission for mechanism b, Wb, is defined in the same way as wa in eq 9, and
where is defined as
and y is defined as the fraction of cation radicalanion radical reactions producing triplets
The behavior of mechanism b as described by eq 14 is interesting. When y = 0 (ie., 100% direct singlet production), one obtains the trivial result
(17) When y > 0, the equation depends greatly upon the magnitude of the triplet quenching term, p. When /3 = 0, eq 14 reduces to Wa
=
(1 -
Wb
(18) If the light-measuring system is accurately calibrated and one can obtain an experimental value for w which is Ob
=
'/Zy)Wa
When y = 1, eq 19 further simplifies and may be written in the form (substituting from eq 8) log W b = -2.90(tr/tr)1" - log P f 1.42
(20)
This expression may explain the slopes more negative than -1.45 observed by several workers3s4in their plots of log Ptr"' vs. (tr/tf)'''. For those values of y and p, which do not lead to simplified equations, eq 14 may have to be graphed for various values of these parameters and compared to plots of experimental data.
Discussion Equations 20 and 8 indicate that the difference in slope (-2.90 instead of -1.45) could provide an unambiguous method of distinguishing between mechanisms a and b. The major experimental difficulty may be in finding a suitable triplet quencher. It must be sufficiently electroinactive so that it will not be oxidized or reduced at the electrode surface or react with the anion or cation radicals. Chandross and Visco5have suggested that the radicals themselves may act as triplet quenchers. Calculations of this mode of quenching are much more complex since they involve the radical concentrations. In that region of the diffusion layer where triplet concentration is greatest (the region of maximum light output2), the radical concentration will be a minimum and the exact value of the concentrations will depend on the rate constant for the anion radical-cation radical reaction. The fact that several workers have obtained data plots close to the theoretical -1.45 slope3** indicates that if the triplet-triplet annihilation mechanism obtains, triplet-radical quenching either does not occur or has only a small effect upon the behavior of the system. Appendix The rate of production of excited triplets and sin~
( 5 ) E. A. Chandross and R. E. Visco, Bell Telephone Laboratories,
Murray Hill, N. J., private
communication.
Volume 70,Number 12 December 1966
STEPHENW. FELDBERG
3930
glets by the counter-ion reaction may be defined as
L = I/cp
(-4-1)
where I is defined following eq 9. Assume that the number of triplets formed is a constant fraction, y, of L. Thus, if T = triplet concentration dT/dt, = y L / A
- k12T2 - kl3C~T
(A-2)
Thus for large values of 8, eq A-8 reduces to
(A-10) or for y = 1 log Wb = -2.90(t,/tf)”’
where A is a reaction volume. Assume A = fA(Dtf)’/’
logf
(A-3)
where f is a constant to be evaluated later. Since klz is probably quite large, the right-hand side of (A-2) may be set equal to zero. The resulting quadratic equation is easily solved
-
- log 0 + 1.12
(A-11)
When y = 1, it is possible to obtain a solution to the problem directly by using the computer technique described p r e v i o ~ s l y and ~ ~ ~thereby ,~ evaluate the constant f. The equation that may be written directly from the computer solution is log Wb = -2.90(k/tr)”’
- log p + 1.40
(A-12)
From eq A-11 and A-12, one can calculate The rate of production of excited singlet by triplettriplet annihilation and by direct singlet production is
ds = Ak1zT2/2 + (1 - y)L dt
(-4-5)
(A-13)
or
f = 0.525
0.5
(A-14)
Substituting this value for f in eq A-8 leads directly to eq 14.
and the rate of singlet light emission is
ds c p z
logf = -0.28
1/2y)0 (A-8)
Acknowledgment. The author wishes to thank Professor R. A. Marcus of the University of Illinois, Urbana, Ill., who suggested that an investigation of quenching effects might permit distinguishing a triplet-triplet annihilation mechanism from a pure singlet mechanism (mechanisms a and b in this paper.) The author also wishes to thank Professor David Roe, Massachusetts Institute of Technology, Cambridge, Mass., Dr. Robert Visco, Bell Telephone Laboratories, Murray Hill, N. J., Dr. Donald Maricle, American Cyanamid, Stamford, Corm., and Dr. Jack Fajer, Brookhaven National Laboratory, for their helpful discussions andsuggestions.
where is defined in eq 15’ and by eq A-3’ The ap proximation for the term (1 X)’”is (for X
