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Submitted on 1 Jan 1985
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QUANTUM BEATS IN THE FLUORESCENCE
DECAY OF TETRACENE CRYSTALS
J. Fünfschilling
To cite this version:
JOURNAL
DE
PHYSIQUE
Colloque C7, suppl6ment au nOIO, T o m e 46, octobre 1985 page C7-377
QUANTUM B E A T S I N T H E FLUORESCENCE DECAY OF TETRACENE CRYSTALS
Physics I n s t . , KZingeZbergstr. 82, CH-4056 BaseZ, SwitzerZmd
Abstract
We have measured the fluorescence decay of tetracene crystals excited with ps-pulses of a dye laser with a time resolution of about 100 ps over 5 decades of the signal intensity. After some 200 ps after the excitation, the observed strongly nonexponential decay is mainly due to geminate recombination of triplet excitons that have been created by fission processes. The decay thus reflects the dynamics of the triplet motion, Superimposed are magnetic field dependent quantum beats that reflect the spin evolution of the triplet pairs. A quasi twodimensional random walk computersimulation yields a very good fit to the data. The resulting triplet hopping rates are smaller than the currently accepted values.
Magnetic field effects on exciton reactions in molecular crystals, such as triplet-triplet fusion or singlet fission, are usually studied with steady-state experiments, i.e. the observed quantity, such as the delayed fluorescence, is monitored as a function of the strength or of the direction of an external magnetic field on a timescale of seconds or longer. On the other hand, the established theories for these effects (developed by Johnson and Merrifield[l] and expanded by Suna [2]) are clearly dynamical theories that work on a timescale of nanoseconds or shorter: in fusion and in fission processes the crucial point is a dynamical equilibrium between the separation of the two involved triplet excitons and their fusion. So far, the results of these theories had to be time-averaged in order to allow a comparison with the steady state experiments.
The fusion process is modified by a magnetic filed dependent quantum beat phenomenon with beat frequencies in the GHz range. In an earlier paper [3] we have demonstrated experimentally the existence of these beats. In this paper we present experiments with much better time resolution and greatly improved dynamic range of the signal, which allows us not only to follow the beats over many cycles, but also to analyse the time decay of the signal in great detail.
EXPERIMENTAL
All experiments are performed with tetracene sublimation flakes. The most important features of the experimental setup are:
(1) The singlet excitons are excited with a synchronously pumped, mode- locked, cavity dumped dye laser operated at 4 MHz. The output is frequency doubled, which results in 5 ps-pulses of 2.5 pJ at 300 nm. (2) The fluorescence of the crystals iB measured (via a monochromator) with the single photon
C7-378 JOURNAL DE PHYSIQUE
counting technique. Both the time resolution (risetime: 70 ps) and the dynamic range (5 decades) are adequate for the experiment. (3) The tetracene crystal is mounted inside a small electromagnet, and its orientation is deduced from the position of the magnetic field resonances. Most experiments were done at 62 Celsius.
THEORY
We will use a description of the time evolution of a triplet pair after its creation by a fission process that is a extension of the approach of Johnson and Merrifield [I]. The starting point is the following kinetic scheme:
I(t) fission a
So
+
he.
S1-
(T,T)-
-3 separation (1) b re-f usion w(t'
)A light pulse I(t) excites the singlet excitons S1, which decay either radiatively (rate constant 5 , leading to the observed fluorescence) or by nonradiative fission into a triplet pair (rate constant a). After the fission process, the triplet separate by diffusion and move through the crystal. Since the lifetime of the triplet excitons in molecular crystals is in the milisecond range, they may meet again and even re-annihilate. After such an re-
annihilation, the singlets can undergo fission again and the diffusion starts anew. To take this possibility into account, the re-annihilation rate in the reaction scheme (1) is denoted by w(t'), where t' is the time elapsed since the last fission process. w(tt) contains all the dynamical information about the triplets. As can be seen from eq.(l), it influences the fluorescence decay and will ultimately be determined from the experiment.
Note that the time-dependence of w(t') includes both, effects of the quantum beats (which are also included in Johnson and Merrifield's theory) as well as effects of diffusion, which we treat in more detail than the rate-constant approach of these authors: we factorize w(t') in the form
where s(tt) depends only on the spin of the triplet pairs
-
it isresponsible for the beats and the magnetic field effects - and d(t') only on the spacial position of the triplets at time t'. w is proportional to the
probability of annihilation, if the two excitogs are on neighbouring lattice sites.
A
coupling between the spin and the spacial motion would, to a first approximation, lead to spin relaxation. Our experiments will show, that the effective spin relaxation rate is negligible on the timescale of the experiment. Eq.(2) can thus be regarded as a very good approximation.Instead of solving eq.(1..2) analytically, which is a formidable task, we try to construct a random-walk model that is based on these equations and that can reproduce our experiment with a minimum of parameters. The stepwise procedure is as follows:
parameters entering in step (3) are adjusted for a best fit.
There are three important parameters: the fission rate into the singlet channel a, the radiative decay rate b (more precisely: all decays other than described by a) and the in-plane hopping rate. With the introduction of a small out-of-plane hopping rate, the fit could be improved, but the influence on the other parameters due to the introduction of a fourth fit-parameter was not very pronounced.
RESULTS
Fig.1 shows two experimental decay curves. In curve a) the magnetic field is in an off-resonance direction, and no beats are expected nor observed. Note the large dynamic range of the experiment and the strongly nonlinear shape of the decay. In curve c), the field is slightly displaced from resonance, at beats are clearly observed during the whole decay. In fact, a more detailed study of the decay of the beat amplitude reveals that there is almost no damping of the beats, which is the confirmation of the negligible spin relaxation mentioned above.
Curve b) is a fit to a) (displaced vertically for clarity, in the scale of the drawing the two curves are practically undistinguishable). The excellent fit possible over the whole dynamic range is a clear confirmation of the validity of the model used.
The parameters of the fit are (in units of lo9 s-I): fission rate
a=5.8, radiative decay rate b=0.032, in-plane hopping rate 13.1 and out-of-plane hopping rate 0.006. The two larger values vary only slightly form fit to fit, the two smaller values are much more sensitive and may vary over a factor of five
.
The values for the hopping rates are at least an order of magnitude smaller than those deduced from steady state experiments [5]. So far, we have no
conclusive explanation for this discrepancy. It may well be that the triplets have some weak attractive interaction. This would decrease the initial hopping rate (our fit is most sensitive on the hopping rate in the beginning of the decay). It would also widen the resonances of the steady state experiments, which in turn would simulate a larger hopping rate. Both effects tend thus to reduce the apparent discrepancy in the observed parameters.
We would like to thank Prof. U.Wild and S.Canonica (ETH Zurich) for the permission to use their excellent laser system. Support from the Swiss National Foundation is gratefully acknowledged.
RERFFINCES
[I] R.C.Johnson and R.E.Merrifield, Phys Rev B1, 896 (1970) [2] A.Suna, Phys Rev B1, 1716 (1970)
[3] M.Chabr,J.Funfschilling, U.P.Wild and 1.Zschokke-Granacher Chem Phys 57, 425 (1981)
[ 4 ] G.Klein, Chem Phys Lett 57, 202 (1978)
JOURNAL DE PHYSIQUE LOG FLUORESCENCE - 1 - LUU A - f i r s - -
