Volume 3$, number
ENERGY
TRANSFER
H. PORT, D. VOGEL Physihlisches Received
Institut.
10 Slarch
1 July 1975
CHEMICAL !‘HYSICS LETTERS
1
WA GUEST EXCITONS
IN ISOTOPIC
MIXED NAPHTHALENE
CRYSTALS
and H.C. WOLF Teilinstitui
3, Universitht Stgttgart.
Gern~~~y
1975
The temperature dependence of the fluorescence spectra ofqegregates in napkthalene-perdcuteronaphthalcnc mixed crysti has been investigated between 1.4 and 70 K and for concentrations up to 50% naphthalene. It is shcwn that the most abundant traps - the monomer guest molecules - transfer energy like a guest cxciton band 46 cm-’ below the host exciton band. With incrusing temperature, the excitation energy is redistributed between the diiferent aggegatc traps by thermal activation into the monomer states. The enegy transfer constant within the monomer exciton band is measured as a function of concentration. It is sugscsted that dipole-dipole interaction between the monomer guests is responsible for the energy transfer via guest esci:ons.
1. Introduction The optical properties of the aggregates in isotopic mixed crystals have been studied previausIy mainly in order to get information on the nearest neighbour intermolecular resonance interaction [l-8]. Careful measurements of the relative intensities of the different aggregate subspectra in the fluorescence spectra of naphthalene (N-ha)-perdeuteronaphthalene (N-d8) mixed crystals gave evidence for an efficient energy transfer between the aggregates without participation of host excitons [9] . The present study on the temperature dependence of fluorescence intensities within the aggregate spectra verifies the tentative interpretation in [9] for an energy transfer via the dilute exciton band formed by the guest monomers. Frqm an analysis of the intensities in the aggregate spectra as a function of concentration and temperature, evidence is given for the existence and action of this guest exciton band. Dipole-dipole interaction seems to be responsible for energy transfer within this band.
2. Experimental
techniques.
The fluorescence spectra of Ndi,/N-lz, talswithN-~~8concentratiqnsc=0.01;1.5;~;6;9;15;
mixed crys-
30; 50% were measured with the same spectrometer as described in [9]. From the photoelectrically recorded spectra the relative intensities of ‘Lhesubspectra were taken essentially by measuring the heights of typical lines within these spestra. These are mainly the 0,O transition (at 3 1540 cm-l for the monomer) and the vibronic transitions 0,0-512 and O,O-937 cm-‘. Superimposed lines were subtracted geometrically. Ifthe temperature dependence of the line width is the same for the different subspectra, the relative intensities of the subspectra as a ftinction of terrlr,erature can be meas. ured in this way without appreciable error.
3.
Aggregate
spectra
at 1.4 K
The fluorescence spectra of the mixed crystals are superposition of emission from monomers, dimers, trimers and higher aggregates. The relative intensities cf these subspectra are concentration and temperature dependent. A survey of al!. subspectra observed and assigned at 1.4 K at different concentrations is given in fig. 1. These rest&s essentially-reconfirm the observations reported in 191. Several additional assignments were possible. For assignment, we used (i) polarization ratios, (ii) estimates of energy shifts caused by superexchange i_nteraction [7] and (iii) ,rhe strong concentration depenhence of relative intenbtieiwithin the aggregate. ‘spectra which will be discussed below. ; 23 2
Volume
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CHEMICAL
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6
PHYSICS
9
LFXTERS
I5
i
A = = -
I
.____
L
r.l
P j_
1 1 6
T
9
20.9 2.21 23.6 25.8
I
a-
I
higher
trimcrr aggrcgater
I5
Fig, 1. Energy scheme of aggregate levels. The energy s&e refers to the monomer level at 31540 cm-‘. contribute to the fluorescence qzectra observed at 1.4 K for different guest concentrations. On the right energy differences between the monomer level and the aggregates are given together with the assip-nent. the aggegzte lines are characterized by these energy values.
4. Temperature
dependence of intensities
At all concentrations investigated, the relative intensities of the different aggregate subspectra are temperature dependent. In fig. 2 it is clearly shown that with increasing temperature the monomer trap intensity in-
Creases whereas the aggregate intensities decrease, especially the dimer spectra. Qualitatively this dependence can be understood as follotis: ,The most abundant .tra:ps -- the monomers are present in such tigh cdncentration that they transfer energy like a guest excitor? band. This band is responsible fz: a redistribution of energy between the different traps. ,At 1;4 K, the excitation energy first absorbed in the host is transferred via the host exciton band to the traps : 24‘
.-.I.:, ‘. .. .’ _,
,. .._...‘.
It is shown which agzegtes hand scale the characteristic In the following figures
according to their concentration. The monomer population is transferred partially to deeper traps. With increasing temperature, a redistribution within the aggregate traps takes place by thermal activation of the shallow traps into the monomer band and retrapping by deeper traps. When the temperature is high enough for thermal activation of even the deepest traps into the monomer band, all traps including the monoiners are in thermal equilibrium with each other and the relative intensities are now proportional to their concentrations. When the temperature increases Further, the total intensity goes
down by thermal activation into the host exciton band - but the relative intensities of the subspectra remain constant. This qu&tative explanation will be confirmed by the following quantitativti discussion..
.
Volume
34, number
CHEMICAL
1
r’s!- -
a= i 9’EZ- -
ez--
PHYSICS
LETTERS
1 July 197.5
Volume
34, ncmber
5. Discussion;
CHE.MlCAL PHYSLCS LETTERS
1
statistical
model of sensitized
fiuorescence
Since for ail concentrations investigated the host emission can be neglected clue to sensitized guest ernission, we have to consider the different trap emissions from N-Jr8 monomers
and aggregates
(1) where p, and phi are the statistical probabilities for 2 specific aggregate A and the monomer M at 2 given guest concentration and E hre the relative capture cross sections, which in our approximation are 1 for a monomer, 2 for a dimer, 3 for a trimer 2nd so on. In calculating the statistical probabilities p, one has to count only those aggregates which are completely surrounded b:q host molecuIes. Only these isolated aggregates contribute to the observed sharp aggregate emission. The probabilities to find isolated N-11, molecules, pairs and trimers respectively nre given by the relations phi =c (1 - C>=, %
where c = q'hr isthe guest concentration, the number of guest molecules II divided by the total number of molecules _N.z are coordktion numbers which count the minimum number of host molecules which must be nearest neighbour to the monomer, dimer, trimer, r&pectivelp, in order to make this guest “isolated”. We used the vdluesz = 9, 13, 16 and 17 (i 25%) for monomers, AS-pairs, AA-pairs and ABA-trimers, respec-
tive!y. This set of z-values was determined by comparison with ihe experimentally observed concent:ation deperidemze of the different trap emission intensities. Table 1 gives the aggregate probabilities 2s calculated fey different guest concentrations. The statistical probability of 2 distinct agg:egatz configuration, for instance of an AA or-y pair (ABA trimer) is only a fraction of
16‘. :
.. . .
PAA =PAB
probability
=Y‘P&
PABA ==+m,,-
For more details, see ref. [lo] .
6. Comparison
with experiment
These statistical considerations are the basis for understanding the observed relative aggregate emission intensities. The fluorescence intensities of aggregate lines se&ztilye to the rnonofner irztetzsiv, IT’ = I,/IkI,
can be
calculated from eqs. (1) 2nd (2) as 2 fun&on of the guest concentrations. The observed intensity ratios I re,obsePed zre always much larger than the ratios which are calculated using eqs. (1) and (2). The factors F=I
rel,obW&-cSuICtlhted
are given in table
1. They increase
with increasing
con-
centration. Apparently
the relative intensities of the aggregates are much larger than expected in the absence of an energy transfer from the monomers into the aggregates. The basic assumption for the statistical description, the exclusive sensitization of aggregate levels via the host band, is not fulfilled. l%e sfroflg deperzdeme of Forz the guest cormtztratiorz ipldicatcs at2 erlera transf‘er rvithirz tlze guest system. A thermally activated en-
transfer vi2 the host exciton band can be excluded since al 1.4 K the value of h-T is small as compared to
ergy
(2)
p-r = c3(1 - c)‘,
‘_
the total pair (trimer)
only.
In the low concentration/deep trap limit the excitation energy is transferred from the host exciton band into the different traps according to their concentration and capture cross suction. The emission intensities of the different 2ggre;ates f,t relative to the emission intensity of the monomer tlap IkI are therefore given by the relation
=c2(1 - #,
1 July 1975
the trap depth of the monomer which is 43 cm-l. A careful analysis of the temperature deperrdeme 2s shown in fig. 3 gives evidence for the mechanism of
this redistribution of energy between the traps: The Arrhenius plots for the aggregate line intensities give as actimtiotz etzergics for thermal depopulatiolz of the ipldividual aggregate traps tlze spectroscopicall) mea.+ rued trap depth below the inotzonzer kw! with a very
good accuracy. This result czn be understood 2s follows: the monomer level is able to transfer energy between traps. it acts as a “dilute” or quasi-exciton band in the crystal.
In the temperature
region between
1.4
and 10 K
all traps are successively depopuleted into the monomer level, according to their depth below the mo-
nomer band. This interpretation explains quantitatitiely both the increase of monomer intensity anti the redistribution of the intensities of different trap states with
Volume 34, number 1
CHEMICAL PHYSICS LETTERS
1 July 1975
Table 1
Concentraticn dependence crystals N+:N-\-irg a)
of statistical
probabilities
p and experimentally
dctcnnined
energy transfer parameters
c(mol 5) 1.5
in isotopic mixed
___-
3
6
9
PM
1.31 x 1oP
2.28 x lo-’
1.44 X LC2
3.85 x 18’
pAEi
1.85 x IO*
6.06 x IO”
1.61 x lo-’
1.38 X 1O-3
5.53 x lo4
1.34 x 1o-3
1.79 X 10-3
-1.61 x lo-’
7.54 x 10-s
1.4i x 10-j
192 196
275 257
PA A
1.77 x lo*
PABA FP
2.61 x 10% AA-pair
AB-piI
14 17
35 39
FT
ABA-trimer
1.3
31
194
li20
k
from AA-pair from AB-pair from ABA-trimcr
1.05 x lo3 1.276 x lo3
1.67 x lo3
5.57 X lo3
1.76 x lo3
5.7
7.15 x lo3 6.67 x lo3 6.79 x lo3
x 10;
a) p -- stntistiul probnbi:ities of monomers, AB-pairs, AA-pairs and ABA trimers isolated, from each other, calculated using ccl. (2). fi- = cxperimcntaliy determined F-values, F = I,,, observed/lrel,calcult~~, at 1.4 K. k = energy tnnsfcr constants k of the monomer/nggregatc system at 1.4 K from eq. (3). ’
increasing temperature (figs. 2 and 3). It is this specific temperature dependence as shown in fig. 3 which justifies the concept of a quasiexciton band.
7. The mechanism
exciton
of energy
transfer
within
the guest
band
In order to elucidate the transfer mechanism within the guest exciton band described above, we determined the transfer constant k For the process of sensitized emission of deeper traps via the monomer band. In order defines
to analyze a transfer
the sensitized constant
I&
= kcG ,
where
IH and IG are host
fluorescence
[ 111 one
k by the equation (3) and guest
intensities,
respec-
and cc is the guest concentration. In our case, we replaced the concentration cG by the weighted statistical probabilities of the aggregates @J2 for pairs, 3pT/2 for Cmers - see above). The k-values at 1.4 K (neglecting thermal detrapping) of the AA-pairs (7.9 cm-l), AB-pairs (15.1 cm-‘) and ABA-trimers (22.1 cm-‘) are given in table 1. For our discussion not the absolute intensities but rather the strong concentration dependence are of primary interest. In order to calculate the dependence of the transfzzr efficiency within the monomer band From the average distance r between the monomer guest mdecuies in the mixed crystal, ,we plotted in fig. 4 the tively
i-l/ K-’ Fig. 3. Intensity of different aggregate lines as a function of the reciprocal temperature, 6% NAB in N-dg, vibronic transition 0,0-937crri‘. To compare relative intensities rhe values for the lines 4.9 cm-‘, 7.9 cm-’ and 15.1 cm-t must be multiplied by a factor of ten. Activation energies AE 8s determined from ihe slope in the high temperature region are listed in the figure.
27
Volume 34, number 1
CHEMICAL
PHYSICS
LETTERS
1 July
1975
band formed by the monomers. From our experiments we cannot say whether or not this energy transfer is due to excitons characterized by a well defined wave vector.
Acknowledgement This work was supported gemeinschaft (SFB 67).
by the Deutsche
Forschungs-
References Fig. 4. Transfer cotstant k for the guest exciton band 3s a function of the square OF phi, the statistical probability for mono-
mers @M is proportional
to rA)_
,empirical transfer constant k as a frrnction of the square of the !Xatisticd probability for monomers, PM. If phi is proportional to rm3, the experimentally determined linear relationship in fig. 4 is equivalent to a proportionality between the efficiency of energy transfer and rs6. According to Fijrster [ 121 such an r-6 dependence can be well understood by dipole-dipole interaction. In conclusion, our experiments suggest enera transfer by dipole-dipole interaction between the monomer guest states in an isotopic rnked crystal at concentrations larger than approximately 0.1%. Since the energy difference between the monomer states and the deeper traps is needed for energy transfer from trap to trap to occur we use the concept of a quasi or dilute exciton
[ 11 E.F. Sheka, Opt. Spectry. 10 (1961) 684. [2] E.R. Bernstein, S.D. Colson, R. KopeLnan and G.-W. Robinson, J. Chem. Phys. 48 (1968) 5596. [3] D. Hanson, J. Chem. Phys. 52 (1970) 3409. [4] V.L. Broude and A.V. Leidermann, JETP Letters 13 (1971) 302. [51 V-L. Broude, A.V. Leidermann and T.G. Tratas, Soviet Phys. Solid State 13 (1972) 3059. [61 H.K. Hong and G.W. Robinson, J. Chem. Phys. 54 (1971) 1369. 171 H.K. Hong and R. Kopelman, 5. Chem. Phys. 55 (1971) 724. iSI C.L. Braun and H.C. Wolf, Chem. Phys. Letters 9 (1971) 260.
(91 K.E. hfauser, H. Port and H-C. Wolf, Chem.
Phys.
1 (1973)
74. Universitit Stuttgart (1974). [lOI D. Vogel, Diplomarboit, IllI H.C. Wolf, in: Advances in atomic and molecular physics, Vol. 3. eds. D.R. Bates and 1. Estermann (Academic New York 1967). [I21 T. F6rster. 2. Elektrochem. 64 (1960) 157.
Press,