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Spin—lattice relaxation in the triplet state of acridine in fluorene
Chemical Physics 90 (19%) North-Holland.
137-146
--
-2 I-
-137
Amsterdam
SPIN-LATTICE IN FLUORENE F. FUJARA’ Frete Uttiwrstriit
RELAXATION
and W. VOLLMANN Beditt.
FB IO. Arttrntullee
IN Tti
TRIPLET
STATE
OF ACRIdINE
’ 14, D-1000
Berlttt 32. Gettttott,
Recewed 28 November 1983: in final form 13 June 1984
Spin-lattice relaxation in the photoexcIted triplet state of a&dine m fluorenr has been me&wed using a transient electron spm nutation method from 20 K up to room temperature, m different magnetic fields and as a function of field orientation The data can be explained v.ith the model of a resonant two-phonon process via the magnetic sublevels of a thermally exctted tnplet state with an excitation energy of = 55 cm-’ and a lifetime of less than 2 ps. The exctted and the loaest triplet state differ in the orientation of their fine-structure tensors. The existence of another thermally ewited triplet state may be derived from the temperature dependence of the fine-structure parameter D.
1. Introduction With the development of time-resolved ESR techniques (electron spin echo, electron spin nutation) it has become possible to measure directly the electron spin dynamics. Thereby spin-lattice relaxation phenomena became accessible, which could earlier only be studied indirectly via cw ESR or via time-resolved phosphorescence as optical observable in photoexcited triplet systems_ In aromatic systems for instance, where radiationless processes dominate the triplet-state kinetics at room temperature, phosphorescence serves as an appropriate observable only at low temperatures [l-3]. It has been our aim to apply a suitable version of the electron spin nutation technique, to doped aromatic crystals in order to study the spin-lattice relaxation of the photoexcited guest molecules in the temperature region between 20 K and room temperature. As a result, we present the first relaxation data which cover such a wide temperature region_ ’ Present- address. Institut m_ Physikalische Chemie. _LJniversitlt Mainz. .Jakob-Welder-Weg 15. D-6500 Mainz, Germany. ’ Present address: Philips Fors~hungslaboratorium Hamburg, Vogt-KZXIn-Strasse 30. D-2000 Hamburg‘ 54. Germany.
When a guest molecule is doped substitutionally into a host crystal, the photoexcited triplet state of the guest molecule may be thermally excited to a nearby “local phonon state”_ Verbeek et al. [1,4] have worked out the idea that in this thermally excited triplet state the guest molecule has molecular axes orIented differently from those in the lowest state. This leads to a characteristic relaxation behaviour of the photoexcited triplet state. By stochastic jumps between the photoexcited triplet state and the local phonon state the initially polarized guest molecule will spin relax, depending on the excitatron lifetime and the orientation of the local phonon state. The theory of this model has been further worked out by one of us [5,6] for the case of only one excited phonon state with an activation energy much larger than the thermal energy. In this paper the theoretical interpretation is generalized to cover the full temperature region. The relax&ion behaviour contrast characteristicalli to that by other mechanisms, e.g., due to a one phonon process-a! low temperatures [3]. 1 The following questions should be answered: ‘Is the r&xation model of a resonant two-phonon process Ga a local ph?non state-
0301-0104/84/$03_00 0 Elsevier Science Publishers B-V_ (North-Holland Physics Publishing Division) -
excitation
energy?
one distinct
Are
there
possibly
more
than
23
DeiaJed ESR spin nutation
excitations? The
applied
method 2. Esperiments
and eqerimental
resuks
“delayed
2. I. Sutnple
created
at
a time
electronic triplet 2. the microwave ble time deiay
r after
nant
of
acridine-d,
tronic
deuterations
hosts and guests. have been examined
of both.
for compari-
B,
with
(nutation)
same
deuteration
creasing
guests (see section Preparation found
neither
for hosts nor
2-4).
and structural
information
can be
be noted that the system
fluorene doped with acridme is photochemically active [7-S] with typical time constants in the mrllisecond
region
for the photochemical
these times are much longer relaxation independent
times to be measured. processes
process.
Since
than the spin-latttce the assumption
nutation
dtfference addition.
of
The
elec-
the rf field
every
r
signal
amplitude relaxation_
is proportional
population In
around
it dies out_ For
transient
volved.
value
has the with
in-
Its ampli-
to the instantaneous the
two
of
the
parts
substates
in-
measurements
were performed using the overdamped spin nutation [10.9]_ Both methcds. the overdamped and the delayed
nutation
spin-lattice
relaxation.
of
is well justified.
transitions.
precesses
but a decreasing
(7)
states a high
the laser pulse and is reso-
-r due to spin-lattice
tude S,,,,
in ref. [7]. It should
until
this characteristic shape
in ref_
triplet
T = 0, producing
the ESR
magnetization
son its well. as will be explained below. It turns out that the relaxation rates are not sensitive to the of the molecules.
one
nutation”
polarization [7]_ As shown in fig. field is switched on with a varia-
For most of our experiments we used a fluorene-hi, single crystal doped with 1000 ppm of 1). Dtfferent
spin
and described
[9]_ By a short laser pulse the acridine are
(fig.
ESR
has been introduced
The band X-
experiments ( = 9 GHz)
and
even
gi\e identical were
carried
and K-band
better
in the
ESR - stgnol Smox(rllau
(=
results
for the
out in both. 24 GHz).
K-band
region.
X-
In the it is
T =70~
t
i -it_
:
Fig 1 Molr~ulsr structure of fhtorene and xridtne. the definiuon of the molrrular axes system (used later in thts work). and the unit-ceil itmcture of the fluorcne host c?stA
5ns
I I t
laser pulse
i : It :
Ftg. 2. Delayed ESR spin nutatton sgnal spm-r&cxatton measurements (see text)
as used
for the
Fujuru.
IV_ E’olin_tinn /
Spar - hirice reIuxutio!t_of triplet -state acridtne m fluorene
139
N+ NO N_ Fig. 3 Magnetic high-field limit.
substates-of
the molecular
tnplet
state m the
sufficient to characterize the triplet state relaxation by just two rate constants. W and W’, as introduced in fig. 3. Because the lifetime of the triplet state [S] is at all temperatures much longer than the observed signal decay times, the populaticn difference between the triplet sublevels can be treated as being changed by relaxation only. Due to the highly spin-selective intersystem crossing [11.12] and the fact that the three spin states are in good approximation eigenfunctions of S=, the initial substate populations are N+(O) = N_(O) # N,(O) very far away from the thermal distribution. Since the three spin substates are approximately equidistant and since the Boltzmann factor can be neglected we keep for all times: N+(T) = N_(r). Thus. the rate equations can be srmplified to: d(N,-ZV&dT=
-3W(N+-N,,),
yielding a mono-exponential spin nutation amplitude S,,
( T) = S,,
(0) e-3’tr-
(1)
decay of our initial
(2)
With the above stated assumptions the measurements are not sensttive to lv’. 2.3. Temperature dependence of the relaxation rate The spin-lattice relaxation rate W has been measured as a function of temperature between 20 and 300 K with the field oriented along the three molecular axes (i.e. B]]x, B]]y, B]]z, the axis system as introduced in fig. 1). The measurements have been performed in both X-band and K-band in the systems acridine-d, doped into fluorene-d&z, as well as fluorene-h,,, both systems yielding the same results within experimental errors. Typical K-band results are plotted in fig. 4. All orientations show the same overall T dependence of. W also for orientations when relaxation rates are different. A further im-
T-’
[10-2K-‘]
Fig 4 Temperature dependence of IV (measured for two molecular onentatlons as mdvzated). Apart from a fast component whch exists only for BII_\ (dashed hne) the tune IS uell described by cq (12) (solid line) as explained in sectlon 3.1
portant observation is that the relaxation rate appears to be the same in the X-band and in the K-band within experimental accuracy (10%). A weak (< 30%) additional fast relaxation component has been measured only for B]]x and T < 150 K. This additional rate is almost independent of temperature. The origin of this spurious relaxation process is not fully understood yet but may be assigned to cross-relaxation effects with neighbouring impurity molecules. The characteristic temperature dependence of the slow relaxation contributton (fig. 4) is apparently unaffected by the fast component. In the following we will therefore only dtscuss the slow component. 2 3. Ilrfluerrce of drfferent deuteration At T = 300 K, B]]x the relaxation rates in several differently deuterated systems, A-d,/Fld,,. A-d,/Fl-h,,, A-h,/Fl-d,,, A-h,/Fl-h,, at o0 = 2n x 9 GHz (X-band) and in A-ds/Fl-hi,, Ad,/Fl-d8h, at o =2~ X 24 GHz (K-band) have been measured. All measurements result in the same value W= (5.8 f 0.3) X 104_s-i, without any systematic deviation. Thus, we conclude that there
130
F- Fqara
W
Voiinra~rn / Sprn -lattice
is no deuteration effect on W within the experimental accuracy. neither for the host nor for the guest. Moreover. W turns out to be the same in the X- and in the K-band. as already stated in section 2.3.
rrfu_ut~~on of trtpIet -stute ucridtne
A
tit Jhorem
ABITI-ASl300Kl [Gauss] x
BII
x
(K-Band1
o
BII
x
Ix-Band)
I
.+ Blly
Z-5. Orienturtort dependence of rite relaxation rate
(K-Band)
CCI BIIv
(x-Band)
.
BIIZ
iK-Band1
*
B II?
(x-Band)
At selected temperatures (T= 93. 150, 300 K) the orientation dependence of W has been measured in the molecular -V-Z plane. as shown in fig. 5. These measurements were carried out m the K-band (at 300 K also in the X-band \\lth identical results. not shown here). It turns out that W is largest along the molecular principal-axes orientatlons. The overall angular shape changes smoothly with varying temperatures. -7.6. Tempera~ttre dependence
of the ftne-smtctrtre
parameters
Another relevant observation is the temperature dependence of the difference. AB = B, - B, of the resonance field values for the high- and lowfield transition with AB being given by (lugh-field limit. isotropic g-tensor [13])
200
T[K]
‘O”
Ftg. 6 hleasured shafts of the difference of the “high-field ’ and the -‘lox\-fkld” resonnnces relatt\e to its value at room tcmperaturtl The mea.urcments are explained b> an Increase of the finr-•-ucturc parameter D toward5 IOU temperatures and are fitted (aohd Ime) by cq (37) a evpkuned m sectlon 3 6
AB=D-3E. AB=D+3E. AB=2D.
(3)
D and E are the fine-structure parameters relative change Al?(T)-AB(300 K) is presented in fig. 6. This quantity is the same for [14]_ The
B/s and Bll_~_ From this finding it may be concluded that the parameter E does not contribute to the temperature dependence of AB(T). Concludmg, we find Blls.
Blj> :
AB( T) - AB(300 = D(T)
Bijz:
AB(T)
- D(300
- AB(300
=Z[D(Z-)-D(300K)].
K) K). K) (4)
where D(T) indicates that the parameter D IS temperature dependent_ Eqs. (4) are in agreement with fig. 6. The overall change of D from 0 to 300 K is = 3% L
i
I
1
6lIP
Bllr,
6 I&Z
2.7.
Temperatare
change
of
tlte fine-swucture
)
FIN 5. Onentnt~on dependence ol IV (logarithmic scale) in the molecular J -_= plane. measured rlt 93. 150 and 300 K. as indxated in the figure.
principal-axes
ortentations
Using cw ESR we measured the temperature dependence of the orientations (P,(T) of the mole-
_cule around. its molecular-x axis B]]v principal-axis orientation_ reach a precision of ~0.2“. The hardly different from zero: j&(300
K)--&(O
Ir)i
_ -by loo&g atthe We were-able to measured shift is ’
+0.2”.
_ -_
(9
A strong directional change of the spin axes such as in ref. [l] could not be measured.
Fig
7. Definttion
of the translt1on
probabilities
IV,_.,
and
rv,_,.
3. Interpretation We assume that for a&dine in fluorene a higher-lying thermally excited triplet state T,“’ exists in addition to the lowest triplet state T,“‘. Thermally induced excitation jumps occur with a rate such that the ESR experiment sees the averaged triplet state (fast-exchange limit). Although some experimental findings indicate the population of a further triplet state Tj’), we start with the assumption that just two triplet states T,“’ and T,‘” are relevant. 3.1. Temperature dependence of the relaxation rate The relaxation rate W measured experiment is given by
1
N(T)=
exp( E,/kT)
- 1_
Especially one has W o_laN(T), r(l)a
N(T)
Combining
W,_,o:N(T)+L + I_
(10)
(8) and (10) yields
WoaN(T)[N(T)+l]/[N(T)+l]=N(T)_
in the ESR
~=po~f$+p,W,.
(6)
where W; is the relaxation rate m T{‘) and where p, is the probabrlity that the excitation is in Ti’) as determined by the Boltzmann distribution:
(3) with p. +pl = 1. We note that eqs. (6) and (7) are modified in a straightforward way if more than two triplet states have to be taken into account. Let us consider the relaxation rate W,. We assume that W, is determined by an Orbach process with TL(l) as intermediate state. According to Orbach 1151one has W. 0: ~o_,~,,_o/~(‘)~
linewidth in Tit). The quantities Wo_.r, WI_o, r(l) can be related to the phonon occupation number N(T); it gives the number of phonons with energy Er as a function of temperature.
_
(8)
where W,_,( W, _o) (see fig. 7) is the probability that the excitation jumps from Tt”j to T{‘) (respectively from T{‘) to Tt”)) and where r(r) is the
(11) For low temperatures we approximate W according to eq. (6) by W, with the consequence that WaN(T),
W=
A exp( E,/kT)
- 1 _
(12)
The best fit of this formula to the measured data is shown in fig. 4, yielding E, = 49 cm-‘. The agreement between theory and experiment is good. There areslight deviations in the temperature range from 150 to 300 K; they can be connected with the violation of our low-temperature approximation and indicate the population of further thermally excited triplet states. Concluding, the analysis of the temperature dependence of the relaxation rate shows the existence of a triplet state T,“‘, which lies = 49 cm-’ above T,(o). \ 3.2. Influence of dtfferent deuteration Different deuteration of guest and host had no influence on the relaxation rate. The only dif-
F_ Fujarra. IV_ Volinmnn
14s
/ Spin - lu~trce reia ration of zn$et -s~ure ucridme m jluorene
ference between hydrogen and deuterium which might be relevant for the reIaxation mechanism discussed here is the mass. But the relative mass difference between a hydrogenated and a deuterated molecule of a&dine or fluorene is small. Therefore. the experimental finding is not surprising. _L?_ Inflrrence of magnetic field srrerrgth We have found that the relaxation rate does not differ in X-band (= 9 GHz) and K-band (- 24 GHz). In order to draw conclusions from this r\perimental result it is necessary to know what the theory predicts for the field dependence_ Under the assumption that the relaxation rate W may be approximated by LV, and that B’,.,.is determined by jumps between T,“) and Tir) it follows from ref. [6] that
Wa [l +(w)‘]-‘.
where ]a) and ]b) are neighbouring Zeeman states and where II(‘) is the hamiltonian of T,<“. It is assumed that the two hamiltoniaus If(O) and Ho’ differ in their fine-structure parameters Do and D, and in the orientation of their fine-structure tensors. The local phonon state which has been investigated in ref. 141is characterized by a different orientation of its Fine-structure tensor only. We allow here additionally Di and D, to be different. because we need this generalization for the discussion of the temperature dependence of the fine-structure parameters (see section 3.6). With respect to the eigenstates of the fine-structure tensor in T,(O) we may write H(O) - If(‘) as
fp'_
@I'=
0
+D,-E
0
o
$D,+E
I 0
0
-
0
(13)
where w is the angular frequency of resonance and 7 is the lifetime of T,“). Assuming that the experimental error is 10% one has to postulate that (2~ x 24 GHz x 7)’ < O-l_
i 0$D~-E
+D,+E
x0
(14)
0
0 0
0 _I
This results in 7 < 2 x to-‘”
fDo
s.
1
(15)
So T:‘) has a lifetime of less than 2 ps. This is so short that the model of fast exchange between Tie) and T:‘) is justified_ 3-J. Orientation dependence of the rela.ration rate
x
with
IV=
AD=
The orientation from ref. [6]:
06) dependence
~~~aI(,IH(O)--H(t)16)j~,
of
FV, can be taken
(17)
-9,
! +=
1
9,
9,
-9,
1 -
08)
*
Here It is assumed that the angles of rotation +,. 9,. 6: are small. The final result is
For the quantitative analysis of the orientation dependence we will restrict ourselves to the Iowtemperature case which is given For temperatures up to = 150 K. Then we know that the relaxation is determined by jumps between Tj”) and T,“) only. So we consider the case where w,.
-9:
34
w,__=
Do-D,. D
-
w,, E,
w,,
=
=
-2E,
D
+
E,
(20)
The orientation dependence has been measured in the molecular -r-z plane. So we define the Zeeman
hamiltonian
H,‘
by _ -
-7.
’ _ = -_ _ (?l)
where q and i are the direction cosines of the magnetic field B with respect _ to the molecular _ axes. With __ Ia)
=
2-m
(-i), .Ib)=(~).
(22)
we obtain ](U]H(O’ - H’lBjb)]z
Combmation
Wa
o,, = 2~ x 2.407 x 10’ s-l,
+ $J+tr,q)2-
(23)
of eqs. (16), (17) and (23) yields
+(Qi,W,,~+$$Jr,4)1-
0,: =2~x1.807x109s-’ and
[@,+(q’--rr’)-AD~~]* (24)
This formula allows us to find relative values for QP_,,, @#V%* @:%_,9 AD from a fit to the measured orientation dependence_ Fig. 8 shows the experimental data at T = 93 K together with a fit curve, which was obtained from eq. (24) with the four relative parameters { +P_,= : q,qz
Summarizing, the orientation dependence of the relaxation rate indicates that T,C’?ahdSTio! differ in the orientation of their fine-structure tensors. A small difference between -D, and Do cannot be excluded. The numerical vaiues [8] w.r, = 2?Tx 0.515 x 109 s-r,
=i[9,w,,(q11-rZ)-~Dqr12 + t(*,~W,,~
It has to be_ noted, however,- that the-fit: is-rather insensitive to the fourth relative parameteri:AD. for example,:- the- two parameter _-sets_ (1-I 1 : ( -0.1) : 0.33) and (1 f-1.1 : (-0.16) : 0) yield ht curves of comparable quality-to that of the Curve -_ _ shown in fig. 8. .
the relative
parameters (1: 1 : (-0.1)) for determine the relative mag@P,=: q,,w,, : +2+_, i nitudes of (p,, 4, &_ They are (1 : 0.75 : 0.35). An independent check of the fit parameters is possrble by comparing the values of W(Bllt) and W(Bllx). which have been experimentally determined at T= 93 K: H’( BIl_r) = 7.4 x lo3 s-‘(
+5%).
W( Bliz) = 13.6 x lo3 s-l(
+5%). .
Thus, : dwt,
= {l:l:(-0.1):0.17}.
: AD} (25)
W(4~)
Q-P= W( BjJz)
= o-54( & 10%) _
(26)
From eq. (24) we find that (27)
W(Bllr)a(~ro,,=)‘+(~,~_,,)2In analogy to eq. (27), W( B&c) is given by
(28)
W(Bllx)a(~,w,=)‘+(~=w,,)‘Combining
Fig 8 Orientation dependence of W at T = 93 K (linear scale) in the molecular y-r plane fitted with eq (24) as explained in section 3 4.
-=
eqs. (27) and (28) yields
[email protected])2~o
-
505
1*+1*
-
-
__
(2%
A comparison between eqs. (26) and (29) indicates that the measured value of W(Bllx) is consistent with the evaluation of the orientation dependence in the -V-Z plane. Concluding. we state that the orientation dependence of the relaxation rate can be explained with the assumption that the triplet state T:” has an orientation of the fine-structure tensor different from that of Tj”)_ The orientation dependence is hardly affected when T,“) and T,“) additionally differ in their fine-structure parameters D, and DO-
35 Temperature chunge princrpal-axes orxentations
of
the
fine-stmctrrre
The result that T:‘) and Tit) hale different orientations of their fine-structure tensors has the consequence that the orientation of the averaged triplet state should change with temperature. The experimental finding is j&(3OOK)-&(O
K)j
~-0.2~.
Under the assumption that onIy contribute to G,(T)-me may write z,(T)
=P~O(P’+P,O:“=P,
and T:”
x 0 +P@,
exp( - E,/kT ‘p”’
Tie)
(30)
)
= 1 + exp( - E,/kT)
“-
(31)
Since G,(O K) = 0. we have for E, = 49 cm-‘: !&(3OOK)-&(OK)i=~,(3OOK)=O.44+,.(32) A comparison
between eqs_ (30) and (32) allows us to find an upper bound for 9,_ It is 1.2O. From the relative magnitudes 1 : 0.75 : 0.35 for +, : 9, : p_ we derive I@,,\< 1.2”.
j+,/jO_9”.
3.6. Temperature
j+zj<0.40.
dependence
changes of the lattice parameters; (ii) an averaging effect where the effective D parameter changes with temperature-dependent weighting factors due to fast exchange between triplet states with dtfferent fine-structure parameters. Comparable reductions of D values have been reported as a consequence of a lattice widening with increasing temperature. As temperature-dependent X-ray data are lacking in the case of the fluorene crystal we cannot be certain whether the observed temperature change of D has to be attributed at least in part to such a lattice effect. Alternatively, we discuss the interpretation with the averaging effect. The experimentally determined quantity is D(T) - D(300 K). see eq. (4) We abbreviate it by .?,D( T). The first idea is to explain the temperature dependence of D with just T,(O) and T,‘“, because these two states gave a good explanation of the temperature dependence of the relaxation rate. As our attempt to approximate D by D=poDo
(34)
+P,D,
failed. it is necessary to introduce a state T,“) which has a much higher activation energy than T:” (see fig. 9). So we have to replace eq. (34) by D =poD,+p,D,
+plD,.
(35)
where D, is the fine-structure parameter in T:‘) and where p, is the corresponding excitation probability_ For this model there are four parameters which determine D(T): E,, E?. Do-D,, Do - D2_ This can be shown ds follows: AD(T)
= D(T)
K) 2
- D(300
1 = c
p,(T)D,-
=
[P,(T)
r-o
c ~,(300 z-o
K)4
(33)
of the fine-stmcture
pammeters
The fine-structure parameter D decreases from 0 to 300 K by = 3% (see fig. 6). This temperature dependence can be attributed to different reasons: (i) a site effect where the electronic molecular orbitals of a&dine and hence the fine-structure parameters change with temperature due to
1-o
-_p,(300
K)] Q-
(36)
Using p. C p1 + p2 = 1 we may write AD@->
= ;
[p,(T)
= (Do + (Do
-~,(300
D,)b,(300 D,)[
K)l(D,
-Do>
K)
~~(300
-P,(T)]
-
T,“’
E,=(315-+
,:‘I
E,=(SS+
,:a’
E,=
Ftg. 9 Energy
0
701
15)
cm-’
cm-’
cm-’
levels of the tnplet states
The best fit of AD(T) to the measured data is shown in fig. 6. The agreement is excellent. Combining the results of several fits we estimate the parameters as follows: E,=(55*15)cm-‘. D, - D, = (10 15)
Ez=(315f70)cm-r, G.
D, - D2 = (140 _+ 10) G. (38)
The values of E, as derived from the temperature dependence of the relaxation rate and from the temperature dependence of AD are consistent_ Even the difference Do - D, is consistent with the maximum tolerable contribution to the relaxation rate (as discussed in section 3.4). The fine-structure parameter decreases from TL(O)via T:‘) to T,‘“. The lowest triplet state Tjsr has a Do of 784 G, whereas Ti”’ has a D, which is 18% less. Concluding, it is possible to explain the temperature dependence of the fine-structure parameter by the averaging effect due to fast exchange with thermally excited triplet states.
4. Discussion The theoretical analysis of the relaxation rate is based on the assumption that the triplet state T,“’ is accompanied by a local phonon state T,C’) which has a different orientation of its fine-structure tensor. The local phonon state, which is trapped at the guest molecule, may invoke properties of guest and host. Since the guest acridine and the host fluorene have .&n.iiar masses and dimensions one may conclude that the local phonon state has properties similar to those of corresponding lattice modes of the pure fluorene crystal. The infrared
and _Raman spectra. df a fluorene single crystal show torsional lattice modes at 44, 46, 66 and 70 cm-’ [16]; this fits weh to the postulated energy of 55 115 cm-’ of T,“) obtained in this work. The temperature dependence of the Eine-structure parameter can be consistently~explained by the averaging effect of fast exchange. One may conclude that the triplet state T,“) has\a fine-structure parameter D which is slightly smaller than that of T{O)_ There is a third triplet state T,“’ at (315 f 70) cm-‘. Its D value is = 140 G smaller than that of T,(O). In the system a&dine in dibenzofurane the temperature dependence of D can be described by the same model with Do - D2 = 80 G. This indicates a strong influence of the host on T(“. Since we cannot rule out temperature-dependent site effects, the above conclusions on D(T) are not fully proven. There are two indications for the existence of a third triplet state T,“‘: (i) slight deviations between theory and the experimental relaxation rates which occur in the temperature region above 150 K, and (ii) optical spectra of a&dine in biphenyl which show vibrational modes at 248, 317 and 374 cm-’ 1171.This fits well to the postulated energy of T,C”.
Acknowledgement We would like to thank Professor D. Stehlik for many fruitful discussions and his continuous encouragement. Several discussions with Dr. C. Winscom are gratefully acknowledged. The work was partly supported by the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich 161).
References [l] P J F. Verbeek. A I M. Drcker and J Schmidt. Chem Phys. Letters 56 (19%) 585 [2] C J. Winscorn. Z Naturforsch. 30a (1975) 571 [3] F Dietz, U. Konzelmarm. H Port and M Schwoerer, Chem Phys. Letters 58 (1978) 565. [4] P-J-F Verbeek. H J den Blanken and J. Schmidt, &hem. Phys. Letters 60 (1979) 358 [S] W. Vollmann. Chem_ Phys 37 (1979) 239. [6] W Volhnann, Chem Phys 57 (1981) 157.
[7] R. Furrer. ;cZ Hemrich. D. Stehhk and H. Zimmcrmann. Chem. Phys. 36 (1979) 27_ [Xj B. Prass. E FLIJ~~ and D. Stehhk. Chem Phys 81 (1983) 175. [9] R. Furrer. F Ft~~arrt. C. Lange_ D. Stehiik. H M Vieth and W Volimann. Chem Phys. Letters 75 (1980) 322. [IO] S S Ktm and S I Weissman. Rev_ Chem. Intermed 3 ( 1979) 107. [Ill R Furrer. G. Gromer. A Kacher. M. Schnocrcr and H C Wolf. Chem Phys 9 (1975) 445
[13] S S. Kim and S I. Weisman. Chem. Phys 27 (1978) 21. [13] S P. rMcGl_ynn. T. Azumi and IM. Kimoshita. Molecular spectroscopy of the triplet state (Prentice-Hall. Englesood Chffs. 1969) 1141 J -Ph Griwt, Chem. Phys. Letters 11 (1971) 267. _ [IS] R Orbach. Proc Roy_ Sot AX4 (1961) 458. [16] A Bree and R Zwarich. J. Chem Phys 49 (196X) 912 [I71 D L. Narva and D.S McClure. Chem. Phys. 56 (1981) 167.
137-146
--
-2 I-
-137
Amsterdam
SPIN-LATTICE IN FLUORENE F. FUJARA’ Frete Uttiwrstriit
RELAXATION
and W. VOLLMANN Beditt.
FB IO. Arttrntullee
IN Tti
TRIPLET
STATE
OF ACRIdINE
’ 14, D-1000
Berlttt 32. Gettttott,
Recewed 28 November 1983: in final form 13 June 1984
Spin-lattice relaxation in the photoexcIted triplet state of a&dine m fluorenr has been me&wed using a transient electron spm nutation method from 20 K up to room temperature, m different magnetic fields and as a function of field orientation The data can be explained v.ith the model of a resonant two-phonon process via the magnetic sublevels of a thermally exctted tnplet state with an excitation energy of = 55 cm-’ and a lifetime of less than 2 ps. The exctted and the loaest triplet state differ in the orientation of their fine-structure tensors. The existence of another thermally ewited triplet state may be derived from the temperature dependence of the fine-structure parameter D.
1. Introduction With the development of time-resolved ESR techniques (electron spin echo, electron spin nutation) it has become possible to measure directly the electron spin dynamics. Thereby spin-lattice relaxation phenomena became accessible, which could earlier only be studied indirectly via cw ESR or via time-resolved phosphorescence as optical observable in photoexcited triplet systems_ In aromatic systems for instance, where radiationless processes dominate the triplet-state kinetics at room temperature, phosphorescence serves as an appropriate observable only at low temperatures [l-3]. It has been our aim to apply a suitable version of the electron spin nutation technique, to doped aromatic crystals in order to study the spin-lattice relaxation of the photoexcited guest molecules in the temperature region between 20 K and room temperature. As a result, we present the first relaxation data which cover such a wide temperature region_ ’ Present- address. Institut m_ Physikalische Chemie. _LJniversitlt Mainz. .Jakob-Welder-Weg 15. D-6500 Mainz, Germany. ’ Present address: Philips Fors~hungslaboratorium Hamburg, Vogt-KZXIn-Strasse 30. D-2000 Hamburg‘ 54. Germany.
When a guest molecule is doped substitutionally into a host crystal, the photoexcited triplet state of the guest molecule may be thermally excited to a nearby “local phonon state”_ Verbeek et al. [1,4] have worked out the idea that in this thermally excited triplet state the guest molecule has molecular axes orIented differently from those in the lowest state. This leads to a characteristic relaxation behaviour of the photoexcited triplet state. By stochastic jumps between the photoexcited triplet state and the local phonon state the initially polarized guest molecule will spin relax, depending on the excitatron lifetime and the orientation of the local phonon state. The theory of this model has been further worked out by one of us [5,6] for the case of only one excited phonon state with an activation energy much larger than the thermal energy. In this paper the theoretical interpretation is generalized to cover the full temperature region. The relax&ion behaviour contrast characteristicalli to that by other mechanisms, e.g., due to a one phonon process-a! low temperatures [3]. 1 The following questions should be answered: ‘Is the r&xation model of a resonant two-phonon process Ga a local ph?non state-
0301-0104/84/$03_00 0 Elsevier Science Publishers B-V_ (North-Holland Physics Publishing Division) -
excitation
energy?
one distinct
Are
there
possibly
more
than
23
DeiaJed ESR spin nutation
excitations? The
applied
method 2. Esperiments
and eqerimental
resuks
“delayed
2. I. Sutnple
created
at
a time
electronic triplet 2. the microwave ble time deiay
r after
nant
of
acridine-d,
tronic
deuterations
hosts and guests. have been examined
of both.
for compari-
B,
with
(nutation)
same
deuteration
creasing
guests (see section Preparation found
neither
for hosts nor
2-4).
and structural
information
can be
be noted that the system
fluorene doped with acridme is photochemically active [7-S] with typical time constants in the mrllisecond
region
for the photochemical
these times are much longer relaxation independent
times to be measured. processes
process.
Since
than the spin-latttce the assumption
nutation
dtfference addition.
of
The
elec-
the rf field
every
r
signal
amplitude relaxation_
is proportional
population In
around
it dies out_ For
transient
volved.
value
has the with
in-
Its ampli-
to the instantaneous the
two
of
the
parts
substates
in-
measurements
were performed using the overdamped spin nutation [10.9]_ Both methcds. the overdamped and the delayed
nutation
spin-lattice
relaxation.
of
is well justified.
transitions.
precesses
but a decreasing
(7)
states a high
the laser pulse and is reso-
-r due to spin-lattice
tude S,,,,
in ref. [7]. It should
until
this characteristic shape
in ref_
triplet
T = 0, producing
the ESR
magnetization
son its well. as will be explained below. It turns out that the relaxation rates are not sensitive to the of the molecules.
one
nutation”
polarization [7]_ As shown in fig. field is switched on with a varia-
For most of our experiments we used a fluorene-hi, single crystal doped with 1000 ppm of 1). Dtfferent
spin
and described
[9]_ By a short laser pulse the acridine are
(fig.
ESR
has been introduced
The band X-
experiments ( = 9 GHz)
and
even
gi\e identical were
carried
and K-band
better
in the
ESR - stgnol Smox(rllau
(=
results
for the
out in both. 24 GHz).
K-band
region.
X-
In the it is
T =70~
t
i -it_
:
Fig 1 Molr~ulsr structure of fhtorene and xridtne. the definiuon of the molrrular axes system (used later in thts work). and the unit-ceil itmcture of the fluorcne host c?stA
5ns
I I t
laser pulse
i : It :
Ftg. 2. Delayed ESR spin nutatton sgnal spm-r&cxatton measurements (see text)
as used
for the
Fujuru.
IV_ E’olin_tinn /
Spar - hirice reIuxutio!t_of triplet -state acridtne m fluorene
139
N+ NO N_ Fig. 3 Magnetic high-field limit.
substates-of
the molecular
tnplet
state m the
sufficient to characterize the triplet state relaxation by just two rate constants. W and W’, as introduced in fig. 3. Because the lifetime of the triplet state [S] is at all temperatures much longer than the observed signal decay times, the populaticn difference between the triplet sublevels can be treated as being changed by relaxation only. Due to the highly spin-selective intersystem crossing [11.12] and the fact that the three spin states are in good approximation eigenfunctions of S=, the initial substate populations are N+(O) = N_(O) # N,(O) very far away from the thermal distribution. Since the three spin substates are approximately equidistant and since the Boltzmann factor can be neglected we keep for all times: N+(T) = N_(r). Thus. the rate equations can be srmplified to: d(N,-ZV&dT=
-3W(N+-N,,),
yielding a mono-exponential spin nutation amplitude S,,
( T) = S,,
(0) e-3’tr-
(1)
decay of our initial
(2)
With the above stated assumptions the measurements are not sensttive to lv’. 2.3. Temperature dependence of the relaxation rate The spin-lattice relaxation rate W has been measured as a function of temperature between 20 and 300 K with the field oriented along the three molecular axes (i.e. B]]x, B]]y, B]]z, the axis system as introduced in fig. 1). The measurements have been performed in both X-band and K-band in the systems acridine-d, doped into fluorene-d&z, as well as fluorene-h,,, both systems yielding the same results within experimental errors. Typical K-band results are plotted in fig. 4. All orientations show the same overall T dependence of. W also for orientations when relaxation rates are different. A further im-
T-’
[10-2K-‘]
Fig 4 Temperature dependence of IV (measured for two molecular onentatlons as mdvzated). Apart from a fast component whch exists only for BII_\ (dashed hne) the tune IS uell described by cq (12) (solid line) as explained in sectlon 3.1
portant observation is that the relaxation rate appears to be the same in the X-band and in the K-band within experimental accuracy (10%). A weak (< 30%) additional fast relaxation component has been measured only for B]]x and T < 150 K. This additional rate is almost independent of temperature. The origin of this spurious relaxation process is not fully understood yet but may be assigned to cross-relaxation effects with neighbouring impurity molecules. The characteristic temperature dependence of the slow relaxation contributton (fig. 4) is apparently unaffected by the fast component. In the following we will therefore only dtscuss the slow component. 2 3. Ilrfluerrce of drfferent deuteration At T = 300 K, B]]x the relaxation rates in several differently deuterated systems, A-d,/Fld,,. A-d,/Fl-h,,, A-h,/Fl-d,,, A-h,/Fl-h,, at o0 = 2n x 9 GHz (X-band) and in A-ds/Fl-hi,, Ad,/Fl-d8h, at o =2~ X 24 GHz (K-band) have been measured. All measurements result in the same value W= (5.8 f 0.3) X 104_s-i, without any systematic deviation. Thus, we conclude that there
130
F- Fqara
W
Voiinra~rn / Sprn -lattice
is no deuteration effect on W within the experimental accuracy. neither for the host nor for the guest. Moreover. W turns out to be the same in the X- and in the K-band. as already stated in section 2.3.
rrfu_ut~~on of trtpIet -stute ucridtne
A
tit Jhorem
ABITI-ASl300Kl [Gauss] x
BII
x
(K-Band1
o
BII
x
Ix-Band)
I
.+ Blly
Z-5. Orienturtort dependence of rite relaxation rate
(K-Band)
CCI BIIv
(x-Band)
.
BIIZ
iK-Band1
*
B II?
(x-Band)
At selected temperatures (T= 93. 150, 300 K) the orientation dependence of W has been measured in the molecular -V-Z plane. as shown in fig. 5. These measurements were carried out m the K-band (at 300 K also in the X-band \\lth identical results. not shown here). It turns out that W is largest along the molecular principal-axes orientatlons. The overall angular shape changes smoothly with varying temperatures. -7.6. Tempera~ttre dependence
of the ftne-smtctrtre
parameters
Another relevant observation is the temperature dependence of the difference. AB = B, - B, of the resonance field values for the high- and lowfield transition with AB being given by (lugh-field limit. isotropic g-tensor [13])
200
T[K]
‘O”
Ftg. 6 hleasured shafts of the difference of the “high-field ’ and the -‘lox\-fkld” resonnnces relatt\e to its value at room tcmperaturtl The mea.urcments are explained b> an Increase of the finr-•-ucturc parameter D toward5 IOU temperatures and are fitted (aohd Ime) by cq (37) a evpkuned m sectlon 3 6
AB=D-3E. AB=D+3E. AB=2D.
(3)
D and E are the fine-structure parameters relative change Al?(T)-AB(300 K) is presented in fig. 6. This quantity is the same for [14]_ The
B/s and Bll_~_ From this finding it may be concluded that the parameter E does not contribute to the temperature dependence of AB(T). Concludmg, we find Blls.
Blj> :
AB( T) - AB(300 = D(T)
Bijz:
AB(T)
- D(300
- AB(300
=Z[D(Z-)-D(300K)].
K) K). K) (4)
where D(T) indicates that the parameter D IS temperature dependent_ Eqs. (4) are in agreement with fig. 6. The overall change of D from 0 to 300 K is = 3% L
i
I
1
6lIP
Bllr,
6 I&Z
2.7.
Temperatare
change
of
tlte fine-swucture
)
FIN 5. Onentnt~on dependence ol IV (logarithmic scale) in the molecular J -_= plane. measured rlt 93. 150 and 300 K. as indxated in the figure.
principal-axes
ortentations
Using cw ESR we measured the temperature dependence of the orientations (P,(T) of the mole-
_cule around. its molecular-x axis B]]v principal-axis orientation_ reach a precision of ~0.2“. The hardly different from zero: j&(300
K)--&(O
Ir)i
_ -by loo&g atthe We were-able to measured shift is ’
+0.2”.
_ -_
(9
A strong directional change of the spin axes such as in ref. [l] could not be measured.
Fig
7. Definttion
of the translt1on
probabilities
IV,_.,
and
rv,_,.
3. Interpretation We assume that for a&dine in fluorene a higher-lying thermally excited triplet state T,“’ exists in addition to the lowest triplet state T,“‘. Thermally induced excitation jumps occur with a rate such that the ESR experiment sees the averaged triplet state (fast-exchange limit). Although some experimental findings indicate the population of a further triplet state Tj’), we start with the assumption that just two triplet states T,“’ and T,‘” are relevant. 3.1. Temperature dependence of the relaxation rate The relaxation rate W measured experiment is given by
1
N(T)=
exp( E,/kT)
- 1_
Especially one has W o_laN(T), r(l)a
N(T)
Combining
W,_,o:N(T)+L + I_
(10)
(8) and (10) yields
WoaN(T)[N(T)+l]/[N(T)+l]=N(T)_
in the ESR
~=po~f$+p,W,.
(6)
where W; is the relaxation rate m T{‘) and where p, is the probabrlity that the excitation is in Ti’) as determined by the Boltzmann distribution:
(3) with p. +pl = 1. We note that eqs. (6) and (7) are modified in a straightforward way if more than two triplet states have to be taken into account. Let us consider the relaxation rate W,. We assume that W, is determined by an Orbach process with TL(l) as intermediate state. According to Orbach 1151one has W. 0: ~o_,~,,_o/~(‘)~
linewidth in Tit). The quantities Wo_.r, WI_o, r(l) can be related to the phonon occupation number N(T); it gives the number of phonons with energy Er as a function of temperature.
_
(8)
where W,_,( W, _o) (see fig. 7) is the probability that the excitation jumps from Tt”j to T{‘) (respectively from T{‘) to Tt”)) and where r(r) is the
(11) For low temperatures we approximate W according to eq. (6) by W, with the consequence that WaN(T),
W=
A exp( E,/kT)
- 1 _
(12)
The best fit of this formula to the measured data is shown in fig. 4, yielding E, = 49 cm-‘. The agreement between theory and experiment is good. There areslight deviations in the temperature range from 150 to 300 K; they can be connected with the violation of our low-temperature approximation and indicate the population of further thermally excited triplet states. Concluding, the analysis of the temperature dependence of the relaxation rate shows the existence of a triplet state T,“‘, which lies = 49 cm-’ above T,(o). \ 3.2. Influence of dtfferent deuteration Different deuteration of guest and host had no influence on the relaxation rate. The only dif-
F_ Fujarra. IV_ Volinmnn
14s
/ Spin - lu~trce reia ration of zn$et -s~ure ucridme m jluorene
ference between hydrogen and deuterium which might be relevant for the reIaxation mechanism discussed here is the mass. But the relative mass difference between a hydrogenated and a deuterated molecule of a&dine or fluorene is small. Therefore. the experimental finding is not surprising. _L?_ Inflrrence of magnetic field srrerrgth We have found that the relaxation rate does not differ in X-band (= 9 GHz) and K-band (- 24 GHz). In order to draw conclusions from this r\perimental result it is necessary to know what the theory predicts for the field dependence_ Under the assumption that the relaxation rate W may be approximated by LV, and that B’,.,.is determined by jumps between T,“) and Tir) it follows from ref. [6] that
Wa [l +(w)‘]-‘.
where ]a) and ]b) are neighbouring Zeeman states and where II(‘) is the hamiltonian of T,<“. It is assumed that the two hamiltoniaus If(O) and Ho’ differ in their fine-structure parameters Do and D, and in the orientation of their fine-structure tensors. The local phonon state which has been investigated in ref. 141is characterized by a different orientation of its Fine-structure tensor only. We allow here additionally Di and D, to be different. because we need this generalization for the discussion of the temperature dependence of the fine-structure parameters (see section 3.6). With respect to the eigenstates of the fine-structure tensor in T,(O) we may write H(O) - If(‘) as
fp'_
@I'=
0
+D,-E
0
o
$D,+E
I 0
0
-
0
(13)
where w is the angular frequency of resonance and 7 is the lifetime of T,“). Assuming that the experimental error is 10% one has to postulate that (2~ x 24 GHz x 7)’ < O-l_
i 0$D~-E
+D,+E
x0
(14)
0
0 0
0 _I
This results in 7 < 2 x to-‘”
fDo
s.
1
(15)
So T:‘) has a lifetime of less than 2 ps. This is so short that the model of fast exchange between Tie) and T:‘) is justified_ 3-J. Orientation dependence of the rela.ration rate
x
with
IV=
AD=
The orientation from ref. [6]:
06) dependence
~~~aI(,IH(O)--H(t)16)j~,
of
FV, can be taken
(17)
-9,
! +=
1
9,
9,
-9,
1 -
08)
*
Here It is assumed that the angles of rotation +,. 9,. 6: are small. The final result is
For the quantitative analysis of the orientation dependence we will restrict ourselves to the Iowtemperature case which is given For temperatures up to = 150 K. Then we know that the relaxation is determined by jumps between Tj”) and T,“) only. So we consider the case where w,.
-9:
34
w,__=
Do-D,. D
-
w,, E,
w,,
=
=
-2E,
D
+
E,
(20)
The orientation dependence has been measured in the molecular -r-z plane. So we define the Zeeman
hamiltonian
H,‘
by _ -
-7.
’ _ = -_ _ (?l)
where q and i are the direction cosines of the magnetic field B with respect _ to the molecular _ axes. With __ Ia)
=
2-m
(-i), .Ib)=(~).
(22)
we obtain ](U]H(O’ - H’lBjb)]z
Combmation
Wa
o,, = 2~ x 2.407 x 10’ s-l,
+ $J+tr,q)2-
(23)
of eqs. (16), (17) and (23) yields
+(Qi,W,,~+$$Jr,4)1-
0,: =2~x1.807x109s-’ and
[@,+(q’--rr’)-AD~~]* (24)
This formula allows us to find relative values for QP_,,, @#V%* @:%_,9 AD from a fit to the measured orientation dependence_ Fig. 8 shows the experimental data at T = 93 K together with a fit curve, which was obtained from eq. (24) with the four relative parameters { +P_,= : q,qz
Summarizing, the orientation dependence of the relaxation rate indicates that T,C’?ahdSTio! differ in the orientation of their fine-structure tensors. A small difference between -D, and Do cannot be excluded. The numerical vaiues [8] w.r, = 2?Tx 0.515 x 109 s-r,
=i[9,w,,(q11-rZ)-~Dqr12 + t(*,~W,,~
It has to be_ noted, however,- that the-fit: is-rather insensitive to the fourth relative parameteri:AD. for example,:- the- two parameter _-sets_ (1-I 1 : ( -0.1) : 0.33) and (1 f-1.1 : (-0.16) : 0) yield ht curves of comparable quality-to that of the Curve -_ _ shown in fig. 8. .
the relative
parameters (1: 1 : (-0.1)) for determine the relative mag@P,=: q,,w,, : +2+_, i nitudes of (p,, 4, &_ They are (1 : 0.75 : 0.35). An independent check of the fit parameters is possrble by comparing the values of W(Bllt) and W(Bllx). which have been experimentally determined at T= 93 K: H’( BIl_r) = 7.4 x lo3 s-‘(
+5%).
W( Bliz) = 13.6 x lo3 s-l(
+5%). .
Thus, : dwt,
= {l:l:(-0.1):0.17}.
: AD} (25)
W(4~)
Q-P= W( BjJz)
= o-54( & 10%) _
(26)
From eq. (24) we find that (27)
W(Bllr)a(~ro,,=)‘+(~,~_,,)2In analogy to eq. (27), W( B&c) is given by
(28)
W(Bllx)a(~,w,=)‘+(~=w,,)‘Combining
Fig 8 Orientation dependence of W at T = 93 K (linear scale) in the molecular y-r plane fitted with eq (24) as explained in section 3 4.
-=
eqs. (27) and (28) yields
[email protected])2~o
-
505
1*+1*
-
-
__
(2%
A comparison between eqs. (26) and (29) indicates that the measured value of W(Bllx) is consistent with the evaluation of the orientation dependence in the -V-Z plane. Concluding. we state that the orientation dependence of the relaxation rate can be explained with the assumption that the triplet state T:” has an orientation of the fine-structure tensor different from that of Tj”)_ The orientation dependence is hardly affected when T,“) and T,“) additionally differ in their fine-structure parameters D, and DO-
35 Temperature chunge princrpal-axes orxentations
of
the
fine-stmctrrre
The result that T:‘) and Tit) hale different orientations of their fine-structure tensors has the consequence that the orientation of the averaged triplet state should change with temperature. The experimental finding is j&(3OOK)-&(O
K)j
~-0.2~.
Under the assumption that onIy contribute to G,(T)-me may write z,(T)
=P~O(P’+P,O:“=P,
and T:”
x 0 +P@,
exp( - E,/kT ‘p”’
Tie)
(30)
)
= 1 + exp( - E,/kT)
“-
(31)
Since G,(O K) = 0. we have for E, = 49 cm-‘: !&(3OOK)-&(OK)i=~,(3OOK)=O.44+,.(32) A comparison
between eqs_ (30) and (32) allows us to find an upper bound for 9,_ It is 1.2O. From the relative magnitudes 1 : 0.75 : 0.35 for +, : 9, : p_ we derive I@,,\< 1.2”.
j+,/jO_9”.
3.6. Temperature
j+zj<0.40.
dependence
changes of the lattice parameters; (ii) an averaging effect where the effective D parameter changes with temperature-dependent weighting factors due to fast exchange between triplet states with dtfferent fine-structure parameters. Comparable reductions of D values have been reported as a consequence of a lattice widening with increasing temperature. As temperature-dependent X-ray data are lacking in the case of the fluorene crystal we cannot be certain whether the observed temperature change of D has to be attributed at least in part to such a lattice effect. Alternatively, we discuss the interpretation with the averaging effect. The experimentally determined quantity is D(T) - D(300 K). see eq. (4) We abbreviate it by .?,D( T). The first idea is to explain the temperature dependence of D with just T,(O) and T,‘“, because these two states gave a good explanation of the temperature dependence of the relaxation rate. As our attempt to approximate D by D=poDo
(34)
+P,D,
failed. it is necessary to introduce a state T,“) which has a much higher activation energy than T:” (see fig. 9). So we have to replace eq. (34) by D =poD,+p,D,
+plD,.
(35)
where D, is the fine-structure parameter in T:‘) and where p, is the corresponding excitation probability_ For this model there are four parameters which determine D(T): E,, E?. Do-D,, Do - D2_ This can be shown ds follows: AD(T)
= D(T)
K) 2
- D(300
1 = c
p,(T)D,-
=
[P,(T)
r-o
c ~,(300 z-o
K)4
(33)
of the fine-stmcture
pammeters
The fine-structure parameter D decreases from 0 to 300 K by = 3% (see fig. 6). This temperature dependence can be attributed to different reasons: (i) a site effect where the electronic molecular orbitals of a&dine and hence the fine-structure parameters change with temperature due to
1-o
-_p,(300
K)] Q-
(36)
Using p. C p1 + p2 = 1 we may write AD@->
= ;
[p,(T)
= (Do + (Do
-~,(300
D,)b,(300 D,)[
K)l(D,
-Do>
K)
~~(300
-P,(T)]
-
T,“’
E,=(315-+
,:‘I
E,=(SS+
,:a’
E,=
Ftg. 9 Energy
0
701
15)
cm-’
cm-’
cm-’
levels of the tnplet states
The best fit of AD(T) to the measured data is shown in fig. 6. The agreement is excellent. Combining the results of several fits we estimate the parameters as follows: E,=(55*15)cm-‘. D, - D, = (10 15)
Ez=(315f70)cm-r, G.
D, - D2 = (140 _+ 10) G. (38)
The values of E, as derived from the temperature dependence of the relaxation rate and from the temperature dependence of AD are consistent_ Even the difference Do - D, is consistent with the maximum tolerable contribution to the relaxation rate (as discussed in section 3.4). The fine-structure parameter decreases from TL(O)via T:‘) to T,‘“. The lowest triplet state Tjsr has a Do of 784 G, whereas Ti”’ has a D, which is 18% less. Concluding, it is possible to explain the temperature dependence of the fine-structure parameter by the averaging effect due to fast exchange with thermally excited triplet states.
4. Discussion The theoretical analysis of the relaxation rate is based on the assumption that the triplet state T,“’ is accompanied by a local phonon state T,C’) which has a different orientation of its fine-structure tensor. The local phonon state, which is trapped at the guest molecule, may invoke properties of guest and host. Since the guest acridine and the host fluorene have .&n.iiar masses and dimensions one may conclude that the local phonon state has properties similar to those of corresponding lattice modes of the pure fluorene crystal. The infrared
and _Raman spectra. df a fluorene single crystal show torsional lattice modes at 44, 46, 66 and 70 cm-’ [16]; this fits weh to the postulated energy of 55 115 cm-’ of T,“) obtained in this work. The temperature dependence of the Eine-structure parameter can be consistently~explained by the averaging effect of fast exchange. One may conclude that the triplet state T,“) has\a fine-structure parameter D which is slightly smaller than that of T{O)_ There is a third triplet state T,“’ at (315 f 70) cm-‘. Its D value is = 140 G smaller than that of T,(O). In the system a&dine in dibenzofurane the temperature dependence of D can be described by the same model with Do - D2 = 80 G. This indicates a strong influence of the host on T(“. Since we cannot rule out temperature-dependent site effects, the above conclusions on D(T) are not fully proven. There are two indications for the existence of a third triplet state T,“‘: (i) slight deviations between theory and the experimental relaxation rates which occur in the temperature region above 150 K, and (ii) optical spectra of a&dine in biphenyl which show vibrational modes at 248, 317 and 374 cm-’ 1171.This fits well to the postulated energy of T,C”.
Acknowledgement We would like to thank Professor D. Stehlik for many fruitful discussions and his continuous encouragement. Several discussions with Dr. C. Winscom are gratefully acknowledged. The work was partly supported by the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich 161).
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