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Temperature dependence of the lifetime of pyrene triplet excimer emission
TEMPERATUiiEDEFENDENCEOF~TH‘ELIl?l?l?IMEOF : -.I' PYRE~T~IPLETEXClME~~E:MiSSION ', :', ,. ;,
,' .._
Q&J. GIJtiMAI’4,~W.I-I. VAN LBEUWEN, J. L.ANGELA4R and J.&W. VAN VGGRST
.,
firtelrtory for Physical Chemistry, Universiry of A msterdatn, Amstwdum, The Nether&& Received 1 Septembk 1971
.
The stab&tion
ent$taIppies of-twodifferent kinds of tripletexcimers of pyrizre are caicukted f&n the tempera-
ture dependence of the triplet lifetime. They are found to Ix 800 cm-’ and 2000 cm”‘.
ments were performed with single crystal fIakes. At tem~ratur~s below 150*K the measurements refer to powdered pyrene.. Table 1 indicates that the delayed excimer fluorescence intensity depends ~ost.quadrati~~y on exciting light intensity, whereas excimer phosphorescence varies Iineariy with excitation intensity. This means that &e triplet life+ne is not mnihiiation controhed.
1. Itlt.roduction
The phosphorescence
of pyrene excimers in single
crystal ,fiakes and powdered samples have been described pre~ously ii, 21. In ikds paper we report the measurement, of the temperature dependence of the lifetime of the broad and structured emission. The stabihsation enthalpies of the triplet excimers with revect to the triplet exciton will be derived from these data..ln oider to account for the influence of the triplet energy transfer upon the triplet lifetime, a description in terms of a random .waik modei for the triplet energy transfer has been used,
2. aesu1ts
3. The model description It is possible to derive the s~ab~~ti~n.en~h~pies of both triplet, excimers from the data in fig. 1 with an extension of a randdm walk model for energy transfer usei by Rosenstock 131. Before proceeding to a derivation of ihe necessary formula, first the gen-
., '.
.tn fig.'1l6g 11~
hasbeen plotted as a function of
t@ereciprocal temperature for the broad triplet exci-
Table I
mer emission (maximum at 13800 cm’&) and the s~ctu~d triplet exeimet {U--Oband at 15200 cm-I). In region I ,omy the broad excimer emission and the ,. delaped singlet excimer fluorescence are observed, in. regiazzu! the structured emission is
@I%.@ iiri&_deerea&~ temper&&
Valuesof tire ,:xponent c re?&ng emissiorrand excjtbg light intensity according to fern P I& Tcm
gradud!ly seen to
accoxqxkcd
by a
173 223 :’
191 153
below 80bK (region HI) the broad emission has ti s&e: +g
I$
:.
‘.
ie.mpkratire regi&sJ tidH lifetike meas&;. ,., ,..
” :
;
.’
Crystal X?.E.F.
'3()@.1.92
decree &IWdelayed exciqer fluorkence [I]. In ,this tempeiature regibn broad and structured exch?r emissions have identical lifetimes. At temperatures what longer iifetime..
powder D.EE.
'_"
-’ ; ‘. I.sl.
:’ ..’
1.94 l’.gi - ..
-” -I -. is, 77 . 1.80 :, ., i: 1.50 :_ ‘, 1; 412 . -.
=j&i’
aystal
broad AXE ..
slTucf.exc* .
&
0.93 .., 1.17 .’ .,: _ f3.57 ; :-.
_.
_. 1.w
:-
_.'
Vohme 11, number 4 *,
CHtiCALPHYSICS
LEITERS.
I November 1971
. ..
I
_ 13 &C’CM-’
Fig. la. Plot of the rate constant (l/r) versus reciprocal temperature. The lifetime was measured at 13800 cm-’ for the
broad excimer. Region I: T > 200°K.
era1 features of the‘ tiodel ‘k4.l W&en. The crystal consists of sites, each site being~composed df ir pGr of pyrene:rkole~uhs. The observed phosphorescence spectra were ascribed to two differerit kinds’of traps. The broad emission‘arises. from excimers ‘resent on lattice defects (trap 3), which concentration wti be defined by afraction q of the total number of sites. The struttured emission originates from +y site after excimer formation (trap 2, regtitar exchrter). Finally, of courSe, a site can contain the uipief energy as a cripfet exeiron (MIed trap 1 for convenience). From the observed temperature dependence of the emission spectra (broad and structured phosphorescence and delayed excimer fluorescence) we infer that the absolute level ordering will be: exciton ? regular excimer > defect excimer. By thermal activation the triplet energy can be transferred through the crystal and the transfer of triplet energy is due to tripIet ex&on and triplet excimer migration. Since f%. 1 shows in the high temperature region an exponential dependence of I/r upon 1/T for the broad excimer phosphorescenk and since also the structured emission is lacking from the phosphores-
t
Fig, lb; Plot, of the rate constant (I/T) versks reciprocal ten&rature. The lifetiine was tkas$red at-t5200 cm-l for the structujred regioi~ iIi: T < 8o"K. : '. -. .’ and at 13800 CIYI”~for the brdad excimer. Region I.k 80”e.y T < 2O_O”K; ., t ._ : : '. : _.' ), 1 : ,529 ‘. .,. ,: .‘. .” ., ;.y ‘.:. ‘_ ,, ‘,_ ,.. . __ 1.. :: ,.’ : ., ,’ ..‘. _, ‘.” ,_, ‘_. ‘. .( ,. ‘. ,: ,’ ., .‘. .. .-_, . ‘. :.-. _‘..
.V+ne !l, number 4
1 November 1971
CHEMICALPHYSIF LETI’ERS
:
cence spectrum, the teniperature-dependence ir.reg.ion i c+n best be described by. 3 thermal equilibrium between defect tripiet.excimers and triplet excitons, de-.
nying the existetice of regular excimeis. The phy$af implication that trap 2 has d&ppeared is. that the average time t&excitation will spend on a regular site is SQsmall (i.e., in the order of an intermolecular vi&ration) that no tirne.is left for excirner formation. Howe!er, trapping on defect-Sites stiU’occur& because no additional molecular motion is needed for exckner : formation. In the model description it is assumed that in the high temperature limit &I exciton wjll reside precisely cr seconds on a site after which it is immediately transferred tq another site. Thus a’tirne unit of I/a can be defined. In the intermediate and low temperature resipn the excitation energy is allowed to stay as regular exm timer on a particular site for several time units. Additionally it is assumed that iP the regular excimer is thermally activated to the exciton IeveJ and wiil transfer its energy to a nei&&&ng site, immediately a new reguk excQner is formed. In the following Li is’defined as the probability per time unit that the excitation energy will lestie a trap of kind i Thus the following quantities are defined for the high temperature region: ?_.I =Ki
+A!#31 =K3 *L31*
For the intermediate ant low temperature region:
t;
t22 = k23 f L,, = kz2 + K,,
exp(--ezl/kn
.
Now, for the high temperature region the probability of finding the excitation in trap 3 after R time units can be calculated. First, the excitation may be transferred within the free exciton level for tz~ units of time, the probability being (I -L1)“l. The probability of stepping on a trap 3 after precisely nL.steps is cakulated to be cq(l - Lt)ml, where c is a constant oforder unity [3]. The excitation lmay then Q&l in trap 3 for n2 units of time, the corresponding probability being (1 -L,)“z . The total probability of fading the excitation in trap 3 after n time units then becomes:
= {cq/(L,-L,
-c&}
((l-4,
-c&-(1
-L3)“)
*
Assuming L 1,.Lj -3 1 this may be approximated by
+Ki =K1 ,
Ls’,= KY SK\
L, =xy
where the t+plet energy transfer is described by the direct transfer.2 + 2 {which neids airnost.sio activation energy, but for which a low probability is assumed) md by the indire& transfer 2 + 1 -+.2,(i.e., excimer to exciton transfer, which nee’ds i,liigher activation anergy), the probability for transfer’from a regular excimsr can be defined by:
+K; =iV1 )
=Ky+U;
,&32 +L32 =K,
id32
+&.
The K’s indicate radiative and non-radiative decay probabiIities * and are assumed to have a veiy small temperature dependence. The probability of thermal activation from a defect excker to an exciton L,, can be written as:
L 3l =,X31ew(-E,l/W. In the intermediate and low temperature region
In the intermediate temperature region (regionl1) the probability that the regular excimer is transferred during j tine units is (m(l -X2)}!. The probabirity that during this transfer it is not trapped by&defect is (I -q)cj. The probabiiity that it wiil stay as a regular excimcr on a particular site for i time units without being transferred is ((1 -&z)(t - tz~)}~. Thus the probab’,lity OFfinding the excitation in trap 2 after n time units becomes:
With the same approximations as used before this gives: P2 7 exp. ~-+I& +c4*oJl -
I.
(2)
CHEMICAL PHYSICSLETTERS
:
For this tempoiature region P3 will be given by
In the iaw temperature region (region‘iil), where alI temperature dependent exponentiab can be neg(41
,
h November 1971.
and K3. The activation energy @in the order of 10 cm-l. From the aMtivation energy of 800 cmsL pthe location of.the exciton ievel fl690Q cmWL)and the 0-O band of the structured emission (I 5200 cm-l), a ground state repuI~a~ of 908 cmMf for the rtigufar excimr is‘obtained. Since the defect excimer gives a broad band with a peak at 13500 ~rn-~, it can be concluded that in this case the ground state.repulsior, will have an average value of XZOOcrnwr. TfreseM& ues an be camped with the pxm~d state repulsive energy obtained from data of the sin&t ex&ner , which is about 2 800 cm- 1 tie]. Thus the: e~~~b~~rn distance for the triplet excimer will be Iar&er than for th$ sikglet excimer .
It is to be noted that, ac#rdiig to the description &tin above, two different kinds of tripbt energy uansfer occur. One h’the direct qSner
4. Discussion In the high temperature region the tri$fet lifetime
obeys fhe equation I/r = 7 X IO7 ex~(-20~/~~. Tjjis means that tg < L, + q and that in f 1) the first ex?one~tiaI can bs neglected because only L3 contains a significant temperature dependence. Thus &?3t= 2000 cm-l, At temperatures between 80°K and 200% (region II) traps 2 and 3 g&e rise to emissions with the same lifetime. Thus the first e~~onenti~ in formula (3) must be the dominant one. The lifetimes of both emissions are then. given by: Fig. 1fr = (I/r)(Kz ‘cqkz3 +cqKzl exp(-eez,/kT)J. 3 shows t~~e.ex~e~eRta~ points together with the theoretical curve, drawn according to 117 = 200 + 9*4 X i04 eq( - NK?/kZ’&&m thf it follows that e21 = 800 cm -1. ..
At low temperatures (region III), it is observed that r3 > 72. This implies li=z + c4k22 3 Kg, so that 73 = @i$ and 72 = ctf(K3 .Ccqk&. The slight teniperature dependence can be attributed to that of iy,
The ~~est~g~ii~~s were supported ir! part by the Netherlands Foundation for‘Chemica1Research (SON) with CnanciaI aid from the Netherhmds Organisation for the Advancement of ?ure Research (ZWO). Referenctls ‘. [I 1 O.L.J. Gijzeman, 3. LangclaaE and .UW. van Viwrst, Chern. Phys. Letters 5 (x970) 26% [2f O.U. Gijmmin,3. .Jan@aa and KWJ. MRVuorti, Qtzm. Phys Letters LI (1971) 526. t31 N.B. Rosenstodc,F&s. Rev. 187 (1969) fL66. f41 ,J.B. Birksa*. Att. IFzzaz, ptoc. F&y. SW. A304 (L968j 291. &5f S. Arm& W-3.Whitten anb AC. B&&c, J.‘Chem. Phys.53 (1970) 2878. ‘, :
‘.
:
.. ..
.,:., ._,. :
” ‘,
+ excher
process, the other the indirect excimer 7 exciton -+ ekcimer process. The relative importance of both processes is dependent an temperatuhtre. Belaw 125°K the direct excimer -+ excimer transfer dominates.
53i
.1 .I
..,._-. _.
..)
,' .._
Q&J. GIJtiMAI’4,~W.I-I. VAN LBEUWEN, J. L.ANGELA4R and J.&W. VAN VGGRST
.,
firtelrtory for Physical Chemistry, Universiry of A msterdatn, Amstwdum, The Nether&& Received 1 Septembk 1971
.
The stab&tion
ent$taIppies of-twodifferent kinds of tripletexcimers of pyrizre are caicukted f&n the tempera-
ture dependence of the triplet lifetime. They are found to Ix 800 cm-’ and 2000 cm”‘.
ments were performed with single crystal fIakes. At tem~ratur~s below 150*K the measurements refer to powdered pyrene.. Table 1 indicates that the delayed excimer fluorescence intensity depends ~ost.quadrati~~y on exciting light intensity, whereas excimer phosphorescence varies Iineariy with excitation intensity. This means that &e triplet life+ne is not mnihiiation controhed.
1. Itlt.roduction
The phosphorescence
of pyrene excimers in single
crystal ,fiakes and powdered samples have been described pre~ously ii, 21. In ikds paper we report the measurement, of the temperature dependence of the lifetime of the broad and structured emission. The stabihsation enthalpies of the triplet excimers with revect to the triplet exciton will be derived from these data..ln oider to account for the influence of the triplet energy transfer upon the triplet lifetime, a description in terms of a random .waik modei for the triplet energy transfer has been used,
2. aesu1ts
3. The model description It is possible to derive the s~ab~~ti~n.en~h~pies of both triplet, excimers from the data in fig. 1 with an extension of a randdm walk model for energy transfer usei by Rosenstock 131. Before proceeding to a derivation of ihe necessary formula, first the gen-
., '.
.tn fig.'1l6g 11~
hasbeen plotted as a function of
t@ereciprocal temperature for the broad triplet exci-
Table I
mer emission (maximum at 13800 cm’&) and the s~ctu~d triplet exeimet {U--Oband at 15200 cm-I). In region I ,omy the broad excimer emission and the ,. delaped singlet excimer fluorescence are observed, in. regiazzu! the structured emission is
@I%.@ iiri&_deerea&~ temper&&
Valuesof tire ,:xponent c re?&ng emissiorrand excjtbg light intensity according to fern P I& Tcm
gradud!ly seen to
accoxqxkcd
by a
173 223 :’
191 153
below 80bK (region HI) the broad emission has ti s&e: +g
I$
:.
‘.
ie.mpkratire regi&sJ tidH lifetike meas&;. ,., ,..
” :
;
.’
Crystal X?.E.F.
'3()@.1.92
decree &IWdelayed exciqer fluorkence [I]. In ,this tempeiature regibn broad and structured exch?r emissions have identical lifetimes. At temperatures what longer iifetime..
powder D.EE.
'_"
-’ ; ‘. I.sl.
:’ ..’
1.94 l’.gi - ..
-” -I -. is, 77 . 1.80 :, ., i: 1.50 :_ ‘, 1; 412 . -.
=j&i’
aystal
broad AXE ..
slTucf.exc* .
&
0.93 .., 1.17 .’ .,: _ f3.57 ; :-.
_.
_. 1.w
:-
_.'
Vohme 11, number 4 *,
CHtiCALPHYSICS
LEITERS.
I November 1971
. ..
I
_ 13 &C’CM-’
Fig. la. Plot of the rate constant (l/r) versus reciprocal temperature. The lifetime was measured at 13800 cm-’ for the
broad excimer. Region I: T > 200°K.
era1 features of the‘ tiodel ‘k4.l W&en. The crystal consists of sites, each site being~composed df ir pGr of pyrene:rkole~uhs. The observed phosphorescence spectra were ascribed to two differerit kinds’of traps. The broad emission‘arises. from excimers ‘resent on lattice defects (trap 3), which concentration wti be defined by afraction q of the total number of sites. The struttured emission originates from +y site after excimer formation (trap 2, regtitar exchrter). Finally, of courSe, a site can contain the uipief energy as a cripfet exeiron (MIed trap 1 for convenience). From the observed temperature dependence of the emission spectra (broad and structured phosphorescence and delayed excimer fluorescence) we infer that the absolute level ordering will be: exciton ? regular excimer > defect excimer. By thermal activation the triplet energy can be transferred through the crystal and the transfer of triplet energy is due to tripIet ex&on and triplet excimer migration. Since f%. 1 shows in the high temperature region an exponential dependence of I/r upon 1/T for the broad excimer phosphorescenk and since also the structured emission is lacking from the phosphores-
t
Fig, lb; Plot, of the rate constant (I/T) versks reciprocal ten&rature. The lifetiine was tkas$red at-t5200 cm-l for the structujred regioi~ iIi: T < 8o"K. : '. -. .’ and at 13800 CIYI”~for the brdad excimer. Region I.k 80”e.y T < 2O_O”K; ., t ._ : : '. : _.' ), 1 : ,529 ‘. .,. ,: .‘. .” ., ;.y ‘.:. ‘_ ,, ‘,_ ,.. . __ 1.. :: ,.’ : ., ,’ ..‘. _, ‘.” ,_, ‘_. ‘. .( ,. ‘. ,: ,’ ., .‘. .. .-_, . ‘. :.-. _‘..
.V+ne !l, number 4
1 November 1971
CHEMICALPHYSIF LETI’ERS
:
cence spectrum, the teniperature-dependence ir.reg.ion i c+n best be described by. 3 thermal equilibrium between defect tripiet.excimers and triplet excitons, de-.
nying the existetice of regular excimeis. The phy$af implication that trap 2 has d&ppeared is. that the average time t&excitation will spend on a regular site is SQsmall (i.e., in the order of an intermolecular vi&ration) that no tirne.is left for excirner formation. Howe!er, trapping on defect-Sites stiU’occur& because no additional molecular motion is needed for exckner : formation. In the model description it is assumed that in the high temperature limit &I exciton wjll reside precisely cr seconds on a site after which it is immediately transferred tq another site. Thus a’tirne unit of I/a can be defined. In the intermediate and low temperature resipn the excitation energy is allowed to stay as regular exm timer on a particular site for several time units. Additionally it is assumed that iP the regular excimer is thermally activated to the exciton IeveJ and wiil transfer its energy to a nei&&&ng site, immediately a new reguk excQner is formed. In the following Li is’defined as the probability per time unit that the excitation energy will lestie a trap of kind i Thus the following quantities are defined for the high temperature region: ?_.I =Ki
+A!#31 =K3 *L31*
For the intermediate ant low temperature region:
t;
t22 = k23 f L,, = kz2 + K,,
exp(--ezl/kn
.
Now, for the high temperature region the probability of finding the excitation in trap 3 after R time units can be calculated. First, the excitation may be transferred within the free exciton level for tz~ units of time, the probability being (I -L1)“l. The probability of stepping on a trap 3 after precisely nL.steps is cakulated to be cq(l - Lt)ml, where c is a constant oforder unity [3]. The excitation lmay then Q&l in trap 3 for n2 units of time, the corresponding probability being (1 -L,)“z . The total probability of fading the excitation in trap 3 after n time units then becomes:
= {cq/(L,-L,
-c&}
((l-4,
-c&-(1
-L3)“)
*
Assuming L 1,.Lj -3 1 this may be approximated by
+Ki =K1 ,
Ls’,= KY SK\
L, =xy
where the t+plet energy transfer is described by the direct transfer.2 + 2 {which neids airnost.sio activation energy, but for which a low probability is assumed) md by the indire& transfer 2 + 1 -+.2,(i.e., excimer to exciton transfer, which nee’ds i,liigher activation anergy), the probability for transfer’from a regular excimsr can be defined by:
+K; =iV1 )
=Ky+U;
,&32 +L32 =K,
id32
+&.
The K’s indicate radiative and non-radiative decay probabiIities * and are assumed to have a veiy small temperature dependence. The probability of thermal activation from a defect excker to an exciton L,, can be written as:
L 3l =,X31ew(-E,l/W. In the intermediate and low temperature region
In the intermediate temperature region (regionl1) the probability that the regular excimer is transferred during j tine units is (m(l -X2)}!. The probabirity that during this transfer it is not trapped by&defect is (I -q)cj. The probabiiity that it wiil stay as a regular excimcr on a particular site for i time units without being transferred is ((1 -&z)(t - tz~)}~. Thus the probab’,lity OFfinding the excitation in trap 2 after n time units becomes:
With the same approximations as used before this gives: P2 7 exp. ~-+I& +c4*oJl -
I.
(2)
CHEMICAL PHYSICSLETTERS
:
For this tempoiature region P3 will be given by
In the iaw temperature region (region‘iil), where alI temperature dependent exponentiab can be neg(41
,
h November 1971.
and K3. The activation energy @in the order of 10 cm-l. From the aMtivation energy of 800 cmsL pthe location of.the exciton ievel fl690Q cmWL)and the 0-O band of the structured emission (I 5200 cm-l), a ground state repuI~a~ of 908 cmMf for the rtigufar excimr is‘obtained. Since the defect excimer gives a broad band with a peak at 13500 ~rn-~, it can be concluded that in this case the ground state.repulsior, will have an average value of XZOOcrnwr. TfreseM& ues an be camped with the pxm~d state repulsive energy obtained from data of the sin&t ex&ner , which is about 2 800 cm- 1 tie]. Thus the: e~~~b~~rn distance for the triplet excimer will be Iar&er than for th$ sikglet excimer .
It is to be noted that, ac#rdiig to the description &tin above, two different kinds of tripbt energy uansfer occur. One h’the direct qSner
4. Discussion In the high temperature region the tri$fet lifetime
obeys fhe equation I/r = 7 X IO7 ex~(-20~/~~. Tjjis means that tg < L, + q and that in f 1) the first ex?one~tiaI can bs neglected because only L3 contains a significant temperature dependence. Thus &?3t= 2000 cm-l, At temperatures between 80°K and 200% (region II) traps 2 and 3 g&e rise to emissions with the same lifetime. Thus the first e~~onenti~ in formula (3) must be the dominant one. The lifetimes of both emissions are then. given by: Fig. 1fr = (I/r)(Kz ‘cqkz3 +cqKzl exp(-eez,/kT)J. 3 shows t~~e.ex~e~eRta~ points together with the theoretical curve, drawn according to 117 = 200 + 9*4 X i04 eq( - NK?/kZ’&&m thf it follows that e21 = 800 cm -1. ..
At low temperatures (region III), it is observed that r3 > 72. This implies li=z + c4k22 3 Kg, so that 73 = @i$ and 72 = ctf(K3 .Ccqk&. The slight teniperature dependence can be attributed to that of iy,
The ~~est~g~ii~~s were supported ir! part by the Netherlands Foundation for‘Chemica1Research (SON) with CnanciaI aid from the Netherhmds Organisation for the Advancement of ?ure Research (ZWO). Referenctls ‘. [I 1 O.L.J. Gijzeman, 3. LangclaaE and .UW. van Viwrst, Chern. Phys. Letters 5 (x970) 26% [2f O.U. Gijmmin,3. .Jan@aa and KWJ. MRVuorti, Qtzm. Phys Letters LI (1971) 526. t31 N.B. Rosenstodc,F&s. Rev. 187 (1969) fL66. f41 ,J.B. Birksa*. Att. IFzzaz, ptoc. F&y. SW. A304 (L968j 291. &5f S. Arm& W-3.Whitten anb AC. B&&c, J.‘Chem. Phys.53 (1970) 2878. ‘, :
‘.
:
.. ..
.,:., ._,. :
” ‘,
+ excher
process, the other the indirect excimer 7 exciton -+ ekcimer process. The relative importance of both processes is dependent an temperatuhtre. Belaw 125°K the direct excimer -+ excimer transfer dominates.
53i
.1 .I
..,._-. _.
..)