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Critical exciton annihilation: Diffusion, percolation or anderson transition?
Journal of lominescence 24/25 (1981) 457—460 North-Holland Publishing Conspany
457
CRITICAL EXCITON ANNIHILATION: OIFFUSION~ PERCOLATION OR ANOERSON TRANSITION?* P. W. Klymko and P. Kopelmnn~ Department nf Chemintry, Univernity of Michigan, Ann Arbor, Mi 48109, U.S.A.
Goeat—Gueat Triplet-Triplet annihilation in highly porified mixed oryntala of naphthalene (goent)— naphthalene—d 8(hoat) waa atodied at 1.8 K via apectrally and time—reaolved phonphorencence and delayed— flooreacence. We find nignificant deviationa from ourrent diffuaion theoriea and homogeneooa kinetion hot connintency with local heterogeneitiea (clonte— rization) and dynamic exciton percolation, an well nn with long—range annihilation (via noperexchnnge) There in negative evidence for nn Andernon trannition.
The trnnnport of excitntionn in dinordered media han neveral interenting nnpectn: 1) Potential obnervntion of an Andernon—Mott tranni— tion [1]. 2( Tentn of corrent theorien on diffunion in dinordered media [2—4] . 3) Search for the effectn of local heterogeneitien (‘clontern’( and their relation with critical phenomena [5]. 4) Simple, reproducible, nyntemn for ntudying the principlen of heterogeneoun kineticn and interface renctionn. 5) The ponnibility of obtaining bio— mimetic nyntemn. 6( The ntudy of energy upconvernion via long-range annihilation (exciton funion) The ntendy—ntnte excitntion (Xe lamp) of highly purified inotopic mixed nnphthnlene cryntaln (C10H8 in C10D8 at 1.8 K) in nhuttered—off and npectrally renolved phonphorencence 1 0-0 1 nnd delayed fluorencence (0u_512(decnyn are monitored an n function of time, light inteonity gueut (C10H8) concentration etc. Cryntnln with 0.1 % mole guent nhow no delayed fluorenceoce (time renolution m 1 me] and junt normal triplet decay curven (r = 2.7 n( . All hont homofunion, heterofunion, prompt fluorencence, rndintive trnpping, ioternyntem cronning etc. are over within 1 mn nod no guent homofunion taken place. However, guent— guent homofunion (triplet—triplet nnoihilntioo( in the phenomenon ntudied at higher guent coocentrationn. The negligible importance of any third channel of decay (i.e. nupertrappiog by impuritien or Xtrnpn) wan demoontrated both npectroncopicnlly nod kioetically (Fig. 1). The abnolute and relative delayed fluorenceoce (DF) and phonphorencence (P) rnten were ntudied an a function of light (3 or— dern of magnitude) and time. An explicit example of n DF decay curve in given in Fig. 1.
*
Supported by WTH Grant 2 P01 MS 08116-1OA1
+
Viuitiog Profeenor, Phynik, lout. 3, Uoiv. of Stuttgart, D — 7000 Stuttgart—SO, W.—Germnoy
O 022—2313/81 /0000—0000/$02.75 © Norgh-Holland
I’ hi Jc/vstlkn, I? An~ic/stiatt/ (ru/sal s/ruins?
455
a—
8% Cryeol Full IntensIty Decay . Delayed Flusrescence
•
Relative Decay at Emissians
5 3
a
n
o
a%d
•
Slape=20
-~
~
-I 5
0
5
f~.1:
SECONDS
10
?sllsl//li/?ltl(sll
5
Sasple Delayed Floorencance and “differeotial” Phosphorenceoco under identical conditions V = meanured phouph. decay rate rsinon “oaturai” one).
5
4 d -2 -l LOG INarmalized Phaspharescence)
0
2. Fig. 2: Test of (OF] For each curve POF and P are at identical decay, tllrm points and initial excitation.
Similar curves have been obtained for different light intonsitioa and guest cooceotrations (4—20 5), with a conatant (tiC ~) ratio of /(Dr) The “differential’ phonphoreaceoce decay ratea (Fig. 1) would be the ooen observed in the li 1’ decay rate rathor theo the real ooo 10.37 a 1mit ) nhtainad the low queat concentration of zero free “natural namples (0.1 5). Fig. 2 nhowa the relative OF and P rataa at variona points in time for given samples. Upon extrapolation of OF Id) and P to t = 0 ooe obtaina in Fig. 3 the effective steady—state annihilation probability en a function of gnest concentration and excitation rate.
/ /
/
Cnest Concentration Oependeoce of Annihilation, at constant excitetino per spent site (probability from phosphorescence and “differen— -
tip~o~~ce
a
0 coNcENTRaTIoN NaPHTHaLcNc e
-
In,, a cent?
te
decays extra-
-
13 IC. K(tntke, 13 Kepc/tntatt
/ Critical cxciten enttilsilutiett
459
The goasicritical behavior of Fig. 3 is interesting hot similar to previous energy traospert work measured vie sopertrappiog [5] . However, the most striking result is fenod in Fig. 2 for the samples at and below the “critical” guest cnoceot~atieo )Cc) While for the 20 5 guest sample )Fig. 2) one gets )OF)c P , en has beeo standard io previous triplet-aooihilatioo work (5,6] , for the 4 8 sample the result in the high exciteo density range is clearly )OF) ~x where X > 2. We note that P is linear with the excitno deosity )io the guest) doe to the monomolecular oatnre of the “natural decay”, and, similarly, OF has usually been expected to be goadratic with excitno deosity doe to the bimolecular oatore of the annihilation process (5,6]. In the limit of long times )t -- w) , or for steady—state conditions, ooe gets from curreot theories of diffusion in disordered media essentially the name answer as from diffusioo theories in homogeneous lattices, oameiy X = 2. On the other hand, the clunteriratioo (“percolation”) approach allows for both X = 2 sod X > 2, depending no specific cooditions, as has recently been demonstrated with the aid of Moote-Carlo calculations (7] 0c )the “critical guest concentration”, where The depeodeoce of )OF) a’ P1 on excitation intensity )Fig. 3) nod no time cannot easily be recoociled with an Aodersoo transition Ii] . This is especially true in view of the further shifts in C~ observed (5] in sopertrappiog experiments on the same systems (C 10H8/ 01008) . The experiments are also ceosinteot with bog—range aooihilatioo (via soperexchaoge (8,9]). In coocbunioo, the annihilation experiments era ont well described by current theories of diffusion in heterogeoeous media. Our system ceo be considered an a medal for heterogeneous kinetics. As both excitation transfer and annihilation processes are most probably limited to the ab crystal plane [5] , this is actually a model system for iotarfacial reactions io synthetic end biological systems. We further believe that cluster-type excitoo annihilation may be importaot for the study of phetosyothetic systems.
[1]
Klafter, J. and Jertoer, J., Chem.Phys.Lett.
[2]
Blomao, A.
[3]
Bbumeo, A., Klafter, 5320.
(4]
Gedzik, K. and Jertoer, J., J.Cham.Phys.
(5]
Fraocis, A.H. sod Kepelmao, R., Excitation Dynamics in Molecular Selids,io Laser Spectroscopy of Solids, ad. Yen W.M. aod Selzar P.M. (Springer, Berlin, 1981) P. 241—302.
[61
Marrifield, R.E. Pure Appl.Chem. 27 )1971) Suoa, A., Phys.Rav. B ±(1970) 1716.
(7]
Mewheosa,
(8]
Sterolicht, H., Miemso, J.Chem.Phys. 38 (1963),
[9]
Jortoer, J. aod Kopelmao
aod Silbey,
P.,
J.Cham.Phys.
J. sod Silbay,
J., Hesheo, J.
49
70 (1979)
72
(1980)
72
(1980)
4471.
481;
(unpublished).
0.0. and Robinson, G.W., 1326; 39 (1963), 1610. (unpublished)
410.
3707.
R., J.Chem.Phys.
and Kepelman, R.
P.
)1977)
457
CRITICAL EXCITON ANNIHILATION: OIFFUSION~ PERCOLATION OR ANOERSON TRANSITION?* P. W. Klymko and P. Kopelmnn~ Department nf Chemintry, Univernity of Michigan, Ann Arbor, Mi 48109, U.S.A.
Goeat—Gueat Triplet-Triplet annihilation in highly porified mixed oryntala of naphthalene (goent)— naphthalene—d 8(hoat) waa atodied at 1.8 K via apectrally and time—reaolved phonphorencence and delayed— flooreacence. We find nignificant deviationa from ourrent diffuaion theoriea and homogeneooa kinetion hot connintency with local heterogeneitiea (clonte— rization) and dynamic exciton percolation, an well nn with long—range annihilation (via noperexchnnge) There in negative evidence for nn Andernon trannition.
The trnnnport of excitntionn in dinordered media han neveral interenting nnpectn: 1) Potential obnervntion of an Andernon—Mott tranni— tion [1]. 2( Tentn of corrent theorien on diffunion in dinordered media [2—4] . 3) Search for the effectn of local heterogeneitien (‘clontern’( and their relation with critical phenomena [5]. 4) Simple, reproducible, nyntemn for ntudying the principlen of heterogeneoun kineticn and interface renctionn. 5) The ponnibility of obtaining bio— mimetic nyntemn. 6( The ntudy of energy upconvernion via long-range annihilation (exciton funion) The ntendy—ntnte excitntion (Xe lamp) of highly purified inotopic mixed nnphthnlene cryntaln (C10H8 in C10D8 at 1.8 K) in nhuttered—off and npectrally renolved phonphorencence 1 0-0 1 nnd delayed fluorencence (0u_512(decnyn are monitored an n function of time, light inteonity gueut (C10H8) concentration etc. Cryntnln with 0.1 % mole guent nhow no delayed fluorenceoce (time renolution m 1 me] and junt normal triplet decay curven (r = 2.7 n( . All hont homofunion, heterofunion, prompt fluorencence, rndintive trnpping, ioternyntem cronning etc. are over within 1 mn nod no guent homofunion taken place. However, guent— guent homofunion (triplet—triplet nnoihilntioo( in the phenomenon ntudied at higher guent coocentrationn. The negligible importance of any third channel of decay (i.e. nupertrappiog by impuritien or Xtrnpn) wan demoontrated both npectroncopicnlly nod kioetically (Fig. 1). The abnolute and relative delayed fluorenceoce (DF) and phonphorencence (P) rnten were ntudied an a function of light (3 or— dern of magnitude) and time. An explicit example of n DF decay curve in given in Fig. 1.
*
Supported by WTH Grant 2 P01 MS 08116-1OA1
+
Viuitiog Profeenor, Phynik, lout. 3, Uoiv. of Stuttgart, D — 7000 Stuttgart—SO, W.—Germnoy
O 022—2313/81 /0000—0000/$02.75 © Norgh-Holland
I’ hi Jc/vstlkn, I? An~ic/stiatt/ (ru/sal s/ruins?
455
a—
8% Cryeol Full IntensIty Decay . Delayed Flusrescence
•
Relative Decay at Emissians
5 3
a
n
o
a%d
•
Slape=20
-~
~
-I 5
0
5
f~.1:
SECONDS
10
?sllsl//li/?ltl(sll
5
Sasple Delayed Floorencance and “differeotial” Phosphorenceoco under identical conditions V = meanured phouph. decay rate rsinon “oaturai” one).
5
4 d -2 -l LOG INarmalized Phaspharescence)
0
2. Fig. 2: Test of (OF] For each curve POF and P are at identical decay, tllrm points and initial excitation.
Similar curves have been obtained for different light intonsitioa and guest cooceotrations (4—20 5), with a conatant (tiC ~) ratio of /(Dr) The “differential’ phonphoreaceoce decay ratea (Fig. 1) would be the ooen observed in the li 1’ decay rate rathor theo the real ooo 10.37 a 1mit ) nhtainad the low queat concentration of zero free “natural namples (0.1 5). Fig. 2 nhowa the relative OF and P rataa at variona points in time for given samples. Upon extrapolation of OF Id) and P to t = 0 ooe obtaina in Fig. 3 the effective steady—state annihilation probability en a function of gnest concentration and excitation rate.
/ /
/
Cnest Concentration Oependeoce of Annihilation, at constant excitetino per spent site (probability from phosphorescence and “differen— -
tip~o~~ce
a
0 coNcENTRaTIoN NaPHTHaLcNc e
-
In,, a cent?
te
decays extra-
-
13 IC. K(tntke, 13 Kepc/tntatt
/ Critical cxciten enttilsilutiett
459
The goasicritical behavior of Fig. 3 is interesting hot similar to previous energy traospert work measured vie sopertrappiog [5] . However, the most striking result is fenod in Fig. 2 for the samples at and below the “critical” guest cnoceot~atieo )Cc) While for the 20 5 guest sample )Fig. 2) one gets )OF)c P , en has beeo standard io previous triplet-aooihilatioo work (5,6] , for the 4 8 sample the result in the high exciteo density range is clearly )OF) ~x where X > 2. We note that P is linear with the excitno deosity )io the guest) doe to the monomolecular oatnre of the “natural decay”, and, similarly, OF has usually been expected to be goadratic with excitno deosity doe to the bimolecular oatore of the annihilation process (5,6]. In the limit of long times )t -- w) , or for steady—state conditions, ooe gets from curreot theories of diffusion in disordered media essentially the name answer as from diffusioo theories in homogeneous lattices, oameiy X = 2. On the other hand, the clunteriratioo (“percolation”) approach allows for both X = 2 sod X > 2, depending no specific cooditions, as has recently been demonstrated with the aid of Moote-Carlo calculations (7] 0c )the “critical guest concentration”, where The depeodeoce of )OF) a’ P1 on excitation intensity )Fig. 3) nod no time cannot easily be recoociled with an Aodersoo transition Ii] . This is especially true in view of the further shifts in C~ observed (5] in sopertrappiog experiments on the same systems (C 10H8/ 01008) . The experiments are also ceosinteot with bog—range aooihilatioo (via soperexchaoge (8,9]). In coocbunioo, the annihilation experiments era ont well described by current theories of diffusion in heterogeoeous media. Our system ceo be considered an a medal for heterogeneous kinetics. As both excitation transfer and annihilation processes are most probably limited to the ab crystal plane [5] , this is actually a model system for iotarfacial reactions io synthetic end biological systems. We further believe that cluster-type excitoo annihilation may be importaot for the study of phetosyothetic systems.
[1]
Klafter, J. and Jertoer, J., Chem.Phys.Lett.
[2]
Blomao, A.
[3]
Bbumeo, A., Klafter, 5320.
(4]
Gedzik, K. and Jertoer, J., J.Cham.Phys.
(5]
Fraocis, A.H. sod Kepelmao, R., Excitation Dynamics in Molecular Selids,io Laser Spectroscopy of Solids, ad. Yen W.M. aod Selzar P.M. (Springer, Berlin, 1981) P. 241—302.
[61
Marrifield, R.E. Pure Appl.Chem. 27 )1971) Suoa, A., Phys.Rav. B ±(1970) 1716.
(7]
Mewheosa,
(8]
Sterolicht, H., Miemso, J.Chem.Phys. 38 (1963),
[9]
Jortoer, J. aod Kopelmao
aod Silbey,
P.,
J.Cham.Phys.
J. sod Silbay,
J., Hesheo, J.
49
70 (1979)
72
(1980)
72
(1980)
4471.
481;
(unpublished).
0.0. and Robinson, G.W., 1326; 39 (1963), 1610. (unpublished)
410.
3707.
R., J.Chem.Phys.
and Kepelman, R.
P.
)1977)