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Intrachain and interchain triplet-triplet exciton annihilation in a quasi-one-dimensional crystal: 1,4-dibromonaphthalene (DBN)
CHEMICAL PHYSICS LETTERS
VoIume 53, number 2
15 January1978
INTIUCHAIN AND INTERCHAIN TRIPLET-TRIPLET EXCITON ANNIHILATION IN A QUASI-ONE-DIMENSXO-NAL CRYSTAL: 1,~DIBROMONAPHTHALENE @BN) H. BOUCHRIHA, V. ERN, J.L. FAVE, C. GUTHMANN and M. SCHOTT Groupe de Physique des Solides de I’E.ff.S. (Laboratoin? asso& au C.N.RS.j. 75.221Paris Cedex 0.5,France
LmivetatW Paris VT..,
Received 25 July 1977 Revised manuscript received 19 September 1977
The modulation of delayed fluorescence in l&dibromonaphthalene by magnetic fields has been studied at room temperature. The analysis of hii field resonance positions shows that, besides annih&tion of triplet excitons in the same onedimensional stack, annihilation also occurs between triplets localized on different, neighbouring, stacks, in particular those corresponding to the two molecules of the asymmetric pair_
1. Introduction
hopping rates inferred from ESR differ by several or-
DBN is known to be a quasi-one-dimensional crystal for triplet excitons, from spectroscopy [l] and direct measurement of the diffusivity [2] - The mono-
ders able ture into
cl&k E+/a
crystal
is made of stacks of molecules
piled up along the c axis. Interstack and intrastack
0
of magnitude [3,4] _ Fig. 1 summarizes the avail(incomplete) information about the crystal struc[S] : there are eight molecules per cell, arranged 4 “asymmetric units” of two molecules each
such as 1 and 1’ (related by no symmetry element).
Hence a splitting between the two sites I and JI, corre-
sin (3
Fig. 1. Projection of DBN crystal structure parallel to the c axis [1,5].
288
Volume 53, number 2
CHEMICAL PHYSICS LETTERS
15 January 1978
spending to primed and unprimed molecules respectively [4], which is 50 cmzl for the lowest triplet Cl].
In this note, triplet-triplet
(TT) annihilation is
studied through the magnetic field modulation of delayed fluorescence (DF) [6]. From the positions of modulation extrema at high field, one can find the zero field (ZF) parameters of the triplet species in-
volved in the interaction. From the dependence of the effect on field strength and direction and on excitation intensity, one can learn about triplet motion and reaction rate [6,7].
2. Experimental setup plates 1 and 2 mm thick were cleaved, or cut using a thread saw, from pure DBN crystal boules. The triplet lifetimes were between 2 and 3 ms at 300 K. The faces were parallel to (ab), (UC’) or (bc’) crystal planes, as determined by conoscopy. The experimental setup was the same as described elsewhere IS]_ The crystal was placed between the pole pieces of an electromagnet, and the magnetic field was rotated in a horizontal plane through 360“. The plate faces could be positioned at any angle from the horizontal with an accuracy of *2O. The samples were iuumlnated from below and excited directly in the lowest triplet state by the 4880 A line of an argon laser, attenuated as needed by neutral density fdters, and through one Corning CS3-70 and one Schott GG495 filters. The delayed fluorescence F was collected by a light guide, and sent onto an EMI 9558 QB PM through one Corning CW-60 and two Schott BGl8 filters. The signal was normalized by measuring A F(_H)/F=[F(H)-F(O)]lF(O). Allexperimentswere performed at low triplet density, nT 2 lOI cme3, where excitor1 decay is mainly monomolecular.
of magnettc
Chentatan
f,e,d
(degrees)
Fig. 2. Variation of the delayed fluorescence when r! 6 kG magnetic field is rotated in the (UC’), (k’), and (ab) planes of DBN.
3. Analysis of high field resonance positions It is weU known [6], that for particular orientations of the magnetic field, “resonance” occurs, corresponding to a degeneracy of pair state energy levels. Whereas in all pure materials studied up to now either two or zero resonances are observed at high magnetic field (9 kG) in any crystal plane, many more are present in DBN (f&2), up to at least 14 (see fig. 3,@ = 60” for instance).
180
90
0 Ot-lenlOtIon
of
maqnettc
field
(degrees)
Fig. 3. Variation of the dekjred fluorescence intensity when a 6 kG magnetic field is rotated in various intermediate planes from (a~?) to (bc’). Sample was positioned by successive rotations (angle @) around the C’ axis.
289
Volume 53, number 2
CHEMICAL
PHYSICS LElTERS
The maximum modulation is 18%. These peaks are not associated w
X)2 + 3(D* + E*)(Ib
Y)2 - 2D* = 0 ,
where D* and E* are the exciton ZF parameters and X, Y, 2 the axes of its ZF tensor_ &is the magnetic field direct&n which direction cosines in the XYZ frame are (H* X), (fi- Y), (fi 2). They can be expressed in terms of the angles 13, @ as defmed in fig. 4. Using the ZF tensor * of DBN obtained by EPR [3,4], the 4 in-chain resonances are found on the con-
15 January
1978
Fig. 4. Definition of angles 8 and v.
tinuous lines in fig. 5. The agreement with experiment (dots) is within the stated accuracy of the tensor (+2 to 5” depending on the plane considered), and of our experiments (*2O). Closer examination of the crystal structure (fig. 1) suggests that at least some interchain interactions might be non-negligible, for instance 1 with 4, or 1 b 90
60
30
0 180
-30
-50
l
* In the original work [3,4], the sign of the molecular direction cosine co@ - c*) of site II was probably misprinted_ It should be -0.3400. The symmetry operations of the factor group were performed on the tensors of molecules 1 and 1’ to generate those of all the other molecules.
290
-90
Fig. 5. Predicted and experimental resonance positions, plotted in (6, I$) coordinates. Dots: experimental results_ Solid lines: intrastack annih&ti~ns. Dashed lines: interstack (asymmetric pair) a@hilation& Dotied Lines:wter$ack an&hSations such
as l-3’ (se-etext). For clarity of tile theoretical lines, expert
mentalpoints &e plotted only in the upper half of the diagram, but results have been taken for all values of 9. For the labelliig of the curves, see table 1.
CHEMICAL
Volume 53, number 2
15 January l.978
PHYSICS LETTERS
Table 1 Correspondence between types of ann&ilation and resonance positions diilayed
in fig. 5
Type of annihilation
Nolecuies involved (fG. 1)
intrastack
1-l; 4-4 2-2; 3-3 1’__1’; 4-4’ 2’-2’; 39-3’
solid line solid line solid tie solid line
interstack interchange equivalent &Wasite)
1-4 2-3 S-4’ 2-3’
solid line solid line solid line solid line
l-2; 1-3; 2-3; 3-4 1’__2’->l’--3’. , 2r-_3~.* 3*_4
dotted line dotted line
interstack non interchange equivalent
l-3’;4-2’: l-2’;4-3’ 2--4’;3--1’;3--4’;2-1’
dotted line dotted line
(imtersitc)
f--1’;4-4’: l-4’: 4-1’ 2--2’;3--3’;2-3’;3-2’
with I’. Two limiting models for the interaction of two triplets in nei~bou~g chains can be considered. Either hopping between these two chains is very fast, and the exciton cannot be considered Iocalized on one chain, but has a ZF tensor obtained by averaging the single-chain ZF tensors; or hopping between the two chains is slow, and one observes a heterofusion, that is the ~tera~tion of two tfiph%s with different ZF tensors. However, since the ZF tensor in the homofusion process is obtained here by averaging ZF tensors corresponding to heterofusion, it is found that, in the present case, both processes yield resonances at the same positions. Moreover, some pairs yieid resonances at positions already corresponding to intraehain interactions (solid lines in fig. 3): pairs 1-4,2-3,1’4’ and 2’-3’. New resonances occur if interactions among other pairs are important. In fig. 3, the dashed lines correspond to the resonances predicted for interchain annihilation in the asymmetric unit pairs such as 1-l’; the dotted lines correspond to pairs 1-3’ and 24’ and all equivalent ones (a total of eight combinations). There remain a few isolated unaccounted for resonances, which might correspond to other interactions. Indeed, up to twenty separate resonances could in principle be seen in some planes. But of course some correspond to viny small interactions, and will not occur. In no case is any resonance predicted in
Label
dashedline f
dashed line
the (a$) plane, and indeed none is observed (fig. 2). Since resonances ~o~espcnding to intrachain TT interactions in chains 1 or I’ are seen at the same time as resonances corresponding to interchain interaction in the l-l’ pair, one can conclude that the latter is a case of “heterofusion” in the sense used above: hops of a triplet from 1 to 1’ are not frequent, but still the l-l’ interaction of large enough to allow TT anniF& lation to occur *_ The observation of these interactions does not invalidate the quasi-one-dimensionality of triplet motion. The occurrence of such interactions however, complicates very much quantitative fitting of the experimental results within Suna’s theory Q’]. A very approximate fitting of the high field resonances in the (bc’) piane was attempted using Merrifield’s theory [ 121, yielding, for the order of magnitude of triplet pair dissociation rates (JQ_~), 108 s”-* for an intrastack pair and lOro s-l for an interstack pair. These results should be considered very preliminary, For comparison, the lifetime of a triplet in a stack, as inferred from ESR [3,4] is aIso of the order of 10-s s, and the intrastack hopping time, as de* At low temperatures, due to the 50 cm-l site splitting, the four chains of site If are depopulated and the corresponding resonances should weaken and disappear. Preliminary experiments at 80 K for magnetic f?eld rotated in the (QC)plane indeed show this.
291
fr_elt pm
15 Jan-
CHEMICAL PlIYSICS LETTERS
Volume 53. number2
1978
the diffusivity [2], is of the order of
4. Variation of delayed fhorescence yield with magnetic field strength The results discussed above were all obtained at high fieId. The variation of the magnetic field effects with field strength was also studied, the results are summarized in figs. 6 and 7. Fig_ 6 shows the anisotropy of the effect in the (ac’) and (bc’) planes under fields of 0.25, 1 and G kG respectively. Fig. 7 shows the field strength dependence of the effect for three special directions in the (ac’) plane. These results are currently under study. Clearly, the gross features of the effect are understood in terms of current theoretical treatment [6,&l 1,121, but, as recently observed in naphthalene [13], not all the results can be accounted for ln this way: reverse resonances exist, for instance for H 1 c’ (fig. 2) at high field, leading to an
-m.
25
_______-__--_
SC00 OO
--_--__-_-_-_
2
‘I
t.4cpctlc
6
7
(KG)
and summary
The existence of the corresponding high field resonances shows that there is enough interstack interaction in DBN to allow am&ilation to occur between triplets localized on different, neighbouring, stacks. This interaction is certainly much smaller than intrastack triplet-triplet interaction. It seems possible that these interstack annihilations
c*
p______,_-__--_--_--_-__-_
1t
Orientation d magnetic field (dagrns)
Fig. 6. Variationof the delayedfluorescenceintensitywhen fieldsof 250,lOOO and 6000 G arerotated in the (ac’) and
Z==
(T,,T, I-
G
(Ti,Tj)
S’
II Ti +TJ
292
5
tireogth
enhancement of fluorescence at all field strengths ln this particular direction (fig. 7) contrary to theoretical expectation.
h +T,
(bc’) planes
4 f&d
Fig. 7. Variation of the delayed fluorescence intensity w&h magnetic field strength, for field appliedin threedirections in the (m’) plane: u and c’ axes, and diction of the main resonance (interstack interaction).
5. IXSC~~OU
cP+P-+
I
t
-9
Fig_8. Schemefor triplet-triplet anGhilationwhen several triplet species T+ coexist and can transforminto one another. Ti, Ti are tripletslocalizedon stacki andj respecti~ely~ where i, j standfdr 1,l’ . ..4’. F&t line is an example of interstackannihilation,second line-of irdstack annihilation. Verticalarrows correspondto diffusionnornialto the C axis, by interstackhoppingof one triplet.
Volume 53, number 2
.
-
CHEMICAL PHYSICS LETTERS
occur because the stack lengths are finite, and most triplets will fiit form interstack pairs before forming an intrastack pair. This can be written, ln Menifield’s chemical kinetic language, as in fig. 8. It is possible that the relative importance of resonance heights can be changed if the average stack length could be sufficiently modified. In our experiments, already some interstack resonances are more intense than the intrastack ones, suggesting that stacks lengths are relatively short. This problem is under investigation (Wolf [14] suggests that “old” crystals have significantly shorter stack lengths than “new” ones).
Acknowledgement This work was supported by the DGRST under contract no. 76-7-0119. This research would not have been possible without the generous gift of crystals by Dr. N. Karl and Mr. J. Ziegler, Kristallabor Stuttgart, and by Dr. G.J. Sloan, DuPont de Nemours, Wilmington, and we are very grateful to them.
15 January 1978
References [l] G. Castro and RM. iiochstrasser, J. Chem Phys. 47 (1967) 2241; RM. Hochstrasser and J.D. Whiteman, J. Chem. Phys. 56 (1972) 5945. [l] V. Em, J. Chem. Phys 56 (1972) 6259. [3]
R. Schmidberger and H.C. Wolf, Chem. Phyr Letters
16 (1972) 402; 25 (1974) 185. [4] R. Schmidberger, Dissertation, Universitlt Stuttgart (1974). [S] J. Trotter, Can. J. Chem. 39 (1961) 1574. [6] C.E. Swenberg and N.E. Ceacintov, in: Organic molecular photophysics, VoL 2, ed. J. Birks (Wiley, New York, 1973) p. 489. 171 A. SUM, Phyb Rev. B l(1970) 1716. [8] H. Bouclxiha, V. Em, J.L. Fave, C. Guthmann and M. Schott, J. Phys. (Paris), submitted for publication.
[9] V. Em, Mol. Cryst. Liquid Cryst. 18 (1972) I. [lo] H. Bouck-iha, M. Schott and J-L. Fave, J. Phys (Paris) 36 (1975) 399_ [ ll] H. Bouchriha, Thesis, Paris (1977). [ 121 R.C. Johnson and R.E. Menifield, Phys Rev. B 1 (1970) 896. [ 131 L. AItwegg, hi. Chabr and I. ZschokkeGranacher, Phys. Rev. B 1% (1976) 1963. [14] H.C. Wolf, Abstracts VIXth Molecular Crystal Symposium, Sarta Barbara, Cal., June l--4,1977.
293
VoIume 53, number 2
15 January1978
INTIUCHAIN AND INTERCHAIN TRIPLET-TRIPLET EXCITON ANNIHILATION IN A QUASI-ONE-DIMENSXO-NAL CRYSTAL: 1,~DIBROMONAPHTHALENE @BN) H. BOUCHRIHA, V. ERN, J.L. FAVE, C. GUTHMANN and M. SCHOTT Groupe de Physique des Solides de I’E.ff.S. (Laboratoin? asso& au C.N.RS.j. 75.221Paris Cedex 0.5,France
LmivetatW Paris VT..,
Received 25 July 1977 Revised manuscript received 19 September 1977
The modulation of delayed fluorescence in l&dibromonaphthalene by magnetic fields has been studied at room temperature. The analysis of hii field resonance positions shows that, besides annih&tion of triplet excitons in the same onedimensional stack, annihilation also occurs between triplets localized on different, neighbouring, stacks, in particular those corresponding to the two molecules of the asymmetric pair_
1. Introduction
hopping rates inferred from ESR differ by several or-
DBN is known to be a quasi-one-dimensional crystal for triplet excitons, from spectroscopy [l] and direct measurement of the diffusivity [2] - The mono-
ders able ture into
cl&k E+/a
crystal
is made of stacks of molecules
piled up along the c axis. Interstack and intrastack
0
of magnitude [3,4] _ Fig. 1 summarizes the avail(incomplete) information about the crystal struc[S] : there are eight molecules per cell, arranged 4 “asymmetric units” of two molecules each
such as 1 and 1’ (related by no symmetry element).
Hence a splitting between the two sites I and JI, corre-
sin (3
Fig. 1. Projection of DBN crystal structure parallel to the c axis [1,5].
288
Volume 53, number 2
CHEMICAL PHYSICS LETTERS
15 January 1978
spending to primed and unprimed molecules respectively [4], which is 50 cmzl for the lowest triplet Cl].
In this note, triplet-triplet
(TT) annihilation is
studied through the magnetic field modulation of delayed fluorescence (DF) [6]. From the positions of modulation extrema at high field, one can find the zero field (ZF) parameters of the triplet species in-
volved in the interaction. From the dependence of the effect on field strength and direction and on excitation intensity, one can learn about triplet motion and reaction rate [6,7].
2. Experimental setup plates 1 and 2 mm thick were cleaved, or cut using a thread saw, from pure DBN crystal boules. The triplet lifetimes were between 2 and 3 ms at 300 K. The faces were parallel to (ab), (UC’) or (bc’) crystal planes, as determined by conoscopy. The experimental setup was the same as described elsewhere IS]_ The crystal was placed between the pole pieces of an electromagnet, and the magnetic field was rotated in a horizontal plane through 360“. The plate faces could be positioned at any angle from the horizontal with an accuracy of *2O. The samples were iuumlnated from below and excited directly in the lowest triplet state by the 4880 A line of an argon laser, attenuated as needed by neutral density fdters, and through one Corning CS3-70 and one Schott GG495 filters. The delayed fluorescence F was collected by a light guide, and sent onto an EMI 9558 QB PM through one Corning CW-60 and two Schott BGl8 filters. The signal was normalized by measuring A F(_H)/F=[F(H)-F(O)]lF(O). Allexperimentswere performed at low triplet density, nT 2 lOI cme3, where excitor1 decay is mainly monomolecular.
of magnettc
Chentatan
f,e,d
(degrees)
Fig. 2. Variation of the delayed fluorescence when r! 6 kG magnetic field is rotated in the (UC’), (k’), and (ab) planes of DBN.
3. Analysis of high field resonance positions It is weU known [6], that for particular orientations of the magnetic field, “resonance” occurs, corresponding to a degeneracy of pair state energy levels. Whereas in all pure materials studied up to now either two or zero resonances are observed at high magnetic field (9 kG) in any crystal plane, many more are present in DBN (f&2), up to at least 14 (see fig. 3,@ = 60” for instance).
180
90
0 Ot-lenlOtIon
of
maqnettc
field
(degrees)
Fig. 3. Variation of the dekjred fluorescence intensity when a 6 kG magnetic field is rotated in various intermediate planes from (a~?) to (bc’). Sample was positioned by successive rotations (angle @) around the C’ axis.
289
Volume 53, number 2
CHEMICAL
PHYSICS LElTERS
The maximum modulation is 18%. These peaks are not associated w
X)2 + 3(D* + E*)(Ib
Y)2 - 2D* = 0 ,
where D* and E* are the exciton ZF parameters and X, Y, 2 the axes of its ZF tensor_ &is the magnetic field direct&n which direction cosines in the XYZ frame are (H* X), (fi- Y), (fi 2). They can be expressed in terms of the angles 13, @ as defmed in fig. 4. Using the ZF tensor * of DBN obtained by EPR [3,4], the 4 in-chain resonances are found on the con-
15 January
1978
Fig. 4. Definition of angles 8 and v.
tinuous lines in fig. 5. The agreement with experiment (dots) is within the stated accuracy of the tensor (+2 to 5” depending on the plane considered), and of our experiments (*2O). Closer examination of the crystal structure (fig. 1) suggests that at least some interchain interactions might be non-negligible, for instance 1 with 4, or 1 b 90
60
30
0 180
-30
-50
l
* In the original work [3,4], the sign of the molecular direction cosine co@ - c*) of site II was probably misprinted_ It should be -0.3400. The symmetry operations of the factor group were performed on the tensors of molecules 1 and 1’ to generate those of all the other molecules.
290
-90
Fig. 5. Predicted and experimental resonance positions, plotted in (6, I$) coordinates. Dots: experimental results_ Solid lines: intrastack annih&ti~ns. Dashed lines: interstack (asymmetric pair) a@hilation& Dotied Lines:wter$ack an&hSations such
as l-3’ (se-etext). For clarity of tile theoretical lines, expert
mentalpoints &e plotted only in the upper half of the diagram, but results have been taken for all values of 9. For the labelliig of the curves, see table 1.
CHEMICAL
Volume 53, number 2
15 January l.978
PHYSICS LETTERS
Table 1 Correspondence between types of ann&ilation and resonance positions diilayed
in fig. 5
Type of annihilation
Nolecuies involved (fG. 1)
intrastack
1-l; 4-4 2-2; 3-3 1’__1’; 4-4’ 2’-2’; 39-3’
solid line solid line solid tie solid line
interstack interchange equivalent &Wasite)
1-4 2-3 S-4’ 2-3’
solid line solid line solid line solid line
l-2; 1-3; 2-3; 3-4 1’__2’->l’--3’. , 2r-_3~.* 3*_4
dotted line dotted line
interstack non interchange equivalent
l-3’;4-2’: l-2’;4-3’ 2--4’;3--1’;3--4’;2-1’
dotted line dotted line
(imtersitc)
f--1’;4-4’: l-4’: 4-1’ 2--2’;3--3’;2-3’;3-2’
with I’. Two limiting models for the interaction of two triplets in nei~bou~g chains can be considered. Either hopping between these two chains is very fast, and the exciton cannot be considered Iocalized on one chain, but has a ZF tensor obtained by averaging the single-chain ZF tensors; or hopping between the two chains is slow, and one observes a heterofusion, that is the ~tera~tion of two tfiph%s with different ZF tensors. However, since the ZF tensor in the homofusion process is obtained here by averaging ZF tensors corresponding to heterofusion, it is found that, in the present case, both processes yield resonances at the same positions. Moreover, some pairs yieid resonances at positions already corresponding to intraehain interactions (solid lines in fig. 3): pairs 1-4,2-3,1’4’ and 2’-3’. New resonances occur if interactions among other pairs are important. In fig. 3, the dashed lines correspond to the resonances predicted for interchain annihilation in the asymmetric unit pairs such as 1-l’; the dotted lines correspond to pairs 1-3’ and 24’ and all equivalent ones (a total of eight combinations). There remain a few isolated unaccounted for resonances, which might correspond to other interactions. Indeed, up to twenty separate resonances could in principle be seen in some planes. But of course some correspond to viny small interactions, and will not occur. In no case is any resonance predicted in
Label
dashedline f
dashed line
the (a$) plane, and indeed none is observed (fig. 2). Since resonances ~o~espcnding to intrachain TT interactions in chains 1 or I’ are seen at the same time as resonances corresponding to interchain interaction in the l-l’ pair, one can conclude that the latter is a case of “heterofusion” in the sense used above: hops of a triplet from 1 to 1’ are not frequent, but still the l-l’ interaction of large enough to allow TT anniF& lation to occur *_ The observation of these interactions does not invalidate the quasi-one-dimensionality of triplet motion. The occurrence of such interactions however, complicates very much quantitative fitting of the experimental results within Suna’s theory Q’]. A very approximate fitting of the high field resonances in the (bc’) piane was attempted using Merrifield’s theory [ 121, yielding, for the order of magnitude of triplet pair dissociation rates (JQ_~), 108 s”-* for an intrastack pair and lOro s-l for an interstack pair. These results should be considered very preliminary, For comparison, the lifetime of a triplet in a stack, as inferred from ESR [3,4] is aIso of the order of 10-s s, and the intrastack hopping time, as de* At low temperatures, due to the 50 cm-l site splitting, the four chains of site If are depopulated and the corresponding resonances should weaken and disappear. Preliminary experiments at 80 K for magnetic f?eld rotated in the (QC)plane indeed show this.
291
fr_elt pm
15 Jan-
CHEMICAL PlIYSICS LETTERS
Volume 53. number2
1978
the diffusivity [2], is of the order of
4. Variation of delayed fhorescence yield with magnetic field strength The results discussed above were all obtained at high fieId. The variation of the magnetic field effects with field strength was also studied, the results are summarized in figs. 6 and 7. Fig_ 6 shows the anisotropy of the effect in the (ac’) and (bc’) planes under fields of 0.25, 1 and G kG respectively. Fig. 7 shows the field strength dependence of the effect for three special directions in the (ac’) plane. These results are currently under study. Clearly, the gross features of the effect are understood in terms of current theoretical treatment [6,&l 1,121, but, as recently observed in naphthalene [13], not all the results can be accounted for ln this way: reverse resonances exist, for instance for H 1 c’ (fig. 2) at high field, leading to an
-m.
25
_______-__--_
SC00 OO
--_--__-_-_-_
2
‘I
t.4cpctlc
6
7
(KG)
and summary
The existence of the corresponding high field resonances shows that there is enough interstack interaction in DBN to allow am&ilation to occur between triplets localized on different, neighbouring, stacks. This interaction is certainly much smaller than intrastack triplet-triplet interaction. It seems possible that these interstack annihilations
c*
p______,_-__--_--_--_-__-_
1t
Orientation d magnetic field (dagrns)
Fig. 6. Variationof the delayedfluorescenceintensitywhen fieldsof 250,lOOO and 6000 G arerotated in the (ac’) and
Z==
(T,,T, I-
G
(Ti,Tj)
S’
II Ti +TJ
292
5
tireogth
enhancement of fluorescence at all field strengths ln this particular direction (fig. 7) contrary to theoretical expectation.
h +T,
(bc’) planes
4 f&d
Fig. 7. Variation of the delayed fluorescence intensity w&h magnetic field strength, for field appliedin threedirections in the (m’) plane: u and c’ axes, and diction of the main resonance (interstack interaction).
5. IXSC~~OU
cP+P-+
I
t
-9
Fig_8. Schemefor triplet-triplet anGhilationwhen several triplet species T+ coexist and can transforminto one another. Ti, Ti are tripletslocalizedon stacki andj respecti~ely~ where i, j standfdr 1,l’ . ..4’. F&t line is an example of interstackannihilation,second line-of irdstack annihilation. Verticalarrows correspondto diffusionnornialto the C axis, by interstackhoppingof one triplet.
Volume 53, number 2
.
-
CHEMICAL PHYSICS LETTERS
occur because the stack lengths are finite, and most triplets will fiit form interstack pairs before forming an intrastack pair. This can be written, ln Menifield’s chemical kinetic language, as in fig. 8. It is possible that the relative importance of resonance heights can be changed if the average stack length could be sufficiently modified. In our experiments, already some interstack resonances are more intense than the intrastack ones, suggesting that stacks lengths are relatively short. This problem is under investigation (Wolf [14] suggests that “old” crystals have significantly shorter stack lengths than “new” ones).
Acknowledgement This work was supported by the DGRST under contract no. 76-7-0119. This research would not have been possible without the generous gift of crystals by Dr. N. Karl and Mr. J. Ziegler, Kristallabor Stuttgart, and by Dr. G.J. Sloan, DuPont de Nemours, Wilmington, and we are very grateful to them.
15 January 1978
References [l] G. Castro and RM. iiochstrasser, J. Chem Phys. 47 (1967) 2241; RM. Hochstrasser and J.D. Whiteman, J. Chem. Phys. 56 (1972) 5945. [l] V. Em, J. Chem. Phys 56 (1972) 6259. [3]
R. Schmidberger and H.C. Wolf, Chem. Phyr Letters
16 (1972) 402; 25 (1974) 185. [4] R. Schmidberger, Dissertation, Universitlt Stuttgart (1974). [S] J. Trotter, Can. J. Chem. 39 (1961) 1574. [6] C.E. Swenberg and N.E. Ceacintov, in: Organic molecular photophysics, VoL 2, ed. J. Birks (Wiley, New York, 1973) p. 489. 171 A. SUM, Phyb Rev. B l(1970) 1716. [8] H. Bouclxiha, V. Em, J.L. Fave, C. Guthmann and M. Schott, J. Phys. (Paris), submitted for publication.
[9] V. Em, Mol. Cryst. Liquid Cryst. 18 (1972) I. [lo] H. Bouck-iha, M. Schott and J-L. Fave, J. Phys (Paris) 36 (1975) 399_ [ ll] H. Bouchriha, Thesis, Paris (1977). [ 121 R.C. Johnson and R.E. Menifield, Phys Rev. B 1 (1970) 896. [ 131 L. AItwegg, hi. Chabr and I. ZschokkeGranacher, Phys. Rev. B 1% (1976) 1963. [14] H.C. Wolf, Abstracts VIXth Molecular Crystal Symposium, Sarta Barbara, Cal., June l--4,1977.
293