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Singlet and triplet channels for triplet-exciton fusion in anthracene crystals
Volume 5. number 3
CHEMICAL PHYSICS LETTERS
SINGLET FOR
TRIPLET-EXCITON
AND
TRIPLET
FUSION
IN
15 March 1970
CHANNELS ANTHRACENE
CRYSTALS
R. P. GROFF, R. E. MERRIFIELD and P. AVAKIAN E.i,du Pant de Nemours and Company, Central Research Department*, ExpeuimentaZ Station, Wilmington, Delaware 19898, USA
Received 23 January 1970
Magnetic behavior of triplet exciton fusion in anthracene crystals shows: fusion via the triplet channel is field independent: 0.22 * 0.01 of the fusions produce singlets; and the electronic fusion matrix elements via singlet and triplet channels are appro.ximately equal.
We have extended the theory [I, 23 of the magnetic field dependence of the rate of pairwise fusion of triplet-exci!ons [3] to include channels leading to triplet final states, and have measured the field dependence of the tofal fusion rate constant in anthracene crystals at room temperature. The theory predicts that in contrast to the singlet channel, the rate constant for fusion via the triplet channel is magnetic-field independent. The experimental results show: (1) the rate constant for fusion via the triplet channel is indeed field independent; (2) at zero field the fraction of fusion events which lead to a singlet final state is 0.22 rt 0.01; and (3) the electronic matrix elements for fusion via the singlet and triplet channels are nearly
the same.
Fusion of two triplet excitors
can lead to both
singlet and triplet final spin states.
(Quintet final
states, which are allowed by the spin selection rules, can be excluded on energetic grounds in most systems.) It is well known that the rate constant for the fusion channel that leads to a singlet exciton is magnetic-field dependent [l-3]. This field dependence has been accounted for as a consequence of the field dependence of the spin wave functions of the nine spin states of the interacting triplet pair and the resulting field dependence of the distribution of singlet amplitude among these states [I, 21 Since the field operate; only on the spin part of the triplet-exciton wave function, all singlet channels will exhibit the same field dependence. The theoretical treatment of fusion via the * Contribution No. 1651.
168
triplet channel is greatly simplified by the symmetry of the exciton pair. The nine pair spin states can be divided into a group of six states which are even under interchange of the two excitons and a group of three states which are odd under this operation. This division into odd and even states is solely a consequence of symmetry and is independent of magnetic field**. The even pair states are (field-dependent) singlet/quintet mixtures while the odd states are pure triplets. Thus fusion events originating in the odd states will lead uniquely to a triplet final state at a field-independent rate ***. Under steady-state conditions the triplet exciton concentration [T~J and the intensity of blue delayed fluorescence r#)per unit VOlUme are given by PI
ai - PITl]
-
qot[Tl]2=0
(1)
and @ = srad[TI12 E $fYtot[T112 , where LY, 8, and Ytot are the absorption coefficients for the incident red light of intensity i, the monomolecular triplet decay rate constant, and the total bimolecular rate constant for triplet** Suna [4] has pointed out that this separation is rigorous only when the pair lifetime is short compared to the spin-lattice relaxation time. This is apparently she case in anthracene. *** A special case of this situation has been considered bv Pope et al. 151. who showed by explicit caloulation of the tripiei pair wave funciions in the zerofield and high-field limits that the triplet channel fusion rate constants in these two limits are equal.
Volume 5. number 3
CHEMICALPHYSICSLETTERS
triplet fusion, respectively. From eqs. (1) and (2) the relation between the experimentally meaeured intensities i and cpcan be expressed z-/w=
A + B+,
(3)
1
where A a Y& and B = Ytot/Yrad. The mechanism in terms of which we interpret our experiment is given in fig. 1. The channels with rate constants y1 and yi lead to singlet excitons S1 and to vibrationally excited singlet molecules SO, respectively. The channel with the rate constant y3 leads to TL either directly or via a higher excited triplet state which decays rapidly to Tl*. The quantities ytot and Y,,d are related to the rate constants appearing in fig. 1 by Ytot = $[(l-W)Yl t 2Yi tYg] and yrad = WI -
So+hv
Fig. 1. Model for triplet exciton
are bimolecular fusion rate constants vibrationally excited singlet molecules SO, ~~%$?excitons T1 ,_ respectively. q is the quantum yield for singlet fluorescence. Since the field dependence
of 7;
15 hfarch 1970
sion channels as follows #+V)vl(O)
+ ri(O)
=
-8l+V)Yl(O) + r\(O) + 73
B(BM2(0) - B(OM2(H)
=R, B(0)A2(B) - B(B)A2(0) where ~3 has been assumed independent of magnetic field in accordake with the above. For materials with a high fluorescence quantum yield (17 = I), R 4 RR, the branching ratio or fraction of fusion events leading to sir@et finai states. Filtered light (6500 - 69GOA) from a IO00 W Xe arc was collimated and allowed to fall on the crystal 193 resting between the poles of an electromagnet. The emitted delayed fluorescence passed through a light guide and suitable redcutoff blue-transmitting filters to a photomultiplier whose output was amplified and fed into a CAT for signal-to-noise enhancement. The Xe arc output and the photomultiplier sensitivity were unaffected by the magnetic field. The exciting light intensity was changed by periodically placing a series of calibrated neutral density fiLters in the exciting beam. Total integration times ranged from 20 - 40 minutes per filter position_ The relative blue (c$) and red (i) light intensities were found and a least squares fit done to eq. f3), to obtain the slope B and intercept A. Fig. 2 shows a typical experimental ptot of i/qversus -for H = 0 and 6 kOe. From a
= 2B(0)A2(0) -
dozen measurements on three crystals we obtain R = 0.22 f 0.01. Since in anthracene the quantum
and 71 are
the same, separate determination of the field dependence Of ytot and yrad prOvideS the necessary information for deducing the field dependence of y and the ratio of the fusion rates leading to sings et and triplet states. This can be done by comparing the relation between @ and i at two different field values, since yrad and yt t are the only magnetic-field dependent factors [39. in the coefficients A and B of eq. (3). Note that only the relative intensities i and @Jneed be determined. The experimentally measured quantities can be related to the rate constants for the various fu* The fntersystem crossing from T2 to S1 is assumed to be negligible. For naphthalene and several other molecules Keller [‘7] has shown that the T -) S intersystem crossing rate is 10 6 times smaller Aan the decay rate T2 - Tl. Radiationless transitions S1 - SO have also been neglected (see ref. [S]).
Fig. 2. Experimental results for a typical anthracene crystal showing the functional dependence of exciting intensity i on delayed fluorescence emission $I for H= 0 and 6 k0e.
169
-Volume 5, number 3
CHEMICALPHYSICSLETTERS
efficiency for fluorescence 77= 1, we conclude that the value of R is an excellent approximation for the value of Rg * t , the fraction of fusion events which lead to singlet final states. The same value of R was found for fields between 1 and 6 kOe in both the on- and off-resonance directions, which confirms that, to within is, Ytot consists of a field-independent part and a part whose field dependence is that of yl_ This is just the expected behavior based on the theoretically
demonstrated
field independence
of 73"
It is interesting that the value of Rg is close * Most reported values for 77in anthracene crystals fall in the range 0.8 -1 [lo-131. Assuming ?j = 0.9 could increase the value of Rg froril that of R by at most 4% (4% represents a maximum increase which occurs only when y;/yl = 0). ? For the related quantity y3/yl in tetracene crystals, the value of 0.4 has been inferred [5] from measurements of the dependence of the relative quantum yield for prompt fluorescence on the intensity of the exciting light. ** Pope et al. [5] have interpreted their measurements on the dependence of the fluorescence quantum yield in tetracene crystals as implying y3(4 kOe) is equal to y3(0) when the field is not in a resonance direction, but is 5% less than ‘y3(0) in the on-resonance direction. 1 Helfrich and Schneider [14] found that the assumption y3 = 3 yl (equivalent to f = 0.4) was consistent with their experimental measurement of fast and slow recombination luminescence under the additional assumption that three times as many triplet as singlet excitons are generated by electron-hole recombtnation. Fourney and Delacote [15] measured recombination luminescence versus a 3 kOe field orientation. By comparing their results with published delayed fluorescence anisotropy. they id&f = 0.4 by assuming
that: (1) the charge carrier recombination rate is field independent; and (2) the triplet channel is the only nonradiative fusion channel.
170
15 March 1970
to l/4, the ratio expected from the statistical weights of the singlet and triplet channels_ This implies the electronic matrix elements for fusion in the two channels must be nearly the same. An upper limit for f (E yrad/ytot) corresponding tori’ 0 can be deduced from RS
-
2R
f=l+R
= 0.36 f 0.02.
we are grateful
crystals
to G. J. Sloan for providing
the
and to A Suna for helpful discussions.
REFERENCES [l] R. E. Merrifield. J. Chem. Phys. 48 (l968) 4318. [2] R. C. Johnson and R. E. Merrifield, Phys. Rev., to be published. [3] R. C. Johnson, R. E. Merrifield. P. Avakian and R. B. Flippen, Phys. Rev. Letters 19 (1967) 285. [4] A. Suna. Phys. Rev., to be published. [5] M. Pope, N. E. Geacintov and F. Vogel, Mol. Cryst. 6 (1969) 83. [G] P. Avakian and R. E. Merrifield, Mol. Cryst. 5 (1968) 37 and references therein. [7] R. A.Keller. Chem. Phys. Letters 3 (1969) 27. [8] W. Siebrand and D. F. Williams, J. Chem. Phys. 49 (1968) 1860. [9] G. J. Sloan, Mol. Cryst. 1 (1966) 161. [lo] E. J. Bowen and E.Mikiewicz, Nature 159 (1947) 706. [ll] E. J. Bowen. E. Mikiewicz and F. W. Smith, Proc. Phys.Soc. (London) A62 (1949) 26. [12] G. T. Wright, Proc. Pbys. Sot. (London) B68 0.955) 241. [13] M. D. Borisov and V. N. Vishnevskii. Izv. Akad. Nauk SSSR Ser. Fiz. 20 (1956) 502. English translation: Bull. Acad. Sci. USSR Phys, Ser. 20 (l956) 459.
[14] W. Helfrich and W. G. Schneider, J. Chem. Phys. 44
(1966) 2902. [15] J. Fourney and G. Delacote,
private communication.
CHEMICAL PHYSICS LETTERS
SINGLET FOR
TRIPLET-EXCITON
AND
TRIPLET
FUSION
IN
15 March 1970
CHANNELS ANTHRACENE
CRYSTALS
R. P. GROFF, R. E. MERRIFIELD and P. AVAKIAN E.i,du Pant de Nemours and Company, Central Research Department*, ExpeuimentaZ Station, Wilmington, Delaware 19898, USA
Received 23 January 1970
Magnetic behavior of triplet exciton fusion in anthracene crystals shows: fusion via the triplet channel is field independent: 0.22 * 0.01 of the fusions produce singlets; and the electronic fusion matrix elements via singlet and triplet channels are appro.ximately equal.
We have extended the theory [I, 23 of the magnetic field dependence of the rate of pairwise fusion of triplet-exci!ons [3] to include channels leading to triplet final states, and have measured the field dependence of the tofal fusion rate constant in anthracene crystals at room temperature. The theory predicts that in contrast to the singlet channel, the rate constant for fusion via the triplet channel is magnetic-field independent. The experimental results show: (1) the rate constant for fusion via the triplet channel is indeed field independent; (2) at zero field the fraction of fusion events which lead to a singlet final state is 0.22 rt 0.01; and (3) the electronic matrix elements for fusion via the singlet and triplet channels are nearly
the same.
Fusion of two triplet excitors
can lead to both
singlet and triplet final spin states.
(Quintet final
states, which are allowed by the spin selection rules, can be excluded on energetic grounds in most systems.) It is well known that the rate constant for the fusion channel that leads to a singlet exciton is magnetic-field dependent [l-3]. This field dependence has been accounted for as a consequence of the field dependence of the spin wave functions of the nine spin states of the interacting triplet pair and the resulting field dependence of the distribution of singlet amplitude among these states [I, 21 Since the field operate; only on the spin part of the triplet-exciton wave function, all singlet channels will exhibit the same field dependence. The theoretical treatment of fusion via the * Contribution No. 1651.
168
triplet channel is greatly simplified by the symmetry of the exciton pair. The nine pair spin states can be divided into a group of six states which are even under interchange of the two excitons and a group of three states which are odd under this operation. This division into odd and even states is solely a consequence of symmetry and is independent of magnetic field**. The even pair states are (field-dependent) singlet/quintet mixtures while the odd states are pure triplets. Thus fusion events originating in the odd states will lead uniquely to a triplet final state at a field-independent rate ***. Under steady-state conditions the triplet exciton concentration [T~J and the intensity of blue delayed fluorescence r#)per unit VOlUme are given by PI
ai - PITl]
-
qot[Tl]2=0
(1)
and @ = srad[TI12 E $fYtot[T112 , where LY, 8, and Ytot are the absorption coefficients for the incident red light of intensity i, the monomolecular triplet decay rate constant, and the total bimolecular rate constant for triplet** Suna [4] has pointed out that this separation is rigorous only when the pair lifetime is short compared to the spin-lattice relaxation time. This is apparently she case in anthracene. *** A special case of this situation has been considered bv Pope et al. 151. who showed by explicit caloulation of the tripiei pair wave funciions in the zerofield and high-field limits that the triplet channel fusion rate constants in these two limits are equal.
Volume 5. number 3
CHEMICALPHYSICSLETTERS
triplet fusion, respectively. From eqs. (1) and (2) the relation between the experimentally meaeured intensities i and cpcan be expressed z-/w=
A + B+,
(3)
1
where A a Y& and B = Ytot/Yrad. The mechanism in terms of which we interpret our experiment is given in fig. 1. The channels with rate constants y1 and yi lead to singlet excitons S1 and to vibrationally excited singlet molecules SO, respectively. The channel with the rate constant y3 leads to TL either directly or via a higher excited triplet state which decays rapidly to Tl*. The quantities ytot and Y,,d are related to the rate constants appearing in fig. 1 by Ytot = $[(l-W)Yl t 2Yi tYg] and yrad = WI -
So+hv
Fig. 1. Model for triplet exciton
are bimolecular fusion rate constants vibrationally excited singlet molecules SO, ~~%$?excitons T1 ,_ respectively. q is the quantum yield for singlet fluorescence. Since the field dependence
of 7;
15 hfarch 1970
sion channels as follows #+V)vl(O)
+ ri(O)
=
-8l+V)Yl(O) + r\(O) + 73
B(BM2(0) - B(OM2(H)
=R, B(0)A2(B) - B(B)A2(0) where ~3 has been assumed independent of magnetic field in accordake with the above. For materials with a high fluorescence quantum yield (17 = I), R 4 RR, the branching ratio or fraction of fusion events leading to sir@et finai states. Filtered light (6500 - 69GOA) from a IO00 W Xe arc was collimated and allowed to fall on the crystal 193 resting between the poles of an electromagnet. The emitted delayed fluorescence passed through a light guide and suitable redcutoff blue-transmitting filters to a photomultiplier whose output was amplified and fed into a CAT for signal-to-noise enhancement. The Xe arc output and the photomultiplier sensitivity were unaffected by the magnetic field. The exciting light intensity was changed by periodically placing a series of calibrated neutral density fiLters in the exciting beam. Total integration times ranged from 20 - 40 minutes per filter position_ The relative blue (c$) and red (i) light intensities were found and a least squares fit done to eq. f3), to obtain the slope B and intercept A. Fig. 2 shows a typical experimental ptot of i/qversus -for H = 0 and 6 kOe. From a
= 2B(0)A2(0) -
dozen measurements on three crystals we obtain R = 0.22 f 0.01. Since in anthracene the quantum
and 71 are
the same, separate determination of the field dependence Of ytot and yrad prOvideS the necessary information for deducing the field dependence of y and the ratio of the fusion rates leading to sings et and triplet states. This can be done by comparing the relation between @ and i at two different field values, since yrad and yt t are the only magnetic-field dependent factors [39. in the coefficients A and B of eq. (3). Note that only the relative intensities i and @Jneed be determined. The experimentally measured quantities can be related to the rate constants for the various fu* The fntersystem crossing from T2 to S1 is assumed to be negligible. For naphthalene and several other molecules Keller [‘7] has shown that the T -) S intersystem crossing rate is 10 6 times smaller Aan the decay rate T2 - Tl. Radiationless transitions S1 - SO have also been neglected (see ref. [S]).
Fig. 2. Experimental results for a typical anthracene crystal showing the functional dependence of exciting intensity i on delayed fluorescence emission $I for H= 0 and 6 k0e.
169
-Volume 5, number 3
CHEMICALPHYSICSLETTERS
efficiency for fluorescence 77= 1, we conclude that the value of R is an excellent approximation for the value of Rg * t , the fraction of fusion events which lead to singlet final states. The same value of R was found for fields between 1 and 6 kOe in both the on- and off-resonance directions, which confirms that, to within is, Ytot consists of a field-independent part and a part whose field dependence is that of yl_ This is just the expected behavior based on the theoretically
demonstrated
field independence
of 73"
It is interesting that the value of Rg is close * Most reported values for 77in anthracene crystals fall in the range 0.8 -1 [lo-131. Assuming ?j = 0.9 could increase the value of Rg froril that of R by at most 4% (4% represents a maximum increase which occurs only when y;/yl = 0). ? For the related quantity y3/yl in tetracene crystals, the value of 0.4 has been inferred [5] from measurements of the dependence of the relative quantum yield for prompt fluorescence on the intensity of the exciting light. ** Pope et al. [5] have interpreted their measurements on the dependence of the fluorescence quantum yield in tetracene crystals as implying y3(4 kOe) is equal to y3(0) when the field is not in a resonance direction, but is 5% less than ‘y3(0) in the on-resonance direction. 1 Helfrich and Schneider [14] found that the assumption y3 = 3 yl (equivalent to f = 0.4) was consistent with their experimental measurement of fast and slow recombination luminescence under the additional assumption that three times as many triplet as singlet excitons are generated by electron-hole recombtnation. Fourney and Delacote [15] measured recombination luminescence versus a 3 kOe field orientation. By comparing their results with published delayed fluorescence anisotropy. they id&f = 0.4 by assuming
that: (1) the charge carrier recombination rate is field independent; and (2) the triplet channel is the only nonradiative fusion channel.
170
15 March 1970
to l/4, the ratio expected from the statistical weights of the singlet and triplet channels_ This implies the electronic matrix elements for fusion in the two channels must be nearly the same. An upper limit for f (E yrad/ytot) corresponding tori’ 0 can be deduced from RS
-
2R
f=l+R
= 0.36 f 0.02.
we are grateful
crystals
to G. J. Sloan for providing
the
and to A Suna for helpful discussions.
REFERENCES [l] R. E. Merrifield. J. Chem. Phys. 48 (l968) 4318. [2] R. C. Johnson and R. E. Merrifield, Phys. Rev., to be published. [3] R. C. Johnson, R. E. Merrifield. P. Avakian and R. B. Flippen, Phys. Rev. Letters 19 (1967) 285. [4] A. Suna. Phys. Rev., to be published. [5] M. Pope, N. E. Geacintov and F. Vogel, Mol. Cryst. 6 (1969) 83. [G] P. Avakian and R. E. Merrifield, Mol. Cryst. 5 (1968) 37 and references therein. [7] R. A.Keller. Chem. Phys. Letters 3 (1969) 27. [8] W. Siebrand and D. F. Williams, J. Chem. Phys. 49 (1968) 1860. [9] G. J. Sloan, Mol. Cryst. 1 (1966) 161. [lo] E. J. Bowen and E.Mikiewicz, Nature 159 (1947) 706. [ll] E. J. Bowen. E. Mikiewicz and F. W. Smith, Proc. Phys.Soc. (London) A62 (1949) 26. [12] G. T. Wright, Proc. Pbys. Sot. (London) B68 0.955) 241. [13] M. D. Borisov and V. N. Vishnevskii. Izv. Akad. Nauk SSSR Ser. Fiz. 20 (1956) 502. English translation: Bull. Acad. Sci. USSR Phys, Ser. 20 (l956) 459.
[14] W. Helfrich and W. G. Schneider, J. Chem. Phys. 44
(1966) 2902. [15] J. Fourney and G. Delacote,
private communication.