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On the intersystem crossing quantum yield determination using external perturbers
Journal of Luminescence 37 (1987) 57-60 North-Holland, Amsterdam
57
SHORT COMMUNICATION ON THE INTERSYSTEM CROSSING USING EXTERNAL PERTURBERS J. NAJBAR
QUANTUM
YIELD DETERMINATION
and A.M. TUREK
Faculiy of Chemistv,
Jagielionian
University, 3 Karasia, 30 060 Krakdw, Poland
Received 15 May 1986 Revised 26 December 1986 Accepted 30 December 1986
A simple derivation of the Medinger and Wilkinson equation for the determination of the intersystem crossing quantum yields @Ox of aromatic molecules using heavy-atom perturbation shows that it is also valid in rigid solution and is independent of the details of the kinetics. It is also shown that under the assumptions of random distribution of the perturber molecules in rate constants from different perturber molecules the rigid solutions and of additivity of the contributions to k, and k, phosphorescence intensity measurements can be used for evaluation of $I”~, if efficient perturbers for the S, 4 T intersystem crossing are applied.
In order to determine the intersystem crossing quantum yield @on it is necessary to monitor the transient or steady state population of the triplet state after So + S, excitation. This can be done using the measurements of the Ti + T, absorption, the energy transfer from the T, state, the intensity of the ESR signal of the triplet molecules or the measurements of the quantum yields of the photochemical reactions originating from the triplet state. These measurements can be more easily accomplished for the molecules in the liquid solutions. In this article we consider two methods using perturbers influencing the rates of the intersystem crossing processes, which can be also used for rigid solutions at low temperatures. The heavy-atom perturbers enhance the S, + T intersystem crossing rate constant k,, and have negligible effect on the fluorescence k& and S, +-+So internal conversion k& rate constants [l-3]. For the samples at low temperatures the phosphorescence measurements are easier to perform than the transient absorption, and the method based on the T-T energy transfer was already applied in the +oTsdetermination [2]. We show that derivation of the equation proposed by Medinger and Wilkinson [2] does not
require any assumption concerning the type of the interaction between the fluorescent molecule and the heavy-atom perturber as well as the details of the kinetics. In the presence of the perturber influencing the S, 4 T intersystem crossing we have (&Y.) + (%X)
+ (Grs)
= 19
(1)
where angle brackets indicate averaging, and +rs = k;srsFs, +os = k&s, +rs = k+ss, 7s = Mkis + k& + k,,). For any type of the averaging based on the superposition scheme we can take out the constant factor from the angle brackets. We obtain C&S) = k;s(rs)~
(Go,> = k%rs).
(2)
Using eqs. (1) and (2) we can get (@FS) -= &S
1-
(&-s)
1 - &$s
(3)
.
Equation (3) can be rearranged to -- 443
(h)
l=&
i
1 . i
(4
Equation (4) is identical to the equation proposed by Medinger and Wilkinson. In this way we have
0022-2313/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
58
J. Najhur, A.M. Turek / Intersystem
crossing quantum yield determination
shown that their equation can be applied under much broader experimental conditions than originally proposed. Here we propose a method using perturbers based on the measurements of the phosphorescence quantum yields and suitably defined lifetimes. The radiative k, and radiationless k,, decay constants of the triplet state are dependent on the presence of the heavy atom perturbers [3]. We assume that the relative configurations of the perturber molecules and the aromatic molecules are random and uncorrelated, and the contributions Ak,,( R) to the rate constants (k,,, k,, k,,) are additive and dependent on the distance between the aromatic molecule and the perturber. In the recent papers [5,6] we have shown that the phosphorescence (P) response function i,“‘(t) after S(t) indirect (I) excitation is given by i:‘(t)
= ([ k&r+pK,(p,
h(p~
s, t) epkzs
ds
)
where p is the mole fraction molecules, RFr(p, =
ee@,
of the perturber
x$(p, s) em@ ds,
dP,
R)t - Ak,(
R)s] }
t) =&r(p,
s=O,
dR,
t),
@CR, S? 1)
s)=$(p,
s=o,
s,
t=O),
S, t=o).
If the integral term in eq. (7) can be neglected for high values of p, then eq. (7) allows for determination of the +‘& by the extrapolation to p = 0. In the special case when the enhancements of the S, -+ T intersystem crossing and the Ti -+ So radiative transitions are such that s) = K,s( P, s) k,O
kh
+p
xexp[ -Ak,(R)t-Ak,,(R)s])R*
t=O), s)=K,(p,
Km( P,
= exp 4rp Dln(l -p i 1RO
(7)
where K,=K(p,
4npjRy{ &r(R)
t)=+(p,
The quantity i~‘(0)/k$&on can be measured directly for different concentrations of the perturber or calculated through eq. (6) from the relative phosphorescence quantum yields (&,T)/+o~ and the mean phosphorescence lifetimes ‘7:’ for concentrations of the perturber ( TG is the phosphorescence lifetime in the absence of the perturber). Using the phosphorescence response function, eq. (5) the right-hand side of eq. (6) can be calculated and we have
K&P,
Xexp[ -AkT(R)t-AkTS(R)S]}-1R2
G(P,
(6)
(5)
x(1-p+p
K,(p,
[61
s, t)]
s, t>
Xexp[ -Ak,(
( c$,) and the mean phosphorescence lifetime ‘~;t defined as zero-order moment of the phosphorescence response function i:‘(t) satisfy the relation
f)
-(ks0-~~s)/oZ‘[k~+pKpr(p, x+(p,
using externcrlperturbers
’
where dR),
KTS(P,
t).
Equation (5) is valid for all concentrations of the perturber including pure perturber solvent p = 1. The mean phosphorescence quantum yield
=4npLo
s) m Ak,,( R) exp( -Ak,(R)s) I-p+pexp(-Ak (R)s)~~~~’ TS
the integral term in eq. (7) can be easily calculated
J. Najbar, A.M. Turek / Intersystem crossing quantum yield determination using external perturbers
59
and we obtain (9) We have obtained here a linear dependence over the whole concentration range; hence this equation cannot be used for determination of the &-s because of the unknown k&. To obtain the proper nonlinear dependence the following inequality should be satisfied:
3.6
0.75 0.5 0.25 0.1
2.6
(10) It means that for a given perturber the ratio of the enhancement of the S, -+ T intersystem crossing to the ki should be greater than the ratio of the enhancement of the radiative phosphorescence transition to the k$ The numerical calculations were carried out assuming that the distance dependence for the enhancement of the S, us T intersystem crossing Ak,s( R) and the radiative phosphorescence transition Ak,(R) are given by Ak,,(R) = kky exp( -axuR), where k&, and cxxY are parameters. The numerical integrations over R in the formulae for K&p, s) and +(p, s) were performed from the distance of the closest approach between the aromatic molecule and the perturber R, = 0.5 nm to R = 3.5 nm. The number density of the perturber was taken to be equal 1.47 X 102* cmP3, which corresponds to the molar volume of the perturber 41 cm3. The $& in all cases was assumed as equal 0.5. In the present calculations slightly different distance dependences for Ak,s(R) and Ak,( R) have been used. To characterize the influence of the perturber on the processes we use the mean values of Akx,(R). They are K, = K&O, O), K,, = K,s(O, 0). The results presented in fig. 1 correspond to namely, 2.2 x lo9 s-l and two values of K,,, 11.3 X lo9 s-l. The ratios K&kg are equal 220 and 1100, respectively. K, is equal 11.08 sP ’ in all cases, whereas kh equals 1.0 s-l, 0.75 s-l, 0.5 ssl, 0.25 s-l and 0.1 s-l, which corresponds to the ratio of Km/k& equaling 11.08, 14.77, 22.16, 44.32 and 110.6, respectively. The K, and K,,
1.c
c
I
0.1
p
, 0.2
Fig. 1. The plots of (eTskn) and (&s) (the insert) versus perturber concentration. The following parameters have been used: kg=lO’s-‘, k’&=0.5x107s-‘, olTs=l.l&‘, 1.5 A-‘, k&=5x103 s-‘, k&=9X10” s-‘(dashedE:si, or 45~10~ s-l (dotted lines). Straight lines represent linear dependences extrapolated from the high-concentration range.
parameters used here represent the typical values found for the aromatic hydrocarbons perturbed by I- ions [6] or ethyl iodide [7]. Straight lines in fig. 1 are the asymptotic lines which represent the dependences of (+TSkPT) at high perturber concentrations. For decreasing Km/k& ratios the calculated curves approach the asymptotic lines at decreasing concentrations of the perturber. Figure 1 shows that if the perturber influences efficiently the S, + T intersystem crossing the extrapolation from higher concentration range to p = 0 is feasible. The insert in fig. 1 shows the calculated (+rS) as a function of p in the same concentration range. In the range of concentrations where ($rsk,) becomes a linear function of p the (&s) has to be very close to 1. Thus, we find that
60
J. Nujbar, A.M.
Turek / Intersystem
crossing quantum yield determinution
it should be possible to design a method of de. . termination of +cs based on phosphorescence measurements, but the perturber must be more efficient for the St -+ T intersystem crossing than for the enhancement of the T -+ S,, radiative transition. The condition (10) can be more easily satisfied for an aromatic compound with relatively high kh and long singlet state lifetime (small kg values). The heavy-atom perturber gives rise to strong radiative phosphorescence transition in aromatic hydrocarbons, so the condition (10) is likely to be satisfied in these cases in which the S, state is of ‘L, type. The other possibility is to apply the paramagnetic perturbers, which give strong enhancement of the S, -+ T ISC, but small enhancement of the Ti + S, radiative transition. The model calculations considered here have been performed under the assumption of spherical symmetry. However, the functions K,(p, s) and +(p, s) have the same form in the more general case when the influence of the perturber on the rate constants depends on the relative orientations of the aromatic molecule and the perturber. We
using externalperturbers
expect that the proposed valid in this more general
method case.
should
be also
Acknowledgement The support of the project CPBP 01.19 is gratefully acknowledged. The authors thank Professor Z.R. Grabowski for valuable comments.
References [l] J.B. Birks, Photophysics [2] [3]
[4] [5] [6] [7]
of Aromatic Molecules (Wiley-Interscience, New York, 1970). F. Wilkinson, in: Organic Molecular Photophysics, Vol. 2, ed. J.B. Birks (Wiley-Interscience, London, 1975) p. 95. S.P. McGlynn, T. Azumi and M. Kinoshita, Molecular Spectroscopy of the Triplet State (Prentice-Hall, Englewood Cliffs, New York, 1969). T. Medinger and F. Wilkinson, Trans. Faraday Sot. 61 (1965) 620. J. Najbar, Chem. Phys. Lett. 90 (1982) 154. J. Najbar, J. Lumin. (to appear). S.E. Webber, Chem. Phys. Lett. 5 (1970) 466.
57
SHORT COMMUNICATION ON THE INTERSYSTEM CROSSING USING EXTERNAL PERTURBERS J. NAJBAR
QUANTUM
YIELD DETERMINATION
and A.M. TUREK
Faculiy of Chemistv,
Jagielionian
University, 3 Karasia, 30 060 Krakdw, Poland
Received 15 May 1986 Revised 26 December 1986 Accepted 30 December 1986
A simple derivation of the Medinger and Wilkinson equation for the determination of the intersystem crossing quantum yields @Ox of aromatic molecules using heavy-atom perturbation shows that it is also valid in rigid solution and is independent of the details of the kinetics. It is also shown that under the assumptions of random distribution of the perturber molecules in rate constants from different perturber molecules the rigid solutions and of additivity of the contributions to k, and k, phosphorescence intensity measurements can be used for evaluation of $I”~, if efficient perturbers for the S, 4 T intersystem crossing are applied.
In order to determine the intersystem crossing quantum yield @on it is necessary to monitor the transient or steady state population of the triplet state after So + S, excitation. This can be done using the measurements of the Ti + T, absorption, the energy transfer from the T, state, the intensity of the ESR signal of the triplet molecules or the measurements of the quantum yields of the photochemical reactions originating from the triplet state. These measurements can be more easily accomplished for the molecules in the liquid solutions. In this article we consider two methods using perturbers influencing the rates of the intersystem crossing processes, which can be also used for rigid solutions at low temperatures. The heavy-atom perturbers enhance the S, + T intersystem crossing rate constant k,, and have negligible effect on the fluorescence k& and S, +-+So internal conversion k& rate constants [l-3]. For the samples at low temperatures the phosphorescence measurements are easier to perform than the transient absorption, and the method based on the T-T energy transfer was already applied in the +oTsdetermination [2]. We show that derivation of the equation proposed by Medinger and Wilkinson [2] does not
require any assumption concerning the type of the interaction between the fluorescent molecule and the heavy-atom perturber as well as the details of the kinetics. In the presence of the perturber influencing the S, 4 T intersystem crossing we have (&Y.) + (%X)
+ (Grs)
= 19
(1)
where angle brackets indicate averaging, and +rs = k;srsFs, +os = k&s, +rs = k+ss, 7s = Mkis + k& + k,,). For any type of the averaging based on the superposition scheme we can take out the constant factor from the angle brackets. We obtain C&S) = k;s(rs)~
(Go,> = k%rs).
(2)
Using eqs. (1) and (2) we can get (@FS) -= &S
1-
(&-s)
1 - &$s
(3)
.
Equation (3) can be rearranged to -- 443
(h)
l=&
i
1 . i
(4
Equation (4) is identical to the equation proposed by Medinger and Wilkinson. In this way we have
0022-2313/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
58
J. Najhur, A.M. Turek / Intersystem
crossing quantum yield determination
shown that their equation can be applied under much broader experimental conditions than originally proposed. Here we propose a method using perturbers based on the measurements of the phosphorescence quantum yields and suitably defined lifetimes. The radiative k, and radiationless k,, decay constants of the triplet state are dependent on the presence of the heavy atom perturbers [3]. We assume that the relative configurations of the perturber molecules and the aromatic molecules are random and uncorrelated, and the contributions Ak,,( R) to the rate constants (k,,, k,, k,,) are additive and dependent on the distance between the aromatic molecule and the perturber. In the recent papers [5,6] we have shown that the phosphorescence (P) response function i,“‘(t) after S(t) indirect (I) excitation is given by i:‘(t)
= ([ k&r+pK,(p,
h(p~
s, t) epkzs
ds
)
where p is the mole fraction molecules, RFr(p, =
ee@,
of the perturber
x$(p, s) em@ ds,
dP,
R)t - Ak,(
R)s] }
t) =&r(p,
s=O,
dR,
t),
@CR, S? 1)
s)=$(p,
s=o,
s,
t=O),
S, t=o).
If the integral term in eq. (7) can be neglected for high values of p, then eq. (7) allows for determination of the +‘& by the extrapolation to p = 0. In the special case when the enhancements of the S, -+ T intersystem crossing and the Ti -+ So radiative transitions are such that s) = K,s( P, s) k,O
kh
+p
xexp[ -Ak,(R)t-Ak,,(R)s])R*
t=O), s)=K,(p,
Km( P,
= exp 4rp Dln(l -p i 1RO
(7)
where K,=K(p,
4npjRy{ &r(R)
t)=+(p,
The quantity i~‘(0)/k$&on can be measured directly for different concentrations of the perturber or calculated through eq. (6) from the relative phosphorescence quantum yields (&,T)/+o~ and the mean phosphorescence lifetimes ‘7:’ for concentrations of the perturber ( TG is the phosphorescence lifetime in the absence of the perturber). Using the phosphorescence response function, eq. (5) the right-hand side of eq. (6) can be calculated and we have
K&P,
Xexp[ -AkT(R)t-AkTS(R)S]}-1R2
G(P,
(6)
(5)
x(1-p+p
K,(p,
[61
s, t)]
s, t>
Xexp[ -Ak,(
( c$,) and the mean phosphorescence lifetime ‘~;t defined as zero-order moment of the phosphorescence response function i:‘(t) satisfy the relation
f)
-(ks0-~~s)/oZ‘[k~+pKpr(p, x+(p,
using externcrlperturbers
’
where dR),
KTS(P,
t).
Equation (5) is valid for all concentrations of the perturber including pure perturber solvent p = 1. The mean phosphorescence quantum yield
=4npLo
s) m Ak,,( R) exp( -Ak,(R)s) I-p+pexp(-Ak (R)s)~~~~’ TS
the integral term in eq. (7) can be easily calculated
J. Najbar, A.M. Turek / Intersystem crossing quantum yield determination using external perturbers
59
and we obtain (9) We have obtained here a linear dependence over the whole concentration range; hence this equation cannot be used for determination of the &-s because of the unknown k&. To obtain the proper nonlinear dependence the following inequality should be satisfied:
3.6
0.75 0.5 0.25 0.1
2.6
(10) It means that for a given perturber the ratio of the enhancement of the S, -+ T intersystem crossing to the ki should be greater than the ratio of the enhancement of the radiative phosphorescence transition to the k$ The numerical calculations were carried out assuming that the distance dependence for the enhancement of the S, us T intersystem crossing Ak,s( R) and the radiative phosphorescence transition Ak,(R) are given by Ak,,(R) = kky exp( -axuR), where k&, and cxxY are parameters. The numerical integrations over R in the formulae for K&p, s) and +(p, s) were performed from the distance of the closest approach between the aromatic molecule and the perturber R, = 0.5 nm to R = 3.5 nm. The number density of the perturber was taken to be equal 1.47 X 102* cmP3, which corresponds to the molar volume of the perturber 41 cm3. The $& in all cases was assumed as equal 0.5. In the present calculations slightly different distance dependences for Ak,s(R) and Ak,( R) have been used. To characterize the influence of the perturber on the processes we use the mean values of Akx,(R). They are K, = K&O, O), K,, = K,s(O, 0). The results presented in fig. 1 correspond to namely, 2.2 x lo9 s-l and two values of K,,, 11.3 X lo9 s-l. The ratios K&kg are equal 220 and 1100, respectively. K, is equal 11.08 sP ’ in all cases, whereas kh equals 1.0 s-l, 0.75 s-l, 0.5 ssl, 0.25 s-l and 0.1 s-l, which corresponds to the ratio of Km/k& equaling 11.08, 14.77, 22.16, 44.32 and 110.6, respectively. The K, and K,,
1.c
c
I
0.1
p
, 0.2
Fig. 1. The plots of (eTskn) and (&s) (the insert) versus perturber concentration. The following parameters have been used: kg=lO’s-‘, k’&=0.5x107s-‘, olTs=l.l&‘, 1.5 A-‘, k&=5x103 s-‘, k&=9X10” s-‘(dashedE:si, or 45~10~ s-l (dotted lines). Straight lines represent linear dependences extrapolated from the high-concentration range.
parameters used here represent the typical values found for the aromatic hydrocarbons perturbed by I- ions [6] or ethyl iodide [7]. Straight lines in fig. 1 are the asymptotic lines which represent the dependences of (+TSkPT) at high perturber concentrations. For decreasing Km/k& ratios the calculated curves approach the asymptotic lines at decreasing concentrations of the perturber. Figure 1 shows that if the perturber influences efficiently the S, + T intersystem crossing the extrapolation from higher concentration range to p = 0 is feasible. The insert in fig. 1 shows the calculated (+rS) as a function of p in the same concentration range. In the range of concentrations where ($rsk,) becomes a linear function of p the (&s) has to be very close to 1. Thus, we find that
60
J. Nujbar, A.M.
Turek / Intersystem
crossing quantum yield determinution
it should be possible to design a method of de. . termination of +cs based on phosphorescence measurements, but the perturber must be more efficient for the St -+ T intersystem crossing than for the enhancement of the T -+ S,, radiative transition. The condition (10) can be more easily satisfied for an aromatic compound with relatively high kh and long singlet state lifetime (small kg values). The heavy-atom perturber gives rise to strong radiative phosphorescence transition in aromatic hydrocarbons, so the condition (10) is likely to be satisfied in these cases in which the S, state is of ‘L, type. The other possibility is to apply the paramagnetic perturbers, which give strong enhancement of the S, -+ T ISC, but small enhancement of the Ti + S, radiative transition. The model calculations considered here have been performed under the assumption of spherical symmetry. However, the functions K,(p, s) and +(p, s) have the same form in the more general case when the influence of the perturber on the rate constants depends on the relative orientations of the aromatic molecule and the perturber. We
using externalperturbers
expect that the proposed valid in this more general
method case.
should
be also
Acknowledgement The support of the project CPBP 01.19 is gratefully acknowledged. The authors thank Professor Z.R. Grabowski for valuable comments.
References [l] J.B. Birks, Photophysics [2] [3]
[4] [5] [6] [7]
of Aromatic Molecules (Wiley-Interscience, New York, 1970). F. Wilkinson, in: Organic Molecular Photophysics, Vol. 2, ed. J.B. Birks (Wiley-Interscience, London, 1975) p. 95. S.P. McGlynn, T. Azumi and M. Kinoshita, Molecular Spectroscopy of the Triplet State (Prentice-Hall, Englewood Cliffs, New York, 1969). T. Medinger and F. Wilkinson, Trans. Faraday Sot. 61 (1965) 620. J. Najbar, Chem. Phys. Lett. 90 (1982) 154. J. Najbar, J. Lumin. (to appear). S.E. Webber, Chem. Phys. Lett. 5 (1970) 466.