ISSN 0030-400X, Optics and Spectroscopy, 2015, Vol. 119, No. 4, pp. 642–655. © Pleiades Publishing, Ltd., 2015. Original Russian Text © V.L. Ermolaev, E.B. Sveshnikova, 2015, published in Optika i Spektroskopiya, 2015, Vol. 119, No. 4, pp. 627–641.
CONDENSED-MATTER SPECTROSCOPY
Limits to the Applicability of the Rule of Equality to Unity of the Sum of Quantum Yields of Fluorescence and Transition to the Triplet State for Complex Organic Molecules in the Condensed Phase (A Review) V. L. Ermolaev and E. B. Sveshnikova ITMO University, St. Petersburg, 197101 Russia e-mail:
[email protected] Received May 5, 2015
Abstract—For different classes of molecules, we have estimated from experimental data the lower limit of the height of S1 levels for which the rule qfl + qT = 1 (qfl is the fluorescence quantum yield, qT is the quantum yield of formation of the triplet state) begins to be violated; i.e., direct nonradiative transition from the S1-state to the ground state appears, the quantum yield of which exceeds measurement errors. We have found that, for compounds of different classes, this limit varies from 15000 to 21000 cm–1. It has been shown that the difference in the limit may be explained in terms of the inductive resonance theory of nonradiative transitions, which takes into account the localization of the electronic transition, its rate constant, and the overlap of the vibronic spectrum of the molecule with the vibrational spectrum of high-frequency vibrations taking into account the variation in the rate constant of the intersystem crossing transition to the triplet state. DOI: 10.1134/S0030400X15100112
INTRODUCTION In 1962–1968, using the triplet–triplet and triplet–singlet energy transfer method, we compared the number of quenched luminescence quanta in energy donors with the number of photons emitted by acceptors [1–8]. This comparison led us to the conclusion that, in photochemically stable complex organic molecules in solutions, electronically excited states are mainly deactivated via the lowest triplet T1-state of the molecule, which means that there is no noticeable internal conversion process S1 V S 0(qIC1) in the molecules. The conclusion that an efficient nonradiative transition from the lowest triplet T1 state to the ground S0 state takes place was also drawn in works in which it was revealed for a series of aromatic hydrocarbons that, upon passage from protonated molecules to deuterated ones, the lifetime of the phosphorescence state considerably increases (see [9] and Table 8.11 in [10]). In 1968, we gathered data that were obtained by different methods (both our data and data available from the literature at that time) on the fluorescence quantum yields (qfl) and quantum yields of formation of the triplet state (qT) (intersystem crossing quantum yield) in solid and liquid solutions [11]. It was found that, for the majority of aromatic hydrocarbons and their derivatives, the sum qfl + qT is close to unity provided that there is no photochemical reaction with a
noticeable yield. This suggested to us that the following rule should be formulated: the sum of fluorescence quantum yield and quantum yield of formation of the triplet state of a molecule from the S1-state is equal to unity (qfl + qT = 1); i.e., the internal conversion process from the lowest singlet excited level S1 V S 0(qIC1) does not proceed (with an accuracy that exceeds measurement errors), i.e., kfl + kISC1 ≫ kIC1. The processes under discussion and their designations are shown in the figure, which presents the energy-level diagram of complex organic molecules and the notation of rate constants of different radiative and nonradiative transitions between levels. For simplicity, the figure omits vibrational levels of electronic states. At the same time, the Vavilov law [12] and the Kasha rule [13], in accordance with which the internal conversion rate constants between excited singlet levels S n(n ≥ 2) V S1 of organic molecules (kIC2) are so high that they considerably exceed the probabilities of emission and transition to the system of triplet levels of the molecule, are well known. Therefore, all molecules excited as a result of the absorption of a radiation quantum in allowed singlet–singlet absorption bands prove to be resided in the first singlet excited state. Kasha extended this rule to transitions from high-lying triplet levels Tn(n ≥ 2) V T1. For the majority of aro-
642
LIMITS TO THE APPLICABILITY OF THE RULE
S3 T2 S2 kIC2
kIC3
hν2
S1 kISC1 T1 hν1
kfl
kIC1
kph kISC2
S0 Scheme of electronic levels and transitions between them in complex organic molecules in the condensed phase. Thick lines indicate positions of electronic levels; thin continuous and dashed lines indicate radiative and nonradiative transitions, respectively. For simplicity, vibrational levels are not shown. Designations: kfl and kph are the fluorescence and phosphorescence radiative rate constants, respectively; kIC1 is the internal conversion rate constant from the S1 level; kIC2 and kIC3 are the internal conversion rate constants from high-lying excited singlet and triplet levels; and kISC1 and kISC2 are the intersystem crossing rate constants from the S1-state to the T1-state and from the T1- state to the S0-state, respectively.
matic compounds and dyes, fluorescence quantum yields from high-lying excited singlet states were measured to be 10–4–10–6 [14, 15], confirming the inferences by Vavilov and Kasha that almost complete conversion of the energy of high-lying excited singlet and triplet levels in the S1 and T1 states takes place. Violation is observed only for some groups of molecules (azulene and its derivatives, thioketones, and porphyrins), in which the energy gap between the lowest S1 and the next S2 singlet excited levels is greater than 7000 cm–1. For them, a noticeable fluorescence S2 → S0 from the second level and the influence of deuteration on its yield are observed. Therefore, only when the molecule finds itself in the S1-state the intersystem crossing rate constant kISC1 to the system of triplet levels can compete with the processes of the fluorescence radiation emission kr = kfl and the internal conversion kIC1 to the ground S0 state. The fulfillment of the rule qfl + qT = 1 was established based on data on yields qfl and qT for a series of aromatic compounds and dyes that fluoresce in the range from 24 000 to 32 000 cm–1 and data on a series of porphyrins fluorescent in the visible range of the spectrum. As has been correctly noted in the dissertation by Plotnikov [16] and monographs by Maier and OPTICS AND SPECTROSCOPY
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Danilova [17, 18], a range of the gap ΔЕ(S1 – S0) should exist in which the values of kIC1 are comparable with the sum kfl + kISC1, and the rule qfl + qT = 1 will not be fulfilled. At present, experimental data have been gathered that testify to the violation of the rule qfl + qT = 1 for organic molecules of different classes, which gives grounds to discuss the fulfillment limits of this rule. The second half of the last century was characterized by the rapid development of various theories of nonradiative transitions, including such transitions in complex organic molecules. This was caused by the intense development of experimental and theoretical works in the field of photonics (luminescence, lasers, photochemistry, photobiology). The physical foundations of the theory of nonradiative transitions have by and large been set out [16, 19, 20]. In subsequent years, the main efforts of theorists were concentrated on the search for methods of approximate calculations of matrix elements of nonradiative transitions. A number of thorough reviews and monographs devoted to the theory of nonradiative transitions in organic molecules appeared [16, 17, 19, 20]. However, to quantitatively calculate rate constants of nonradiative transitions in complex organic molecules, one had to introduce many not always substantiated approximations. As early as 1960, Hutchison and Mangum [21] revealed that the deuteration of aromatic molecules affects the decay time of their phosphorescence. Robinson and Frosch [22] explained this observation by a change in the overlap of vibrational wave functions (the Franck–Condon factor). This influence indicates that high-frequency СН groups, which contribute little to the formation of the phosphorescence vibronic spectrum of these molecules, actively participate in the nonradiative deactivation of the T1-state. In 1971, we proposed an inductive resonance theory of nonradiative transitions, in which the nonradiative transition was considered as a result of the inductive interaction between the electric dipole of the electronic transition and purely vibrational transitions of the vibrational absorption spectra which are overlapped in the fundamental or overtone (combination frequencies) range of the spectrum with the radiation spectrum of the electronic transition. Initially, we applied this approach to the deactivation of tricharged lanthanide ions [23]; then, it was extended to ions of transition metals and complex organic molecules [10, 24–30]. Under this approach, the rate constant of the nonradiative transition between electronic levels is proportional to the rate constant of the corresponding radiative transition (if the nature of the transition between levels under comparison is the same, e.g., there are electric dipole transitions) and the Förster overlap integral of the corresponding normalized radiation spectrum with vibrational absorption spectra. This approach makes it possible to calculate the probabilities of nonradiative transitions by the Förster for-
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Table 1. Rate constants of radiative (kr) and nonradiative (knr) transitions from sublevels of triplet states of 1-halogensubstituted derivatives of naphthalene in a 1,2,4,5tetramethylbenzene crystal at 1.4 K in accordance with data from [37] k, s–1
1FN
1ClN
1BrN
k rx
0.056
1.3
k ry
0.013
0.46
8.3
k rz
0.0035
0.6
0.3
x k nr
0.86
6.16
y k nr
1.17
4.4
65.5
z k nr
0.21
0.21
3.6
23
132
1FN denotes 1-fluoronaphthalene, 1ClN is 1-chloronaphthalene, and 1BrN is 1-bromonaphthalene. We introduced corrections using more exact data on absolute fluorescence and phosphorescence quantum yields of 1-halogen-substituted naphthalene derivatives [1, 2] instead of the data from our earlier work [38], which were used by the authors in their calculations of the values of kr and knr.
mula, in which the overlap of the observed vibronic radiation spectrum with the measured vibrational absorption spectrum of groups of atoms that receive this energy and that are not involved in the formation of the vibronic spectrum. The inductive resonance theory of nonradiative transitions received recognition and was experimentally confirmed in works of a series of research groups engaged in studies of luminescent and lasing properties of glasses, crystals, and organic lanthanide complexes (see review [30], as well as [31–35]). It was also briefly described in monographs [19, 20]. Calculation of rate constants of nonradiative transitions by the Förster formula for electronic–vibrational energy transfer yielded quantitative agreement with experiment for lanthanide ions in solutions, glasses, and a number of crystals, as well as for ions of transition metals in solid and liquid solutions, including transitions with a strong vibronic coupling in Mn2+ ions [10, 26, 27, 36]. In 1973, we extended our approach to nonradiative transitions in complex organic molecules in solutions [24]. In 1976, Bodunov [25] proposed to calculate the Franck–Condon factor in the expression for the probability of nonradiative transitions in organic molecules in terms of an approximation in which vibrations involved in the nonradiative transition are separated into two types. Vibrations of the first type cause a nonradiative transition in a complex organic molecule and are called “promoting–accepting vibrations.” For energy gaps between electronic levels that correspond to energies exceeding 4000–5000 cm–1, vibrations of this type are vibrations of O–H, C–H, N–H, O–D, C–D, and N–D groups. Vibrations of this type pos-
sess a high anharmonicity and manifest themselves in the short-wavelength range of the IR vibrational absorption spectrum as overtone and combination frequencies, ensuring the overlap of the radiation spectrum corresponding to the nonradiative transition under consideration with the vibrational absorption spectrum of the molecule. These vibrations cause (provoke, promote) the nonradiative transition in a molecule and accept a part of the exchanging energy of the electronic transition. As promoting–accepting vibrations, not the only above-listed vibrations with the participation of hydrogen or deuterium can act, but also (when the energy gap between electronic levels is small) other groups of vibrations that are active in the IR absorption spectrum. Vibrations of the second type in the molecule are accepting vibrations; for the most part, they are totally symmetric vibrations, which experience a shift in the equilibrium position upon the electronic transition under consideration, as well as nontotally symmetric vibrations, which change their frequency upon the considered electronic transition. These vibrations actively manifest themselves in the absorption and radiation spectra of this electronic transition in the molecule. The possibility of this separation of vibrations for organic molecules makes it possible to replace the calculation of the Franck– Condon factor in the matrix element of the nonradiative transition by the calculation of the overlap integral between the luminescence spectrum of the molecule and the absorption spectrum of vibrations that are resonant with the radiation. The dependence of the probability of nonradiative transitions on the rate constant of the corresponding radiative transition is confirmed by an approximate proportionality between the radiative and nonradiative rate constants of transitions from some magnetic sublevels of the triplet state of aromatic compounds, which was noted in a series of works. Table 1 presents data that were reported by Azumi and Saigusa [37] on the probabilities of radiative (kr) and nonradiative (knr) transitions from sublevels of triplet states of 1-halogen-substituted derivatives of naphthalene molecules. The directly proportional dependence of knr on quantity k r × I fl (ν)ε vib (ν)ν −4d ν that is predicted by the inductive resonance theory of nonradiative transitions makes it possible to describe experimentally observed regular features of the behavior of knr in organic molecules. As was shown in [24], calculation of this integral makes it possible to quantitatively estimate the difference in the excitation energy distributions between СС- and СН-vibrations in aromatic molecules and molecules of dyes. It also explains the difference in knr for the same values of ΔЕel in dyes and in aromatic molecules, which is caused by this distinction. Since the rate constant of the nonradiative transition is proportional to the overlap integral, it follows from this that molecules vibronic transitions in which
∫
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Table 2. Quantum yields of fluorescence (qfl), transition to the triplet state (qT), and internal conversion (qIC1) in aromatic hydrocarbons E(S1),
E(T1),
cm–1
cm–1
Naphthalene Naphthalene
31750 31750
21250 21250
0.29 0.21
0.71 0.71
Naphthalene
31750
21250
0.38
–
п-Terphenyl
29900
21800
0.11
Phenanthrene
28900
21700
Chrysene
27700
Pyrene-h10
qfl + qT
qIC1
Matrix
Т, K
Ref.
1.0 0.92
0.0 0.08
ethanol + ether C2H5OH
77 293
1 42
–
–
C2H5OH
77
43
0.93
1.04
0.0
n-С6Н14
293
44
0.13
0.80
0.93
0.07
C2H5OH
293
42
20000
0.17
0.82
0.99
0.01
C2H5OH
293
42
26830
16970
0.72
0.27
0.99
0.01
C2H5OH
293
42
Pyrene-h10
26830
16970
0.78
1.0
0.0
PMM
77
39
Pyrene-d10
26900
17000
1.0
0.0
PMM
77
39
1:2-Benzanthracene-h12
26000
16500
Anthracene
27000
Anthracene 9,10-Diphenylanthracene Naphthacene
Molecule
qfl
0.79
qT (qph)
0.22 (0.0024) 0.21 (0.01)
0.18
0.79
0.97
0.03
n-С6Н14
293
44
14900
0.30
0.70
1.00
0.0
C2H5OH
293
42, 45
26580
14920
1.00 0.93
0.0 0.07
293
46
13500
0.71 0.12
n-С6Н14
24 400
0.29 0.81
Liquid paraffin
293
45
20 950
10200
0.29
0.63
0.92
0.08
n-С6Н14
293
46
Naphthacene
21100
10300
0.10
0.62
0.72
0.28
C6H6
293
47
Naphthacene
21000
10300
0.16
0.66
0.82
0.18
C2H5OH
293
48
Naphthacene
21100
10300
0.16
0.63
0.79
0.21
C6H6
293
49
Rubrene
18500
9300
1.0
0.01
1.0
0.0
C6H12
293
47
Penthacene
17000
7700
n-С6Н14
293
46
Penthacene
16592
7700
2
50
Penthacene
16592
7700
1.9
51
Penthacene Hexacene
17088 14500
7700 6500
1.7 293
52 46
0.09
0.16
0.25
0.75
0.66
0.03
0.69
0.31
0.70
0.03
0.73
0.27
0.26 0.01
0.01 0.045
0.27 0.055
0.73 0.95
Crystalline naphthalene Crystalline naphthalene n-Tetradecane n-С6Н14
All experiments on determining qT and qfl were done either in glassy solutions at low temperatures or in deoxygenated liquid solutions at room temperature. The fluorescence quantum yield qfl was determined by conventional methods. Main methods of determination of qT were triplet–triplet energy transfer, pulsed or laser photolysis, or sensitized triplet–triplet annihilation.
have radiation spectra that decay slower to low frequencies have a high relative probability of the nonradiative transition. The validity of this conclusion was demonstrated upon comparison of the quenching efficiency of T1-states in glassy solutions of pyrene and acriflavine molecules at 77 K, which have roughly the same heights of Т1 levels, but the phosphorescence spectrum of acriflavine decays much more steeply to smaller frequencies than the corresponding spectrum of pyrene. Correspondingly, the ratio of the phosphorescence radiation rate constant (kph) to the rate constant of the corresponding nonradiative transition (kISC2) at 77 K changes from 0.46 for acriflavine (E(T1) = 17100 cm–1) (see Chapter 8 in [10]) to 0.01 OPTICS AND SPECTROSCOPY
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for pyrene-h10 and 0.07 for pyrene-d10 (E(T1) = 17000 cm–1) [39]. In order to quantitatively calculate knr of molecules in terms of inductive resonance theory, as well as in terms of any other theory of nonradiative transitions, it is necessary to know where the given electronic (vibronic) transition is located in the molecule and how it is extended to the region in which groups of atoms are arranged that interact with this transition and that provoke the nonradiative transition. It has been shown in [40, 41] that the deuteration of NHand ОH-groups affects kISC2 of the Т1-state in molecules of naphthylamines and naphthols more considerably than the deuteration of СН-groups of rings. It
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was found that the difference between the contributions of these groups to the deactivation is caused by different degrees of participation of these groups in the π-conjugation and by the localization of the electronic transition near these substituent groups. It is also known that the participation in the nonradiative transition of СН-groups of aromatic rings depends on their positions in the rings (see Table 8.11 on p. 244 in [10]). It is rather difficult to take into account these factors in calculations of rate constants of nonradiative transitions. There is another factor that affects the nonradiative transition rate constant in an organic molecule, namely, the mutual orientation of the dipole moment that corresponds to the radiative vibronic transition and the transition moment that corresponds to the promoting–accepting vibrational transition that interacts with it. At the same energy gap between singlet levels, values of knr for molecules from different classes differ from each other and it is hard to expect that there is for them unified lower limit ΔЕel of the fulfillment of the rule qfl + qT = 1. The limit of the fulfillment of this rule depends also on the variation of the probability of the intersystem crossing transition kISC1, which depends on gap ΔЕST to the nearest triplet level, on the nature of the transition, and on whether the molecule contains a heavy atom. Therefore, in order to determine the applicability limit of this rule and to compare observed differences between values of kIC1 for compounds from different classes with predictions of the inductive resonance theory of nonradiative transitions [10, 23–30], we gathered experimental data on fluorescence quantum yields and on yields of the transition to the triplet state for different classes of organic compounds. We begin our consideration with aromatic hydrocarbons, for which the amount of experimental data on fluorescence quantum yields and triplet-state formation is the greatest. Then we consider carbonyl- and amine-substituted derivatives of aromatic hydrocarbons; dyes; porphyrin-substituted derivatives; fullerenes; and, finally, benzene and its methyl- and nitrile-substituted derivatives. AROMATIC HYDROCARBONS Table 2 contains data on quantum yields of photoprocesses of interest in solutions of naphthalene and more complex aromatic hydrocarbons. The table also presents data on positions of the lowest excited singlet (S1) and triplet (T1) levels, matrices, and temperatures of experiments. It is seen from this table that data on the sum of quantum yields that were obtained for one and the same compound by different authors under the same measurement conditions can differ almost by 10% (e.g., for naphthacene). Therefore, the appearance of the internal conversion process can be reliably fixed only for those compounds, for which qfl + qT ≤
0.9. Comparison of data on the quantum yields of penthacene measured under different experimental conditions (Table 2) convincingly proves that the choice of these conditions has an influence on the value of qT of this compound and, as a consequence, on the observed probability of internal conversion. All this makes it possible to determine only some threshold value of the height of the S1-level for the fulfillment of the rule qfl + qT = 1 for aromatic hydrocarbons. When putting forward this rule [11], we dealt with molecules of aromatic hydrocarbons the heights of S1levels of which were between 32000 and 24000 cm–1. In 1997, Nijegorodov et al. [46] have suggested that 24000 cm–1 is the lower energy boundary of S1-compounds for which the rule qfl + qT = 1.0, i.e., kfl + kISC1 much greater than kIC1, is fulfilled. However, consideration of data of Table 2 shows that the internal conversion process in aromatic hydrocarbons that exceeds the measurement error appears only for compounds the height of the lowest singlet excited level S1 of which is in the range 21 000 cm–1 or lower (naphthacene, penthacene, hexacene). The dependence of the sum qfl + qT for this compound on the kind of the matrix and the equality of this sum to unity for rubrene (ΔЕel = 18500 cm–1) indicate that it is necessary to simultaneously take into account the variation in values of the intersystem crossing rate constant (kISC1) in these systems. It is seen from the spectra of naphthacene, penthacene, and hexacene presented by Nijegorodov et al. in [46] that the width of the fluorescence spectra and the intensity decay of the spectra in the frequency scale are roughly the same; therefore, one should expect that, in the series of these compounds, the rate constant of the internal conversion between the S1- and S0-levels would systematically increase. Attention should be paid to the fact that, at the same height of the triplet T1-level of molecules of the aromatic hydrocarbon, an efficient process of its nonradiative deactivation (qISC2) is observed: naphthalene, pyrene, phenanthrene, chrysene, and 1:2-benzanthracene. In this case, one can compare the rate constants of radiative and nonradiative transitions taken from the literature for different molecules that have approximately the same energy gap between the S1 and S0 levels for molecules of one kind and have the same energy gap between the T1 and S0 states for molecules of the other kind. For penthacene-h14 in a Shpolskii matrix at 1.7 K, the ratio of the rate constant of the internal conversion that proceeds from the S1 level lying at 17100 cm–1 to the rate constant of the corresponding radiative S1 → S0 transition (i.e., the ratio of internal conversion quantum yield qIC1 to the fluorescence quantum yield) is approximately equal to 3 at a value of the rate constant of the radiative transition equal to 1 × 107 s–1 and the rate constant of the internal conversion between the same levels equal to 3 × 107 s–1. At the
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Table 3. Quantum yields of fluorescence (qfl), transition to the triplet state (qT), phosphorescence (qph), and internal conversion (qIC1) in aromatic ketones and amines E(S1),
E(T1),
cm–1
cm–1
Benzaldehyde
26750
Benzophenone
qfl
qT
qph
qfl + qT
qIC1
Matrix
24950
0.00
1.00
0.49
1.00
0.0
ethanol + ether
77
1
26000
24250
0.00
1.00
0.74
1.00
0.0
ethanol + ether
77
1
Benzophenone
26000
24250
0.00
–
0.88
–
–
ethanol
77
43
Acetophenone
27500
25750
0.00
1.00
0.62
1.00
0.0
ethanol + ether
77
1
m-Iodo-benzaldehyde
26250
24750
0.00
1.00
0.64
1.00
0.0
ethanol + ether
77
1
Methyl-2-naphthyl ketone
26800
20800
0.00
1.00
0.05
1.00
0.0
toluene
293
7
2-Methoxy-naphthalene
30775
20 600
0.47
0.50
–
0.97
0.03
toluene
293
7
Triphenyamine
29 000
24500
0.04
1.05
0.8
1.09
0.0
toluene
293
8
Carbazole
29300
24600
0.36
0.55
0.07
0.91
0.09
toluene
293
7
Molecule
Т, K Ref.
All data presented in Table 3 were obtained either by the method of triplet–triplet energy transfer or in glassy solutions at 77 K in an ethanol + ether matrix (2 : 1 volume mixture of ethanol with diethyl ether) or in deoxygenated liquid toluene at 293 K.
same time, the rate constant of the nonradiative transition between the lowest triplet T1-level of pyrene-h10, which lies at the same height (16970 cm–1), and the ground S0 singlet level is approximately equal to 1.7 s–1 at a value of the radiative rate constant of 0.045 s–1; the ratio is knr/kr = 37 (in accordance with the data obtained by Lim and coworkers in a solution in EPA at 77 K [53]). The value of knr varies approximately in a parallel to the corresponding kr. The tenfold difference between the values of knr/kr for the fluorescence of penthacene and phosphorescence of pyrene is explainable in terms of consideration of differences in the values of the overlap integrals between their vibronic and vibrational absorption spectra. It is related to a slower decay of the intensity of the phosphorescence spectrum of pyrene toward low frequencies compared to the fluorescence spectrum of penthacene. It was noted previously that Stokes losses for the majority of investigated aromatic compounds (i.e., the shift of the center of gravity of the phosphorescence spectrum with respect to the position of the corresponding electronic level) are noticeably greater than Stokes losses in fluorescence spectra of the same compounds [5]. Therefore, for the majority of aromatic hydrocarbons, the probability of the internal conversion of energy from their S1-state to the S0-state becomes comparable with the probability of radiation and transition to the triplet state only at Е(S1) ≤ 21000 cm–1. It follows from this that the rule qfl + qT = 1 for these hydrocarbon molecules is not fulfilled. OPTICS AND SPECTROSCOPY
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DERIVATIVES OF AROMATIC HYDROCARBONS Furthermore, we will try to determine (based on experimental data on photophysical properties available from the literature) where this boundary passes for molecules of other types. Table 3 summarizes data on photoprocesses in some derivatives of aromatic hydrocarbons. The energies of S1-states of the presented compounds lie between 26 000 and 31 000 cm–1, and the yield of the internal conversion process (qIC1) in them is not high. We failed to determine the applicability limit of the rule for simple derivatives of aromatic compounds because data on qfl and qT for derivatives of naphthacene and penthacene are unavailable. DYES The next class of compounds for which it was of interest to verify the applicability limit of the rule qfl + qT = 1.0 consisted of fluorescent dyes. Table 4 presents data on quantum yields of fluorescence and formation of the triplet state of xanthene, acriflavine, and oxazine dyes. Consideration of these classes of dyes is of interest, since they are widely used in fluorescence, chemical, and biological analysis, as well as in laser technics. For trypaflavine (E(S1) = 21740 cm–1) [54], fluorescein dianion (E(S1) = 20 400 cm–1) [55], and rhodamine 6G cation (E(S1) = 19 000 cm–1) [55], the values of the sum qfl + qT are close to 1.0. The deviation of this sum from 1.0 is within the range of measurement error. These dyes contain oxygen or nitrogen atoms in their structure, which are capable of exchanging protons bonded with them for deuterium with OD-groups of the solvent. This explains the fact
648
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Table 4. Quantum yields of fluorescence (qfl), transition to the triplet state (qT), and internal conversion (qIC1) in solutions of acridine, xanthene, and oxazine dyes E(S1), cm—1 E(T1), cm–1
Molecule
qfl
qT
qfl+qT
qIC1
Matrix
0.0
C2H5OH
90
54
Т, K
Ref.
Trypaflavine
21740
17200
0.61
0.45
1.05
Fluorescein2–
20 400
19 000
0.92
≤0.08
≥0.92
≤0.08
H 2O
293
55
Fluorescein2–
20 420
19 000
0.98
≤0.02
≥0.98
≤0.02
D2O
293
55
Fluorescein2–
0.95
≤0.05
H 2O
293
57
20 400
19 000
0.92
Rhodamine
6G+
19 000
17720
0.90
≤0.10
≥0.90
≤0.10
H 2O
293
55
Rhodamine
6G+
19 030
17730
0.98
≤0.02
≥0.98
≤0.02
D2O
293
55
Rhodamine 6G
+
18880
17770
0.95
≤0.05
≥0.95
≤0.05
C2H5OH
293
55
Rhodamine 6G Eosin Y
+
18880
17770
0.98
≤0.02
≥0.98
≤0.02
C2H5OD
293
55
0.2
0.8
1.00
0.00
H 2O
293
57
293
57
0.032
19230
14600
Eosin Y
19157
14600
0.56
0.44
1.00
0.00
CH3OH
Oxazine 9
16100
~13000
0.56
