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Effect of solvent polarity on non-radiative processes in xanthene dyes: the acid form of rhodamine B in nitrile solvents
J. Photochem.
Photobiol. A: Chem., 64 (1992) 307-314
307
Effect of solvent polarity on non-radiative processes in xanthene dyes: the acid form of rhodamine B in nitrile solvents Kelly G. Case$, Department
Yavuz Onganer and Edward L. Quitevistt
of Chemisty
and Biochemistry,
Texas T&h University, Lubbock
lX
79409 (USA)
(Received August 5, 1991; accepted November 1, 1991)
The fluorescence lifetimes of the acid form of rhodamine l3 in nitrile solvents were measured as a function of temperature. Non-radiative rate constants were calculated from the fluorescence lifetimes and quantum yields. Arrhenius plots of the non-radiative rate constants were linear. The value of the non-radiative activation energy was, within experimental error, the same for all the solvents studied and equal to 3.4f0.3 kcal mol-‘. However, at constant temperature, the natural logarithm of the non-radiative rate constant increased linearly with the solvent polarity parameter I&(30). The dependence of the non-radiative rate on solvent polarity can be explained by a model involving a planar-pyramidal change at the xanthene-amine bond. On the basis of this model, a comparison of the non-radiative rate of the dye in alcohols and nitriles shows that the dependence on solvent polarity is due to specific solute-solvent interactions at the amino and carboxyphenyl groups.
1. Introduction
Although the photophysical properties of rhodamine B and related xanthene dyes in solution have been extensively studied, the role of the molecular structure and
solvent in &-So internal conversion, the main non-radiative process in these dyes [l, 21, is still controversial [3-91. Internal conversion in rhodamine l3 is associated with the rigidity at the xanthene-amine bond (Fig. 1). This rigidity determines the temperature dependence
of the fluorescence
properties
of these dyes. For example,
the fluorescence
quantum yield is unity and independent of temperature for rhodamine 101, where the diethylamino groups are rigidly held to the xanthene ring by methylene bridges, but decreases with temperature for rhodamine B, where the groups are not rigidly held [IO-13). Several models have been proposed to explain the effect of solvent and molecular structure on internal conversion in xanthene dyes. The first was the intramolecular rotation model [l, 23. In this model, rotation about the xanthene-amine bond causes internal conversion. The rate of this rotation and, hence, the rate of internal conversion decrease as the solvent viscosity and the size of the amino groups are increased [14, 151. However, this behavior is not observed for most rhodamine dyes [4-9, 16191. ‘Present address: Shock Dynamics Laboratory, Department University, Pullman, WA 99164, USA. “Author to whom correspondence should be addressed.
lOlO-f5030/92/$5.00
of Physics, Washington State
Q 1992 - Elsevier Sequoia. All rights reserved
w
LJ
0)
(b) ?
ff
N-Et
EVN
Lactone
Fig. 1. Resonance structures a-c of the acid form of rhodamine B (RBH+) of lactone.
and the structure
For example, the non-radiative rate constant k,,for rhodamine B has the same value in ethylene glycol as in ethanol, even though ethylene glycol has a higher viscosity than ethanol [4], and the fluorescence lifetimes and quantum yjelds are greater for dyes with monoethylamino groups than for dyes with diethylamino groups [8]. In the twisted-intramolecular-charge-transfer (TICT) model of Rettig and coworkers 120-221, internal conversion occurs via the TICT state. This state is characterized by electron transfer from the amino groups to the xanthene ring and by rotation about the xanthene-amine bond. The formation of the TICT state depends on solvent polarity and on the donor-acceptor properties of the amino group and the xanthene ring. Because intramolecular rotation is also involved, the rigidity of the molecule and solvent viscosity influence the formation of the TICT state. To explain the photophysical properties of rhodamine dyes, Lopez Arbeloa and coworkers [3-91 proposed the umbrella-like-motion (ULM) model. In this model, a structural change in the amino groups (Fig. 1) from a planar structure (resonance structures a and c, quinoid structures) to a pyramidal structure (resonance structure b, a carbocation structure) results in internal conversion in the excited state, This umbrella-like motion changes the xanthene-amine bond from a double bond to a single bond and moves the positive charge from the amino group to the xanthene group. The transformation disrupts the T-electron system at the xanthene-amine bond and causes the amino group to rotate. In resonance structure b, rotation of the amino group does not disrupt the v-electron system, and hence does not lead to internal conversion. In systems where resonance structures a and c have higher statistical weights than resonance structure b, internal conversion is inhibited because of the high electron density in the xanthene-amine bond. Stabilizing the positive charge at either the g-carbon atom or the amino nitrogen prevents the disruption of the n= electron system at the xanthene-amine bond, and hence decreases the probability for internal conversion. In rhodamine dyes, the PhCOOR group is sterically hindered from being coplanar with the xanthene ring, and is essentially perpendicular to it. In this configuration,
309
the negative field of the COOR group can stabilize the positive charge at the g-carbon atom. Increasing this xanthene-COOR interaction increases the statistical weight of the resonance structure b, whereas increasing the molecular interactions at the amino nitrogen atom increases the statistical weight of resonance structures a and c. Solvent coupling at the PhCOOR group reduces the xanthene-COOR interaction and thus destabilizes the positive charge at the g-carbon atom, whereas solvent coupling at the amino group stabilizes the positive charge on the amino nitrogen atom. Therefore, in the ULM model, the solvent influences internal conversion in rhodamine dyes through specific solute-solvent interactions at the amino and PhCOOR groups. Recently, we have introduced a two-state model [17, 181 that quantitatively relates k,, to the solvent polarity parameter E,(30) [23]. We used this model to explain the linear increase in Ink,,, with &(30) and the linear increase in the non-radiative activation energy E, with Em for the acid form of rhodamine B (RBH+) in normal alcohols. In the two-state model, a fluorescent state A*, which can only decay radiatively to the ground singlet state S,,, is in rapid equilibrium with a non-emissive state B*, which can only decay to So via internal conversion. In the original two-state model, A* was the planar state and B* was a twisted state. The non-radiative rate constant for this model is given by km=ki,KA*B*
(1)
where KAaB*is the equilibrium constant between A* and B* and ki, is the rate constant for internal conversion from B*. The temperature dependence of k,, arises from the temperature dependence of KAeB. through the equation KACBh=exp( - AG,-BnllW)
(2)
where AG A*B. is the Gibbs free energy difference between A* and B*. In this model, E, is therefore equal to AGALBL.According to the energy gap law 124-261, ki, can be expressed as ki=a exp(- &IO)
(3)
where IYis a constant and AElo is the &-So energy gap for B*. In the two-state model, A&, and AGAeB. are assumed to be linear functions of E430) AGA.,s = AG,.,.’
+ HE430)
- 30)
(4)
A.&J = AElQO+ y(ET(30) - 30)
(5)
where p and y are constants and AGAeB.’ and AE,,” are the Gibbs free energy difference and the energy gap in a non-polar solvent respectively. The variation in k,, for RBH+ in normal alcohols results from the polarity dependence of AG*T and AElo. Combining eqns. (l)-(5) yields the relation km a exp(- (p/RT+
K)(J?&(~O)
-
30))
exp(
-
AG,.,.“/ZW)
(6)
where K= ay. Therefore, a plot of ln k, vs. &(30) is linear, with a slope equal to -(p/K?+ K), and a plot of E, tm E430) is linear, with a slope equal to @. In this paper, we report new fluorescence data for RBH’ in nitriles. Rhodamine B is a lactone (Fig. 1) in aprotic solvents, such as the nitriles [2, 271. However, the addition of a drop of acid to solutions of the dye in aprotic solvents converts the lactone to RBH+. Although E, did not vary with solvent polarity, k,,, at constant temperature increased with E430) for RBH’ in nitriles. The results for RBH+ in
310
nitriles and alcohols the two-state model,
2. Experimental
[17, 181 agree with the ULM model but not with the TICT model.
and a modified
version
of
details
Rhodamine B perchlorate (Kodak, laser grade) showed a single spot on a thin layer chromatography (TLC) plate and was used without further purification. The solvents acetonitrile (C&H,N), valeronitrile (C,H,N), hexanenitrile (C,HHN), heptylwere vacuum distilled and stored in a cyanide (C,H,,N) and octylnitrile (qH1,N) desiccator prior to use. To convert the lactone to the acid, a drop of trifluoroacetic acid (250 ~1 or less) was added to 4 ml samples of nitrile solutions of rhodamine B (approximately 2~ 10e6 M). Relative fluorescence quantum yields from corrected fluorescence spectra at 25 “C were calculated with respect to rhodamine B in acidic ethanol (&=0.49) [28, 291. Fluorescence decay curves were measured with standard time-correlated photon counting techniques using excitation at 577 nm from a cavity-dumped rhodamine-6G dye laser that was synchronously pumped by a mode-locked argon-ion laser. The details of the apparatus have been described previously [17, 18, 301. The fluorescence was collected with a lens at right angles to the excitation and passed through a double monochromator set at 605 nm. A polarizer, set to 54.7” (“magic angle”) with respect to the polarization of the excitation light, was placed between the collection lens and the sample to remove molecular reorientation effects. The samples were contained in a 1 cm cuvette which was maintained to rt 1 “C with a heat pump and temperature controller. The fluorescence decay curves were fitted by single-exponential decays using a convolute-and-compare non-linear least-squares program. The fluorescence lifetimes were obtained from fits to the decay curves which gave reduced chi-squares of less than 1.2. The fluorescence lifetimes were measured at different temperatures for each solvent.
3. Results The photophysical parameters Tf, & and the absorption and emission maxima (&, and h,,) at 25 “C are listed in Table 1. The unacidified dye solutions were colorless, but turned pink after adding trifluoroacetic acid. The absorption and emission maxima at approximately 556 and 583 nm respectively confirm that RBH+ and not the lactone was present in the acidified soIutions. The radiative and non-radiative rate constants k, and k,,, listed in Table 1 were obtained from the fluorescence lifetime rf and the quantum yield & using the equations k,= &f/Tf and km,= (l/Tf) -%. At constant temperature, k,, increased with solvent polarity, whereas k, was independent of solvent polarity. Since k, is independent of temperature for RBH+ [13], the value of km at each temperature was obtained by using the value of Tf at these temperatures and the values of k, listed in Table 1. Arrhenius plots of k,, over the range of temperatures studied were linear for each solvent (Fig. 2). The non-radiative activation energies E, obtained from these plots are listed in Table 1. Within experimental error, the value of E, was the same for all the nitriles. The average of the values of E, listed in Table 1 is 3.4f0.3 kcal mol-‘.
311 TABLE
1
Photophysical properties of RBHC in nitrile solvents at 25 “C Solvent
&b=
&”
k: (10s s-l)
k,: (108 s-r)
E.b (kcal mol-‘)
&(30) (kcal mol-r)
& GH3N
556 583
l-62&0.02
0.21
1.3
4.9
3.8
46.0
CJH9N
557 584
2.15 f 0.01
0.26
1.2
3.4
3.0
43.7
G&IN
557 584
2.17 f 0.05
0.28
1.3
3.3
3.3
42.0
CsHrsN
556 583
2.45 f0.01
0.36
1.5
2.6
3.7
41.1
W&N
556 582
2.51 f0.05
0.32
1.3
2.7
3.4
40.3
Wncertainty, f 1 nm. bUncertainty, 10%. O ‘ btained from refs. 23 and 31.
Fig. 2. Arrhenius plots of the non-radiative rate constant k,, for RBH+ in QH,N (A); CsHgN (X); C&LnN (Cl); CaH,sN (0) and G,Hr,N (a). The lines are linear least-squares fits to the data with a correlation of better than 0.99. Activation energies are listed in Table 1. 4. Discussion
In the TICT model, the energy of the TICT state mainly determines the nonradiative rate. Increasing the solvent polarity decreases the energy of the TICI’ state [20,21]. Solvent effects are taken into account by a polarity-dependent E,. For example, by assuming that E, is a linear function of &(30), Hicks et al. [31] were able to explain the dependence of the photophysics of the TICT compound dimethylaminobenzonitrile on solvent polarity. If internal conversion for IZEIH+ involves the formation of the TICT state, ink, should increase and E, should decrease with Er(30). These trends were not observed for RBH+ in nitriles. Although In k,, increased linearly with
312 of &(30) (Table 1). The TICT ET(30) (Fig. 3), E, was constant and independent model also predicts that, because nitriles are less polar than alcohols, the values of E, in nitriles should be greater than in alcohols and, correspondingly, the values of k,,, in nitriles should be Iess than in alcohols. However, these predictions do not agree with the data. The measured values of E, are lower in nitriles (approximately 3.4 kcal mol-‘) than in alcohols (5.2 kcal mol-’ or less) 117, 183, and the measured values of k,, in nitriles (4.9X10’ s-l or less) are greater than in alcohols (3.0X 10s s-l or less) [17, 181. The photophysical properties of RBH+ in nitriles and alcohols can be explained by the ULM model. To help us quantitatively interpret the data, we first introduce a mechanism that is similar to the two-state model [17, 181. This new mechanism deviates from the two-state model by allowing B* to be in rapid equilibrium with not only A* but also with the excited pyramidal state P* A *-
‘It-l
1k. i
kz = k-z
kl
;
SO
P*
ki, So
J
This new mechanism is consistent with the ULM model, because &-So internal conversion occurs only in the intermediate state B* and not in the pyramidal state P*. The same expression for k,,, as given by eqn. (I), is obtained from this mechanism by applying the steady state approximation to B* and P* and assuming kicek-1, with KA.B.=kl/ k_l. In terms of the ULM model, the difference in the values of E, and k,, for nitriles vs. alcohols reflects a difference in the strength of attraction between the soivent dipoles and the positively charged amino group. Because nitriles are less polar than alcohols, the positively charged amino group is less stable in nitriles than in alcohols. The. statistical weights of resonance structures a and c and the electron density in the xanthene-amine bond are less in nitriles than in alcohols. The energy needed to change the xanthene-amine bond is less in nitriles than in alcohols or, alternatively, AGAW . in nitriles is less than in alcohols_
40
42
44 Ed
46
40
kcallmol
Fig. 3. Plot of Ink,,, for RBH+ VS. polarity of nitriles at 25 “C. Slope, 0.108; intercept, 15.0; correlation, 0.96.
313 For RBH+, E, has a weak, but noticeable, dependence on solvent polarity in alcohols [17, 181, but is essentially independent of solvent polarity in nitriles. We believe that this difference is caused by hydrogen-bonding effects. Alcohols can form hydrogen bonds with the PhCOOH group. The hydrogen bond weakens the xanthene-COOH interaction and, consequently, decreases the statistical weight of resonance structure b relative to that of resonance structures a and c. The shift in the relative weights of the resonance structures leads to a higher electron density in the xanthene-amine bond. Thus, a hydrogen bond between an alcohol and the COOH group increases the barrier for the planar-pyramidal change or, alternatively, increases the value of AGAoB.. Since the strength of the hydrogen bond parallels the solvent polarity in the alcohols, E, increases with solvent polarity in the alcohols. Although dipole-dipole interactions can occur between nitriles and the COOH group, they are not as strong as the hydrogen bonds formed between alcohols and the COOH group. Hence, E, should not show much of a dependence on solvent polarity, and p-0 in eqn. (4) for RBHf in nitriles. in nitriles must therefore be The dependence of k, on the solvent for RBH+ mainly due to the dependence of ki, on the solvent polarity. A plot of In k,, vs. &(30) is linear with a slope of 0.108 mol kcal-‘. If eqn. (6) describes k,, the value of this slope must be equal to -@/RT+ IC). This implies that K is equal to -0.108 mol kcal-‘, since p=O. In contrast, K= - 0.51 mol kcal-’ and p = 0.23 for RBH+ in alcohols [17, 181. Thus, for nitriles and alcohols, AE10 decreases with solvent polarity. A plausible explanation for this result, based on the ULM model, is that B* has more planar than pyramidal character. Solute-solvent interactions that stabilize the positive charge on the amino nitrogen atom will also tend to increase delocalization in the r-electron system and shrink the energy gap for B *. It should also be noted that the absolute value of K is about a factor of two greater in alcohols than in nitriles. This is consistent with the hypothesis that B* has more planar than pyramidal character. Because resonance structures a and c contribute to the electronic structure of B*, the amino nitrogen atoms in B* must have some positive charge. Therefore, if the magnitude of K is a measure of the strength of solute-solvent coupling for B*, the absolute value of K should be larger in the more polar solvent.
5. Conclusions We have accounted for the dependence of k,, on solvent polarity for RBH+ using the ULM model and a modified version of the two-state model. By comparing the non-radiative rate of RBH+ in nitriles with that in alcohols, we have found that the dependence on solvent polarity is due to specific solvent-solute interactions at the amino group and the PhCOOH group. These interactions, according to the ULM model, affect the non-radiative rate by modulating the relative statistical weights of the quinoid and carbocation resonance structures. We hypothesize that internal conversion occurs from an intermediate state that has more planar than pyramidal character. This hypothesis explains the dependence of the energy gap at the intermediate state on solvent polarity.
Acknowledgment This research was supported Institutes of Health.
by the Robert
A. Welch
Foundation
and the National
314
References H. Drexhage, Laser Focus, 9 (1973) 35. K. H. Drexhage, in F. P. Schzer (ed.), .Dye Laseq Springer, Berlin, 1977. I. Lopez Arbeloa and K. K. Rohatgi-Mukherjee, Chem. Phys. Lett., 128 (1986) 474. I. tipez Arbeloa and K K. Rohatgi-Mukherjee, Chem. Phys. Lett., 129 (1986) 607. F. Lopez Arbeloa, I. Urrecha Aguirresacona and I. Lopez Arbeloa, Chem. Phys., I30 (1989) 371. F. Lopez Arbeloa, A. Costela and I. Mpez Arbeloa, 1. Photochem. Photobiol. A: Chem., 55 (1990) 97. F. L6pez Arbeloa, T. L6pez Arbeloa, E. Gil Lage, I. Mpez Arbeloa and F. C. De Schryver, J. Photochem. PhotobioL A: Chem., 56 (1991) 313. T. Lopez Arbeloa, M. J. Est&ez, F. Mpez Arbeloa, I. Urrebra Aguirresacona and I. Lopez Arbeloa, .I. Lumin., 48/49 (1991) 400. F. upez Arbeloa, T. Liipez Arbeloa, M. J. Tapia Est&ez and I. tipez Arbeloa, J. Phys. Chem., 95 (1991) 2203. B. G. Huth, G. I. Farmer and M. R. Kagan, J. A&. Phys., 40 (1969) 5145. T. Karsten and K Kobs, A Phys. Chem., 84 (1980) 1871. R. F. Kubin and A. N. Fletcher, J. Cumin., 27 (1982) 455. L. B.-A. Johansson and A. Niemi, .I. Phys. Chem., 91 (1987) 3020. C. J. Tredwell and A. D. Osborne, J Chem. Sot., Furuday Trans. 2, 76 (1980) 1627. A. D. Osborne, J. Chem. Sot., Faraday Trans. 2, 76 (1980) 1638. M. J. Snare, F. E. Treloar, K P. Ghiggino and P. J. Thistlewaite, I. Photochem., 28 (1982) 335. F. G. Casey and E. L. Quitevis, J Phys. Chem., 92 (1988) 6590. K. G. Casey and E. L. Quitevis, Proc. SPIE-hat. Sot. Opt. Eng., 910 (1988) 144. T.-L. Chang and W. L. Borst, J. Chem. Phys., 93 (1990) 4724. W. Rettig, Angew. Chem., Int. Ed. En& 25 (1986) 971. M. Vogel, W. Rettig, R. Sens and K. H. Drexhage, Chem. Phys. Lett., 147 (1988) 452. M. Vogel, W. Rettig, R. Sens and K. H. Drexhage, Chem. Phys. Lett., 147 (1988) 461. C. Reichardt, Solvents and SoZvent Effects in Organic Chemistry, VCH, New York, 1988. W. Siebrand, .I. Chem. Phys., 46 (1967) 440. W. Siebrand, J. Chem. Phys., 47 (1967) 2411. R. Englman and J. Jortner, Mol. Phys., 18 (1970) 145. F. Barigelletti, Chem. Phys. Lett., 140 (1987) 603. J. Ferguson and A. W.-H. Mau, Aust. J. Chem, 26 (1973) 1617. P. J. Sadowski and G. R. Fleming, Chem. Phys. Lett., 57 (1978) 526. J. Lee, R. D. Griffin and G. W. Robinson, J. Chem. Phys., 82 (1985) 4920. J. Hicks, M. Vandersali, Z. Babarogic and K. B. Eisenthal, Chem. Phys. Left., 216 (1985) 18.
1 K.
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29 30
31
Photobiol. A: Chem., 64 (1992) 307-314
307
Effect of solvent polarity on non-radiative processes in xanthene dyes: the acid form of rhodamine B in nitrile solvents Kelly G. Case$, Department
Yavuz Onganer and Edward L. Quitevistt
of Chemisty
and Biochemistry,
Texas T&h University, Lubbock
lX
79409 (USA)
(Received August 5, 1991; accepted November 1, 1991)
The fluorescence lifetimes of the acid form of rhodamine l3 in nitrile solvents were measured as a function of temperature. Non-radiative rate constants were calculated from the fluorescence lifetimes and quantum yields. Arrhenius plots of the non-radiative rate constants were linear. The value of the non-radiative activation energy was, within experimental error, the same for all the solvents studied and equal to 3.4f0.3 kcal mol-‘. However, at constant temperature, the natural logarithm of the non-radiative rate constant increased linearly with the solvent polarity parameter I&(30). The dependence of the non-radiative rate on solvent polarity can be explained by a model involving a planar-pyramidal change at the xanthene-amine bond. On the basis of this model, a comparison of the non-radiative rate of the dye in alcohols and nitriles shows that the dependence on solvent polarity is due to specific solute-solvent interactions at the amino and carboxyphenyl groups.
1. Introduction
Although the photophysical properties of rhodamine B and related xanthene dyes in solution have been extensively studied, the role of the molecular structure and
solvent in &-So internal conversion, the main non-radiative process in these dyes [l, 21, is still controversial [3-91. Internal conversion in rhodamine l3 is associated with the rigidity at the xanthene-amine bond (Fig. 1). This rigidity determines the temperature dependence
of the fluorescence
properties
of these dyes. For example,
the fluorescence
quantum yield is unity and independent of temperature for rhodamine 101, where the diethylamino groups are rigidly held to the xanthene ring by methylene bridges, but decreases with temperature for rhodamine B, where the groups are not rigidly held [IO-13). Several models have been proposed to explain the effect of solvent and molecular structure on internal conversion in xanthene dyes. The first was the intramolecular rotation model [l, 23. In this model, rotation about the xanthene-amine bond causes internal conversion. The rate of this rotation and, hence, the rate of internal conversion decrease as the solvent viscosity and the size of the amino groups are increased [14, 151. However, this behavior is not observed for most rhodamine dyes [4-9, 16191. ‘Present address: Shock Dynamics Laboratory, Department University, Pullman, WA 99164, USA. “Author to whom correspondence should be addressed.
lOlO-f5030/92/$5.00
of Physics, Washington State
Q 1992 - Elsevier Sequoia. All rights reserved
w
LJ
0)
(b) ?
ff
N-Et
EVN
Lactone
Fig. 1. Resonance structures a-c of the acid form of rhodamine B (RBH+) of lactone.
and the structure
For example, the non-radiative rate constant k,,for rhodamine B has the same value in ethylene glycol as in ethanol, even though ethylene glycol has a higher viscosity than ethanol [4], and the fluorescence lifetimes and quantum yjelds are greater for dyes with monoethylamino groups than for dyes with diethylamino groups [8]. In the twisted-intramolecular-charge-transfer (TICT) model of Rettig and coworkers 120-221, internal conversion occurs via the TICT state. This state is characterized by electron transfer from the amino groups to the xanthene ring and by rotation about the xanthene-amine bond. The formation of the TICT state depends on solvent polarity and on the donor-acceptor properties of the amino group and the xanthene ring. Because intramolecular rotation is also involved, the rigidity of the molecule and solvent viscosity influence the formation of the TICT state. To explain the photophysical properties of rhodamine dyes, Lopez Arbeloa and coworkers [3-91 proposed the umbrella-like-motion (ULM) model. In this model, a structural change in the amino groups (Fig. 1) from a planar structure (resonance structures a and c, quinoid structures) to a pyramidal structure (resonance structure b, a carbocation structure) results in internal conversion in the excited state, This umbrella-like motion changes the xanthene-amine bond from a double bond to a single bond and moves the positive charge from the amino group to the xanthene group. The transformation disrupts the T-electron system at the xanthene-amine bond and causes the amino group to rotate. In resonance structure b, rotation of the amino group does not disrupt the v-electron system, and hence does not lead to internal conversion. In systems where resonance structures a and c have higher statistical weights than resonance structure b, internal conversion is inhibited because of the high electron density in the xanthene-amine bond. Stabilizing the positive charge at either the g-carbon atom or the amino nitrogen prevents the disruption of the n= electron system at the xanthene-amine bond, and hence decreases the probability for internal conversion. In rhodamine dyes, the PhCOOR group is sterically hindered from being coplanar with the xanthene ring, and is essentially perpendicular to it. In this configuration,
309
the negative field of the COOR group can stabilize the positive charge at the g-carbon atom. Increasing this xanthene-COOR interaction increases the statistical weight of the resonance structure b, whereas increasing the molecular interactions at the amino nitrogen atom increases the statistical weight of resonance structures a and c. Solvent coupling at the PhCOOR group reduces the xanthene-COOR interaction and thus destabilizes the positive charge at the g-carbon atom, whereas solvent coupling at the amino group stabilizes the positive charge on the amino nitrogen atom. Therefore, in the ULM model, the solvent influences internal conversion in rhodamine dyes through specific solute-solvent interactions at the amino and PhCOOR groups. Recently, we have introduced a two-state model [17, 181 that quantitatively relates k,, to the solvent polarity parameter E,(30) [23]. We used this model to explain the linear increase in Ink,,, with &(30) and the linear increase in the non-radiative activation energy E, with Em for the acid form of rhodamine B (RBH+) in normal alcohols. In the two-state model, a fluorescent state A*, which can only decay radiatively to the ground singlet state S,,, is in rapid equilibrium with a non-emissive state B*, which can only decay to So via internal conversion. In the original two-state model, A* was the planar state and B* was a twisted state. The non-radiative rate constant for this model is given by km=ki,KA*B*
(1)
where KAaB*is the equilibrium constant between A* and B* and ki, is the rate constant for internal conversion from B*. The temperature dependence of k,, arises from the temperature dependence of KAeB. through the equation KACBh=exp( - AG,-BnllW)
(2)
where AG A*B. is the Gibbs free energy difference between A* and B*. In this model, E, is therefore equal to AGALBL.According to the energy gap law 124-261, ki, can be expressed as ki=a exp(- &IO)
(3)
where IYis a constant and AElo is the &-So energy gap for B*. In the two-state model, A&, and AGAeB. are assumed to be linear functions of E430) AGA.,s = AG,.,.’
+ HE430)
- 30)
(4)
A.&J = AElQO+ y(ET(30) - 30)
(5)
where p and y are constants and AGAeB.’ and AE,,” are the Gibbs free energy difference and the energy gap in a non-polar solvent respectively. The variation in k,, for RBH+ in normal alcohols results from the polarity dependence of AG*T and AElo. Combining eqns. (l)-(5) yields the relation km a exp(- (p/RT+
K)(J?&(~O)
-
30))
exp(
-
AG,.,.“/ZW)
(6)
where K= ay. Therefore, a plot of ln k, vs. &(30) is linear, with a slope equal to -(p/K?+ K), and a plot of E, tm E430) is linear, with a slope equal to @. In this paper, we report new fluorescence data for RBH’ in nitriles. Rhodamine B is a lactone (Fig. 1) in aprotic solvents, such as the nitriles [2, 271. However, the addition of a drop of acid to solutions of the dye in aprotic solvents converts the lactone to RBH+. Although E, did not vary with solvent polarity, k,,, at constant temperature increased with E430) for RBH’ in nitriles. The results for RBH+ in
310
nitriles and alcohols the two-state model,
2. Experimental
[17, 181 agree with the ULM model but not with the TICT model.
and a modified
version
of
details
Rhodamine B perchlorate (Kodak, laser grade) showed a single spot on a thin layer chromatography (TLC) plate and was used without further purification. The solvents acetonitrile (C&H,N), valeronitrile (C,H,N), hexanenitrile (C,HHN), heptylwere vacuum distilled and stored in a cyanide (C,H,,N) and octylnitrile (qH1,N) desiccator prior to use. To convert the lactone to the acid, a drop of trifluoroacetic acid (250 ~1 or less) was added to 4 ml samples of nitrile solutions of rhodamine B (approximately 2~ 10e6 M). Relative fluorescence quantum yields from corrected fluorescence spectra at 25 “C were calculated with respect to rhodamine B in acidic ethanol (&=0.49) [28, 291. Fluorescence decay curves were measured with standard time-correlated photon counting techniques using excitation at 577 nm from a cavity-dumped rhodamine-6G dye laser that was synchronously pumped by a mode-locked argon-ion laser. The details of the apparatus have been described previously [17, 18, 301. The fluorescence was collected with a lens at right angles to the excitation and passed through a double monochromator set at 605 nm. A polarizer, set to 54.7” (“magic angle”) with respect to the polarization of the excitation light, was placed between the collection lens and the sample to remove molecular reorientation effects. The samples were contained in a 1 cm cuvette which was maintained to rt 1 “C with a heat pump and temperature controller. The fluorescence decay curves were fitted by single-exponential decays using a convolute-and-compare non-linear least-squares program. The fluorescence lifetimes were obtained from fits to the decay curves which gave reduced chi-squares of less than 1.2. The fluorescence lifetimes were measured at different temperatures for each solvent.
3. Results The photophysical parameters Tf, & and the absorption and emission maxima (&, and h,,) at 25 “C are listed in Table 1. The unacidified dye solutions were colorless, but turned pink after adding trifluoroacetic acid. The absorption and emission maxima at approximately 556 and 583 nm respectively confirm that RBH+ and not the lactone was present in the acidified soIutions. The radiative and non-radiative rate constants k, and k,,, listed in Table 1 were obtained from the fluorescence lifetime rf and the quantum yield & using the equations k,= &f/Tf and km,= (l/Tf) -%. At constant temperature, k,, increased with solvent polarity, whereas k, was independent of solvent polarity. Since k, is independent of temperature for RBH+ [13], the value of km at each temperature was obtained by using the value of Tf at these temperatures and the values of k, listed in Table 1. Arrhenius plots of k,, over the range of temperatures studied were linear for each solvent (Fig. 2). The non-radiative activation energies E, obtained from these plots are listed in Table 1. Within experimental error, the value of E, was the same for all the nitriles. The average of the values of E, listed in Table 1 is 3.4f0.3 kcal mol-‘.
311 TABLE
1
Photophysical properties of RBHC in nitrile solvents at 25 “C Solvent
&b=
&”
k: (10s s-l)
k,: (108 s-r)
E.b (kcal mol-‘)
&(30) (kcal mol-r)
& GH3N
556 583
l-62&0.02
0.21
1.3
4.9
3.8
46.0
CJH9N
557 584
2.15 f 0.01
0.26
1.2
3.4
3.0
43.7
G&IN
557 584
2.17 f 0.05
0.28
1.3
3.3
3.3
42.0
CsHrsN
556 583
2.45 f0.01
0.36
1.5
2.6
3.7
41.1
W&N
556 582
2.51 f0.05
0.32
1.3
2.7
3.4
40.3
Wncertainty, f 1 nm. bUncertainty, 10%. O ‘ btained from refs. 23 and 31.
Fig. 2. Arrhenius plots of the non-radiative rate constant k,, for RBH+ in QH,N (A); CsHgN (X); C&LnN (Cl); CaH,sN (0) and G,Hr,N (a). The lines are linear least-squares fits to the data with a correlation of better than 0.99. Activation energies are listed in Table 1. 4. Discussion
In the TICT model, the energy of the TICT state mainly determines the nonradiative rate. Increasing the solvent polarity decreases the energy of the TICI’ state [20,21]. Solvent effects are taken into account by a polarity-dependent E,. For example, by assuming that E, is a linear function of &(30), Hicks et al. [31] were able to explain the dependence of the photophysics of the TICT compound dimethylaminobenzonitrile on solvent polarity. If internal conversion for IZEIH+ involves the formation of the TICT state, ink, should increase and E, should decrease with Er(30). These trends were not observed for RBH+ in nitriles. Although In k,, increased linearly with
312 of &(30) (Table 1). The TICT ET(30) (Fig. 3), E, was constant and independent model also predicts that, because nitriles are less polar than alcohols, the values of E, in nitriles should be greater than in alcohols and, correspondingly, the values of k,,, in nitriles should be Iess than in alcohols. However, these predictions do not agree with the data. The measured values of E, are lower in nitriles (approximately 3.4 kcal mol-‘) than in alcohols (5.2 kcal mol-’ or less) 117, 183, and the measured values of k,, in nitriles (4.9X10’ s-l or less) are greater than in alcohols (3.0X 10s s-l or less) [17, 181. The photophysical properties of RBH+ in nitriles and alcohols can be explained by the ULM model. To help us quantitatively interpret the data, we first introduce a mechanism that is similar to the two-state model [17, 181. This new mechanism deviates from the two-state model by allowing B* to be in rapid equilibrium with not only A* but also with the excited pyramidal state P* A *-
‘It-l
1k. i
kz = k-z
kl
;
SO
P*
ki, So
J
This new mechanism is consistent with the ULM model, because &-So internal conversion occurs only in the intermediate state B* and not in the pyramidal state P*. The same expression for k,,, as given by eqn. (I), is obtained from this mechanism by applying the steady state approximation to B* and P* and assuming kicek-1, with KA.B.=kl/ k_l. In terms of the ULM model, the difference in the values of E, and k,, for nitriles vs. alcohols reflects a difference in the strength of attraction between the soivent dipoles and the positively charged amino group. Because nitriles are less polar than alcohols, the positively charged amino group is less stable in nitriles than in alcohols. The. statistical weights of resonance structures a and c and the electron density in the xanthene-amine bond are less in nitriles than in alcohols. The energy needed to change the xanthene-amine bond is less in nitriles than in alcohols or, alternatively, AGAW . in nitriles is less than in alcohols_
40
42
44 Ed
46
40
kcallmol
Fig. 3. Plot of Ink,,, for RBH+ VS. polarity of nitriles at 25 “C. Slope, 0.108; intercept, 15.0; correlation, 0.96.
313 For RBH+, E, has a weak, but noticeable, dependence on solvent polarity in alcohols [17, 181, but is essentially independent of solvent polarity in nitriles. We believe that this difference is caused by hydrogen-bonding effects. Alcohols can form hydrogen bonds with the PhCOOH group. The hydrogen bond weakens the xanthene-COOH interaction and, consequently, decreases the statistical weight of resonance structure b relative to that of resonance structures a and c. The shift in the relative weights of the resonance structures leads to a higher electron density in the xanthene-amine bond. Thus, a hydrogen bond between an alcohol and the COOH group increases the barrier for the planar-pyramidal change or, alternatively, increases the value of AGAoB.. Since the strength of the hydrogen bond parallels the solvent polarity in the alcohols, E, increases with solvent polarity in the alcohols. Although dipole-dipole interactions can occur between nitriles and the COOH group, they are not as strong as the hydrogen bonds formed between alcohols and the COOH group. Hence, E, should not show much of a dependence on solvent polarity, and p-0 in eqn. (4) for RBHf in nitriles. in nitriles must therefore be The dependence of k, on the solvent for RBH+ mainly due to the dependence of ki, on the solvent polarity. A plot of In k,, vs. &(30) is linear with a slope of 0.108 mol kcal-‘. If eqn. (6) describes k,, the value of this slope must be equal to -@/RT+ IC). This implies that K is equal to -0.108 mol kcal-‘, since p=O. In contrast, K= - 0.51 mol kcal-’ and p = 0.23 for RBH+ in alcohols [17, 181. Thus, for nitriles and alcohols, AE10 decreases with solvent polarity. A plausible explanation for this result, based on the ULM model, is that B* has more planar than pyramidal character. Solute-solvent interactions that stabilize the positive charge on the amino nitrogen atom will also tend to increase delocalization in the r-electron system and shrink the energy gap for B *. It should also be noted that the absolute value of K is about a factor of two greater in alcohols than in nitriles. This is consistent with the hypothesis that B* has more planar than pyramidal character. Because resonance structures a and c contribute to the electronic structure of B*, the amino nitrogen atoms in B* must have some positive charge. Therefore, if the magnitude of K is a measure of the strength of solute-solvent coupling for B*, the absolute value of K should be larger in the more polar solvent.
5. Conclusions We have accounted for the dependence of k,, on solvent polarity for RBH+ using the ULM model and a modified version of the two-state model. By comparing the non-radiative rate of RBH+ in nitriles with that in alcohols, we have found that the dependence on solvent polarity is due to specific solvent-solute interactions at the amino group and the PhCOOH group. These interactions, according to the ULM model, affect the non-radiative rate by modulating the relative statistical weights of the quinoid and carbocation resonance structures. We hypothesize that internal conversion occurs from an intermediate state that has more planar than pyramidal character. This hypothesis explains the dependence of the energy gap at the intermediate state on solvent polarity.
Acknowledgment This research was supported Institutes of Health.
by the Robert
A. Welch
Foundation
and the National
314
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1 K.
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20 21 22 23 24 25 26 27 28 29 30
31