J . Phys. Chem. 1988, 92, 6590-6594
6590
Acknowledgment. We thank Prof. J. Jortner, Tel Aviv, for many stimulating discussions and Prof. M. Klingenberg, Munchen, for putting the single photon counting apparatus at our disposal. We gratefully acknolwedge the financial support of the Deutsche Forschungsgemeinschaft, the Volkswagenstiftung, and the Alfried
Krupp von Bohlen und Halbach-Stiftung. Registry No. A I , 1498-71-1; AID, 99397-67-8; A2D, 99397-68-9; AN, 79760-50-2; A ~ ~ N 116785-54-7; D, ~1,42211-34-7;PID, 9939765-6; P2D, 99397-66-7; PN, 96763-47-2; P14ND, 101969-95-3; PlSND, 110538-62-0; P26ND, 116785-55-8.
Effect of Solvent Polarity on Nonradiative Processes in Xanthene Dyes: Rhodamine B in Normal Alcohols Kelly G. Casey’ and Edward L. Quitevis* Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409 (Received: February 22, 1988; In Final Form: May 6,1988)
The fluorescence lifetime of rhodamine B in a series of normal alcohols (C,H,,,OH, n = 1-6) was measured as a function of temperature. The nonradiative rate constants were calculated from the fluorescence lifetimes and quantum yields. Activation energies were obtained from Arrhenius plots of the nonradiative rate constant. The variation of the nonradiative rate constant with solvent polarity and temperature was consistent with a photophysical mechanism that involves equilibrium between the planar and twisted configurations of the diethylamino groups on the xanthene ring of rhodamine B and internal conversion from the twisted configuration. The activation energy is equal to the free energy difference between the twisted and planar configurations. The solvent polarity dependence of the free energy difference and of the rate constant for internal conversion from the twisted configuration determines the variation of the nonradiative rate constant with solvent. When solvent polarity effects are taken into account by using the parameter ET(30),the nonradiative rate constant shows weak or no dependence on the solvent viscosity.
Introduction Solvent effects are important in determining the photophysical properties of dye molecules in solution. Dye molecules are often used to probe the local environment in biological’ and synthetic polymericZ systems. Many of these molecules are used as laser dyes.3 A complete understanding of solvent effects is needed to interpret such experiments or to improve the performance of dye lasers. The role of the solvent in determining the photophysics of molecules can be divided into dynamic and static solvent effects. Dynamic solvent effects are caused by collisions with the solvent molecules. These effects are important in excited-state relaxation processes involving photoinduced torsional motion about chemical These effects are manifested by a viscosity-dependent nonradiative rate constant k,. During the past several years, there have been numerous theoretical studies to understand the molecular basis of this viscosity dependen~e.’~ The earliest studies involved Kramers’ modelI4 in conjunction with the laws of hydrodynamic~.’~The conformational change is represented as solute motion governed by a one-dimensional torsional potential energy surface, with the motion modified by two Brownian effects arising from solvent dynamics: a hydrodynamic drag (obeying macroscopic hydrodynamic equations) and a random fluctuating force (buffeting by the solvent). The rate constant that results from this model is given by the activated barrier crossing formula kb = A ( q ) exp(-E2/RT) (1) where E: is a solvent-independent barrier height and A ( q ) is a preexponential factor which depends nonlinearly on the solvent viscosity. The validity of this simple model is limited to molecular systems for which hydrodynamics and one-dimensional torsional potentials are valid and static solvent-solute effects are unimpor tan t . Static solventsolute coupling effects can be divided into specific short-range solventsolute interactions and universal interactions.l 6 The bulk influence of the solvent as a dipolar medium depends on the dielectric constant and the index of refraction and gives *To whom correspondence should be addressed. ‘Robert A. Welch Foundation Predoctoral Fellow. 0022-3654 I 8 8 12092-6590$01.50/0
rise to the universal interactions. Both interactions affect the shape and separation of the potential energy surfaces and therefore affect the barrier heights. The issue of static solvent effects in the torsional dynamics of molecules is beginning to be addressed quantitatively. For example, static solvent effects play a major role in the torsionally
(1) Ainsworth, S.; Flanagan, M. T. Biochim. Biophys. Acta 1969, 194, 213. (2) Snare, M. J.; Tan, K. L.; Treloar, F. E. J . Macromol. Sci., Chem. 1982,
A17, 189. (3) Drexhage, K. H. In Dye Lasers; Schafer, F. P., Ed.; Springer-Verlag: Berlin, 1978; pp 144-193. (4) (a) Fleming, G. R. Chemical Applications of Ultrafast Spectroscopy; Oxford University Press: New York, 1986; pp 179-195. (b) Fleming, G. R.; Courtney, S . H.; Balk, M. W. J . Chem. Phys. 1985,83, 215, and references cited therein. (5) Rothenberger, G.; Negus, D. K.; Hochstrasser, R. M. J . Chem. Phys. 1983, 79, 5360. (6) (a) Velsko, S. P.; Fleming, G. R. J . Chem. Phys. 1982, 76, 3553. (b) Keery, K. M.;Fleming, G. R. Chem. Phys. Lett. 1982, 93, 322. (7) Barbara, P. F.; Rand, S. D.; Rentzepis, P. M. J . Am. Chem. SOC.1981, 103, 2156. (8) (a) Flom, S. R.; Nagarajan, V.; Barbara, P. F. J . Phys. Chem. 1986, 90. 2085. (b) Brearlev. A. M.: Flom.’ S. R.: Naearaian. Barbara. P. F. I . , I V.: I J . Phys. Chem. 1986,’90, 2092. (9) (a) Sundstrom, V.; Gillbro, T.;Bergstrom, H. Chem. Phys. 1982, 73, 439. (b) Ben-Amotz, D.; Harris, C. B. Chem. Phys. Lett. 1985,119, 305, and references cited therein. (10) (a) Velsko, S. P.; Waldeck, D. H.; Fleming, G . R. J . Chem. Phys. 1983, 78, 249. (b) Velsko, S. P.; Fleming, G. R. Chem. Phys. 1982, 65, 59. (11) Shank, C. V.; Ippen, E. P.; Teschke, 0.;Eisenthal, K. B. J . Chem. Phys. 1977, 67, 5547. (12) (a) Tredwell, C. J; Osborne, A. D. J . Chem. SOC.,Faraday Trans. 2 1980, 76, 1627. (b) Osborne, A. D. J. Chem. SOC.,Faraday Trans. 2 1980, 76, 1638. (13) (a) Lee, J.; Zhu, S.-B.; Robinson, G. W. J . Phys. Chem. 1987, 91, 4273. (b) Bagchi, B.; Oxtoby, D. W. J . Chem. Phys. 1983, 78, 2735. (c) Grote, R. F.; Hynes, J. T.J . Chem. Phys. 1980, 73, 2715. (14) Kramers, H. A. Physica 1940, 7 , 284. (15) See for example: McCaskill, J. S.; Gilbert, R. G. Chem. Phys. 1979, 44, 389. (16) Birks, J. B. The Photophysics of Aromatic Molecules; Wiley-Interscience: New York, 1970. I
0 1988 American Chemical Societv
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 6591
Rhodamine B in Normal Alcohols
TABLE I: Comparison of Photophysical Parameters for Rhodamine B (Acid) with Solvent Polarity and Viscosity of Normal Alcohols at 25 O C solvent 7, c p ET(30)P kcal/mol Xmnx,d nm 7f, ns 4; lO"k,,cf s-I 1o-%g :, s-I methanol ethanol 1-propanol 1-butanol 1-pentanol 1-hexanol
0.549' 1.14' 1.98' 2.73b 3.75b 5.10b
55.5 51.9 50.7 49.9 49.1 48.8
55 1 552 553 553 553 553
2.00 f 0.02 2.30 0.01 2.74 f 0.05 2.76 f 0.01 2.89 f 0.05 3.07 f 0.06
*
0.40 0.49 0.49 0.59 0.53 0.62
2.0 2.1 1.8 2.1 1.8 2.1
3.0 2.2 1.9 1.5 1.6 1.2
'Obtained from the CRC Handbook. bMeasuredwith viscometer. cFrom ref 31. duncertainty is f l nm. CUncertaintyis 10%. /Calculated from eq 2c. XCalculated from eq 2d.
induced charge-transfer dynamics of p(dimethy1amino)benzonitrile (DMABN)." DMABN exhibits dual fluorescence from a nonpolar planar state and a twisted intramolecular chargetransfer (TICT) state. The barrier height is a strong function of the solvent polarity due to the large dipole moment change. The functional dependence of the twisting rate on solvent viscosity is removed by correcting for the solvent polarity. Rhodamine B is an example of a molecule where both static and dynamic solvent effects can be examined. Its photophysics and spectral characteristics have been studied as a function of dye concentration,'* visc~sity,'~ temperature,z0 solvent polarity,21and pH.ZZ Rhodamine B exists in either the acidic (protonated) or basic (zwitterionic) form, depending on the pH of the solution.z'~22 The visible absorption and fluorescence spectra for the S transition show a slight red shift with increasing solvent polarity, with the shift being larger for the basic than the acidic form. Despite all the work to date, the detailed role of the solvent in the photodynamics of rhodamine B is still controversial.21 The fluorescence quantum yield of rhodamine B is unity at low temperaturesZb and in viscous solvents such as glycerol.' The temperature dependence of the fluorescence lifetime and quantum yield arises from the rotation of the diethylamino groups on the xanthene ring:'
19
This is substantiated by the fact that the fluorescence quantum yield of rhodamine 101, where the diethylamino groups are immobilized in the planar configuration, is near unity.= The increase in the fluorescence quantum yield in rigid rhodamine dyes could be attributed to a decrease in the density of states from the absence of low-frequency modes. However, nonradiative processes in rhodamine dyes are promoted by high-frequency hydrogenic modes.3 Consequently, the reduction in the density of states in rhodamine 101 cannot be the primary reason for the increased ~~~
~~
(17) (a) Hicks, J.; Vandersall, M.; Babarogic, Z.; Eisenthal, K. B. Chem. Phys. Lett. 1985, 116, 18. (b) Wang, Y.; McAuliffe, M.; Novak, F.; Eisenthal, K. B. J. Phys. Chem. 1981,85, 3736. (18) Selwyn, J. E.; Steinfeld, J. I. J. Phys. Chem. 1972, 76, 762. (19) Moog, R. S.;Ediger, M. D.; Boxer, S. G.; Fayer, M. D. J . Phys. Chem. 1982,86, 4694. (20) (a) Johnansson, L. B.-& Niemi, A. J. Phys. Chem. 1987, 91, 3020. (b) Kubin, R. F.; Fletcher, A. N. J. Lumin. 1982, 27,455. ( c ) Karsten, T.; Kobs, K. J. Phys. Chem. 1980.84, 1871. (d) Huth, B. G.; Farmer, G. I.; Kagan, M. R. J. Appl. Phys. 1969, 40, 5145. (21) (a) Snare, M.J.; Treloar, F. E.; Ghiggino, K. P.; Thistlewaite, P. J. J. Photochem. 1982,18, 335. (b) Arbeloa, I. Lopez; Rohatgi-Mukherjee, K. K. Chem. Phys. Letr. 1986, 128, 474. (22) (a) Faraggi, M.; Peretz, P.; Rosenthal, I.; Weintraub, D. Chem. Phys. Lett. 1984,103,310. (b) Sadkowski, P. J.; Fleming, G. R. Chem. Phys. Lett. 1978, 57, 526. (c) Ferguson, J.; Mau, A. W.-H. Aust. J. Chem. 1973, 26, 1617. (d) Ferguson, J.; Mau, A. W.-H. Chem. Phys. Lett. 1972, 17, 543.
fluorescence over nonrigid rhodamine dyes. In this paper we show that the photophysical data can be understood in terms of a mechanism involving internal conversion from a nonemissive twisted state which is in equilibrium with a fluorescent planar state. Our results indicate that the variation of k,, with solvent and temperature for rhodamine B in normal alcohols can be quantitatively explained by this model, if the SI-So energy gap for internal conversion from the nonemissive state and the activation energy are linear functions of the solvent polarity parameter ET(30).
Experimental Section Rhodamine B perchlorate (Kodak, laser grade) showed a single spot on a TLC plate and was used without further purification. The alcohols were dried over calcium hydride, purified by fractional distillation, and stored in a desiccator prior to use. Viscosities of the solvents were obtained from the literature or from measurements with a Brooldeld viscometer. To shift the acid-base equilibrium, a drop of trifluoroacetic acid (1250 pL) was added to 4-mL samples of rhodamine B (=2 X lod M). Relative fluorescence quantum yields from corrected fluorescence spectra at 25 OC were calculated with respect to rhodamine B in acidic ethanol (& = 0.49).2zb Fluorescence decay curves were measured with standard time-correlated photon-counting techniques using excitation from a synchronously pumped, mode-locked rhodamine 6G dye laser, which was cavity-dumped to yield an interpulse spacing of =78 ns. The details of the apparatus have been previously des~ribed.~' The solutions were excited at 577 nm, and the fluorescence was collected with a lens at right angles to the excitation and passed through a double monochromator to a photomultiplier. To eliminate molecular reorientation effects, a polarizer set at the "magic angle" of 5 4 . 7 O was included in the collection optics. The temperature of the fluorescence cell was maintained to f 1 O C with a heat pump and a temperature controller. The entire fluorescence decay curves were fit to single-exponential decays by using nonlinear least-squares deconvolution. Fluorescence lifetimes were obtained from decay curves that gave fits with reduced x2 of less than 1.2. Results The fluorescence lifetimes were checked between 590 and 620 nm and found to be independent of wavelength. N o dual emission was observed. Fluorescence lifetimes at 605 nm and quantum yields for rhodamine B in a series of normal alcohols at 25 OC are tabulated in Table I. The nonradiative rate constant k,,, and the radiative rate constant k, in Table I were calculated from the ~ the photofluorescence lifetime Tf and the quantum yield q ! ~via physical equations (1/Tf)
= kr + knr
k, = df/7f k,, = (1/7f)
- k,
(2a) (2c) (2d)
The nonradiative rate constant is extremely sensitive to the solvent, (23) Lee, J.; Griffin, R. D.; Robinson, G. W. J. Chem. Phys. 1985, 82, 4920.
6592
Casey and Quitevis
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988
TABLE 11: Summary of Arrhenius Parameters for Rhodamine B solvent 10-12A,,," s-1 E,," kcal/mol 1O4A,,,,b s-' 5.2 f 0.4 4.09 methanol 2.0 i 0.1 ethanol 1.0 f 0.1 5.0 f 0.4 13.6
1-propanol
0.19 f 0.04 0.20 f 0.03 0.10 f 0.02 0.07 f 0.03
1-butanol
1-pentanol 1-hexanol
AC,p,b kcal/mol
4.75
4.1 f 0.5 4.3 f 0.5 3.8 f 0.6 3.7 i 0.5
7.36
5.78 4.16
-0.7 -0.1 -0.7 -0.4 -0.6 -0.7
10-9A s-I 2.48 1.22 0.22 0.26 0.12
K-I
81
EBIC kcal/mol
E,, kcal/mol
4.6 4.4
2.62d 3.09d 4.36d
3.5
3.6
5.27' 5.32e
3.2 3.1
0.08
5.56e
Arrhenius parameters for kn,. bArrheniusparameters for k,, (eq 12). 'Arrhenius parameters for k,JT (eq 13). dObtained from data in CRC Handbook and plot of 9 = 9o exp(E,/RT). CObtainedfrom ref lob. (I
20 1
2 0 18'
3.2
3.0
3.4
1
1
18' 50
3.6
J
60
55
65
ET(30) / kcalimol
1O O O f l (K'l)
Figure 1. Arrhenius plot of the nonradiative rate constant k,,, for rhodamine B in 1-hexanol. A,, = (7.0 f 3.0) X 10'os-l, E, = 3.7 f 0.5 kcal/mol, correlation = 0.97.
whereas the radiative rate constant is not (Table I). Since k, is relatively independent of temperature,*Oa the temperature dependence of q is associated with that of k,. In general, k , can be separated into temperature-independent and -dependent parts:
Figure 2. Plot of the logarithm of k,, for rhodamine B in alcohol-water mixtures versus the polarity at 1.4 CPand 23 OC: (a) 8.5% C2HSOH/ 91.5% HZO, (b) 13% CHjOH/87% H20, (c) 68% CH3OH/32% H20, (d) 94% CzHSOH/6%H20. Slope = 0.104 f 0.02, intercept = 13.1 f 1.5, correlation = 0.99. k,, were obtained from ref 21a. and ET(30) values were calculated (see Appendix).
Since the fluorescence quantum yield of rhodamine B approaches unity at low temperatures, k,: = 0, and k,, is solely determined by the temperature-dependent term k,( 0. Fluorescence lifetimes for rhodamine B were measured at different temperatures in each of the solvents. The values of k,, at each temperature were calculated from eq 2d by using the values of k, listed in Table I. A typical Arrhenius plot of k,, for rhodamine B in 1-hexanol is given in Figure 1. Temperature-independent contributions to the nonradiative rate constant would cause curvature in the Arrhenius plot at low temperatures. For example, Arrhenius plots of k,, for 3,3'-diethyloxadicarbocyanine iodide in polar solvents show marked curvature at low temperatures due to a temperature-independent contribution to the nonradiative rate constant.Iob Arrhenius plots for rhodamine B in all the solvents studied show no curvature over the temperature range of these measurements. The activation energies E, and preexpoiential factors A , are listed in Table 11.
Discussion These results can be explained by the following two-state model:
1l Y Q1
48
'
' 50
'
52
54
56
ET(30)1 kcal/mol
Figure 3. Plot of In k,, for rhodamine B versus polarity of alcohols at 25 "C. Slope = 0.12 f 0.02, intercept = 12.8 f 1.1, correlation = 0.95.
of dual fluorescence. Internal conversion, which is the primary nonradiative process in rhodamine dyes, from the twisted state and not from the planar state accounts for the fluorescence quantum yield being nearly unity at low temperatures20c and in viscous solvents like glycer01.~ The rate law that follows from applying the steady-state approximation to S,(et) is given by d[S1(8p)l/dt = -(k + knr)[s~(ep)l
I
I
SO
SO
kic
where k, is the radiative rate constant, kp, is the rate constant for rotation from the planar state a t 8, to the twisted state at Ot, ktp is the corresponding reverse rate constant, and kic is the internal conversion rate constant in the twisted state. This model is consistent with a Stokes-shifted fluorescence risetime of less than 1 P S ? ~which is much shorter than the risetime (==lo-150 ps) of the Stokes-shifted emission from TICT ~tates,"~**~ and the absence (24) Mourou, G.; Malley, M. M. Chem. Phys. Left. 1975, 32, 476.
(4)
where The decrease of the nonradiative rate constants can be correlated with an increase in the solvent viscosity (Table I). The values of k,, can be empirically fit to C/v' with C = 2.362 X lo8 s-l, a = 0.380, and a correlation coefficient of 0.98. This value of a lies within the range of 0.23-1.00 previously found for other molecules undergoing photoinduced conformational changes and showing dynamic solvent effects.6J0 However, the isoviscosity data (25) Su, S.-G.:Simon, J . D.J . Phys. Chem. 1986, 90, 6475.
Rhodamine B in Normal Alcohols
7 6-
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 6593
1
I
7
-0
O
-
L
s
/
// 1
-
3-
-
i
16.0
2
of Snare et which were obtained for alcohol-water mixtures at 23 O C and 1.4 cP, indicate that the variation with solvent cannot be solely a viscosity effect. A plot of the logarithm of k,, versus the solvent polarity parameter ET(30)is linear (Figure 2). (The calculation of ET(30) values for the alcohol-water mixtures is described in the Appendix). The logarithm of the k,, values in Table I also varies linearly with ET(30)values (Figure 3). Despite the 2 O C temperature difference and the fact that the solvent viscosity is not constant for the data in Figure 3, the slopes of both the plots in Figures 2 and 3 are, within experimental error, equal. The effects of temperature and solvent polarity on the nonradiative processes of rhodamine B are quantitatively consistent with the mechanism described above if kic 32 kcal/mol. The rate constant corrected for solvent polarity is given by
kcor, = knr exp[(@’/RT + K)(ET(30) - 3o)i = Acm, exp(-ACp,O/RT) (12) Since AG,? is nearly zero, Arrhenius plots of k,,, are relatively flat (Figure 5). If k,, is independent of viscosity, both the preexponential factor and the activation energy extracted from Arrhenius plots of k , will not vary with the solvent. The values of AC,: (Table 11) are constant within the =0.5 kcal/mol experimental error in the activation energy and give an average value of -0.5 kcal/mol, which agrees well the value calculated from the intercept of E, versus ET(30). Errors in the intercept of Arrhenius plots due to uncertainty in the data are the primary cause for the lack of constancy in A,,,, (Table 11). We think that the dependence of the activation energy on solvent polarity originates from a change in dipole moment associated with the internal twisting of the diethylamino group about the C N bond. The absence of a dipole moment change upon excitatioq2’ which results in the absorption maximum A,, not being a strong function of the solvent polarity, would not be inconsistent with this idea. Steady-state fluorescence and absorption spectra are associated with optical transitions between the planar ground and excited states, whereas internal conversion occurs from the twisted excited state, which can have a dipole moment different from that of the planar excited state. Rettig27 has recently postulated that a TICT state is formed by the internal twisting of the diethylamino groups, coupled with electron transfer from the amino nitrogen to a r* orbital extending over the xanthene ring, and that the electron-withdrawing carboxyphenyl group attached to the xanthene ring stabilizes the TICT state. (27) Rettig, W . Angew. Chem., Int. Ed. Engl. 1986, 25, 971
alcohols.
Although our conclusions support the claims of Snare et aL2Ia that static solvent effects determine the photophysics of rhodamine B, our model differs from theirs. In our two-state model, solvent and temperature effects are explained by solvent polarity, whereas in the single-minimum potential model both rotational diffusion and solvent polarity must be invoked. In their single-minimum potential model, thermal excitation in the SI state changes the torsional angle, without going over a barrier, to a new value where the S1-So gap is smaller. The variation of k , with solvent polarity is explained by an energy gap law, where the Sl-So gap is proportional to l/&,,ax. However, this explanation is not consistent with the fact that A,, for rhodamine B in alcohol solvents is relatively constant, changing by at most 2 nm or
