4874
J. Phys. Chem. 1992, 96,4874-4878
Solvent Effects on the Photolsomerizatlon Rates of the Zwltterlonic and the Cationic Forms of Rhodamlne 6 in Protic Solvents Tzyh-Lee Chang**+and Herbert C . Cheung Department of Biochemistry, University of Alabama at Birmingham, UAB Station, CH 19, Room 520, Birmingham, Alabama 35294 (Received: June 5, 1991; In Final Form: March 9, 1992)
Solvent effects on the nonradiative rate have been investigated for the zwitterionic form of rhodamine B dissolved in water-methanol mixtures, water-ethanol mixtures, monoalcohols (C3-C10),ethylene glycol, and glycerol. The effect of solvent polarity is considered in the Arrhenius-type equation by introducing a polarity dependence into the activation energy and the effect of solvent viscosity is taken into account by including a fractional-viscosityfactor in the preexponential coefficient. This empirical expression has been found to describe satisfactorily the photoisomerization rates of rhodamine B in the above solvents. We also studied solvent effects on the nonradiative rates of the cationic form of rhodamine B in alcoholic solutions. We found that the effect of solvent polarity is stronger for the zwitterionic form than for the cationic form. However, the effect of solvent viscosity is about the same for both forms.
sumed a linear dependence of the height on ET(30),which is an Introduction empirical solvent polarity parameter proposed by Dimroth et a1.30 The effects of microenvironment on the excited state dynamics In this work we continued to adopt the idea that the barrier height of small organic molecules in well-characterized solvents are still is dependent on solvent polarity. Preferably, we used ETN,a poorly understood. An understanding of these effects will facilitate normalized polarity parameter recommended by Reichardt et al.," application of these molecules to investigate unknown microeninstead of ET(30)as the solvent polarity parameter. Thus a linear vironments. Spectroscopic techniques have been widely used, for dependence of the barrier height Eb on ETNcan be formulated this purpose, to study the solute-solvent interaction for dye with water and tetramethylsilane (TMS) as reference solvents: molecules in various solvent systems. Of particular interest in these studies are both the ground-state and excited-state spectral Eh = Eho -4- 32.4BETN (1) parameters of the dyes as related to their chemical species and to the macroscopic properties of the solvents. Rhodamine B has where Ehois the barrier height in TMS having an ETNof 0.000 been studied in this manner with specific reference to two pheand the factor 32.4 is the difference of ET(30) between water (63.1 nomena: (1) its ionic and isomeric forms as a function of solvent kcal/mol) and TMS (30.7 kcal/mol). The parameter ,d determines composition and solvent system,l-I2and (2) the effects of solvent how strongly Eh varies with solvent polarity and is dimensionless. conditions on the spectral parameters including fluorescence The polarity-dependent nonradiative rate can then be expressed quantum yield?J3J4lifetime,I5absorption and emission s p e ~ t r a , ~ ~ J ~as and rotational relaxation time.18.19The mechanism by which the excited state rhodamine B interacts with solvent molecules has also been investigated.'6v20-2Z On the basis of the high quantum yields for both rhodamine 101, which has a rigid structure, and rhodamine B in glycerol, where kM0is a constant. To correct for the solvent polarity effect, a highly viscous solvent, DrexhageZ0suggested that the torsional knris modified as follows: motion of the diethylamino groups is involved in the nonradiative processes. Snare et a1.I6 concluded that the internal conversion rate increased when the S1-So energy separation was lowered. (3) They suggested that no crossover of an energy barrier is required because thermal excitation in the S1 state would change the In the present work, we studied the excited-state dynamics of torsional angle to a new value corresponding to a smaller +So rhodamine B in a series of water-methanol mixed solvents and gap. In contrast to the model proposed by Snare et al., we adopted, compared the results with those previously obtained for rhodamine the Grabowski model23and showed that the nonradiative rate of B in water-ethanol mixed solvents.z The ,k values of rhodamine rhodamine B could be regarded essentially as the rotation rate B in all of these low-viscosity solvents (all these solvents have for transition from the excited planar state to the excited twisted viscosities 12.6cp) do not show an apparent dependence of solvent ~ t a t e . * ~This . ~ ~connection between the nonradiative rate and the viscosity. To further examine the possible viscusity effect, we also rotation rate enabled us to associate the activation energy of the studied this dye dissolved in a medium-viscosity solvent (ethylene nonradiative processes with the barrier height (Eh)for transition glycol) and a high-viscosity solvent (glycerol). Our results led from the planar state to the twisted state. Vogel et a1.21invesus to establish a general expression for the nonradiative rate by tigated several rhodamine dyes with different substitution groups including parameters for both solvent polarity and solvent viscosity and concluded that the nonradiative deactivation was influenced effects. This expression was then used to examine all previous by solvent polarity and other factors (solvent viscosity and temdata and the data in this work for the zwitterionic form of rhoperature). The effect of solvent polarity on the isomerization rate damine B in dilute protic solvents and to study solutesolvent was also found for a few other molecules aside from rhodamine interaction on the cationic (protonated) form of rhodamine B in dyes. For instance, Fleming and his ~ o - w o r k e r s suggested ~.~~ that alcoholic solvents. the activation energy from the planar to twisted configuration decreases in polar solvents based on their studies of diphenyl Experimental Section butadiene. Similarly, Hicks et al.28929also found that the barrier Rhodamine B was purchased from Sigma Chemical Co. and height in the isomerization decreased with increasing solvent used as received. Distilled deionized water and 100% ethanol were polarity for (dimethy1amino)benzonitrile in solutions. They asused. All other solvents were used without further purification and were obtained from the following sources: ethylene glycol + Present address: Institute of Atomic and Molecular Sciences, Academia (spectrophotometric grade) and glycerol (spectrophotometric Sinica, P.O. Box 23-166, Taipei, Taiwan 10764, Republic of China. 0022-3654/92/2096-4814$03 .00/0 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 4875
Rhodamine B in Protic Solvents
TABLE I: Spectroscopic Data for Rhodamine B in a Series of Water-Methanol Mixed Solvents, Ethylene Glycol, a d Glycerol" Sbb (nm) kmb (4 ETNc vd (CP) df 7 (ns) lo-%,, (s-I) 10-'k,,
CHj0H:HZO
1oo:o
90:10 80:20 70:30 60:40 50:50 30:70 10:90 0:100
ethylene glycol glycerol
545.0 545.5 547.5 548.0 549.0 550.0 551.5 552.0 553.5 552.0 554.5
569.6 571.7 572.4 573.3 574.8 576.6 577.4 579.2 580.8 578.2 580.8
0.762 0.793 0.831 0.863 0.893 0.920 0.963 0.993 1.ooo
0.790 0.812
0.555 0.857 1.124 1.361 1.558 1.655 1.554 1.131 0.890 16.79 954
0.52 0.51 0.49 0.48 0.45 0.43 0.38 0.33 0.30 0.60 0.66
1.89 2.01 2.19 2.29 2.51 2.65 3.10 3.74 4.24 1.34 0.929
2.54 2.44 2.33 2.27 2.19 2.15 2.00 1.79 I .65 2.99 3.66
(s-I) 1.76 1.70 1.64 1.55 1.55 1.51 1.54 1.69 1.88
OThe methanol-water compositions are volume percent. bEstimated errors =&l nm, CFromrefs 30 and 33. dFrom refs 37 and 38,the viscosities of the mixtures at 25 O C were estimated by ?,,(mixture) = qzo(mixture) X volume percent (H,O) X 725(H20)/820(H2O) + ?,,(mixture) X volume percent (MeOH) X r/,5(MeOH)/~,o(MeOH).eEstimated errors =*lo%. For mixtures, refractive indices at 20 O C (ref 38) were used. grade) from Aldrich, methanol (HPLC grade) from Fisher, and propanol, butanol, and pentanol (all analyzed reagents) from Baker. Absorbance was measured with a Beckman DU-40 spectrophotometer using 1-cm cell paths. The absorbance of rhodamine B was kept 10.15 at the absorption maximum in order to "ize possible dimerization in aqueous solutions.s*8-'0The corrected fluorescence spectra were measured with a Perkin-Elmer MPF-66 spectrofluorimeter, and the fluorescence quantum yield was determined by a comparative method using a dilute solution of rhodamine B in ethanol (4 = 0.65)32and 530-nm excitation. For quantum yield determinations, a quadratic correction for refractive index and percent absorption of solution were applied. The apparatus used for fluorescence lifetime measurementswas described in detail e l ~ e w h e r e . An ~ ~ excitation polarizer was used for vertically polarized exciting light and an emission polarizer was rotated at 54.7O relative to the vertical direction to eliminate bias due to anisotropy effects. All spectral measurements were carried out at 25 OC. Lifetimes and quantum yields of rhodamine B were also measured for both the zwitterionic and cationic forms in ethylene glycol at 40 OC. ReSult.9 In addition to the zwitterionic and cationic forms, a third species of rhodamine B in dilute solution is the colorless lactone which does not contribute to the absorption and fluorescence emission in the visible region of i n t e r e ~ t . ~ J l JThe ~ structures of the zwitterionic, cationic, and lactonic forms of rhodamine B are shown in Figure 1. In dilute concentration rhodamine B dissolved in ethanol showed an absorption peak and an emission peak at 542.0 and 568.0 nm, respectively. Addition of one drop of 1 M NaOH to a 3-mL solution of the dye in ethanol did not change the absorption spectrum, but a drop of concentrated HCl shifted the absorption peak to 553.0 nm. A red shift of the absorption peak was also observed with increasing dye concentration. These spectral changes have been previously observed and are consistent with a shift of the acid + base (cation * zwitterion) equilibrium, indicating that rhodamine B at dilute concentration in protic solvents is largely in the zwitterionic form.24 Faraggi et a1.6 determined the acid * base equilibrium constant for rhodamine B in ethanol to be 8.7 and concluded that the degree of acid dissociation to yield the zwitterionic form was 0.98 at 10" M. Lopez Arbeloa and Ruiz Ojeda5 determined that the equilibrium constant for the dimer + monomer transition of rhodamine B in aqueous solution was 2100 M-I at 20 OC. Therefore, the mole fraction of monomeric rhodamine B is close to unity at 10" M. Hmckley et al." found that in the lactone + zwitterion equilibrium 70.6% of rhodamine B dissolved in ethanol is in the zwitterionic form in the concentration range of (6-8) X lo4 M, on the basis of a reference molar absorptivity for the zwitterionic form of c = 13.0 X lo4 M-' cm-'. These findings suggest that the best preparation of rhodamine B for investigation of its zwitterions is a dilute solution in the micromolar range, and this is the concentration range used in the present work.
b
a
C Figure 1. Structures of rhodamine B in its (a) zwitterionic, (b) cationic. and (c) lactonic forms.
18.54
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1
Figure 2. Plot of the nonradiative rates In k, vs solvent polarity parameters ETNfor rhodamine B dissolved in water-methanol mixed solvents. The data are taken from Table I. The least-squares line yields a slope of 3.117 (@= -0.0570) and an intercept of 16.61 with a correlation coefficient of 0.965.
Table I lists the spectral parameters for rhodamine B in water-methanol mixtures. Both the absorption and emission peaks show a red shift with increasing water content similar to the results previously obtained for the dye in water-ethanol mixtures.2s The solvent polarity parameter ET^ is associated with Y,2,and ET(30) which are correlated with each other by the equations: Y = 0.416322- 35.877 and E ~ ( 3 0=) 0.7522 - 7.87?3 The calculated values of ETN,34 solvent viscosity ( q ) , measured quantum yields (+), and lifetimes ( 7 ) are also listed in Table I. The nonradiative rates (k",)were calculated from $ and T and are given in Table I. By using eq 2, we obtained 6 = -0.0570 from a plot of In k,, vs ETN(Figure 2). We then substituted this value of 6 in eq 3 to calculate the polarity-corrected nonradiative rates ( J C ~ ) , also listed in Table I. The mean of the k,, values is 1.65 X lo7 s-l with a standard deviation of 0.122 X lo7 s-l. To compare the present results for rhodamine B in water-methanol mixed solvents
4876 The Journal of Physical Chemistry, Vol. 96, No. 12, 1992
TABLE 11:
Spectroscopic Data for the Cationic Form of RhodPmiw
h b b (nm) methanol ethanol propanol butanol pentanol ethylene glycol glycerol
Xc,'
552.0 553.0 553.5 554.0 555.0 558.0 562.0
(nm) 577.1 577.5 578.2 579.0 579.7 584.2 586.4
Chang and Cheung
B in Alcoholsa
ET^' 0.762 0.654 0.617 0.602 0.568 0.790 0.812
(CP) 0.555 1.075 1.950 2.570 3.722 16.79 954 tld
#Je
0.40 0.46 0.52 0.54 0.54 0.51 0.59
(ns) 2.17 2.38 2.41 2.50 2.62 2.78 3.53
T
10-*k,, (s-') 2.77 2.27 1.99 1.84 1.76 1.76 1.16
10%,'
(s-l)
1.13 1.13 1.11 1.08 1.12 1.07 1.13
OThe cationic form of rhodamine B was prepared by addition of a trace of concentrated HC1 to a solution of rhodamine B dissolved in the alcohols. *Estimated errors =fl nm. CFromref 30. dFrom refs 37 and 38. eEstimated errors =&IO%.
20.04
I
20'o
. / I
20.0
19.5
19.5
19.0
19.0
f Glycerol 18.0 4
0.60
0.70
0.80
0.90
1.00
I
1.10
E:
Figure 3. Plot of the nonradiative rates In k,, vs solvent polarity parameters ETNfor rhodamine B in two solvent systems: (0) water-ethanol mixed solvents, data taken from ref 25 and corrected for solvent refractive index; (0)water-methanol mixed solvents from the present work. Note that the deviation of ethanol from the line will be less pronounced if the calculated ETN (0.643)is used instead of that from ref 30 (ETN= 0.654); see ref 34. The least-squares line yields a slope of 3.1 12 (fl = 4.0569) and an intercept of 16.60with a correlation coefficient of 0.981. Also shown are the In k,, values for the zwitterionic form of rhodamine B in ethylene glycol (A) and glycerol (v).
with previous results obtained for the dye in water-ethanol mixed solvent^,^^*^^ we pooled the calculated k,, values for these two solvent systems as shown in Figure 3. A linear least-squares fit of these composite data yielded a value of -0.0569 for 8. With this new estimated 8 value we recalculated k, for the two solvent systems and obtained a mean value of 1.63 X lo7 s-I. The fit shown in Figure 3 cannot tell us a significant dependence of viscosity effect. However, the possibility exists that solvent viscoSity may play a role in determining the nonradiative rate when the viscosity is significantly higher than those of water-alcohol mixtures. To examine this issue we measured the spectral parameters of rhodamine B dissolved in ethylene glycol and glycerol and calculated the corresponding nonradiative rates k,, (Table I). These two values are compared in Figure 3 with the k, values for the two low-viscosity solvent systems. It is clear that the polarity-dependent k,, values for ethylene glycol and glycerol are significantly lower than those predicted by eq 2 for low-viscosity systems. Using the new estimate of the mean of the polarity-free nonradiative rate (1.63 X 1O7 s-I) from low-viscosity solvents, the Piscosity-free" and polarity-dependent nonradiative rates k,, can be readily calculated from eq 3. These values are 1.90 X lo8 s-] and 2.03 X lo8 s-' for ethylene glycol and glycerol, respectively. Thus the observed k,, for rhodamine B in these two solvents are 29 and 54% smaller than the predicted values, respectively, and the smaller rates are likely due to viscosity restriction of the dye molecules in their immediate surroundings. Thii analysis indicates the need to introduce a viscosity parameter into the expression for k,,. To shift the zwitterionic form to the cationic form, we added 10 fiL of concentrated HCl to a 3-mL sample of rhodamine B dissolved in several alcohols. This small volume of HCI (-0.33%) is assumed not to cause a significant change of the ETN and t) of alcohols. Table I1 lists the spectral parameters for protonated rhodamine B in the alcohols, and Figure 4 shows a plot of In k,, vs ETN.
-
; -c
C
5
18.0
L. 18.0
4
0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 N
ET
Figure 4. Plot of the nonradiative rates In k, vs solvent polarity parameters ETNfor the cationic form of rhodamine B dissolved in methanol, ethanol, propanol, butanol, pentanol, ethylene glycol, and glycerol (0). The data were taken from Table 11. A second plot of In IC', vs ETN according to eq 4 is also shown (0) for comparison. k', (=k,q") include a correction factor (11") to account for viscosity effect. The least-squares line for the second plot yields a slope of 1.081 (@= -0,0197)and an intercept of 18.52with a correlation coefficient of 0.975.
Discussion In the current modified model, the nonradiative rate can be regarded as the barrier-crossing rate from the planar state to the twisted state. This model provides a reasonable explanation for the high quantum yield ( E 1) of rhodamine 101 because of its inability to rotate due to its rigid s t r u ~ t u r e . ' ~ Drexhage20 J~ reported that the fluorescence quantum yield of rhodamine B is viscosity-dependent, but Alobaidi et al.36 disagreed with this finding. If the rotation rate depends on solvent viscosity, it would be justified to ascribe the high quantum yield for rhodamine B in high-viscosity solvents (e.g., poly(viny1 alcohol))16to the restricted rotation motion. This idea has been strengthened in the present work. The experimental k,, values for rhodamine B in glycerol (t) = 954 cp at 25 "C) is 54% reduced compared with the value predicted from low-viscosity solvents, whereas the corresponding reduction is only 29% for ethylene glycol (t) = 16.79 cp at 25 0C).37,38 Since the reduction of k,, by high viscosity is not linear, we propose to include a fractional-viscosity dependence into the preexponential coefficient in eq 2. Equation 2 is then modified as follows:
where C is a constant, t) is solvent viscosity in units of cp, and the parameter a! determines how strongly k, is influenced by friction. Equation 2 can be treated as an approximation of eq 4 if all solvent viscosities are close to 1 cp (i.e., k,O in eq 2 approximately equals the constant C in eq 4). Since eq 2 can describe satisfactorily the mixtures studied except ethylene glycol and glycerol, we can estimate a! by computing In (k,(predicted)/k,(experimental))/ln t) for these two higher-viscosity solvents. The computed a! values are 0.12 and 0.1 1 for ethylene glycol and glycerol, respectively. The fitted 9, (=-0.0569) obtained from mixtures was also used to find k, for rhodamine B in normal alcohols (c3-c10).24s35In contrast to our previous results which showed no significant dependence of k,, on solvent viscosity,24the plot of In k, vs -In t) for these eight alcohols yields a slope of 0.13 and a correlation
Rhodamine B in Protic Solvents
The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 4811
solved dye is in a local environment less viscous than the solvents. It is possible that the diethylamino groups do not sense the full restriction of the structure of poly(ethy1ene oxide) because methanol could occupy the surrounding solvation cage. As a 19.5 matter of fact, the constant lifetime observed in this mixed system I 'E A! can be attributed to this solvation effect by the lower-viscosity 5 methanol. By using multiple linear regression for the data of cationic form 16.5 of rhodamine B (Table 11), we obtain an intercept = 18.525, a = 0.124, and j3 = -0.0197. A plot of In k',,, vs ETN is shown in Figure 4. After correcting for both polarity and viscosity effects, 17.5 4 a plot of In kk, vs ETN yields a slope of 3.1 X with a 0.45 0.55 0.65 0.75 0.85 0.95 1.05 correlation coefficient of 1.2 X and a plot of In kk, vs In 7 yields a slope of 5.9 X with a correlation coefficient of E: 5.9 X lO-I4. These results are similar to those obtained from the Figure 5. Plot of In Pnr vs ETNaccording to eq 4 for rhodamine B zwitterionic form. The values of kk, are listed in Table 11. By dissolved in water-methanol mixtures (0),water-ethanol mixtures (0, comparing the values of a and j3 between the zwitterionic and data taken from ref 25 and corrected for solvent refractive index), alcationic forms, we can see that the effect of solvent polarity is cohols from Cp to C,,, ( 0 ,data taken from ref 24 and corrected for stronger for the zwitterionic form than for the cationic form. solvent refractive index), ethylene glycol (A), and glycerol (V). k'nr (=knrf) includes a correction factor (9") to account for viscosity effect. However, the effect of solvent viscosity is about the same for both The least-squares line yields a slope of 3.404 (@= -0.0622) and an forms. intercept of 16.386 with a correlation coefficient of 0.997. It is interesting to examine the role of carboxyphenyl group of rhodamine B in the rotational dynamics. By assuming the coefficient of 0.97. The present result can be ascribed to the for both the zwitterionic and the cationic forms refractive index correction, which was neglected b e f ~ r e . " * ~ ~ , ~microenvironments ~ to be about the same in the same solvent, the different values of From the above results, we come to the conclusion that eq 4 might cu and j3 fitted from the nonradiative rates between these two forms be applicable to a large range of solvent viscosities and, therefore, can only be attributed to their different characteristics in response a more general polarity-dependent and viscosity-dependent exto the same micropolarity and microviscosity. DrexhageZocompression for the nonradiative rate. pared the quantum yields of the zwitterionic and cationic forms We have reexamined the data obtained from water-methanol in ethanol and attributed the greater quantum yield of the former mixtures, water-ethanol mixtures, alcohols (C3-Clo), ethylene to the negative charge at the COO-group which increases the glycol, and glycerol, by using multiple linear regression.39 The *-electron density near the remote amino groups. , T o further fitted results yield an intercept = 16.386, cu = 0.120, and fl = understand how different intramolecular forces in the zwitterionic -0.0622 as compared with j3= -0.0569 obtained from eq 2 with form (between the carboxylate ion group and the amino groups) data from low-viscosity solvents (without correction for viscosity and the cationic form (between the carboxyl group and the amino effect). The best estimate of the viscosity parameter cu from the groups) are responsible for the different rotation rates, we need composite data is very close to those determined from ethylene to take into account intermolecular interactions between the dye glycol, glycerol, and alcohols (C3-Cl0). From the multiple linear and its immediate surroundings. The intercept of the multiple regression fits, the correlation coefficient between In k,, and ETN regression fit (In C- E?/RZ") is 16.386 for the zwitterionic and is 0.96, between In k,, and In 7 is -0.54, and between In q and 18.525 for the cationic form. By assuming the constant C of both ETNis -0.30. The large correlation coefficient between In k, and forms to be about the same, we can estimate that the barrier height ETNand the small coefficient between In k, and In 7 indicate that of the zwitterionic form is 1.27 kcal/mol higher than that of the polarity effect dominates the viscosity effect for rhodamine B in cationic form in TMS. In ethanol the barrier is lowered by 1.32 these solvents. The even smaller correlation coefficient between kcal/mol for the zwitterionic form and by 0.42 kcal/mol for the In 7 and ETNindicates that there might be no significant relacationic form. However, this relative drop (0.90 kcal/mol) still tionship between them. cannot offset the E: difference (1.27 kcal/mol) so that the barrier Figure 5 shows a semilogarithmic plot of k i , (=knrWa)vs ETN height for the zwitterionic form is still higher than the cationic for the data obtained from water-methanol mixtures, waterform. In this case, the effect of solvent viscosity does not make ethanol mixtures, alcohols (C3-C10), ethylene glycol, and glycerol. a significant difference because the ratio of 7-u for the two rhoIt should be noted that without correction for viscosity effect the damine B species is essentially unity. Therefore, k,, is smaller data obtained for low-viscosity solvents (Figure 3) show a slight for the zwitterionic form due to a higher barrier and hence may curvature at high values of ETN. With this correction the curbe responsible for its comparatively larger quantum yield and vatgure is less pronounced (Figure 5 ) , indicating that the more lifetime. general expression is appropriate even for low-viscosity solvents. In order to determine the constant C and Eho in eq 4, we To correct for both solvent viscosity and solvent polarity effects, measured the quantum yield and lifetime of the zwitterionic and we can write cationic forms in ethylene glycol at a second temperature (40 "C). k 6 r = kcorV' (5) The quantum yield and lifetime of the zwitterionic form are 0.49 and 2.48 ns, respectively, and the corresponding values for the A plot of In k", vs ETN yields a slope of 2.5 X with a cationic form are 0.40 and 2.21 ns. The data from the two correlation coefficient of 8.8 X and a plot of In kkrvs In temperatures enabled us to determine E: from eq 4 using the best 7 yields a slope of 3.8 X with a correlation coefficient of fitted values of a and fl and literature values of polarity and 1.1 X lW3. Both plots show random distributions with essentially v i s ~ o s i t y .This ~ ~ ~procedure ~ yielded Eho = 6.76 kcal/mol for horizontal slopes. These plots are expected if both the polarity the zwitterionic form and Eho= 5.26 kcal/mol for the cationic and viscosity effects are corrected in the expression for kk,. form. The difference between these values (1 S O kcal/mol) is close Equation 4 can now be regarded as a more appropriate expression to that (1.27 kcal/mol) deduced from multiple regression analysis to describe the nonradiative rate of rhodamine B in a variety of solvent systems including those with low viscosities. by assuming the same C values for both forms. From the intercepts obtained from multiple regression analysis and the above Our previous results of rhodamine B in methanol-poly(ethy1ene values of Eho,C is 1.18 X lo1*s-I for the zwitterionic form and oxide) mixed solvents showed that the lifetime of rhodamine B 7.98 X 10" s-l for the cationic form. is essentially independent of viscosity up to ~ 3 cp." 0 This finding appears to differ from our present results that the rotation motion Theoretically, multiple linear regression should also reveal is dependent on both solvent polarity and solvent viscosity. The solvent effects on the nonradiative rates for the dye dissolved in apparent discrepancy may be due to the possibility that the disa solvent at various temperatures. In practice, it is simpler to
4878 The Journal of Physical Chemistry, Vol. 96, No. 12, 1992
unravel both solvent polarity and solvent viscosity effects in a constant-temperature study because the temperature factor can be ruled out. Generally, the fitted results obtained from temperature studies are expected to have larger uncertainties than thme obtained from constant-temperature studies. It is noteworthy that the polarity effect may not be pronounced in a temperature study because the variation of ETNis relatively small (e.g., AETN N 0.07 for all methanol, ethanol, and ethylene glycol between 0 and 60 oC).40 Since the viscosity changes are usually more sensitive to temperature (e.g., 2.3-fold variation for methanol, 3-fold for ethanol, and 8-fold for ethylene glycol between 0 and 60 OC),3’ the viscosity effect may become comparable with or even greater than the polarity effect in a temperature study. Finally, we would like to address the lactone + zwitterion equilibrium. Johansson and Niemi4’ did a temperature study on the fluorescence quantum yield and lifetime of rhodamine B (
