J. Phys. Chem. 1982, 86,4205-4211
systems, one should use azethoxyl, rather than doxyl, nitroxides. Acknowledgment. We are grateful to Professor Z. Luz for helpful discussions. This study was made possible in part by funds granted by the Charles H. Revson Foundation (to E.M.). The statements made and views expressed, however, are solely the responsibility of the author (E.M.). This research was also supported, in part, by NIH-NIGMS, National Research Service Award GM07932 (to M.S.B.).
Appendix In this Appendix we briefly discuss the considerations in determining the parameters needed for simulating the azethoxyl spectra, once the doxyl spectra had been simulated. We also suggest a means by which the simulations might be improved. The doxyl and azethoxyl spectra are of almost identical length, although the doxyl probe is 10-20% wider than is the azethoxyl. We might therefore expect to see some difference in N(azethoxy1) relative to N(doxy1) and, hence, in the diffusion constants. Assuming a half-length of 10 A, N = 4 gives a half-width of 2.8 A; a 10% decrease in width gives N = 4.5.14 For such a relative change in width, only R,,should be significantly affected; l4 we therefore set R,(doxyl) = R,(azetoxyl). Spectra simulated with larger values of N gave poorer fits to the azethoxyl spectra than those obtained with N = 4.5. Looking at the experimental spectra, one might think that there is a 20 "C temperature shift between the doxyl and azethoxyl spectra and that the differences in the spectra of the two types of probes is not due to a molecular tilt for the azethoxyls but, rather, due to much higher diffusion constants for the azethoxyls than for the doxyls. Such a possibility has been dismissed by the above-mentioned geometric considerations. On the other hand, a 60" molecular tilt for the azethoxyls is equivalent to the commonly assumed 0" molecular tilt for the doxyls, 60" and
4205
0" being the respective azethoxyl and doxyl molecular tilts for the all-trans conformations of the nitroxide-bearing portions of the chains. Interpretation of the spectral differences between the two types of probes by invoking a 60" molecular tilt thus seems to be the most straightforward hypothesis. Furthermore, to "erase" this tilt would require both a significant and persistent distortion of the chain and require that this distortion be induced by glycerol. This is physically untenable. The doxyl simulations are better fits to the experimental spectra than are the azethoxyl spectra. In the latter, the greatest discrepancy is the relative magnitude of the lowfield line to the central line in the incipient slow-motion spectra. Varying the tilt angle over the range 55-65" did not improve the fit. For the doxyl spectra, this problem also occurs, although to an apparently lesser extent. It has been found previously that considerable improvement of spectral fits in this region can be achieved by consideration of coupling between solvent and solute motions, e.g., by consideration of fluctuating torques, slowly relaxing local structure, or anisotropic v i s ~ o s i t y . ~ Our ~ ~ *computer ~~ programs allow us to consider, besides the parameters discussed in the text, only anisotropic viscosity which, although physically untenable for glycerol, was found to have similar spectral consequences as the other coupling mechanisms. Inclusion of such a coupling mechanism improves simulations with respect both to relative intensities of the spectral lines and to anomalous hyperfine shifts.6i23Illustrated for the 65" doxyl spectrum in Figurg 5a is the improyedAsimylationAobtainedby introducing N = 4, with N = R,,/R,, Riland R, denoting principal values of the fictitious viscosity tensor. It is very likely that N # 1 would have a similar effect on the azethoxyl spectra; unfortunately, our simulation programs do not allow us to include both anisotropic viscosity and molecular tilt. (23)J. S.Hwang, R. P. Mason, L.-P. Hwang, and J. H. Freed, J.Phys. Chem., 79,489 (1975). See, for example, Figure 9.
Effect of Viscosity and Temperature on Torsional Relaxation of Molecular Rotors Raflk 0. Loutfy' and Bradley A. Arnold Xerox Research Centre of Canada, Mississauga. Ontario, L5L lJ9 Canada (Received: Februafy 72, 1982; In Final Form: July 13, 1982)
The effect of solvent viscosity and temperature on the fluorescence quantum yield of p-(dimethylamino)benzylidenemalononitrile(1) and julolidinemalononitrile(3) has been studied in ethyl acetate, dimethyl phthalate, and glycerol. In the low-viscosity solvent, ethyl acetate, when temperature and viscosity variations are studied, a hydrodynamic model with a stick boundary condition gives an accurate and consistent description of the dynamics of the torsional motion of the probes. However, in medium- and high-viscositysolvents deviations from the hydrodynamic model are seen. In these solvents the free-volume concept was found to provide an accurate description of the solvent viscosity-temperature behavior and the probe torsional relaxation dynamics.
Introduction
The dynamics of reorientation relaxation of molecules in solution has been extensively investigated by various picosecond spectroscopic technique^.'-^ Most of the (1)T. J. Chuang and K. B. Eisenthal, Chem. Phys. Lett., 11, 368 (1971). (2) H. J. Eichler, U. Klein, and D. Langhaus, Chem. Phys. Lett., 67, 21 (1979). (3) J. R. Taylor, M. C. Adams, and W. Sibbett, Appl. Phys., 21, 13 (1979).
studies have been performed on ionic dyes in a variety of s o h n t s in order to test the validity of the Debye(4) D. Welford, W. Sibbett, and J. R. Taylor, Opt. Commun., 34,175 (1980). (5)P.F.Barbara, S. D. Rand, and P. M. Rentzepis, J.Am. Chem. Soc., 103,2156 (1981). (6)C. Tredwell and A. D. Osborne, J. Chem. Soc., Faraday Trans. 2, 76,1627 (1980). (7) R. W. Wijnaendts Van Rasandt and L. DeMaeyer, Chem. Phys. Lett., 78,219 (1981). (8)A. Von Jena and H. E. Lessing, Chem. Phys. Lett., 78,187 (1981).
0022-3654/82/2086-4205$01.25/00 1982 American Chemical Society
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The Journal of Physical Chemistry, Vol. 86, No. 21, 1982
Stokes-Einstein (DSE) hydrodynamic model. In this model the orientational relaxation time, 70r, is given by 7or = c ( ? / T ) (1) where q is the shear viscosity of the solvent and C is a geometry-dependent rotational friction coefficient of the particle. For a stick boundary condition C = 4ra3/3k, where a is a molecular hydrodynamic radius. The applicability of eq 1 to describe the dependence of 70ron q / T has been confirmed by most technique^.'^^^^^^ However, a number of exceptions have been reported. Both crystal violet and fluorescien in hydrogen-bonding solvents rotate at a much slower rate than expected from a stick boundary condition. A strong solvent attachment to the dye molecules forming a rigid complex has been suggested as the cause of the slow rotation? In high-viscosity solvents such as ethylene glycol and glycerol, deviation from the hydrodynamic prediction has been seen with all dyes studied.1,6J Generally, the rotational diffusion is found to be considerably faster than expected in these solvents. These deviations have been attributed to saturation of the retarding influence of viscosity9Jo or to specific solvent n e t w ~ r k . ' ~There ~ ~ ~ Jis~ still enough uncertainty about the competing influence of molecular structure of the rotating particles, solute-solvent and solvent-solvent interactions, and boundary conditions which calls for further experiments on a great variety of solute-solvent systems to clarify some of these problems. In particular, very little information is available on the dominant relaxation processes in high-viscosity solvents. We have chosen to study the reorientation relaxation of two neutral dyes (p(dialky1amino)benzylidenemalononitriles) with a different molecular volume in three functionally different solvents (ethyl acetate, dimethyl phthalate, and glycerol) over a wide viscosity range and as a function of temperature. Varying the ratio q / T for a single solvent by temperature change and for a series of solvents at constant temperature should assist in establishing the dominant solvent relaxation process and distinguishing between DSE diffusion and free-volume-dependent viscosity-controlled diffusion. The temperature studies will also enable the activation energy for the reorientation dynamics to be obtained and compared with the activation energy of the solvent viscosity. We have recently described a novel phenomenon associated with the effect of media rigidity on the fluorescence intensities of a series of donor-acceptor dyes, p-(dialkylamino)benzylidenemalononitriles 1-3.11 These dyes exC H2C H$C@ph
CH3
I
I
2
1
n &C
N Hr
'CN
3
hibit an exceptionally high rate for internal conversion, .=loll s-l, and this rate is viscosity dependent. The ex(9)D.H.Waldeck and G. R. Fleming, J.Phys. Chem., 85,2614(1981). (10)S.A. Rice and G. A. Kenney-Wallace, Chem. Phys., 47,161(1980). (11)R. 0.Loutfy and K. Y. Law, J. Phys. Chem., 84, 2804 (1980); Macromolecules, 14,587 (1981);R. 0.Loutfy, ibid., 14,270 (1981).
tremely fast deactivation rate of the singlet excited state of these materials was attributed to torsional re1axation.l' We have shown that environmental factors resisting the internal molecular rotation of these dyes lead to a decrease in the nonradiative decay rate, k,,, and consequently an increase in the fluorescence yield. These dyes are, therefore, excellent microscopic probes that could yield valuable information about hydrodynamic interactions in various solvents. Recently Law12reported the effect of viscosity on the fluorescence quantum yield of 2 in alcoholic solvents over a narrow viscosity range and at a constant temperature and attributed the effect to molecular rotation of surrounding solvent molecules. In this work, the dependence of the fluorescence yield of 1 and 3 upon solvent viscosity in aprotic and protic solvents and temperature has been investigated to study their photochemical dynamics, with particular emphasis on excited-state conformational relaxation. It is believed that these compounds exhibit viscosity-dependent torsional motion," which permits us to explore ultrafast solvent relaxation processes.
Experimental Section Materials. p(Dimethy1amino)benzylidenemalononitrile (1) and julolidinemalononitrile (3) were purified as described previously." Ethyl acetate and dimethyl phthalate were analyzed and reagent grade, respectively, from Baker and glycerol was certified grade from Fisher. All solvents were used without further purification. General Techniques. The measurements were done at relatively low dye concentration (2 X mol/L) to avoid aggregation and dimer formation. Absorption spectra were recorded with a Cary 17 spectrophotometer. Fluorescence spectra were taken on a Perkin-Elmer MPF-4 spectrofluorimeter which was equipped with a differential corrected spectra unit (DCSU-2). Fluorescence quantum yields were determined by comparison with the fluorescence of 3 in ethyl acetate (@f = 3.0 X which has been calibrated with a fluorescence standard GG21 (@f = 0.494, from Hellma) as previously described." The optical densities of all the samples studied were 10.8 at the absorption maxima. For the temperature-dependent fluorescence studies, measurements were carried out by using a specially designed electrically heated copper block which was fitted into the sample compartment. The temperature of the copper block was controlled to within f O . l "C by using a temperature controller unit RKc.DB-4,while the sample temperature was monitored separately by using a Bailey thermocouple probe immersed into the solution and connected to a Bailey instrument digital meter (Model BAT-12). The samples were excited with 430-nm light and the relative fluorescence yield change was monitored at the emission maximum. The viscosities of the solvents were determined by using capillary-type viscometers, Cannon Obbelhude dilutiontype viscometers, which were submerged in a variabletemperature oil bath. This type of measurement yields the kinematic viscosity which is density dependent. We measured the densities of the solvents at different temperatures (by immersing the viscometer in a constanttemperature bath) and calculated the thermal expansion coefficient of each solvent in order to obtain the dynamic viscosity (q). The viscosities of glycerol between 0 and 90 "C were also measured by the cone-and-plate rheometric method and the results were in excelleiit agreement with the above results. ~~~~
~~~
(12)K.Y.Law, Chem. Phys. Lett., 75,545 (1980);Photochem. Photobiol., 33, 799 (1981).
Torsional Relaxation of Molecular Rotors
The Journal of Physical Chemistry, Vol. 86,No. 21, 1982
4207
TABLE I: Absorption and Fluorescence Data of 1 and 3 in Organic Solvents at 25 "C dye 1 solvent
Il,a
ethyl acetate dimethyl phthalate glycerol
cp
fa
0.44 14 954
6.0 8.5 42.5
~m,
423 431 442
dye 3
a,/10-~ , , A
hFb
469 477 487
0.89 2.5 21.0
b
447 464 469
kFb
af/10-3
488 500 508
3.0 11.0 100.0
a R. C. Weast, "CRC Handbook of Chemistry and Physics", 60th ed., CRC Press, Boca Raton, FL, 1980. accuracy r 0 . 2 nm.
0.6
In nm,
FLUORESCENCE
-
CN in Ethylacetate
10
-
Tor (psec)
400
450
500
550
WAVELENGTH (nm)
Flgure 1. Absorption and fluorescence emission spectra of 1 and 3 in glycerol at room temperature.
Results Absorption and Fluorescence. Figure 1 displays the absorption and emission spectra of 1 and 3 in glycerol at 25 "C. Both dyes exhibit an intense (em= = 5 X lo4 M-' cm-') absorption band in the blue and a weak fluorescence emission band in the green region of the spectrum. The widths of the absorption and emission bands were found to be the same in all solvents and at all temperatures. However, the absorption and fluorescence maxima of 3 are always shifted to the red by about 1300 and 850 cm-', respectively, compared to 1. This shift is attributed to the lower ionization potential of 3. The absorption and fluorescence spectra data of I and 3 in the solvent studied at 25 "C are given in Table I. The absorption maximum (A-) and fluorescence maximum (A,) of both 1 and 3 shift to longer wavelength by -20 nm when the dielectric constant of the solvent increases from 6 (ethyl acetate) to 42.5 (glycerol), consistent with our earlier conclusion that the SIstate is a T,T* with considerable charge-transfer character." It has been shown previously that the quantum yield of fluorescence, af, of the (dialky1amino)benzylidenemalononitriles is not sensitive to the dielectric constant of the medium;"J2 however, it is very sensitive to the viscosity. Since the intrinsic internal rotation time, qro,of these probes is much smaller (110-12 s) than the orientation relaxation time, T,,, of the surrounding media, thus, the internal rotation time, rir,is predominantly determined by r,, (i.e., rir = r,,). Therefore, the orientation relaxation times, io,, of 1 and 3 in the various solvents can thus be obtained from the measured quantum yield of fluorescence, an via 701
=
TI[@f/(@O
-
@dl
(2)
where a0is the limiting fluorescence quantum yield attainable when internal rotation of the dye has ceased and r, is the intrinsic radiative lifetime of the excited state. The limiting fluorescence quantum yield, a0,for 1 and 3 were found by experiments at 77 K to approach unity and 7,'s measured by using single-photon counting technique a t 77 K were 3.5 and 3.6 ns, respectively.
1.0
0.5 103qlT
1.5
cP.K-'
Flgure 2. Plots of Orientation relaxatlon times ( T ~against ) the viscosity over temperature ( q l T ) for dyes 1 and 3 in ethyl acetate.
Effect of Solvents. A nonlinear dependence of rO1of 1 and 3 on solvent viscosity at constant temperature was seen. The trend is for T,, to be smaller than expected by the DSE hydrodynamic model. At 25 "C in glycerol T,, is 100 times smaller and in dimethyl phthalate it is 10 times smaller than the hydrodynamic predictions. The deviation is found to increase with increasing temperature. It is apparent from these results that there is no simple relation between rarand 7 of the series of solvents studied and an obvious saturation effect is observed. Nonetheless, a plot of log T,, or log @f (T,, = .,af) against log q gives a reasonably good straight line with a slope much less than unity. The slopes of the linear region are 0.53 and 0.51 for 1 and 3, respectively, which are less than the value of 0.62 found for 2 in alcoholic solvents.12 In addition, the slope (exponent) was found to decrease with an increase in measurement temperature. In a theoretical treatment, Forster and Hoffmann13 derived the equation af = B# (where x is between 'I3 and 2/3) and produced a good fit, to this function, of the fluorescence quantum yield data of the triphenylmethane dye crystal violet using x = 2/3. This 2 / 3 power viscosity-dependent afhas also been reported for carbocyanine dyes314and the rhodamine dye fast acid violet 2Ra6 These results suggest a free-volume-dependent relaxation process rather than DSE diffusion in the high-viscosity region. Temperature Effects. Low-Viscosity Solvent. The variation of T,, as a function of 7 1 T for the fluorescence probes 1 and 3 in ethyl acetate is shown in Figure 2. The results displayed in Figure 2 show that the variation of T,, with q / T is essentially linear within the range of experimental data. The linearity of rol with respect to TIT observed here is consistent with simple hydrodynamic (13) Th.Forster and G. Hoffmann, 2. Phys. Chem. (Frankfurt am Main), 75, 63 (1971).
Loutfy and Arnold
The Journal of Fhysical Chemistry, Vol. 86, No. 21, 1982
4200
[ "/T)"2 Ethylacetate
Dimethylphthalate
Glycerol
,./*
10-1
,'
9
9
w
a
3 $
7
10-2
4
0
6
Y
70,
5
(psec)
z 10-3
4
5a
3
U
2 10.~ 1( I
1
0
20
10
'1
T (10-3cP/K)
('IT j 2 ] 1
2
(
I'
5 1''
5
3
'
a
10
/
1
2 " T (cP K l
3
4
5 'I
I
10-1
I
1
100
10'
'
15
/ i160,
Figure 5. Dependence of the fluorescence quantum yield of 1 and 3 on DIT in (0)ethyl acetate, (0) dimethyl phthalate, and (0)glycerol.
consistent data and provide less ambiguous tests of hydrodynamic predictions. Activation Energy for Solvent Viscosity. It is wellknown that the mobility (7-l) of many solvents exhibits Arrhenius-type behavior, so that 7-l
0
, 10-2
'i (r) cPK-'
40
30
Figure 3. Dependence of Orientation relaxation times (7w)of 1 and 3 on v l T (0,A) and (v/T)"* (0, A) in dimethyl phthalate.
80
I
10
15
T (cP K 'I
Figure 4. Orientation relaxation times (a) of 1 and (b) of 3 in glycerol as a functlon of viscosity over temperature in the range of 10-130 OC.
theories which also predict that the slope, C, should increase with increasing molecular size. The slopes of the r, against q / T plots shown in Figure 2 do in fact increase with increasing the size of the rotating phenyl group. A least-squares analysis of the data provided slopes of 2350 and 7270 ps K/cP for 1 and 3, respectively, and intercepts near zero as expected from relation 1. These values of C are in good agreement with those computed on the basis of stick boundary conditions using hydrodynamic radii of 2.36 and 3.43 8, for 1 and 3, respectively. These hydrodynamic radii are in satisfactory agreement with the molecular radii of these dyes estimated from molecular models. Medium- and High- Viscosity Solvents. The orientation relaxation time, T ~of~ 1 ,and 3 in dimethyl phthalate and glycerol deviates from the linear viscosity dependence as seen in Figures 3 and 4,respectively. Nevertheless, for a given solvent, plots of 70r against (q/Tlxgive reasonably good straight lines, using x = 1 / 2 for dimethyl phthalate and 3/4 for glycerol, indicating agreement with the Forster and Hoffmann scheme. Figure 5 shows the dependence of the quantum yield of fluorescence of dyes 1 and 3 on q/T for the three solvents studied. The results displayed in Figure 5 show that +,p((q/W with x = 1in ethyl acetate, x = '/2 in dimethyl phthalate, and x = 3 / 4 in glycerol for temperatures between 10 and 95 "C. For a given dye, the data from each solvent lie on a separate curve. This is due to the large differences in the activation energies of the solvent viscosity. I t seems clear from these results that studies of viscosity-dependent phenomena in a series of different solvents at a constant temperature do not provide an unambiguous method of testing hydrodynamic predictions. The temperature-variation studies give more
= 70-l exp(-Wq)/kT)
(3)
Figure 6, a and b, shows plots of In 71-l vs. 1/T for ethyl acetate and dimethyl phthalate. Excellent straight lines are obtained for these solvents over the temperature range of interest. A least-squares analysis of the data provided activation energies of 1.64 and 5.5 kcal/mol for ethyl acetate and dimethyl phthalate, respectively. The plot of In 9-l vs. 1/T for glycerol is nonlinear (see Figure 6c). The observed curvature in the Arrhenius plot of glycerol suggests that the dominant relaxation mechanism is not a simple thermally activated process, which would exhibit a linear Arrhenius plot as in the case of ethyl acetate or dimethyl phthalate. I t seems that a major change in the physical structure of glycerol occurs at high temperatures >60 OC. The slope of the linear portion of the In q-' vs. 1/T plot for glycerol gives an activation energy of 14.9 kcal/mol. Activation Energy for the Rate of Orientation Relaxation. In their study of the reorientation dynamics of 3,3'-diethyloxadicarbocyanine iodide in alcoholic solvents, Waldeck and Flemingg combined eq 1 and 2 and derived the following relation for a single exponential decay with a stick hydrodynamics: T kor = - exp(-aE(d/kTl (4) CDO Thus, plots of In (kor/T)vs. 1/T should be linear with slope AE(7)/k. Figure 6a-c shows such plots for 1 and 3 in ethyl acetate and dimethyl phthalate and glycerol, respectively. The data for these solvents studied are listed in Table 11. The orientation relaxation rate activation energy, hE(k,,), parallels the viscosity activation energy and is essentially independent of the size of the probe only in ethyl acetate. For dimethyl phthalate and glycerol AE!(kor)is much less (3-5 kcal) than A E ( q ) and also dependent on the fluorescent probe size. For dye 3 AE(kor)is 1kcal larger than hE(ko,) of the smaller dye 1 in both dimethyl phthalate and glycerol. In a study of the reorientation relaxation of rhodamine 6G in glycerol, Rice and Kenney-Wallacelo similarly found that AE(kor)I2.15 kcal/mol as compared with AE(q) of 16.2 kcal/mol. It was suggested that the solute is relatively unhindered in its rotation within a
-
The Journal of Physical Chemistry, Vol. 86, No. 21, 1982 4209
Torsional Relaxation of Molecular Rotors
m
100
a. Ethylacefate
io9
c.Glycerol
io9 10-2
3.0
107
10-2
108
2.5
-
3.5
2.5
3.0
3.5
1 0 0 0 / T (K-')
Figure 6. Plots of In q-' vs. l/Tfor (a) ethyl acetate, (b) dimethyl phthalate, and (c) glycerol and plots of In ( k , / T ) vs. l/Tfor dyes 1 and 3 in
the three solvents. TABLE 11: Activation Energies for Internal-Rotation Rate ( A E (kor)) and Solvent Viscosity ( A E ( q ) ) AE
solvent
a
In kcal/mol.
dye 3
dye 1
1.9 2.4 9.9Bb
ethyl acetate dimethyl phthalate glycerol
A , s-l K-l
(kO#
dye 1
dye 3
2.7 X 10''' 2.2 x 1O'O 6.8 X 10l4
4.5 x 109 1.8 x 109 8.9 x 10l4
AE(q)'
1.64 5.5 14.gb
1.61 3.24 10.96b
For temperatures between 1 0 and 60 " C .
TABLE 111: Effect of Viscosity and Temperature on the Fluorescence Quantum Yield of 1
TABLE IV: Effect of Viscosity and Temperature on the Fluorescence Quantum Yield o f 3 Glycerol
Glycerol
T,K 296.7 308.0 319.7 330.3 341.2 351.4 358.8 366.3
q , CP @f/lO-' T, K 1040 2.1 372.3 1.1 377.8 420 0.6 381.9 173 95 0.39 387.3 54 0.27 392.2 34 0.21 397.6 25 0.17 402.3 19 0.15
q , CP
@ f/
10-2
T,K
15 13 12 10 8.4 7.3 6.5
0.14 0.13 0.125 0.12 0.115 0.11 0.10
q , CP
~ ~ ~ 0 - 3
277.3 283.4 288.7 294.8 299 303.7 309.3 313.8 315.7
Dimethyl Phthalate
T, K
q , CP
@f/10-3
297.5 304.3 320.9 333.1 340.8
13.7 8.5 5.1 4.1 3.5
2.5 2.0 1.6 1.4 12
T, K 349.7 358.0 368.6 378.2
2.9 2.5 2.0 1.8
1.1 1.0 0.90 0.83
Ethyl Acetate
T,K
q , CP
295.2 298.0 301.4 312.7
0.44 0.43 0.413 0.373
@ f / i o - 4 T, K 9.5 8.9 8.3 7.1
329.7 340.6 348.8
q , CP
0.328 0.301 0.286
~ ~ ~ 0 - 4
@f
0.48 0.30 0.20 0.13 0 10 0.075 0.055 0.044 0.038
318.7 324.3 329.2 337.3 346.0 351.6 360.8 371.0 381.0
186 143 98 65 44 34 24 16 12
0.034 0.027 0.022 0.015 0.011 0.0094 0.007 0.0048 0.0044
Dimethyl Phthalate
T,K
q , CP
@f/lO-'
T, K
296.6 306.3 314.0 321.0 328.0 335.8 343.0
14.3 9.7 7.3 5.8 4.8 3.9 3.3
1.2 0.95 0.80 0.70 0.62 0.55 0.49
351.9 359.5 367.1 375.5 383.0 390.2 396.4
q , CP @ f / 1 O W 2
2.8 2.4 2.0 1.8 1.6 1.4 1.3
0.44 0.40 0.37 0.34 0.32 0.30 0.28
Ethyl Acetate
5.9 5.1 4.9
T,K 295.0 298.0 303.2 313.9 320.0
solvent cage and that simple hydrodynamics was therefore inappropriate.
Discussion The fluorescence quantum yields (af)obtained from dye 1 and 3 in various solvents as a function of viscosity and temperature are summarized in Tables I11 and IV, respectively. The lifetime of SIof 3 increased from 11 ps in low-viscosity, room-temperature ethyl acetate to 44 ps in dimethyl phthalate to almost 500 ps in glycerol and approaches the radiative lifetime of 3600 ps in rigid glasses. A solvent-dependent, excited-state relaxation process must therefore be proposed. Since these dyes exhibit very little triplet yields, the main pathway for nonradiative deactivation of the excited state is internal conversion. The
rl, cp 7100 3500 2000 1200 850 590 380 250 225
- 3 q , CP ~ ~ 1 1 0 - 3 rl cp ~ ~ ~ 0T,K 0.442 3.1 324.9 0.34 2.3 0.43 3.0 329.9 0.327 2.1 0.40 2.8 0.317 2.0 334.2 0.368 2.5 338.4 0.306 1.9 0.353 2.4 340.5 0.302 1.8
absence of change in fluorescence emission maximum between room temperature and 77 K and the approach of afto unity at 77 K indicate that the emitting states must be those excited states which maintain a ground-state conformation. Previous work11J2has shown that for molecular rotors such as l and 3 torsional motion in the excited state is capable of inducing radiationless decay, S1 S., It has also been suggested on the basis of substantial increases in the fluorescence quantum yield in highly viscous solvents, polymers, and frozen glasses that the torsional motion responsible for inducing radiationless decay is hindered by the viscous drag of the solvent.
-
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Loutfy and Arnold
The Journal of Physical Chemistry, Vol. 86,No. 21, 1982
Fbtation of the aryl group in the excited state is considered the rate-determining step, leading to rapid internal conversion to the ground state. The effect of solvent on the torsional relaxation of molecular rotors encompasses a number of factors, namely, the motion of the solvent molecules out of the path of the rotating group, the strength and rate of breaking of solute-solvent vs. solvent-solvent interactions, and the size of the gaps in the solvent relative to the size of the rotating group. Past studies of the torsional relaxation of c a r b ~ c y a n i n etri,~~~ phenyl~nethane,'~ and rhodamine dyes6 in a series of solvents have always been interpreted in terms of the Forster and Hoffmann scheme. However, recently Waldeck and Fleming have shown that, when temperature and viscosity variations are studied in a single solvent, hydrodynamics with a stick boundary condition gives an accurate description of carbocyanine dye torsional relaxation. From our viscosity and temperature studies on the torsional relaxation of dyes 1 and 3 we will attempt to describe the various relaxation processes encountered in low-, mediumand high-viscosity solvents. Low-Viscosity Solvents. The linearity of r,, with respect to qlT observed for 1 and 3 in ethyl acetate is consistent with simple hydrodynamic theories. The intercepts were very close to zero and the slope increased with the molecular size of the probe as should be the case for simple DSE hydrodynamics. In addition, the torsional relaxation rate's activation energies, hE(k,,), paralleled the solvent viscosity activation energy AE(q);see Table 11. It is evident from these results that for low-viscosity solvents (q < 2 cP) simple hydrodynamics gives a remarkably accurate description of the torsional motion dynamics of dyes l and 3 and that the macroscopic viscosity is an appropriate measure of the friction on the rotating probe molecule. Medium- and High-Viscosity Solvents. Moderate to severe deviation from the hydrodynamic prediction is seen with dimethyl phthalate and glycerol as solvent. This type of behavior has previously been attributed to a saturation of the retarding influence of the solventgJOviscosity or to specific solvent netw0rk.l~~ This phenomena occurs when the solvent relaxation becomes too slow; at such point, free-volume availability becomes the controlling factor in the torsional relaxation of the probe. The importance of the free volume of the solvent on the molecular relaxation process of the S1states has been clearly demonstrated in the study of af of 1-3 in the polymerization of methyl methacry1ate.l' The temperature dependence of viscosity, q ( T ) , of many simple, small-molecule liquids was shown to arise largely from its dependence on free volume,14-16 in a manner analogous to the use of free-volume concepts in accommodating ~ ( 7 'for ) p~lymers.'~J*For these systems, the free-volume fraction shrinks with decreasing temperature to about 0.025 at the glass transition temperature, Tg,and q ( T ) is correlated in terms of free-volume expansion be(14)A. K.Doolittle, J. Appl. Phys., 22, 1471 (1951);23, 236 (1952). (15)M. L. Williams, R. F. Landel, and J. D. Ferry, J.Am. Chem. SOC., 77,3701 (1955). (16)J. H. Hildebrand and R. H. Lamoreaux, J.Phys. Chem.,77,1471 (1973). (17)A. Bondi, 'Physical Properties of Molecular Crystals, Liquids and Glasses", Wiley, New York, 1968. (18)J. D. Ferry, "ViscoelasticProperties of Polymers",2nd ed.,Wiley, New York, 1970. (19)T.G. Fox, Jr., and P. J. Flory, J. Am. Chem. SOC.,70,2384(1948); J.Polym. Sci., 14, 315 (1954). (20)F.Bueche, J. Chem. Phys., 21, 1850 (1953);'Physical Properties of Polymers", Interscience, New York, 1962,Chapter 5. (21)H. H. Meyer and J. D. Ferry, Trans. SOC.Rheol., 9,343 (1965). (22)A. J. Barlow, J. Lamb, and A. J. Matheson, Proc. R. SOC.London. Ser. A, 292, 322 (1966)
I
-14.5
-05 1 F F
. .
u 150
200
-
250
300
(T-Tg)'K
u
-10.5 b. Glycerol
80
120
160
200
(T-Tg) OK
Flgure 7. Temperature dependence of viscosity of q for (a) dimethyl phthalate and (b) glycerol. Each q(T) curve was independently fitted by the WLF model, eq 8, as represented by the solid line.
tween T gand roughly T g+ 100 K.23 The dependence of free volume on temperature is taken by several author^^^^^ to be the difference between the thermal expansion coefficient, a,above and below the glass transition temperature. Thus
f = f g + a(T - T,)
(5)
where f and f g are the free-volume fractions at given temperatures T and Tg,respectively. An expression of liquid viscosity in terms of the free volume of the solvent has been derived by D~olittle:'~ 7 =
A expVo/f)
(6)
Here A depends on the nature of the liquid, and f, and f are the occupied and free-volume fractions, respectively. Combination of eq 5 and 6 and assuming that f , >> f gives15 log q / q g = -(1/2.303fg)(T- T g ) / [ V g / a+) ( T - T,)] (7) Taking the constants f = 0.025 and a = 4.8 X deg-l leads to the well-known h F equation for the temperature dependence of viscosity of polymers and glass-forming liquids: log q / q g = -17.44(T - T,)/[51.6 + ( T - T,)]
(8)
A limited number of small-molecule liquids have been analyzed by this m e t h ~ d . ' ~ pThe ~ ~ -applicability ~~ of the glass transition model developed for polymers-invoking, free-volume concepts to correlate q ( T ) for dimethyl phthalate and glycerol was tested. Results of the q / q g vs. T - T, correlations are shown in Figure 7. Each set of q ( T ) data was fitted to eq 8 by least squares to yield the corresponding values of Tgand q . Dimethyl phthalate gives T g = 108 K and qg = 6 X lo1! CPwhile glycerol gives T g = 187 K and qg = 6.5 X 1014cP. The WLF prediction for the T dependence of q for dimethyl phthalate and glycerol (23)T.Soesanto and M. C. Williams, J. Phys. Chem., 86,3338(1981).
The Journal of Physical Chemistry, Vol. 86, No. 21, 1982 4211
Torsional Relaxation of Molecular Rotors
temperature dependence of viscosity will relate to specific details of solvent molecular structure rather than the free volume. The slopes of the In Qf against l / f plots shown in Figure 8 for the probes 1 and 3 were 0.43 and 0.51 in dimethyl phthalate and 0.69 and 0.76 in glycerol, respectively. The slope is consistently greater for the larger probe. Combining eq 6 and 11,the relationship between the dye fluorescence quantum yield and viscosity can be derived as @f
10-41
I
I
I
I
I
I
I
8
9
10
11
12
13
14
15
16
l/f
Figure 8. Dependence of the fluorescence quantum yield, a,, of 1 and 3 on the freevolume fraction of the solvent, (A)dimethyl phthalate and (0)glycerol.
as seen in Figure 7 is entirely satisfactory. This tends to reinforce the general principle of utilizing free volume in evaluation of viscosity-dependent relaxation processes. Therefore, in medium- and high-viscosity solvents when the WLF equation is applicable the rotation-dependent, nonradiative decay rate, k,, should be linked to the media free-volume fraction, f according to
k, = kmo exp(-xfo/f)
(9)
Here kn2 is the free-rotor reorientation rate and x is a constant for the particular probe. The nonradiative decay rate, k,,, is related to the fluorescence yield according to knr
= kr(l/@f- 1)
(10)
Equation 9 can be substituted into eq 10 to yield the fluorescence-dependent free volume Qf
= (kr/k,2) exp(xf,/f)
(11)
Plotting In af vs. l / f should yield a straight line with a slope equal to xf,. Figure 8 shows such plots for dyes 1 and 3 in both dimethyl phthalate and glycerol. The free volume of the solvents was calculated from eq 5 using f = 0.025, a(dimethy1 phthalate) = 3.5 X deg-', and a(glycero1)= 4.4 X lo4 deg-'.I5 The linearity of In Qf with respect to l / f observed here supports the validity of the free-volume concepts as the controlling factor of torsional motion of excited states and also as the dominant determinant of the q ( T ) behavior of these solvents. Deviations from the WLF model are expected at high temperature when the free volume is plentiful. Indeed, a slight deviation can be seen for dye l in glycerol at high temperature. This must be expected, since the free volume available for molecular relaxation will be large; in addition, for ordinary liquids far above their glass transition temperature the
= Bh/T)"
(12)
where B = (k,/kmo)(T/A)".Plots of log Qf vs. log q / T were shown in Figure 5. The slopes of these plots give the exponent x , which has been found to agree extremely well with those obtained above. The above relationships indicate that the fluorescence yield of dyes which exhibit rotation-dependent, nonradiative decay will increase with decreased free volume and increase of viscosity of the solvent. The viscosity dependence of afarises from the dependence of q on the free volume for solvent systems whose free volume is small enough to cause high viscosity. For low-viscosity solvents or at very high temperatures much above the solvent glass transition temperature, when free volume is plentiful, the free-volume concept becomes inappr~priate.~J~ In the smaller, lower-viscosity solvent studied in this work, the results show that simple hydrodynamics gives a remarkably accurate description of the torsional motion dynamics of the molecular rotors 1 and 3 and that the macroscopic viscosity is an appropriate measure of the friction on the rotating probe molecule. However, in medium- and high-viscosity solvents the free-volume concept was found to describe accurately the torsional relaxation of the probe, and the WLF equation, based on free-volume concepts and used widely with polymers, is found to characterize the temperature dependence of solvent viscosity, q ( T ) , extremely well. In its full form, the torsional relaxation rate, k,,, of molecular rotors can be derived by combining eq 1,9, and 11 to give k,,h/T) = A
+ B(v/T)'-"
(13)
The quantity k,,*(q/T) should be independent of the solvent viscosity if the DSE hydrodynamic model is operative and should depend on the viscosity to a power of 1- x if the free volume is a controlling factor. Indeed, the product of k,, and q/T is found to be independent of viscosity for 1 and 3 in ethyl acetate and dependent on viscosity to a power of -0.5 in dimethyl phthalate and to a power of -0.255 in glycerol.
Conclusions We have used the SIstate of two neutral molecular rotors with different molecular sizes to study the dynamics of the torsional motion in a series of solvents as a function of viscosity and temperature. It was shown that studies of viscosity-dependent phenomena in a series of different solvents at a constant temperature do not yield an unambiguous method of testing the solvent relaxation mechanism, in agreement with previous observations on other large molecular dye systems. On the other hand, the temperature-variation studies gave more consistent data and should provide a less ambiguous test of the dominant solvent relaxation mechanism.
