J. Phys. Chem. 1992, 96, 190-194
190
pendence of Gs(t)is conveniently detected by measuring the excitation anisotropy r,. The excitation anisotropy of TBPe at high reduced concentrations shows a wavelength dependence over the first vibronic band a t all temperatures. By the red edge of the absorption spectrum there is a pronounced increase of the excitation anisotropy. By the blue edge, and over the higher vibronic bands, r,(X) varies much less, although small oscillations can be detected. The temperature dependence of these oscillations is small. A careful examination shows that r,(h) is slightly larger on the red edge of every vibronic band. In our determination of r(t) we excited the second vibronic band, where the value of r, is equal to the average value of r,(A). These observations and the broad bandwidth of the excitation pulse used exclude dispersive energy migration as being the explanation for the observed increase of K below 250 K. More likely explanations are a change of S and/or a spatial-orientational correlation associated with the phase transition. (27) Weber, G.; Shinitzky, M. Proc. Natl. Acad. Sci. U.S.A. 1970,65, 823. (28) Marcus, A. H.; Fayer, M. D. J . Chem. Phys. 1991, 94, 5622.
Acknowledgment. We gratefully acknowledge the computer assistance of Bosse Medhage. We are indebted to Mrs. Eva VikstrBm for skillful technical assistance. This work was supported by the Swedish Natural Science Research Council (Ku8676-301). Appendix
Finally, the influence of the excluded volume around the initially excited donor molecule has been investigated. Assume that energy transfer occurs in a 2D surface of infinite size and that the excluded volume is characterized by a radius of Re. The time evolution of the excitation probability of the initial molecule reads In G;d,e(t)= -2apX-’Lm(1 - exp[-Xw(r)t])r dr = c
- ~ ~ - * / 3 ( t / ~ ) 1 / 3 [ r ( 2 / -3 ) (7(2/3,w/R3 + [1 - ~ ~ ~ ( - w / R ~ ) l R ~ (A7) w-~’~~l
- (;S2d,e(t)I 0.01 we find that Re I 0.27& For the case of (;Sa(?) for DD transfer and Re I0.24Ro for DT. Registry No. TBPe, 80663-92-9; DOPC, 4235-95-4.
Holographic Grating Relaxation Studies of Photoprocesses of Azobenzenes in Polymer Hosts C. H. Wang* and J. L. Xia Department of Chemistry, University of Nebraska, Lincoln, Nebraska 68588-0304 (Received: April 15, 1991; In Final Form: July 25, 1991)
Laser-induced holographic grating relaxation spectroscopy is used to investigate the lifetime and diffusion processes of azobenzene, methyl red, and methyl yellow in several amorphous polymer matrices. The lifetime associated with the cis-trans isomerization of azobenzene is found to be significantly lengthened by the presence of a small amount of toluene in the azo/polymer system. The activation energy associated with the lifetime of the azo dye is found to be correlated with the steric hindrance of the side groups attached to the azo linkage.
Introduction
Laser-induced holographic grating relaxation (HGR) provides a low-background, sensitive detection technique for investigating dynamic processes in condensed matter. The technique involves with first inducing a transient grating by two coherent laser beams (the writing beams) and then probing the state of the grating by diffraction of another laser beam (the reading beam). The transient diffraction signal contains information about the time-dependent change and the transport properties of the sample. A change of the optical refractive index or adsorption coefficient can be detected by using this technique.] as small as Several types of photochromous dyes have been used as dynamic probes in the HGR experiment. Nonreversible diketone dyes have been extensively used in this laboratory for the measurement of the mutual diffusion coefficient in the amorphous dye/polymer system.* We are concerned in this paper with the HGR study of reversible azobenzene derivatives in several amorphous polymer hats. The photochromous properties of the azobenzene derivatives are associated with the trans-cis isomerization through the azo bond.3 The photochromous property of the azo dye is used to generate the optical grating. Rondelez et al.4 were the first to apply the HGR technique to study the photoprocesses of methyl (1) Either, H.; Sale, G.;Stall, H. J. Appl. Phys. 1973, 44, 5383. (2) See, for example: Zhang, J.; Wang, C. H. Macromolecules 1987, 20, 2296. (3) Zimmerman, G.; Chow, L. Y.; Paik, U. J. J . Am. Chem. SOC.1958, 80, 3258. Ross, D. L.; Blanc, J. In Phofochromism Techniques of Chemistry; Vol. 3, Brown, G . H., Ed.; Wiley-Interscience: New York, 1971; Vol. 3. (4) Rondelez, F.; Hervet, H.; Urbach, W. Chem. Phys. Leu. 1978,53,138. Hervet, H.; Urbach, W.; Rondelez, F. J . Chem. Phys. 1978, 68, 2725.
0022-3654/92/2096-190$03.00/0
red (MR) in a polymer glass and in liquid crystals. Wesson et al. used M R to investigate the dynamics of polymer gels.5 Gong et al. reported the HGR study of the M R lifetime in poly(methy1 methacrylate) (PMMA) and in polystyrene (PS).6 Lodge et aL7+ used the H G R technique to investigate translational diffusion processes of azobenzene (AB), methyl red (MR), and methyl yellow (MY) in PS/toluene and in poly(viny1 acetate) (PVAc)/toluene solutions. Xia et al. studied the tracer diffusion coefficient of methyl red in poly(ethy1ene glycol).l0 When used as the diffusion probe in the HGR experiment, unlike the nonreversible diketone dyes, the azo dye is complicated by the finite lifetime associated with the cis-trans isomerization process. To obtain reliable diffusion data, the lifetime associated with the cis to trans isomerization must be considered, and careful measurements at several crossing angles are needed for separating the lifetime effect from diffusion. In the study of the tracer diffusion coefficients of azo dyes in various amorphous polymers, we have determined the lifetime of the cis azobenzene in bulk PVAc at 23 OC to be 92 s; this is in contrast to the lifetime of about lo4 s, reported by Huang et al. (5) Wesson, J. H.; Takezoe, H.; Yu, H.; Chen, S. P. J . Appl. Phys. 1982, 53, 6513. (6) Gong, S. S.; Christensen, D.; Zhang, J.; Wang, C. H. J. Phys. Chem. 1987, 91, 4505. (7) Lee, J . A,; Lodge, T. P. J . Phys. Chem. 1987, 91, 5546. (8) Lodge, T. P.; Lee, J. A. and Frick, T. S. J . Polym. Sci., Part E. Polym. Phys. 1990, 28, 2607. (9) Frick, T. S.; Huang, W. J.; Tirrell, M.; Lodge, T. P. J . Polym. Sci., Part E. Polym. Phys. 1990, 28, 2629. (10) Xia, J . L.; Gong, S. S . ; Wan& C. H. J . Phys. Chem. 1987, 91, 5805.
0 1992 American Chemical Society
Photoprocesses of Azobenzenes in the PVAc/toluene solution a t 35 O C . I I This suggests that, by adding toluene to bulk PVAc, the lifetime of cis-AB is lengthened by more than a 100-fold compared with the value in the pure bulk state. To ascertain that the two experimental results are not in contradiction, we have carried out experiments to examine the effect of adding toluene to PVAc on the H G R intensity curve. In this paper we report the results of such studies. In addition, we have also studied the temperature dependence of the cis-trans isomerization process of azobenzene (AB), methyl red (MR), and methyl yellow (MY) in polystyrene (PS) and in poly(methy1 methacrylate) (PMMA) to obtain the activation energy. We have also found that the activation energy is related to the torsional angle the azo linkage with respect to the phenyl rings. Experimental Section
PMMA (Mw= 200000, T = 107 "C) and PS (Mw= 300000, Ts = 100 "C) were purchased from Aldrich Chemical Co. PVAc with a molecular weight of 35 000 was purchased from Polysciences, Inc. Polymers were washed to remove any plasticizer that was added in the manufacturing process. This purification step is very important, as the presence of small amounts of additives in the polymer can cause the diffusion coefficient to increase several 100-fold.I2 The sample used in the experiment was prepared first by mixing approximately 0.2% wt of the azo dye (MR, MY, or AB) with the dried polymer powder. To investigate the effect of additives, we also added different amounts of toluene in PVAc containing AB. Since the lifetime is very sensitive to a trace amount of toluene, to obtain reliable concentration data, we used a large amount of the PVAc. Test tubes containing a desirable amount of the samples were sealed under the nitrogen atmosphere and then placed in an oven, set at the temperature about 50 O C above the glass transition temperature of the polymer. The sample became homogeneous after several days of heating and annealing in the oven. The homogeneous sample was cooled to room temperature and then cut to a 0.5 mm thick disk. The sample disk bordered by a Teflon spacer was sandwiched between two optical quality glass plates. The whole sample assembly was mounted in a specially designed copper holder which was placed in a temperature-controlled oven with glass windows to permit the transmission of laser beams. After thermal equilibrium was reached, a holographic grating was induced by crossing two equal intensity coherent beams from an argon ion laser operating at wavelength X = 488.0 nm. The crossing angle was varied from 3.6O to 15'. The optical setup employed in the experiment was discussed in ref 10. To ascertain the homogeneity of the sample, the holographic gratings were written at several sample locations. All gratings yield similar relaxation data, indicating that dyes and additive molecules are uniformly mixed in the polymer. Holographic Grating Relaxation and Photoprocesses. Adding the azo dye to the polymer changes the background refractive index of the polymer no to n. Since the concentration of the azo dyes is small, 6n (= n - no)is assumed to be proportional to the concentration of the azo molecules. Upon the interaction of the sample with the laser beams, 6n becomes nonuniform and is a periodic function of position. The photochemical reaction gives rise to a spatial variation of the trans and cis isomers of the azobenzene molecules. Mutual diffusion takes place during and after the photochemical process. Diffusion and the thermal-activated process that reverts cis to trans isomer cause the concentration of trans and cis isomers to be time dependent. The change of the azobenzene concentration imposes spatial and temporal modulations of 6n. With a small azo dye concentration, we can write 6n(r,t) = (an/acA)6cA(r,t)+ (an/acB)6cB(r,t) (1) where 6CA(r,t)and 6CB(r,t)are the local concentration change of the trans and cis isomers of the azo dye molecules, respectively. (11) Huang, W. J.; Friek, T.S.;Landry, M. R.; Lee, J. A.; Lodge, T. P.; Tirrell, M.AIChE J . 1987, 33, 573. (12) Wang, C. H.; Xia, J. L.; Yu, L. Macromolecules 1991, 24, 224.
The Journal of Physical Chemistry, Vol. 96, No. 1, 1992 191 The kinetic equations needed for describing the concentration variations of trans and cis isomers in the presence of both diffusion and photochemical processes are
where, in eqs 2 and 3, we have assumed Fick's law of diffusion and the reaction kinetics are reversible first order. In the above, we only consider one-dimensional diffusion equations, as the dye diffusion in the direction transverse to the grating vector will not change the H G R intensity. Here DA and DB are the tracer diffusion coefficients of the trans and cis isomers, respectively. The diffusion coefficients are different because molecules A and B have different shapes. The quantities kl and kl are the rate constants of the forward and reverse reactions, respectively. The rate constants kl and may depend on the intensities of the writing and reading laser beams. We consider only the case where kl 9600
0 0.2 0.5 1.0 1.7
0 6.0 X lo-' 7.0 X 1.0 X 2.0 X
8000 900 665 640 600
4.1 5.4 8.2 11 12.8
& 5.0 X lo-* 7.0 X 1.0 X 10-1 1.4 X 10-1 1.7 X 10-1
(8)
The effect of the reading laser radiation on the lifetime of the azobenzenes has been described in ref 6. One can obtain eq 8 by setting both DA and DBin eq 5 to zero. Thus, the quantity 7 is interpreted as the lifetime of AB in cis form, as 7-l = k-,. The quantity a can be considered as the coherent background intensity, since it represents the portion of the intensity scattered from the fixed grating. The fit gives 7 = 92 s for AB in pure PVAc. This is more than a 100-fold faster than the lifetime of l o 4 s reported in ref 9 for their 92.5 wt % PVAc/toluene solution at 35 O C . We have found that introduction of a small amount of toluene into the AB/PVAc system significantly lengthens the HGR curve. As shown in Figure 1 at about 1% toluene concentration, the HGR curve does not exhibit any signifkant decay even after 4 h. Further addition of toluene results in a gradual shortening of the relaxation curve; at the concentration higher than lo%, the HGR curve appears to reach an asymptotic lifetime value of about 600 s. At 4% toluene concentration, both lifetime and diffusion contribute to the decay of the HGR intensity curve. Diffusion and the lifetime effect were separated by measurements at several crossing angles. The diffusion coefficient of about cm2/s obtained is in good agreement of the value reported by Lodge et a1.8 Due to the large lifetime variation with the toluene concentration, we plot in Figure 3 log 7 versus I&, the volume fraction of toluene. The toluene concentration dependence of 7 is also given in Table I. The cis-trans isomerization of azobenzene occurs by first breaking the double azo bond through the A u* transition, followed by the rotation of the two phenyl rings about the remaining single Q bond.* The lifetime of azobenzene in cis form in amorphous glassy polymers is closely related to the available free volume in the system.lS Decreasing the available free volume in the medium hinders the rotation of the cis back to the thermodynamically preferred trans isomer, and hence lengthening the lifetime. Introducing additives to the polymer increases free volume; however, the significant lengthening of the lifetime from 92 s in pure PVAc to a lifetime value of more than 150-fold (>1.4 X 104s) in the 1% toluene concentration would suggest that the cis form has been stabilized by the presence of toluene, despite the increase of free volume by the presence of toluene.
The time constant 7 obtained from the fit does not depend on the crossing angle of the two coherent laser beams. However, it depends on the wavelength and the reading laser (see Figure 2).
(1 5 ) Dubini-Paglia, E.;Beltrame, P. L.; Marcandall, B.; Carniti, P.; Seves, A,; Vincini, L.J. Appl. Polym. Sci. 1986, 31, 1251.
h
u
s: 0.01 -. c,
c
1
0.005
I
I
I
I
I
0
2
4
G
8
sin'ei2 x103
Figure 2. Reciprocal of relaxation time constants T plotted vs sin2(8/2) in the azobenzene/PVAc system at 23 OC. The relaxation time is obtained from fitting the HGR intensity curve to eq 15. Note the lifetime constants are affected by the wavelength of reading laser beam. A and 0 represent the experimental data at X = 488.0 and 632.8 nm, respec-
tively. The solid lines are drawn to guide the eyes. Note the 488.0-nm radiation shortens the lifetime considerably. benzene (AB) and different amounts of toluene in PVAc at 23 OC. At the 1 wt % toluene concentration, the diffraction intensity does not display a noticeable decay over 4 h; at 4.1 % toluene, the intensity curve shows a monotonous decay, but at 11% toluene it exhibits a decay-rise and then decay shape. The intensity curve for the 4.1% toluene sample does not correspond to a single exponential; it can, however, be fit to the sum of two exponential decay functions. Both the 4.1% and the 11% intensity curves can be fit rather accurately to eq 5. The 11% requires the sign of Q to be opposite to that of 8. The theoretical fits are shown as smooth curves in Figure 1 . The HGR intensity curve, Z(t), of AB in PVAc exhibits a very interesting behavior when toluene at low concentration is present. Without toluene the HGR intensity curve of AB in pure PVAc at 23 O C displays a monotonous decay. The decay curve can be fit to the equation. Z(t) = (a
+ fie-'/')*
-
The Journal of Physical Chemistry, Vol. 96, No. 1 , 1992 193
Photoprocesses of Azobenzenes
. w
c
-14
0.6
0
2
1
I
I
4
G
8
I
1
0
0.7
I
1
0.8
0.9
1.o
0,
2
sir?e/2)x10'
Figure 4. Relaxation time constants (fA, T B ) of azobenzene in 4.1% toluene/PVAc system plotted vs sin2 (0/2) at 23 "C to show that fA (curve A) is associated with trans-azobenzene diffusion and fB (curve B)
with the diffusion and lifetime of the cis form. It is possible that physical association of AB with toluene has occurred. The association is expected to prevent the cis to trans isomerization to take place. The presence of toluene at low concentration leads to a long decay but does not affect the peak diffraction intensity, suggesting that AB is well dispersed in the PVAc host. At 1% toluene concentration, there are about two toluene molecules per AB statistically dispersed in PVAc. However, continuous lengthening of the lifetime is not expected as toluene concentration is increased further, as the available AB molecules have already been taken up by toluene. As a matter of fact, as more toluene is added to PVAc, available free volume is greatly i n c r d , the increased available free volume is expected to decrease physical association, thus allowing isomerization to take place. Because only after the &-AB molecules that have been dissociated from toluene can they undergo the ?r O* transition and be isomerized back to the trans form. As a result, the lifetime of &AB in the 10% toluene concentration is expected to be longer than that in bulk PVAc. Unfortunately, NMR and infrared absorption spectroscopyare not sensitive to detect evidence of physical association at such a azo dye low concentration. Therefore, the physical association between AB and toluene as the proposed mechanism for the observed lifetime lengthening requires further proof. When both translational diffusion and cis to trans isomerization mechanisms are operative, the HGR curve depends on the amplitude of the grating vector. As mentioned above, to separate out the diffusion and lifetime mechanisms, the HGR intensity curve Z(t) for each sample at fixed temperature is measured as a function of the crossing angle 8. The intensity curves obtained are next fit to eq 5 to obtain the relaxation times and rB. The relaxation times are then plotted with respect to sin2 (8/2). A representative plot for the relaxation times versus sin2 ( 8 / 2 ) for the sample containing 4.1% toluene is shown in Figure 4. Both and rB-lare proportional to sinZ( 8 / 2 ) . Since the 7A-l versus sinZ(8/2) plot has a zero intercept, and the I ~ - Idisplays a finite intercept, in accordance with eqs 13 and 14 the finite intercept is assigned to be equal to k , ,or 7-I. The slopes are proportional to the diffusion coefficients. Investigation of the sample at the condition when both diffusion and lifetime mechanisms contribute to the intensity decay is particularly useful, as by doing this an unequivocal assignment of the relaxation times can be made. The relaxation time associated with the zero intercept is associated with the diffusion of the trans isomer, and the relaxation time with a finite intercept is associated with relaxation involving both the lifetime and diffusion mechanisms of the cis isomer. Shown in Figure 5 are the tracer diffusion data of AB in PVAc at 23 O C plotted as a function of the polymer concentration in the PVAc/toluene system. The diffusion data of Lee and Lodge' at two temperatures are also included for comparison. Except for no differentiation of the cis from the trans diffusion coefficients in the data of Lee and Lodge, the agreement between the two sets of data is satisfactory.
-
Figure 5. Tracer diffusion coefficients of azobenzene in the trans and in the cis form in PVAc at 23 "C plotted as a function of toluene concentration. The horizontal axis is the polymer fraction $I~,equal to 1 -
&. Solid circles are for trans and empty circles are for cis. The diffusion data of Lee and Lodge (A are data at 15 "C and A are at 35 "C) reported in ref 7 are included for comparison.
The HGR technique is used often to extract only one relaxation time, by fitting the decay curve to the type of equation given byI6 Z ( t ) = (be-'/'
+ a)2 + y
(9) where CY is interpreted as the coherent background and y is the incoherent background, including noise, stray light intensity contributions, etc. The relaxation time I is then related either to the lifetime or to the diffusion process. The incoherent background y is not of interest as it can be subtracted from the raw data. However, in order to obtain reliable diffusion data, one needs to handle the coherent background with some care. One source of the coherent background arises from the scattered intensity from the static grating, corresponding to I ~ - '= 0 in eq 5 as discussed above; the other may arise from the intensity associated with the fixed phase difference between two coherent beams. In the heterodyne setup, one can insert a Babinet phase compensator in the optical path of the reference beam and adjust the compensator to remove the intensity contribution due to the finite phase difference before recording the HGR intensity. The coherent background arising from the fixed phase difference can hence be eliminated. However, the coherent background owing to the scattered intensity from the static grating cannot be eliminated. Nevertheless, when diffusion occurs,the scattered intensity from the static grating also becomes time dependent, and as such, it is no longer considered as the coherent background. Because of their different shapes and polarities, the photochromous dye molecules generally have different transport properties in the ground and isomerized states. Thus, one expects at least two diffusion coefficients to be inherently associated with the HGR spectroscopy. With a HGR spectrometer having sufficient contrast, it should be possible to resolve the two relaxation rates connecting diffusion of the dye molecule in the ground and excited states simultaneously. In the present case, the molecule in the ground state is in the trans form and in the excited state the cis form of azobenzene. Using our spectrometer, we have obtained the diffusion coefficients for azobenzene in W A C containing 4.1% toluene, to be equal to 8.1 X l@I3 cm2/s for the trans form and equal to 1.1 X lo-" cmz/s for the cis form. The cis form of AB diffuses more than 30% faster than does the trans form. However, if the data are fit to eq 9, it would be impossible to obtain diffusion coefficients of different isomers. The diffraction intensity curves, Z ( t ) , for AB/PMMA, MY/ PMMA, and MR/PMMA systems at 43 OC are plotted versus log ( t ) in Figure 6. We use the logarithmic scale for the time axis to display the difference in the decay behavior. AB decays slowest; next is MY; MR has the fastest decay among the three. The curves with noise are the experimental results, and the smooth curves represent the best fit of the experimental ones to eq 9. At 43 O C , the diffraction intensity curves for the three samples do (16) See,for example, the method of data analysis given in refs 4 and 5 , and a recent paper: Ehlich, D.; Sillescu, H.Macromolecules 1990,23,600.
194 The Journal of Physical Chemistry, Vol. 96, No. 1, 1992
-------I
’------
=I
Wang and Xia
I
28
30
32
34
1 / T X Id (K-’) Log t
(SCC)
Figure 6. Diffraction light intensity (I) plotted as a function of time log t in AB/PMMA, MY/PMMA, and MR/PMMA systems at 43 O C . The curves with noise represent the experimental results, and the smooth curves represent the best fit to eq 16. The lifetime constants obtained from the fit are 986 s for AB, 79 s for MY, and 12 s for MR. TABLE 11: Correlation of the Lifetimes of AB, MY, MR in PMMA with the Torsion Anele of Azo Linkage azo compds torsion angle,’ deg T, s azobenzene 84 986 methyl yellow 81 79 methyl red 78 12 With respect to the N=N bond.
not show any dependence on the crossing angle of the laser beams. The decay is due to the finite lifetime of the cis isomer. The lifetime data obtained from the fit are given in Table 11. While the lifetime is closely associated with the energy dissipation behavior of the photoexcited state. To quantitatively account for the lifetime behavior, quantum mechanical calculations are needed. However, qualitatively it may be correlated to the steric hindrance of the side groups attached to the azo linkage. MY and MR differ from AB by having larger substituted side groups on the azo linkage, and they have shorter lifetimes. For the three azobenzenes studied, the lifetime decreases with increasing the size of the side groups. Using an energy-minimizing program, we have found that the geometry of the cis isomers of the three azobenzenes are not p1anar.l’ According to the molecular model, the two phenyl rings in &-AB are torqued about 8 4 O with respect to the azo bond. On the other hand, the corresponding angles for cis-MY and cis-MR are 81’ and 78O, respectively. The difference in the lifetime among the three azobenzenes appears to correlate with the torsional angles: the smaller the torsional angle, the shorter the lifetime. (17) The software program that we used in this work is
ALCHEMY 11,
provided by Tripos Associates, St. Louis, MO. The program allows one to predict the geometry of the molecule by minimizing the configurational energy of the molecule.
Figure 7. Lifetimes of cis isomer of AB in PS (curve 1) and PMMA (curve 2), and MY in PMMA (curve 3) plotted as a function of reciprocal temperature. The Arrhenius type temperature dependence gives the activation energy E,: 4.9 kcal/mol for AB in PS, 7.5 kcal/mol for AB in PMMA, and 5.5 kcal/mol for MY in PMMA.
We have also studied the temperature dependence of the lifetime for the three azobenzenes in PS and in PMMA. In Figure 7, we plot In T versus 1/T. Over the range between 293 and 353 K, the temperature dependence is Arrhenius, with the activation energy equal to 4.9 kcal/mol for AB in PS; however, it is 7.5 kcal/mol for AB in PMMA. The activation energy is 5.5 kcal/mol for MY in PMMA. The magnitude of the activation energy is consistent with the one usually observed for the cis-trans isomerization processes involving the azo bond. Despite a similar glass temperature for PS and PMMA, the much larger activation energy observed for AB in PMMA than for AB in PS indicates that AB is better stabilized in PMMA than in PS. The greater stabilization may be due to the interaction of cis-AB with the ester group. In PMMA, MY has a lower activation energy than AB. The smaller activation energy for MY indicates that the thermal barrier for isomerization is significantly less than that for AB, possibly due to large side groups of MY. In summary, we have studied the relaxation behavior of the holographic gratings induced in azobenzenes in several amorphous polymer hosts. The lifetime of AB in PVAc is found to be lengthened by the presence of toluene. The effect is more important for toluene present at low concentration. Above 1% toluene concentration, the lifetime levels off and reaches an asymptotic value. We have provided a mechanism to account for the observation. The activation energies of several azobenzenes in the polymer host have been determined. Using an energy-minimization program to determine the structure of cis isomer, we have correlated the activation energy with the steric hindrance and the torsional angle of the azobenzene. Acknowledgment. This work is financially supported by a grant from the Office of Naval Research. ResrStry NO. MR, 493-52-7; PMMA, 901 1-14-7; DS, 9003-53-6; AB, 103-33-3; MY, 60-1 1-7; PVAc, 9003-20-7; toluene, 108-88-3.
