Wavelength Dependence of the Reorientation Efficiency of Azo Dyes

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Wavelength Dependence of the Reorientation Efficiency of Azo Dyes in Polymer Matrixes Sergey Yu Grebenkin, and Arkadiy B. Meshalkin J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b03171 • Publication Date (Web): 07 Aug 2017 Downloaded from http://pubs.acs.org on August 13, 2017

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The Journal of Physical Chemistry

Wavelength Dependence of the Reorientation Efficiency of Azo Dyes in Polymer Matrixes Sergey Grebenkin∗,† and Arkadiy B. Meshalkin‡ †Voevodsky Institute of Chemical Kinetics and Combustion, Institutskaya 3, Novosibirsk, 630090, Russian Federation ‡Kutateladze Institute of Thermophysics, Lavrentieva, 1, Novosibirsk, 630090, Russian Federation E-mail: [email protected]

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Abstract Irradiation with linearly polarized light of azobenzene-containing polymeric matrixes causes reorientation of azobenzene molecules. In this study, the optical lightinduced anisotropy of amorphous poly(alkyl methacrylates) (PAMAs) doped with an azo compound was measured at different temperatures and at two irradiation wavelengths. To describe a decrease in the efficiency of anisotropy formation with temperature, a model of molecule reorientation is suggested which includes the probability of molecule reorientation per one isomerization as a basic parameter. The probability of molecule reorientation was found to depend on irradiation wavelength. Comparing the anisotropy time profiles at different irradiation wavelengths, we concluded that, upon each photon absorption, the molecule most likely makes an attempt to reorient even without isomerization, i.e. the reorientation occurs by a mechanism predicted by Persico and co-workers in their theoretical works. Also, we infer that the reorientation is facilitated by the photon energy absorbed by a molecule.


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Introduction Irradiation of azobenzene-containing amorphous solids leads to the appearance of the optical anisotropy of the samples in the form of optical dichroism and birefringence. 1–10 Two processes are responsible for the creation of anisotropy: i) hole burning in the initially uniform angular distribution of azo molecules (caused by the orientation-dependent probability of cis-trans isomerization), and ii) light-induced reorientation of azo molecules which is con′

′′

sidered to be the result of the isomerization events: trans(θ)→cis(θ )→trans(θ ), where θ, ′

′′

θ and θ stand for angular coordinates of the molecules which define their orientations. Both these processes underlie the theoretical models of anisotropy formation in glassy matrixes. 3,11–17 The two simplest models, the conical 11,14 and fully correlated 14 ones, represent the evolution of angular distribution of the molecules in the cases of highly mobile and immobile environments, respectively, e.g. in glassy matrixes near and much below glass transition temperature, Tg . The conical model postulates that, following isomerization, the transition dipole moment of molecule rotates by the same value with equal probability with respect to its previous direction. In the context of the fully correlated model, each isomer of azo mol′

ecule returns to its initial orientation after back isomerization: trans(θ)→cis(θ )→trans(θ), i.e., there is no reorientation of the molecule. A basic parameter of both models is the angle by which the transition dipole of azo molecule at irradiation wavelength rotates due to isomerization (rotation angle). The anisotropy formation in the films of poly(alkyl methacrylate)s can be well described by a combination of the conical and fully correlated models. 18 However, rotation angles extracted from the anisotropy curves decrease strongly with a decrease in temperature, which is hard to interpret, since, at T ≪ Tg , lowering of temperature leads to the slowdown of polymer dynamics and does not cause changes in polymer structure. We assume that the apparent temperature dependence of the rotation angles is a hint about the temperature dependence of the reorientation probability of azo molecules. Development of the model of 3 ACS Paragon Plus Environment


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anisotropy formation which involves the reorientation probability was the first aim of the present work. At temperatures much below Tg , the rotation of molecules is strongly hindered, which reflects the fact that the dynamics of their environments is slowed down. At the same time, their reorientation caused by cis-trans photoisomerization can run in a short time. 12,19 Comparing these facts, one can assume that a photon energy somehow influences the dynamics of the polymer environment of azo molecule. A limited number of data are available on the influence of light energy transferred to the matrix on polymer dynamics. Comparing the data on thermal erasure of in-plane birefringence of dense self-assembled monolayer of azo molecules covalently bonded to a glass substrate with the photo-erasure, the authors of ref 20 concluded that, in the course of the photo-erasure, each absorbed photon causes “photofluidization” of the local environment of azo moiety. The hypothesis of enhancing the molecular mobility in azo-containing polymers when irradiating with light (so-called “softening”) was suggested 10,21,22 to explain the formation of the relief grating (SRG) 23,24 (discovered in 1995) on the surface of polymer films when irradiated with an interference pattern of coherent light much below Tg . Softening of the film of pDR1M upon illumination with circularly polarized visible light at temperature much below Tg was detected by measuring the response of the polymer surface to a constant load. 25 A decrease in viscosity was estimated to be more than two orders of magnitude. Also, the increase in the elastic compliance of thin films of PMMA doped with an azo compound 26 and in the plate compliance of azobenzene side chain polymer film under irradiation with visible light were detected. 27,28 These data have been interpreted to be evidences of softening the polymer matrix upon repetitive isomerization of azo molecules. Above Tg , a speeding-up of the molecular dynamics in multilayers of azo-polymer upon light illumination was detected using x-ray photon correlation spectroscopy. 29 Up to now the effect of photon energy on the mobility of molecules in polymer matrixes and, in particular, on the reorientation of azo molecules is poorly understood. To our


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knowledge, there are no direct evidences of enhancing the reorientation of azo molecules by photon energy which is released into the matrix following molecule excitation. However, it can be expected that the “photofluidization” facilitates the reorientation of azo molecules in bulk polymers and, therefore, lies at the basis of the reorientation mechanism. The second aim of the present work was to elucidate the effect of photon energy on the efficiency of the reorientation of azo molecules. In this study, we analyze the temperature and wavelength dependence of anisotropy formation in azo-doped poly(alkyl methacrylate)s. Using the developed model, we estimate the probabilities of the reorientation of a model azo compound per one trans→cis→trans cycle at different temperatures and at two wavelengths. We show that the probability of reorientation per one isomerization cycle depends on the wavelength of irradiation. In conclusion, we suggest an interpretation of the observed wavelength dependence of reorientation probability.

Experimental Methods The experimental technique has been described in detail elsewhere. 18,30 Here, we give only the most important features. The concentration of azo compound, 1-naphthyl-p-azo-methoxybenzene (NAMB), in polymeric films (poly(ethyl methacrylate) (PEMA), Mw = 515 000, Tg = 336 K; poly(n-butyl methacrylate) (PnBMA), Mw = 337 000, Tg = 288 K; and poly(n-hexyl methacrylate) (PnHexMA), Mw = 400 000, Tg = 268 K) was about 5 × 10−3 mol/l. The anisotropy of the samples was generated by linearly polarized light with the wavelength of 405 or 546 nm. The rate constant of dark cis → trans isomerization of NAMB in PnBMA was measured in the range 283–313 K and extrapolated to lower temperatures. Its value was estimated to be 3 × 10−8 s−1 at 243 K. Due to such a low rate constant, the dark isomerization does not affect the anisotropy and absorbance in the temperature range studied. Both the cis → trans and trans → cis isomerizations are considered to be induced only by light.



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In the course of irradiation, the sample absorbances measured at the wavelength of maximum absorption of trans isomer (382 nm) with light polarized transversely (Abs⊥ ) and parallel (Abs∥ ) to the polarization of irradiation were recorded. The anisotropy and isotropic absorbance were calculated as:

Anisotropy(t) = Abs⊥ (t) − Abs∥ (t),

Abs(t) =

Abs∥ (t) + 2Abs⊥ (t) . 3

The extinction coefficients of trans NAMB at 253 K in MMA at the wavelength of maximum absorption (381.5 nm), 405 and 546 nm were measured to be 19700 ± 1000, 14200±1000 and 45±5 l mole−1 cm−1 , respectively. The extinction coefficient of trans NAMB at 253 K in ethanol at the wavelength of maximum absorption (380 nm) was measured to be 19400 ± 1000 l mole−1 cm−1 . Using this value and the relative spectra of isomers (see Supporting Information: Figure S1), the extinction coefficients of cis NAMB at 253 K in ethanol at 380 and 405 nm were determined to be 880 ± 80 and 1200 ± 100 l mole−1 cm−1 , respectively. The extinction coefficients of cis NAMB at 253 K in ethanol at 546 nm (104 ± 15 l mole−1 cm−1 ) was determined using the relative spectra of the isomers and spectra of high-concentration solution of NAMB before (100% in trans) and after 405 nm irradiation. The spectra of trans NAMB in methyl methacrylate (MMA) and ethanol are close to each other (the spectrum of trans NAMB in MMA is red-shifted by 1.5 nm relative to the spectrum in ethanol). Therefore, the extinction coefficients of cis NAMB in MMA were taken to be equal to those in ethanol; in turn, the extinction coefficients of NAMB in the polymers were taken to be equal to those in MMA. From the initial parts of the absorbance time profiles of NAMB/PnHexMA film irradiated at 233 K (these time profiles are nearly exponential), we estimated the quantum yields of trans→cis isomerization induced by 546 and 405 nm irradiation: ϕ546 t→c = 0.27 ± 0.06 and ϕ405 t→c = 0.087 ± 0.02. Also, in separate experiments, the quantum yields of NAMB 6 ACS Paragon Plus Environment

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trans→cis isomerization were obtained to be ϕ546 t→c = 0.25 ± 0.06 (in PnHexMA at 223 K) and ϕ405 t→c = 0.092 ± 0.015 (in PnBMA at 243 K).

Modeling Approach The Dynamical Model The experimental data were interpreted with the help of the dynamical model which was developed on the basis of the conical model 11,14 by imposing the following conditions. We postulate that, after isomerization, a molecule most probably will return into the previous ′

isomeric state with the previous orientation, e.g.: trans(θ) → cis(θ ) → trans(θ). With a less probability each isomer can be formed in a new orientation characterized by angular ′′

′

′′

coordinates θ , e.g.: trans(θ) → cis(θ ) → trans(θ ); all allowed new orientations of each isomer are considered to be equally probable. Schematically, the reorientational process is depicted in Figure 1.

Figure 1: Schematic representation of the reorientational process specified by the dynamical model. Dotes represent the orientations of cis (c) and trans (t) isomers of the same molecule. Arrows reflect the transcis isomerization process. At temperatures much below Tg , the transitions between the isomers in fixed orientations occur many times until the orientation of one of them is changed. A basic parameter of the model is the probability, Preor , that a molecule changes its orientation following the isomerization. At temperatures much below Tg , where the molecular mobility is “frozen out”, Preor → 0 and the dynamical model becomes the fully correlated 7 ACS Paragon Plus Environment


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model: any azo molecule has only one orientation in the cis and one orientation in the trans form. With increase in temperature, Preor increases and, at high enough temperature, becomes close to 1. As a result, at high temperature, the dynamical model transforms to the conical one (see Supporting Information: Note 2 for more details about the dynamical model). The reorientation of cis-NAMB itself has a minor effect on the anisotropy because of a weak absorption of the cis isomer at probe wavelength (the ratio of the absorption cross sections of trans and cis isomers of NAMB at probe wavelength was determined to be 22). Therefore, the change in anisotropy is mainly caused by the reorientation of trans molecules ′

′′

following the trans(θ) → cis(θ ) → trans(θ ) cycle. In the context of the dynamical model, the reorientation of trans isomer occurs with the probability Preor upon cis → trans isomerization, irrespective of whether the cis isomer was reoriented at the preceding isomerization or not. Therefore, the probability of the reorientation of trans isomer after trans→cis→trans cycle equals Preor . Just this parameter was estimated from experiment.

Fitting Procedure The parameters of the dynamical model are as follows: i) the rate parameters of light-induced trans→cis and cis→trans isomerizations, kt→c ≡ Iσt ϕt→c and kc→t ≡ Iσc ϕc→t , where I is the light intensity, σt and σc are the cross sections of trans and cis molecules, and ϕt→c and ϕc→t are the quantum yields of trans→cis and cis→trans isomerizations, respectively, ii) the angle, α, by which the transition dipole moment (at irradiation wavelength) rotates owing to isomerization, iii) the probability of reorientation, Preor , iv) the amplitude of molecules librations 30 (fast rotational oscillations of molecules), Ω. Also, the model includes the rotational diffusion constants which have been found from the fit of anisotropy decay 30 and are essentially the rotational diffusion constants of trans8 ACS Paragon Plus Environment

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NAMB (because the cross section of trans isomer at probe wavelength is much greater than that of cis). We set these constants to be the same for both isomers since modeling the anisotropy formation in NAMB/PnHexMA showed that the anisotropy changes only slightly when the rotational diffusion constants of cis NAMB are set to be 10 times less than those of trans NAMB. The time profiles of the anisotropy decay of PnBMA and PnHexMA films doped with NAMB reflect a heterogeneity 31,32 of the polymer matrixes: the anisotropy decay can be fitted with a sum of at least four exponential functions. 30 Therefore, we considered that there are four dynamically different types of the chromophore environments. Consequently, the measured anisotropy and absorbance were fitted with a sum of four individual curves. To simplify the fitting procedure, we postulated the equality of Ω for all the azo molecules in a given matrix at a given temperature. Besides, we postulated the equality of α for all the molecules at all temperatures. The temperature dependence of chromophore reorientation is ascribed to such a dependence of the Ω and Preor,i , where i denotes the type of chromophore environment (i = 1, . . . , 4, the less index corresponds to the more mobile environment). The value of α was set equal to 50.4◦ , the value obtained from fitting the anisotropy formation in the films of PEMA, where the majority of molecules do not reorient at measured temperatures. 18 Thus, the fitting parameters for each pair of curves (absorbance and anisotropy) were the kc→t,i , kt→c,i , Ω and Preor,i . To fit the absorbance and anisotropy at a given temperature, first, the rate parameters kc→t,i and kt→c,i were estimated from the fit of the absorbance time profile. The absorbance time profiles are nearly biexponential and were satisfactorily fitted on the conditions that kc→t,1 = kc→t,2 = kc→t,3 and kt→c,1 = kt→c,2 = kt→c,3 . Then, the libration amplitude Ω and the probability parameters Preor,i were estimated from the fit of anisotropy time profile. These two steps were repeated until a satisfactory fitting quality of both the anisotropy and absorbance has been achieved. The molecules with a larger diffusion constant were considered to have a higher reorientation probability. Below, we omit the subscript i in the



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notations kc→t,i , kt→c,i and Preor,i where appropriate. While the time profiles of isotropic absorbance are nearly biexponential, the satisfactory fit of the anisotropy was obtained using the set of all parameters Preor,i being different (except the cases when the anisotropy was formed at high temperatures). These facts reflect a different sensitivity of the two processes, viz., isomerization and rotation, to the heterogeneity of polymer matrix: the isomerization is much less sensitive to the difference in the environment than the reorientation. It is known that the trans→cis isomerization of azobenzene takes place even when azobenzene is included in the cyclodextrin cavity and cannot rotate (Bortolus, 1987). In addition, the isomerization rate of NAMB in PEMA is close to the rate of isomerization in PnHexMA, while no rotation of the majority of NAMB molecules in PEMA was observed. Formally, the isotropic absorbance is simply proportional to the trans isomer fraction, while the anisotropy reflects the angular distribution of azo molecules. Therefore, if the reorientation of molecules takes place, the time dependencies of anisotropy and absorbance are different.

Results Wavelength Dependence of Reorientation Probability Figure 2 presents the typical time profiles of anisotropy induced by linearly polarized irradiation with the wavelengths of 546 and 405 nm in PnHexMA and PnBMA films doped with NAMB; Abs0 stands for the absorbance before irradiation. The dependence of reorientation probability on the irradiation wavelength was revealed by modeling the anisotropy formation. The modeling procedure was as follows. First, the time profiles of anisotropy and absorbance recorded in the course of irradiation with 405 nm light were fitted (insets of Figure 2, only the time profiles of anisotropy are shown); as a result of the fit, the values of Ω and Preor were obtained. Then, using the obtained parameters, the time profile of the absorbance recorded in the course of irradiation with 546 nm light was fitted (not 10 ACS Paragon Plus Environment

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0

5

10

15

20

25

0.12 546 nm Irradiation

Anisotropy/Abs0

0.10 0.08

Anisotropy/Abs0

0.15

0.06

405 nm Irradiation

0.10

0.04

PnHexMA, 223 K

0.05

0.02

Irradiation time / 1000 s

0.00

0.00 0.14

0

1

2

546 nm Irradiation

0.12

Anisotropy/Abs0

0.10

Anisotropy/Abs0

0.08

0.15

0.06

405 nm Irradiation

0.10

0.04

PnBMA, 243 K

0.05

0.02

Residuals

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Irradiation time / 1000 s

0.00

0.00 0.01 0.00 -0.01 0

0

1

2

3

5 10 15 Irradiation time / 1000 s

Figure 2: Anisotropy time profiles of the NAMB-doped PnHexMA (top panel) and PnBMA films at 223 and 243 K, respectively, in the course of irradiation with linearly polarized light at 546 nm. The dash lines represent the anisotropy simulated with the same reorientational parameters as those obtained from fitting the “405 nm induced” anisotropy. The solid lines represent the fit of the anisotropy obtained by varying the Preor . Insets show the anisotropy time profiles in the course of irradiation at 405 nm, lines are the fitting curves. Residuals with respect to the data on anisotropy formation in PnBMA under 546 nm irradiation are shown below the respective data. 546 546 shown) and the rate parameters kt→c and kc→t were determined. Finally, the time profile of

the anisotropy formed under irradiation at 546 nm was simulated using all the parameters 546 546 , Ω and Preor . , kc→t determined: kt→c

The simulated “546 nm induced” time profiles are shown in Figure 2 by dash lines. In the simulations, we took into account the non-collinearity of the transition dipole moments of NAMB at probe wavelength (382 nm) and at 546 nm; the angle between the transition



dipole moments of NAMB at 382 and 546 nm was determined to be 32.5◦ . 34 ( T -Tg) / K

( T -Tg) / K

-30-40-50 -60 -70 -80 1

Reorientation probability per isomerization cycle, Preor,i

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-20

-30

-40

-50

i=1

i=1

0.1

PnHexMA

PnBMA

0.01 1

i=2

i=2

i=3

i=3

i=4

i=4

0.1 0.01 1 0.1 0.01 1 0.1

No Rotation

0.01

4.2 4.5 4.8 5.1 5.4

3.8

4.0

4.2

1000 K / T

1000 K / T

Figure 3: Probabilities of light-induced reorientation, Preor,i , of NAMB molecule in PnHexMA (left column) and PnBMA (right column) after trans→cis→trans cycle. Panels, from top to bottom, represent the reorientation probabilities of the molecules in i-th environment; the larger index i corresponds to the smaller mobility of molecules. In PnBMA, azo molecules are not able to reorient in the environment of 4-th type. Circles: irradiation at 405 nm; crosses: irradiation at 546 nm. Reorientation probabilities less than 0.004 are not shown. Errors are given by the symbol size. The arrows mark the data which have been used to estimate the probability of reorientation upon photon absorption (see text). As seen from Figure 2, the experimental anisotropy induced by 546 nm light grows much slower than the simulated one. Too slow growth of the anisotropy induced by 546 nm light was observed in the NAMB-doped films of PnHexMA and PnBMA also at other temperatures. In terms of the dynamical model, the slow growth of the anisotropy under irradiation at 546 nm, compared to the anisotropy induced by 405 nm irradiation, points to the less probability of molecule reorientation under 546 nm irradiation. Then, to fit the anisotropy formed by 546 nm light, we varied the probabilities Preor , while keeping fixed all other 12 ACS Paragon Plus Environment

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parameters. The fitting curves are shown in Figure 2 by solid lines.

< Preor >

1

0.1

Ω / degree

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50 45 40 35 3.6

4.0

4.4 4.8 1000 K / T

5.2

5.6

Figure 4: Top panel: The average probability of the light-induced reorientation of NAMB molecule in PnHexMA (circles) and PnBMA (squares) after trans→cis→trans cycle. Full symbols: irradiation at 405 nm. Empty symbols: irradiation at 546 nm. The lines are a guide for the eye. Bottom panel: The amplitude of NAMB librations in PnHexMA (circles) and PnBMA (squares). Figure 3 presents the probabilities of NAMB reorientation following trans→cis→trans cycle in different environments of PnBMA and PnHexMA at 546 and 405 nm irradiations, extracted from the anisotropy formation curves. The larger index i corresponds to the less mobile environment. Top panel of Figure 4 shows the reorientation probability averaged over all environments, < Preor >. This figure demonstrates the wavelength dependence of reorientation probability in a more convincing form, as the average values depend only a little on the form of distribution. For PnBMA, the data do not include the non-rotating molecules (≈ 14% of all molecules), the reorientation probability for which is zero in the temperature range studied. Bottom panel of Figure 4 demonstrates an increase in the libration amplitude of NAMB with temperature; the anisotropy cannot be fitted in the whole temperature range using a single value of Ω.



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Discussion Possible Reasons for the Wavelength Dependence of the Reorientation Probability In this section we discuss possible reasons for the wavelength dependence of the reorientation probability. We start with the consideration of isomerization mechanism and proceed with the analysis of reorientation mechanism involving light-enhanced changes in the environments of azo molecules.

Hypothesis Involving Different Isomerization Mechanisms Upon absorption of the photons with wavelengths of 546 and 405 nm, NAMB molecule is excited to the S1 (n − π ∗ ) and S2 (π − π ∗ ) states, respectively. One can assume that the isomerization trajectory depends on the initially excited state, and, therefore, the value of the rotation angle α depends on the excitation wavelength. In such a case, the seeming dependence of the reorientation probability on wavelength reflects the actual wavelength dependence of the rotation angle α. However, Lu et al., 35 by means of a femtosecond fluorescence, showed that the trans→cis isomerization of azobenzene derivatives proceeds in the S1 (most probably) or S0 states irrespective of the initial excitation, either to the S1 or the S2 state. Conti et al., 36 using ab initio calculations, have found that, upon excitation of both the S2 and S1 states, the isomerization of azobenzene occurs predominantly by the same route. Persico and co-workers 37,38 relying on the results of semiempirical calculations, have concluded that the isomerization of both azobenzene isomers takes place on the S1 potential surface by the same (rotational) mechanism. We conclude that the wavelength dependence of the reorientation probability cannot be explained by a difference in isomerization paths upon excitation of NAMB molecule to different states: in the same polymeric environment, the isomerization trajectory (and the 14 ACS Paragon Plus Environment

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rotation angle) should not depend on the excitation wavelength.

Hypothesis Involving Light-Enhanced Changes in the Environment of Azo Molecule According to the concept of “photofluidization”, 20 the absorption of a photon by azo molecule results in enhancing the dynamics of the polymer environment thereby facilitating its rearrangement; in turn, in a more mobile environment, a molecule reorients with higher probability. The energy of 405 nm photon (3.06 eV) is higher than the energy of 546 nm one by ≈ 0.8 eV. A larger probability of reorientation might be expected upon absorption of a photon with higher energy. Within the limits of the conventional mechanism of reorientation, the reorientation occurs only upon isomerization event. It seems surprising that an increase in photon energy only by 0.8 eV could cause such a strong increase in the reorientation probability upon single isomerization event which is demonstrated in Figures 3,4. Recently, Persico and co-workers 39,40 carried out a computational study of the photoorientation of azobenzene in ethylene glycol and concluded that the molecule can be reoriented due to an excitation-deactivation process without isomerization. They supposed that “any chromophore undergoing large amplitude geometry relaxation during its excited state dynamics can develop anisotropy”. 40 With this in mind, we assume that the azo molecule changes its orientation following trans→cis→trans isomerization cycle due to numerous attempts of reorientation. These attempts are associated with each photon absorption and −1 their number per isomerization cycle equals ϕ−1 t→c + ϕc→t .

We can assume that the reorientation of azo molecule without isomerization is accompanied by the redistribution of free volume in the vicinity of the molecule. The redistribution of free volume near guest molecules after their electronic excitation was suggested earlier to explain the nonphotochemical hole burning in the electronic absorption bands of the molecules imbedded in amorphous solids at low temperatures (Small, 1993; Small, 2001). The basis of both phenomena is the redistribution of free volume which is triggered by the electronic



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excitation of molecules. To conclude, we remark that there are two wavelength-dependent parameters which can influence the probability of the molecule reorientation following the isomerization cycle: i) the photon energy and ii) the quantum yield of isomerization.

Influence of Photon Energy on the Reorientation Probability To confirm the effect of photon energy on the reorientation efficiency, we suppose the opposite situation, i.e., consider the hypothesis that the photon energy does not influence the reorientation efficiency and a molecule reorients after each photon absorption with the probability which is independent of wavelength. In that case, the probability of reorientation in −1 the course of trans→cis→trans cycle is proportional to ϕ−1 t→c + ϕc→t . It is known that the

quantum yield of trans→cis isomerization of azobenzene and its derivatives in solutions upon n → π ∗ excitation exceeds that upon π → π ∗ excitation, 33,43,44 therefore such a hypothesis is qualitatively consistent with our experimental results. To test this hypothesis, the quantum yields values are required. The quantum yields of trans→cis isomerization induced by 546 and 405 nm irradiation were taken to be ϕ546 t→c = 0.25 546 and ϕ405 t→c = 0.092 (they have been obtained in separate measurements of ϕt→c in PnHexMA

at 223 K and ϕ405 t→c in PnBMA at 243 K). From the absorbance steady-state level, the quantum yield of cis→trans isomerization of NAMB in PnHexMA at 223 K under irradiation at 546 nm, ϕ546 c→t , was estimated to be 0.57. This value is close to the quantum yield of cis→trans isomerization of azobenzene in hydrocarbon solvents upon excitation to the S1 state (≈0.55 33,43,45 ). The quantum yield of cis→trans isomerization of NAMB at 405 nm, 405 546 ϕ405 c→t , was estimated to be 0.43. Thus, the value of the quantum yields ratio ϕc→t /ϕc→t was

estimated to be about 1.33. In the temperature range 193–233 K, for the most mobile NAMB molecules (75% of the 405 total number) in PnHexMA, the ratio ϕ546 t→c /ϕt→c remains equal to 2.7 within the accuracy

of ±0.15. For the slowest 25% molecules, it decreases to ≈ 1.4 at 193 K. This decrease 16 ACS Paragon Plus Environment

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is in qualitative accordance with literature data: it is known that the quantum yield of trans→cis isomerization of free azobenzene in solution upon n → π ∗ excitation is larger than upon π → π ∗ excitation, while for the sterically hindered azobenzene they are close to each other 33,46,47 (it has been shown by quantum chemistry calculations that such a quantum yield behavior is due to the competition between the S1 → S0 internal conversion and the rotation around the N = N bond 36–38,48 ). The main conclusion which we draw from these data is that, in the temperature range studied, for any NAMB molecule in PnHexMA, the 405 value of ϕ546 t→c /ϕt→c does not exceed 2.7. By a similar argument, the same conclusion was

made concerning NAMB in PnBMA. In turn, the quantum yield of cis→trans isomerization of azo molecules only slightly depends on temperature 44 and to a lesser extent is sensitive to the steric confinements of the molecules 33,47 than the quantum yield of trans→cis isomerization. Therefore, we considered 405 the ratio ϕ546 c→t /ϕc→t to be equal to 1.33 in the whole temperature range measured. 405 546 405 Under conditions that ϕ546 t→c /ϕt→c 6 2.7 and ϕc→t /ϕc→t ≈ 1.33, an upper bound for the

ratio of the numbers of photon absorbed during trans→cis→trans cycles in the cases of 405 and 546 nm irradiations is deduced to be 2.7. However, Figure 3 demonstrates that, for 405 546 some environments and temperatures, the ratio Preor /Preor (upper index denotes irradiation

wavelength) is much higher than 2.7. We conclude that the hypothesis that the molecule can be reoriented after each photon absorption with the probability which is independent of wavelength is not correct: the probability of the reorientation of azo molecule in some environments after absorption of the 405 nm photon is higher than after absorption of the 546 nm one. We speculate that the higher probability of molecule reorientation after absorption of the 405 nm photon (excitation to S2 state) is due to the larger vibrational energy of the molecule following the decay to S1 state from which the molecule deactivates with or without isomerization. 48 The excess of vibrational energy (the energy of 405 nm photon is higher than that of 546 nm one by ≈ 0.8 eV) probably provides a more effective molecule reorientation



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which takes place in the S1 and vibrationally excited ground states.

Reorientation of Azo Molecules in Different Environments The following conclusions can be drawn from the data in Figure 3. First, the probability of the molecules reorientation in the environments of high mobility (the most mobile regions at high temperatures) is unity for both wavelengths. That means that in highly mobile regions every trans→cis→trans cycle results in molecule reorientation irrespective of wavelength. Second, the probability of the reorientation in the environments of low mobility (i = 3, 4) at low temperatures is much less than unity for both wavelengths; a possible difference between 405 546 Preor and Preor is within the accuracy of the analysis. Besides, in a constrained environment,

the quantum yields of trans→cis isomerization upon n → π ∗ and π → π ∗ excitations become 405 close to each other; 33,46,47 this factor also leads to the decrease of the difference between Preor 546 and Preor .

We did not find a clear correlation between the isomerization quantum yield and reorientation probability of a molecule. From fitting the anisotropy and absorbance time profiles, we found the isomerization quantum yields of molecules in the most mobile environments (i = 1, 2, 3) to be close to each other. At the same time, the reorientation probabilities of the molecules in these environments differ strongly, see Figure 3. Besides, the isomerization of NAMB in PEMA takes the same time as in PnHexMA, while the majority of NAMB molecules do not reorient in PEMA. These results are in line with the fact that the isomerization of even essentially sterically constrained azo moieties, such as in azobenzenophanes 46 and azobenzene capped crown ether, 47 takes place with high quantum yields.


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Rough Estimation of the Reorientation Probability per One Photon Absorption To get an idea of the values of the reorientation probabilities per one photon absorption, we λ make their rough estimations. Let qreor,iso and qreor denote the probabilities that, upon a

photon absorption, a molecule will be reoriented with and without isomerization, respectively. For simplicity, we put the probabilities of reorientation accompanied with isomerization λ to be the same at both wavelengths and for both isomerization directions while the qreor

to be dependent on wavelength, λ. Also, the probabilities of the reorientation without λ isomerization under light with a given wavelength, qreor , were set to be the same for cis

and trans molecules. We neglect the difference in the average angle of the rotation of trans molecule following the trans→cis→trans cycle in the cases of different mechanisms of reorientation. λ On conditions that qreor,iso , qreor ≪ 1, a rough estimate for the probability of molecule

reorientation after trans→cis→trans cycle can be written as 1

λ λ Preor ≈ 1 − (1 − qreor,iso )2 (1 − qreor ) φt→c

1 −2 c→t

+φ

.

(1)

For each environment type at selected temperature, only two equations 1 can be written (for 546 405 546 405 Preor and Preor ) which contain three unknown parameters: qreor,iso , qreor and qreor . Therefore,

we can only estimate the accessible regions for each parameter. For the environment of 2-nd type in PnHexMA at 213 K (marked data in Figure 3), the value of qreor,iso was found to lie in the range from 0.04 to 0.077. When the qreor,iso runs from 405 546 from 0.039 to 0.03 (see Supporting runs from 0.022 to 0 and the qreor 0.037 to 0.077, the qreor λ are anticorrelated: the larger Information: Note 2 and Figure S2). The qreor,iso and qreor λ . Thus, the probability of the molecule reorientation the qreor,iso is, the less are the qreor

without isomerization upon absorption of 405 nm photon is more than that upon absorption of 546 nm photon at least by a factor of 1.8. 19 ACS Paragon Plus Environment


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Comments on Fitting Procedure and Validity of Obtained Parameters Here, we briefly discuss how the approximations made to fit the experimental data affect fitting results and conclusions. The first approximation consists in setting the same value of Ω for all molecules at a given temperature in a given polymer. The use of the distribution of Ω results in somewhat better fitting of experimental curves and, in some extent, influences the parameters Preor , but it does not change the conclusions about the wavelength dependence of Preor . The second approximation consists in setting the α to be independent of polymer and temperature. We found that some variation in α (which is considered to be independent of the site in a polymer matrix) leads to a change in Ω and Preor ; however, the Preor changes in a similar manner at both irradiation wavelengths, 405 and 546 nm. Therefore, the variation in α does not change the conclusion about the wavelength dependence of Preor . In the context of this paper, the crucial assumption is that the α is independent of wavelength. Formally, introducing the dependence of α on wavelength, temperature and site in a polymer matrix, we can obtain a good description of the anisotropy induced both by 405 and 546 nm irradiations at all temperatures. However, physically, the wavelength dependence of Preor seems to be more probable than the wavelength dependence of α. The arguments are as follows: i) the assumption that α depends on temperature results in physically implausible values of this parameter (several degrees) at low temperatures, while a small Preor seems to be reasonable, ii) it is hard to explain why the α increases from ≈ 30◦ to ≈ 60◦ when the wavelength of irradiation changes from 546 to 405 nm, while the wavelength dependence of Preor in combination with the Persico’s hypothesis of molecule rotation without isomerization seems to be plausible. At the same time, we cannot completely exclude the temperature dependence of α. If so, the temperature dependence of Preor will be weaker than that reported here.


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Conclusions The formation of light-induced anisotropy in poly(alkyl methacrylates) doped with azo molecules can be consistently described in the framework of the model including temperaturedependent probability of molecule reorientation upon the trans→cis→trans (cis→trans→cis) isomerization cycle and using a single temperature- and site-independent value of the rotation angle. Due to heterogeneity of the polymer matrixes, the reorientation probability depends on the environment of azo molecule. Most likely, there are two mechanisms of lightinduced reorientation: the first one (conventional) connects the reorientation of a molecule with the isomerization event, and the second one, suggested for the first time by Persico and co-workers in their theoretical works, involves the reorientation of azo molecule following photon absorption and electronic excitation without subsequent isomerization. The probability of molecule reorientation following trans→cis→trans cycle was found to be dependent on the irradiation wavelength. Two factors contribute to the wavelength dependence of the reorientation probability: i) the photon energy, and ii) the quantum yield of isomerization which determines the number of reorientation attempts. The observed dependence of the reorientation probability on wavelength indicates that the reorientation of a molecule is facilitated by the energy of absorbed photon.

Supporting Information Available The following files are available free of charge.

Figure S1: UV-vis absorption spectra of

NAMB. Note 1: Details about the dynamical model. Note 2 and Figure S2: Estimation of the reorientation probabilities per one photon absorption.

Acknowledgement The authors are grateful to Galina Dultseva for assistance in the preparation of the manu-



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script. The authors thank B. Bolshakov for kindly providing NAMB. The authors gratefully thank Dr. V. Syutkin for fruitful discussions.

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Wavelength Dependence of the Reorientation Efficiency of Azo Dyes

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