Article pubs.acs.org/JPCB
Study of Molecular Dynamics in Poly(n‑alkyl methacrylates) by Light Induced Absorption Anisotropy S. Grebenkin,* B. Bol’shakov, and V. M. Syutkin Institute of Chemical Kinetics and Combustion, Novosibirsk, 630090, Russian Federation S Supporting Information *
ABSTRACT: Formation of absorbance anisotropy under linearly polarized irradiation at 405 nm in films of poly(ethyl methacrylate) (PEMA), poly(n-butyl methacrylate) (PnBMA), and poly(n-hexyl methacrylate) (PnHexMA) doped with azo compound has been studied in a wide temperature range below Tg. The anisotropy formation kinetics has been well described under the assumption that there are two types of environments in the polymer matrixes: mobile and immobile. The mobile environment allows the dopant to reorient in the course of cis−trans−cis isomerization cycle and the immobile environment does not. The fraction of mobile environments was estimated to be 0.12 in PEMA, 0.65 in PnBMA, and 1.0 in PnHexMA. An increase in the fraction of mobile environments within the series PEMA−PnBMA−PnHexMA have been associated with an increase in the size of alkyl nanodomains. The average angle of transition dipole rotation upon isomerization and the amplitude of molecules librations have been estimated in the temperature range studied.
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INTRODUCTION The phenomenon of light-induced optical anisotropy in azocontaining amorphous solids has been reported for the first time by Neporent and Stolbova in 1961.1 They have observed an optical dichroism (different absorption of light with different polarizations) of a solution of azo in poly(vinyl alcohol) below Tg after irradiation of the sample with linearly polarized light. They supposed that the anisotropy arises due to light-induced cis−trans isomerization of azo molecules. A period of intensive study of the optical anisotropy had started much later, in early 90s.2−11 The interest to the issue was aroused by a probable application of azo-containing polymers in technologies for information storage and optical switches.12−14 Along with dichroism, optical anisotropy manifests itself in the form of birefringence.15−18 A common model used to describe anisotropy generation takes into account the following processes: (i) photoisomerization, which can be presented as the disappearance of a molecule with some orientation in one isomeric state and the appearance of a molecule in another isomeric state, (ii) the dark cis−trans isomerization, and (iii) rotational diffusion.19,20 The reorientation of azo molecules following the trans−cis−trans isomerization cycle constitutes the light-induced angular redistribution. The main question at issue for the angular redistribution concerns the orientation of transition dipole after cis−trans isomerization. A variety of models of angular redistribution was suggested. The simplest one is the model of purely correlated turns: it is assumed that each molecule has just one orientation in cis form and one orientation in trans form.20 The second important model is the conical model, which implies the transition dipole changing its direction upon isomerization by a fixed angle with equal probability relative to the initial direction.19,20 Several other models were also introduced.21,22 © 2014 American Chemical Society
Suggested models qualitatively reproduce the majority of the anisotropy generation features, whereas a quantitative description, as a rule, is not achievable due to the heterogeneity23 of a medium. In the present paper, we propose an approach for quantitative description of anisotropy formation in heterogeneous medium. The approach is based on the usage of two simplest models: the model of purely correlated turns (purely correlated model) and the conical model. These models can be easily discriminated because the former one does not include angular redistribution, and anisotropy is formed by a pure angular hole burning mechanism.20 In the framework of the approach, the conical and purely correlated models describe reorientation of molecules in the mobile and immobile environments, respectively. It has been shown by dielectric and mechanical spectroscopy, X-ray, and calorimetric methods that in poly(n-alkyl methacrylates) (PnAMA), side chains aggregate in alkyl nanodomains.24−27 This phenomenon, named nanophase separation,24 was observed in PnAMA with four and more alkyl carbons in side chain. The alkyl nanodomains preserve high mobility at temperatures much below conventional Tg of polymer.25,28 Thus, PnAMAs are the amorphous polymers that include the mobile and immobile regions in natural way; the volume fractions of these regions change monotonically with the side chain length. The proposed approach has been applied to describe light induced reorientation of azo molecules in poly(n-ethyl methacrylate) (PEMA), poly(n-butyl methacrylate) (PnBMA), Received: May 1, 2014 Revised: July 27, 2014 Published: July 28, 2014 9800
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Figure 1 shows the optical absorption spectra of NAMB in PnBMA before irradiation and after 1 min of irradiation with polarized light of 405 nm. The steady state fraction of trans isomer decreases with temperature. In PnBMA, its value was estimated to be 70 and 21% upon irradiation with the wavelength of 405 nm at 193 and 253 K, respectively. At the beginning of irradiation, about 94% of light is absorbed by the samples. Therefore, the light intensity is not constant throughout the sample. In addition, the intensity changes inside the sample in the course of isomerization. Nevertheless, in case of dynamically homogeneous matrix, the kinetics of cis−trans isomerization of NAMB follows the firstorder law within a good accuracy; the light intensity can be considered to be constant in time and space throughout the sample and be equal to an effective value, which is several times less than the intensity of incident light. In the case of heterogeneous matrix, the isomerization kinetics of dynamically equivalent molecules also follows the first-order law within a good accuracy (see Supporting Information, Note and Figure S1). For this reason, we will consider light intensity to be constant in time and space.
and poly(n-hexyl methacrylate) (PnHexMA) matrixes. First, we present the time profiles of anisotropy formation in polymers studied and argue that the mechanism of anisotropy formation is different in these polymers. Then, we describe quantitatively the anisotropy development. Finally, we sketch a picture of the rotational dynamics of azo molecules in these polymers.
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EXPERIMENTAL METHODS The experimental technique has been described in detail elsewhere.29,30 Here, basic details only are given. PEMA (Mw = 515 000 by GPC, Tg = 336 K) and PnBMA (Mw = 337 000 by GPC, Tg = 288 K) were purchased from Aldrich and PnHexMA (Approx. Mw = 400 000, Tg = 268 K) was purchased from Scientific Polymer Products, Inc. 1-naphthyl-p-azo-methoxybenzene (NAMB) was synthesized in our laboratory in accordance with ref 31. The chemical structure of NAMB and monomeric units are given in Figure 1. The concentration of azo in the polymers was about 5 × 10−3 mol/L.
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EXPERIMENTAL RESULTS The time profiles of anisotropy formation in the polymers studied are essentially different, see Figures 2, 4, and 5. We will discuss them one by one. The denotation Abs0 stands for Abs(0).
Figure 1. UV−vis absorption spectrum of NAMB in PnBMA before irradiation (top curve) and after 1 min of irradiation with Z-polarized light of 405 nm. Probe light is polarized along Y axis (middle curve) and Z axis (bottom curve), T = 233 K. The inset shows the chemical structures of NAMB and monomeric units of PEMA (n = 2), PnBMA (n = 4), and PnHexMA (n = 6). Figure 2. Formation of the optical anisotropy in PEMA under linearly polarized irradiation at 405 nm. Inset shows the initial parts of the curves. The lines are fitting curves.
To generate optical anisotropy, the samples were irradiated with linearly polarized (along Z axis) light with a wavelength of 405 nm (polarizer from LOMO PLC with the extinction ratio of 500 at 405 nm). The light of 405 nm was isolated from the radiation of a high-pressure mercury arc lamp. The photon flux (measured with the power meter Thorlabs PM120) at 405 nm was (8.3 ± 0.9) × 1015 photons s−1 cm−2. The polymer films were oriented at an angle of 45° both to the irradiation and probe beams, which propagated along Y and X axes, respectively. The probe beam (382 nm) was polarized either along Z or along Y axis. We define the anisotropy and the isotropic absorbance as
Anisotropy Formation in PEMA. Figure 2 represents anisotropy formation kinetics in PEMA. At 243 and 273 K, the time profiles are typical of the anisotropy formed by the angular hole burning mechanism.19,32,33 This mechanism excludes angular redistribution of molecules and suggests only one orientation for each isomer. The fast initial anisotropy growth (0 < t < 50 s) is caused by isomerization of the molecules oriented predominantly along Z axis. The following slow decrease is due to isomerization of the rest molecules. The nonzero steady state level testifies to a nonzero value of the angle between the transition dipoles of cis and trans isomers (if this angle is zero, then the asymptotic value of anisotropy must be zero). Slow anisotropy growth at long times (t > 1000 s) at 203 K testifies to an angular redistribution of a small fraction of molecules. At higher temperatures, the anisotropy curves do not display a sign of the angular redistribution. We conclude
Anisotropy(t ) = Abs Y (t ) − AbsZ (t )
Abs(t ) =
Abs Z (t ) + 2Abs Y (t ) 3
where AbsY and AbsZ are the sample absorbances measured at 382 nm with light polarized transversely and parallel to the polarization of irradiation, respectively, t is time. 9801
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that at 243 and 273 K, the rotational diffusion of these molecules is too fast, therefore they contribute negligibly to the anisotropy. Depicted in Figure 3 anisotropy decay kinetics confirms this assumption: a small fraction of molecules exhibits fast rotation at 243 K and no rotation is observed at 203 K.
Figure 5. Formation of the optical anisotropy in PnBMA under linearly polarized irradiation at 405 nm. The lines are fitting curves. Figure 3. Time profiles of anisotropy decay following 30 s of irradiation with linearly polarized light of 405 nm, NAMB in PEMA.
(compare with PnHexMA). Suggestion of the angular redistribution is in harmony with the observation of the noticeable rotational diffusion of NAMB in PnBMA in the range 243−263 K.30 At 193 K, the angular redistribution becomes apparent. We interpret these results as a reflection of two essentially different types of environments. The azo molecules located in the environments of the first type are able to reorient during the trans−cis−trans cycle and the molecules located within the environment of the second type are unable to do so. Thus, the matrix of PnBMA represents an intermediate case between PEMA and PnHexMA.
Thus, in PEMA, the anisotropy is formed predominantly by a pure hole burning mechanism. Anisotropy Formation in PnHexMA. Anisotropy formation in PnHexMA is shown in Figure 4. The time profiles
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MODELING OF ANISOTROPY FORMATION: APPROACH We suppose that the change in the direction of each transition dipole upon isomerization is governed, depending on the environment, by either the conical or purely correlated reorientation mechanism. In the former case, upon isomerization, the transition dipole rotates equally probably relative to the initial direction by a fixed angle. In the latter case, a molecule has just one orientation in each, cis or trans, isomeric form. We postulate that in case of the arrested rotation of a molecule the reorientation mechanism is purely correlated, otherwise it is conical. We also assume that the dynamical parameters of a molecule (the rotational diffusion constant, isomerization quantum yields, and angle of transition dipole rotation upon isomerization) do not change during experimental time. Figure 6 demonstrates a principal difference between the conical and purely correlated models. At the same values of effective rate constants of isomerization, kt→c ≡ Iσtϕtc and kc→t ≡ Iσcϕct, and the angle of transition dipole rotation upon isomerization, α, the models result in close initial parts of the anisotropy time profiles and strongly different curves at longer times. Here, I is the effective light intensity (see Supporting Information: Note, Figure S1), σt and σc are the cross sections of trans and cis molecules when the transition dipole of a molecule is parallel to light polarization, and ϕtc and ϕct are the quantum yields of trans → cis and cis → trans isomerization, respectively. For both models, the initial growth of anisotropy is due to the trans → cis isomerization of the molecules oriented mainly along light polarization. That is, at small times, angular hole burning is the predominant process irrespective of the model. Therefore, the characteristic time of the initial rise in anisotropy is the same for both models (this time can be estimated as 3(2.23Iσtϕtc)−1, ref 19). At longer times, the
Figure 4. Formation of the optical anisotropy in PnHexMA under linearly polarized irradiation at 405 nm. The lines are fitting curves.
have characteristic features of the angular redistribution: (i) there is no maximum observed in the time profiles besides a tiny one that can be found on the curve obtained at 233 K, (ii) the steady state level of anisotropy increases with temperature decrease. The latter is caused by two factors. The first one is the decrease in the rotational diffusion of azo. It was shown that the rotational diffusion of NAMB in PnHexMA slows down strongly in the temperature range measured.30 The second factor is an increase in the steady state fraction of strongly absorbing trans isomer with a decrease in temperature. In the case of pure hole burning, an increase in the steady state fraction of trans isomer leads to a decrease in anisotropy. At 193 K, the absorption of probe light polarized transversely to the polarization of irradiation (AbsY) increases at long times (Supporting Information, Figure S2). Such behavior is a signature of the angular redistribution. We conclude that the matrix of PnHexMA allows the azo molecules to rotate during the trans−cis−trans isomerization cycle. Anisotropy Formation in PnBMA. The kinetics of anisotropy formation in PnBMA bears the stamps of both the hole burning and angular redistribution (see Figure 5). In the range 243−263 K, the anisotropy time profiles have the maximum which is a typical sign of hole burning (as is the case with PEMA). On the other hand, an increase in anisotropy with a decrease in temperature points to the angular redistribution 9802
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rotate) was described with the conical model also using single parameter set. Accordingly, the anisotropy and absorbance time profiles were fitted each with a sum of two curves. The fraction of nonrotating molecules was determined to be 0.88 at all temperatures. The anisotropy fitting curves are depicted in Figure 2. The absorbance curves also were well fitted (see Supporting Information Figure S3). PnHexMA. In PnHexMA, all the molecules can rotate, therefore, to fit the anisotropy formation, only the conical model was used. At the same time, the anisotropy decay reflects the heterogeneity of matrix and was described using discrete distribution of molecules over rotational times consisting of four groups.30 Therefore, the anisotropy formation kinetics were fitted with a sum of four curves; each curve was simulated using the conical model with individual parameters set (kc→t, kt→c, α and Ω). The anisotropy fitting curves are shown in Figure 4; the absorbance curves were also well fitted. PnBMA. The anisotropy time profiles shown in Figure 5 indicate the existence of two main types of environments in PnBMA: the environments of the first type allow azo molecules to rotate and the environments of the second type do not. At the same time, the anisotropy decay was satisfactorily described on the assumption of four dynamically different ensembles of molecules.30 For this reason, to fit the anisotropy formation curves, we used a four-ensemble distribution of azo molecules. The rotational times of two “slowest” ensembles greatly exceed the times of anisotropy formation at the same temperature; therefore, the molecules of the two “slowest” ensembles were considered as nonrotating ones. We tried to fit the anisotropy formation in PnBMA using only the purely correlated or only the conical model. Neither of the two fits were successful. The reason is that the conical model gives too slow initial anisotropy growth, whereas the purely correlated model provides too fast one (for the observed steady-state value of anisotropy). Only a combination of these models results in good fitting of the experimental data. The best fit was obtained using the purely correlated model for two “slowest” ensembles (with weights of 0.21 and 0.14) and the conical model for two “fastest” ones (with weights of 0.34 and 0.31). Figure 5 shows the fitting curves. The ensemble weights are the same at all temperatures.
Figure 6. Anisotropy time profiles simulated with the conical model and model of purely correlated turns using the following parameters: α = 46°, kt→c = 0.1 s−1, kc→t = 0.025 s−1. No rotational diffusion and librations.
conical model gives an increase in anisotropy due to the angular redistribution, whereas the purely correlated model gives an anisotropy decrease. As a result, the conical model gives much higher steady-state anisotropy level than the purely correlated one. For the same steady-state value of anisotropy, the conical model gives a smaller initial rate of anisotropy formation than the purely correlated model. This difference in the initial rates allows us to discriminate between these two models and choose the appropriate one. The dynamical heterogeneity of the matrixes was introduced via a set of dynamically different ensembles of azo molecules. In the cases of PnBMA and PnHexMA, we used a discrete distribution consisting of four groups of probe molecules because the decay of light induced anisotropy was described using such a distribution.30 The weights of distribution and the constants of rotational diffusion were obtained from fitting the anisotropy decay curves earlier.30 The previous study30 of anisotropy formation in PnBMA and PnHexMA shows that the librations34−39 of molecules strongly decrease the anisotropy level. Thus, the fitting parameters for ith ensemble are the effective rate constants, kt→c,i and kc→t,i, the angle of transition dipole rotation upon isomerization, αi, and the amplitude of librations, Ωi. The time profiles of isotropic absorbance strongly depend on rate parameters, kt→c,i and kc→t,i, and to a smaller extent on αi and Ωi. Therefore, at first, the estimates of kt→c,i and kc→t,i were obtained from fitting the absorbance time dependence (using least-squares fit); we considered the steady state isomer ratios to be independent of i. The anisotropy time profile strongly depends on all the parameters; however, to fit the anisotropy, only the parameters αi and Ωi were varied. The steps “absorbance fit−anisotropy fit” were repeated until a good fitting quality was obtained (typical fitting result is shown in Supporting Information Figure S3). The general equations for the conical model was derived elsewhere,30 the equations for the purely correlated model are given in Appendix.
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DISCUSSION Peculiarities of Anisotropy Formation. Figure 2 demonstrates a nonmonotonic temperature dependence of the anisotropy steady-state level in PEMA: at 243 K, the anisotropy is greater than at 203 and 273 K. Such a surprising temperature behavior is easily understood in the context of the purely correlated model. According to this model, the steadystate anisotropy is zero when the content of trans isomer is zero because, in this case, the angular distribution of cis molecules is isotropic. Also, the anisotropy is zero if the content of trans isomer equals 100%. Between the two zeros, the anisotropy necessarily has a maximum (a typical dependence of the steadystate anisotropy on the steady-state content of cis isomer is shown in Figure S4 of the Supporting Information). The steady-state content of cis isomer decreases when temperature decreases because the quantum yield of trans → cis isomerization of azo-compounds decreases with lowering temperature.40 Taking the α and Ω as they were obtained from fitting the anisotropy formation kinetics at 243 K (56 and 32°, respectively) and varying the ratio kt→c/kc→t, we simulated a set of anisotropy formation time profiles. The maximum steady-
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FITTING RESULTS PEMA. The majority of the molecules do not rotate in PEMA. We described the evolution of their angular distribution with the purely correlated model using a single parameter set for all these molecules. That is, we did not find a dispersion in the rotation angles and libration amplitude for these molecules. The reorientation of the rest of the molecules (which can 9803
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state anisotropy was found at cis isomer fraction of ≈50% (Supporting Information, Figure S4). From the temperature dependence of the steady-state absorbance (obtained in a separate experiment), the steady-state cis fraction was estimated to be 50% at ≈200 K. However, the value of steady-state anisotropy at 243 K exceeds that at 203 K. Hence, the maximum is closer to 243 K. The shift of the maximum to a higher temperature is probably caused by a decrease in rotation angle α with a decrease in temperature. The temperature dependence of α will be presented in the next section. Strongly pronounced features of the angular hole burning are most likely a consequence of low concentration of azo compound and low irradiation intensity. If a high concentration of azo is used, the azo molecules influence each other and the anisotropy time profiles can bear a stamp of angular redistribution even in “stiff” polyimide matrix.16 Within the approach of effective orientation potential,41−43 it has been shown that both the high irradiation intensity and high concentration of azo are required to produce changes in polymeric environments.42 The time profiles of anisotropy formation in PnHexMA are typical for the case of rotating molecules. A decrease in temperature leads to an increase in anisotropy level due to both the decrease in rotational diffusion and increase in the content of trans isomer. Simultaneously, the angular redistribution slows down, which can be interpreted to be due to a decrease in rotational angle α. The most interesting feature of anisotropy formation in PnBMA is the disappearance of the maximum on the curve at the lowest temperature, see Figure 5. In PnBMA, two-thirds of molecules can rotate and one-third cannot. The anisotropy formed by the latter molecules always has a maximum. In case of rotating molecules, the existence of the maximum is determined by two competitive processes: angular redistribution and trans → cis isomerization. In the beginning of irradiation (the first stage of the anisotropy formation), both processes lead to an increase in anisotropy, AbsY(t) − AbsZ(t), as both processes decrease the AbsZ(t). At the second stage, isomerization leads to a decrease in anisotropy because the molecules directed mainly along the Y axis react. Simultaneously, angular redistribution brings about the anisotropy increase. Depending on the relation between the rates of trans → cis isomerization and of angular redistribution, the anisotropy can increase or decrease. At high temperatures, the steady-state content of trans isomer is low (21% at 253 K); therefore, the rate of trans → cis isomerization is high, and a decrease in AbsY(t) caused by the isomerization prevails over an increase due to the angular redistribution. As a result, the anisotropy decreases, and we observe the maximum. At 193 K, the steady-state content of trans isomer is high (about 70%); therefore, angular redistribution dominates and no maximum is observed (see Figure 5). To sum up, the anisotropy formation in the studied matrixes looks as follows. There are two main types of environment: the mobile one, which allows a molecule to rotate, and the immobile one, which does not. The molecules located in mobile environments participate in three processes: (i) cis− trans isomerization, (ii) photoinduced orientation, and (iii) rotational diffusion. The molecules from the immobile environments are involved in isomerization only. Rotational Angles and Libration Amplitudes. The average rotation angles, , and the libration amplitude, , are presented in Figure 7 for all the polymers. Only the
Figure 7. Average angles of transition dipole rotation per one photoisomerization act (405 nm) (a) and libration amplitudes (b). Circles: PEMA (only nonrotating molecules). Triangles: PnHexMA. Solid squares: PnBMA (nonrotating molecules). Open squares: PnBMA (rotating molecules). Semifilled squares: PnBMA (the average over all molecules). The bars reflect the accuracy of the analysis. The lines are a guide for the eye.
data on nonrotating molecules (fraction 0.88) are shown for PEMA; the parameters for rotating molecules are not presented because their accuracy is poor. For PnBMA, the for the rotating (total fraction 0.65) and nonrotating molecules are shown separately. The figure demonstrates an increase in the rotation angle with temperature. In the case of PEMA, this increase is much weaker (if any) than in the cases of PnBMA and PnHexMA. Within the accuracy of the analysis, the amplitude of probe libration in PEMA does not change in the range studied, whereas in PnBMA and PnHexMA, it changes considerably. The uncertainties in evaluation of rotational angle and libration amplitude for an individual ensemble of the probes in PnBMA and PnHexMA are high. However, the uncertainties in evaluation of the average (over all molecules) values and are much smaller: when another “good” set of fitting parameters is obtained, an increase in the parameter α (or Ω) for one ensemble is compensated by its decrease for another one (ones). On the basis of the results of many fits, we estimated the errors for average values and as they are shown in Figure 7 by bars. We tried different distributions of molecules over mobile and immobile environments. In case of PnBMA, we also simulated the anisotropy formation considering the molecules from one and from three slowest ensembles as nonrotating ones. The anisotropy formation in PnHexMA also was simulated assuming that the molecules from the slowest ensemble cannot rotate. In all the cases, the average values of α and Ω changed with temperature in a similar manner to those shown in Figure 7, although the fitting quality was worse. Physical meaning of parameter α for PEMA and for PnHexMA is not the same. In the former case, α is the angle between two stable directions (for cis and trans) of the transition dipole. In the case of PnHexMA, α has a sense of the effective angle of the transition dipole rotation upon one 9804
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The fraction of mobile environments increases with an increase in the length of side chain: only 12% of azo molecules embedded in PEMA have mobile environments, whereas in PnHexMA, all the molecules are located in such environments. The mobile environments are considered to be the alkyl nanodomains formed by the side chains. The immobile environments most probably are formed by the main chains. The angle by which the transition dipole rotates upon isomerization of azo in PEMA (in immobile environments) depends only slightly on temperature (if at all). For the probes located in mobile environments, in PnBMA and PnHexMA matrixes, this angle decreases strongly with a decrease in temperature. In a similar manner, the amplitude of molecules libration in PEMA does not depend on temperature, whereas that in PnBMA and PnHexMA decreases as temperature decreases.
isomerization event. We speculate that in PnHexMA (as well as, in PnBMA, in the mobile environments), not each trans−cis− trans isomerization cycle leads to reorientation of the molecule. The more the number of “unsuccessful” trans−cis−trans cycles, the less the apparent angle α is. Thus, if molecules are able to rotate, their angular redistribution can be described with the conical model, and α is the measure of this ability. Manifestation of Alkyl Nanodomains in the Dynamics of Azo Molecules. In polymeric matrixes with long alkyl side chains (with the number of the alkyl carbons four and more), alkyl groups aggregate and form nanodomains with a typical size of 0.5−2 nm.24−26,28,44 In these nanodomains, the side chains preserve high mobility even below conventional glass temperature of polymer. The size of nanodomains depends on the length of side chain. The distance between the main chains that border the nanodomains, in PEMA, PnBMA, and PnHexMA, are 1.0, 1.2, and 1.43 nm, respectively, according to the data of Hiller et al.26 and 1.0, 1.3, 1.6 nm according to Arbe et al.44 The sizes of mobile nanodomains is smaller than these distances; however, they increase with side chain length in the similar manner. Our findings can be interpreted within the concept of such nanodomains. We infer that there is a correlation between the nanodomain size and the fraction of azo molecules located in mobile environments. Actually, the majority of azo molecules have immobile environments in PEMA. At the same time, the fraction of mobile environments in PnBMA amounts to 65%, and in PnHexMA, it reaches 100%. In the plane of rings, the trans molecule of NAMB is 0.83 nm wide and 1.5 nm long (estimated using Persico’s data for azobenzene.45) The voids that are detected in pure PnAMAs have a typical size of only 0.5−0.6 nm.46 Hence, for the molecule to rotate, the surrounding polymeric chains must be displaced. The mobility of main chains is frozen out in the temperature range studied, whereas the alkyl nanodomains retain high mobility.24 As the length of side chain increases, the volume fraction of alkyl nanodomains increases. Accordingly, the fraction of azo molecules located in mobile environments increases. In PEMA, the libration amplitude Ω does not depend on temperature and rotation angle α depends weakly (if at all), whereas in PnBMA and PnHexMA, they change noticeably with temperature. The absence of temperature dependence of α and Ω in the case of PEMA also can be explained in terms of alkyl nanodomains if we assume that the mobility of azo molecules in PEMA mainly reflects the dynamics of backbone chains, which is “frozen” at temperatures below Tg. In turn, in PnBMA and particularly in PnHexMA, the majority of molecules border on the alkyl nanodomains. The dynamics of the nanodomains is not “frozen” and affects the dynamics of probe molecules. An increase in relaxation rate in the nanodomains with temperature causes an increase in the mobility of azo molecules.
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APPENDIX: GENERAL EQUATIONS OF THE PURELY CORRELATED MODEL We assume that only one orientation of trans isomer and one orientation of cis isomer are possible for each azo molecule. The angle between the transition dipoles of cis and trans isomers, α, is assumed to depend on the environment of the molecule. The direction of transition dipole of trans molecule is specified by the polar, θ, and axial, φ, angles in spherical coordinates. At fixed α, the orientation of transition dipole of cis molecule is defined by the angles θ and φ of the related trans molecule and by the azimuthal angle −π < γ ≤ π with respect to the transition dipole of trans molecule. We denote the absorption cross sections of molecules at probe wavelength for light polarized along the transition dipole pr by σpr t and σc , and the angular distribution functions by nt(θ, φ, γ) and nc(θ, φ, γ). Here and below, indexes c and t stand for cis and trans. Because of axial symmetry (irradiation light is polarized along Z), the angular distributions of isomers do not depend on φ. Then we can omit φ: nt,c(θ,γ) ≡ nt,c(θ, φ, γ). 2πnt(θ,γ)sin θ dθ dγ expresses the number of trans molecules in 1 cm3 with transition dipole directions lying in the range from θ to θ + dθ that can convert to the cis molecules with relative orientation specified by the γ lying in the range [γ, γ + dγ]; 2πnc(θ, γ)sin θ dθ dγ expresses the number of such cis molecules. The absorbances of trans and cis isomers measured with Z and Y-polarized light are given by the following equations: Abs Zt , c = 0.434 × 8πσt pr, c ×
π
∫0 ∫0
π /2
nt , c(θ , γ )
(C1 + C2cos2 θt , c)sin θ dθ dγ Abs Yt , c = 0.434 × 8πσt pr, c ×
π
∫0 ∫0
π /2
nt , c(θ , γ )
⎛ C2 2 ⎞ ⎜C + sin θt , c ⎟sin θ dθ dγ ⎝ 1 ⎠ 2
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CONCLUSIONS Formation of anisotropy in the matrixes of PEMA, PnBMA, and PnHexMA reflects the existence of the environments of the two general types: mobile and immobile. The mobile environments allow the molecules to change their orientation in a series of trans−cis−trans conversions, and the immobile environments do not allow it to do this. In the latter case, the molecule has only one orientation for each isomer.
with
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C1 =
2 − cos Ω(3 − cos2 Ω) 6(1 − cos Ω)
C2 =
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cos θt = cos θ
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cos θc = cos α cos θ + sin α sin θ cos γ
θt and θc are the angles between axis Z and the transition dipoles of trans and cis molecule, coefficients C1 and C2 arise from the librations of azo molecules. The librations of molecules about average directions were taken into account by averaging the absorbances over transition dipole directions restricted by a cone with an opening angle of 2Ω.30 If there are no librations (Ω = 0), then C1 = 0, C2 = 1. The kinetic equations for the angular distribution functions are of the form d n t (θ , γ ) = −Iσtϕtc(C1 + C2cos2 θ )nt (θ , γ ) dt 2 + Iσϕ c ct (C1 + C 2 cos θc)nc (θ , γ )
dnc(θ , γ ) = Iσtϕtc(C1 + C2cos2 θ )nt (θ , γ ) dt 2 − Iσϕ c ct (C1 + C 2 cos θc)nc (θ , γ )
where I is the effective light intensity (see Supporting Information, Note), σt and σc are the absorption cross sections at a wavelength of irradiation for the polarization parallel to the transition dipole, ϕtc and ϕct are the quantum yields for trans → cis and back isomerization, respectively. The initial conditions are nt(θ,γ) = N/8π2, nc(θ,γ) = 0, where N is the concentration of azo molecules.
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ASSOCIATED CONTENT
S Supporting Information *
Note regarding the kinetics of photoisomerization. Figure S1: The kinetics of photoisomerization in the case of strong light absorption. Figure S2: Time profiles of absorbances (AbsY and AbsZ) of NAMB in PnHexMA in the course of irradiation with linearly polarized light of 405 nm at 193 K. Figure S3: The example of fitting of the absorbance and anisotropy time profiles. Figure S4: Dependence of the steady-state anisotropy on cis isomer fraction for the case of nonrotating molecules. This material is available free of charge via the Internet at http://pubs.acs.org/.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported, in part, by the Russian Foundation for Basic Research, project No 08-03-00632-a. REFERENCES
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