J. Phys. Chem. B 2008, 112, 15369–15375
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Dynamical Heterogeneity in Glassy o-Terphenyl. 2. Measurement of Environment Structure Lifetime Using Reversible Reactions S. Yu. Grebenkin* Institute of Chemical Kinetics and Combustion, NoVosibirsk 630090, Russian Federation ReceiVed: May 23, 2008; ReVised Manuscript ReceiVed: September 25, 2008
A new method is proposed for measuring the lifetime of heterogeneities in a glassy matrix. UV-vis absorption spectroscopy has been used to monitor the kinetics of photoinduced cisftrans isomerization of 1-naphthylazomethoxybenzene (NAMB) in o-terphenyl (OTP) below Tg. The dependence of isomerization rate on the duration of dark interval after generation of cis molecules was established; an increase in the dark interval causes a decrease in isomerization rate. This dependence is shown to be due to the change in the local environment of NAMB molecules. The time required for the environment to change was estimated over a temperature range of 234 (Tg - 9 K) to 241.5 K (Tg - 1.5 K). The change in the environment of the guest molecules has been interpreted in terms of the exchange processes. The values obtained for the exchange time coincide with the rotation times of the NAMB molecule. Also, it is shown that the time of structural rearrangement of the environment near the fast reacting molecules is of the same order of magnitude as the time of structural rearrangement of the environment near the slow reacting ones. 1. Introduction In the last two decades, the dynamics of supercooled liquids and glasses has been studied extensively. This problem is considered in a series of reviews1-6 and many original works in some of which the novel methods for studying dynamics in disordered media have been developed. The most extensively used method for studying relaxation in the disordered phase is the dielectric spectroscopy.7-19 It allows investigations over wide time and temperature ranges. The NMR method is used to study the rotation of molecules and polymeric segments over the time ranges of 10-4 to 102 s at temperatures slightly above Tg.20-24 The probe rotation times in amorphous media are measured using optical methods such as photobleaching technique,25-29 single molecule spectroscopy (SMS),30-35 and second harmonic generation.36-38 These methods allow one to obtain rotation times over a wide temperature range, including glass transition temperature. The dynamics in amorphous media has been also studied using ESR method39,40 and the method of solvation dynamics.41,42 To date, it has been established that (1) the dynamics in amorphous media is heterogeneous, that is, the characteristic times of molecular motions in different regions of a matrix are different (spatially heterogeneous dynamics), (2) with time the region of high mobility can transform into that of low mobility and vice versa (dynamical heterogeneity). The average period during which the molecular mobility of a region remains constant is referred to as “lifetime of the heterogeneity”2 or “exchange time”.28 In the framework of the concepts of medium heterogeneity, the lifetime and length scale of heterogeneous regions are of most interest. In the present work, we shall restrict our consideration to the heterogeneity lifetime. Note that the size of heterogeneities is estimated, as a rule, at several nanometers. For example, it was estimated that “OTP is homogeneous on * To whom correspondence should be addressed. E-mail: grebenk@ ns.kinetics.nsc.ru.
length scales greater than 2.5 nm at Tg”.26 In poly(vinyl acetate) (PVA), the value of 3 nm at Tg +10 K43 was obtained for the heterogeneities length scale. Few literature data are available on exchange time. The exchange times were measured by the photobleaching technique27-29 in OTP and polystyrene at Tg or slightly higher, by the method of multipulse NMR in low-molecular weight and polymeric substances at temperatures above Tg21,22,24,44 and by the single molecule spectroscopy.30,33-35 In addition, the exchange time was estimated by means of solvation dynamics,45 dielectric hole burning,18 and atomic force microscopy techniques.46 Note that most of the works devoted to the measurement of exchange times were performed at temperatures exceeding the glass transition temperature. Only some data were obtained at temperatures below Tg.34,46 Since in different works the measurements were made over different temperature ranges and using different substances, a direct comparison of results is impossible. Nevertheless, one can make a qualitative comparison that reveals some inconsistency in the data. Thus, the results from NMR and dielectric measurements indicate that the exchange time and the time of R-relaxation are the values of the same order of magnitude. At the same time, the data provided by SMS testify that the exchange time exceeds even the rotation time of probe molecules by an order of magnitude or more. Thus, the ratios between the exchange time and the time of rotation, τex/τrot, measured by SMS30 and NMR22 methods in OTP differ from each other by more than order of magnitude. R. Zondervan et al.35 using the SMS estimated the τex/τrot for a large probe molecule in glycerin at Tg + 22.5 K, at the minimum, as 105. Further, the data of photobleaching experiments indicate a strong temperature dependence of τex/τrot in OTP whereas the results of SMS measurements in OTP30 and dielectric measurements in PVA46 do not show signs of such a dependence. New experimental data are required on the exchange processes and their times. The present work reports the exchange times in OTP at temperatures below Tg. The process, which is
10.1021/jp806159b CCC: $40.75 2008 American Chemical Society Published on Web 11/11/2008
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Figure 1. The chemical structure of NAMB.
sensitive to matrix heterogeneity and change in environment is the kinetics of the cisftrans isomerization of probe molecules. The monomolecular reactions in amorphous matrices have been studied for a long time. The most frequently used reactions are the cis-trans isomerizations of azo-compounds47-53 and stilbenes50,51,54,55 and isomerization of merocyanines.56-58 There also are examples of more rare reactions, for example, racemization.59 The method used in this work is as follows. Under exposure to short-wavelength light, the probe molecules of azocompounds are converted from the trans form into the cis one. The inverse reaction induced by long-wavelength light is started within period, τdark, after formation of cis molecules. The change of probe molecule environment manifests itself in the change of the cisftrans isomerization quantum yield with varying duration of τdark. The idea of the method resembles that of solvation dynamics approach.41,42 The principle common for both of these methods is the formation of a new state of guest molecule and monitoring of the response of the medium to this event. Earlier, in the same system (NAMB/OTP) the lifetime of environment nearby the cis particles whose quantum yield of cisftrans isomerization is lower than average have been measured below Tg.60 It is interesting to compare the new data with the previous ones. 2. Experimental Section 2.1. Experimental Details. The experimental technique has been fully described elsewhere.60 Here, we just mention the most important details. The isomerization kinetics was monitored by measuring sample absorbance at the wavelength of the absorption maximum of the trans isomer (388 nm). A 500 W high-pressure mercury arc lamp was used as a source of irradiation light. The required lines of the mercury spectrum were isolated using standard sets of colored glass filters. The sample was prepared by the following procedure. A Pyrex ampule (rectangular cross section of 1 mm × 8 mm) filled with the solution of NAMB in OTP (a concentration of 4 × 10-4 mol/L) was kept at 373-393 K for 20 h under dry air. On heating, the ampule was sealed. Before each measurement, the ampule was kept at 373-393 K for 2 h. After heating, the ampule was housed in a temperature-controlled cell and kept for 17 h at the experimental temperature. Thereafter, the sample (containing the NAMB in the trans form) was irradiated with 405 nm light for 1 min to convert about 30% of probe molecules into the cis form. At each temperature, the initial mole fraction of the cis isomer was almost the same in all the experiments. The kinetics of cisftrans isomerization induced by the 546 nm light was measured following the different dark pauses, τdark, after the irradiation with 405 nm light. The ampules were irradiated in the direction parallel to the 8 mm edges. The probe beam was transverse to the irradiation one. The rate of dark cisftrans isomerization in the temperature range used in this work is quite negligible. The chemical structure of NAMB is depicted in Figure 1.
Figure 2. Kinetic curves for induced by light at 546 nm cisftrans isomerization of NAMB in OTP following the different dark pauses (indicated in figure) after generation of the cis isomer. Lines are results of fitting the data with the KWW equation.
2.2. Isotropic Irradiation Procedure. To simulate isotropic irradiation, the sample was irradiated alternately along the horizontal X and Y axes during equal periods. Here, the XYZ system is rigidly bound to the sample. To irradiate the sample along the Y axis, it was turned around the Z axis through 90°. The sample was irradiated along the X axis through the set of neutral glasses (total transmittance at 546 nm is 0.695) and along Y through the polarizer (transmittance at 546 nm for unpolarized light is 0.351). The polarizer was used to obtain a horizontally polarized light. If the time periods are short, this irradiation procedure is equivalent to the simultaneous irradiations along axes X, Y, and Z with light of identical intensity. Under these conditions, the mean effective light intensity is equal to (0.695 + 0.351)/2 ) 0.523 au. 2.3. Values under Measurement. To obtain isomerization kinetics, the absorptions of the horizontally Absh and vertically Absv polarized probe light were measured at the same time. The combination of these values
Abs(t) ≡
Absh(t) + 2Absv(t) 3
(1)
provides the value that is independent of angular particle distribution under our experimental conditions and directly proportional to the isomeric composition. Hereafter, absorbance denotes the value determined in accordance with eq 1. 3. Results 3.1. The Dependence of CisfTrans Photo Isomerization Kinetics on the Duration of the Dark Pause after Formation of Cis Molecules. Figure 2 shows the kinetics of NAMB photo isomerization at various τdark. The isomerization slows down with an increase in the duration of the dark pause. To obtain time characteristics of the isomerization, the kinetic curves were
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approximated by the Kohlrausch-Williams-Watts (KWW) equation
Abs(t) - Abs∞ ) (Abs(0) - Abs∞)e-(t/τKWW)
β
(2)
where, Abs(t), Abs(0), and Abs∞ are the current, initial, and steady-state sample absorbance values. Figure 3 demonstrates the dependence of parameters τKWW and β on the duration of the dark pause at two extreme temperatures of the range measured. 3.2. Probable Reasons for a Decrease in the Rate of CisfTrans Isomerization after Formation of Cis Isomer. There are two reasons which can cause the decrease in isomerization rate with increasing τdark. The first one is the rotation of cis molecules. A short-term (1 min) irradiation with light at 405 nm results in only partial conversion of trans molecules into cis ones and therefore leads to photoselection.61 Mainly, those trans molecules are converted into cis ones whose transition dipoles lie in the plane transverse to the light beam. If the directions of the transition dipoles of both the parent trans molecule (for light 405 nm) and the obtained cis molecule (for light 546 nm) coincide, the probability of subsequent cisftrans isomerization induced by 546 nm irradiation will be maximum just upon cis molecule formation. The rotation of the cis molecule results in an increase in the angle between the transition dipole and the light polarization. This leads to a decrease in the rate of cisftrans isomerization. The decrease is the greater, the longer is the dark pause. To verify this hypothesis, special experiments have been performed involving “isotropic” irradiation, which excludes the dependence of isomerization probability on molecule orientation. The details of this experiment are described in the experimental section of the paper. The kinetics obtained under the “isotropic” irradiation was compared with that obtained under irradiation along the X axis. To obtain the “one-direction” kinetics, the sample was irradiated along X with unpolarized light through the set of neutral glasses providing total transmittance of 0.533 at 546 nm. The value of filter transmittance was chosen to provide approximately the same total photon flux in the “isotropic” and “one-direction” irradiation methods. The kinetic curves obtained using “isotropic” irradiation are shown in Figure 4 for dark pauses of 30 s and 2 h. The isomerization kinetics depends on τdark even in case of “isotropic” irradiation. Moreover, the kinetics does not depend on the type of irradiation. Since a decrease in the cisftrans isomerization rate with increasing τdark is not due to the reorientation of molecule transition dipoles, the only reason for this phenomenon is a change in their local environment. Two interpretations of this change can be suggested. The first one is as follows. The change in the local environment is due to the exchange processes. Initially, all probe molecules are in the trans form. In an equilibrium matrix, there is some equilibrium distribution of their environments over configurations. The irradiation with 405 nm light for 1 min leads to only partial conversion of trans molecules into the cis form (about 30%). At first, the loose trans molecules react; they have the highest isomerization rate (“fast” molecules). Therefore, the partial conversion results in isomerization mainly of loose trans molecules. Under the conditions of heterogeneity, the rates of forward and back reactions in a matrix are correlated.58 Therefore, the cis molecules obtained in such a way are the “fast” cis molecules. Thus, the used method allows to select
the environments with loose probe molecules. With time, due to the exchange processes, the distribution of cis molecules over isomerization rates tends to equilibrium. The equilibration time is the time required for the environment to change; that is the exchange time. The second interpretation of the change in the environment of probe molecules consists of the following: the change is caused by a structural relaxation of the matrix around the cis molecule. What does it mean? Immediately after transfcis isomerization the environment of a cis molecule “remembers” the geometry of trans molecule and does not fit the geometry of sic molecule. At this time, the probability of the back process is the highest. Because of the structural relaxation, the matrix fits the geometry of cis molecule. In the course of relaxation, the probability of the back process diminishes and reaches a minimum when the matrix becomes fitted to the cis molecule. If we choose the second interpretation, then we have to discuss two subcases. To illustrate these subcases, consider two different equilibrium samples. The first equilibrium sample (“cissample”) contains only the cis molecules. There is some distribution of the cis molecules over their surroundings; the surroundings of some molecules are looser and those of other molecules are more clamped. Also, consider the second equilibrium sample containing only the trans molecules (“transsample”). Short-term irradiation leads to partial conversion of trans molecules and the cis molecules generated are the “fastest” ones. In the first subcase, the cis molecules generated in the “transsample” have the same environment (or close) as a fraction of cis molecules in the “cis-sample” have. If so, then a change in the reactivity of the generated cis molecules does not differ from the change in the reactivity of the corresponding (fast) fraction of cis molecules in the “cis-sample”. And inasmuch as the reactivity of cis molecules in the “cis-sample” changes due to the exchange process, the reactivity of cis molecules in the “trans-sample” changes due to the exchange process also. To summarize, if short photolysis creates cis molecules with environments, which are present in an equilibrium matrix, then the reactivity relaxation is due to the exchange processes and the relaxation time is the exchange time. One can see that this subcase of the interpretation based on the structural relaxation does not differ from the interpretation based on the exchange processes. The second subcase is as follows. The short photolysis creates cis molecules that have the surroundings atypical for an equilibrium sample. These surroundings never exist around cis molecules in equilibrium matrix. The rate of transformation of the atypical surroundings to the typical ones can differ from the rate discussed above, that is, from the exchange rate. If so, the time of reactivity relaxation does not coincide with the exchange time. Then the question arises. What kind of environment do the cis molecules formed in equilibrium matrix have? Is this environment of the first (typical) or of the second (atypical) kind? We cannot answer this question unambiguously because we have no experimental way to determine it. However, the following arguments in favor of the exchange process interpretation can be presented. Short-term irradiation causes the isomerization of mainly loose molecules. It seems likely that the isomerization of loose molecules does not disturb the matrix. In this case, the rearrangements of host molecules after the isomerization proceed in the same way as they do in an equilibrium matrix. On the basis of this, the decrease of
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cisftrans conversion rate will be interpreted below in terms of exchange process. 3.3. Exchange Time Calculation. The exchange time was estimated using the exchange model described in ref 60. The essence of the model is as follows. To describe the kinetics of isomerization under the conditions of heterogeneity, a trimodal distribution of particles over effective rate constants of isomerization was used. It was assumed that each particle belongs to one of three ensembles whose weights Ci and effective rate constants ki are determined by local environment. The transition of molecules from the i-th to the j-th ensemble occurs with the probability Wij. To reduce the number of independent Wij values, it was assumed that the probability of transition from ensemble k to ensemble i is proportional to the equilibrium weight of the i-th ensemble, which can be written as
Wki C ieq ) eq Wkj Cj
(3)
Figure 3. Dependence of the isomerization time τKWW (circles) and parameter β (triangles) on the dark interval between the cis isomer formation and cisftrans isomerization. Lines represent the exponential fit to the τKWW.
Here, Ceq i is the equilibrium weight of the i-th ensemble in the absence of irradiation. In addition, taking into account the principle of detailed balance
Wij C jeq ) eq Wji Ci
(4)
we can express the Wij values in terms of only one parameter of transition probability (e. g., W12) and the equilibrium weights Ceq i . Considering that C1(t) + C2(t) + C3(t) ) 1, all the Wij values are expressible in terms of W12, C1eq, and C2eq. On irradiation with 546 nm light, the steady-state fraction of the trans isomer is about five times as high as that of the cis isomer. Therefore, in simulations, the transfcis isomerization was neglected. As a result, the set of kinetic equations describing the cisftrans isomerization is of the form
dCi(t) ) -kiCi(t) dt
∑ WijCi(t) + ∑ WjiCj(t) j*i
Figure 4. First-order plots for induced by light at 546 nm isomerization of NAMB in OTP. Triangles, irradiation along one direction; circles, “isotropic” irradiation. Values of dark pauses are indicated in the figure.
(5)
j*i
The values of Ci(0) and ki were determined at each temperature from the kinetic curves obtained after a minimum dark pause (30 s). The Ci(0) values obtained were set equal for the kinetic curves for all values of the τdark at a given temperature. eq The W12, Ceq 1 , and C2 were found from the numerical solution of eq 5, which provides the best coincidence between the calculated and experimental kinetic curves. Data fitting was performed as follows. First, at a given temperature the curve for the maximum value of τdark was fitted. The resulting Ceq i values were used to fit the rest of the curves at a given temperature. At 239 and 241.5 K all kinetic curves can be fitted using one set of Ceq i (for each temperature). At 236.5 K a satisfactory fitting of the curve at τdark ) 5 min can be performed only for the set of Ceq i differing from that used for the other τdark values (50, 160, 720 min). At 234 K for the curves at τdark of 3 and 15 min, acceptable fitting gives the Ceq i set differing substantially from that for the larger τdark values (150 min, 440 min, and 72 h). Most probably, this is due to the nonexponential character of the environment relaxation.
Figure 5. First-order plots for photo isomerization of NAMB in OTP at different dark pauses: 30 s, 3 min, 440 min, and 72 h (from top to bottom), 234 K. Solid lines are results of fitting the data with the model described in the text.
As an example, the fitting parameters for the experimental data at 241.5 K are cited below. The values of 0.86, 0.12, and 0.02 were obtained for the initial weights, C1(0),..., C3(0), and the values of 0.44, 0.45, and 0.11 for the equilibrium ones, Ceq 1 ,..., C3eq, respectively. The corresponding values of k1-1,..., k3-1 are 0.19, 2.6, and 16.0 min, respectively. Figure 5 depicts the typical simulated kinetic curves (234 K). Note that in the experiments performed, the equilibrium distribution was achieved only at the two highest temperatures of the range measured, 239 and 241.5 K, for the maximum duration of the dark pause. The conclusion about the achieve-
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Figure 6. Arrhenius plot for the exchange time. Empty circles, data estimated using the model described in the text; crosses, data estimated from the time dependence of τKWW; filled circles, data from the work.60 Also the rotation times63 are shown (triangles).
ment of equilibrium distribution was drawn from the invariability of isomerization kinetics with further increase in the dark pause. At 236.5 K, the maximum duration was 12 h. From reference 62, it is concluded that the OTP relaxation is completed mainly at times of about 13 h. Therefore, the kinetic curve obtained at 236.5 K after 12 h dark pause is close to the equilibrium one. At 234 K, the relaxation is very slow and there is no assurance that this process is completed during the longest dark pause (72 h). The ensemble average exchange time is determined using the equation:
τex )
∑ i
C ieq
∑ j*i Wij
(6)
For a given temperature, a set of τex values was obtained from the individual fitting of all kinetic curves, except the curve recorded after the dark pause of 30 s. Figure 6 shows the Arrhenius plot for the mean τex which was obtained by averaging individual τex values. The error bars represent one standard deviation. The figure shows also the previous data on the exchange time measured using variable light intensity method60 and the time of NAMB molecules rotation.63 The figure demonstrates the close agreement of all the values. The exchange time can be estimated in a simpler way. To this end, the dependence of τKWW on τdark was approximated in terms of the exponential law
τKWW (τdark) ) (τini - τ∞)e-τdark/τrel
(7)
where τini and τ∞ are the initial and steady-state τKWW values, τrel is the relaxation time. As mentioned above, the τ∞ values were reliably determined at 239, 241.5 K and at 236.6 K (taking into account the literature data).62 The relaxation time at 234 K was determined by fitting the experimental dependence of τKWW on τdark involving τ∞ as a fitting parameter. Figure 6 shows that relaxation times, τrel, obtained in this way (denoted by crosses) differ only slightly from those determined using the exchange model. 4. Discussion 4.1. Probability of a Molecule to Isomerize, and the Lifetime of its Environment. As Figure 6 shows, the exchange times determined in this work are close to those measured using the variable light intensity approach.60 A ratio of these values
is 1:4 at 241.5 and 1:10 at 239 K. At 234 K, they coincide within experimental accuracy. The fact that the exchange times measured by these two methods are close to each other, calls for a more detailed consideration. Actually, the variable light intensity method was used to measure the lifetime of environment near the cis molecules having the lowest quantum yield (clamped molecules). In this case, the changes of environment manifest themselves as an increase in the quantum yield of cisftrans isomerization upon sample storage in the dark. At the same time, the method presented here is used to measure the lifetime of environment near the molecules having the highest quantum yield (loose molecules). This makes it clear that the lifetime of environment near the loose and clamped particles are the values of the same order of magnitude. At the same time, the probabilities of the isomerization of these particles differ greatly. For example, at 234 K, an effective isomerization rate constant of the loosest 30% of the particles differs by more than 2 orders of magnitude from that of the most clamped 20%. It is concluded then that there is no strong correlation between the probability of cisftrans isomerization of a molecule and the lifetime of its environment. The lifetimes of environments of all the molecules are close to each other. To some extent, these results are similar to those obtained in ref 46 where the lifetime of the environment of the most rapidly relaxing PVA segments coincides with the mean time of R-relaxation. 4.2. The Exchange Time and the Rotation Time. The data in Figure 6 demonstrate that the exchange time obtained in the present work coincides with the rotation time of NAMB molecules. This means that the rotation of NAMB molecule occurs simultaneously with the rearrangement of the neighboring molecules. It is very likely that the rotation of the molecule results from a cooperative rearrangement involving neighboring molecules. The literature data say in favor of this conclusion. The rotation times of tetracene molecules in OTP25 are in close agreement with the rotation times of OTP molecules.64 On the other hand, the rotation times of NAMB molecules in OTP63 coincide with those of tetracene. Hence, the rotation times of OTP molecules closely matched that of NAMB. As the rotation of host molecules causes the environment changes the exchange time and the time of host molecule rotation are close to each other. The issue of the relation between the rotation time and the exchange time has been studied in a number of works. M. Ediger and co-workers using the photobleaching technique have established that the lifetime of tetracene molecule environment in polystyrene29 exceeds the mean rotation times of the tetracene molecules at Tg by about 2 orders of magnitude. This ratio amounts to 540 for the OTP matrix at Tg + 1.28 As it was said above the rotation times of tetracene and NAMB molecules in OTP are in good agreement. An extremely high ratio between the heterogeneity lifetime and the rotation time of the large probe molecule in glycerol at temperatures higher than Tg (190 K) was obtained in the work,35 using the single molecule spectroscopy. It was established that over the range 195-210 K the exchange time is longer at least by a factor of 100 than the mean rotation time of the probe particle. At 212.5 K the ratio of these times exceeds 105. Such an unusual behavior is assigned by the authors to the formation of a network of solid-like “walls” with the probe molecules “segregated in the fluid domains”. On the other hand, there is a series of works, showing that the τex is the value of the same order of magnitude as the τrot or
15374 J. Phys. Chem. B, Vol. 112, No. 48, 2008 only 1 order of magnitude larger. L. Deschenes and D. Vanden Bout30 using the single molecule spectroscopy have measured the exchange time in the OTP matrix. The ratio τex/τrot evaluated from the data on rotation of Rhodamine 6G at Tg + 2 (245 K), Tg + 5, and Tg + 10 K to be 2.5, 10, and 55, respectively.65 Environment exchange was found to be roughly 300 times slower than the R-relaxation time. Note that a Rhodamine 6G molecule is larger than the molecules of tetracene and NAMB, therefore it rotates slower. The similar results were obtained in ref 33. It was shown by means of SMS that the exchange time exceeds by an order of magnitude the rotation time of Rhodamine 6G molecules in the polymethylacrylate matrix at the temperature Tg + 9 K. Using the method of multidimensional NMR it has been established that the exchange times in PVA21 and polystyrene44 are comparable with the reorientation times of polymeric segments at the temperature slightly exceeding Tg. Close values of the exchange time and the rotation time was found by the NMR method in toluene24 and o-terphenyl22 matrices. The authors of46 used the atomic force microscope technique to demonstrate that the heterogeneity lifetime in PVA films is comparable at temperatures slightly below Tg, with the mean R-relaxation time. Note that the heterogeneity lifetime was measured in the high-frequency tail region of the R peak. The method of dielectric hole burning spectroscopy indicates that the heterogeneity lifetime is comparable with the time of R-relaxation in the matrices of propylene carbonate and glycerol18 just above Tg. As follows from the above, the results of various experiments differ noticeably in the estimation of the ratio between the heterogeneity lifetime and the rotation time. Whereas the results of the measurements using photobleaching technique28 and single molecule spectroscopy35 testify in favor of the high value, the other data of the single molecule spectroscopy30,33 as well as those of multidimensional NMR and dielectric measurements rather indicate the closeness of the times of molecular motions to the exchange time. The present work also reports the exchange time close in value to the rotation one. At present, the reasons of this divergence are unclear. One of the possible reasons is that different experimental methods use different dynamical selection, that is, estimate exchange times based on the behavior of the fastest or the slowest molecules. The sample history also can be of major importance for the dynamics in amorphous phase. It is known that even at Tg + 50 K the OTP samples can be produced with and without longrange density fluctuations, depending on the procedure of preparation.66 The striking effect of the annealing on rheological behavior of glycerol and OTP above Tg has been reported by M. Orrit and co-workers.67 Finally, the sensitivity of different methods to a change in local environment may vary widely. New data on the heterogeneity lifetime obtained by different methods for the same medium can clarify the reason for the disagreements. 5. Conclusions Reversible photoinduced monomolecular reactions present a convenient tool for measuring the time of the environment rearrangement in glassy matrixes under conditions of dynamical heterogeneity. An advantage of such reactions arises from two features. First, the forward reaction, if conducted partially, results in the formation of most reactive product molecules. Thus, the partial conversion allows to select the environments with loose probe molecules. Second, the equilibration of the distribution
Grebenkin of product molecules over reaction rates can be separated in time from the back reaction. A new method, based on the measurement of the cis-trans photoisomerization kinetics, has been used to estimate the time of the environment rearrangement in OTP matrix over a temperature range of 234 (Tg - 9 K) to 241.5 K (Tg - 1.5 K). It has been shown that (a) the time required for the environment to change coincides with the rotation time of the probe molecules and (b) the time of structural rearrangements of the environment near the fast reacting molecules is of the same order of magnitude as that near the slow reacting ones. Acknowledgment. The author thanks A. Alturmesov and V. Vyazovkin for assistance in the preparation of samples. The author is grateful to B. Bolshakov for kindly providing NAMB. The author gratefully acknowledge fruitful discussions with V. Syutkin. This work was supported by the funds of interdisciplinary integration project of Siberian Branch of Russian Academy of Science No. 50 and by the Russian Foundation for Basic Research, Project No. 08-03-00550-a. References and Notes (1) Ediger, M. D.; Angell, C. A.; Nagel, S. R. J. Phys. Chem. 1996, 100, 13200. (2) Sillescu, H. J. Non-Cryst. Solids 1999, 243, 81. (3) Angell, C. A.; Ngai, K. L.; McKenna, G. B.; McMillan, P. F.; Martin, S. W. J. Appl. Phys. 2000, 88, 3113. (4) Ediger, M. D. Annu. ReV. Phys. Chem. 2000, 51, 99. (5) Ngai, K. L. J. Non-Cryst. Solids 2000, 275, 7. (6) Richert, R. J. Phys.: Condens. Matter 2002, 14, R703. (7) Johari, G. P.; Goldstein, M. J. Chem. Phys. 1970, 53, 2372. (8) Wu, L.; Nagel, S. R. Phys. ReV. B 1992, 46, 11198. (9) Wagner, H.; Richert, R. J. Phys. Chem. B 1999, 103, 4071. (10) Richert, R. Europhys. Lett. 2001, 54, 767. (11) Richert, R. J. Chem. Phys. 2005, 123, 154502. (12) Huang, W.; Richert, R. J. Chem. Phys. 2006, 124, 164510. (13) Garwe, F.; Schonhals, A.; Lockwenz, H.; Beiner, M.; Schroter, K.; Donth, E. Macromolecules 1996, 29, 247. (14) Alegria, A.; Goitiandia, L.; Telleria, I.; Colmenero, J. Macromolecules 1997, 30, 3881. (15) Goitiandia, L.; Alegria, A. J. Chem. Phys. 2004, 121, 1636. (16) Lunkenheimer, P.; Wehn, R.; Schneider, U.; Loidl, A. Phys. ReV. Lett. 2005, 95, 055702. (17) Lunkenheimer, P.; Wehn, R.; Loidl, A. J. Non-Cryst. Solids 2006, 352, 4941. (18) Schiener, B.; Chamberlin, R. V.; Diezemann, G.; Bohmer, R. J. Chem. Phys. 1997, 107, 7746. (19) Lunkenheimer, P.; Loidl, A. Chem. Phys. 2002, 284, 205. (20) Dries, Th.; Fujara, F.; Kiebel, M.; Rossler, E.; Sillescu, H J. Chem. Phys. 1988, 88, 2139. (21) Heuer, A.; Wilhelm, M.; Zimmermann, H.; Spiess, H. W. Phys. ReV. Lett. 1995, 75, 2851. (22) Bohmer, R.; Hinze, G.; Diezemann, G.; Geil, B.; Sillescu, H. Europhys. Lett. 1996, 36, 55. (23) Bohmer, R.; Hinze, G.; Jorg, T.; Qi, F.; Sillescu, H. J. Phys.: Condens. Matter 2000, 12, A383. (24) Hinze, G. Phys. ReV. E 1998, 57, 2010. (25) Cicerone, M. T.; Ediger, M. D. J. Phys. Chem. 1993, 97, 10489. (26) Cicerone, M. T.; Blackburn, F. R.; Ediger, M. D. J. Chem. Phys. 1995, 102, 471. (27) Cicerone, M. T.; Ediger, M. D. J. Chem. Phys. 1995, 103, 5684. (28) Wang, C.-Y.; Ediger, M. D. J. Phys. Chem. B 1999, 103, 4177. (29) Wang, C.-Y.; Ediger, M. D. J. Chem. Phys. 2000, 112, 6933. (30) Deschenes, L. A.; Vanden Bout, D. A. J. Phys. Chem. B 2002, 106, 11438. (31) Vallee, R. A. L.; Cotlet, M.; Hofkens, J.; De Schryver, F. C.; Mullen, K. Macromolecules 2003, 36, 7752. (32) Vallee, R. A. L.; Tomczak, N.; Kuipers, L.; Vancso, G. J.; Van Hulst, N. F. Phys. ReV. Lett. 2003, 91, 038301. (33) Schob, A.; Cichos, F.; Schuster, J.; Von Borczyskowski, C. Eur. Polym. J. 2004, 40, 1019. (34) Adhikari, A. N.; Capurso, N. A.; Bingemann, D. J. Chem. Phys. 2007, 127, 114508. (35) Zondervan, R.; Kulzer, F.; Berkhout, G. C. G.; Orrit, M. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 12628.
Dynamical Heterogeneity in Glassy o-Terphenyl (36) Dhinojwala, A.; Wong, G. K.; Torkelson, J. M. J. Chem. Phys. 1994, 100, 6046. (37) Hooker, J. C.; Torkelson, J. M. Macromolecules 1995, 28, 7683. (38) Hall, D. B.; Deppe, D. D.; Hamilton, K. E.; Dhinojwala, A.; Torkelson, J. M. J. Non-Cryst. Solids 1998, 235 (237), 48. (39) Andreozzi, L.; Bagnoli, M.; Faetti, M.; Giordano, M. J. Non-Cryst. Solids 2002, 303, 262. (40) Vorobiev, A. Kh.; Gurman, V. S.; Klimenko, T. A. Phys. Chem. Chem. Phys. 2000, 2, 379. (41) Wendt, H.; Richert, R. Phys. ReV. E 2000, 61, 1722. (42) Yang, M.; Richert, R. Chem. Phys. 2002, 284, 103. (43) Tracht, U.; Wilhelm, M.; Heuer, A.; Feng, H.; Schmidt-Rohr, K.; Spiess, H. W. Phys. ReV. Lett. 1998, 81, 2727. (44) Kuebler, S. C.; Heuer, A.; Spiess, H. W. Phys. ReV. E 1997, 56, 741. (45) Richert, R. J. Chem. Phys. 2001, 115, 1429. (46) Russell, E. V.; Israeloff, N. E. Nature 2000, 408, 695. (47) Sung, C. S. P.; Lamarre, L.; Chung, K. H. Macromolecules 1981, 14, 1839. (48) Lamarre, L.; Sung, C. S. P. Macromolecules 1983, 16, 1729. (49) Yu, W.-C.; Sung, C. S. P.; Robertson, R. E. Macromolecules 1988, 21, 355. (50) Victor, J. G.; Torkelson, J. M. Macromolecules 1987, 20, 2241. (51) Victor, J. G.; Torkelson, J. M. Macromolecules 1988, 21, 3490. (52) Mita, I.; Horie, K.; Hirao, K. Macromolecules 1989, 22, 558. (53) Anseth, K. S.; Rothenberg, M. D.; Bowman, C. N. Macromolecules 1994, 27, 2890.
J. Phys. Chem. B, Vol. 112, No. 48, 2008 15375 (54) Imamura, Y.; Yamaguchi, Y.; Tran-Cong, Q. J. Polym. Science B: Polym. Phys. 2000, 38, 682. (55) Ilieva, D.; Nedelchev, L.; Petrova, Ts.; Dragostinova, V.; Todorov, T.; Nikolova, L.; Ramanujam, P. S. J. Opt. A: Pure Appl. Opt. 2006, 8, 221. (56) Richert, R. Chem. Phys. 1988, 122, 455. (57) Richert, R. Macromolecules 1988, 21, 923. (58) Richert, R.; Heuer, A. Macromolecules 1997, 30, 4038. (59) Park, J.-W.; Ediger, M. D.; Green, M. M. J. Am. Chem. Soc. 2001, 123, 49. (60) Grebenkin, S.; Yu.; Bol’shakov, B. V. J. Phys. Chem. B 2007, 111, 5921. (61) Michl, J.; Thulstrup, E. W. Spectroscopy with Polarized Light: Solute Alignment by Photoselection, Liquid Crystal, Polymers, and Membranes; Wiley: New York, 1995. (62) Cicerone, M. T.; Ediger, M. D. J. Chem. Phys. 1992, 97, 2156. (63) Grebenkin, S. Yu.; Bol’shakov, B. V. J. Phys. Chem. B 2006, 110, 8582. (64) Fujara, F.; Geil, B.; Sillescu, H.; Fleischer, G. Z. Phys. B: Condens. Matter 1992, 88, 195. (65) The error in the determination of these values from the data given in the paper is about 100%. (66) Patkowski, A.; Glaser, H.; Kanaya, T.; Fischer, E. W. Phys. ReV. E 2001, 64, 031503. (67) Zondervan, R.; Xia, T.; Van der Meer, H.; Storm, C.; Kulzer, F.; Van Saarloos, W.; Orrit, M. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 4993.
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