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Effect of Pressure on Tautomers’ Equilibrium in Supercooled Glibenclamide Drug: Analysis of Fragility Behavior Z. Wojnarowska,* K. Adrjanowicz, K. Kaminski, L. Hawelek, and M. Paluch Institute of Physics, UniVersity of Silesia, ul. Uniwersytecka 4, 40-007 Katowice, Poland ReceiVed: May 15, 2010; ReVised Manuscript ReceiVed: September 19, 2010
In this work, we investigated the relaxation dynamics of supercooled and glassy glibenclamide drug in conditions of high compression using broadband dielectric spectroscopy. Glibenclamide, an oral antidiabetic drug, belongs to the group of organic compounds which reveal amide-imidic acid tautomerism. Our studies reveal that application of pressure does not change the shape of dielectric loss spectrum of this pharmaceutical, whereas it probably influences the tautomers’ concentration in the examined sample. Because every tautomer may influence the unique physical properties like the glass transition temperature, we have also focused on the analysis of pressure dependence of fragility, mP(P). In contradiction to the others active pharmaceutical ingredients (API) like verapamil hydrochloride, indomethacin or ibuprophen, in the case of glibenclamide drug slightly increasing trend of fragility was observed. On the other hand, pressure measurements confirmed the validity of suggestions concerning the origins of two secondary relaxations in glibenclamide presented in our previous paper (Wojnarowska et al. Mol. Pharmaceutics 2010, 7, 1692-1707). It is worth noting that until now the system which reveals tautomerism has never been analyzed in condition of high compression. Introduction In the last decades, understanding of the physical nature of dynamic processes in a glass-forming liquid became an important goal in the fields of organic, inorganic, and polymeric glasses as well as in the case of amorphous pharmaceuticals or food preservation.1 Amorphous solids have attracted an interest of pharmaceutical scientists because of the continuous increase in the number of insoluble drug molecules. However, limitations of amorphous systems such as physical instability and higher chemical reactivity act as a hurdle in their extensive commercialization.2,3 Therefore, it is important to understand the molecular and thermodynamic factors that control solubility and stability of amorphous drugs. At present, the most commonly used parameters to characterize the glass-forming liquids are glass transition temperature (Tg) and fragility. It is worth noting that fragility is one of the key topics of many publications related to the glass-forming liquids.4 The concept of “fragility” was introduced by Angell in order to classify the glass-forming materials in the three groups: “fragile”, “intermediate”, and “strong”, depending on the temperature variations of the R-relaxation process.5 In so-called Angell plot (the plot of the logarithm of relaxation time or viscosity vs Tg/T), “strong” means the liquid for which the Angell plot is linear whereas the “fragile” liquid exhibits a notable deviation from Arrhenius behavior. Much of the interest in fragility arises from the possibility of identifying general principles which underlie the supercooled dynamics, by drawing correlations between fragility and other dynamic and thermodynamic properties. It has been established that fragility is related to many other liquid properties like nonexponentiality6,7 (correlation between non-Debye and non-Arrhenius relaxation) or diffusional properties of supercooled liquids.8,9 On the other * To whom correspondence should be addressed. E-mail: zwojnaro@ us.edu.pl.
hand, it was shown that it is also related to the tendency of glass to crystallization.10 Although fragility is usually determined at atmospheric pressure, an interesting issue is the study of effect of high pressure on this value. Understanding of the fragility’s behavior in these conditions becomes crucial because it provides complete information about relaxation dynamics in the amorphous materials. There are lots of experimental data which show that pressure usually reduces the fragility.11 The only exceptions to this rule are some hydrogen-bonded materials, such as glycerol12 and polypropylene glycol.13 From this point of view, it is also interesting to analyze the fragility behavior in compounds which reveal tautomerism, being the special case of structural isomerism.14 This phenomenon is commonly observed in the case of organic compounds and it is still a subject of intense research, despite decades of investigation. It is important to mention that this kind of material has never been analyzed in the condition of high compression. Very recently, using broadband dielectric spectroscopy, we have studied the molecular dynamics and tautomerism phenomenon of vitrified glibenclamide (GCM) drug, which is an oral hypoglycemic agent of the sulphonylurea group.15 In our previous paper, we have shown that in dielectric loss spectra one can distinguish two wellpronounced relaxation processes: structural R-relaxation and secondary γ-process. Moreover, the analysis of ε′′(f) in terms of KWW function revealed the existence of “excess wing” attributed to the true Johari-Goldstein process based on Ngai’s coupling model.1 Furthermore, experimental work connected with computational simulations reported in our next work has provided fresh insights into the kinetics of amide-imidic acid tautomerism of GCM drug.16 Moreover, it was shown that the value of steepness index determined for the amide-imidic acid mixture was almost 14 units higher than that calculated for the imide-rich sample. We have found that this change in fragility during the tautomerization process
10.1021/jp104444q 2010 American Chemical Society Published on Web 10/28/2010
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is connected with the different tautomers concentration in the examined samples. Since one of the advantages of the dielectric spectroscopy method is that it can be relatively easily adapted to the high-pressure experiments, the analysis of tautomerism phenomenon under compression is also possible. In this communication, we have applied dielectric spectroscopy to investigate the effect of pressure on fragility and tautomers equilibrium in GCM drug. Moreover, we will try to answer the question whether or not the influence of pressure on the dielectric relaxation will provide any insight into the nature of an excess wing in GCM? Experimental Section The sample under test was glibenclamide (GCM) drug. The sample was supplied by Polpharma as a white powder and was used as received. The starting material was completely crystalline with the melting point equal to 440 K. For the pressuredependent dielectric measurements we used capacitor, filled with the vitrified anhydrous GCM sample, which was next placed in the high-pressure chamber and compressed using the silicone fluid via a piston in contact with a hydraulic press. The sample was in contact only with stainless steel and Teflon. Pressure was measured by the Nova Swiss tensometric pressure meter with a resolution of 0.1 MPa. The temperature was controlled within 0.1 K by means of a liquid flow provided by a thermostatic bath. We measured real (ε′) and imaginary (ε′′) part of dielectric permittivity of GCM in the frequency range 10-2-106 Hz. We have performed six isothermal dielectric measurements in the temperature range 368-393 K, each of them with the same pressure intervals equal to 15 MPa. Applied experimental procedure enabled us to simply generate five isobaric curves. The latter isobar (at p ) 390 MPa) was additionally measured in order to check the pressure effect on the secondary relaxations. Results and Discussion A. Pressure Analysis of the Structural Relaxation’s Behavior. Isothermal and isobaric dielectric measurements were performed at T ) 368, 373, 378, 383, 388, and 393 K and at P ) 70, 100, 130, 160, and 190 MPa. In Figure 1, representative isobaric (panel a) and isothermal (panel b) dielectric loss spectra are presented. As can be seen, the increase of pressure brings about the same effect on structural relaxation process as lowering the temperature, i.e., shifting of the R-peak toward lower frequencies. Moreover, it is clearly visible that the R-relaxation exhibits quite strong pressure sensitivity. Squeezing of liquid from ambient pressure to 200 MPa causes the maximum of R-loss peak to move almost 6 decades in frequencies. One should note that Figure 1 presents the isothermal and isobaric curves obtained after subtracting the dc conductivity. This procedure was applied because the structural relaxation peak was influenced by dc conductivity. The strong contribution of dc conductivity observed in the ε′′ spectra of GCM is characteristic of the pressure measurement of a number of other systems and it can be easily explained. It is well-known that dc conductivity in some systems is mainly a thermally activated process which consequently exhibits only weak pressure sensitivity. Thus, taking into account that the overwhelming majority of high-pressure measurements were performed at high temperature (above 358 K), the great contribution of the dc conductivity to the loss spectra is understandable.
Figure 1. Loss spectra obtained (a) during isothermal measurement carried out at T ) 383 K (p ) 10-190 MPa) and (b) isobaric measurements performed at p ) 130 MPa (T ) 373-398 K).
The analysis of glibenclamide spectra measured at ambient pressure shows that the shape of the R-relaxation peak is practically independent of temperature. It means that the structural relaxation process observed at atmospheric pressure holds the time-temperature superposition principle.1 From this point of view, it is interesting to examine the behavior of the spectral shape of ε′′ also at elevated pressure. Using the data recorded at different temperature and pressure conditions, which have approximately the same frequency of R-peak ( fmax), one can check whether or not the shape of the structural relaxation process is pressure dependent. The superposed dielectric loss spectra obtained at different thermodynamic conditions (P, T) are presented in Figure 2. It is easily seen that distribution of the R-relaxation times is invariant in the T-P plane. Our result is in accordance with recent findings reported by Ngai et al.17 These authors demonstrated, for almost 40 materials including molecular glass formers and amorphous polymers of diverse chemical structure, that the principle of temperature-pressure superpositioning of the R-dispersion at constant relaxation time is valid. As can be seen, glibenclamide drug is the next example of this rule. Next we analyzed a series of isobaric and isothermal measurements to determine the relaxation times τR defined as the inverse of frequency of the R-peak maximum, fmax-1. The obtained data were then used to construct two relaxation maps.
Relaxation Dynamics of Glibenclamide Drug
Figure 2. A comparison of the dielectric loss spectra of glibenclamide obtained for different temperature and pressure combinations reported in the figure, with approximately the same structural relaxation time.
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Figure 4. Temperature dependence of the activation volume ∆V.
and log τR(P) are not linear. Therefore, to describe them the VFT equation18–20 and its pressure counterpart,12 respectively, were used:
(
DTT0 T - T0
)
(1)
(
DPP P0 - P
)
(2)
τR ) τ0 exp
τR ) τ0 exp
From the data presented in Figure 3b and using the commonly known equation21
(
∆V ) 2.303RT
Figure 3. Structural relaxation times obtained during isobaric (a) and isothermal measurements (b). Solid lines are temperature VFT and its pressure counterpart fits.
Variations in log10 τR with temperature at elevated pressure are shown in Figure 3a, while Figure 3b presents the behavior of the structural relaxation times as a function of pressure. As can be seen, the experimentally observed dependences of log τR(T)
∂ log τR ∂p
)
T
(3)
one can calculate the activation volume defined as the difference between the volumes occupied by a molecule in activated and nonactivated states.22 Since ∆V is pressure dependent, we have calculated the value at a pressure Pg for which τR ) 1 s. This procedure enables us to avoid the extrapolation of the pVFT fit curves to the value of τR ) 100 s, which could cause larger calculation errors. The obtained results are presented in Figure 4. It can be seen that the activation volume increases with decreasing temperature, from ∆V ) 94 cm3 /mol at 393 K to 139 cm3/mol at 368 K. The observed behavior of ∆V for glibenclamide drug is characteristic of many other materials and can be considered as a specific feature of the dynamic of supercooled liquids and amorphous polymers. Since the activation volume reflects the volume required for relaxation, its increase with lowering temperature is often attributed to an increase in the cooperativity of the relaxation process. It is wellknown that as a measure of cooperativity23 degree one can usually take the coupling parameter n in the KohlrauschWilliams-Watts function.24 Moreover, the literature data shows that the increase in the cooperativity should be connected with the broadening of R-process.25 However, in the previous part of this paper it was shown that for glibenclamide drug the time-temperature-pressure superposition principle is valid. Thus, in this case the correlation between the ∆V and n is not satisfied valid. The decreasing trend of ∆V with temperature
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mP )
Figure 5. Pressure dependence of glass transition temperature. The solid line represents the fit to the Andersson and Andersson equation.
reflects probably the fact that thermal energy contribution to the molecular dynamics becomes more important at high pressures. Herein, we also focus on the general correlation between the stretching exponent βKWW and fragility. Some time ago, it was established that fragile material (large m) has a small βKWW parameter and vice versa.6 Taking into account that in the case of GCM the R-process width is pressure independent, one can expect that the value of fragility should be constant in the applied pressure range. To check the effect of pressure on fragility behavior, first we have determined the values of the glass transition temperature and the glass transition pressure for glibenclamide drug. As it was mentioned previously, to avoid the extrapolation of VFT fits in our analysis we have taken Tg (and Pg) as temperature (or pressure) at which τR ) 1 s. The obtained values of Tg for isobaric and Pg for isothermal condition are depicted in Figure 5. It is clearly seen that experimentally determined glass-transition temperature of glibenclamide drug is strongly dependent on pressure. The value of Tg is changing almost 15% with increasing pressure from 0.1 to 235 MPa. It is also evident that Tg increases with pressure in a nonlinear fashion. This behavior, commonly observed for the glassforming liquids, can be described with use the empirical equation proposed by Andersson and Andersson.26,27
(
Tg ) k1 1 +
)
k2 P k3
1/k2
(4)
The best fit (solid line in Figure 5) was obtained for the k1 ) 344.36, k2 ) 3.86, and k3 ) 1382. By dividing k1/k3, one can also estimate the value of the pressure coefficient of the glass transition temperature in the limit of low pressures. It is equal to 249 K/GPa for GCM. This value is similar to that obtained for the van der Waals materials (200-300 K/GPa) and significantly larger than values achieved for typical hydrogenbonding systems, for example, glycerol (40 K/GPa)28 or sorbitol (43 K/GPa).29 It is interesting that, using the above classification, GCM can be regarded as a typical van der Waals liquid, despite the fact that this compound can form weak hydrogen bonds. From the VFT fits to the temperature dependences of the structural relaxation times at different isobaric conditions, we have estimated the steepness index, mP7
∂log10(τ) ∂(Tg /T)
|
P)const,T)Tg
(5)
where Tg is the glass transition temperature defined previously as Tg ) T(τR ) 1 s). It is worth noting that fragility is a single parameter that provides information about how quickly the glass transition temperature is approached during cooling of the liquid. The values of the steepness index determined at different pressures for GCM are displayed in the inset panel of Figure 6. On the one hand, the behavior of experimental points in the inset of Figure 6 suggests that fragility slightly increases with pressure. On the other hand, taking into account the size of error bars, one could conclude that mP does not depend on compression. To ensure what is the real mP(P) behavior for GCM drug, the isobaric relaxation data was additionally plotted in Tg/T representation. Obtained in this way, the so-called “Angell plot” is depicted in Figure 6. It is worth noting that using Angell plot one can easily estimate the influence of pressure on fragility: different slopes of Tg-normalized isobars log τR(Tg/T) near Tg/T ) 1 means different values of the steepness index. From Figure 6, we can see that the slopes in Tg/T are rather increasing with pressure. It means that fragility of GCM, indeed, slightly increases in the studied pressure range. In the case of a great majority of glassy pharmaceuticals, the steepness index is decreasing with pressure, i.e., the drug becomes “stronger” at elevated pressure. Here, one can recall, e.g., ibuprofen,30 indomethacine,31 or verapamil hydrochloride.32 It is worth noting that GCM drug can be classified as a van der Waals liquid although it can form very weak H-bonds. Therefore, one should rather expect the decreasing trend of mP(P).11 This uncommon behavior of fragility observed for GCM has been reported previously only in the case of hydrogenbonded systems, e.g., for glycerol and polypropylene glycol. In these cases the increasing trend of mP was explained by the complete or nearly complete reduction of hydrogen bonds with applying pressure. In the case of GCM, the increase of mP is probably related to the change of equilibrium concentration between amide and imidic acid forms. As it was mentioned in Introduction, vitrified glibenclamide exists in equilibrium between two tautomeric forms, amide and imidic acid, respectively. In our previous work16 we have shown that in the freshly prepared glass one can observe a high concentration of imidic acid forms. However, after a while this equilibrium is disturbed and we can detect the continuous increase of the amide concentration. Moreover, we have shown that every tautomer may have its unique physical properties. Consequently, the nonequilibrated and equilibrated samples are characterized by different values of both the glass transition temperature and fragility. It is worth noting that dielectric measurements carried out at ambient pressure shows that there is 11 K and 14 units difference in the glass transition temperature and fragility, respectively, between both examined materials.16 Thus, one can suppose that the decrease of imide concentration brings about increase in both Tg and mP. It is worth noting that the pressure measurements of glibenclamide were carried out after the long temperature stabilization. Moreover, the lowest temperature at which the dielectric loss spectra were collected was equal to 363 K. Therefore, one can be sure that the sample under test was equilibrated. Taking into account the results obtained at ambient pressure, i.e., the increasing steepness index with decreasing concentration of imidic acid form, one can suppose that the fragility behavior observed under pressure is probably due to the change in the quantity of imidic acid forms.
Relaxation Dynamics of Glibenclamide Drug
Figure 6. Angell plot of the relaxation times estimated for all isobaric processes observed in the investigated sample; the inset presents the isobaric fragility vs pressure.
It has been pointed out by Angell that on the basis of the value of fragility one can simply identify the structure stability of glass formers. According to the above idea, fragile liquids are structurally less stable than the strong are.10 In accordance with this criterion, we can assume that amorphous glibenclamide in condition of high compression is less stable than at ambient pressure. However, one should remember that in the case of GCM stability of amorphous drug is also determined by the proportionality between tautomeric forms. The literature reports that this kind of equilibrium detected in the glassy state reduces strongly the tendency to crystallization. As it was stated above, because the number of imide acid forms probably decreases with pressure one can suppose that the examined system should exhibit the greater crystallization tendency in high pressure conditions. B. Pressure Analysis of the Secondary Relaxation Processes. In this part of the paper, we focus on the analysis of the secondary relaxation process detected in the dielectric loss spectra of glibenclamide. In our previous work we have shown that at ambient pressure one can identify two secondary relaxation processes in the dielectric spectra: well-pronounced γ-relaxation below the glass transition temperature, and the excess wing which was identified as a hidden JG relaxation.1 Moreover, we have shown that the γ-process may originate from some intramolecular motion of a small part of the GCM molecule. Similarly as for the data taken at ambient pressure in the case of high-pressure measurements, γ-relaxation becomes visible only in the glassy state. To see the effect of pressure on the secondary relaxations, we have performed isobaric measurements at P ) 390 MPa over a wide range of temperatures. The obtained dielectric spectra are presented in Figure 7. One can observe the dominant γ-relaxation peak which moves to lower frequencies with decreasing temperature. Moreover, in the region of minimum between γ- and R-relaxation processes, another peak emerges. This new relaxation mode has been not seen in the ε′′ spectra obtained at ambient pressure. As can be seen in Figure 7, this relaxation process becomes more separated and visible with decreasing temperature. This suggests that its activation energy is much greater than that of the γ one. Analysis of the loss spectra presented in this plot with the use of Cole-Cole functions enabled us to determine relaxation times of these two secondary processes and then calculate its activation energies. The temperature dependence of β- and γ-relaxation
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Figure 7. Dielectric loss spectra obtained from isobaric measurements at P ) 390 MPa performed in the temperature range T ) 393-263 K. In the inset panel the representative dielectric loss spectrum collected at 293 K is depicted.
Figure 8. Relaxation map of the glibenclamide. Blue circles denote γ-relaxation times obtained at ambient pressure while the green squares and yellow triangles are respectively β- and γ-relaxation times obtained from measurements carried out at P ) 390 MPa. Solid lines are Arrhenius fits to the temperature dependences of secondary relaxation times.
times was included in the relaxation map depicted in Figure 8. From fitting the Arrhenius equation to the experimental data, the following values of activation energies for both modes have been calculated: Eβ ) 79.63 ( 2 kJ/mol and Eγ ) 43.6 ( 1.5 kJ/mol. As can be seen, the activation energy for the γ-process practically does not change when compared to the ambient pressure value (49.24 ( 1 kJ/mol). Moreover, in the relaxation map presented in Figure 8 it is clearly seen that the secondary γ-relaxation is practically independent of pressure. This is a clear evidence that γ-relaxation has an intramolecular origin. Thus, it is related to the motions of a part of the GCM molecule. It is worth reminding that the sensitivity to pressure is one of the most important criteria used to classify the secondary relaxation as a “genuine” JG process. For glibenclamide, the pressure invariance of the γ-peak indicates that this secondary relaxation is a non-JG relaxation. In addition, we found that the large value of the activation energy estimated for the β-relaxation suggests that this process can be the true JG
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relaxation and it is related to the motions of a whole molecule of drug. This investigation is consistent with predictions based on the coupling model, presented in our previous paper.1 Conclusion In the present work, using the BDS technique we have investigated the molecular dynamics of amorphous glibenclamide drug. It is worth reminding that glassy GCM exists in equilibrium between two constitutional isomers: the so-called amide and imidic acid. Herein, we have shown that tautomers’ equilibrium is probably pressure dependent and it may be manifested by the changes in the fragility. In the experimental pressure range the slightly increasing trend of fragility was observed. On the basis of the data presented in our previous work, we have found that, with increasing pressure, concentration of imidic acid forms probably decreases. Thus, one can suppose that at elevated pressure the examined material will reveal a greater crystallization tendency. Finally, in the glassy state of GCM, we have detected two secondary relaxations. On the basis of detailed analysis of the dielectric loss spectra measured at 390 MPa, we have found that the “excess wing”, observed in the ε′′ spectra collected at ambient pressure, is a hidden JG relaxation with the activation energy equal to 79.63 kJ/mol. Acknowledgment. The authors Z.W., K.A., K.K., and M.P. are deeply thankful for the financial support of their research within the framework of the project entitled “From Study of Molecular Dynamics in Amorphous Medicines at Ambient and Elevated Pressure to Novel Applications in Pharmacy” (Contract No. TEAM/2008-1/6), which is operated within the Foundation for Polish Science Team Programme cofinanced by the EU European Regional Development Fund. Moreover, K.K. thanks FNP for awarding grants within the framework of the START Programme (2009). References and Notes (1) Wojnarowska, Z.; Grzybowska, K.; Adrjanowicz, K.; Kaminski, K.; Paluch, M.; Hawelek, L.; Wrzalik, R.; Dulski, M.; Sawicki, W.; Mazgalski, J.; Tukalska, A.; Bieg, T. Mol. Pharmaceutics 2010, 7, 16921707.
Wojnarowska et al. (2) Shamblin, S. L.; Tang, X.; Chang, L.; Hancock, B. C.; Pikal, M. J. J. Phys. Chem. B 1999, 103, 4113–4121. (3) Shamblin, S. L.; Hancock, B. C.; Dupuis, Y.; Pikal, M. J. J. Pharm. Sci. 2000, 89, 417–427. (4) Angell, C. A.; Ngai, K. L.; McKenna, G. B.; McMIllan, P. F.; Martin, S. W. J. Apply. Phys. 2000, 88, 3113. (5) Angell, C. A. J. Non-Cryst. Solids 1991, 131-133, 13–31. (6) Bo¨hmer, R.; Ngai, K. L.; Angell, C. A.; Plazek, D. J. J. Chem. Phys. 1993, 99, 4201. (7) Plazek, D. J.; Ngai, K. L. Macromolecules 1991, 24, 1222. (8) Angell, C. A.; Pool, P. H.; Shao, J. NuoVo Cimento A 1994, 16, 883. (9) Roland, C. M.; Ngai, K. L. J. Chem. Phys. 1996, 104, 2967. (10) Hancock, B.; Shamblin, S. L. Thermochim. Acta 2001, 380, 95– 107. (11) Roland, C. M.; Hensel-Bielowka, S.; Paluch, M.; Casalini, R. Rep. Prog. Phys. 2005, 68, 1405–1478. (12) Paluch, M.; Casalini, R.; Hensel-Bielowka, S.; Roland, C. M. J. Chem. Phys. 2002, 116, 9839. (13) Andersson, S. P.; Andersson, O. Macromolecules 1998, 31, 2999. (14) Smith, M. B.; March, J. AdVanced Organic Chemistry, 5th ed.; Wiley Interscience: New York, 2001; pp 1218-1223. (15) Mutalik, S.; Udupa, N. J. Pharm. Sci. 2004, 93, 4, 1577. (16) Wojnarowska, Z.; Wlodarczyk, P.; Kaminski, K.; Hawelek, L.; Paluch, M. J. Chem. Phys. 2010, 133, 094507. (17) Ngai, K. L.; Casalini, R.; Capaccioli, S.; Paluch, M.; Roland, C. M. J. Chem. Phys. B 2009, 109, 17356. (18) Vogel, H. Phys. Z. 1921, 22, 645. (19) Fulcher, G. J. Am. Ceram. Soc. 1923, 8, 339. (20) Tammann, G.; Hesse, W.; Anorg, Z. Allg. Chem. 1926, 156, 245. (21) Leyser, H.; Schulte, A.; Doster, W.; Petry, W. Phys. ReV. E 1995, 51, 5899. (22) Glasstone, S.; Laidler, K. J.; Eyring, H. Theory of Rate Processes; McGraw-Hill: New York, 1941. (23) Richert, R.; Blumen, A. Disorder Effects on Relaxational Processes; Springer: Heidelberg, Germany, 1993. (24) Williams, G.; Watts, D. C. Trans. Faraday Soc. 1970, 66, 80. (25) Paluch, M.; Casalini, R.; Best, A.; Patkowski, A. J. Chem. Phys. 2002, 117, 7624. (26) Andersson, S. P.; Andersson, O. Macromolecules 1998, 31, 2999. (27) Avramov, I. J. Non-Cryst. Solids 2005, 351, 3163. (28) O’Reilly, J. M. J. Polym. Sci. 1962, 57, 429. (29) Atake, T.; Angell, C. A. J. Phys. Chem. 1979, 83, 3218. (30) Adrjanowicz, K.; Kaminski, K.; Wojnarowska, Z.; Dulski, M.; Hawelek, L.; Pawlus, S.; Paluch, M. J. Phys. Chem. B 2010, 114, 6579. (31) Wojnarowska, Z.; Adrjanowicz, K.; Wlodarczyk, P.; Kaminska, E.; Kaminski, K.; Grzybowska, K.; Wrzalik, R.; Paluch, M.; Ngai, K. L. J. Phys. Chem. B 2009, 113, 12536. (32) Wojnarowska, Z.; Paluch, M.; Grzybowski, A.; Adrjanowicz, K.; Grzybowska, K.; Kaminski, K.; Wlodarczyk, P.; Pionteck, J. J. Chem. Phys. 2009, 131, 104505.
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