Relaxation in Poly(vinyl acetate) - American Chemical Society

Jul 17, 2009 - ature Tg (i.e., R relaxation) in simple glass forming liquids and polymers .... butyl rubber (CIIR).49,50 The asymmetrical broad mechan...
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J. Phys. Chem. B 2009, 113, 11147–11152

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Dynamic Crossover of r′ Relaxation in Poly(vinyl acetate) above Glass Transition via Mechanical Spectroscopy Xuebang Wu* and Zhengang Zhu Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, P.O. Box 1129, Hefei, Anhui, P. R. China ReceiVed: April 16, 2009; ReVised Manuscript ReceiVed: June 28, 2009

The molecular relaxation dynamics of poly(vinyl acetate) (PVAc) has been studied by mechanical spectroscopy above the glass transition temperature (Tg) within a frequency range from 1 mHz to 100 Hz. The temperaturedependent mechanical spectra reveal the existence of two relaxation modes: R, ascribed to the glass transition, and R′, which may be related to the softening dispersion, composed of the sub-Rouse modes and the Rouse modes. The R′ mode has a weaker temperature dependence than the R mode. Furthermore, the R′ mode from the frequency-domain spectra exhibits a similar dynamic crossover at temperature TB ∼ 387 K as the R mode through the temperature dependence of relaxation time, relaxation strength, and shape parameter. However, the crossover of the R′ mode occurs at a time of about 0.08 s, longer than 10-6-10-7 s for the R mode by dielectric spectroscopy. According to the coupling model, the crossover is suggested to be caused by the strong increase of intermolecular cooperativity below TB. I. Introduction The dynamics of relaxation near the glass transition temperature Tg (i.e., R relaxation) in simple glass forming liquids and polymers has been extensively studied for a number of years.1-7 The dynamics of simple glass formers and polymers usually shows non-Arrhenius behavior and nonexponentiality.1 The temperature dependence of dynamic properties such as relaxation time or viscosity is found to be non-Arrhenius and could be addressed by the Vogel-Fulcher-Tamman8 (VFT) equation. The spectral shapes are found to be strongly non-Debye (with monohydroxy alcohols as an exception9) and phenomenologically described in terms of the Kohlrausch-Williams-Watts10 (KWW) relaxation function. In addition, the dynamics of R relaxation in simple glass forming liquids often exhibits a dynamic crossover8,11 at a temperature of TB ) (1.2-1.3) Tg, usually revealed as a change in the temperature dependence of the relaxation time at a time of 10-6-10-7 s. The crossover has also been found in some polymeric systems12-14 but has not been explored as a general feature. The crossover in simple glass-forming liquids and polymers has been assigned by Murthy15 to be the liquid-liquid transition, designated by Boyer and considered as a transformation of the liquid from one dynamic regime to another. On the contrary, Kisliuk et al.12 believe that the crossover is strongly different from the thermodynamic liquid-liquid transition, where the crossover is dynamic in origin and the liquid-liquid transition is not evidenced. The crossover for the R relaxation is found to be caused by the change of intermolecular cooperativity in local segmental motion according to the coupling model.11,16 Recent studies suggest that the breakdown of time-temperature superposition (TTS) is closely related to the crossover temperature TB, and increase in molecular weight results in increase of TB.17,18 In the glass to rubber softening dispersion of polymers, three distinct viscoelastic mechanisms contribute to the softening dispersion from the local segmental motion, the sub-Rouse modes, and the Rouse modes.19-22 The local segmental motion * Corresponding author. E-mail: [email protected].

time has the strongest temperature dependence responsible for glass transition. The Rouse modes are the weakest and dominate the viscoelastic response in the glass-rubber transition region and contain in the order of 50 or more backbone bonds. The sub-Rouse modes are intermediate in character between the local segmental relaxation and the Rouse modes, involving segments larger than the couple of conformers involved in local segmental relaxation, while they contain fewer chain units than the shortest Gaussian submolecules described by the Rouse modes. The subRouse modes may involve in the order of 10 backbone bonds, and may have retained to some degree the intermolecular cooperativity of the R relaxation, but there is little known about them.22 Poly(vinyl acetate) (PVAc) is a typical amorphous and polar polymer and is often chosen to test the current aspects of various theories related to glass transition. Many experimental techniques have been exploited to study the dynamics of PVAc in the equilibrium (above Tg) or nonequilibrium state, including dielectric spectroscopy (DS),16,23-27 mechanical spectroscopy,19,28 quasielastic neutron scattering (QENS),26,29 positron annihilation lifetime spectroscopy (PALS),30,31 electron spin resonance (ESR),32-34 nuclear magnetic resonance (NMR),35 atomic force microscopy (AFM),36 thermally stimulated current technique (TSC),37-39 differential scanning calorimetry (DSC),40 and single molecular spectroscopy.41 In the glassy state, studies on structural relaxation (often called “physical aging”) of PVAc have been carried out to understand the changing relaxation dynamics as the nonequilibrium glass evolves toward and into equilibrium.38-40 The R relaxation of PVAc has been examined since as far back as 1941,28 and available results16,23,24 show strong non-Debye and non-Arrhenius dynamics. TSC measurements37 exhibit a liquid-liquid transition at a temperature Tll ∼ (1.1-1.2) Tg, showing a Vogel behavior. Recently, several experiments32-35 on PVAc have pointed out a heterogeneous character on the molecular level of the dynamics near Tg. QENS measurements indicate the existence of dynamic heterogeneities in PVAc even at temperatures far above Tg.26 The viscoelastic behaviors of PVAc reveal two dispersions between glassy and

10.1021/jp903523x CCC: $40.75  2009 American Chemical Society Published on Web 07/17/2009

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steady state behavior.19 Moreover, a dynamic crossover temperature TB at 383-387 K is revealed by the characteristic times of dielectric spectroscopy for the R relaxation in PVAc at a time of about 10-6-10-7 s.16,26 The crossover is due to the change of intermolecular cooperativity below TB according to the coupling model.11,16 However, there is little about the dynamics of the sub-Rouse modes in PVAc above Tg and the exact nature of the dynamics of PVAc in the glass to rubber softening dispersion is far from being well understood. The mechanical spectroscopy (also termed internal friction) technique is one of the most powerful tools to probe the relaxation dynamics in soft matter such as biological matter and polymers on a large temperature range and frequency scale.42-45 The mechanical loss of a material is caused by conformational changes leading to a phase shift between stress and strain during periodic excitations and a damping of a free vibration sample. The higher the phase shift, the higher the damping of the material will be. Damping is maximal when the period of molecular motions becomes comparable to the time scale of the experiment. Thus, different relaxation processes lead to mechanical loss peaks. On the other hand, the relaxation time of the Rouse modes has much weaker temperature dependence than the local segmental relaxation time τR in the softening dispersion. The mechanical loss peak for the Rouse modes would not shift if the local segmental dynamics changes. Therefore, the mechanical loss peak could be used as a measure of the frequency of the Rouse dynamics. In the present paper, we have investigated the viscoelastic behaviors of PVAc and focus on the dynamic evolution of the sample above Tg over a relatively broad frequency range using mechanical spectroscopy. Our aim is to understand the origin of the dynamics in the glass to rubber softening dispersion.

II. Experiment The polymer investigated in this study is poly(vinyl acetate) with chemical formula [-CH2CH(OCOCH3)-]n. The sample used was supplied by Alfa Aesar with a weight-average molecular weight Mw of 50 kg/mol (Mw/Mn ) 1.8, as determined by means of gel permeation chromatography using polystyrene as a standard). Prior to the measurements, samples were kept at 430 K in a vacuum for at least 24 h to remove any moisture content as structural relaxation of PVAc is known to be sensitive to moisture content. The DSC measurement showed a glass transition at 312 K. The mechanical spectroscopy measurements were conducted on a developed low-frequency inverted torsion pendulum using the forced-vibration method. The apparatus proposed here consists of the traditional torsion shaft equipped with two coaxial cylindrical cells for liquid samples. The details of the device can be found elsewhere.46 In the measurements, the inner cylinder is forced into torsional vibration by a time-dependent force F(t) ) F0 sin(ωt). The angular displacement function of the cylinder, A(t), is measured optically. In the case here, the response of the argument can be expressed as A(t) ) A0 sin(ωt - φ), where φ is the phase difference between F(t) and A(t). The mechanical loss of the oscillating system, characterized by Q-1, is given by

Wu and Zhu

Q-1 )

1 ∆W 1 ) 2π W 2π

∫ F dA ∫0π/2 dW - 41 ∆W

)

1 F0A0π sin φ ) tan φ (1) 2π 1/ F A cos φ 2 0 0

where ∆W and W are the dissipated energy and the maximum stored energy per cycle, respectively. In the measurement, the mechanical loss Q-1 and the relative modulus G ()F0/A0) are measured as functions of temperature and frequency. To ensure a linear response, the measurements were carried out with a torsion strain amplitude of 3.0 × 10-5. In the nonisothermal test, the experimental parameters are as follows: a temperature cooling rate of 1.0 K/min and frequencies (f) ranging from 0.05 to 8.0 Hz. In the isothermal test, the measurements were performed in a wide frequency range of 10-3 to 102 Hz. In all tests, the samples were protected by argon with a pressure of 0.1 MPa to avoid oxidation and degradation. III. Results and Discussion The complex mechanical spectra (Q-1 and G) of PVAc are shown in Figure 1 at five frequencies in the temperature range 300-470 K. Unlike other amorphous polymers whose mechanical loss peak, generally about 30 K wide, is located near the glass transition region, the dynamic mechanical loss peak of PVAc covering a temperature range from 320 to 420 K shows an asymmetrical broad structure with a shoulder at the lowtemperature side. Such a phenomenon is the same as other polymers such as polyisobutylene (PIB)21,47,48 and chlorinated butyl rubber (CIIR).49,50 The asymmetrical broad mechanical loss peak could be well fitted by two peaks (R and R′ peaks) with distributions in relaxation time using a nonlinear fitting method.51,52 The details of the fitting results are given only at 0.5 Hz for clarity, as shown in Figure 1. Evidently, there are two relaxation mechanisms responsible for the R and R′ peaks. For simplicity, we describe the processes as the R and R′ relaxation modes, respectively. Note that the R′ mode exhibits a stronger frequency dependence than the R mode. For example, as the frequency varies from 2.0 to 0.2 Hz, the R peak shifts from about 342 to 333 K with an interval of 9 K; however, the R′ peak shifts from 379 to 361 K with a large interval of 18 K. So the R′ peak moves to lower temperature faster than the shoulder peak with decreasing frequency. As a result, the whole loss peak becomes narrower and narrower, and the R peak is almost superposed by the R′ peak at low frequencies due to the encroachment of the slow process toward the R process. On the contrary, as the frequency increases, the R peak and the R′ peak can be more and more clearly discerned from each other. A similar phenomenon has been observed in CIIR.50 To define the origin of these modes, we checked their reproducibility and verified that they were not caused by the interaction between polymer melts and the sample cell. Moreover, since the maximum temperature of the R peak agrees approximately with the glass transition temperature determined by DSC measurement, the R peak is associated with the glass transition and is known to be ascribed to the cooperative rearrangement of chain segments when Tg is approached.53 On the other hand, the R′ mode has a much longer relaxation time and is more sensitive to frequency than the R mode (Figure 1). Compared with the creep behavior of PVAc by Plazek,19 the R′ mode is likely to be the contribution from chain modes within the softening dispersion, composed of the sub-Rouse modes and

Dynamic Crossover of R′ Relaxation in PVAc

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Figure 1. Temperature-dependent mechanical spectra (mechanical loss Q-1 and relative modulus G) of PVAc at 0.05, 0.1, 0.2, 0.5, and 2.0 Hz. The dotted lines are the fitting of the R and R′ peaks at 0.5 Hz. Two peaks appear explicitly. Figure 3. Frequency-domain mechanical spectra of PVAc at different temperatures above Tg. (a) Relative modulus G measured at different temperatures. (b) Mechanical loss Q-1 at different temperatures, where the symbols are experimental data points and the solid lines are the total fitting results. The fitting peak (dashed line) and the fitting background (short dotted line) are down for the results at 384.7 K. (c) The fitting mechanical loss peaks at several temperatures between 365 and 413 K indicated in part d. (d) The normalized master curves of PVAc.

Figure 2. Temperature dependence of relaxation frequency ωp (s-1) obtained from the temperature-dependent mechanical spectra of PVAc. The solid lines are the linear least-squares Arrhenius fitting curves.

the Rouse modes. This explains why the Q-1 of the R′ mode is so much larger than that of the R mode. A similar phenomenon has been observed in polyisobutylene (PIB)21,22 and chlorinated butyl rubber (CIIR),49,50 where for PIB the sub-Rouse modes can be resolved from the Rouse modes because of the broad width of PIB. These peaks shift to higher temperatures with the increase of frequency, demonstrating that they are associated with relaxation processes, whereas the peak height or relaxation strength hardly changes with temperature. For a relaxation process, the relaxation τ generally follows the Arrhenius law54

τ ) τ0 exp(E/kBT)

(2)

where τ0 is the pre-exponential factor (or the relaxation time at infinite temperature), E denotes the activation energy of the relaxation process, and kB is the Boltzmann constant. It is wellknown that at the peak position the condition ωpτp ) 1 is fulfilled,54 where ω ) 2πf is the angular frequency of the measurement and the subscript p denotes values at peak position. Therefore, the relaxation parameters E and τ0 can be determined from the temperature-dependent mechanical spectra at different frequencies or from the frequency-domain spectra at different temperatures. If we plot ln(ωp) as a function of the reciprocal of peak temperature (Arrhenius plots), a linear relation would be obtained according to eq 2. The so-called Arrhenius plots for the two mechanical loss peaks are shown in Figure 2, where the solid lines are the linear least-squares fittings. The relaxation parameters E1 ) 2.57 eV, τ01 ) 1.5 × 10-39 s for the R peak and E2 ) 1.59 eV, τ02 ) 6.9 × 10-23 s for the R′ peak are obtained from these fitting lines. Here, τ01 and τ02 are so small and unrealistic, indicating that they are cooperative relaxation processes.45 Note that the R′ mode has a weaker temperature

dependence of relaxation time than the R mode (Figure 2), which is consistent with that found in PIB.21,22 To get a better insight of the dynamics of PVAc in the glass to rubber softening dispersion, the frequency-domain mechanical spectra of PVAc at different temperatures above Tg have been measured, as shown in Figure 3. Compared with the result in Figure 1, the mechanical loss peak observed in Figure 3 is associated with the R′ mode. The frequency fm at which Q-1 takes the maximum value shifts to higher frequency with increasing temperature (Figure 3b). This is a direct consequence of decreasing relaxation time, τm ()1/(2πfm)), and mainly shows the increasing mobility of polymeric chains at higher temperatures. The complex mechanical loss-frequency peak can be fitted by a peak with a distribution in relaxation time using a modified Debye equation55,56

tan φ )

(1/2)∆ sin(βπ/2) cosh(βz) + cos(βπ/2)

(3)

where ∆ is the relaxation strength, z ) ln(ωτ), and β (0 < β e 1) is the distribution parameter of relaxation time (β ) 1 corresponds to the standard Debye relaxation). The analysis of the curves in Figure 3b with eq 3 and an exponential background of ln f suggest that one peak fitting is very satisfactory and there is no trace of another peak in the frequency-domain mechanical spectra, where the background may consist of the intrinsic damping of the apparatus and the damping caused by the highfrequency secondary relaxation. From the results shown in Figure 3b, it is clear that the position of the R′ mode is closely related to the temperature and measuring frequency. The temperature dependence of mean relaxation time τ could be obtained by fitting the peak with a distribution in relaxation time by eq 3. As is well-known, relaxation times of amorphous polymers and glass-forming liquids vary strongly as the temperature is lowered toward their glass transition temperatures. In the thermodynamic equilibrium, i.e., above Tg, the temperature dependence of relaxation times τ(T) in these systems deviates strongly from a simple thermally

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Figure 5. Temperature dependence of relaxation strength ∆ for PVAc. -1

Figure 4. Variation of relaxation frequency ωp (s ) obtained from the frequency-domain mechanical spectra of PVAc against the inverse of temperature. The two VFTs are shown by solid lines, the details of which are given in the text. The inset shows the plots of [d(-ln τ)/ dT]-1/2 against temperature. The crossover temperature is the intersection of two solid lines which correspond to two VFTs shown in this figure.

activated behavior or the Arrhenius behavior. The strong nonArrhenius character of the dynamics of the R′ mode in PVAc can be seen from Figure 4 where the relaxation frequency ωp against the inverse of temperature is plotted from the frequencydomain mechanical spectra. Usually, for such systems, an excellent representation of the complex temperature dependence of τ(T) could be described by the well-known VFT law:

τ ) τ0′ exp[E/kB(T - T0)]

(4)

where τ0′ is the pre-exponential factor, T0 is the critical temperature (or “Vogel temperature”), and B is a pseudoactivation energy. However, a close examination of data over a wide temperature range where the R′ mode occurs reveals that τ(T) cannot be described accurately by a single VFT law over the entire temperature range and one usually requires separate VFT laws in the high-temperature and low-temperature regimes. To analyze more deeply the temperature dependencies, a derivative method is used.57 For a dependency according to the VFT law, one gets

[d(-ln τ)/dT]-1/2 )

() B kB

-1/2

(T - T0)

(5)

Accordingly, plotting the experimental data using eq 5 would result in linearity if a single VFT law is followed by the relaxation times over the entire temperature range. The slop and intercept of the straight line can be used to calculate back the corresponding VFT law. The results of such an analysis are shown in the inset of Figure 4, where it can be seen that [d(-ln τ)/dT]-1/2 versus T for PVAc is not linear over the entire temperature range. Data well below 387 K lie on one straight line, and data well above 387 K lie on another. This means that two VFT equations are required to describe the full temperature dependence of the relaxation time, with the temperature dependence changing in the vicinity of crossover temperature TB ∼ 387 K. The details of these obtained VFTs are as follows: (1) Low-T VFT: log τ0 ) -4.8, B ) 792.3, T0 ) 295 K. (2) High-T VFT: log τ0 ) -3.2, B ) 228.4, T0 ) 340 K. These VFT fits can be seen in Figure 4. The deviations from the single VFT law can also be realized26,58 approximately in terms of the ratio of the product of VFT parameters B for

the low-T and high-T VFT laws, respectively. As this ratio increases, the deviations from the single VFT law become more and more apparent. As can be realized from Figure 4, we found the above-mentioned ratio to be 3.2 and hence the deviation from the single VFT law in the case of PVAc seems to not be strong compared to 6.3 for a trimer of vinyl acetate (3VAc).27 TTS is the basic principle widely used for analysis of dynamics in supercooled liquids and polymers, expressing the fact that the shape of the response function remains the same when the system is cooled.59-61 When TTS is applied, the response only shifts its characteristic time and amplitude if the liquid is cooled. Here, we analyze the frequency-dependent mechanical loss to investigate whether TTS is obeyed. A normalized master curve of the loss data for PVAc above Tg is plotted in Figure 3d. This plot shows that the shape of the relaxation process varies rapidly below TB with lowering T, while it changes very slowly above TB, indicating that TTS breaks down in the entire temperature range. The failure of TTS is related to the crossover temperature TB due to the different friction mechanism for the segmental relaxation and the Rouse modes.17 Another proof of the crossover is the variation of relaxation strength ∆ and shape parameter β of PVAc. Figure 5 shows the temperature dependence of ∆ of PVAc. It can be seen that above TB the relaxation strength decreases slowly with increasing temperature. Generally, because of the enhanced thermal energy with increasing temperature, ∆ of a cooperative relaxation decreases due to the decreased cooperativity, and that of a noncooperative local relaxation increases because of the increased dipole fluctuation angle and the fraction of mobile groups.62,63 Thus, the change in ∆ with temperature can be a useful tool for indicating the extent of cooperativity of a particular relaxation. The fact that ∆ is a decreasing function of temperature suggests the decreased cooperativity of the R′ mode. On the other hand, the shape parameter β also exhibits an obvious change around TB. That is, it shows a slow increase above TB (Figure 6). Here, the shape parameter indicates that the relaxation peaks are somewhat broader than a standard Debye peak.54 This is also shown in Figure 3d. The sub-Rouse modes have a smaller intermolecular coupling than that of the local segmental mode.22 The coupling model64 (CM) is appropriate for describing this kind of intermolecular coupling. The basis of the CM is the putative existence of a temperatureinsensitive crossover time, tc, equal to about 2 ps for molecular liquids. According to the CM, the correlation function φ(t) is very different in two regions separated by tc. That is, for t < tc,

φ(t) ) exp[-(t/τ*)]

(6)

Dynamic Crossover of R′ Relaxation in PVAc

J. Phys. Chem. B, Vol. 113, No. 32, 2009 11151 liquid-liquid transition temperature Tll of PVAc by others.37,69 We estimated TB ∼ 387 K, while Tll has been estimated as ∼358 K. The liquid-liquid transition was ascribed to a third order thermodynamic transition,69,70 while the crossover is purely dynamic in origin, without any thermodynamic nature. IV. Conclusion

Figure 6. Temperature dependence of shape parameter β and coupling parameter n for PVAc. The change in T dependence at TB is apparent. The dashed lines are a guide to the eyes.

and for t > tc,

φ(t) ) exp[-(t/τ)1-n]

(7)

Here, τ and τ* are the relaxation time measured experimentally and the primitive (noncooperative) relaxation time, while n is the coupling parameter that can be considered as an indicator of the degree of correlation or cooperativeness in the relaxation process originating from the mutual interactions (0 e n < 1). In the CM, n increases with increasing molecular interaction strength and comparisons of the values of n for different glassformers at their respective Tg reveal differences in intermolecular coupling strength. The temperature dependence of n also reflects how intermolecular coupling changes with temperature. According to ref 56, the parameter n is equivalent to (1 - β) in some aspects. So the value of n could be calculated by fitting the Q-1-f spectrum with eq 3, and the temperature variation of n of PVAc is shown in Figure 6. It can be seen that with decreasing temperature the value of n varies slowly above TB and exhibits a rapid increase toward a large value at Tg. This indicates a strong increase of intermolecular cooperativity below TB, which leads the dynamics of the system to become heterogeneous and nonexponential.11,16 It is known that for the R mode of PVAc the dynamics shows a crossover at 383-387 K and at a time of 10-6-10-7 s by dielectric spectroscopy, whereas it exhibits no crossover at TB for the terminal relaxation.16,26 This difference was accounted for in terms of the different coupling parameters for the R relaxation and the terminal relaxation.16 Here, we show that the sub-Rouse modes also have a similar dynamic crossover at TB ∼ 387 K through the change of T dependence in relaxation time, relaxation strength, and coupling parameter. Interestingly, this τ(TB) is about 0.08 s, much larger than the relaxation time at the crossover in the temperature dependence of τR. According to the coupling model, the crossover is suggested to be due to the change of the intermolecular coupling because the sub-Rouse modes follow the local segmental mode in behavior. In the previous dielectric measurement of amorphous polymers, the R′ mode is usually called the liquid-liquid transition.65 The nature of the transition used to be attributed to the breakage of short-range intermolecular interaction and the onset of motion of melts,66 the change in the state of localized order,65 and the slippage of chain entanglements and chain ends.48,67 However, the occurrence of liquid-liquid transition is discredited by Plazek and co-workers.68 Here, we prove that there is no transition in the softening dispersion zone, and the only change is the variation of the intermolecular coupling. Moreover, our estimate of TB in PVAc is larger than an earlier estimate of the

The study by mechanical spectroscopy of PVAc above Tg shows the existence of the R mode, related to the glass transition, and another relaxation mode, R′, which might be associated with the softening dispersion, composed of the sub-Rouse modes and the Rouse modes. The R′ mode shows a dynamic crossover at about 387 K through the temperature dependence of different mechanical parameters, viz., relaxation time, shape parameter, and relaxation strength. The crossover temperature is consistent with the value TB ∼ 383-387 K obtained by the dielectric data but for the R mode at much shorter time than 0.08 s for the R′ mode. According to the coupling model, it is suggested that the crossover is a direct consequence of the strong increase in intermolecular cooperativity below TB. There is no transition in the softening dispersion zone of polymers, and the only change is the variation of intermolecular coupling at TB. Acknowledgment. The authors wish to thank Dr. Qiaoling Xu, Prof. Changsong Liu, and Prof. Jiapeng Shui for very helpful discussions. The financial support of National Natural Science Foundation of China (50803066, 10874182, and 10674135) is gratefully acknowledged. References and Notes (1) Angell, C. A.; Ngai, K. L.; et al. J. Appl. Phys. 2000, 88, 3113. (2) Dalnoki-Veress, K.; Forrest, J. A.; et al. Phys. ReV. E 2001, 63, 031801. (3) Deschenes, L. A.; Vanden Bout, D. A. Science 2001, 292, 255. (4) Leon, C.; Ngai, K. L.; Roland, C. M. J. Chem. Phys. 1999, 110, 11585. (5) Casalini, R.; Ngai, K. L.; Roland, C. M. J. Chem. Phys. 2000, 112, 5181. (6) Schneider, U.; Brand, R.; Lunkenheimer, P.; Loidl, A. Phys. ReV. Lett. 2000, 84, 5560. (7) Caliskan, G.; Kisliuk, A.; Novikov, V. N.; Sokolov, A. P. J. Chem. Phys. 2001, 114, 10189. (8) Kremer, F., Scho¨nhals, A., Eds. Broadband Dielectric Spectroscopy; Springer: Berlin, 2003. (9) Murthy, S. S. N. J. Phys. Chem. B 1996, 100, 8508. (10) Williams, G.; Watts, D. C. Trans. Faraday Soc. 1970, 66, 80. (11) Casalini, R.; Ngai, K. L.; Roland, C. M. Phys. ReV. B 2003, 68, 014201. (12) Kisliuk, A.; Matherson, R. T.; Sololov, A. P. J. Polym. Sci., Part B: Polym. Phys. 2000, 38, 2785. (13) Bergman, R.; Borjesson, L.; Torell, L. M.; Fontana, A. Phys. ReV. B 1997, 56, 11619. (14) Kriegs, H.; Gapinski, J.; et al. J. Chem. Phys. 2006, 124, 104901. (15) Murthy, S. S. N. J. Polym. Sci., Part B: Polym. Phys. 1993, 31, 475. (16) Ngai, K. L.; Roland, C. M. Polymer 2002, 43, 567. (17) Sokolov, A. P.; Hayashi, Y. J. Non-Cryst. Solids 2007, 353, 3838. (18) Pawlus, S.; Kunal, K.; Hong, L.; Sokolov, A. P. Polymer 2008, 49, 2918. (19) Plazek, D. J. Polym. J. 1980, 12, 43. (20) Santangelo, P. G.; Ngai, K. L.; Roland, C. M. Macromolecules 1993, 26, 2682. (21) Plazek, D. J.; Chay, I. C.; Ngai, K. L.; Roland, C. M. Macromolecules 1995, 28, 6432. (22) Ngai, K. L.; Plazek, D. J.; Rizos, A. K. J. Polym. Sci., Part B: Polym. Phys. 1997, 35, 599. (23) (a) Mashimo, S.; Nozaki, R.; Yagihara, S.; Takeishi, S. J. Chem. Phys. 1982, 77, 6259. (b) Nozaki, R.; Mashimo, S. J. Chem. Phys. 1987, 87, 2271. (24) Alegria, A.; Guerrica-Echevarria, E.; Goitiandia, L.; Telleria, I.; Colmenera, J. Macromolecules 1995, 28, 1516. (25) Roland, C. M.; Casalini, R. Macromolecules 2003, 36, 1361. (26) Tyagi, M.; Alegria, A.; Colmenero, J. J. Chem. Phys. 2005, 122, 244909.

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J. Phys. Chem. B, Vol. 113, No. 32, 2009

(27) Tyagi, M.; Alegria, A.; Colmenero, J. Phys. ReV. E 2007, 75, 061805. (28) McCrum, N. G.; Read, B. E.; Williams, G. Anelastic and Dielectric Effects in Polymeric Solids; Wiley: London, 1967. (29) Mukhopadhyay, R.; Alegria, A.; Colmenero, J.; Frick, B. Macromolecules 1998, 31, 3985. (30) Wang, C. L.; Hirade, T.; et al. J. Chem. Phys. 1998, 108, 4654. (31) Ngai, K. L.; Bao, L. R.; Yee, A. F.; Soles, C. L. Phys. ReV. Lett. 2001, 87, 215901. (32) Andreozzi, L.; Cianflone, F.; Donati, C.; Leporini, D. J. Phys.: Condens. Matter 1996, 8, 3795. (33) Faetti, M.; Giordano, M.; Leporini, D.; Pardi, L. Macromolecules 1999, 32, 1876. (34) Barbieri, A.; Gorini, G.; Leporini, D. Phys. ReV. E 2004, 69, 061509. (35) (a) Schmidt-Rohr, K.; Spiess, H. W. Phys. ReV. Lett. 1991, 66, 3020. (b) Tracht, U.; Wilhelm, M.; Heuer, A.; Feng, H.; Schmidt-Rohr, K.; Spiess, H. W. Phys. ReV. Lett. 1998, 81, 2727. (36) (a) Walther, L. E.; Israeloff, N. E.; Russell, E. V.; Gomariz, H. A. Phys. ReV. B 1998, 57, R15112. (b) Russell, E. V.; Israeloff, N. E. Nature (London) 2000, 408, 695. (37) Dias, A. B.; Correia, N. T.; Mouraramos, J. J.; Fernandes, A. C. Polym. Int. 1994, 33, 293. (38) Alegria, A.; Goitiandia, L.; Colmenero, J. Polymer 1996, 37, 2915. (39) Goitiandia, L.; Alegria, A. J. Non-Cryst. Solids 2001, 287, 237. (40) Svoboda, R.; Pustkova, P.; Malek, J. Polymer 2008, 49, 3176. (41) Adhikari, A. N.; Capurso, N. A.; Bingemann, D. J. Chem. Phys. 2007, 127, 114508. (42) Muzeau, E.; Perez, J.; Johari, G. P. Macromolecules 1991, 24, 4713. (43) (a) Haramina, T.; Kirchheim, R. Macromolecules 2007, 40, 4211. (b) Haramina, T.; Kirchheim, R.; Tibrewala, A.; Peiner, E. Polymer 2008, 49, 2115. (44) Castellano, C.; Generosi, J.; Congiu, A.; Cantelli, R. Appl. Phys. Lett. 2006, 89, 233905. (45) Wu, X. B.; Zhu, Z. G. Appl. Phys. Lett. 2007, 90, 251908. (46) Zhu, Z. G.; Zu, F. Q.; Guo, L. J.; Zhang, B. Mater. Sci. Eng., A 2004, 370, 427. (47) Fitzgerald, E. R.; Grandine, L. D.; Ferry, J. D. J. Appl. Phys. 1953, 24, 650.

Wu and Zhu (48) Sanders, J. F.; Ferry, J. D. Macromolecules 1974, 7, 681. (49) Zhu, Y. C.; Zhou, W.; et al. J. Phys. Chem. B 2007, 111, 11388. (50) Wu, J. R.; Huang, G. S.; et al. Polymer 2007, 48, 7653. (51) Yuan, L. X.; Fang, Q. F. Acta Met. Sinica 1998, 34, 1016. (52) Wang, X. P.; Fang, Q. F. J. Phys.: Condens. Matter 2001, 13, 1641. (53) Munch, E.; Pelletier, J. M.; Sixou, B.; Vigier, G. Phys. ReV. Lett. 2006, 97, 207801. (54) Nowick, A. S.; Berry, B. S. Anelastic Relaxation in Crystalline Solids; Academic: New York, 1972. (55) Ang, C.; Yu, Z.; Cross, L. E. Phys. ReV. B 2000, 62, 228. (56) Wang, X. P.; Fang, Q. F. Phys. ReV. B 2002, 65, 064304. (57) Stickel, F.; Fischer, E. W.; Richert, R. J. Chem. Phys. 1995, 102, 6251. (58) Richert, R. Physica A 2000, 287, 26. (59) Ding, Y.; Sokolov, A. P. Macromolecules 2006, 39, 3322. (60) Maggi, C.; Jakobsen, B.; Christensen, T.; Olsen, N. B.; Dyre, J. C. J. Phys. Chem. B 2008, 112, 16320. (61) Plazek, D. J. J. Non-Cryst. Solids 2007, 353, 3783. (62) Scho¨nhals, A. In Dielectric Spectroscopy of Polymer Materials: Fundamentals and Applications; Runt, J. P., Fitzgerald, J. J., Eds.; American Chemical Society: Washington, DC, 1997; p 107. (63) Jin, X.; Zhang, S. H.; Runt, J. Macromolecules 2003, 36, 8033. (64) Ngai, K. L. In Disorder Effects on Relaxation Processes; Richert, R., Blumer, A., Eds.; Springer: Berlin, 1994. (65) (a) Dudognon, E.; Berne`s, A.; Lacabanne, C. Macromolecules 2002, 35, 5927. (b) Dudognon, E.; Berne`s, A.; Lacabanne, C. J. Non-Cryst. Solids 2002, 671, 307–310. (c) Dudognon, E.; Berne`s, A.; Lacabanne, C. Polymer 2002, 43, 5175. (66) (a) Pucic, I.; Ranogajec, F. J. Polym. Sci., Part B: Polym. Phys. 2001, 39, 129. (b) Pucic, I.; Ranogajec, F. Macromol. Chem. Phys. 2001, 202, 1844. (67) Langley, N. R.; Ferry, J. D. Macromolecules 1968, 1, 353. (68) Plazek, D. J. J. Polym. Sci., Part B: Polym. Phys. 1982, 20, 1533. (69) Boyer, R. F.; Miller, R. L. Macromolecules 1984, 17, 365. (70) Boyer, R. F. Polym. Eng. Sci. 1979, 19, 732.

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