Arrhenius relaxation behavior

The concept of fragility is a qualitative one and is related to deviations of the relaxation time of a liquid from Arrhenius-like behavior and to the topology of the potential energy landscape of the system. The classification of liquids into strong and fragile thus provides a fundamental framework for quantitatively describing equilibrium and dynamical properties of supercooled liquids and glassy states of matter [1-6,8,9,22,37,38,52,54—56,88-91,103]. 

To measure the departure from an Arrhenius-like behavior and to decrease the ambiguity in the use of fragility as a quantitative probe of the liquid state, the so-called F1/2 metric has been introduced. It is defined as the value of Tg/T at the midway of the relaxation time on a log scale, specifically, between the high-temperature phonon vibration lifetimes 10 14 s and the relaxation time at Tg, namely, i Tg), which is generally taken to be 102s [37], An advantage of this definition is that the midway values for the relaxation time are readily and accurately accessible by viscosimetric and by dielectric measurements [37,43], Let T /2 be temperature at which x = 10 6s. Now define a quantity Fx /2 as follows [37,43] ... 

Process B was observed to pass through all three phase transitions, and it was found to be non-Arrhenius with distinct changes in its relaxation behavior delineated by the phase transitions. In the same manner as for Process A the characteristic relaxation time tb was extracted from the peak maximum of the dielectric losses, s"(a), T), (Fig. 21). 

Fig. 10. Transition map for the mixture of hydrophilic Aerosil with PDMS [27] the relaxation of chain units outside the adsorption layer is represented by symbol , anisotropic motion of chain units inside the adsorption layer is shown by symbol 0, the slowest chain motion related to adsorption-desorption processes in the adsorption layer is designated by symbol O the data of the fu t two relaxation processes are fitted by the WLF function, the tempoature dependence of the slowest relaxation shows the Arrhenius-like behavior for comparison data from previous h Ty and NMR experiments , mechanical , and dielectric spectroscopy are given...

Fast relaxation processes ( , 0) show a Williams-Landel-Ferry (WLF) type temperature dependence which is typical for the dynamics of polymer chains in the glass transition range. In accordance with NMR results, which are shown in Fig. 9, these relaxations are assigned to motions of chain units inside and outside the adsorption layer (0 and , respectively). The slowest dielectric relaxation (O) shows an Arrhenius-type behavior. It appears that the frequency of this relaxation is close to 1-10 kHz at 240 K, which was also estimated for the adsorption-desorption process by NMR (Fig. 9) [9]. Therefore, the slowest relaxation process is assigned to the dielectric losses from chain motion related to the adsorption-desorption. 

Cerveny investigated the development of the dynamic glass transition in styrene-butadiene copolymers by dielectric spectroscopy in the frequency range from 10 to 10 Hz. Two processes were detected and attributed to the alpha- and beta-relaxations. The alpha relaxation time has a non-Arrhenius temperature behavior that is highly dependent on styrene content... 

In some epoxy systems ( 1, ), it has been shown that, as expected, creep and stress relaxation depend on the stoichiometry and degree of cure. The time-temperature superposition principle ( 3) has been applied successfully to creep and relaxation behavior in some epoxies (4-6)as well as to other mechanical properties (5-7). More recently, Kitoh and Suzuki ( ) showed that the Williams-Landel-Ferry (WLF) equation (3 ) was applicable to networks (with equivalence of functional groups) based on nineteen-carbon aliphatic segments between crosslinks but not to tighter networks such as those based on bisphenol-A-type prepolymers cured with m-phenylene diamine. Relaxation in the latter resin followed an Arrhenius-type equation. 

Abstract For three liquids, salol, propylene carbonate, and o-terphenyl, we show that the relaxation time or the viscosity at the onset of Arrhenius behavior is a material constant. Thus, while the temperature of this transition can be altered by the application of pressure, the time scale of the dynamics retains a characteristic, pressure-independent value. Since the onset of an Arrhenius temperature-dependence and the related Debye relaxation behavior signify the loss of intermolecular constraints on the dynamics, our result indicates that intermolecular cooperativity effects are governed by the time scale for structural relaxation. 

Relaxation Phenomena Hilczer et al. [2002] studied the relaxation behavior of nanoceramic-polymer composites. The smdy focused on a PVDF/PZT composite with 30-nm particles. The dielectric relaxation time of PVDF as well as that of the low-temperature component followed VFTH [Eq. (13.2)]. By contrast, the relaxation time of the high-temperature component obeyed the Arrhenius equation. It is interesting to note that the activation enthalpy increased strongly in composites. The effect was ascribed to the wide-angle oscillation of dipolar groups of PVDF. 

Figure 12 Dielectric relaxation behavior of PMPS. (a) Relaxation map. Solid lines are fits of the VF equation to the low- and high-temperature data. The dash-dotted line is an MCT fit where the dashed line is an Arrhenius fit to the high-temperature data, (b) Derivative plot of the data shown in (a), (c) f As vs. 1/7. Lines are linear regressions to the low-and high-temperature data.

By simply quenching bom melt, the o form (crystal form II) is formed, which is not ferroelectric. In this polymer three dielectric transitions may be delected, the p transition at about —(KTC. Ok o. transition near —10 and the a, transition near 1S0 C The p transition exhibits an Arrhenius-like relaxation behavior with an activatioo enthalpy of SO kJAnol it is attributed to local motions in the amorphous as well as in the crystalline state. The a. tiansitioo has a WLF-type relaxatkm beluvior it is attributed to the glass Iransitioa of the amorphous part The a, tiansitioo is attributed to motioos in the crystalline phase, but most probably not within the lamellae but in the partially... 

The relaxation behavior of amorphous polymers was dominated by two processes, the glass-rubber transition and the terminal flow region, which are both characterized by a temperature dependence given by the WLF equation. For polyethylene, one cannot expect a flow transition because flow is suppressed by the crystallites in the sample. The fact is that for linear polyethylene, i.e., polyethylene with high crystallinity, there is no WLF-controlled process at all. The numerous measurements in the literature provide clear evidence that the two processes observed in linear polyethylene, a and 7, are both based on activated mechanisms obeying the Arrhenius law. The process... 

This approach has been applied extensively in recent years to polymers [16,27-31]. From comparisons of segmental relaxation times for various polymers made on the basis of 7g-scaled Arrhenius plots, correlations between the shape of the relaxation function and chemical structure have been demonstrated [3,16,32,33]. Fragility plots are also useful in interpreting the relaxation behavior of polymer blends, since the relaxation function itself is complicated due to inhomogeneous broadening [34-37]. 

The effect of including attractive interactions with the walls is essentially to reduce the acceptance rate of the algorithm as more monomers get adsorbed on the walls. The relaxation times show an Arrhenius behavior, similar to the result on Fig. 9 in Sec. III. 

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