Vogel-Fulcher-Tammann equation temperature dependence

Figure 80 Temperature dependencies of conductivities for PEO brushes with short side chains (MW = 300g moi ) at various UCF3SO3 doping levels (symbols are experimental data lines are fits with the Vogel-Fulcher-Tammann equation). The vertical dashed line indicates the range of room temperature (295 K). Reprinted from Zhang, Y. ...

Unfortunately, reliable experimental estimates of the configurational entropy are unavailable to enable explicit application of the AG model for polymer fluids. Instead, the temperature dependence of t in polymer melts is often analyzed in terms of the empirical Vogel-Fulcher-Tammann-Hesse (VFTH) equation [103],... 

A Vogel-Fulcher-Tammann-Hesse equation can be used to characterize the temperature dependence of the relaxation times for these six different degrees of cure, 0.70, 0.75, 0.80, 0.825, 0.90, and 0.95 ... 

It appears, however, that the mode-coupling theory is not able to explain some of the most significant slow-relaxation processes of these more complex glass formers. In particular, it cannot explain the success of the Vogel-Fulcher-Tammann-Hesse (VFTH) equation for the temperature-dependence of the relaxation time near the glass transition. The mode-coupling theory predicts instead a power-law dependence of the longest relaxation... 

E0 and the infinite temperature relaxation time To are independent of temperature, and (ii) in the isotropic phase near the I-N transition, the temperature dependence of ts2(T) shows marked deviation from Arrhenius behavior and can be well-described by the Vogel-Fulcher-Tammann (VFT) equation ts2(T) = TyFrQxp[B/(T — TVFF), where tvff, B, and tvft are constants, independent of temperature. Again these features bear remarkable similarity with... 

In the a-process, the viscosity and consequently the relaxation time increase drastically as the temperature decreases. Thus, molecular dynamics is characterized by a wide distribution of relaxation times. A strong temperature dependence presenting departure from linearity or non-Arrhenius thermal activation is present, owing to the abrupt increase in relaxation time with the temperature decrease, thus developing a curvature near T. This dependence can be well described by the Vogel-Fulcher-Tammann-Hesse (VFTH) equation [40, 41], given by Equation 2.1 ... 

Fig. 19. Temperature dependence of the shift factors of the viscosity (T), terminal dispersion ( ), and softening dispersion (0) of app from Ref. 73. The temperature dependence of the local segmental relaxation time determined by dynamic light scattering ( ) (30) and by dynamic mechanical relaxation (o) (74). The two solid lines are separate fits to the terminal shift factor and local segmental relaxation by the Vogel-Fulcher-Tammann-Hesse equation. The uppermost dashed line is the global relaxation time tr, deduced from nmr relaxation data (75). The dashed curve in the middle is tr after a vertical shift indicated by the arrow to line up with the shift factor of viscosity (73). The lowest dashed curve is the local segmental relaxation time tgeg deduced from nmr relaxation data (75).

That the viscosities of the ILs are highly sensitive to the temperature is evident from the data presented in Table 7.1. The temperature dependence of the viscosity of morpholinium ILs, depicted in Figure 7.2, is found to be better represented by the Vogel-Fulcher-Tammann (VFT) equation [63], an equation widely used to describe the temperature dependence of the viscosity of glass-forming substances compared to the Arrhenius equation. 

The average a-relaxation time of polymers exhibit a dramatic sensitivity to temperature as Tg is approached. Figure 3.1b shows the temperature dependence of the average a-relaxation time as a function of inverse temperature normalized to Tg for an amorphous polymer. The temperature dependence of the average a-relaxation (or viscosity) can be well described by the Vogel-Fulcher-Tammann-Hesse (VFTH) equation [64-66]... 

Normal liquids exhibit Arrhenius tempCTature depoidaice of the typical lime scale of spontaneous fluctuations. However, once below Ihdr T , a steep super-Anhenius temperature dependence of such time scale is observed. This, in a more or less wide temperature range, is often described by the so-called Vogel Vogel-Fulcher-Tammann (VFT) equation [62, 166, 178] t= Tq exp (B/(T - Tq)). Here r is the relaxation time relevant for spontaneous fluctuations, to a pre-exponential factor, and B and To the Vogel activation energy and temperature, respectively. 

Before proceeding further, it is appropriate to discuss some aspects of molecular mobility of amorphous solids as it affects stability. The temperature dependence of molecular motion in amorphous systems is described by the empirical Vogel-Tammann-Fulcher (VTF) equation ... 

The temperature dependence of relaxation in glass-forming liquids is often described by the Vogel-Tammann-Fulcher (VTF) equation... 

The conductivity of ionic liquids often exhibits classical linear Arrhenius behavior above room-temperature. However, as the temperature of these ionic liquids approaches their glass transition temperatures (Tg) the conductivity displays significant negative deviation from linear behavior. The observed temperature-dependent conductivity behavior is consistent with glass-forming liquids, and is often best described using the empirical Vogel-Tammann-Fulcher (VTF) equation. 

One of the important properties of a polymer electrolyte leading to its development activity is the ionic conductivity. Temperature dependence on the conductivity of amorphous polymer electrolytes generally follows the Vogel-Tammann-Fulcher [VTF] equation [14] ... 

It is remarkable that the free-volume-based Doolittle equation devised to explain the temperature dependence of the viscosity of a generic simple atomic liquid can account so well both for the viscous behavior of metallic glass alloys through the Vogel, Fulcher, and Tammann (VFT) equation representation discussed in Chapter 1 and for the behavior of the much more complex sub-cooled... 

The viseosities of the 1,3-dialkylimidazoilium aluminium ehloride and l-mefliyl-3-ethylimidazolium aluminium bromide ionie liquids have also been reported for different eompositions and temperatures. For both the ehloroaluminate and bromoaluminate ionie liquids the temperature dependence was found not to have an Arrhenious type curve, with non-linear plots of Inq vs. 1/T. In these studies the temperature range used was wider than that of the N-alkylpyridinium. This non-Arrhenius behavior is characteristic of glass forming melts. Here the three parameter Vogel-Tammann-Fulcher (VFT) equation ... 

The temperature dependence of the dynamic viscosity t of a liquid close to its glass temperature Tg can be described by the Vogel-Tammann-Fulcher (VTF) equation [43-45] or by the Theory of free volume introduced by Doolittle [46 8], Cohen and Turnbull [49, 50]. An exponential dependence from the reciprocal temperature 1/T is found (see (8.8)). 

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