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Vogel-Fulcher-Tammann equation, 8-relaxation dependence

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 ... [Pg.143]

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... [Pg.216]

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... [Pg.295]

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 ... [Pg.17]

The relaxation-time dependence could be described by the Vogel-Fulcher-Tammann-Hesse equation [88] ... [Pg.232]

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). 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).
Segmental relaxation is a non-Arrhenius process having a time scale with a temperature dependence that follows the Vogel-Fulcher-Tammann-Hesse (VFTH) equation (27) ... [Pg.163]

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]... [Pg.51]

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. [Pg.267]

The temperature dependence of relaxation in glass-forming liquids is often described by the Vogel-Tammann-Fulcher (VTF) equation... [Pg.83]


See other pages where Vogel-Fulcher-Tammann equation, 8-relaxation dependence is mentioned: [Pg.211]    [Pg.169]    [Pg.194]    [Pg.324]    [Pg.499]    [Pg.10]    [Pg.129]    [Pg.242]    [Pg.335]    [Pg.24]    [Pg.852]    [Pg.40]    [Pg.236]    [Pg.421]    [Pg.8]    [Pg.121]   


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