Vogel-Fulcher-Tammann-Hesse VFTH equation

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],... 

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... 

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 ... 

If the free volume shows a linear expansion with the temperature, Vf = Ef(T- T ), where Ef=dVf IdT is its specific thermal expansivity and Tq < Tg is the temperature where the (linearly extrapolated) free volume disappears, one obtains from Eq. (11.7) the well-known Vogel-Fulcher-Tammann-Hesse (VFTH) equation [Vogel, 1921 Fulcher, 1925 Tammann and Hesse, 1926] ... 

This equation is a special form of the empirical Vogel-Fulcher-Tammann-Hesse (VFTH) equation [78-80],... 

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]... 

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