Vogel-Fulcher-Tamman-Hesse

The parameters for P4tBCHM are summarized in Table 2.6 The temperature dependence of the a relaxation in the frequency domain can be conveniently analyzed by means of the Vogel-Fulcher-Tamman-Hesse (VFTH) equation [88-90] which was empirically formulated as ... 

Fig. 2.23 Vogel-Fulcher-Tamman-Hesse plots for P2tBCHM ( ) and P4tBCHM ( ). (From ref. [32])...

On the other hand, as in the analysis of the previous systems the temperature dependence of the a relaxation follow the Vogel-Fulcher-Tamman-Hesse (VFTH) [88-90], The 7% values obtained are 337 5 and 274 5 for PBCHM and PBCHMM respectively. By this way and using equation (2.31) the m parameter obtained are 1579 and 1804 and the relative free volumes at Tg are 3.2 and 2.6% for PCBuM and PCHBMM, respectively, in good agreement with the free volume theory. 

VFTH Vogel, Fulcher, Tamman, Hesse equation... 

It was shown in Figure 12.4 that, in the case of glass-rubber relaxation, the linearity of the plot of peak E" or the peak of tan d versus the reciprocal of the peak temperature, was lost. Consequently, the Vogel-Fulcher-Tamman-Hesse... 

The non-Arrhenius-type fluids widely exist. The typical cases include the Vogel-Fulcher-Tamman (VFT) type (Vogel 1921 Fulcher 1925 Tatnmann and Hesse 1926),... 

Currently, the dependence of t on temperature is deduced from viscosity-temperature measurements. At T < T, the temperature dependence of T obeys an Arrhenius law, but this dependence is much more complex at T > T. In the latter case it is referred to an empirical Vogel-Tamman-Fulcher (VTF) law (Vogel, 1921 Tamman and Hesse, 1926 Fulcher, 1925). 

At the time of development of free volume theory, two important empirical equations of viscosity were known. They are the Doolittle (1951) equation (3.01) and the Vogel, Tamman and Fulcher (VTF) equation (3.02) (Vogel, 1921, Fulcher, 1923, Tammann and Hesse, 1926), which are given below. 

The temperature dependence of the ionic conductivities for the HBP-SA and the HBP-SA-co-HBP-Ac membrane in the temperature range of 60-150°C is shown in Fig. 13.1. Ionic conductivity data of the polymer and electrolyte membrane are typically interpreted using the Vogel-Tamman-Fulcher (VTF) equation (Vogel, 1921 Tammann and Hesse, 1926 Fulcher, 1925) ... 

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