Vogel-Tamman-Fulcher temperature

Following the general trend of looldng for a molecular description of the properties of matter, self-diffusion in liquids has become a key quantity for interpretation and modeling of transport in liquids [5]. Self-diffusion coefficients can be combined with other data, such as viscosities, electrical conductivities, densities, etc., in order to evaluate and improve solvodynamic models such as the Stokes-Einstein type [6-9]. From temperature-dependent measurements, activation energies can be calculated by the Arrhenius or the Vogel-Tamman-Fulcher equation (VTF), in order to evaluate models that treat the diffusion process similarly to diffusion in the solid state with jump or hole models [1, 2, 7]. 

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). 

To see more clearly the temperature effect on ion conduction, the logarithmic molal conductivity was plotted against the inverse of temperature, and the resultant plots showed apparent non-Arrhenius behavior, which can be nicely fitted to the Vogel— Tamman-Fulcher (VTF) equation ... 

Experimental measures of molecular mobility within glasses have proven technically difficult because of the long time spans required. General behavior is described by the Vogel-Tamman-Fulcher (VTF) Model, valid for temperatures near Tg, where viscosity increases in a double exponential relationship with decreasing temperature (Angell, 1991) ... 

The temperature dependence of the conductivity is described by the Vogel—Tamman— Fulcher equation. ... 

Glasses and polymer electrolytes are in a certain sense not solid electrolytes but neither are they considered as liquid ones. A glass can be regarded as a supercooled liquid and solvent-free polymer electrolytes are good conductors only above their glass transition temperature (7 ), where the structural disorder is dynamic as well as static. These materials appear macroscopically as solids because of their very high viscosity. A conductivity relation of the Vogel-Tamman-Fulcher (VTF) type is usually... 

The usual expressions for visco-elastically related properties of amorphous polymers (and of the amorphous regions in semi-crystalline polymers) are the essentially similar Vogel-Tamman-Fulcher (VTF) and Williams-Landel-Ferry (WLF) relationships [30, 45 7]. These can be applied to the dependence of conductivity, a, on absolute temperature, T, for polymer electrolytes, whereupon they have the form... 

The motion of ions (i.e. conductivity) in polymer electrolytes appears to occur by a liquid-like mechanism in which the movement of ions through the polymer matrix is assisted by the large amplitude segmental motion of the polymer backbone. Ionic conductivity primarily occurs in the amorphous regions of the polymer [4,5]. The temperature dependence of the conductivity of polymer electrolytes is best related by the Vogel-Tamman-Fulcher (VTF) equation... 

A conductivity study on PVC-PMMA-LiAsFg-DBP polymer blend electrolyte by S. Rajendran, T. Uma, and T. Mahalingam (Rajendran et al., 2000) revealed the effect of PVC-PMMA blend ratio on ionic conductivity. The temperature dependence of the conductivity of the polymer films obeys the Vogel-Tamman-Fulcher (VTF) relationship. 

Type I. The conductivity of these compounds follows a free volume law in all experimental temperature ranges, reflected by a VTF (Vogel-Tamman-Fulcher) equation ... 

In parallel with the Williams-Landel-Ferry (WLF) equation, the Vogel-Tamman-Fulcher (VTF) equation is used to express the temperature dependency of conductivity ... 

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) ... 

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 ... 

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. 

Since most of ILs including polymer systems show upper convex curvature in the Arrhenius plot, and not a straight line, the temperature dependence of the ionic conductivity is expressed by Vogel-Fulcher-Tamman (VFT) equation [7] ... 

Most of the liquids obey Eq. (9.2) if the temperature interval is not too large. However, for glass-forming melts, the viscosity of which ranges from 1 Pa to 10 " Pa, the Vogel-Fulcher-Tamman equation is frequently used... 

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