Vogel-Fulcher-Tamman

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 ... 

Another approach has been developed by Bruno and Della Monica [24-26], This work takes the Vogel-Tamman-Fulcher (VTF) equation, which has been used to rationalize transport properties in molten salts and glassy electrolytes, and modifies it for nonaqueous solutions. The work follows the development of Angell and co-workers [27,28], who carried out a similar development for aqueous solutions. The expression used is... 

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. ... 

In the case of polymers, different expressions for the conductivity are used, such as the Vogel-Tamman-Fulcher (VTF) relationship ... 

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... 

---