Viscosity Fulcher relation

As the exponential relation does not describe viscosity over a wider temperature range, various empirical equations have been suggested for practical purposes the Fulcher-Tammann relationship has found the widest application ... 

The theoretical explanation of the Fulcher-Tammann relation is based either on the free volume theory or on the concept of the temperature-dependent size of structural units taking part in viscous flow (cf. Doremus, 1973). The Fulcher-Tammann relation predicts a rapid increase of viscosity to an infinite value at To, while in fact in the transformation range approaches a constant and relation (6) is thus complied with. 

As mentioned above, all molecular liquids that have been studied at viscosities above 1 cP (D< 1 X 10 cm sec) have been found to depart the behavior described by (3) in a way that requires the activation energy to increase continuously and in an accelerating manner as the temperature decreases. Over much of the range, the behavior is described by a simple empirical modification of the Arrhenius relation, often called the VTF or Fulcher equation... 

It is well known that the viscosity of a liquid decreases upon heating. This would usually be expected to fit to an Arrhenius type of behavior. That is, the natural logarithm of the viscosity should vary in a linear manner with temperature. All of the I Ls for which the temperature dependence of the viscosity has been studied deviate from this behavior [7, 9, 11, 14, 20]. Rather, they fit a Vogel-Tammann-Fulcher interpretation where the viscosity of the IL at any given temperature is better related to a material-specific temperature such as the difference between the temperatare of the study and the glass transition temperature of the IL. 

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... 

Below the fast process in frequency, the so-called primary a-process is observed [80, 99] which governs the viscosity [100] and is directly related to the glass transition. The temperature dependence of the relaxation time t is described not by the Arrhenius equation but by the Vogel-Fulcher type ... 

At temperatures T > (melting temperature), the dependence of viscosity on temperature is controlled by the Arrhenius equation. In most materi als, in the temperature range from to (glass transition temperature), the temperature decrease results in an increase of activation energy ( ), which relates to the fact that molecules do not move as individuals, but in a coordinated maimer. At T > Tg, viscosity is satisfactorily described by the so called VTF (Vogel Fulcher Tammany) equation ijj. = A.exp D.Tq/(T Tq) or WLF (Williams—Landel—Ferry) equation Oj. = exp [Cjg.(T—Tg)]/[C2g (T-Tg)], where ijj, = viscosity at temperature T, j. = ratio of viscosities at T and Tg, or the ratio of relaxation times r and tg at temperatures T and Tg and A, D, Tg, Cjg and are constants. Parameters and are considered universal... 

Equation (5.121) relates ap to the temperature dependence of the viscosity. Numerous experiments were carried out to measure this function. They led to a specific result. As it turns out, for the majority of polymer systems, rjo(T) is well represented by an empirical equation known as the Vogel-Fulcher law . It has the form... 

One of the most convenient tools for practical determination of fictitious temperatures is thermomechanometry [396] see Fig. 54, where the time dependence of fictitious temperature can be obtained on the basis of the Tool-Narayanaswami relation [391,396,400] by the optimization of viscosity measurements (logr] T,Tf versus temperatures) using the Vogel-Fulcher equation again. 

The viscosity ( q)-temperature (T) relation of strong glass-forming liquids follows the Vogel-Fulcher-Tammann model [9] ... 

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