Viscosity Vogel-Tamman-Fulcher

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). 

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) ... 

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... 

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. 

A more attractive equation derived by Vogel [27], Fulcher [28], and Tamman [29] gives viscosity from an exponential function that is currently written in the form (VTF equation) ... 

The Arrhenius plot of the viscosity of the ILs is not a straight line but a Vogel-Fulcher-Tamman (VFT) type curve. Since ionic conductivity is the inverse of the viscosity (Eq. (3.8)), it also obeys the VFT equation. 

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... 

Two mathematical expressions, the Arrhenian equation and the Vogel-Fulcher-Tamman equation, are commonly used to express the temperature dependence of the viscosity of glass forming melts. At one extreme, we find that the viscosity can often be fitted, at least over limited temperature ranges, by an Arrhenian expression of the form ... 

An equation that does fit the data originated from attempts to fit the temperature dependence of the viscosity. The Vogel-Fulcher, or Vogel-Fulcher-Tamman (VFT), equation for x T), viz. 

A formula often used to fit viscosity vs temperature data for inorganic glasses is the Vogel-Fulcher-Tamman (VFT) equation. 

Viscosities were calculated using the Vogel, Fulcher, Tamman, and Hesse (VFTH) equation. 

Figure 11.7 shows the viscosity of the NS2 liquid at ambient pressure as a function of inverse temperature, and it can be seen that the computed value [107] is in very good agreement with experimental measurements from Bockris et al. [108] and from Neuville [109]. To gain additional insight into the relaxational behavior, we use a functional form for the viscosity-temperature behavior given by the Vogel-Fulcher-Tamman law [111] ... 

However, as anticipated above, the glass transition phenomenology involving structural processes in polymer materials rarely follows simple Arrhenius laws, and especially near Tg (where decreasing the temperature by 10 K can produce an increase of x and r of, say, three orders of magnitude), the dramatic increase of the viscosity and of the characteristic structural relaxation time is much better described by the Vogel-Fulcher-Tamman (VFT) equation ... 

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