Equations Fulcher-Tamman

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. 

VFTH Vogel, Fulcher, Tamman, Hesse 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. 

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... 

Several other equations have been suggested to overcome the shortcomings of the Arrhenius equation. The most widely used is the Vogel-Fulcher-Tamman equation (also called the Vogel-Fulrath equation) ... 

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. 

Molten salt approaches such as the Vogel-Fulcher-Tamman (VFT) equation have been used repeatedly for analyzing the temperature dependence of transport properties W T) such as diffusion, conductance, and fluidity, or of relaxation processes ... 

The relationship between the relaxation time and the temperature between glass transition and melting is described by several empirical equations. The one of the most commonly employed Vogel-Fulcher-Tamman (VFT) equation is given by (Mauro etal. 2009 Yu 2001)... 

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 ... 

Figure 9.30 Dp of 20 nm radius probes as a function of T in 2/3 neutralized 596 kDa polyacrylic acid 0.1 M NaCl 0.1 wt% Triton X-100 at concentrations 0 (0) 3 ( ), 6 (A), 8 (0), and 15 (V) g/1 and fits at each c to the Vogel-Fulcher-Tamman equation, using the same Tg at every c, after Phillies, et u/.(51).

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]. 

The WLF relation was an extension of the Vogel-Tamman-Fulcher (VTF) empirical equation (Vogel, 1921 Tamman and Hesse, 1926 Fulcher, 1925) which was originally formulated to describe the properties of supercooled liquids and, given in its original form, is... 

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