Fulcher

Figure C2.1.15. Schematic representation of tire typicai compiiance of a poiymer as a function of temperature. (C) VOGEL-FULCHER AND WILLIAMS-LANDEL-FERRY EQUATIONS...

On the other hand, polymeric materials show universal aspects of glass transition behavior, just like other materials. For instance, the classical Vogel-Fulcher behavior... 

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 dramatic slowing down of molecular motions is seen explicitly in a vast area of different probes of liquid local structures. Slow motion is evident in viscosity, dielectric relaxation, frequency-dependent ionic conductance, and in the speed of crystallization itself. In all cases, the temperature dependence of the generic relaxation time obeys to a reasonable, but not perfect, approximation the empirical Vogel-Fulcher law ... 

In spite of the problems associated with the static structure, the coarsegrained model for BPA-PC did reproduce the glass transition of this material rather well the self-diffusion constant of the chains follows the Vogel-Fulcher law [187] rather nicely (Fig. 5.10),... 

Fig. 5.10. Plot of the inverse logarithm of the self-diffusion constant of BPA-PC, for a length N = 20 of the coarse-grained chains, vs. temperature. Straight line indicates the Vogel-Fulcher [187] fit. From [28]...

Fig. 6.4. Vogel-Fulcher plot of the chain diffusion constants D for the three different polycarbonate modifications, as indicated in the figure, for N = 20 model monomers...

Table 6.1 Activation energies A0 [K] (below) and Volgel-Fulcher temperatures Tvf [K] (above) for experiment and simulation. While the error bar for TVf is fairly small, it is significant ( 30%) for the experimental determination of A0 due to the large polydisper-sity of the typical commerical samples... 

Fulcher SM Rifaximin Combined Study of Effects on Fertility and Embryo-Fetal Toxicity in CD Rats by Oral Gavage Administration. Eye, Huntington Life Sciences, 2000. 

Kamens, R.M., Guo, Z., Fulcher, J.N., Bell, D.A. (1988) Influence of humidity, sunlight, and temperature on daytime decay of polyaromatic hydrocarbons on atmospheric soot particles. Environ. Sci. Technol. 22, 103-108. 

Figure 2 Sketch of typical temperature dependencies of the viscosity r of glass-forming systems. The viscosimetric Tg of a material is defined by the viscosity reaching 1013 Poise. Strong glass formers show an Arrhenius temperature dependence, whereas fragile glass formers follow reasonably well a Vogel-Fulcher (VF) law predicting a diverging viscosity at some temperature T0.

Tk is often close to the Vogel-Fulcher temperature T0 discussed in connection with Figure 2, which is determined by fitting the Vogel-Fulcher relation5-8 to the temperature dependence of the structural relaxation time of the melt9 using Eq. [3] ... 

To interpret the cooling rate dependence of the glass transition temperature, one can use the Vogel-Fulcher law discussed in the section on the... 

Applying this prediction to the cooling rate dependence of a break points in the specific volume curves, one obtains a Vogel-Fulcher temperature of To = 0.35 that agrees well with that determined from the temperature dependence of the diffusion constant in this model, which is T = 0.32. 

Figure 9 Chain center of mass self-diffusion coefficient for the bead-spring model as a function of temperature (open circles). The full line is a fit with the Vogel-Fulcher law in Eq. [3]. The dashed and dotted lines are two fits with a power-law divergence at the mode-coupling critical temperature. 

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