In general, the WLF equation holds over the temperature range T to (T + lOO C). [Pg.170]

This is the well-known WLF equation. In the temperature range from Tg to Tg + 100 °C, most polymers obey the WLF equation. The averaged constants Cl = 17.44 and Ci = 51.6. Normally B 1, one may obtain /, = 0.025. fg appears to be independent of the molecular structures, thus the glass transition is also referred as an equal-free-volume transition verified by the experiments. It can be proved that WLF equation is actually a reflection of VFT-type liquids. [Pg.114]

The WLF equation applies to amorphous polymers in the temperature range of Tg to about Tg + lOO C. In this equation J is the reference temperature, these days taken to be the T, while and C2 are constants, initially thought to be universal (with Cx = 17.44 and C2 = 51.6), but now known to vary somewhat from polymer to polymer. These experimental observations bring up a number of interesting questions. What is the molecular basis of the time-temperature superposition principle What is the significance of the log scale and what does the superposition principle tell us about the temperature dependence of relaxation behavior And what about the temperature dependence of a7 at temperatures well below 2 [Pg.467]

The question we now wish to address concerns the WLF equation. Why does the temperature dependence of the shift factor have this form for temperatures ranging from the T into the terminal flow region [Pg.468]

WLF equation provides a good description of the temperature dependence of dynamics for non-crystalline polymers in the temperature range Eg < r < Eg + 100 K. The choice of reference temperature is completely [Pg.338]

For numerical results, the WLF equation has been found to be good for the temperature range Tg to (Tg + 50). The merit of the equation lies in its generality as no particular chemical structure is assumed other than a linear amorphous polymer above Tg. For polymer scientists and rheologists over the last four decades, the WLF equation has provided a mainstay both in utility and theory. [Pg.111]

The WLF formula shows that the ionic conductivity of the polymer electrolyte is shown in the temperature range higher than Tg. Ionic conductivity decreases rapidly if its temperature goes below that of Tg. The EO unit is recognized as the most excellent structure from the ionic dissociation viewpoint. The ion is transported coupled with the oxyethylene chain motion in amorphous polymer domain. However, oxyethylene structure easily becomes crystalline. Therefore, in order to accelerate the quick molecular motion of the polymer chain and quick ion diffusion, it is important to lower the crystallization of polymer matrixes. The methods for inhibiting the crystallization of the polymer are, for example, to introduce the polyethylene oxide chain into the low Tg polymer such as polysiloxane and phosp-hazene, or to introduce the asymmetric units such as ethylene oxide/propylene oxide (EO/PO) into polymer main chain. [Pg.415]

If accuracy is needed, the WLF equation should be used, or alternatively, an Arrhenius expression, suitable for the temperature range. [Pg.129]

It should be emphasized that data of good precision covering a broad temperature range are needed to distinguish between the Arrhenius and WLF relationships. [Pg.154]

One further point should be made. The WLF equation can correctly predict the relaxation behavior of incompatible systems, but for temperature ranges limited to one transition. For incompatible polyblends that exhibit two transitions, the equation will yield satisfactory results if applied to each transition separately. [Pg.66]

The correlation time of the motions involved in intramolecular excimer formation is defined as the reciprocal of the rate constant ki for this process. Its temperature dependence can be interpreted in terms of the WLF equation for polymers at temperatures ranging from the glass transition temperature Tg to roughly Tg +100° [Pg.239]

Equation (10-59) or (10-58) is known as the William-Landels-Ferry (WLF) equation. It applies to all relaxation processes, and therefore also for the temperature dependence of the viscosity (see Section 7.6.4). Its validity is limited to a temperature range from Tg to about Tg + 100 K. Outside this temperature range the expansion coefficient ai varies, not linearly, but with the square root of temperature. [Pg.412]

In attempts to better understand dendrimer intramolecular morphology, considerable attention was devoted to the fractional free volume near the glass temperature [40, 49, 50], Because all of the studies were performed within the WLF temperature range, the data were analyzed using the equation [Pg.350]

The master curve in the form of stiffness versus frequency can be created by fitting the experimentally determined shift factors to a mathematical model. With a multifrequency measurement, frequencies beyond the measurable range of the DMA can be achieved by using the superposition method based on the Williams-Landel-Ferry (WLF) equation [60, 61]. For a temperature range above the T, it is generally [Pg.34]

In this equation, a is the conductivity, A is a constant proportional to the number of carrier ions, B is a constant, and To is the temperature at which the configurational entropy of the polymer becomes zero and is close to the glass transition temperature (Tg). The VTF equation fits conductivity rather well over a broad temperature range extending from Tg to about Tg +100 K. Equation [3.2] is an adaptation of the William-Landel-Ferry WLF relationship developed to explain the temperature dependence of such polymer properties as viscosity, dielectric relaxation time and magnetic relaxation rate. The fact that this equation can be applied to conductivity implies that, as with these other properties, ionic [Pg.77]

This relationship for Newtonian viscosity is valid normally for temperatures higher than 50 °C or more above the Tg. The utility of the Arrhenius correlation can be limited to a relatively small temperature range for accurate predictions. The viscosity is usually described in this exponential function form in terms of an activation energy, Af, absolute temperature T in Kelvin, the reference temperature in Kelvin, the viscosity at the reference T, and the gas law constant Rg. As the temperature approaches Tg for PS (Tg = 100°C), which could be as high as 150°C, the viscosity becomes more temperature sensitive and is often described by the WLF equation [10] [Pg.102]

In 1955, major questions concerning the flow laws for polymer q tems still remained unanswered, however. Conclusive evidence that a is unity for short chains at constant f was lacking. The importance of polymer coil dimensions in addition to (or instead o chain length per se in the dependence of rj on molecular parameters was unknown. Similarly, the relation of Zg for different pol5miers to characteristic molecular dimensions was unknown. The usefulness of the WLF relation over a wide temperature range and the universality of the parameters in the WLF relation for a wide variety of materials 220) had not been demonstrated. [Pg.263]

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