Williams-Landel-Ferry type equation

No simple reaction kinetic was found to describe the thermal dedoping process. It can be described using a master-plot technique. This master plot can be fitted with a Williams-Landell-Ferry type equation [491]. A reduction of the number... 

In some epoxy systems ( 1, ), it has been shown that, as expected, creep and stress relaxation depend on the stoichiometry and degree of cure. The time-temperature superposition principle ( 3) has been applied successfully to creep and relaxation behavior in some epoxies (4-6)as well as to other mechanical properties (5-7). More recently, Kitoh and Suzuki ( ) showed that the Williams-Landel-Ferry (WLF) equation (3 ) was applicable to networks (with equivalence of functional groups) based on nineteen-carbon aliphatic segments between crosslinks but not to tighter networks such as those based on bisphenol-A-type prepolymers cured with m-phenylene diamine. Relaxation in the latter resin followed an Arrhenius-type equation. 

The same free volume also occurs in the Williams-Landel-Ferry dynamic glass-transition-temperature equation (see Section 10.5.2). The free-volume fraction is independent of the polymer type. It has a value of about 2.5% (Table 5-7). 

The choice of equation for determining the temperature dependence of MFI is mainly governed by whether T < Tg + 100 otT > Tg + 100. At temperatures relatively closer to Tg, free volume and its changes with temperature play a dominant role. Hence, the (Williams-Landel-Ferry) WLF-type Eq. (4.15) could provide better estimates. At temperatures greater than Tg + 100, the temperature dependence of MFI is decisively affected by overcoming of the forces of inter-molecular interactions, in which case the Arrhenius-type Eq. (4.14) would give better predictions. 

However, the L-H model differs in several important macromoleeular details that distinguish it from small moleeule morphology. Following the ad hoe assumption that the first e qjonential in the erystallization equation (A12) may be approximated by a Vogel or modified Williams-Landel-Ferry (WLF) type of term,, Eq. (A 12) beeomes... 

Arrhenius plots of the ionic conductivity of amorphous polymer electrolytes, such as PPO-based electrolytes, frequently do not lie on a simple straight line, but rather, on a positively curved line (Fig. 3) [11]. Such curves are well represented by a Williams-Landel-Ferry (WLF) type equation [13] ... 

In conclusion, the viscosity of polymer melts depends on shear conditions (rates or stresses), on the molecular weights, and on the temperature. While Newtonian liquids obey an Arrhenius type dependence on temperature, on the other hand, polymer melts follow suit only at temperatures that exceed 100 C above the glass transition temperature (Tg). At the intermediate range, a generalized WLF equation (named after its founders Williams, Landel and Ferry) is applicable ... 

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