Williams-Landel-Ferry kinetics

Recently, Peleg el al.129 have made a case for applying non-Arrhenius and non-Williams-Landel-Ferry kinetics to the Maillard reaction, since its reactivity is only noticeable above a certain temperature. They show that a relatively simple, empirical log-logistic relationship,... 

An alternative approach to describe nucleation from the amorphous state utilizes the glass transition temperature (Tg) concept (Williams et al. 1955 Slade and Levine 1991). Based on this approach, molecular mobility below Tg is sufficiently limited to kinetically impede nucleation for very long times. Amorphous systems, at temperatures above Tg, nucleate at a rate depending on the temperature difference above Tg. Williams et al. (1955) suggested that the rate of nucleation increases rapidly at temperatures just above Tg according to a kinetic expression given by the WLF (Williams-Landel-Ferry) 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... 

The fractional free volume f, which is the ratio of the free volume to the overall volume, occupies a central position in tr5nng to understand the molecular origins of the temperature dependence of viscoelastic response. The main assumption of the free-volume theory is that the fractional free volume assumes some universal value at the glass transition temperature. The Williams-Landel-Ferry (WLF) equation for the thermal dependence of the viscosity tj of polymer melts is an outgrowth of the kinetic theories based on the free volume and Eyring rate theory (35). It describes the temperature dependence of relaxation times in polymers and other glass-forming liquids above Tg (33-35). The ratio of a mechanical or dielectric relaxation time, Tm or ra, at a temperature T to its value at an arbitrary reference temperature To can be represented by a simple empirical, nearly universal function. 

However, because measurements are kinetically determined, this is a less accurate form of the equation. Very often it is observed that the measured shift factors, defined for different properties, are independent of the measured property. In addition, if for every polymer system, a different reference temperature is chosen, and ap is expressed as a function of T — rj, then ap turns out to be nearly universal for all polymers. Williams, Landel and Ferry believed that the universality of the shift factor was due to a dependence of relaxation rates on free volume. Although the relationship has no free volume basis, the constants and may be given significance in terms of free volume theory (Ratner, 1987). Measurements of shift factors have been carried out on crosslinked polymer electrolyte networks by measuring mechanical loss tangents (Cheradame and Le Nest, 1987). Fig. 6.3 shows values of log ap for... 

Since the value of / < 0.159 [120] and T < then it is apparent that in the case of glassy polymers energy of the thermal oscillations of order kT is not sufficient for microvoid formation kT < ej. The second problem requiring explanation and repeatedly discussed [48, 80, 147,148] is the absolute value of f, which within the frameworks of the kinetic theory is estimated according to Equation 1.33. The values 0.050-0.100 were obtained for different polymers [157], which is much more than the generally accepted value of = 0.025 0.003 for most polymers within the frameworks of the Williams, Landel and Ferry concept (WLF) [8, 145,146]. 

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