Arrhenius factor viscosity dependence

PPG (at higher temperatures) behaves like a typical pseudoplastic non-Newtonian fluid. The activation energy of the viscosity in dependence of shear rate (284-2846 Hz) and Mn was detected using a capillary rheometer in the temperature range of 150-180°C at 3.0-5.5 kJ/mol (28,900 Da) and 12-13 kJ/mol (117,700 Da) [15]. The temperature-dependent viscosity for a PPG of 46 kDa between 70 and 170°G was also determined by DMA (torsion mode). A master curve was constructed using the time-temperature superposition principle [62] at a reference temperature of 150°G (Fig. 5) (Borchardt and Luinstra, unpublished data). A plateau for G was not observed for this molecular weight. The temperature-dependent shift factors ax were used to determine the Arrhenius activation energy of about 25 kJ/mol (Borchardt and Luinstra, unpublished data). 

Of all the physico-chemical properties, it is the rheology which shows the strongest temperature dependence. For instance, the decrease in apparent viscosity at a fixed shear rate is well represented by the Arrhenius-type exponential expression the pre-exponential factor and the activation energy are then both fimctions of shear rate. It is thus customary to denote the temperature dependence using rheological constants such as the power-law consistency coefficient and flow behaviour index. It is now reasonably well established that the flow behaviour index, n, of suspensions, polymer melts and solutions is nearly independent of temperature, at least over a range of 40-50°C, whereas the consistency coefficient exhibits an exponential dependence on temperature, i.e. 

Rate constants for free radical propagation increase with decreasing polymer free radical resonance stabilization (Table 20-2). The activation energies, however, are more or less independent of the constitution. Consequently the rate constants are predominantly determined by the preexponential factors of the Arrhenius equation. In addition, they also depend on the viscosity of the reaction medium to a slight extent. 

The S-factor model was originally developed by Yorston and Liebergott (1965) and was based on the assumption that a correlation exists between the lignin content of the solid phase in the reaction and the pulp viscosity. The widely accepted delignification rate equation, in the form also later reported by Hagberg and Schobn (1973) in 1973, was used to model delignification and relate the pulp viscosity to that. The Arrhenius temperature dependency of the reaction had already been confirmed and this was used in equation 1. 

In such cases the rate constant may be controlled either by diffusion or by chemical factors depending on the conditions. Evidence for the simultaneous roles of diffusion and activation control has also been found for some other reactions in highly viscous solvents, in that they show curved Arrhenius plots, indicating that the rate is controlled by diffusion at low temperatures where the viscosity is highest, but by chemical activation at ordinary temperatures. Examples include the reactions of CO with haemoglobin and myoglobin in aqueous glyerol [10,c,d]. Reactions of simple radicals such as H- and HO- with solvated electrons... 

Both constants used in the Arrhenius equation (Eq. 4.1) have to be more closely defined. In order to determine whether these two values are dependent on processing parameters, the above relationships are compared with measured data. The relationship found between reduction in viscosity and the various influencing factors has the following mathematical form [607] ... 

In the study of dielectric relaxation, temperature is an important variable, and it is observed that relaxation times decrease as the temperature increases. In Debye s model for the rotational diffusion of dipoles, the temperature dependence of the relaxation is determined by the diffusion constant or microscopic viscosity. For liquid crystals the nematic ordering potential contributes to rotational relaxation, and the temperature dependence of the order parameter influences the retardation factors. If rotational diffusion is an activated process, then it is appropriate to use an Arrhenius equation for the relaxation times ... 

In this chapter, we have presented the rheological behavior of homopolymers, placing emphasis on the relationships between the molecular parameters and rheological behavior. We have presented a temperature-independent correlation for steady-state shear viscosity, namely, plots of log ri T, Y) r](jiT) versus log or log j.y, where Tq is a temperature-dependent empirical constant appearing in the Cross equation and a-Y is a shift factor that can be determined from the Arrhenius relation for crystalline polymers in the molten state or from the WLF relation for glassy polymers at temperatures between and + 100 °C. 

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