Arrhenius relationship between shift factor

The Arrhenius relationship (Eq. 2) between shift factor aj, and temperature T is commonly used for secondary relaxation phenomena (4). To is the reference temperature and E. is the activation energy. 

This transposition for amorphous polymers is accomplished using a shift factor ( x) calculated relative to a reference temperature T, which may be equal to Tg. The relationship of the shift factor to the reference temperature and some other temperature T, which is between Tg and T + 50 K, may be approximated by the Arrhenius-like Equation. 

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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