WLF Equation for the Shift Factor

Williams, R.F. Landel and J.D. Ferry (1955 see also Ferry, (1980)) applied the TTSP to a large number of polymers and found empirically the following expression for the shift factor, 

The development of the above equation has been shown to be of great importance and has become widely used. It is commonly known as the WLF equation and must be one of the most referenced equations ever in the polymer literature. Eq. 7.6 was thought to be a universal equation for 

Equation 7.6 can be developed from Doolittle s concept of free volume of a liquid. In Chapter 4 it was noted that the specific volume varies with temperature during quenching as shown in Fig. 4.27 and can be used to identify the degree of crystallinity as well as the melt temperature, T.  

Above the Tg the fractional free volume can be expressed as (see Aklonis and McKnight, (1983)), 

The ratio of the natural log of viscosity at any temperature to that at the T will give after simplification. 

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