Free Volume and the Williams-Landel-Ferry Equation

3 Free Volume and the Williams-Landel-Ferry Equation  

The free volume theory is based on the concept introduced by Doolittle which describes the nonlinear behaviour of the viscosity of a liquid as Tg is approached  

The value of the parameter / can be defined as /g at the glass transition temperature and allowed to increase with a value af which is equal to the liquid 

The viscosity at any temperature T divided by the value at the glass transition temperature is then expressed by 

The constants 17.4 and 51.6 are nearly universal and can be used to describe the behaviour of a wide range of materials. The value of 17.4 for the first constant implies that the fractional free volume at Tg is 0.025, i.e. of the order of 2.5% for most materials. The second constant 51.6 is the ratio fgjoLf and this would arise if the value of f were equal to 4.8 x 10 K . There are several other theories that exist, but despite its simplicity the WLF theory has been foimd to be very successful in describing a significant volume of data. 

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