Temperature Dependence of the Viscoelastic Functions

The viscoelastic functions of polymeric materials are strongly temperature-dependent. Molecular models suggest that the source of this dependence is a factor in the decay constants, the same factor in all of them, which is very sensitive to temperature. This would imply that if the factor is denoted by a T), where T is the absolute temperature, and 

This observation is totally confirmed by experimental observation, for a wide range of polymers, as discussed by Ferry (1970) who also refers to the original literature. Apart from the temperature dependence through a(T), there is an overall factor in the viscoelastic functions which depends on temperature [Ferry (1970)]. However, it is frequently the case that this overall variation can be neglected compared with the effect of a(T), An exception to this may occur at times for which the viscoelastic functions are very slowly varying. In the present discussion, we shall ignore it. 

In practice, a(T) is determined empirically rather than from any fundamental theoretical considerations. A reference temperature Tq is selected and a(To) is set equal to unity. If follows that G(t,To), J(t,To) are the universal curves Go( ), yo( ) with One may then fill in the detailed structure of a T) by taking measurements at different temperatures. 

Williams, Landel and Ferry (1955) have given an empirical expression for a T)y applicable to a wide variety of polymeric materials, for temperatures not too different from the glass transition temperature Tg of the polymer. Their expression contains material-dependent parameters. In its simplest form, there is only one such parameter, the glass transition temperature Tg. This approximate universal expression is given by 

The combining of time and temperature dependence in the manner described above is referred to as the time-temperature superposition principle. Materials which have this property are sometimes referred to as thermorheologically simple materials. 

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