Time-temperature superposition viscoelastic region

Fortunately for linear amorphous polymers, modulus is a function of time and temperature only (not of load history). Modulus-time and modulus-temperature curves for these polymers have identieal shapes they show the same regions of viscoelastic behavior, and in each region the modulus values vary only within an order of magnitude. Thus, it is reasonable to assume from such similarity in behavior that time and temperature have an equivalent effect on modulus. Such indeed has been found to be the case. Viscoelastic properties of linear amorphous polymers show time-temperature equivalence. This constitutes the basis for the time-temperature superposition principle. The equivalence of time and temperature permits the extrapolation of short-term test data to several decades of time by carrying out experiments at different temperatures. 

Chapters 8 and 9 have introduced the concepts of the glass transition and rubber elasticity. In particular. Section 8.2 outlined the five regions of viscoelasticity, and Section 8.6.1.2 derived the WLF equation.This chapter treats the subjects of stress relaxation and creep, the time-temperature superposition principle, and melt flow. Parts of this topic are commonly called rheology, the science of deformation and flow of matter. 

Also, even when the data are obtainable only over one or two decades of the logarithmic frequency scale at any one time, the viscoelastic functions can be traced out over a much larger effective range by making measurements at different temperatures, and by applying time-temperature superposition (TTS) for flexible homopolymers (see Chapter 6). In many instances, the effect of an increase in temperature is nearly equivalent to an increase in time or a decrease in frequency, as molecular viscoelastic theories suggest (see Chapter 4). When properly applied, TTS yields plots in terms of reduced variables that can be used with considerable confldence to deduce the effect of molecular parameters, and also to predict viscoelastic behavior in regions of the time or frequency scale not experimentally readily accessible (see Chapters 4 and 6). 

Tr = 150 °C. The master curve clearly displays the five different characteristic viscoelastic regions or physical states noted in Fig. 5.2, with respect to the time or frequency axis. The superposition process underscores the fact that the viscoelastic properties of polymers depend more strongly on temperature than time, with changes in modulus and other properties over several orders of magnitude occurring over a modest temperature range (in this case -40 °C). 

The master curve so obtained corresponds to the compliance in the region of linear viscoelasticity. Because of this, it is interesting to compare the master curve with that obtained using the temperature-time superposition (shown in Figure 12.3). The latter curve is shown in Figure 12.8 as the dashed line. It is seen that both master curves agree with each other fairly closely. 

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