Polymer dynamics time-temperature superpositioning

Whatever the selected method (static, monotonous, or dynamic), it gives access to a limited range of timescales. For example it is almost impossible to perform static experiments in times less than 1 s, or dynamic tests at frequencies lower than 10 1 Hz, or tensile tests at strain rates higher than 103 s-1. These timescales are, however, indirectly accessible because the polymers generally obey a time-temperature superposition principle ... 

Detailed analysis of the isothermal dynamic mechanical data obtained as a function of frequency on the Rheometrics apparatus lends strong support to the tentative conclusions outlined above. It is important to note that heterophase (21) polymer systems are now known to be thermo-rheologically complex (22,23,24,25), resulting in the inapplicability of traditional time-temperature superposition (26) to isothermal sets of viscoelastic data limitations on the time or frequency range of the data may lead to the appearance of successful superposition in some ranges of temperature (25), but the approximate shift factors (26) thus obtained show clearly the transfer viscoelastic response... 

It is noteworthy that even in miscible polymers of similar molecular structure, viz. 1,4-polyiso-prene with 1,2-polybutadiene, the time-temperature superposition fails. The polymers having glass transition temperatures separated by 60°C preserve their different dynamics in the blends [Kan-nan and Komfield, 1994]. Thus, even miscible systems can be rheologicaUy complex. The rheological behaviors of blends in the vicinity of the phase separation are of great fundamental importance. They will be discussed in Part 7.4.3. 

Although time-temperature superpositioning can be very useful, in the glass transition (softening) zone of the viscoelastic response, polymers are ther-morheologically complex. This breakdown of time-temperature superpositioning is caused by the weaker temperature dependence of the chain dynamics... 

Yu et al. (2011) studied rheology and phase separation of polymer blends with weak dynamic asymmetry ((poly(Me methacrylate)/poly(styrene-co-maleic anhydride)). They showed that the failure of methods, such as the time-temperature superposition principle in isothermal experiments or the deviation of the storage modulus from the apparent extrapolation of modulus in the miscible regime in non-isothermal tests, to predict the binodal temperature is not always applicable in systems with weak dynamic asymmetry. Therefore, they proposed a rheological model, which is an integration of the double reptation model and the selfconcentration model to describe the linear viscoelasticity of miscible blends. Then, the deviatirMi of experimental data from the model predictions for miscible... 

Figures 9.4 and 9.5 show G and G" for two linear polymers, a poly(vinyl methyl ether) (PVME) with a molecular weight of 138,000 and a polystyrene (PS) with a molecular weight of 123,000, respectively. The data for each polymer have been moved horizontally along the frequency axis until they form a single curve. There is a substantial region of overlap, extending over three decades of frequency, so the superposition is clearly established. The shift factors needed to obtain overlap of the curves are shown as inserts. The reference temperature for each case was taken to be 84 °C this temperature has no significance other than being a convenient value for the particular application for which the data were obtained, which was a study of phase separation in blends of the two polymers. One of the significant uses of time-temperature superposition is made evident by focusing on the open and closed symbols in the PVME curves. The dynamic moduli are available over five orders...

Ding, Y. Sokolov, A. P. (2006). Breakdown of time temperature superposition principle and universality of chain dynamics in polymers. Macromolecules 39(9) 3322-3326. 

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