Thermorheological simplicity and complexity

It is not a trivial problem to obtain a complete characterization of a material responding over many decades of time. The brute force method would be to carry out experiments over many decades of time. More efficient is to employ more than one instrument, and cover a time span that includes high frequencies. This is now possible with broad dielectric spectroscopy, with which the frequency reuige from 10 to 10 can be attained by using different techniques - time domain spectroscopy, frequency response analysis using AC-bridges, and coaxial line reflectrometry. Of course, each isothermal experiment has to be repeated at various temperatures in order to determine the temperature dependence. 

It is common to measure some viscoelastic quantity at constmt frequency (or isochronally) over a series of temperatures, thus efficiently gaining a view of all viscoelastic mechanisms. However, since the relaxation function is temperature dependent, employing temperature as the independent variable convolutes the time and temperature dependencies, yielding data that are not amenable to theoretical analysis. The convenience of sweeping temperature at fixed test frequency comes at the expense of rigor. 

Often the assumption is made that a material is thermorheologically simple, meaning all mechanisms contributing to the response have the same temperature dependence. In this situation, temperature only changes the relrixation time, not the shape of the relaxation function. Accordingly, the principle of time-temperature superpositioning can be applied. The measured quantities are shifted 

Of course, thermorheological complexity does not necessarily mean that 

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