Measurement time-temperature superposition procedure

Time-temperature superposition was first suggested by H. Leaderman who discovered that creep data can be shifted on the horizontal time scale in order to extrapolate beyond the experimentally measured time frame (9-10). The procedure was shown to be valid for any of the viscoelastic functions measured within the linear viscoelastic range of the polymer. The time-temperature superposition procedure was first explicitly applied to experimental data by... 

Viscoelastic Master Curves. In order to evaluate whether a given material is suitable for a particular damping application we need to know its viscoelastic properties over a broad range of temperature and frequency. However, in most instances we can measure these quantities only over a limited range of temperature or frequency. The data are then extended to other temperatures and frequencies by using the time-temperature-superposition procedure (5, 6) to form viscoelastic master curves that correlate the data and extend its utility. 

Since we are interested in this chapter in analyzing the T- and P-dependences of polymer viscoelasticity, our emphasis is on dielectric relaxation results. We focus on the means to extrapolate data measured at low strain rates and ambient pressures to higher rates and pressures. The usual practice is to invoke the time-temperature superposition principle with a similar approach for extrapolation to elevated pressures [22]. The limitations of conventional t-T superpositioning will be discussed. A newly developed thermodynamic scaling procedure, based on consideration of the intermolecular repulsive potential, is presented. Applications and limitations of this scaling procedure are described. 

Fig. 26. Influence of the temperature on logar of 9.9 wt% PVC/DOP. (O) Measuroimits correspond-ing with the extrapoktion procedure (A) measurements correspond with the normal application of the time-temperature superposition pincipfe (see Fig. 24). The full line corresponds with the WLF-equation (reference tenq)erature 1°Q. Re oduced from Physical Networks, Polymers and Gels [Ref. 12] by the courtesy of Chapman Hall...

In friction force microscopy (also called lateral force microscopy, LFM), on the contrary, these lateral forces are measured and may yield important insight into friction forces, their dependence on particular phases, and orientation of the underlying polymer or environmental conditions. Due to the difficulties in obtaining truly quantitative friction force data and the dependence of friction forces on load and scan velocity (due to the time-temperature superposition principle) [14], which all require tedious experimental procedures, friction force microscopy is not widely used in the analysis of polymer morphologies. 

Time-temperature superposition is of interest in two contexts. For the experimentalist it is the basis of a technique for substantially increasing the range of times or frequencies over which linear behavior can be determined. And for the polymer scientist, it may provide additional information about molecular structure. It was Ferry [1] who first provided a scientific basis for this procedure. The essence of the concept is that if all the relaxation phenomena involved in G t) have the same temperature dependency, then changing the temperature of a measurement will have the same effect on the data as shifting the data horizontally on the log(time) or log(frequency) axis. Let us say that a change in the temperature from a reference value Tg to a different temperature T has the following effect on all the relaxation times ... 

A final comment seems to be pertinent. In most cases actual measurements are not made at the frequencies of interest. However, one can estimate the corresponding property at the desired frequency by using the time (fre-quency)-temperature superposition techniques of extrapolation. When different apparatuses are used to measure dynamic mechanical properties, we note that the final comparison depends not only on the instrument but also on how the data are analyzed. This implies that shifting procedures must be carried out in a consistent manner to avoid inaccuracies in the master curves. In particular, the shape of the adjacent curves at different frequencies must match exactly, and the shift factor must be the same for all the viscoelastic functions. Kramers-Kronig relationships provide a useful tool for checking the consistency of the results obtained. 

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