Uniqueness of Relaxation Times Determined by Dielectric Spectroscopy.

Dielectric spectroscopy (DS) is extremely powerful to study molecular dynamics, be-cause of the very broad frequency range. Often multiple processes superimpose resulting in spec-tra that expand over several orders of magnitude, with some of the contributions partially hidden. For illustration, we selected two examples, (i) normal mode of high molar mass polymers partial-ly hidden by conductivity and polarization and (ii) contour length fluctuations partially hidden by reptation using the well-studied polyisoprene melts as example. The intuitive approach to de-scribe experimental spectra and to extract relaxation times is the addition of two or more model functions. Here, we use the empirical Havriliak-Negami (HN) function to illustrate the ambigui-ty of the extracted relaxation time, despite an excellent agreement of the fit with experimental data. We show that there are an infinite number of solutions for which a perfect description of experimental data can be achieved. However, a simple mathematical relationship indicates uniqueness of the pairs of the relaxation strength and relaxation time. Sacrificing the absolute value of the relaxation time enables to find the temperature dependence of the parameters with a high accuracy. For the specific cases studied here, the time temperature superposition (TTS) is very useful to confirm the principle. However, the derivation is not based on a specific tempera-ture dependence, hence, independent from the TTS. We compare new and traditional approaches and find the same trend for the temperature dependence. The important advantage of the new technology is the knowledge of the accuracy of the relaxation times. Relaxation times deter-mined from data for which the peak is clearly visible are the same within the experimental accu-racy for traditional and new technology. However, for data where a dominant process hides the peak substantial deviations can be observed. We conclude that the new approach is particularly helpful for cases in which relaxation times need to be determined without having access to the associated peak position.