Effect of incomplete datasets on the calculation of continuous relaxation spectra from dynamic-mechanical data

In this article, the effect of an incomplete frequency range on relaxation spectra calculated with the new spline-based method (Stadler and Bailly, Rheol Acta 48(1):33-49, 2009) presented before is discussed. The range, in which the spectrum can be determined, is limited by the range of the input data, but not directly by the inverse frequency. The actual limits depend on the range of input data. Depending on the shape of the spectrum the relaxation spectrum can be determined from the input data in a range up to three decades larger than the input data. This can be explained by the influence of the modes outside the inverse frequency range. For this purpose, a new concept, the relevance factor analysis, was introduced, which allows for a determination of the limits of spectrum calculation. The characteristic relaxation times are discussed in comparison for to the calculation of J_e⁰ and η₀ from the spectrum.