Rigorous analysis of the linear viscoelastic behavior of thermo-rheologically complex amorphous materials

It is well-known that linear viscoelastic response of amorphous materials, including both low molecular weight and polymeric, as probed in mechanical and dielectric relaxation experiments is thermo-rheologically complex. A common approach to analyzing viscoelastic data is to use a combination of phenomenological functions such as stretched exponential, Havriliak-Negami, etc. manifesting as distinct peaks in the relaxation spectrum. Unfortunately, not only the location on the time axis but also the shape and the spectral strength of these peaks is required to change with temperature rendering such representation merely a curve fit. A brute force Prony series expansion has also been tried, where the relaxation times are typically assumed to be evenly spaced on the logarithmic scale. The resulting set of Debye peaks of varying strength also lacks physical interpretation. We propose a different approach where all processes have the same strength, but the corresponding relaxation times are dictated by the data. When broad temperature interval comprising sub-Tg and above Tg regions is investigated a complete relaxation map emerges. Examples of the relaxation map will be shown for several materials, including epoxy systems of varying architecture.