BOTTS: broadband optimized time-temperature superposition for vastly accelerated viscoelastic data acquisition

Modern materials design strategies take advantage of the increasing amount of materials property data available and increasingly complex algorithms to take advantage of those data. However, viscoelastic materials resist this trend towards increased data rates due to their inherent time-dependent properties. Therefore, viscoelasticity measurements present a roadblock for data collection in an important aspect of material design. For thermorheologically simple (TRS) materials, time-temperature superposition (TTS) made relaxation spectrum measurements faster relative to, for example, very long creep experiments. However, TTS itself currently faces a speed limit originating in the common logarithmic discrete frequency sweep (DFS) mode of operation. In DFS, the measurement time is proportional (by a factor much greater than one) to the lowest frequency of measurement. This state of affairs has not improved for TTS for half a century or more. We utilize recent work in experimental rheometry on windowed chirps to collect three decades of complex modulus data simultaneously, resulting in a ∼500% increase in data collection. In BOTTS, we superpose several isothermal chirp responses to produce a master curve in a fraction of time required by the traditional DFS-TTS technique. The chirp responses have good, albeit nontrivial, signal-to-noise properties. We use linear error propagation and a noise-weighted least squares approach to automatically incorporate all the data into a reliable shifting method. Using model thermoset polymers, we show that DFS-TTS and BOTTS results are comparable, and therefore BOTTS data represent a first step towards a faster method for master curve generation from unmodified rheological measurement instruments. By applying a broadband "chirp" to a viscoelastic sample tested with a typical DMA, one can collect complex modulus data at many frequencies at once. This approach dramatically accelerates the collection of viscoelastic data from polymer samples.