BOTTS: Rapid viscoelastic master curves through broadband optimized time-temperature superposition of windowed chirps from widely available DMA equipment

Modern materials design strategies take advantage of the increasing amount of materials property data available and increasingly complex algorithms to take advantage of that data. However, viscoelastic materials resist this trend towards increased data rates due to the very material time-dependence that should be measured. Therefore, viscoelasticity measurements present a roadblock for data collection in an important aspect of material design. For thermorheologically simple materials, time-temperature superposition (TTS) has for many years provided a method to accelerate relaxation spectrum measurements 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, 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. Furthermore, the three-decade chirp response is recorded in the time it would take to collect only the lowest frequency data point of a traditional DFS experiment, resulting in a 500% speedup in data collection. In BOTTS, we superpose several isothermal chirp responses to produce a master curve in a fraction of the time of 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 in a reliable shifting method. Using model thermoset polymers, we show DFS-TTS and BOTTS results are comparable, and therefore BOTTS data represent a first step towards a fast, reproducible method for master curve generation from existing rheological measurement instruments.