σOWCh: Optimally Windowed Chirp rheometry using combined motor transducer/single head rheometers

Recent advances in rheometry exploiting frequency-modulated (chirp) waveforms have dramatically reduced the time required to perform linear viscoelastic characterisation of complex materials. However, the technique was optimised for ‘separate motor transducer’ instruments, in which the drive motor imposing the strain deformation is decoupled from the torque transducer. Whilst the use of optimised windowed chirps (OWCh) using other rheometers has been recently reported in the literature, no systematic study concerning the use of ‘combined motor transducer’ instruments (in which the motor and transducer subsystems are integrated into a single ‘head’) has been undertaken. In the present study, we demonstrate the use of OWCh rheometry using combined motor transducer/single-head rheometers using a stress-controlled operating principle, thus avoiding the reliance on complicated and instrument-specific feedback control systems that would be required to perform strain-controlled experiments. The use of stress-controlled chirps requires a modification to the established OWCh analysis protocol such that the complex viscosity ${\eta }^{\ast }\left(\omega \right)$ is used as an intermediate proxy function for ultimately computing the complex modulus $G^{\ast }\left(\omega \right)$. This approach negates the effect of the strain offset that is inherent to stress-controlled oscillatory rheometry. Secondly, a correction algorithm and operational criteria for identifying inertial artefacts is established before we consider the impact of chirp digitisation on data acquisition. The use of stress-controlled OWCh rheometry (which we term Stress-OWCh, i.e. $\sigma$OWCh) is demonstrated for a diverse range of material classes including, Newtonian calibration fluids (silicone oil), polymer solutions (polyethylene oxide in water), an entangled polymer melt (polydimethylsiloxane), worm-like micellar systems (cetylpyridinium chloride/sodium salicylate), time-evolving critical gels (gelatin) and aging elastoviscoplastic materials (Laponite®). This novel implementation of chirp waveforms using a single-head rheometer will facilitate the wider adoption of OWCh rheometry and allow the benefits of frequency-modulation techniques to be exploited where separate motor transducer instruments are unavailable/unsuitable.