Influence of initial phase angle on optimally windowed strain-controlled chirp ( <i>γ</i>  − OWCh) rheometry

Optimally windowed chirp rheometry—a technique employing both frequency and amplitude-modulated exponential chirps—is gaining popularity for its ability to precisely capture the linear viscoelastic spectrum of complex materials while dramatically reducing the experimental time required to acquire data. To date, the chirp signals used for characterizing the linear viscoelasticity of such materials have featured a high time-bandwidth product (TB&amp;gt;50), calculated as the product of chirp duration or experiment time (Towc) and frequency bandwidth (Δω). However, for time-evolving materials, it is essential to also adjust the chirp duration (Towc) according to the characteristic mutation timescale, τmu(t) of the material to ensure time-translation invariance (Towc≪τmu(t)) during experiments. For rapidly mutating materials, the values of the time-bandwidth product TB thus systematically decrease as the chirp duration is progressively reduced during the mutation process. However, the signal must also be sufficiently long, relative to the material’s inherent relaxation timescale (τ), to ensure that a steady-state periodic viscoelastic response is obtained. To explore the trade-offs between these two competing conditions, we perform exploratory numerical simulations using canonical constitutive models: the classical Maxwell model, characterized by a single dominant relaxation time and the fractional Maxwell model, which compactly and accurately captures the broad relaxation spectra typical of many viscoelastic materials. For highly viscoelastic systems and/or rapidly mutating samples, we show that when employing short exponential chirp sequences, substantially improved accuracy can be obtained by shifting the initial phase of the chirp waveform through a single new phase offset parameter, φ0. Experimental validation tests performed on wormlike micellar solutions, a pressure-sensitive adhesive, and a UV-curable acrylate system—each having relaxation times comparable to the signal duration—further demonstrate that adjusting the initial phase significantly enhances the data quality of linear viscoelastic measurements made with optimally windowed chirp protocols.