A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS)

Characterizing purely viscous or purely elastic rheological nonlinearities is straightforward using rheometric tests such as steady shear or step strains. However, a definitive framework does not exist to characterize materials which exhibit both viscous and elastic nonlinearities simultaneously. We define a robust and physically meaningful scheme to quantify such behavior, using an imposed large amplitude oscillatory shear (LAOS) strain. Our new framework includes new material measures and clearly defined terminology such as intra-/intercycle nonlinearities, strain-stiffening/softening, and shear-thinning/thickening. The method naturally lends a physical interpretation to the higher Fourier coefficients that are commonly reported to describe the nonlinear stress response. These nonlinear viscoelastic properties can be used to provide a “rheological fingerprint” in a Pipkin diagram that characterizes the material response as a function of both imposed frequency and strain amplitude. We illustrate our new ...

New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear

We introduce a comprehensive scheme to physically quantify both viscous and elastic rheological nonlinearities simultaneously, using an imposed large amplitude oscillatory shear (LAOS) strain. The new framework naturally lends a physical interpretation to commonly reported Fourier coefficients of the nonlinear stress response. Additionally, we address the ambiguities inherent in the standard definitions of viscoelastic moduli when extended into the nonlinear regime, and define new measures which reveal behavior that is obscured by conventional techniques.

Fingerprinting Soft Materials: A Framework for Characterizing Nonlinear Viscoelasticity

The application of oscillatory shear strain leads, in the non-linear regime, to the appearance of higher harmonic contributions in the shear stress response. These contributions can be analyzed as spectra in Fourier space with respect to their frequencies, amplitudes and phase angles. In this article, we present several theoretical and practical aspects of measuring Fourier rheology spectra with high sensitivity. Using the hardware of a conventional rheometer, Fourier rheology spectra with a signal-to-noise ratio of about 18,000:1 for a single acquisition were obtained. This allowed the observation of harmonics up to the 21st harmonic. Signal averaging can further increase the sensitivity.

High Sensitivity Fourier-Transform Rheology

Recently, large-amplitude oscillatory shear has been studied in great detail with emphasis on its impact on the material response. Here we present a conceptually different, robust methodology based on viewing the stress waveforms as representing a sequence of physical processes. This novel approach provides the viscous and elastic contributions while overcoming the problems with infinite series encountered by Fourier transformation. Application to a soft colloidal star glass leads to the unambiguous determination and quantification of rate-dependent static and dynamic yield stresses, the rationalization of the response to strain sweeps and the post-yield regime by introducing the apparent cage modulus, and a connection to the steady-shear stress, all from a single-amplitude experiment. We propose that this approach is generic, but focus in this contribution only on a yield stress material which exhibits repeating cycles of (i) elastic extension, (ii) yielding, (iii) flow, and (iv) reformation. We show tha...

A sequence of physical processes determined and quantified in LAOS: Application to a yield stress fluid

A very high molecular weight, narrow molecular weight distribution polystyrene, having a molecular weight of 8.42×106, was investigated using a sliding plate rheometer. The solvent was diethyl phthalate. The solution exhibited wall slip during steady shear, even at very low shear rates and exhibited a marked normal‐stress‐driven secondary flow at high shear rates. However, there was no evidence of slip during the oscillatory shear tests. Using fast Fourier transform analysis, the results of the oscillatory shear tests on this solution are presented in terms of response surfaces in a space based on a Pipkin diagram (strain‐rate amplitude versus frequency). These reveal the linear and nonlinear regimes and the approach to a purely elastic regime at high frequencies. Wagner’s constitutive equation predicts the major trends in the experimental data but does not provide quantitative predictions over the entire range of experimental parameters.

Sliding plate rheometer studies of concentrated polystyrene solutions: Large amplitude oscillatory shear of a very high molecular weight polymer in diethyl phthalate

Two high molecular weight, narrow distribution polystyrenes dissolved in tricresyl phosphate were studied using a sliding plate rheometer. Shear stress and birefringence measurements in step strain allowed the determination of N3 for both solutions. Start-up of steady simple shear and large amplitude oscillatory shear measurements revealed that the critical shear stress for slip for both solutions is around 2500 Pa and that slip is dynamic in nature, allowing rheological measurements above the critical stress to be made at sufficiently high frequencies. The critical stress value was used in conjunction with data from the literature to develop a relationship between critical stress and concentration. Large-amplitude oscillatory shear stress measurements revealed that the solutions exhibit a limiting behavior at high strain rate amplitudes in the intermediate frequency range when the dependence on strain rate amplitude becomes small. Birefringence measurements showed that at high frequencies, where the time scale of the deformation is short, the oscillatory component of N3 vanished. This was found to occur at lower frequencies for the lower molecular weight solution. In contrast, the average value of the third normal stress difference, reflected in the zeroth harmonic, was found to vary little between the two solutions.

Sliding plate rheometer studies of concentrated polystyrene solutions: Nonlinear viscoelasticity and wall slip of two high molecular weight polymers in tricresyl phosphate

Michael J. Reimers

Papers

Sliding plate rheometer studies of concentrated polystyrene solutions: Large amplitude oscillatory shear of a very high molecular weight polymer in diethyl phthalate

Sliding plate rheometer studies of concentrated polystyrene solutions: Nonlinear viscoelasticity and wall slip of two high molecular weight polymers in tricresyl phosphate