Fingerprinting Soft Materials: A Framework for Characterizing Nonlinear Viscoelasticity

By R. Ewoldt, G. H. McKinley, Anette E. Hosoi. 2007

391 citations recorded by the source corpus.

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. PACS numbers: 83.60.Df, 83.85.Ns, 83.80.Qr, 83.80.Lz ∗Electronic address: peko@mit.edu 1 ar X iv :0 71 0. 55 09 v1 [ co nd -m at .s of t] 2 9 O ct 2 00 7 Biopolymer networks [1, 2, 3], wormlike micelles [4], colloidal gels [5], and metastable soft solids in general [6], can be classified as nonlinear viscoelastic materials and as such have been of interest to experimentalists for many decades (e.g. [7]). The biological and industrial processes associated with these materials often involve large deformations, yet standard methods of characterizing their nonlinear rheological properties rely on techniques designed for small strains. In this Letter, we develop a new and systematic framework for quantifying the nonlinear viscoelastic response of soft materials which enables us to describe a unique “rheological fingerprint” of an a priori unknown substance. Both the elastic and viscous characteristics of a material can be examined simultaneously by imposing an oscillatory shear strain, γ(t) = γ0 sin(ωt), which consequently imposes a phase-shifted strain-rate γ̇(t). Here ω is the imposed oscillation frequency, γ0 is the maximum strain amplitude and t is time. At small strain amplitudes when the response is linear, the material is commonly characterized by the viscoelastic moduli G′(ω), G′′(ω), as determined from the components of the stress in phase with γ(t) and γ̇(t), respectively. For a purely elastic linear solid, the elastic modulus G′ is equivalent to the shear modulus G. Similarly, for a purely viscous Newtonian fluid with viscosity μ, the loss modulus G′′ = μω. However, these viscoelastic moduli are not uniquely defined once the material response becomes nonlinear, since higher order harmonics emerge. For convenience the moduli are often determined by the coefficients of the first harmonic, G1 and G ′′ 1 (see Eqn. 1). These measures of the viscoelastic moduli are arbitrary and often fail to capture the rich nonlinearities that appear in the raw data signal [8]. An example of such rich behavior is shown in the large amplitude oscillatory shear (LAOS) results from a wormlike micelle solution in Fig. 1. The periodic stress response σ(t;ω, γ0) at steady state is plotted against either γ(t) or γ̇(t), the simultaneous phase-shifted inputs. These parametric plots are commonly called Lissajous curves (or more accurately, BowditchLissajous curves [21]). In this parameter space, a linear viscoelastic response appears as an ellipse which is progressively distorted by material nonlinearity. We refer to the σ(t) vs. γ(t) curves (Fig. 1a) as elastic Lissajous curves to distinguish them from the viscous Lissajous curves (Fig. 1b) which plot σ(t) as a function of the shear-rate γ̇(t). The most common method of quantifying LAOS tests is Fourier transform (FT) rheology [9]. For a sinusoidal strain input γ(t) = γ0 sinωt, the stress response can be represented as

Subfields: Cell Biology, Fluid Flow and Transfer Processes, Pulmonary and Respiratory Medicine

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Citations in the corpus

On secondary loops in LAOS via self-intersection of Lissajous–Bowditch curves (2010, methodology): “The MITlaos software is used to determine the Fourier coefficients, Chebyshev coefficients, elastic/viscous stress decomposition, and the corresponding viscoelastic moduli.”
Mapping thixo-elasto-visco-plastic behavior (2017, background): “Adapted from Ewoldt et al. (2007) and Ewoldt (2014) which describe the materials in more detail space of this material property map, lines of constant viscoelastic relaxation time τve = η/G thus correspond to 45◦ lines with equation pS ≡ log10(τve) = pV − pM .”