|Abstract:||Viscoelastic materials, such as crosslinked networks of synthetic and biological polymers, exhibit a nonlinear rheological response to mechanical deformation. Oscillatory shear is a popular deformation protocol for viscoelastic characterization, both linear and nonlinear, the latter referred to as large amplitude oscillatory shear (LAOS). However, the accompanying nonlinear material response in LAOS is challenging to interpret and requires non-trivial material descriptions. The goal of this thesis is to provide a new paradigm of nonlinear rheological characterization using oscillatory shear deformation as well as to demonstrate applications of nonlinear viscoelastic materials, involving stimuli responsive polymer-colloid composites.
A nonlinear viscoelastic response in LAOS is high dimensional, covering the entire range of the 2D Pipkin space of deformation amplitude and frequency. A low-dimensional language and framework is introduced for viscoelastic characterization using asymptotic material functions in oscillatory shear, referred to as medium amplitude oscillatory shear (MAOS). These material functions, four in number, emerge from an asymptotic expansion in deformation amplitude and depend only on the oscillatory frequency. They carry physically meaningful inter- and intra-cycle information, for example, softening/stiffening and thickening/thinning of the stress response. For the first time, experimental measurements are shown for all four asymptotic nonlinearities.
Parallel disk measurements in the MAOS regime require a correction for the apparent stress response. In this regime, the derivatives appearing in the general stress correction are constant over the range of interest, and this allows exact single-point corrections for all four asymptotic nonlinearities. Experimental measurements are presented for the asymptotically-nonlinear signals on an entangled polymer melt, using both parallel disk and cone fixtures. The corrected (amplified) parallel disk signals match the measurements with the cone.
Using a fourth order fluid expansion, universal frequency scaling and interrelations are derived for asymptotic nonlinearities in the terminal regime, defined by the limit of De<<1. Experimental measurements, consistent with such predictions, are presented for an entangled polymer melt in the terminal regime. Beyond the terminal regime, at higher frequencies, signs and magnitudes cannot be universally predicted, leaving these as free parameters that depend on the specifics of the material microstructure or constitutive model.
A library of expectations of signatures (or fingerprints) is developed for all four asymptotically-nonlinear material functions for seven nonlinear constitutive models. The fingerprints are different in magnitude, frequency-scaling, curve shapes and sign changes, and distinguish the models. They obey the terminal regime inter-relations and frequency scaling, and are driven by strain-rates at small De and strains at large De. Some constitutive models exhibit multiple sign changes at intermediate De and there may be no universal behavior of asymptotically-nonlinear fingerprints in this regime. Therefore, frequency-dependent signatures can be material-specific.
Frequency-dependent asymptotically-nonlinear fingerprints are presented for a strain stiffening transiently-crosslinked polymeric hydrogel of aqueous polyvinyl alcohol (PVA) cross-linked by sodium tetraborate (borax). A transient network model with strain-stiffening elements is developed, and this predicts the asymptotically-nonlinear signatures of the PVA-Borax system that no other model predicts. The quantitative agreement provides fit parameters that are related to molecular features and network architecture. In conclusion, asymptotically-nonlinear descriptions enable structure-rheology insight, constitutive model development, and model selection for soft materials.
As examples of nonlinear viscoelastic materials, polymer/colloid composites are developed with field responsive nonlinear elastic mechanical properties. A large mesh semi-flexible network of bovine fibrin is nonlinear elastic and stiffening, and serves as the scaffold. Methods are described to fabricate fibrin-colloid composites that preserve network integrity and nonlinear stiffening properties. The strain-stiffening fibrin network is combined with stimuli-responsive colloids that respond to temperature and magnetic field, resulting in field-controllable elastic stiffening of the network.