Transient, nonlinear rheology and apparent yield stress of nanoparticle-organic hybrid materials

Nanoparticle-organic hybrid materials (NOHMs) consist of hard inorganic nanocores densely grafted with polymer chains. Even in the absence of solvents, NOHMs can exhibit fluid behavior since the grafted polymers fill the interstitial space between the cores like an incompressible fluid. Experiments indicate that NOHMs show rheological characteristics similar to soft glassy materials [P. Agarwal, H. Qi, and L.A. Archer, Nano Lett. 10, 111 (2010)]. We use the soft glassy rheology (SGR) model to predict the NOHMs rheology with and without solvent. Within this framework, we model NOHMs as mesoscopic elements trapped in cages formed by their neighbors. Using a density functional theory, we obtain the associated energy barrier as an input parameter to the SGR model as a function of the nanocores, polymers, and solvent properties. Mechanical loading reduces the energy barrier thus facilitating hops out of the trap by thermal fluctuations. Due to thermal and mechanical relaxations, NOHMs show Newtonian behavior over very long time scales. However, over a broader range of time scales of usual rheological characterization (or more importantly processing flow times), they act like yield stress materials. We examine how the apparent yield stress depends on the method of characterization such as startup shear or strain sweep oscillatory flow and on the time scale (shear rate, frequency) of the rheological probe.