Linking the rheology of thermal amorphous materials to molecular-scale physics

Amorphous materials transition from solid-like to liquid-like behaviour (yield) under large stresses. Their constituent elements are caged in metastable configurations due to their neighbours. Microscale interactions between these elements lead to a large energy barrier to break the cages and trigger a plastic rearrangement. Thermal fluctuations can alter the yielding point as the elements hop to new configurations in anticipation. This work bridges the gap between molecular-scale physics and bulk rheology in thermal amorphous materials by connecting a classical density functional theory to a thermally activated elastoplastic model (EPM). We use a model system of solvent-free polymer-grafted nanoparticles which show rheological characteristics similar to those of soft glassy materials. We formulate the evolution of the free energy in a deforming array of polymer-grafted nanoparticles to obtain the energy landscape as an input to our EPM. We examine how the apparent yield stress depends on the shape of the energy landscape, thermal fluctuations and the rate of deformation. Our general scaling analyses reveal different regimes of structural relaxation governed by the applied shear rate and the inherent time scale for thermal hops. The complex interplay between mechanical loading and thermal fluctuations is further characterized by performing a variety of shear tests with different deformation history. The proposed framework provides an understanding of the yielding transition by integrating across a vast range of length and time scales.