A framework to link the rheology of thermal amorphous materials to molecular-scale physics

In amorphous materials, the constituent elements or particles are trapped in metastable configurations due to their neighbors. Under small stresses, these configurations deform elastically, but under large stresses, they rearrange plastically. In thermal amorphous materials, the energy barrier to rearrangement is only moderately larger than the thermal energy. Thus, under mechanical loading, yielding is aided by thermal effects. However, the physics of the yielding transition and the role of thermal fluctuations in this dynamical phase transition are not well understood. We propose a classical density functional theory to obtain molecular-level information concerning the many-body potential between a few polymer-grafted nanoparticles with random configurations and show how the free energy of the system changes from one configuration to another. Then, we introduce a thermally activated elastoplastic model that links the free energy landscape to the bulk rheology. We show how thermal fluctuations can alter the yielding point as the elements hop to new configurations in anticipation. Our theoretical results agree with experiments for a model system of polymer-grafted nanoparticles exhibiting rheological characteristics similar to those of soft glassy materials. By allowing for any functional form of the energy landscape, our framework is applicable to all thermal amorphous materials.