(257h) Linking Molecular-Level Information to the Rheology of Polymer-Grafted Nanoparticles

Amorphous materials can be categorized as athermal (e.g., foams and emulsions) and thermal (e.g., colloidal glasses and metallic glasses), depending on the size of their constituent elements. These materials deform elastically when subjected to small deformation but undergo yielding and begin to flow plastically under large deformation. In these materials, the constituent elements are in metastable configurations or cages due to the presence of their neighbors. Under deformation, the elements locally store elastic energy until a yielding point where they plastically rearrange as they break the cages. Despite extensive studies on athermal materials through elastoplastic models, the origin of the yielding transition and the effects of thermal fluctuations on this dynamical phase transition remain poorly understood. Depending on the energy landscape, the presence of thermal fluctuations alters the yielding point as the elements can hop to new configurations in anticipation. In this work, we obtain the molecular-level information by a classical density functional theory and connect it to the bulk response in thermal amorphous materials through a thermally activated elastoplastic system. To test our theoretical framework, we use a model system of polymer-grafted nanoparticles. We formulate the evolution of the free energy in a deforming periodic array of grafted nanoparticles with and without solvent. We show that the energy barrier to nanostructure relaxation arises from the configurational entropy of the grafted polymers, the entropy of the solvent molecules, and the enthalpic affinity between the grafted polymers and the solvent molecules. Then, we use this information as input for our thermally activated elastoplastic model, which predicts the rheological response of the material via a Fokker-Planck equation. We examine how the apparent yield stress depends on the material properties, such as core volume fraction, grafting density, molecular weight of the grafted polymers, and solvent volume fraction. Scaling analysis based on our thermally activated elastoplastic model reveals different regimes of structural relaxations governed by the applied rate of mechanical deformation and the inherent timescale for thermal hops. We calculate the timescale for thermal hops based on the molecular-level information and further characterize the complex interplay between mechanical loading and thermal fluctuations by performing a variety of shear tests in the presence of a history of deformation. The results, which are in agreement with our experiments, show a stress overshoot in start-up shear tests and a maximum in the loss modulus in strain-sweep oscillatory tests, both indicative of cage breakage in these materials.

This work is supported by National Science Foundation (CBET: Fluid Dynamics Award 2135617)