Modeling mechanophore activation within a crosslinked glassy matrix

Mechanically induced reactivity is a promising means for designing self-reporting materials. Mechanically sensitive chemical groups called mechanophores are covalently linked into polymers in order to trigger specific chemical reactions upon mechanical loading. These mechanophores can be linked either within the backbone or as crosslinks between backbone segments. Mechanophore response is sensitive to both the matrix properties and placement within the matrix, providing two avenues for material design. A model framework is developed to describe reactivity of mechanophores located as crosslinks in a glassy polymer matrix. Simulations are conducted at the molecular and macromolecular scales in order to develop macroscale constitutive relations. The model is developed specifically for the case of spiropyran (SP) in lightly crosslinked polymethylmethacrylate (PMMA). This optically trackable mechanophore (fluorescent when activated) allows the model to be assessed in terms of observed experimental behavior. The force modified potential energy surface (FMPES) framework is used in conjunction with ab initio steered molecular dynamics (MD) simulations of SP to determine the mechanophore kinetics. MD simulations of the crosslinked PMMA structure under shear deformation are used to determine the relationship between macroscale stress and local force on the crosslinks. A continuum model implemented in a finite element framework synthesizes these mechanochemical relations with the mechanical behavior. The continuum model with parameters taken directly from the FMPES and MD analyses under predicts stress-driven activation relative to experimental data. The continuum model, with the physically motivated modification of force fluctuations, provides an accurate prediction for monotonic loading across three decades of strain rate and creep loading, suggesting that the fundamental physics are captured.