Time-Scale Bridging in Atomistic Simulations of Epoxy Polymer Mechanics Using Nonaffine Deformation Theory

Developing a deep understanding of macroscopic mechanical properties of amorphous systems, which lack structural periodicity, has posed a key challenge, not only at the level of theory but also in molecular simulations. Despite significant advancements in computational resources, there is a vast time scale disparity, more than 6 orders of magnitude, between mechanical properties probed in simulations compared to experiments. Using the theoretical framework of nonaffine lattice dynamics (NALD), based on the instantaneous normal modes analysis determined through the dynamical matrix of the system, we study the viscoelastic response of a cross-linked epoxy system of diglycidyl ether of bisphenol A (DGEBA) and poly(oxypropylene) diamine, over many orders of magnitude in deformation frequency, below the glass transition temperature. Predictions of the elastic modulus are satisfactorily validated against the nonequilibrium molecular dynamics simulations in the high-frequency regime and against experimental data from dynamic mechanical analysis at frequencies ∼1 Hz, hence successfully bridging the time scale gap. The comparison shows that nonaffine displacements at the atomic level account for nearly 2 orders of magnitude reduction in the low-frequency elastic modulus of the polymer glass, compared to affine elasticity estimates. The analysis also reveals the role of internal stresses (as reflected in the instantaneous normal modes), which act to strengthen the mechanical response.