Atomistic framework for glassy polymer viscoelasticity across twenty frequency decades

Glassy polymers are central to engineering applications, yet their viscoelastic response over broad frequency and temperature ranges remains difficult to characterize. We extend non-affine deformation theory by incorporating a time-dependent memory kernel within the generalized Langevin equation for atomistic non-affine motions, yielding frequency-dependent mechanical response. Applied to poly(methyl methacrylate), the method captures the shear modulus and relaxation spectrum over more than twenty decades of frequency, from hundreds of terahertz to the millihertz regime, thus bridging polymer mechanics from ordinary to extreme scales. Our predictions show quantitative consistency with independent estimates from oscillatory-shear molecular dynamics, Brillouin scattering, ultrasonic spectroscopy, split-Hopkinson testing, and dynamic mechanical analysis, thereby demonstrating a unified theoretical-computational route for multiscale characterization of polymer glasses.