Viscoelastic dynamics of complex soft materials from mechanical testing to terahertz frequencies via atomistic modeling

Viscoelastic properties of the materials provide key insights into the structural and dynamical behavior of glasses. Elastic moduli such as Young's and the shear modulus characterize the response of the material, but their frequency and temperature dependence are challenging to determine across the wide spectral range accessible to experiments. We investigate a microscopic non-affine framework that exploits the mathematical description of atomic-scale displacements under deformation to overcome the intrinsic timescale limitations of atomistic molecular dynamics, thus enabling the computation of mechanical responses at experimental accessible frequencies that bridge the dynamic mechanical analysis to Brillouin scattering regimes. We study poly(methyl methacrylate)  polymer below the glass transition temperature by using atomistic molecular dynamics simulations to explore the characteristics of the underlying potential energy surface. From the atomistic configurations, we compute the vibrational density of states (vDOS) and affine force-field correlators, which are then used to evaluate the complex shear modulus. A time-dependent memory kernel is implemented to capture the primary and secondary relaxation decays of the shear modulus in the frequency domain, thus bridging the mechanical testing (Hz-kHz) to Brillouin (GHz), and THz regimes. We also show the temperature dependence of the shear modulus, which serves as an order parameter that distinguishes the liquid and glassy phases in both experiments and theory.