  We study the viscoelastic response of amorphous polymers using theory and
simulations. By accounting for internal stresses and considering instantaneous
normal modes (INMs) within athermal non-affine theory, we make parameter-free
predictions of the dynamic viscoelastic moduli obtained in coarse-grained
simulations of polymer glasses at non-zero temperatures. The theoretical
results show very good correspondence with rheology data collected from
molecular dynamics simulations over five orders of magnitude in frequency, with
some instabilities that accumulate in the low-frequency part on approach to the
glass transition. These results provide evidence that the mechanical glass
transition itself is continuous and thus represents a crossover rather than a
true phase transition. The relatively sharp drop of the low-frequency storage
modulus across the glass transition temperature can be explained
mechanistically within the proposed theory: the proliferation of
low-eigenfrequency vibrational excitations (boson peak and nearly-zero energy
excitations) is directly responsible for the rapid growth of a negative
non-affine contribution to the storage modulus.
