  The structure and vibrational density of states (VDOS) of polymer glasses are
investigated using numerical simulations based on the classical Kremer-Grest
bead-spring model. We focus on the roles of chain length and bending stiffness,
the latter being set by imposing three-body angular potentials along chain
backbones. Upon increasing the chain length and bending stiffness, structural
reorganisation leads to volumetric expansion of the material and build-up of
internal stresses. The VDOS has two dominant bands: a low frequency one
corresponding to inter- and intra-chain non-bonding interactions and a high
frequency one corresponding principally to vibrations of bonded beads that
constitute skeletal chain backbones. Upon increasing the steepness of the
angular potential, vibrational modes associated with chain bending gradually
move from the low-frequency to the high-frequency band. This redistribution of
modes is reflected in a reduction of the so-called Boson peak upon increasing
chain stiffness. Remarkably, the finer structure and the peaks of the
high-frequency band, and their variations with stiffness, can, for short
chains, be explained using an analytical solution derived for a model triatomic
molecule. For longer chains, the qualitative evolution of the VDOS with chain
stiffness is similar, although the distinct peaks observed for short chains
become increasingly smoothed-out. Our findings can be used to guide a
systematic approach to interpretation of Brillouin and Raman scattering spectra
of glassy polymers in future work, with applications in polymer processing
diagnostics.
