This manuscript explores the connection
between the fast relaxation
processes in an undeformed polymer glass and essential trends in the
mechanical toughness, a nonlinear mechanical property that is of practical
interest for engineering polymers with high impact strength. We quantify
the time scale of the molecular relaxations in the subnanosecond regime
for a quiescent polycarbonate glass using inelastic and quasi-elastic
neutron scattering and then correlate these processes with the macroscopic
brittle-to-ductile transition (BDT), which demarcates a change in
the dominant mechanism of failure and a marked increase in the material
toughness. We show that the macroscopic phenomenon of the BDT corresponds
to a change in the dominant dynamical process at the nanoscale. The
brittle regime is characterized by collective vibrational modes (the
so-called Boson peak) with a characteristic time scale τ ≈
0.5–0.8 ps, while slower collective relaxations with τ
≈ 3 ps become dominant above the BDT. We further establish
that the onset of ductility coincides with the appearance of anharmonicity
in the mean-square atomic displacement ⟨u
2⟩ on a picosecond time
scale, emphasizing that fast anharmonic molecular motions are important
for energy dissipation. This builds upon our previous report correlating
toughness with the amplitude of these anharmonic fluctuations across
a wide range of polycarbonate glasses. Brillouin light scattering
measurements are used to characterize the bulk and shear moduli of
the material, revealing a concomitant upturn in Poisson’s ratio
in the region of the BDT, a phenomenon that has been reported in metallic
and oxide glasses. The ratio of transverse acoustic mode velocity
and the Boson peak frequency is used to estimate the length scale
for these processes, indicating that the dynamic heterogeneities are
collective across 100–1000s of atoms. These length scales are
strikingly similar to the activation volume of yield derived from
mechanical measurements, suggesting that these fast and collective
relaxation processes may be related to the mechanisms of yield.