  Optical phonons serve as the fast and efficient carriers of energy across
periodic polymers due to their delocalization, large group velocity because of
covalent bonding and large energy quantum compared to that for acoustic
phonons, as it was observed in a number of recent measurements in different
oligomers. However, this transport is dramatically sensitive to anharmonic
interactions, including the unavoidable interaction with acoustic phonons
responsible for the transport decoherence, suppressing ballistic transport at
long distances. Here we show that this decoherence is substantially suppressed
if the group velocity of optical phonons is less than the sound velocity of
acoustic phonons; otherwise ballistic transport is substantially suppressed by
a Cherenkov's like emission of acoustic phonons. This conclusion is justified
considering energy and momentum conservation during phonon absorption or
emission and supported by the numerical evaluation of lifetimes of the optical
phonons. It is also consistent with the recent experimental investigations of
ballistic optical phonon transport in oligomers with minor exception of
relatively short oligophenylenes.
