Maximum propagation speed and Cherenkov effect in optical phonon transport through periodic molecular chains

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 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-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 the lifetimes of the optical phonons. It is also consistent with the recent experimental investigations of ballistic optical phonon transport in oligomers with the minor exception of relatively short oligophenylenes.