  Understanding phonon transport at a molecular scale is fundamental to the
development of high-performance thermoelectric materials for the conversion of
waste heat into electricity. We have studied phonon and electron transport in
alkane and oligoyne chains of various lengths and find that due to the more
rigid nature of the latter, the phonon thermal conductances of oligoynes are
counter intuitively lower than that of the corresponding alkanes. The thermal
conductance of oligoynes decreases monotonically with increasing length,
whereas the thermal conductance of alkanes initially increases with length and
then decreases. This difference in behaviour arises from phonon filtering by
the gold electrodes and disappears when higher-Debye-frequency electrodes are
used. Consequently a molecule that better transmits higher-frequency phonon
modes, combined with a low-Debye-frequency electrode that filters high-energy
phonons is a viable strategy for suppressing phonon transmission through the
molecular junctions. The low thermal conductance of oligoynes, combined with
their higher thermopower and higher electrical conductance lead to yield a
maximum thermoelectric figure of merit of ZT = 1.4, which is several orders of
magnitude higher than for alkanes.
