Thermal conductance through molecular wires

We consider phononic heat transport through molecular chains connecting two thermal reservoirs. For relatively short molecules at normal temperatures we find, using classical stochastic simulations, that heat conduction is dominated by the harmonic part of the molecular force-field. We develop a general theory for the heat conduction through harmonic chains in three-dimensions. Our approach uses the standard formalism that leads to the generalized (quantum) Langevin equation for a system coupled to a harmonic heat bath, however the driving and relaxation terms are considered separately in a way that leads directly to the steady-state response and the heat current under nonequilibrium driving. A Landauer-type expression for the heat conduction is obtained, in agreement with other recent studies. We used this general formalism to study the heat conduction properties of alkane. We find that for relatively short (1-30 carbon molecules) the length and temperature dependence of the molecular heat conduction results from the balance of three factors: (i) The molecular frequency spectrum in relation to the frequency cutoff of the thermal reservoirs, (ii) the degree of localization of the molecular normal modes and (iii) the molecule-heat reservoirs coupling. The fact that molecular modes at different frequency regimes have different localization properties gives rise to intricate dependence of the heat conduction on molecular length at different temperature. For example, the heat conduction increases with molecular length for short molecular chains at low temperatures. Isotopically substituted disordered chains are also studied and their behavior can be traced to the above factors together with the increased mode localization in disordered chain and the increase in the density of low frequency modes associated with heavier mass substitution. Finally, we compare the heat conduction obtained from this microscopic calculation to that estimated by considering the molecule as a cylinder characterized by a macroscopic heat conduction typical to organic solids. We find that this classical model overestimates the heat conduction of single alkane molecules by about an order of magnitude at room temperature. Implications of the present study to the problem of heating in electrically conducting molecular junctions are pointed out.