Thermal conductance through molecular wires

Abstract

We consider phononic heat transport through molecular chains connecting two thermal reservoirs. For relatively short molecules at normal temperatures 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 3-dimensions. A Landauer-type expression for the heat conduction is obtained, in agreement with other recent studies. We use this formalism to study the heat conduction properties of alkanes. For relatively short (1-30 carbon atoms) chains the length and temperature dependence of the molecular heat conduction result 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 temperatures. For example, the heat conduction increases with molecular length for short molecular chains at low temperatures. Similar considerations apply for isotopically substituted disordered chains. 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.