Length dependence of the electronic transparence (conductance) of a molecular wire

The electronic transparence of a single molecular wire connecting the two electrodes of a metal-insulating-metal nanojunction decreases exponentially with its length. The transparence attenuation can be quite small depending of the homo-lumo gap of the molecule and of electronic interaction of the wire ends with the electrodes. For a 10 nm long polyene connecting two nano-electrodes, a 100 mV bias voltage will lead to a tunnelling current intensity in the 10 pA range.