We investigate the electronic transmission properties of polymers whic
h consist of a dimerized backbone chain with randomly distributed side
chains of length 2m. The system is connected to perfect left-hand and
right-hand metallic leads, and the transmission spectrum is computed.
We find 2m - 2 high-transmission and 2 low-transmission peaks which r
eflect resonant extended states in the random system and the gap edges
of the dimerized backbone chain, respectively. The temperature depend
ence of the conductivity is shown to be very sensitive to the position
of the Fermi level. The tunnelling current at zero temperature in the
presence of a bias voltage gives a region of negative differential co
nductivity, which is due to a competition between the opening of a tra
nsmission window by the applied bias and the suppression of the transm
ission peaks by the electric field.