Interaction of Torsional Oscillations with Polarons and Bipolarons in Conjugated Polymer

We propose a model for the electronic interaction associated with torsional and bond length vibrations in quasi one dimensional chains of conjugated polymers. The model admits conformational bond length objects like polarons and bipolarons and torsional modes of vibration. It is shown that the dynamics of these objects can be studied by numerically integrating the corresponding time-dependent equations of motion for the bond length, ring torsion angle and pi-electrons. An extension of the PPP and SSH models is numerically solved using the Time-Dependent Hartree-Fock approximation. An wide range of conducting polymers is simulated by varying the moment of inertia of the monomers (ranging from polypyrrole to poly(3-hexyl)thiophene). The stereometric interactions between chains are parametrically considered with different torsional potentials. The results show that polarons and bipolarons are trapped between the antinodes of torsional vibration modes with wave length larger than their width. This effect damps down their mobility. It is also found that torsional vibration modes with very long wave lengths or wave lengths shorter than the width of polarons and bipolarons produces almost no effect on their propagation.