Polaron and bipolaron stability on paraphenylene polymers

Polyparaphenylene is the prototypical conjugated polymer containing phenyl rings and its properties are good references for a family of derived polymers. We investigate the structure, stability, and dynamics of polarons and bipolarons in polyparaphenylene chains under an applied electric field. To do this, we use a bidimensional SSH Hamiltonian model with the Hubbard extension, i.e., with local and nearest-neighbor Coulomb interaction, which has been designed to work with general hexagonal lattices, from which polyparaphenylene can be seen as a prominent case. Using the time-dependent Hartree-Fock approximation, we calculate the structural characteristics, the maximum field strength, supported before polarons and bipolarons gets unstable, and the maximum velocity achieved by these charge carriers. We obtained the polaron and bipolaron terminal velocity to be 0.51 Å/fs and 1.15 Å/fs, respectively. The maximum field strength determined by our calculations is 0.54 mV/Å and 0.80 mV/Å, respectively. Our results are in good agreement with other theoretical methods and experiments.