Comparative theoretical study of the doping of conjugated polymers: Polarons in polyacetylene and polyparaphenylene

Defect-state calculations on all-trans polyacetylene and polyparaphenylene have been performed in the framework of the adiabatic Hückel Hamiltonian with $\sigma$-bond compressibility. In polyacetylene, the study of the energetics of the separation of the radical (neutral defect) -ion (charged defect) pair induced upon doping indicates that the two defects tend to remain in close proximity, resulting in the formation of a polaron. The binding energy of the polaron is estimated to be about 0.05 eV with this model. Absorption spectra at low doping levels are shown to be compatible with polaron formation, thus demonstrating the nonuniqueness of the previously proposed soliton model in explaining these absorption data. At higher doping levels, interaction between polarons leads to the formation of charged solitons carrying no spin. In polyparaphenylene, defects are always correlated in pairs due to the absence of a degenerate ground state. At low doping, polarons with a binding energy estimated at 0.03 eV are formed on ionization of polyparaphenylene. The related deformation of the lattice is relatively sof, in agreement with crystallographic data on biphenyl anions, and extends over about five rings. Increasing the doping level leads to the formation of bipolarons (doubly charged defects) that require a stronger deformation of the lattice and carry no spin. The possibility of a conduction mechanism in polyparaphenylene involving motion of bipolarons is consistent with magnetic data indicative of very low Pauli susceptibility in the metallic regime of Sb${\mathrm{F}}_5$-doped polyparaphenylene.