Counterion Control and the Electronic Structure of Polarons and Bipolarons in Doped Conjugated Polymers

When an electron is removed from a conjugated polymer, such as poly(3-hexylthiophene-2,5-diyl) (P3HT), the remaining hole and associated changein the polymer backbone structure from aromatic to quinoidal are referred to as a polaron. Bipolarons are created by removing the unpaired electron from an already-oxidized polymer segment. In electrochemically-doped P3HT films, polarons and bipolarons are readily observed, but in chemically-doped P3HT films, bipolarons rarely form. We explain this observation by studying the effects of counterion position on the formation of polarons, strongly coupled polarons, and bipolarons using both spectroscopic and X-ray diffraction experiments and time-dependent density functional theory (TD-DFT) calculations. The counterion positions control whether two polarons spin-pair to form a bipolaron or whether they strongly couple without spin-pairing. When two counterions lie close to the same polymer segment, bipolarons can form, with an absorption spectrum that is blueshifted from that of a single polaron. Otherwise, polarons at high concentrations do not spin-pair, but instead J-couple, leading to a redshifted absorption spectrum. The counterion location needed for bipolaron formation is accompanied by a loss of polymer crystallinity, so that bipolarons can form only in disordered regions of conjugated polymer films. Our TD-DFT calculations of polarons and bipolarons predict absorption spectra that match well with experiment, providing strong evidence that TD-DFT is correctly capturing the electronic structure of the doped material. Several groups, however, who looked at the energies of the Kohn-Sham orbitals from (non-time-dependent) DFT calculations, have recently argued that the traditional band picture is incorrect for doped conjugated polymers. Instead, these non-time-dependent DFT calculations suggest that polaron creation causes only one unoccupied state to move into the band gap near the valence band edge while half-filled states in the conduction and valence bands bend downward in energy. To understand the discrepancy, we also performed an analysis using natural transitional orbitals (NTOs) that shows that our TD-DFT calculations indeed reproduce the traditional band picture of polarons and bipolarons. Taken together, our experimental and theoretical results argue that controlling the counterion location and using the properly level of theory is critical to understanding the electronic structure of polarons and bipolarons on doped conjugated polymers.