Multi-Charge Complexes and Spin Pairing in Electrochemically Doped Conjugated Polymers

Several novel devices rely on electrochemical doping pi-conjugated polymers (CP’s), with applications spanning energy conversion, energy storage, bioelectronics, and neuromorphic computing, to name a few. The process involves introducing electronic charges in the polymer, which then draw ions with an opposite charge from an electrolyte contact solution into the polymer to maintain charge neutrality. For many of these devices, high doping levels and excellent transport of the injected charges within the polymer is desirable for improved performance. As the polymer is doped, the spin density initially increases with charge carrier density before plateauing and even moderately dropping as more electronic charges are injected. This suggests a transition from polarons, singly charged carriers with a spin, to bipolarons, which are spinless doubly charged carriers, or other multi-charge carriers with reduced spin being formed as a result of spin pairing. The formation of multi-charge carriers is often associated with a deterioration of charge transport. As such, a better understanding of spin pairing in electrochemically doped polymers can provide an avenue to further improve performance and even open up new applications requiring high-spin concentrations. We use first-principles calculations on p-type P3HT and n-type P(NDI2O-T2) polymers based on density functional theory (DFT) and time-dependent density functional theory (TD-DFT) to examine spin pairing in doped CP’s. We perform calculations on charged single oligomer chains in all possible spin configurations for a given number of excess charges, in the presence of counterions. In the simple case of two excess charges, we find that when the two charges are forced to be sufficiently close to one another as dictated by the counterions positions, short-range exchange interactions can lead to a singlet-triplet gap inversion, making the bipolaron state (singlet) more stable than the two-polaron state (triplet). We subsequently consider charge complexes containing more charges, up to six holes or electrons, to simulate higher doping levels. We observe that spin pairing occurs more readily as the number of charges in the complex increases; the low multiplicity spin states become energetically favorable at larger inter-counterion distances, with more negative energy gaps relative to the highest spin state. Our TD-DFT calculations of the optical absorption spectrum of the doped oligomer chains show charged features at various doping levels that are in good agreement with experiment.