Understanding Bipolarons in Conjugated Polymers Using a Multiparticle Holstein Approach

A Holstein-based model for mid-IR polaron absorption in π-conjugated polymers with nondegenerate ground states is expanded to include singlet bipolarons. In addition to hole hopping, the model includes electron–vibration coupling involving the prominent aromatic-quinoidal mode, as well as Coulombic interactions between (hole) polarons and between polarons and dopant anions. Compared to single polarons, the mid-IR band for bipolarons is red-shifted by up to 0.2 eV depending on the level of disorder. The red shift reflects the enhanced hole delocalization in the bound bipolaron complex and is in good agreement with recent measurements on electrochemically doped P3HT.