Understanding Bipolarons in Conjugated Polymers Using a Multiparticle Holstein Approach

Abstract

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.

Structural and Dynamic Disorder, Not Ionic Trapping, Controls Charge Transport in Highly Doped Conducting Polymers

“…The occurrence of a Coulomb gap at the Fermi level has been reported in recent kinetic Monte Carlo simulations, , which, hinging on the assumption of charges localized on molecular units, could not grasp the effect of electron–electron interactions in limiting the size of carriers wave packets. In contrast, very recent work by Qarai et al suggests that hole–hole repulsion may itself drive delocalization by screening the trapping potential of the dopant ions . These findings suggest that the overall effect of hole–hole interactions is nontrivial and may under some conditions be beneficial to charge transport.…”

“…In contrast, very recent work by Qarai et al suggests that hole–hole repulsion may itself drive delocalization by screening the trapping potential of the dopant ions. 53 These findings suggest that the overall effect of hole–hole interactions is nontrivial and may under some conditions be beneficial to charge transport.…”

Lewis acid–base pair doping of p-type organic semiconductors

“…32 In a two-polaron model, P1 can redshift further, matching electrochemical doping experiments, 40 but without hole-hole repulsions, bipolarons can localize and blueshift P1. 41 At 1 eq. BCF : BPO doping, the P3HT peak was completely bleached.…”

Quantifying Polaron Mole Fractions and Interpreting Spectral Changes in Molecularly Doped Conjugated Polymers

“…[9] For the remainder of this article, we define the doping efficiency as the mole fraction of SP sites that are fully ionized regardless of whether they are "free," and it will be referred to as the polaron mole fraction (Θ). [22,23] Recent studies demonstrate that a larger driving force for doping (ΔE) generally results in higher free charge carrier formation, [3,9,10] but it is difficult to determine a direct functional relationship because the available dopants and SPs are highly variable in size, solubility, and molecular structure, making a systematic comparison from published values practically impossible.…”