Exciton localization in polymers with static disorder

Using configuration interaction-singles calculations of realistic models of conjugated polymers and by employing a mapping onto the single-particle Anderson model, we investigate the role of thermally induced static disorder on the properties of excitons in conjugated polymers. We use poly(para-phenylene) as a model system, where the off-diagonal disorder arises from fluctuations in the torsional angles and the diagonal disorder arises from fluctuations in the local relative permittivity. We make the following observations and conclusions: (1) disorder localizes excitons. The exciton localization length defines the exciton conjugation length. (2) Excitons are randomly spatially localized along the chain, with the localization length generally increasing as the excitation energy increases (up to the band center). These define localization or conjugation segments. Generally, the conjugation segments overlap and are not spatially distinct. (3) Triplet excitons are more localized than singlet excitons, because of their smaller band widths. (4) The standard deviation of the Gaussian random disorder, $\ensuremath{\sigma}$, satisfies $\ensuremath{\sigma}\ensuremath{\sim}\sqrt{T}$, where $T$ is the temperature. (5) Mapping onto the Anderson model indicates that the conjugation length, $⟨\ensuremath{\ell}⟩$, scales as $⟨\ensuremath{\ell}⟩\ensuremath{\sim}{\ensuremath{\sigma}}^{\ensuremath{-}2/3}$ at the edges of the band and $⟨\ensuremath{\ell}⟩\ensuremath{\sim}{\ensuremath{\sigma}}^{\ensuremath{-}3/2}$ at the center of the band. (6) The correlation length of the torsion angles in poly(para-phenylene) scales as ${\ensuremath{\sigma}}^{\ensuremath{-}2}$. Thus, there is no direct quantitative correlation between exciton conjugation lengths and conformational disorder. (7) The absorption inhomogeneous line width scales approximately as $\sqrt{T}$. (8) For realistic values of disorder in poly(para-phenylene) $⟨\ensuremath{\ell}⟩\ensuremath{\sim}8$ repeat units for the lowest excited singlet and increases to $\ensuremath{\sim}20$ repeat units at the absorption maximum. The absorption line width is $\ensuremath{\sim}0.5\text{ }\text{eV}$. We use these results to draw further conclusions about electronic processes in conjugated polymers.