Absorption in regio-regular poly(3-hexyl)thiophene thin films: Fermi resonances, interband coupling and disorder

Abstract

Absorption in conjugated polymer aggregates is studied theoretically, taking into account excitonic (intermolecular) coupling, exciton–phonon (EP) coupling and site-energy disorder, all treated on equal footing within a generalized Holstein Hamiltonian with numerically generated eigenmodes and energies. The analysis deals primarily with the weak excitonic coupling regime, which for polymers, corresponds to J 0 ≲ 0.4 ω 0 where J 0 is the nearest neighbor excitonic coupling and ω 0 (≈1400 cm −1) is the frequency of the ring breathing/stretching mode coupled to the molecular electronic transition with Huang–Rhys factor, λ 2 ≈ 1. Disorder is characterized by a Gaussian distribution of molecular transition frequencies of width σ. Absorption spectra are calculated under the two-particle approximation (TPA) as well as the less accurate, but computationally more efficient single-particle approximation (SPA). Fermi resonances (FRs) arise due to the coupling between the optically allowed single-particle states (vibronic excitons) and the dark two-particle states. In the motional narrowing limit FRs are clearly resolved. Further increases in σ cause the FRs to merge into a single peak for each vibronic band. At this point the SPA becomes accurate for the entire spectrum. The SPA also provides the basis for simplified analytical expressions for the peak intensity ratios, from which the free exciton bandwidth, W, can be determined. Analytical expressions are also obtained for the peak-positions within the vibronic progression. Application to regio-regular poly(3-hexyl)thiophene films shows the exciton bandwidth, W, to be in the range 0.8 ω 0– ω 0. The model also accounts for the irregular peak spacings observed in experiment.