Excitons in disordered polymers

We investigate the effects of disorder on Frenkel excitons in disordered conjugated polymers. In these materials, the principal effect of the disorder is to modify the transfer integrals appearing in the exciton Hamiltonian by changing the angle of relative rotation between polymeric units in a random manner. It is assumed that the transfer integrals have the form t cos(ϕk−ϕk+1) where ϕk denotes the orientation angle of the kth unit. We focus on two types of angular disorders: segmental disorder, which is characterized by infrequent, large fluctuations in Δφ and a continuous disorder marked by small fluctuations in each Δφ. We calculate the density of states and inverse localization lengths for the exciton modes in long chains by mode-counting techniques and the absorption spectra in shorter chains by direct matrix diagonalization. Particular emphasis is placed on relating the features of absorption spectra to distribution and localization of the underlying exciton modes. Comparison is made with the spectra obtained by assuming that the disorder arises from random fluctuations in inter-unit bond length.