Transport of Quasilocalized Excitons in Molecular Crystals

Abstract

A model is presented for electron–phonon coupling in molecular crystals and its effect on transport of excitons and charge carriers in aromatic hydrocarbon crystals. The model differs from the usual ones in that the coupling is taken quadratic instead of linear in the vibrational coordinates. It is shown that this coupling dominates in aromatic hydrocarbons, leading to large frequency shifts in out‐of‐plane molecular vibrations on electronic excitation or ionization. The present study is limited to weak intermolecular electronic coupling, implying quasilocalized excitons (or electrons). There are then two limiting modes of diffusion, governed by the rate either of exciton transfer between molecules or of phonon transfer. In either limit, at high temperatures, transport occurs by incoherent jumps between adjacent molecules (hopping) and increases or decreases gently with temperature, while at low temperatures, coherent transport decreasing rapidly with increasing temperature occurs. The diffusion coefficient is larger for normal than for deuterated aromatic hydrocarbons except for hopping transport in the slow‐exciton limit. The observed temperature dependence and deuterium effect of triplet exciton diffusion in the $\mathrm{c\prime }$ direction of anthracene are reproduced by the model in this case. The transition from hopping to coherent diffusion is not readily observable for anthracene, but may be observable for naphthalene or benzene. Preliminary results indicate that the model also accounts satisfactorily for the magnitude and temperature dependence of charge‐carrier mobilities in anthracene.