Mobility of Holes in Oligo- and Polyfluorenes of Defined Lengths

The high-frequency mobility of positive charges (holes) moving along the backbones of an extensive data set of 7 oligomers (<i>n</i> = 2–16) and 6 polymers (⟨<i>n</i>⟩ = 26–138) of fluorene was measured using pulse-radiolysis time-resolved microwave conductivity (PR-TRMC) in benzene. As expected, at 8.9 GHz, the measured isotropic ac mobility, μ_ac,meas^iso, was observed to be strongly dependent on the lengths of the chains due to the charges encountering chain ends during one microwave cycle. Values of the measured mobility, μ_ac,meas^iso, ranged from 5 × 10^–4 cm²/(V s) for an <i>n</i> = 2 repeat unit oligomer to 0.18 cm²/(V s) for a polymer with an average length of ⟨<i>n</i>⟩ = 86 repeat units. Global fits to the entire set of lengths extracted the chain-length-independent intramolecular mobility, μ_ac^intra, using the Kubo formula, assuming normal diffusion along the contour of the molecule with reflecting boundary conditions at the ends. The effects of chain conformation, chain defects, polymer length distributions, and a finite polaron length on μ_ac,meas^iso were considered quantitatively. The best fit to the whole data set, taking into account the polymer length distributions, suggests μ_ac^intra = 1.1 cm²/(V s). The fit was improved slightly by implementing randomly spaced barriers to transport along the chain with an average spacing of ∼40 repeat units, although at this spacing, the estimate of μ_ac^intra was not affected. These barriers could represent defects in the polymer or dihedral angles between repeat units, giving poor electronic coupling that persists for times greater than the 50 ps period of the microwaves. In this defect model, the best fit for their average spacing depended strongly on the chain conformation used, while the predicted intramolecular mobility did not. This estimate of the frequency of defects, a new aspect of this work, is less accurate because coiling of chains and defects have similar effects on the measured mobilities, and each can mask the effect of the other. The present data set also shows that there are few, if any, traps having depths substantially greater than thermal energy for holes on polyfluorene. The value of 1.1 cm²/(V s) is tightly constrained by the mobility of charges on the oligomers. Should the diffusion model break down for short chains and only be applicable to longer polymers, the intrachain mobility may be able to take both larger and smaller values (∼0.7–3 cm²/(V s)), although the data points to this being reasonably unlikely. It is shown that measurements of the imaginary part of the conductivity could be used in the future to clarify the mobility if this is the case