Brownian dynamics simulations of charge mobility on conjugated polymers in solution.

A model is developed for the mobility of a charge carrier along a conjugated polymer dissolved in solution, as measured by time-resolved microwave conductivity. Each unit cell of the polymer is assigned a torsional degree of freedom, with Brownian dynamics used to include the effects of solvent on the torsions. The barrier to torsional motion is substantially enhanced in the vicinity of the charge, leading to self-trapping of the charge onto a planarized region of the polymer chain. Within the adiabatic approximation used here, motion arises when regions of the polymer on either side of the charge fluctuate into planarity and the wavefunction spreads in the corresponding direction. Well-converged estimates for the mobility are obtained for model parameters where the adiabatic approximation holds. For the parameters expected for conjugated polymers, where crossing between electronic surfaces may lead to breakdown in the adiabatic approximation, estimates for the mobility are obtained via extrapolation. Nonadiabatic contributions from hopping between electronic surfaces are therefore ignored. The resulting mobility is inversely proportional to the rotational diffusion time, trot, of a single unit cell about the polymer axis in the absence of intramolecular forces. For trot of 75 ps, the long-chain mobility of poly(para-phenylene vinylene) is estimated to be between 0.09 and 0.4 cm(2)∕Vs. This is in reasonable agreement with experimental values for the polymer, however, the nonadiabatic contribution to the mobility is not considered, nor are effects arising from stretching degrees of freedom or breaks in conjugation.