Charge mobility induced by Brownian fluctuations in π-conjugated polymers in solution

We study the motion of a doped charge in a π-conjugated polymer chain in solution subject to Brownian fluctuations. Specifically, we take poly(para-phenylene) to be our model system where the Brownian fluctuations cause rotational motion of the phenylene rings. The instantaneous torsional fluctuations cause Anderson localization of the charge wavefunction, with the lower-energy spectrum being composed of local ground states and the higher-energy spectrum being composed of quasi-extended states. At low temperatures, additional charge localization occurs via torsional relaxation. The dynamical torsional fluctuations lead to two distinct modes of motion of the charge: adiabatic and non-adiabatic. Adiabatic motion is a ‘crawling’ motion of the charge along the polymer chain while the charge remains in its local ground state. Non-adiabatic motion is a rapid ‘hopping’ motion as the charge is excited into higher energy quasi-extended states and travels ballistically along the chain before relaxing into a local ground state. The adiabatic motion dominates at low temperatures, and exhibits a linear temperature dependence and thus a constant zero-field charge mobility. Non-adiabatic motion begins to dominate as the temperature is increased, as the charge is thermally excited into higher energy states. At high temperatures the diffusion constant becomes almost temperature independent, indicating a decrease in the charge mobility with increasing temperature, which we attribute to the charge localization length being a decreasing function of temperature at high temperatures.