Theory of charge hopping along a disordered polymer chain

We built a model of charge transport in a single disordered polymer chain starting from a model Hamiltonian of the system. The parameters entering the Hamiltonian determine both the density of states (DOS) and the hopping rate unlike the most common modelling strategies of transport in polymeric materials that parametrize both the DOS and the hopping rate from the outset. This model incorporates the effect of variable delocalization of one-electron states and is designed to link atomistic calculations of polymeric systems with full device models in multiscale modelling protocols. The initial and final states for the hopping process are determined by static disorder and further stabilized by polaronic effects. The coupling between these states is due to the residual (and much smaller) dynamic disorder. We find that, at lower static disorder, long-distance hopping events become more frequent, i.e. the hopping range and disorder are not unrelated parameters, as commonly assumed. The availability of low energy relatively delocalized states promotes long range displacement of charge and it can be at the origin of the high mobility observed in some polymers. The description of the hopping rates from the model Hamiltonian also allows the identification of the breakdown of the incoherent transport limit.