Escape rate of a charge carrier from a semiconducting polymer chain

Charge carriers in amorphous semiconducting polymers diffuse rapidly along the polymer chains, hopping less frequently to neighboring chains. The escape time required on average to hop to a neighboring chain affects the design of new polymers and determines the relative importance of other system parameters such as polymer rigidity or polymer molecular weight. We provide a general expression for the escape rate, which lends itself to a more simplified and transparent expression in the limit of vanishing reorganization energy. The escape rate appears to be more sensitive to disorder and temperature than the intra-chain transport. We show how the parameters required for the evaluation of this rate can be derived from a combination of classical and quantum chemical models already used to characterize semiconducting polymers, and we provide an illustration based on two realistic polymeric materials.