How Many Parameters Actually Affect the Mobility of Conjugated Polymers?

Abstract

We describe charge transport along a polymer chain with a generic theoretical model depending in principle on tens of parameters, reflecting the chemistry of the material. The charge carrier states are obtained from a model Hamiltonian that incorporates different types of disorder and electronic structure (e.g., the difference between homo- and copolymer). The hopping rate between these states is described with a general rate expression, which contains the rates most used in the literature as special cases. We demonstrate that the steady state charge mobility in the limit of low charge density and low field ultimately depends on only two parameters: an effective structural disorder and an effective electron-phonon coupling, weighted by the size of the monomer. The results support the experimental observation [N. I. Craciun, J. Wildeman, and P. W. M. Blom, Phys. Rev. Lett. 100, 056601 (2008)PRLTAO0031-900710.1103/PhysRevLett.100.056601] that the mobility in a broad range of (polymeric) semiconductors follows a universal behavior, insensitive to the chemical detail.