Charge Diffusion in Semiconducting Polymers: Analytical Relation between Polymer Rigidity and Time Scales for Intrachain and Interchain Hopping

We study the charge diffusion of semiconducting polymer bulk using simplified coarse grained models to investigate the relation between charge diffusion coefficient and the characteristics time of intrachain and interchain hopping, tau(1) and tau(2). We consider the process of charge diffusion in several standard models of polymer chains (rigid chain, Gaussian chain, worm-like chain), and we achieve an analytical expression for the diffusion coefficient in terms of the characteristic times and the geometric parameters defining the chain models. The diffusion depends only on the intrachain hopping for the rigid chain and on the geometric average of intrachain and interchain hopping times for the Gaussian chain (the least rigid model), with an analytical interpolation available between two limits. The model highlights the importance of large persistence lengths for improved transport properties. In all cases, it is incorrect to consider the slower interchain hopping as the rate-determining step for the charge transport.