Percolation, Tie-Molecules, and the Microstructural Determinants of Charge Transport in Semicrystalline Conjugated Polymers

Semiconducting polymers play an important role in a wide range of optical and electronic material applications. It is widely accepted that the polymer ordering impacts charge transport in such devices. However, the connection between molecular ordering and device performance is difficult to predict due to the current need for a mathematical theory of the physics that dictate charge transport in semiconducting polymers. We present an analytical and computational description of semicrystalline conjugated polymer materials that captures the impact of polymer conformation on charge transport in heterogeneous thin films. We first develop an analytical theory for the statistical behavior of a polymer chain emanating from a crystallite, predicting the average distance to the first kink that would trap a charge. This analysis is used to define the conditions where percolation would lead to efficient transport through a semicrystalline material. We then establish a model that predicts the multiscale charge transport. This model is used to identify the speed limits of charge transport at short and long time scales for varying fraction of crystallinity. This work provides a rational framework to connect molecular organization to device performance