The potential of conjugated polymers to compete with inorganic materials in the field of semiconductor is conditional on fine-tuning of the charge carriers mobility. The latter is closely related to the material morphology, and various studies have shown that the bottleneck for charge transport is the connectivity between well-ordered crystallites, with a high degree of pi-pi stacking, dispersed into a disordered matrix. However, at this time there is a lack of theoretical descriptions accounting for this link between morphology and mobility, hindering the development of systematic material designs. Here we propose a computational model to predict charge carriers mobility in conducting polymer PEDOT depending on the physicochemical properties of the system. We start by calculating the morphology using molecular dynamics simulations. Based on the calculated morphology we perform quantum mechanical calculation of the transfer integrals between states in polymer chains and calculate corresponding hopping rates using the Miller-Abrahams formalism. We then construct a transport resistive network, calculate the mobility using a mean-field approach, and analyze the calculated mobility in terms of transfer integrals distributions and percolation thresholds. Our results provide theoretical support for the recent study [Noriega et al., Nat Mater 12, 1038 (2013)] explaining why the mobility in polymers rapidly increases as the chain length is increased and then saturates for sufficiently long chains. Our study also provides the answer to the long-standing question whether the enhancement of the crystallinity is the key to designing high-mobility polymers. We demonstrate, that it is the effective pi-pi stacking, not the long-range order that is essential for the material design for the enhanced electrical performance. This generic model can compare the mobility of a polymer thin film with different solvent contents, solvent additives, dopant species or polymer characteristics, providing a general framework to design new high mobility conjugated polymer materials.
Poly(3,4-ethylenedioxythiophene) (PEDOT) is a conducting polymer that is used in a wide range of applications such as electronics, optoelectronics, and bio-electronics, where the fundamental understanding of the charge transport, and in particular of the electrical conductivity sigma, is a prerequisite to develop new high performance devices. There are many reports in the literature where the conductivity of archetypical conducting polymer PEDOT doped with tosylate (PEDOT:TOS) exhibits a dry negative temperature coefficient, d sigma/dT < 0, which is strikingly different from the activated-type behavior with d sigma/dT > 0 commonly observed in most conducting polymers. This unusual temperature dependence was attributed to the transition from the photon-assisted hopping to the metallic behavior, which is however difficult to rationalize taking into account that this transition occurs at high temperatures. In order to understand the origin of this unusual behavior, multiscale mobility calculations in PEDOT:TOS for the model of hopping transport were performed, where changes in the morphology and the density of states (DOS) with the temperature were explicitly taken into account. The morphology was calculated using the Molecular Dynamics simulations, and the hopping rates between the chains were calculated quantum-mechanically following the Miller-Abrahams formalism. Our results reproduce the observed negative temperature coefficient, where however the percolation analysis shows that this behavior mainly arises because of the changes in morphology upon heating when the system becomes less ordered. This results in a less efficient pi-pi stacking and hence lower mobility in the system. We therefore conclude that experimentally observed negative mobility temperature coefficient in conducting polymers at high temperatures is consistent with the hopping transport, and does not necessarily reflect the transition to a metallic band-like transport. Based on our multiscale modeling, we introduce a simple Gaussian Disorder Model for the efficient mobility calculations, where the DOS broadening is a function of the temperature, and where the transfer integral distribution is a bimodal distribution evolving with temperature.