Modelling charge and exciton transport in polymeric and molecular systems

Abstract

In this thesis some fundamental aspects of charge transport and exciton dynamics in organic semiconductors are explored from a theoretical and computational point of view. After a brief review of the field of organic electronics, the theoretical methods most commonly used to describe exciton dynamics and charge transport are summarised, with an emphasis on the specific methods employed in this thesis (chapter 1). A very general kinetic rate of hopping between electronic states in the incoherent regime is then derived (chapter 2). This rate contains the most commonly used rates (Miller-Abrahams, Marcus, Marcus-Levich-Jortner) as special cases. The excitonic couplings between molecules determine the properties of excited states in biological and artificial molecular aggregates. A large number of excitonic couplings in these systems are computed (chapters 3 and 4) including both the Coulombic and the short-range (non-Coulombic) contributions as well as the thermal fluctuation of the coupling (dynamic disorder). The effect of thermal fluctuations in crystalline materials is found to be important when evaluating exciton dynamics (chapter 3). The short-range component of the coupling needs to be included when the interacting molecules are in close contact (chapter 3). The characteristics of charge transport in disordered polymers depend in principle on many parameters. With the aim of accounting for the complicated nature of these materials, a very general charge transport model is presented here (chapter 5). A detailed electronic structure with variable localization of the electronic states is obtained from a simple model Hamiltonian depending on just a few parameters. Using the hopping rate derived in chapter 2, the charge mobility along disordered polymer chains is computed. The proposed model includes features of both variable range hopping (VRH) and mobility edge (ME) models, but it starts from fewer assumptions. Donor-acceptor copolymers have a narrower transport band which in principle should result in lower mobility. Instead, the narrower band is found to enhance mobility if the other parameters are kept constant. By exploring the large parameter space of this model, the temperature dependence of mobility is found to follow a universal Arrhenius behaviour in agreement with experimental data (chapter 6). The activation energy for transport depends only on the effective electronic disorder of the polymer chain. When the 3D structure of the polymer chains and the role of inter-chain hopping are also considered (chapter 7), the mobility is found to be linearly dependent on the persistence length. The activation energy is found to depend only on the electronic disorder and not on chain rigidity