Modelling charge and exciton transport in polymeric and molecular systems

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

Exciton dynamics in phthalocyanine molecular crystals

The exciton transport properties of an octa(butyl)-substituted metal-free phthalocyanine (H2-OBPc) molecular crystal have been explored by means of a combined computational (molecular dynamics and electronic structure calculations) and theoretical (model Hamiltonian) approximation. The excitonic couplings in phthalocyanines, where multiple quasi-degenerate excited states are present in the isolated chromophore, are computed with a multistate diabatization scheme which is able to capture both short- and long-range excitonic coupling effects. Thermal motions in phthalocyanine molecular crystals at room temperature cause substantial fluctuation of the excitonic couplings between neighboring molecules (dynamic disorder). The average values of the excitonic couplings are found to be not much smaller than the reorganization energy for the excitation energy transfer, and the commonly assumed incoherent regime for this class of materials cannot be invoked. A simple but realistic model Hamiltonian is proposed to study the exciton dynamics in phthalocyanine molecular crystals or aggregates beyond the incoherent regime

A very general rate expression for charge hopping in semiconducting polymers

We propose an expression of the hopping rate between localized states in semiconducting disordered polymers that contains the most used rates in the literature as special cases. We stress that these rates cannot be obtained directly from electron transfer rate theories as it is not possible to define diabatic localized states if the localization is caused by disorder, as in most polymers, rather than nuclear polarization effects. After defining the separate classes of accepting and inducing nuclear modes in the system, we obtain a general expression of the hopping rate. We show that, under the appropriate limits, this expression reduces to (i) single-phonon rate expression or (ii) the Miller-Abrahams rate or (iii) a multi-phonon expression. The description of these limits from a more general expression is useful to interpolate between them, to validate the assumptions of each limiting case, and to define the simplest rate expression that still captures the main features of the charge transport. When the rate expression is fed with a range of realistic parameters the deviation from the Miller-Abrahams rate is large or extremely large, especially for hopping toward lower energy states, due to the energy gap law

How many parameters actually affect the mobility of conjugated polymers?

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)] that the mobility in a broad range of (polymeric) semiconductors follows a universal behavior, insensitive to the chemical detail

Theory of charge hopping along a disordered polymer chain

We built a model of charge transport in a single disordered polymer chain starting from a model Hamiltonian of the system. The parameters entering the Hamiltonian determine both the density of states (DOS) and the hopping rate unlike the most common modelling strategies of transport in polymeric materials that parametrize both the DOS and the hopping rate from the outset. This model incorporates the effect of variable delocalization of one-electron states and is designed to link atomistic calculations of polymeric systems with full device models in multiscale modelling protocols. The initial and final states for the hopping process are determined by static disorder and further stabilized by polaronic effects. The coupling between these states is due to the residual (and much smaller) dynamic disorder. We find that, at lower static disorder, long-distance hopping events become more frequent, i.e. the hopping range and disorder are not unrelated parameters, as commonly assumed. The availability of low energy relatively delocalized states promotes long range displacement of charge and it can be at the origin of the high mobility observed in some polymers. The description of the hopping rates from the model Hamiltonian also allows the identification of the breakdown of the incoherent transport limit

Unexpectedly Large Couplings Between Orthogonal Units in Anthraquinone Polymers

Directly linked polyanthraquinones have relatively large electronic couplings between charge-localized states despite near-orthogonality of the monomer units. By using density functional theory (DFT) and ab initio molecular dynamics (AIMD) simulations, we investigate this unusual coupling mechanism and show that this is due to strong lone pair-pi interactions, which are maximized around orthogonal conformations. We find that such materials are largely resilient to dynamic disorder and are promising for organic electronics applications