A general framework for consistent estimation of charge transport properties via random walks in random environments

A general framework is proposed for the study of the charge transport properties of materials via random walks in random environments (RWRE). The material of interest is modeled by a random environment, and the charge carrier is modeled by a random walker. The framework combines a model for the fast generation of random environments that realistically mimic materials morphology with an algorithm for efficient estimation of key properties of the resulting random walk. The model of the environment makes use of tools from spatial statistics and the theory of random geometric graphs. More precisely, the disordered medium is represented by a random spatial graph with directed edge weights, where the edge weights represent the transition rates of a Markov jump process (MJP) modeling the motion of the random walker. This MJP is a multiscale stochastic process. In the long term, it explores all vertices of the random graph model. In the short term, however, it becomes trapped in small subsets of the state space and makes many transitions in these small regions. This behavior makes efficient estimation of velocity by Monte Carlo simulations a challenging task. Therefore, we use aggregate Monte Carlo (AMC), introduced in [T. Brereton et al., Methodol. Comput. Appl. Probab., 16 (2014), pp. 465-484], for estimating the velocity of a random walker as it passes through a realization of the random environment. In this paper, we prove the strong consistency of the AMC velocity estimator and use this result to conduct a detailed case study, in which we describe the motion of holes in an amorphous mesophase of an organic semiconductor, dicyanovinyl-substituted oligothiophene (DCV4T). In particular, we analyze the effect of system size (i.e., number of molecules) on the velocity of single charge carriers

Backbone chemical composition and monomer sequence effects on phenylene polymer persistence lengths

Despite a vast body of the literature devoted to the use of phenylene polymers in the fabrication of graphene nanoribbons, the study of the physical properties of these precursors still poses open questions whose answers will certainly contribute to the design of more efficient/precise synthesis protocols. Particularly, persistence length measurements combined with size exclusion chromatography techniques assign both semiflexible to semirigid structures depending on the molecular weight of the precursor (Narita et al. Nat. Chem. 2014, 6, 126-132). Peculiarly, these results suggest an apparent structural change upon increasing the length of the polymers. To address this puzzle, we use single-chain models to study the stiffness of polyphenylene precursors in a theta-like solvent as a function of chain composition and monomer sequence. Steric effects are isolated by considering random walk chains with segment length distributions and the position of monomers determined by the nature of the arene substitution along the backbone. Moreover, two homopolymer limiting cases are defined, that is, meta and para sequences, by associating two types of monomers to each possible substitution pattern. We consider, within these two limiting cases, chains with different compositions and monomer sequences. We compute persistence lengths, mean square end-to-end distances, and gyration and hydrodynamic radii. We find that distinct values of the persistence length for apparently the same chain chemistry are the result of different mixing ratios and the arrangement along the chain of the two positional isomers of the same monomer. Finally, we discuss the relation between two-dimensional density of the number of crossings and the length of polyphenylene segments as they would occur upon strong chain adsorption onto a substrate

Charge transport in organic crystals : role of disorder and topological connectivity

We analyze the relationship among the molecular structure, morphology, percolation network, and charge carrier mobility in four organic crystals: rubrene, indolo[2,3-b]carbazole with CH3 side chains, and benzo[1,2-b:4,5-b']bis[b]benzothiophene derivatives with and without C4H9 side chains. Morphologies are generated using an all-atom force field, while charge dynamics is simulated within the framework of high-temperature nonadiabatic Marcus theory or using semiclassical dynamics. We conclude that, on the length scales reachable by molecular dynamics simulations, the charge transport in bulk molecular crystals is mostly limited by the dynamic disorder, while in self-assembled monolayers the static disorder, which is due to the slow motion of the side chains, enhances charge localization and influences the transport dynamics. We find that the presence of disorder can either reduce or increase charge carrier mobility, depending on the dimensionality of the charge percolation network. The advantages of charge transporting materials with two- or three-dimensional networks are clearly shown

Impact of mesoscale order on open-circuit voltage in organic solar cells

Structural order in organic solar cells is paramount: it reduces energetic disorder, boosts charge and exciton mobilities, and assists exciton splitting. Owing to spatial localization of electronic states, microscopic descriptions of photovoltaic processes tend to overlook the influence of structural features at the mesoscale. Long-range electrostatic interactions nevertheless probe this ordering, making local properties depend on the mesoscopic order. Using a technique developed to address spatially aperiodic excitations in thin films and in bulk, we show how inclusion of mesoscale order resolves the controversy between experimental and theoretical results for the energy-level profile and alignment in a variety of photovoltaic systems, with direct experimental validation. Optimal use of long-range ordering also rationalizes the acceptor-donor-acceptor paradigm for molecular design of donor dyes. We predict open-circuit voltages of planar heterojunction solar cells in excellent agreement with experimental data, based only on crystal structures and interfacial orientation