Polaron hopping barriers and rates in semiconducting polymers.

Conjugated polymers are potential next-generation materials for organic electronic devices. The ability of these materials to transport charges is a key factor limiting their performance. Charge carriers in conjugated polymers are localized by disorder and polaronic effects. Charge transport in these materials is often described by thermally activated hopping, with a rate given by Marcus theory. The polaron hopping activation energy determines the temperature dependence of the Marcus rate. This energy barrier is dictated by the transition state, in which the charge carrier is equally divided between the initial and final locations. The prefactor for the polaron hopping rate is set by the charge tunneling rate between the initial and final locations. We use a tight-binding polaron model, in which charge carriers are stabilized by both nuclear reorganization and polarization of the surrounding dielectric, to compute the activation energy, charge tunneling rate and overall rate constant for intrachain and interchain charge hopping processes in poly(3-hexylthiophene) (P3HT) crystalline lamellae and amorphous melts. Charge transport in these two environments is limited by interchain hopping processes. Both hopping barriers and rates predicted by the model are in good agreement with experiments on a variety of crystalline and amorphous P3HT materials. Qualitatively, the barriers largely depend on how well the transition state is stabilized by polarization effects, and on the hopping integral between the initial and final locations, both of which penalize hopping over longer distances.

Thermal Fluctuations Lead to Cumulative Disorder and Enhance Charge Transport in Conjugated Polymers.

All conjugated polymers examined to date exhibit significant cumulative lattice disorder, although the origin of this disorder remains unclear. Using atomistic molecular dynamics (MD) simulations, the detailed structures for single crystals of a commonly studied conjugated polymer, poly(3-hexylthiophene-2,5-diyl) (P3HT) are obtained. It is shown that thermal fluctuations of thiophene rings lead to cumulative disorder of the lattice with an effective paracrystallinity of about 0.05 in the π-π stacking direction. The thermal-fluctuation-induced lattice disorder can in turn limit the apparent coherence length that can be observed in diffraction experiments. Calculating mobilities from simulated crystal structures demonstrates that thermal-fluctuation-induced lattice disorder even enhances charge transport in P3HT. The mean inter-chain charge transfer integral is enhanced with increasing cumulative lattice disorder, which in turn leads to pathways for fast charge transport through crystals.

Energetics of exciton binding and dissociation in polythiophenes: a tight binding approach.

Organic photovoltaics offer a potential low-cost alternative to inorganic solar cells. Crucial to the performance of these devices is the generation of free charges, which occurs through the dissociation of excitons. Here we study excitons in polythiophenes, their stability and energetics of dissociation and separation into charge carriers. Excitons are excited electron and hole pairs bound by Coulomb interactions. To separate into unbound charges, the exciton binding energy must be overcome. We use a tight binding Hamiltonian to describe the exciton binding energy and its dissociation potential, for an exciton confined to a single polymer chain. Our model accounts for polaronic effects, arising from reorganization of nuclei and from polarization of the surrounding dielectric, which stabilize the separated carriers and thereby affect the exciton dissociation potential. We examine the effects of an applied electric field on the dissociation potential, and relate the field strength necessary to unbind the hole-electron pair to the maximum attractive Coulomb force between them. We apply our model to study the exciton at a donor-acceptor interface on a block-copolymer. Interfacial polarization alters the exciton binding potential, rendering the hole-electron pair easier to unbind.

Polaron formation mechanisms in conjugated polymers.

In semiconducting polymers, interactions with conformational degrees of freedom can localize charge carriers, and strongly affect charge transport. Polarons can form when charges induce deformations of the surrounding medium, including local vibrational modes or dielectric polarization. These deformations then interact attractively with the charge, tending to localize it. First we investigate vibrational polaron formation in poly(3-hexylthiophene) [P3HT], with a tight-binding model for charges hopping between adjacent rings, coupled to ring distortions. We use density functional theory (DFT) calculations to determine coupling constants, including the "spring constant" for ring distortions and the coupling to the charge carrier. On single chains, we find only broad, weakly bound polarons by this mechanism. In 2d crystalline layers of P3HT, even weak transverse hopping between chains destabilizes this polaron. Then, we consider polarons stabilized by dielectric polarization, described semiclassically with a polarizable continuum interacting with the carrier wavefunction. In contrast to vibrational polarons, we find dielectrically stabilized polarons in P3HT are narrower, more strongly bound, and stable in 2d crystalline layers.

Tight binding model of conformational disorder effects on the optical absorption spectrum of polythiophenes.

Semiconducting polymers are soft materials with many conformational degrees of freedom. The limited understanding of how conformational disorder affects their optoelectronic properties is a key source of difficulties that limits their widespread usage in electronic devices. We develop a coarse-grained approach based on the tight binding approximation to model the electronic degrees of freedom of polythiophene chains, taking into account conformational degrees of freedom. Particularly important is dihedral disorder, which disrupts extended electronic states. Our tight binding model is parameterized using density functional theory (DFT) calculations of the one-dimensional band structures for chains with imposed periodic variations in dihedral angles. The model predicts valence and conduction bands for these chain conformations that compare well to DFT results. As an initial application of our model, we compute the optical absorption spectrum of poly(3-hexylthiophene) chains in solution. We observe a broadening of the absorption edge resulting from dihedral disorder, just shy of the experimental broadening. We conclude that the effects of molecular disorder on the optoelectronic properties of conjugated polymer single chains can be mostly accounted for by torsional disorder alone.

Combination of Counterion Size and Doping Concentration Determines the Electronic and Thermoelectric Properties of Semiconducting Polymers.

In both chemical and electrochemical doping of organic semiconductors (OSCs), a counterion, either from the electrolyte or ionized dopant, balances the charge introduced to the OSC. Despite the large influence of this counterion on OSC optical and electronic response, there remains substantial debate on how a fundamental parameter, ion size, impacts these properties. This work resolves much of this debate by accounting for two doping regimes. In the low-doping regime, the Coulomb binding energies between charge carriers on the OSC and the counterions are significant, and larger counterions lead to decreased Coulomb interactions, more delocalized charge carriers, and higher electrical conductivities. In the high-doping regime, the Coulomb binding energies become negligible due to the increased dielectric constant of the films and a smoothing of the energy landscape; thereby, the electrical conductivities depend primarily on the extent of morphological disorder in the OSC. Moreover, in regioregular poly(3-hexylthiophene), rr-P3HT, smaller counterions lead to greater bipolaron concentrations in the low-doping regime due to the increased Coulomb interactions. Emphasizing the impact of the counterion size, it is shown that larger counterions can lead to increased thermoelectric power factors for rr-P3HT.

New Chemical Dopant and Counterion Mechanism for Organic Electrochemical Transistors and Organic Mixed Ionic-Electronic Conductors.

Organic mixed ionic-electronic conductors (OMIECs) have varied performance requirements across a diverse application space. Chemically doping the OMIEC can be a simple, low-cost approach for adapting performance metrics. However, complex challenges, such as identifying new dopant materials and elucidating design rules, inhibit its realization. Here, these challenges are approached by introducing a new n-dopant, tetrabutylammonium hydroxide (TBA-OH), and identifying a new design consideration underpinning its success. TBA-OH behaves as both a chemical n-dopant and morphology additive in donor acceptor co-polymer naphthodithiophene diimide-based polymer, which serves as an electron transporting material in organic electrochemical transistors (OECTs). The combined effects enhance OECT transconductance, charge carrier mobility, and volumetric capacitance, representative of the key metrics underpinning all OMIEC applications. Additionally, when the TBA+ counterion adopts an "edge-on" location relative to the polymer backbone, Coulombic interaction between the counterion and polaron is reduced, and polaron delocalization increases. This is the first time such mechanisms are identified in doped-OECTs and doped-OMIECs. The work herein therefore takes the first steps toward developing the design guidelines needed to realize chemical doping as a generic strategy for tailoring performance metrics in OECTs and OMIECs.