Poly(3-decylthiophene) radical anions and cations in solution: single and multiple polarons and their delocalization lengths in conjugated polymers

The effect of an electric field on the reaction kinetics of a charge carrier migrating within a one-dimensional chain

The aim of this study is to suggest a novel approach for estimating the intramolecular mobility of a charge carrier that migrates within a polymer chain and is involved in a pair reaction with a particle located on the same chain. The approach is based on the effect of an external electric field on the migration rate and, consequently, the kinetics of the reaction. As a first step, this problem is considered a stochastic one-step process with absorbing and reflecting boundaries, and an analytical solution is obtained in the case that the second reactant is immobile. With the use of computer simulations of stochastic migration, the effect of the mobility of both reactants and the influence of the Coulomb interaction between them are considered. It is found that the ratio of the pair reaction rates with and without an external field is relatively little dependent on these factors and that the analytical expressions derived can be applied to estimate the relative mobility of recombining particles with accuracy better than a factor of two in many realistic situations.

Operando Characterization of Organic Mixed Ionic/Electronic Conducting Materials

Operando characterization plays an important role in revealing the structure-property relationships of organic mixed ionic/electronic conductors (OMIECs), enabling the direct observation of dynamic changes during device operation and thus guiding the development of new materials. This review focuses on the application of different operando characterization techniques in the study of OMIECs, highlighting the time-dependent and bias-dependent structure, composition, and morphology information extracted from these techniques. We first illustrate the needs, requirements, and challenges of operando characterization then provide an overview of relevant experimental techniques, including spectroscopy, scattering, microbalance, microprobe, and electron microscopy. We also compare different in silico methods and discuss the interplay of these computational methods with experimental techniques. Finally, we provide an outlook on the future development of operando for OMIEC-based devices and look toward multimodal operando techniques for more comprehensive and accurate description of OMIECs.

Improving Intramolecular Hopping Charge Transport via Periodical Segmentation of π-Conjugation in a Molecule

The development of several-nanometer-scale π-conjugated systems for efficient intramolecular hopping charge transport remains a significant challenge. To construct localized electronic structures at the same energy in a molecule, a series of oligothiophenes, with lengths up to 10 nm and periodically twisted structures, was synthesized. Single-molecule conductance measurements of the twisted molecules revealed resistances lower than those of planar oligothiophenes. This study provides a rational molecular design to improve the intramolecular hopping charge transport in materials.

UV-to-IR Absorption of Molecularly p-Doped Polythiophenes with Alkyl and Oligoether Side Chains: Experiment and Interpretation Based on Density Functional Theory

The UV-to-IR transitions in p-doped poly(3-hexylthiophene) (P3HT) with alkyl side chains and polar polythiophene with tetraethylene glycol side chains are studied experimentally by means of the absorption spectroscopy and computationally using density functional theory (DFT) and tight-binding DFT. The evolution of electronic structure is calculated as the doping level is varied, while the roles of dopant ions, chain twisting, and π-π stacking are also considered, each of these having the effect of broadening the absorption peaks while not significantly changing their positions. The calculated spectra are found to be in good agreement with experimental spectra obtained for the polymers doped with a molybdenum dithiolene complex. As in other DFT studies of doped conjugated polymers, the electronic structure and assignment of optical transitions that emerge are qualitatively different from those obtained through earlier "traditional" approaches. In particular, the two prominent bands seen for the p-doped materials are present for both polarons and bipolarons/polaron pairs. The lowest energy of these transitions is due to excitation from the valence band to a spin-resolved orbitals located in the gap between the bands. The higher-energy band is a superposition of excitation from the valence band to a spin-resolved orbitals in the gap and an excitation between bands.

Inverted Region in Bimolecular Electron Transfer in Solution Enabled by Delocalization

Rate constants for bimolecular electron transfer (ET) increased with driving force, -ΔG°, reached a plateau, and then decreased in an inverted region. This rate data was described well by electron transfer theory subject to a diffusion-controlled limit. These were for ET from radical anions of polydecylthiophene (P3DT) to a series of acceptors in THF solution. When the donor was the smaller anion of quaterthiophene (T₄^•-) the inverted region was much less prominent and still less so for when the donor was the anion of bithiophene (T₂^•-). Description of the data using ET theory identifies smaller electronic couplings for the highly delocalized P3DT anions as enabling the inverted behavior: The presence of a Marcus inverted region is a consequence of delocalized electronic states. The results further imply that electronic couplings smaller than usually found for molecules in contact could boost efficiency of energy storage by electron transfer and identifies size-mismatch as an important concept in control of electronic couplings.

Polaron and Exciton Delocalization in Oligomers of High-Performance Polymer PTB7

A key characteristic of organic photovoltaic cells is the efficient charge separation in the active layer. Sufficient delocalization of the positive polaron in organic photovoltaics is considered essential for the effective separation of the opposite charges and the suppression of recombination. We use light-induced EPR and ENDOR spectroscopy combined with DFT calculations to determine the electronic structure of the positive polaron in PTB7-type oligomers. Utilizing the superior spectral resolution of high-frequency (130 GHz) D-band EPR, the principal components of the g tensors were determined. Pulsed ENDOR spectroscopy at X-band allowed the measurement of ¹H hyperfine coupling constants. A comparison of g tensors and ¹H hyperfine coupling constants of the PTB7-type oligomers with the high-performance PTB7 polymer revealed a delocalization of the positive polaron in the polymer over about four monomeric units, corresponding to about 45 Å in length. Our current study thus not only determines the polaron delocalization length in PTB7 but also validates the approach combining EPR/ENDOR spectroscopy with DFT-calculated magnetic resonance parameters. This is of importance in those cases where oligomers of defined length are not easily obtained. In addition, the delocalization of the neutral triplet exciton was also determined in the oligomers and compared with polymer PTB7. The analysis revealed that the neutral triplet exciton is substantially more delocalized than the positive polaron, exceeding 10 monomeric units.

Mechanisms of IR amplification in radical cation polarons

Break down of the Born-Oppenheimer approximation is caused by mixing of electronic and vibrational transitions in the radical cations of some conjugated polymers, resulting in unusually intense vibrational bands known as infrared active vibrations (IRAVs). Here, we investigate the mechanism of this amplification, and show that it provides insights into intramolecular charge migration. Spectroelectrochemical time-resolved infrared (TRIR) and two-dimensional infrared (2D-IR) spectroscopies were used to investigate the radical cations of two butadiyne-linked conjugated porphyrin oligomers, a linear dimer and a cyclic hexamer. The 2D-IR spectra reveal strong coupling between all the IRAVs and the electronic π-π* polaron band. Intramolecular vibrational energy redistribution (IVR) and vibrational relaxation occur within ∼0.1-7 ps. TRIR spectra show that the transient ground state bleach (GSB) and excited state absorption (ESA) signals have anisotropies of 0.31 ± 0.07 and 0.08 ± 0.04 for the linear dimer and cyclic hexamer cations, respectively. The small TRIR anisotropy for the cyclic hexamer radical cation indicates that the vibrationally excited polaron migrates round the nanoring on a time scale faster than the measurement, i.e. within 0.5 ps, at 298 K. Density functional theory (DFT) calculations qualitatively reproduce the emergence of the IRAVs. The first singlet (S1) excited states of the neutral porphyrin oligomers exhibit similar IRAVs to the radical cations, implying that the excitons have similar electronic structures to polarons. Our results show that IRAVs originate from the strong coupling of charge redistribution to nuclear motion, and from the similar energies of electronic and vibrational transitions.

Impact of morphology on polaron delocalization in a semicrystalline conjugated polymer

We investigate the delocalization of holes in the semicrystalline conjugated polymer poly(2,5-bis(3-alkylthiophene-2-yl)thieno[3,2-b]thiophene) (PBTTT) by directly measuring the hyperfine coupling between photogenerated polarons and bound nuclear spins using electron nuclear double resonance spectroscopy. An extrapolation of the corresponding oligomer spectra reveals that charges tend to delocalize over 4.0-4.8 nm with delocalization strongly dependent on molecular order and crystallinity of the PBTTT polymer thin films. Density functional theory calculations of hyperfine couplings confirm that long-range corrected functionals appropriately describe the change in coupling strength with increasing oligomer size and agree well with the experimentally measured polymer limit. Our discussion presents general guidelines illustrating the various pitfalls and opportunities when deducing polaron localization lengths from hyperfine coupling spectra of conjugated polymers.

Electronic Delocalization in the Radical Cations of Porphyrin Oligomer Molecular Wires

The radical cations of a family of π-conjugated porphyrin arrays have been investigated: linear chains of N = 1-6 porphyrins, a 6-porphyrin nanoring and a 12-porphyrin nanotube. The radical cations were generated in solution by chemical and electrochemical oxidation, and probed by vis-NIR-IR and EPR spectroscopies. The cations exhibit strong NIR bands at ∼1000 nm and 2000-5000 nm, which shift to longer wavelength with increasing oligomer length. Analysis of the NIR and IR spectra indicates that the polaron is delocalized over 2-3 porphyrin units in the linear oligomers. Some of the IR vibrational bands are strongly intensified on oxidation, and Fano-type antiresonances are observed when activated vibrations overlap with electronic transitions. The solution-phase EPR spectra of the radical cations have Gaussian lineshapes with linewidths proportional to N^-0.5, demonstrating that at room temperature the spin hops rapidly over the whole chain on the time scale of the hyperfine coupling (ca. 100 ns). Direct measurement of the hyperfine couplings through electron-nuclear double resonance (ENDOR) in frozen solution (80 K) indicates distribution of the spin over 2-3 porphyrin units for all the oligomers, except the 12-porphyrin nanotube, in which the spin is spread over about 4-6 porphyrins. These experimental studies of linear and cyclic cations give a consistent picture, which is supported by DFT calculations and multiparabolic modeling with a reorganization energy of 1400-2000 cm^-1 and coupling of 2000 cm^-1 for charge transfer between neighboring sites, placing the system in the Robin-Day class III.

Extreme electron polaron spatial delocalization in π-conjugated materials

The electron polaron, a spin-1/2 excitation, is the fundamental negative charge carrier in π-conjugated organic materials. Large polaron spatial dimensions result from weak electron-lattice coupling and thus identify materials with unusually low barriers for the charge transfer reactions that are central to electronic device applications. Here we demonstrate electron polarons in π-conjugated multiporphyrin arrays that feature vast areal delocalization. This finding is evidenced by concurrent optical and electron spin resonance measurements, coupled with electronic structure calculations that suggest atypically small reorganization energies for one-electron reduction of these materials. Because the electron polaron dimension can be linked to key performance metrics in organic photovoltaics, light-emitting diodes, and a host of other devices, these findings identify conjugated materials with exceptional optical, electronic, and spintronic properties.

Electron Spin Relaxation of Hole and Electron Polarons in π-Conjugated Porphyrin Arrays: Spintronic Implications

Electron spin resonance (ESR) spectroscopic line shape analysis and continuous-wave (CW) progressive microwave power saturation experiments are used to probe the relaxation behavior and the relaxation times of charged excitations (hole and electron polarons) in meso-to-meso ethyne-bridged (porphinato)zinc(II) oligomers (PZnn compounds), which can serve as models for the relevant states generated upon spin injection. The observed ESR line shapes for the PZnn hole polaron ([PZnn](+•)) and electron polaron ([PZnn](-•)) states evolve from Gaussian to more Lorentzian as the oligomer length increases from 1.9 to 7.5 nm, with solution-phase [PZnn](+•) and [PZnn](-•) spin-spin (T2) and spin-lattice (T1) relaxation times at 298 K ranging, respectively, from 40 to 230 ns and 0.2 to 2.3 μs. Notably, these very long relaxation times are preserved in thick films of these species. Because the magnitudes of spin-spin and spin-lattice relaxation times are vital metrics for spin dephasing in quantum computing or for spin-polarized transport in magnetoresistive structures, these results, coupled with the established wire-like transport behavior across metal-dithiol-PZnn-metal junctions, present meso-to-meso ethyne-bridged multiporphyrin systems as leading candidates for ambient-temperature organic spintronic applications.