Design Rules to Maximize Charge-Carrier Mobility along Conjugated Polymer Chains

Detailed Complementary Consistency: Wave Function Tells Particle How to Hop, Particle Tells Wave Function How to Collapse

In mixed quantum-classical dynamics, the quantum subsystem can have both wave function and particle-like descriptions. However, they may yield inconsistent results for the expectation value of the same physical quantity. We here propose a novel detailed complementary consistency (DCC) method based on the principle of detailed internal consistency. Namely, the wave function along each trajectory tells the particle how to hop, while the particle tells the wave function how to collapse based on active states in the trajectory ensemble. As benchmarked in a diverse array of representative models with localized nonadiabatic couplings, DCC not only achieves fully consistent results (i.e., identical populations calculated based on wave functions and active states) but also closely reproduces the exact quantum results. Due to the high performance, our new DCC method has great potential to give a consistent and accurate mixed quantum-classical description of general nonadiabatic dynamics after further development.

A Review of Polyolefin-Insulation Materials in High Voltage Transmission; From Electronic Structures to Final Products

This review focuses on the use of polyolefins in high-voltage direct-current (HVDC) cables and capacitors. A short description of the latest evolution and current use of HVDC cables and capacitors is first provided, followed by the basics of electric insulation and capacitor functions. Methods to determine dielectric properties are described, including charge transport, space charges, resistivity, dielectric loss, and breakdown strength. The semicrystalline structure of polyethylene and isotactic polypropylene is described, and the way it relates to the dielectric properties is discussed. A significant part of the review is devoted to describing the state of art of the modeling and prediction of electric or dielectric properties of polyolefins with consideration of both atomistic and continuum approaches. Furthermore, the effects of the purity of the materials and the presence of nanoparticles are presented, and the review ends with the sustainability aspects of these materials. In summary, the effective use of modeling in combination with experimental work is described as an important route toward understanding and designing the next generations of materials for electrical insulation in high-voltage transmission.

Coarse-Grained Model for Prediction of Hole Mobility in Polyethylene

Electrical conductivity measurements of polyethylene indicate that the semicrystalline structure and morphology influence the conductivity. To include this effect in atomistic charge transport simulations, models that explicitly or implicitly take morphology into account are required. In the literature, charge transport simulations of amorphous polyethylene have been successfully performed using short oligomers to represent the polymer. However, a more realistic representation of the polymer structure is desired, requiring the development of fast and efficient charge transport algorithms that can handle large molecular systems through coarse-graining. Here, such a model for charge transport simulations in polyethylene is presented. Quantum chemistry calculations were used to define six segmentation rules on how to divide a polymer chain into shorter segments representing localized molecular orbitals. Applying the rules to amorphous systems yields distributions of segments with mode and median segment lengths relatively close to the persistence length of polyethylene. In an initial test, the segments of an amorphous polyethylene were used as hopping sites in kinetic Monte Carlo (KMC) simulations, which yielded simulated hole mobilities that were within the experimental range. The activation energy of the simulated system was lower compared to the experimental values reported in the literature. A conclusion may be that the experimental result can only be explained by a model containing chemical defects that generate deep traps.

Charge carrier dynamics in conducting polymer PEDOT using ab initio molecular dynamics simulations

As conducting polymers become increasingly important in electronic devices, understanding their charge transport is essential for material and device development. Various semi-empirical approaches have been used to describe temporal charge carrier dynamics in these materials, but there have yet to be any theoretical approaches utilizing ab initio molecular dynamics. In this work, we develop a computational technique based on ab initio Car-Parrinello molecular dynamics to trace charge carrier temporal motion in archetypical conducting polymer poly(3,4-ethylenedioxythiophene) (PEDOT). Particularly, we analyze charge dynamics in a single PEDOT chain and in two coupled chains with different degrees of coupling and study the effect of temperature. In our model we first initiate a positively charged polaron (compensated by a negative counterion) at one end of the chain, and subsequently displace the counterion to the other end of the chain and trace polaron dynamics in the system by monitoring bond length alternation in the PEDOT backbone and charge density distribution. We find that at low temperature (T = 1 K) the polaron distortion gradually disappears from its initial location and reappears near the new position of the counterion. At the room temperature (T = 300 K), we find that the distortions induced by polaron, and atomic vibrations are of the same magnitude, which makes tracking the polaron distortion challenging because it is hidden behind the temperature-induced vibrations. The novel approach developed in this work can be used to study polaron mobility along and between the chains, investigate charge transport in highly doped polymers, and explore other flexible polymers, including n-doped ones.

Learning Decoherence Time Formulas for Surface Hopping from Quantum Dynamics

Surface hopping simulations have achieved great success in many different fields, but their reliability has long been limited by the overcoherence problem. We here present a general machine learning assisted approach to identify optimal decoherence time formulas for surface hopping using exact quantum dynamics as references. In order to avoid computationally expensive force calculations, we use the nuclear kinetic energy and the adiabatic energy difference to iteratively generate the descriptor space. Through multilayer screening of the candidate descriptors and discrete optimization of the relevant parameters, we obtain new energy-based decoherence time formulas. As benchmarked in thousands of diverse multilevel systems and six standard scattering models, surface hopping with our new decoherence time formulas nearly reproduces the exact quantum dynamics while maintaining high efficiency. Thereby, our approach provides a promising avenue for systematically improving the accuracy of surface hopping simulations in complex systems from quantum dynamics data.

Computational Approaches for Organic Semiconductors: From Chemical and Physical Understanding to Predicting New Materials

While a complete understanding of organic semiconductor (OSC) design principles remains elusive, computational methods─ranging from techniques based in classical and quantum mechanics to more recent data-enabled models─can complement experimental observations and provide deep physicochemical insights into OSC structure-processing-property relationships, offering new capabilities for in silico OSC discovery and design. In this Review, we trace the evolution of these computational methods and their application to OSCs, beginning with early quantum-chemical methods to investigate resonance in benzene and building to recent machine-learning (ML) techniques and their application to ever more sophisticated OSC scientific and engineering challenges. Along the way, we highlight the limitations of the methods and how sophisticated physical and mathematical frameworks have been created to overcome those limitations. We illustrate applications of these methods to a range of specific challenges in OSCs derived from π-conjugated polymers and molecules, including predicting charge-carrier transport, modeling chain conformations and bulk morphology, estimating thermomechanical properties, and describing phonons and thermal transport, to name a few. Through these examples, we demonstrate how advances in computational methods accelerate the deployment of OSCsin wide-ranging technologies, such as organic photovoltaics (OPVs), organic light-emitting diodes (OLEDs), organic thermoelectrics, organic batteries, and organic (bio)sensors. We conclude by providing an outlook for the future development of computational techniques to discover and assess the properties of high-performing OSCs with greater accuracy.

An Amorphous n-Type Conjugated Polymer with an Ultra-Rigid Planar Backbone

High charge carrier mobility polymer semiconductors are always semi-crystalline. Amorphous conjugated polymers represent another kind of polymer semiconductors with different charge transporting mechanism. Here we report the first near-amorphous n-type conjugated polymer with decent electron mobility, which features a remarkably rigid, straight and planar polymer backbone. The molecular design strategy is to copolymerize two fused-ring building blocks which are both electron-accepting, centrosymmetrical and planar. The polymer is the alternating copolymer of double B←N bridged bipyridine (BNBP) unit and benzobisthiazole (BBTz) unit. It shows a decent electron mobility of 0.34 cm²  V^-1  s^-1 in organic field-effect transistors. The excellent electron transporting property of the polymer is possibly due to the ultrahigh backbone stiffness, small π-π stacking distance, and high molecular weight.

Screening semiconducting polymers to discover design principles for tuning charge carrier mobility

We employ a rapid method for computing the electronic structure and orbital localization characteristics for a sample of 36 different polymer backbone structures. This relatively large sample derived from recent literature is used to identify the features of the monomer sequence that lead to greater charge delocalization and, potentially, greater charge mobility. Two characteristics contributing in equal measure to large localization length are the reduced variation of the coupling between adjacent monomers due to conformational fluctuations and the presence of just two monomers in the structural repeating units. For such polymers a greater mismatch between the HOMO orbitals of the fragments and, surprisingly, a smaller coupling between them is shown to favour greater delocalization of the orbitals. The underlying physical reasons for such observations are discussed and explicit and constructive design rules are proposed.

Thermally activated intra-chain charge transport in high charge-carrier mobility copolymers

Disordered or even seemingly amorphous, donor–acceptor type, conjugated copolymers with high charge-carrier mobility have emerged as a new class of functional materials, where transport along the conjugated backbone is key. Here, we report on non-adiabatic molecular dynamics simulations of charge-carrier transport along chains of poly (indacenodithiophene-co-benzothiadiazole), within a model Hamiltonian parameterized against first-principles calculations. We predict thermally activated charge transport associated with a slightly twisted ground-state conformation, on par with experimental results. Our results also demonstrate that the energy mismatch between the hole on the donor vs the acceptor units of the copolymer drives localization of the charge carriers and limits the intra-chain charge-carrier mobility. We predict that room-temperature mobility values in excess of 10 cm2 V−1 s−1 can be achieved through proper chemical tuning of the component monomer units.

A reciprocal-space formulation of surface hopping

Surface hopping has seen great success in describing molecular phenomena where electronic excitations tend to be localized, but its application to materials with band-like electronic properties has remained limited. Here, we derive a formulation of fewest-switches surface hopping where both the quantum and classical equations of motion are solved entirely in terms of reciprocal-space coordinates. The resulting method is directly compatible with band structure calculations and allows for the efficient description of band-like phenomena by means of a truncation of the Brillouin zone. Using the Holstein and Peierls models as examples, we demonstrate the formal equivalence between real-space and reciprocal-space surface hopping and assess their accuracy against mean-field mixed quantum-classical dynamics and numerically exact results. Having very similar equations of motion, reciprocal-space surface hopping can be straightforwardly incorporated in existing (real-space) surface hopping implementations.

Modeling Non-adiabatic Dynamics in Nanoscale and Condensed Matter Systems

Rapid, far-from-equilibrium processes involving excitation of electronic, vibrational, spin, photon, topological, and other degrees of freedom form the basis of modern technologies, including electronics and optoelectronics, solar energy harvesting and conversion to electrical and chemical energy, quantum information processing, spin- and valleytronics, chemical detection, and medical therapies. Such processes are studied experimentally with various time-resolved spectroscopies that allow scientists to track system's evolution on ultrafast time scales and at close to atomistic level of detail. The availability of various forms of lasing has made such measurements easily accessible to many experimental groups worldwide, to study atoms and small molecules, nanoscale and condensed matter systems, proteins, cells, and mesoscopic materials. The experimental work necessitates parallel theoretical efforts needed to interpret the experiments and to provide insights that cannot be gained through measurements due to experimental limitations.Non-adiabatic (NA) molecular dynamics (MD) allows one to study processes at the atomistic level and in the time domain most directly mimicking the time-resolved experiments. Atomistic modeling takes full advantage of chemical intuition and principles that guide design and fabrication of molecules and materials. It provides atomistic origins of quasi-particles, such as holes, excitons, trions, plasmons, phonons, polarons, polaritons, spin-waves, momentum-resolved and topological states, electrically and magnetically polarized structures, and other abstract concepts. An atomistic description enables one to study realistic aspects of materials, which necessarily contain defects, dopants, surfaces, interfaces, passivating ligands, and solvent layers. Often, such realistic features govern material properties and are hard to account for phenomenologically. NA-MD requires few approximations and assumptions. It does not need to assume that atomic motions are harmonic, that electrons are Drude oscillators, that coupling between different degrees of freedom is weak, that dynamics is Markovian or has short memory, or that evolution occurs by exponential kinetics of transitions between few states. The classical or semiclassical treatment of atomic motions constitutes the main approximation of NA-MD and is used because atoms are 3-5 orders of magnitude heavier than electrons. NA-MD is limited by system size, typically hundreds or thousands of atoms, and time scale, picoseconds to nanoseconds. The quality of NA-MD simulations depends on the electronic structure method used to obtain excited state energies and NA couplings.NA-MD has been largely popularized and advanced in the chemistry community that focuses on molecules. Modeling far-from-equilibrium dynamics in nanoscale and condensed matter systems often has to account for other types of physics. At the same time, condensed phase NA-MD allows for approximations that may not work in molecules. Focusing on the recent NA-MD developments aimed at studying excited state processes in nanoscale and condensed phases, this Account considers how the phenomena important on the nanoscale can be incorporated into NA-MD and what approximations can be made to increase its efficiency with complex systems and processes.

Long-Range Interactions Boost Singlet Exciton Diffusion in Nanofibers of π-Extended Polymer Chains

Raising the distance covered by singlet excitons during their lifetimes to values maximizing light absorption (a few hundred nm) would solve the exciton diffusion bottleneck issue and lift the constraint for fine (∼10 nm) phase segregation in bulk heterojunction organic solar cells. In that context, the recent report of highly ordered conjugated polymer nanofibers featuring singlet exciton diffusion length, L_D, in excess of 300 nm is both appealing and intriguing [Jin, X.; et al. Science 2018, 360 (6391), 897-900]. Here, on the basis of nonadiabatic molecular dynamics simulations, we demonstrate that singlet exciton diffusion in poly(3-hexylthiophene) (P3HT) fibers is highly sensitive to the interplay between delocalization along the polymer chains and long-range interactions along the stacks. Remarkably, the diffusion coefficient is predicted to rocket by 3 orders of magnitude when going beyond nearest-neighbor intermolecular interactions in fibers of extended (30-mer) polymer chains and to be resilient to interchain energetic and positional disorders.

Rapid Method for Calculating the Conformationally Averaged Electronic Structure of Conjugated Polymers

We developed a rapid method to calculate the average electronic structure properties of large ensembles of conjugated polymer chains sampling their conformational space. This is achieved by using the localized molecular orbital (MO) method to rapidly compute the MOs and their energies for isolated polymer chains and through using a calibration scheme to further correct the obtained energies by comparison with a few accurate calculations. The method is applied to the study of the density of states and orbital localization characteristics for five polymers. It is shown that all key properties of the individual chain related to the charge mobility can be rationalized in terms of the properties of the constituent monomers, their interaction, and the conformational flexibility of the chain. More specifically we identify the features that lead to greater charge delocalization. Finally, we discuss the prospect of using this method for a computational high-throughput screening of conjugated polymers.

Intrinsically stretchable organic light-emitting diodes

Soft and conformable optoelectronic devices for wearable and implantable electronics require mechanical stretchability. However, very few researches have been done for intrinsically stretchable light-emitting diodes. Here, we present an intrinsically stretchable organic light-emitting diode, whose constituent materials are all highly stretchable. The resulting intrinsically stretchable organic light-emitting diode can emit light when exposed to strains as large as 80%. The turn-on voltage is as low as 8 V, and the maximum luminance, which is a summation of the luminance values from both the anode and cathode sides, is 4400 cd m^-2 It can also survive repeated stretching cycles up to 200 times, and small stretching to 50% is shown to substantially enhance its light-emitting efficiency.

Branching Corrected Mean Field Method for Nonadiabatic Dynamics

When nonadiabatic dynamics are described on the basis of trajectories, severe trajectory branching occurs when the nuclear wave packets on some potential energy surfaces are reflected while those on the remaining surfaces are not. As a result, the traditional Ehrenfest mean field (EMF) approximation breaks down. In this study, two versions of the branching corrected mean field (BCMF) method are proposed. Namely, when trajectory branching is identified, BCMF stochastically selects either the reflected or the nonreflected group to build the new mean field trajectory or splits the mean field trajectory into two new trajectories with the corresponding weights. As benchmarked in six standard model systems and an extensive model base with two hundred diverse scattering models, BCMF significantly improves the accuracy while retaining the high efficiency of the traditional EMF. In fact, BCMF closely reproduces the exact quantum dynamics in all investigated systems, thus highlighting the essential role of branching correction in nonadiabatic dynamics simulations of general systems.