A multiscale description of charge transport in conjugated oligomers

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.

Microstructural Model of Indacenodithiophene-co-benzothiadiazole Polymer: π-Crossing Interactions and Their Potential Impact on Charge Transport

Morphological and electronic properties of indacenodithiophene-co-benzothiadiazole (IDTBT) copolymer with varying molecular weights are calculated through combined molecular dynamics (MD) and quantum chemical (QC) methods. Our study focuses on the polymer chain arrangements, interchain connectivity pathways, and interplay between morphological and electronic structure properties of IDTBT. Our models, which are verified against GIWAXS measurements, show a considerable number of BT-BT π-π interactions with a (preferential) perpendicular local orientation of polymer chains due to the steric hindrance of bulky side chains around IDT. Although our models predict a noncrystalline structure for IDTBT, the BT-BT (interchain) crossing points show a considerable degree of short-range order in spatial arrangement which most likely result in a mesh-like structure for the polymer and provide efficient pathways for interchain charge transport.

Efficient Surface Hopping Approach for Modeling Charge Transport in Organic Semiconductors

The trajectory surface hopping (TSH) method is nowadays widely applied to study the charge/exciton transport process in organic semiconductors (OSCs). In the present study, we systematically examine the performance of two approximations in the fewest switched surface hopping (FSSH) simulations for charge transport (CT) in several representative OSCs. These approximations include (i) the substitution of the nuclear velocity scaling along the nonadiabatic coupling vector (NCV) by rescaling the hopping probability with the Boltzmann factor (Boltzmann correction (BC)) and (ii) a phenomenological approach to treat the quantum feedback from the electronic system to the nuclear system (implicit charge relaxation (IR)) in the OSCs. We find that charge mobilities computed by FSSH-BC-IR are in very good agreement with the mobilities obtained by standard FSSH simulations with explicit charge relaxation (FSSH-ER), however, at reduced computational cost. A key parameter determining the charge carrier mobility is the reorganization energy, which is sensitively dependent on DFT functionals applied. By employing the IR approximation, the FSSH method allows systematic investigation of the effect of the reorganization energies obtained by different DFT functionals like B3LYP or ωB97XD on CT in OSCs. In comparison to the experiments, FSSH-BC-IR using ωB97XD reorganization energy underestimates mobilities in the low-coupling regime, which may indicate the lack of nuclear quantum effects (e.g., zero point energy (ZPE)) in the simulations. The mobilities obtained by FSSH-BC-IR using the B3LYP reorganization energy agree well with experimental values in 3 orders of magnitude. The accidental agreement may be the consequence of the underestimation of the reorganization energy by the B3LYP functional, which compensates for the neglect of nuclear ZPE in the simulations.

Why does solvent treatment increase conductivity of PEDOT:PSS? Insight from molecular dynamics simulations

Poly(3,4-ethylenedioxythiophene):polystyrenesulfonate (PEDOT:PSS) is one of the most important conducting polymers. In its pristine form its electrical conductivity is low, but it can be enhanced by several orders of magnitude by...

Multiscale modelling of charge transport in P3HT:DIPBI bulk heterojunction organic solar cells

Charge transport properties of a P3HT:DIPBI bulk heterojunction solar cell are modelled by kinetic Monte Carlo simulations based on a morphology obtained from coarse-grained molecular dynamics. Different methods for calculating the hopping integrals entering the charge transfer rates are compared and calibrated for hole transport in amorphous P3HT. The influence of intermolecular and intramolecular charge transfer on the total charge carrier mobility and hence the power conversion efficiency is investigated in detail. An analysis of the most probable pathways with low resistance for hole transport is performed, establishing a connection between charge mobility and morphology.

Performance of Mixed Quantum-Classical Approaches on Modeling the Crossover from Hopping to Bandlike Charge Transport in Organic Semiconductors

In the present study, several mixed quantum-classical (MQC) methods are applied to on-the-fly nonadiabatic molecular dynamics simulations of hole transport in molecular organic semiconductors (OSCs). The tested MQC methods contain the mean-field Ehrenfest (MFE), trajectory surface hopping (TSH) approaches based on Tully's fewest switches surface hopping (FSSH) and the global flux surface hopping (GFSH), the latter in the diabatic/adiabatic representation, and a Landau-Zener type trajectory surface hopping (LZSH). We also tested several correction schemes which were proposed to identify trivial crossings and to remove unphysical long-range charge transfers due to decoherence corrections. In addition, several cost-effective approaches for the nuclear velocity adjustment after an energy-allowed/energy-forbidden hop are investigated with respect to detailed balance and internal consistency conditions. To model a broad spectrum of OSCs with different charge transport characteristics, we derived from the anthracene structural model the construction of two additional models by uniformly scaling down the electronic couplings by the factors of 0.1 and 0.5. Anthracene shows a bandlike charge transport mechanism, characterized by slightly delocalized charge carriers 'diffusing' through the crystal. For smaller couplings, the mechanism changes to a hopping type, characteristically differing in the charge delocalization and temperature dependence. The MFE and corrected adiabatic TSH approaches are able to quantitatively reproduce the expected behavior, while the diabatic LZSH method fails for large couplings, as do approaches which are based on the hopping of localized charge between neighboring sites. Moreover, we find that while the hole mobility of the anthracene crystal simulated using the celebrated Marcus theory is in good agreement with the experimental value, its agreement has to be regarded as an accident due to the overestimation of the prefactor in the Marcus rate equation.

Effect of site energy fluctuation on charge transport in disordered organic molecules

Effect of dynamics of site energy disorder on charge transport in organic molecular semiconductors is not yet well-established. In order to study the relationship between the dynamics of site energy disorder and charge transport, we have performed a multiscale study on dialkyl substituted thienothiophene capped benzobisthiazole (BDHTT-BBT) and methyl-substituted dicyanovinyl-capped quinquethiophene (DCV5T-Me) molecular solids. In this study, we explore the structural dynamics and correlated charge transport by electronic structure calculations, molecular dynamics, and kinetic Monte-Carlo simulations. We have also proposed the differential entropy dependent diffusion and charge density equations to study the electric field drifted diffusion property and carrier density. In this investigation, we have addressed the transformation mechanism from dynamic to static disorder in the extended stacked molecular units. Here, the decrease in the charge transfer rate due to site energy fluctuations reveals the dispersion transport along the extended π-stacked molecules. Furthermore, the calculated current density for a different set of site energy difference values shows the validity and the limitations of the Einstein relation. Based on the calculated ideality factor, we have classified the charge transport in these molecules as either the Langevin or the Shockley-Read-Hall type mechanism. Through the calculated mobility, current density, and ideality factor analysis, we categorize the applicability of molecules of interest for photovoltaic or light emitting diode applications.

Multiscale modeling of charge transfer in polymers with flexible backbones

In order to evaluate carrier transfer properties in polymers with flexible backbones, we have proposed a simplified multi-scale modeling approach combining molecular dynamics simulations, first-principles calculations and kinetic Monte Carlo simulations.

Structural determinants in the bulk heterojunction

Photovoltaics is one of the key areas in renewable energy research with remarkable progress made every year. Here we consider the case of a photoactive material and study its structural composition and the resulting consequences for the fundamental processes driving solar energy conversion. A multiscale approach is used to characterize essential molecular properties of the light-absorbing layer. A selection of bulk-representative pairs of donor/acceptor molecules is extracted from the molecular dynamics simulation of the bulk heterojunction and analyzed at increasing levels of detail. Significantly increased ground state energies together with an array of additional structural characteristics are identified that all point towards an auxiliary role of the material's structural organization in mediating charge-transfer and -separation. Mechanistic studies of the type presented here can provide important insights into fundamental principles governing solar energy conversion in next-generation photovoltaic devices.

Getting excited: challenges in quantum-classical studies of excitons in polymeric systems

A combination of classical molecular dynamics (MM/MD) and quantum chemical calculations based on the density functional theory (DFT) was performed to describe the conformational properties of diphenylethyne (DPE), methylated-DPE and poly para phenylene ethynylene (PPE). DFT calculations were employed to improve and develop force field parameters for MM/MD simulations. Many-body Green's function theory within the GW approximation and the Bethe-Salpeter (GW-BSE) equation were utilized to describe the excited states of the systems. The reliability of the excitation energies based on the MM/MD conformations was examined and compared to the excitation energies from DFT conformations. The results show an overall agreement between the optical excitations based on MM/MD conformations and DFT conformations. This allows for the calculation of excitation energies based on MM/MD conformations.

Theoretical modeling of charge transport in triphenylamine–benzimidazole based organic solids for their application as host-materials in phosphorescent OLEDs

The dynamic disorder and electric field effects on charge transport in triphenylamine–benzimidazole based molecular solids have been investigated using electronic structure calculations, molecular dynamics and Monte-Carlo simulations. During the charge propagation, the energy loss of the carrier in each hopping step is monitored by Monte-Carlo simulation. We derive a survival probability correlated momentum–energy distribution for drift-diffusion analysis and we demonstrate the dispersion initiated charge trapping mechanism which is indeed ideal for light emission efficiency via recombination. In the present model, the proposed carrier drift energy–current density expression and Shockley diode current density equation are used to study the current density–voltage characteristics; accordingly the ideality factor (∼1.8–2.0) dictates the deviation of Einstein's classical diffusion–mobility relation (where the ideality factor is unity). The dual mechanism of electric field assisted site energy gap on coherent-like transport and the electric field stretched dispersion on recombination are observed in tris(3′-(1-phenyl-1H-benzimidazole-2-yl)biphenyl-4-yl)amine (TBBI) and tris(4′-(1-phenyl-1H-benzimidazole-2-yl)biphenyl-4-yl)amine (TIBN) molecular systems, which can be used as host materials in organic light emitting diodes (OLEDs). We find the transport going from coherent to incoherent, due to the conversion mechanism of dynamic to static disorder. This can also be a controlled by applied electric field. By adjusting the applied electric field, film thickness and changing the π-stacked molecular aggregation via substitutions, one can fix the dispersive parameter and accordingly calculate the charge transport properties to design efficient host-materials for photovoltaic and light emitting diode devices.

Dynamic disorder and electric field affect the charge (hole and electron) transport in host-materials for OLEDs.

Highly Planarized Naphthalene Diimide-Bifuran Copolymers with Unexpected Charge Transport Performance

The synthesis, characterization, and charge transport performance of novel copolymers PNDIFu2 made from alternating naphthalene diimide (NDI) and bifuran (Fu2) units are reported. Usage of potentially biomass-derived Fu2 as alternating repeat unit enables flattened polymer backbones due to reduced steric interactions between the imide oxygens and Fu2 units, as seen by density functional theory (DFT) calculations and UV-vis spectroscopy. Aggregation of PNDIFu2 in solution is enhanced if compared to the analogous NDI-bithiophene (T2) copolymers PNDIT2, occurring in all solvents and temperatures probed. PNDIFu2 features a smaller π-π stacking distance of 0.35 nm compared to 0.39 nm seen for PNDIT2. Alignment of aggregates in films is achieved by using off-center spin coating, whereby PNDIFu2 exhibits a stronger dichroic ratio and transport anisotropy in field-effect transistors (FET) compared to PNDIT2, with an overall good electron mobility of 0.21 cm2/(V s). Despite an enhanced backbone planarity, the smaller π-π stacking and the enhanced charge transport anisotropy, the electron mobility of PNDIFu2 is about three times lower compared to PNDIT2. Density functional theory calculations suggest that charge transport in PNDIFu2 is limited by enhanced polaron localization compared to PNDIT2.

Study of the cold charge transfer state separation at the TQ1/PC71 BM interface

Charge transfer (CT) state separation is one of the most critical processes in the functioning of an organic solar cell. In this article, we study a bilayer of TQ1 and PC₇₁ BM molecules presenting disorder at the interface, obtained by means of Molecular Dynamics. The study of the CT state splitting can be first analyzed through the CT state splitting diagram, introduced in a previous work. Through this analysis, we identify the possibility of CT state splitting within Marcus Theory in function of the electric field. Once the right range of electric fields has been identified, we perform Kinetic Monte Carlo simulations to estimate percentages and times for the CT state splitting and the free charge carriers collection. Statistical information extracted from these simulations allows us to highlight the importance of polarization and to test the limits of the predictions given by the CT state splitting diagram. © 2017 Wiley Periodicals, Inc.

Thermodynamics of a Compressible Maier-Saupe Model Based on the Self-Consistent Field Theory of Wormlike Polymer

This paper presents a theoretical formalism for describing systems of semiflexible polymers, which can have density variations due to finite compressibility and exhibit an isotropic-nematic transition. The molecular architecture of the semiflexible polymers is described by a continuum wormlike-chain model. The non-bonded interactions are described through a functional of two collective variables, the local density and local segmental orientation tensor. In particular, the functional depends quadratically on local density-variations and includes a Maier–Saupe-type term to deal with the orientational ordering. The specified density-dependence stems from a free energy expansion, where the free energy of an isotropic and homogeneous homopolymer melt at some fixed density serves as a reference state. Using this framework, a self-consistent field theory is developed, which produces a Helmholtz free energy that can be used for the calculation of the thermodynamics of the system. The thermodynamic properties are analysed as functions of the compressibility of the model, for values of the compressibility realizable in mesoscopic simulations with soft interactions and in actual polymeric materials.

Simulating charge transport in organic semiconductors and devices: a review

Charge transport simulation can be a valuable tool to better understand, optimise and design organic transistors (OTFTs), photovoltaics (OPVs), and light-emitting diodes (OLEDs). This review presents an overview of common charge transport and device models; namely drift-diffusion, master equation, mesoscale kinetic Monte Carlo and quantum chemical Monte Carlo, and a discussion of the relative merits of each. This is followed by a review of the application of these models as applied to charge transport in organic semiconductors and devices, highlighting in particular the insights made possible by modelling. The review concludes with an outlook for charge transport modelling in organic electronics.

Theoretical Study of the Charge-Transfer State Separation within Marcus Theory: The C60-Anthracene Case Study

We study, within Marcus theory, the possibility of the charge-transfer (CT) state splitting at organic interfaces and a subsequent transport of the free charge carriers to the electrodes. As a case study we analyze model anthracene-C60 interfaces. Kinetic Monte Carlo (KMC) simulations on the cold CT state were performed at a range of applied electric fields, and with the fields applied at a range of angles to the interface to simulate the action of the electric field in a bulk heterojunction (BHJ) interface. The results show that the inclusion of polarization in our model increases CT state dissociation and charge collection. The effect of the electric field on CT state splitting and free charge carrier conduction is analyzed in detail with and without polarization. Also, depending on the relative orientation of the anthracene and C60 molecules at the interface, CT state splitting shows different behavior with respect to both applied field strength and applied field angle. The importance of the hot CT in helping the charge carrier dissociation is also analyzed in our scheme.

Charge transport network dynamics in molecular aggregates

Due to the nonperiodic nature of charge transport in disordered systems, generating insight into static charge transport networks, as well as analyzing the network dynamics, can be challenging. Here, we apply time-dependent network analysis to scrutinize the charge transport networks of two representative molecular semiconductors: a rigid n-type molecule, perylenediimide, and a flexible p-type molecule, [Formula: see text] Simulations reveal the relevant timescale for local transfer integral decorrelation to be [Formula: see text]100 fs, which is shown to be faster than that of a crystalline morphology of the same molecule. Using a simple graph metric, global network changes are observed over timescales competitive with charge carrier lifetimes. These insights demonstrate that static charge transport networks are qualitatively inadequate, whereas average networks often overestimate network connectivity. Finally, a simple methodology for tracking dynamic charge transport properties is proposed.

P3HT:DiPBI bulk heterojunction solar cells: morphology and electronic structure probed by multiscale simulation and UV/vis spectroscopy

The effect of different annealing protocols on the morphology and light absorption of a P3HT:DiPBI mixture is studied by theory and experiment.

The Next Breakthrough for Organic Photovoltaics?

While the intense focus on energy level tuning in organic photovoltaic materials has afforded large gains in device performance, we argue here that strategies based on microstructural/morphological control are at least as promising in any rational design strategy. In this work, a meta-analysis of ∼150 bulk heterojunction devices fabricated with different materials combinations is performed and reveals strong correlations between power conversion efficiency and morphology-dominated properties (short-circuit current, fill factor) and surprisingly weak correlations between efficiency and energy level positioning (open-circuit voltage, enthalpic offset at the interface, optical gap). While energy level positioning should in principle provide the theoretical maximum efficiency, the optimization landscape that must be navigated to reach this maximum is unforgiving. Thus, research aimed at developing understanding-based strategies for more efficient optimization of an active layer microstructure and morphology are likely to be at least as fruitful.

Design rules for charge-transport efficient host materials for phosphorescent organic light-emitting diodes

The use of blue phosphorescent emitters in organic light-emitting diodes (OLEDs) imposes demanding requirements on a host material. Among these are large triplet energies, the alignment of levels with respect to the emitter, the ability to form and sustain amorphous order, material processability, and an adequate charge carrier mobility. A possible design strategy is to choose a π-conjugated core with a high triplet level and to fulfill the other requirements by using suitable substituents. Bulky substituents, however, induce large spatial separations between conjugated cores, can substantially reduce intermolecular electronic couplings, and decrease the charge mobility of the host. In this work we analyze charge transport in amorphous 2,8-bis(triphenylsilyl)dibenzofuran, an electron-transporting material synthesized to serve as a host in deep-blue OLEDs. We show that mesomeric effects delocalize the frontier orbitals over the substituents recovering strong electronic couplings and lowering reorganization energies, especially for electrons, while keeping energetic disorder small. Admittance spectroscopy measurements reveal that the material has indeed a high electron mobility and a small Poole-Frenkel slope, supporting our conclusions. By linking electronic structure, molecular packing, and mobility, we provide a pathway to the rational design of hosts with high charge mobilities.

Simulations of nematic homopolymer melts using particle-based models with interactions expressed through collective variables

We develop a hybrid Monte Carlo approach for modelling nematic liquid crystals of homopolymer melts. The polymer architecture is described with a discrete worm-like chain model. A quadratic density functional accounts for the limited compressibility of the liquid, while an additional quadratic functional of the local orientation tensor of the segments captures the nematic ordering. The approach can efficiently address large systems parametrized according to volumetric and conformational properties, representative of real polymeric materials. The results of the simulations regarding the influence of the molecular weight on the isotropic-nematic transition are compared to predictions from a Landau-de Gennes free energy expansion. The formation of the nematic phase is addressed within Rouse-like dynamics, realized using the current model.

Microscopic Simulations of Charge Transport in Disordered Organic Semiconductors

Charge carrier dynamics in an organic semiconductor can often be described in terms of charge hopping between localized states. The hopping rates depend on electronic coupling elements, reorganization energies, and driving forces, which vary as a function of position and orientation of the molecules. The exact evaluation of these contributions in a molecular assembly is computationally prohibitive. Various, often semiempirical, approximations are employed instead. In this work, we review some of these approaches and introduce a software toolkit which implements them. The purpose of the toolkit is to simplify the workflow for charge transport simulations, provide a uniform error control for the methods and a flexible platform for their development, and eventually allow in silico prescreening of organic semiconductors for specific applications. All implemented methods are illustrated by studying charge transport in amorphous films of tris-(8-hydroxyquinoline)aluminum, a common organic semiconductor.

Density-functional based determination of intermolecular charge transfer properties for large-scale morphologies

Theoretical studies of charge transport in organic conducting systems pose a unique challenge since they must describe both extremely short-ranged and fast processes (charge tunneling) and extremely long-ranged and slow ones (molecular ordering). The description of the mobility of electrons and holes in the hopping regime relies on the determination of intermolecular hopping rates in large-scale morphologies. Using Marcus theory these rates can be calculated from intermolecular transfer integrals and on-site energies. Here we present a detailed computational study on the accuracy and efficiency of density-functional theory based approaches to the determination of intermolecular transfer integrals. First, it is demonstrated how these can be obtained from quantum-chemistry calculations by forming the expectation value of a dimer Fock operator with frontier orbitals of two neighboring monomers based on a projective approach. We then consider the prototypical example of one pair out of a larger morphology of tris(8-hydroxyquinolinato)aluminium (Alq(3)) and study the influence of computational parameters, e.g. the choice of basis sets, exchange-correlation functional, and convergence criteria, on the calculated transfer integrals. The respective results are compared in order to derive an optimal strategy for future simulations based on the full morphology.