Understanding structure-mobility relations for perylene tetracarboxydiimide derivatives

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.

Multi-level aggregation of conjugated small molecules and polymers: from morphology control to physical insights

Aggregation of molecules is a multi-molecular phenomenon occurring when two or more molecules behave differently from discrete molecules due to their intermolecular interactions. Moving beyond single molecules, aggregation usually demonstrates evolutive or wholly emerging new functionalities relative to the molecular components. Conjugated small molecules and polymers interact with each other, resulting in complex solution-state aggregates and solid-state microstructures. Optoelectronic properties of conjugated small molecules and polymers are sensitively determined by their aggregation states across a broad range of spatial scales. This review focused on the aggregation ranging from molecular structure, intermolecular interactions, solution-state assemblies, and solid-state microstructures of conjugated small molecules and polymers. We addressed the importance of such aggregation in filling the gaps from the molecular level to device functions and highlighted the multi-scale structures and properties at different scales. From the view of multi-level aggregation behaviors, we divided the whole process from the molecule to devices into several parts: molecular design, solvation, solution-state aggregation, crystal engineering, and solid-state microstructures. We summarized the progress and challenges of relationships between optoelectronic properties and multi-level aggregation. We believe aggregation science will become an interdisciplinary research field and serves as a general platform to develop future materials with the desired functions.

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.

Visualizing the helical stacking of octahedral metallomesogens with a chiral core

A combination of grazing-incidence X-ray diffraction and molecular dynamics simulation studies led to the visualization of the stacking structure of a helical columnar liquid crystal formed by enantiopure octahedral metallomesogens with ΔΛ chirality. The helical structure was elucidated as a hybrid of two major proposed structures.

Interplay between Charge Carrier Mobility, Exciton Diffusion, Crystal Packing, and Charge Separation in Perylene Diimide-Based Heterojunctions

Two of the key parameters that characterize the usefulness of organic semiconductors for organic or hybrid organic/inorganic solar cells are the mobility of charges and the diffusion length of excitons. Both parameters are strongly related to the supramolecular organization in the material. In this work we have investigated the relation between the solid-state molecular packing and the exciton diffusion length, charge carrier mobility, and charge carrier separation yield using two perylene diimide (PDI) derivatives which differ in their substitution. We have used the time-resolved microwave photoconductivity technique and measured charge carrier mobilities of 0.32 and 0.02 cm2/(Vs) and determined exciton diffusion lengths of 60 and 18 nm for octyl- and bulky hexylheptyl-imide substituted PDIs, respectively. This diffusion length is independent of substrate type and aggregate domain size. The differences in charge carrier mobility and exciton diffusion length clearly reflect the effect of solid-state packing of PDIs on their optoelectronic properties and show that significant improvements can be obtained by effectively controlling the solid-state packing.

Perylene-Based Liquid Crystals as Materials for Organic Electronics Applications

Columnar phases formed by the stacking of disclike molecules with an intimate π-π overlap forms a 1D pathway for the anisotropic charge migration along the columns. Columnar phases have great potential in organic electronic devices to be utilized as active semiconducting layers in comparison to organic single crystals or amorphous polymers in terms of processability, ease of handling, and high charge carrier mobility. Intelligent molecular engineering of perylene and its derivatives provided access to tune the physical properties and self-assembly behavior. The columnar phase formed by perylene derivatives has great potential in the fabrication of organic electronic devices. There are several positions on the perylene molecule, which can be functionalized to tune its self-assembly, as well as optoelectronic properties. Thus, many liquid-crystalline molecules stabilizing the columnar phase, which are based on perylene tetraesters, perylene diester imides, and perylene bisimides, have been synthesized over the years. Their longitudinal and laterally extended derivatives, bay-substituted derivatives exhibiting a columnar phase, are reported. In addition, several liquid-crystalline oligomers and polymers based on perylene derivatives were also reported. All such modifications provide an option to tune the energy levels of frontier molecular orbitals with respect to the work function of the electrodes in devices and also the processability of such materials. In this feature article, we attempt to provide an overview of the molecular design developed to tune the applicable properties and self-assembly of perylene derivatives as well as recent developments related to their application in the fabrication of organic solar cells, organic light-emitting diodes, and organic field-effect transistors.

Computational Design of Two-Dimensional Perovskites with Functional Organic Cations

Two-dimensional (2D) halide perovskites are a class of materials in which 2D layers of perovskite are separated by large organic cations. Conventionally, the 2D perovskites incorporate organic cations as spacers, but these organic cations also offer a route to introduce specific functionality in the material. In this work, we demonstrate, by density functional theory calculations, that the introduction of electron withdrawing and electron donating molecules leads to the formation of localized states, either in the organic or the inorganic part. Furthermore, we show that the energy of the bands located in the organic and inorganic parts can be tuned independently. The organic cation levels can be tuned by changing the electron withdrawing/donating character, whereas the energy levels in the inorganic part can be modified by varying the number of inorganic perovskite layers. This opens a new window for the design of 2D perovskites with properties tuned for specific applications.

Introducing correlations into carrier transport simulations of disordered materials through seeded nucleation: impact on density of states, carrier mobility, and carrier statistics

Disorder in organic semiconductors has made it challenging to achieve performance gains; this is a result of the many competing and often nuanced mechanisms effecting charge transport. In this article, we attempt to illuminate one of these mechanisms in the hopes of aiding experimentalists in exceeding current performance thresholds. Using a heuristic exponential function, energetic correlation has been added to the Gaussian disorder model (GDM). The new model is grounded in the concept that energetic correlations can arise in materials without strong dipoles or dopants, but may be a result of an incomplete crystal formation process. The proposed correlation has been used to explain the exponential tail states often observed in these materials; it is also better able to capture the carrier mobility field dependence, commonly known as the Poole-Frenkel dependence, when compared to the GDM. Investigation of simulated current transients shows that the exponential tail states do not necessitate Montroll and Scher fits. Montroll and Scher fits occur in the form of two distinct power law curves that share a common constant in their exponent; they are clearly observed as linear lines when the current transient is plotted using a log-log scale. Typically, these fits have been found appropriate for describing amorphous silicon and other disordered materials which display exponential tail states. Furthermore, we observe the proposed correlation function leads to domains of energetically similar sites separated by boundaries where the site energies exhibit stochastic deviation. These boundary sites are found to be the source of the extended exponential tail states, and are responsible for high charge visitation frequency, which may be associated with the molecular turnover number and ultimately the material stability.

Intra-molecular Charge Transfer and Electron Delocalization in Non-fullerene Organic Solar Cells

Two types of electron acceptors were synthesized by coupling two kinds of electron-rich cores with four equivalent perylene diimides (PDIs) at the α-position. With fully aromatic cores, TPB and TPSe have π-orbitals spread continuously over the whole aromatic conjugated backbone, unlike TPC and TPSi, which contain isolated PDI units due to the use of a tetrahedron carbon or silicon linker. Density functional theory calculations of the projected density of states showed that the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for TPB are localized in separate regions of space. Further, the LUMO of TPB shows a greater contribution from the orbitals belonging to the connective core of the molecules than that of TPC. Overall, the properties of the HOMO and LUMO point at increased intra-molecular delocalization of negative charge carriers for TPB and TPSe than for TPC and TPSi and hence at a more facile intra-molecular charge transfer for the former. The film absorption and emission spectra showed evidences for the inter-molecular electron delocalization in TPB and TPSe, which is consistent with the network structure revealed by X-ray diffraction studies on single crystals of TPB. These features benefit the formation of charge transfer states and/or facilitate charge transport. Thus, higher electron mobility and higher charge dissociation probabilities under J_sc condition were observed in blend films of TPB:PTB7-Th and TPSe:PTB7-Th than those in TPC:PTB7-Th and TPSi:PTB7-Th blend films. As a result, the J_sc and fill factor values of 15.02 mA/cm², 0.58 and 14.36 mA/cm², 0.55 for TPB- and TPSe-based solar cell are observed, whereas those for TPC and TPSi are 11.55 mA/cm², 0.47 and 10.35 mA/cm², 0.42, respectively.

Effects of Structural and Energetic Disorders on Charge Transports in Crystal and Amorphous Organic Layers

Understanding charge transports in organic films is important for both fundamental science and practical applications. Here, contributions of off-diagonal (structural) and diagonal (energetic) disorders to charge transports were clarified using molecular-based multiscale simulation. These disorders, important for understanding charge transport in organic systems, are investigated by comparing crystal and amorphous aggregates of N,N'-diphenyl-N,N'-bis(1-naphthyl)-1,1'-biphenyl-4,4'-diamine (NPD). Although NPD has been used as a hole transport material, it also exhibits comparable electron mobility experimentally. The experimental mobility and its electric field dependence in amorphous layers were reasonably reproduced by the multiscale simulation, confirming the electron transport properties of NPD. We assumed that the structural disorder would lower mobilities; however, the mobilities were found to be independent of the degree of structural disorder. Energetic disorder markedly lowered charge mobility instead. Charge migration in crystals was dominated by maximum electronic coupling pairs, whereas small electronic coupling pairs significantly contributed to charge transport in amorphous aggregate.

Cooperative supramolecular polymerization of a perylene diimide derivative and its impact on electron-transporting properties

H-bonding-promoted supramolecular polymerization of a perylene diimide (PDI) building block and its impact on charge carrier mobility.

Novel multifunctionalized peryleneteracarboxylic/amine supramolecules for electrochemical assay

In this work, a series of novel multifunctionalized peryleneteracarboxylic supramolecules were synthesized based on hydrogen bonding interactions between 3,4,9,10-perylenetetracarboxylic acid (PTCA) and amines, which possess large specific surface area, good membrane-forming properties and high stability. Importantly, an interesting phenomenon was found in that these series of supramolecules could conciliate disorderly redox peaks of PTCA and result in a pair of well-defined redox peaks, which were able to act as redox carriers for charge-generation and electron-transportion. And the probable mechanism for this phenomenon was discussed for the first time in detail through the integration of theoretical with practical research. To further reveal the advantages of these novel multifunctionalized supramolecule nanomaterials, PTCA/triethylamine (PTCA/TEA) was chosen as the best candidate for a redox carrier to participate in a "signal-on" aptasensor for thrombin (TB) detection by employing Fe₃O₄ magnetic beads (MBs) as a good enzyme mimic to catalyze the PTCA/TEA for signal amplification. As a result, a wide linear detection range of 0.0001-50 nM is acquired with a relatively low detection limit of 0.05 pM. And the proposed aptasensor exhibited good specificity and acceptable reproducibility and stability. After all, the explorations between PTCA and amines would set up a meaningful basis in seeking multifunctionalized supramolecule nanomaterials based on PTCA for extending the application of PTCA in a wider range of fields, and exploring the essential reason for the referred peculiar phenomenon for PTCA.

A self-assembled lysinated perylene diimide film as a multifunctional material for neural interfacing

We report the design, synthesis and structure-property investigation of a new perylene diimide material (PDI-Lys) bearing lysine end substituents. Water processed films of PDI-Lys were prepared and their self-assembly, morphology and electrical properties in both inert and air environments were theoretically and experimentally investigated. With the aim of evaluating the potential of PDI-Lys as a biocompatible and functional neural interface for organic bioelectronic applications, its electrochemical impedance as well as the adhesion and viability properties of primary neurons on the PDI-Lys films were studied. By combining theoretical calculations and electrical measurements we show that due to conversion between neutral and zwitterionic anions, the PDI-Lys film conductivity increased significantly upon passing from air to an inert atmosphere, reaching a maximum value of 6.3 S m^-1. We also show that the PDI-Lys film allows neural cell adhesion and neuron differentiation and decreases up to 5 times the electrode/solution impedance in comparison to a naked gold electrode. The present study introduces an innovative, water processable conductive film usable in organic electronics and as a putative neural interface.

Theoretical insights on morphology and charge transport properties of two-dimensional N,N′-ditridecylperylene-3,4,9,10-tetra carboxylic diimide aggregates

An integrated computational approach, based on molecular dynamics and density functional theory, reveals an interplay between morphology, processing and charge transport properties in layered aggregates of PTCDI-C13.

Charge carrier mobility in organic molecular materials probed by electromagnetic waves

Charge carrier mobility is an essential parameter providing control over the performance of semiconductor devices fabricated using a variety of organic molecular materials. Recent design strategies toward molecular materials have been directed at the substitution of amorphous silicon-based semiconductors; accordingly, numerous measurement techniques have been designed and developed to probe the electronic conducting nature of organic materials bearing extremely wide structural variations in comparison with inorganic and/or metal-oxide semiconductor materials. The present perspective highlights the evaluation methodologies of charge carrier mobility in organic materials, as well as the merits and demerits of techniques examining the feasibility of organic molecules, crystals, and supramolecular assemblies in semiconductor applications. Beyond the simple substitution of amorphous silicon, we have attempted to address in this perspective the systematic use of measurement techniques for future development of organic molecular semiconductors.

Anisotropy of the n-type charge transport and thermal effects in crystals of a fluoro-alkylated naphthalene diimide: a computational investigation

The anisotropy of the n-type charge transport of a fluoro-alkylated naphthalene diimide is investigated in the framework of the non-adiabatic hopping mechanism. Charge transfer rate constants are computed within the Marcus-Levich-Jortner formalism including a single effective mode treated quantum-mechanically and are injected in a kinetic Monte Carlo scheme to propagate the charge carrier in the crystal. Charge mobilities are computed at room temperature with and without the influence of an electric field and are shown to compare very well with previous measurements in single-crystal devices which offer a superior substrate for testing molecular models of charge transport. Thermally induced dynamical effects are investigated by means of an integrated computational approach including molecular dynamics simulations coupled to quantum-chemical evaluation of electronic couplings. It is shown that charge transport occurs mainly in the b,c crystallographic plane with a major component along the c axis which implies an anisotropy factor in very good agreement with the observed value.

Tilt orientationally disordered hexagonal columnar phase of phthalocyanine discotic liquid crystals

The structures of the discotic liquid crystalline (LC) phase of metal-free octa-substituted phthalocyanine (Pc) derivatives were investigated using molecular dynamics (MD) simulations. Special attention was paid to the LC phase structure of the non-peripheral octa-hexyl substituted Pc-derivatives that were recently found to show very high carrier mobilities for the discotic LCs. We obtained spontaneous transition to the columnar hexagonal (Col_{h}) LC phase in a melting simulation from the crystal structure obtained using an x-ray diffraction study. In this simulated Col_{h} structure, the Pc-core normal vectors were tilted 47{∘} from the column axis in parallel within each column, but the tilting directions are disordered between columns. We also found that the inter-core distance was not as large as previously suggested (0.4-0.5 nm) but similar to the common value (0.36 nm). This may resolve the contradiction between the high carrier mobility of the non-peripheral substituted Pcs, because larger inter-core separations degrade the mobilities.

High charge carrier mobility and efficient charge separation in highly soluble perylenetetracarboxyl-diimides

In this communication we report on the synthesis and charge mobility of highly soluble perylenebisimid derivatives.

Order induced charge carrier mobility enhancement in columnar liquid crystal diodes

Discotic molecules comprising a rigid aromatic core and flexible side chains have been promisingly applied in OLEDs as self-organizing organic semiconductors. Due to their potentially high charge carrier mobility along the columns, device performance can be readily improved by proper alignment of columns throughout the bulk. In the present work, the charge mobility was increased by 5 orders of magnitude due to homeotropic columnar ordering induced by the boundary interfaces during thermal annealing in the mesophase. State-of-the-art diodes were fabricated using spin-coated films whose homeotropic alignment with formation of hexagonal germs was observed by polarizing optical microscopy. The photophysical properties showed drastic changes at the mesophase-isotropic transition, which is supported by the gain of order observed by X-ray diffraction. The electrical properties were investigated by modeling the current-voltage characteristics by a space-charge-limited current transport with a field dependent mobility.

Hierarchically structured microfibers of "single stack" perylene bisimide and quaterthiophene nanowires

Organic nanowires and microfibers are excellent model systems for charge transport in organic semiconductors under nanoscopic confinement and may be relevant for future nanoelectronic devices. For this purpose, however, the preparation of well-ordered organic nanowires with uniform lateral dimensions remains a challenge to achieve. Here, we used the self-assembly of oligopeptide-substituted perylene bisimides and quaterthiophenes to obtain well-ordered nanofibrils. The individual nanofibrils were investigated by spectroscopic and imaging methods, and the preparation of hierarchically structured microfibers of aligned nanofibrils allowed for a comprehensive structural characterization on all length scales with molecular level precision. Thus, we showed that the molecular chirality resulted in supramolecular helicity, which supposedly serves to suppress lateral aggregation. We also proved that, as a result, the individual nanofibrils comprised a single stack of the π-conjugated molecules at their core. Moreover, the conformational flexibility between the hydrogen-bonded oligopeptides and the π-π stacked chromophores gave rise to synergistically enhanced strong π-π interactions and hydrogen-bonding. The result is a remarkably tight π-π stacking inside the nanofibrils, irrespective of the electronic nature of the employed chromophores, which may render them suitable nanowire models to investigate one-dimensional charge transport along defined π-π stacks of p-type or n-type semiconductors.

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.

Comparison of the electronic structure of different perylene-based dye-aggregates

Aggregates of functionalized polycyclic aromatic molecules like perylene derivatives differ in important optoelectronic properties such as absorption and emission spectra or exciton diffusion lengths. Although those differences are well known, it is not fully understood if they are caused by variations in the geometrical orientation of the molecules within the aggregates, variations in the electronic structures of the dye aggregates or interplay of both. As this knowledge is of interest for the development of materials with optimized functionalities, we investigate this question by comparing the electronic structures of dimer systems of representative perylene-based chromophores. The study comprises dimers of perylene, 3,4,9,10-perylene tetracarboxylic acid bisimide (PBI), 3,4,9,10-perylene tetracarboxylic acid dianhydride (PTCDA), and diindeno perylene (DIP). Potential energy curves (PECs) and characters of those electronic states are investigated which determine the optoelectronic properties. The computations use the spin-component-scaled approximate coupled-cluster second-order method (SCS-CC2), which describes electronic states of predominately neutral excited (NE) and charge transfer (CT) character equally well. Our results show that the characters of the excited states change significantly with the intermolecular orientation and often represent significant mixtures of NE and CT characters. However, PECs and electronic structures of the investigated perylene derivatives are almost independent of the substitution patterns of the perylene core indicating that the observed differences in the optoelectronic properties mainly result from the geometrical structure of the dye aggregate. It also hints at the fact that optical properties can be computed from less-substituted model compounds if a proper aggregate geometry is chosen.

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.