Computationally Linking Molecular Features of Conjugated Polymers and Fullerene Derivatives to Bulk Heterojunction Morphology

Effect of Materials Parameters on the Shape of Face-On Lamellae in Semi-Conducting Polymers: Insights From Qualitative Theory

Polymer semiconductors frequently form crystals or mesophases with lamellae, that comprise alternating layers of stacked backbones and side chains. Controlling lamellar orientation in films is essential for obtaining efficient charge carrier transport. Herein, lamellar orientation is investigated in an application-relevant setup: lamellae assembled on a substrate that strongly favors face-on orientation, but exposed to a film surface that promotes orientation along an "easy" direction, other than face on. It is assumed that the face-on order propagates from the substrate, but the lamellae bend to reduce their surface energy. A qualitative free-energy model is developed. The deformation is investigated as a function of film thickness, effective Young modulus, anchoring coefficient, and easy direction at the free surface. The calculations highlight the importance of elastic constants - lamellae can substantially deform already when Young moduli are only an order of magnitude smaller than the values that are reported for crystals. Softer Young moduli are expected when lamellar assembly occurs in a non-solidified mesophase that can be an equilibrium or (more speculatively) a transient state prior to crystallization. The alternative scenario of a two-layered film is also evaluated, where edge-on and face-on grains form, respectively, at the free surface and substrate.

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.

PyThinFilm: Automated Molecular Dynamics Simulation Protocols for the Generation of Thin Film Morphologies

The performance of organic optoelectronic devices, such as organic light-emitting diodes (OLEDs) and organic solar cells (OSCs), is intrinsically related to the molecular-scale morphology of the thin films from which they are composed. However, the experimental characterization of morphology at the molecular level is challenging due to the often amorphous or at best semicrystalline nature of these films. Classical molecular modeling techniques, such as molecular dynamics (MD) simulation, are increasingly used to understand the relationship between morphology and the properties of thin-film devices. PyThinFilm (github.com/ATB-UQ/PyThinFilm) is an open-source Python package which allows fully automated MD simulations of thin film growth to be performed using vacuum and/or solution deposition processes. PyThinFilm utilizes the GROMACS simulation package in combination with interaction parameters from the Automated Topology Builder (atb.uq.edu.au). Here, PyThinFilm is described along with an overview of applications in which PyThinFilm has been used to study the thin films of organic semiconductor materials typically used in OLEDs and OSCs.

Mesoscopic Modeling of a Highly-Ordered Sanidic Polymer Mesophase and Comparison With Experimental Data

Board-shaped polymers form sanidic mesophases: assemblies of parallel lamellae of stacked polymer backbones separated by disordered side chains. Sanidics vary significantly with respect to polymer order inside their lamellae, making them “stepping stones” toward the crystalline state. Therefore, they are potentially interesting for studying crystallization and technological applications. Building on earlier mesoscopic models of the most disordered sanidics Σ_d, we focus on the other extreme, near-crystalline order, and develop a generic model that captures a highly ordered Σ_r mesophase. Polymers are described by generic hindered-rotation chains. Anisotropic nonbonded potentials, with strengths comparable to the thermal energy, mimic board-like monomer shapes. Lamellae equilibrated with Monte Carlo simulations, for a broad range of model parameters, have intralamellar order typical for Σ_r mesophases: periodically stacked polymers that are mutually registered along their backbones. Our mesophase shows registration on both monomer and chain levels. We calculate scattering patterns and compare with data published for highly ordered sanidic mesophases of two different polymers: polyesters and polypeptoids. Most of the generic structural features that were identified in these experiments are present in our model. However, our mesophase has correlations between chains located in different lamellae and is therefore closer to the crystalline state than the experimental samples.

The interplay of interfaces, supramolecular assembly, and electronics in organic semiconductors

Organic semiconductors, which include a diverse range of carbon-based small molecules and polymers with interesting optoelectronic properties, offer many advantages over conventional inorganic semiconductors such as silicon and are growing in importance in electronic applications. Although these materials are now the basis of a lucrative industry in electronic displays, many promising applications such as photovoltaics remain largely untapped. One major impediment to more rapid development and widespread adoption of organic semiconductor technologies is that device performance is not easily predicted from the chemical structure of the constituent molecules. Fundamentally, this is because organic semiconductor molecules, unlike inorganic materials, interact by weak non-covalent forces, resulting in significant structural disorder that can strongly impact electronic properties. Nevertheless, directional forces between generally anisotropic organic-semiconductor molecules, combined with translational symmetry breaking at interfaces, can be exploited to control supramolecular order and consequent electronic properties in these materials. This review surveys recent advances in understanding of supramolecular assembly at organic-semiconductor interfaces and its impact on device properties in a number of applications, including transistors, light-emitting diodes, and photovoltaics. Recent progress and challenges in computer simulations of supramolecular assembly and orientational anisotropy at these interfaces is also addressed.

Solution Processing Dependent Bulk Heterojunction Nanomorphology of P3HT/PCBM Thin Films

Mixtures of poly(3-hexyl-thiophene) (P3HT) and phenyl-C61-butyric acid methyl ester (PCBM) have been widely employed as donor and acceptor materials, respectively, for the active layer of the bulk heterojunction (BHJ) organic solar cells. Experiments are able to provide only limited insights on the dynamics of blend morphology of these organic materials because of the challenges in extracting microstructural characterization amidst the poor contrast in electron microscopy. We present results from coarse-grained molecular dynamics simulations (CGMD) describing the morphological evolution of P3HT/PCBM active layer under solution processing in chlorobenzene (CB). We examine the impact of various processing parameters such as weight ratio, degree of polymerization (DOP), thermal annealing, and preheating on the BHJ active layers using morphological characterizations from atomic trajectories. Simulated diffraction patterns are compared with experimental results of X-ray diffraction and Small Angle X-ray Scattering (SAXS). Both simulated scattering and experimental X-ray diffraction and X-ray scattering measurements reveal increase in crystallinity for P3HT upon annealing until PCBM weight fraction ∼50%. The solubility of PCBM being greater in CB than that of P3HT facilitates the phase separation of the polymer during early stages of solvent evaporation. An increase in the average size of the P3HT domain relative to the preannealed morphology, is due to phase segregation and crystallization of the polymer upon annealing. Percolation for PCBM remains unchanged until PCBM constitutes at least one-half of the composition. Although 1.0:2.0 weight ratio is predicted to be ideal for balanced charge transport, 1.0:1.0 weight ratio is the most beneficial of overall power conversion based on exciton generation and charge separation at the interface. DOP of P3HT molecules is another important design variable as larger P3HT molecules tend to entangle more often deteriorating molecular order of P3HT phase in the active layer. Preheating the ternary mixture of P3HT, PCBM, and CB modifies the structural order and morphology of the BHJ due to changes in PCBM diffusion into the P3HT phase.

Generic Model for Lamellar Self-Assembly in Conjugated Polymers: Linking Mesoscopic Morphology and Charge Transport in P3HT

We develop a generic coarse-grained model of soluble conjugated polymers, capable of describing their self-assembly into a lamellar mesophase. Polymer chains are described by a hindered-rotation model, where interaction centers represent entire repeat units, including side chains. We introduce soft anisotropic nonbonded interactions to mimic the potential of mean force between atomistic repeat units. The functional form of this potential reflects the symmetry of the molecular order in a lamellar mesophase. The model can generate both nematic and lamellar (sanidic smectic) molecular arrangements. We parametrize this model for a soluble conjugated polymer poly(3-hexylthiophene) (P3HT) and demonstrate that the simulated lamellar mesophase matches morphologies of low molecular weight P3HT, experimentally observed at elevated temperatures. A qualitative charge-transport model allows us to link local chain conformations and mesoscale order to charge transport. In particular, it shows how coarsening of lamellar domains and chain extension increase the charge carrier mobility. By modeling large systems and long chains, we can capture transport between lamellar layers, which is due to rare, but thermodynamically allowed, backbone bridges between neighboring layers.

Optimization and Validation of Efficient Models for Predicting Polythiophene Self-Assembly

We develop an optimized force-field for poly(3-hexylthiophene) (P3HT) and demonstrate its utility for predicting thermodynamic self-assembly. In particular, we consider short oligomer chains, model electrostatics and solvent implicitly, and coarsely model solvent evaporation. We quantify the performance of our model to determine what the optimal system sizes are for exploring self-assembly at combinations of state variables. We perform molecular dynamics simulations to predict the self-assembly of P3HT at ∼350 combinations of temperature and solvent quality. Our structural calculations predict that the highest degrees of order are obtained with good solvents just below the melting temperature. We find our model produces the most accurate structural predictions to date, as measured by agreement with grazing incident X-ray scattering experiments.

Structural Correlations and Percolation in Twisted Perylene Diimides Using a Simple Anisotropic Coarse-Grained Model

Large, twisted, and fused conjugated molecular architectures have begun to appear more prominently in the organic semiconductor literature. From a modeling perspective, such structures present a challenge to conventional simulation techniques; atomistic resolutions are computationally inefficient, while traditional isotropic coarse-grained models do not capture the inherent anisotropies of the molecules. In this work, we develop a simple coarse-grained model that explicitly incorporates the anisotropy of these molecular architectures, thereby providing a route toward analyzing π-stacking, and thus qualitative electronic structure, at a computationally efficient coarse-grained resolution. Our simple coarse-grained model maintains relative orientations of conjugated rings, as well as inter-ring dihedrals, that are critical for understanding electronic and excitonic transport in bulk systems. We apply this model to understand structural correlations in several recently synthesized perylene diimide (PDI)-based organic semiconductors. Twisted and nonplanar molecular architectures are found to promote amorphous morphologies while maintaining local π-stacking. A graph theoretical network analysis demonstrates that these twisted molecules are more likely to form percolating three-dimensional pathways for charge motion than strictly planar molecules, which show connectivity in only one dimension.

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.

Photoluminescence Properties of Polymorphic Modifications of Low Molecular Weight Poly(3-hexylthiophene)

The structural and photoluminescence (PL) properties of thin films of poly(3-hexylthophene) (P3HT) with molecular weights (MWs) of 3000 and 13,300 have been investigated. Although high MW P3HT always self-organizes into one packing structure (form I), low MW P3HT forms two different packing structures (forms I and II) depending on the fabrication conditions. In this work, several fabrication techniques have been examined to obtain form II samples with little inclusion of a form I component. It is found that drop-cast thin films of low MW P3HT (form II) exhibit a PL spectrum that is different from that of form I and does not contain the form I component. The PL spectrum can thus be attributed to form II. The differences in PL properties between forms I and II can be understood in terms of weakened interchain interactions due to the longer interchain distance in form II.

The correspondence between the conformational and chromophoric properties of amorphous conjugated polymers in mesoscale condensed systems

For π-conjugated polymers, the notion of spectroscopic units or "chromophores" provides illuminating insights into the experimentally observed absorption/emission spectra and the mechanisms of energy/charge transfer. To date, however, no statistical analysis has revealed a direct correspondence between chromophoric and conformational properties-with the latter being fundamental to polymer semiconductors. Herein, we propose a "persistence length" calculation to re-evaluate chain conformation over a full conjugation length. The mesoscale condensed systems of MEH-PPV and MEH-PPV/C₆₀ hybrid (system size ∼10 × 10 × 10 nm³) are utilized as two prototypical model systems, along with a full range of segmental lengths (2-20-mer) and five lowest singlet excited states to hint at the generality of the features presented. We demonstrate, for the first time, that two properly re-defined conformational factors that characterize chain folding and planarity, respectively, capture excellently the population distribution of chromophores in both systems investigated. In contrast, the conventional strategy of utilizing two adjacent monomer units to characterize (local) chain conformation results in only an inconspicuous correlation between the two, as previously reported. It is further shown that chain folding-and not chain planarity-is more relevant in capturing the associated oscillator strength for the first excited state, where the transient dipole moments are known to align with the chain conformation, although the corresponding excitation energy and exciton size seem relatively unaffected. The observed effects of C₆₀ on the MEH-PPV adsorption spectra also agree with recent experimental trends. Overall, the present findings are expected to aid future multiscale computer simulations and spectroscopy-data interpretations for polymer semiconductors and their hybrid systems.

Bulk Heterojunction Morphologies with Atomistic Resolution from Coarse-Grain Solvent Evaporation Simulations

Control over the morphology of the active layer of bulk heterojunction (BHJ) organic solar cells is paramount to achieve high-efficiency devices. However, no method currently available can predict morphologies for a novel donor–acceptor blend. An approach which allows reaching relevant length scales, retaining chemical specificity, and mimicking experimental fabrication conditions, and which is suited for high-throughput schemes has been proven challenging to find. Here, we propose a method to generate atom-resolved morphologies of BHJs which conforms to these requirements. Coarse-grain (CG) molecular dynamics simulations are employed to simulate the large-scale morphological organization during solution-processing. The use of CG models which retain chemical specificity translates into a direct path to the rational design of donor and acceptor compounds which differ only slightly in chemical nature. Finally, the direct retrieval of fully atomistic detail is possible through backmapping, opening the way for improved quantum mechanical calculations addressing the charge separation mechanism. The method is illustrated for the poly(3-hexyl-thiophene) (P3HT)–phenyl-C61-butyric acid methyl ester (PCBM) mixture, and found to predict morphologies in agreement with experimental data. The effect of drying rate, P3HT molecular weight, and thermal annealing are investigated extensively, resulting in trends mimicking experimental findings. The proposed methodology can help reduce the parameter space which has to be explored before obtaining optimal morphologies not only for BHJ solar cells but also for any other solution-processed soft matter device.

Enhanced Computational Sampling of Perylene and Perylothiophene Packing with Rigid-Body Models

Molecular simulations have the potential to advance the understanding of how the structure of organic materials can be engineered through the choice of chemical components but are limited by computational costs. The computational costs can be significantly lowered through the use of modeling approximations that capture the relevant features of a system, while lowering algorithmic complexity or by decreasing the degrees of freedom that must be integrated. Such methods include coarse-graining techniques, approximating long-range electrostatics with short-range potentials, and the use of rigid bodies to replace flexible bonded constraints between atoms. To understand whether and to what degree these techniques can be leveraged to enhance the understanding of planar organic molecules, we investigate the morphologies predicted by molecular dynamic simulations using simplified molecular models of perylene and perylothiophene. Approximately, 10 000 wall-clock hours of graphics processing unit-accelerated simulations are performed using both rigid and flexible models to test their efficiency and predictive capability with the two chemistries. We characterize the 1191 resulting morphologies using simulated X-ray diffraction and cluster analysis to distinguish structural transitions, summarized by four phase diagrams. We find that the morphologies generated by the rigid model of perylene and perylothiophene match with those generated by the flexible model. We find that ordered, hexagonally packed columnar phases are thermodynamically favored over a wide range of densities and temperatures for both molecules, in qualitative agreement with experiments. Furthermore, we find the rigid model to be more computationally efficient for both molecules, providing more samples per second and shorter times to equilibrium. Owing to the structural accuracy and improved computational efficiency of modeling polyaromatic groups as rigid bodies, we recommend this modeling choice for enhancing the sampling in polyaromatic molecular simulations.

Addition of P3HT-grafted Silica nanoparticles improves bulk-heterojunction morphology in P3HT-PCBM blends

We present molecular dynamics simulations of a ternary blend of P3HT, PCBM and P3HT-grafted silica nanoparticles (SiNP) for applications in polymer-based solar cells. Using coarse-grained models, we study the effect of SiNP on the spatial arrangement of PCBM in P3HT. Our results suggest that addition of SiNP not only alters the morphology of PCBM clusters but also improves the crystallinity of P3HT. We exploit the property of grafted SiNP to self-assemble into a variety of anisotropic structures and the tendency of PCBM to preferentially adhere to SiNP surface, due to favorable interactions, to achieve morphologies with desirable characteristics for the active layer, including domain size, crystallinity of P3HT, and elimination of isolated islands of PCBM. As the concentration of SiNP increases, the number of isolated PCBM molecules decreases, which in turn improves the crystallinity of P3HT domains. We also observe that by tuning the grafting parameters of SiNP, it is possible to achieve structures ranging from cylindrical to sheets to highly interconnected network of strings. The changes brought about by addition of SiNP shows a promising potential to improve the performance of these materials when used as active layers in organic photovoltaics.

Morphology and Performance of Polymer Solar Cell Characterized by DPD Simulation and Graph Theory

The morphology of active layers in the bulk heterojunction (BHJ) solar cells is critical to the performance of organic photovoltaics (OPV). Currently, there is limited information for the morphology from transmission electron microscopy (TEM) techniques. Meanwhile, there are limited approaches to predict the morphology /efficiency of OPV. Here we use Dissipative Particle Dynamics (DPD) to determine 3D morphology of BHJ solar cells and show DPD to be an efficient approach to predict the 3D morphology. Based on the 3D morphology, we estimate the performance indicator of BHJ solar cells by using graph theory. Specifically, we study poly (3-hexylthiophene)/[6, 6]-phenyl-C₆₁butyric acid methyl ester (P3HT/PCBM) BHJ solar cells. We find that, when the volume fraction of PCBM is in the region 0.4 ∼ 0.5, P3HT/PCBM will show bi-continuous morphology and optimum performance, consistent with experimental results. Further, the optimum temperature (413 K) for the morphology and performance of P3HT/PCBM is in accord with annealing results. We find that solvent additive plays a critical role in the desolvation process of P3HT/PCBM BHJ solar cell. Our approach provides a direct method to predict dynamic 3D morphology and performance indicator for BHJ solar cells.

Combined deterministic-stochastic framework for modeling the agglomeration of colloidal particles

We present a multiscale model, based on molecular dynamics (MD) and kinetic Monte Carlo (kMC), to study the aggregation driven growth of colloidal particles. Coarse-grained molecular dynamics (CGMD) simulations are employed to detect key agglomeration events and calculate the corresponding rate constants. The kMC simulations employ these rate constants in a stochastic framework to track the growth of the agglomerates over longer time scales and length scales. One of the hallmarks of the model is a unique methodology to detect and characterize agglomeration events. The model accounts for individual cluster-scale effects such as change in size due to aggregation as well as local molecular-scale effects such as changes in the number of neighbors of each molecule in a colloidal cluster. Such definition of agglomeration events allows us to grow the cluster to sizes that are inaccessible to molecular simulations as well as track the shape of the growing cluster. A well-studied system, comprising fullerenes in NaCl electrolyte solution, was simulated to validate the model. Under the simulated conditions, the agglomeration process evolves from a diffusion limited cluster aggregation (DLCA) regime to percolating cluster in transition and finally to a gelation regime. Overall the data from the multiscale numerical model shows good agreement with existing theory of colloidal particle growth. Although in the present study we validated our model by specifically simulating fullerene agglomeration in electrolyte solution, the model is versatile and can be applied to a wide range of colloidal systems.

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.

Influence of Molecular Conformations and Microstructure on the Optoelectronic Properties of Conjugated Polymers

It is increasingly obvious that the molecular conformations and the long-range arrangement that conjugated polymers can adopt under various experimental conditions in bulk, solutions or thin films, significantly impact their resulting optoelectronic properties. As a consequence, the functionalities and efficiencies of resulting organic devices, such as field-effect transistors, light-emitting diodes, or photovoltaic cells, also dramatically change due to the close structure/property relationship. A range of structure/optoelectronic properties relationships have been investigated over the last few years using various experimental and theoretical methods, and, further, interesting correlations are continuously revealed by the scientific community. In this review, we discuss the latest findings related to the structure/optoelectronic properties interrelationships that exist in organic devices fabricated with conjugated polymers in terms of charge mobility, absorption, photoluminescence, as well as photovoltaic properties.

Phase behavior and complex crystal structures of self-assembled tethered nanoparticle telechelics

Motivated by growing interest in the self-assembly of nanoparticles for applications such as photonics, organic photovoltaics, and DNA-assisted designer crystals, we explore the phase behavior of tethered spherical nanoparticles. Here, a polymer tether is used to geometrically constrain a pair of nanoparticles creating a tethered nanoparticle "telechelic". Using simulation, we examine how varying architectural features, such as the size ratio of the two end-group nanospheres and the length of the flexible tether, affects the self-assembled morphologies. We demonstrate not only that this hybrid building block maintains the same phase diversity as linear triblock copolymers, allowing for a variety of nanoparticle materials to replace polymer blocks, but also that new structures not previously reported are accessible. Our findings imply a robust underlying ordering mechanism is common among these systems, thus allowing flexibility in synthesis approaches to achieve a target morphology.

Theory and simulation studies of effective interactions, phase behavior and morphology in polymer nanocomposites

Polymer nanocomposites are a class of materials that consist of a polymer matrix filled with inorganic/organic nanoscale additives that enhance the inherent macroscopic (mechanical, optical and electronic) properties of the polymer matrix. Over the past few decades such materials have received tremendous attention from experimentalists, theoreticians, and computational scientists. These studies have revealed that the macroscopic properties of polymer nanocomposites depend strongly on the (microscopic) morphology of the constituent nanoscale additives in the polymer matrix. As a consequence, intense research efforts have been directed to understand the relationships between interactions, morphology, and the phase behavior of polymer nanocomposites. Theory and simulations have proven to be useful tools in this regard due to their ability to link molecular level features of the polymer and nanoparticle additives to the resulting morphology within the composite. In this article we review recent theory and simulation studies, presenting briefly the methodological developments underlying PRISM theories, density functional theory, self-consistent field theory approaches, and atomistic and coarse-grained molecular simulations. We first discuss the studies on polymer nanocomposites with bare or un-functionalized nanoparticles as additives, followed by a review of recent work on composites containing polymer grafted or functionalized nanoparticles as additives. We conclude each section with a brief outlook on some potential future directions.