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.

Development of hybrid coarse-grained atomistic models for rapid assessment of local structuring of polymeric semiconductors

Decades of work in the field of computational study of semiconducting polymers using atomistic models illustrate the challenges of generating equilibrated models for this class of materials. While adopting a coarse-grained model can be helpful, the process of developing a suitable model is particularly non-trivial and time-consuming for semiconducting polymers due to a large number of different interactions with some having an anisotropic nature. This work introduces a procedure for the rapid generation of a hybrid model for semiconducting polymers where atoms of secondary importance (those in the alkyl side chains) are transformed into coarse-grained beads to reduce the computational cost of generating an equilibrated structure. The parameters are determined from easy-to-equilibrate simulations of very short oligomers and the model is constructed to enable a very simple back-mapping procedure to reconstruct geometries with atomistic resolution. The model is illustrated for three related polymers containing DPP (diketopyrrolopyrrole) to evaluate the transferability of the potential across different families of polymers. The accuracy of the model, determined by comparison with the results of fully equilibrated simulations of the same material before and after back-mapping, is fully satisfactory for two out of the three cases considered. We noticed that accuracy can be determined very early in the workflow so that it is easy to assess when the deployment of this method is advantageous. The hybrid representation can be used to evaluate directly the electronic properties of structures sampled by the simulations.

Transfer Learned Designer Polymers For Organic Solar Cells

Organic photovoltaic (OPV) materials have been examined extensively over the past two decades for solar cell applications because of the potential for device flexibility, low-temperature solution processability, and negligible environmental impact. However, discovery of new candidate OPV materials, especially polymer-based electron donors, that demonstrate notable power conversion efficiencies (PCEs), is nontrivial and time-intensive exercise given the extensive set of possible chemistries. Recent progress in machine learning accelerated materials discovery has facilitated to address this challenge, with molecular line representations, such as Simplified Molecular-Input Line-Entry Systems (SMILES), gaining popularity as molecular fingerprints describing the donor chemical structures. Here, we employ a transfer learning based recurrent neural (LSTM) model, which harnesses the SMILES molecular fingerprints as an input to generate novel designer chemistries for OPV devices. The generative model, perfected on a small focused OPV data set, predicts new polymer repeat units with potentially high PCE. Calculations of the similarity coefficient between the known and the generated polymers corroborate the accuracy of the model predictability as a function of the underlying chemical specificity. The data-enabled framework is sufficiently generic for use in accelerated machine learned materials discovery for various chemistries and applications, mining the hitherto available experimental and computational data.

Elasto-morphology of P3HT:PCBM bulk heterojunction organic solar cells

Predicting the mechanical properties of organic semiconductors is important when using these materials in flexible electronics applications. For instance, knowledge of the mechanical and thermal stability of thin film organic solar cells (OSCs) is critical for the roll-to-roll production of photovoltaic devices and their use under various operating conditions. Here, we examine the thermal and elasto-mechanical properties of the conjugated donor polymer poly-(3-hexylthiophene) (P3HT) and the interpenetrating mixtures of P3HT and phenyl-C₆₁-butyric acid methyl (PCBM) ester bulk heterojunction (BHJ) active layers under the application of unidirectional tensile deformation using coarse-grained molecular dynamics (CGMD) simulations. The predictions are validated against previous experimental reports as well as with earlier modeling results derived using different intermolecular force fields. Our results reveal that PCBM molecules behave as anti-plasticizers when mixed with P3HT and tend to increase the tensile modulus and glass transition temperature, while decreasing the crack-onset strain relative to pure P3HT. The variations in the mechanical properties with the composition of the BHJ active layer suggest that, in the presence of small oligomers as additives in the BHJ, the P3HT:PCBM mixture resists the anti-plasticizing effect of PCBM molecules due to the low tensile modulus of the short polymer chains.

Manipulation of PBDT-DTNT:PCBM photoactive layers for a stability increment by core–shell and core–mantle–shell supramolecules

Two types of core–shell and core–mantle–shell supramolecules were designed based on grafted-CNTs and PBDT-DTNT chains and employed in the active layers of PBDT-DTNT:PC₇₁BM solar cells to stabilize morphology and performance.

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.

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.

Impact of Low Molecular Weight Poly(3-hexylthiophene)s as Additives in Organic Photovoltaic Devices

Despite tremendous progress in using additives to enhance the power conversion efficiency of organic photovoltaic devices, significant challenges remain in controlling the microstructure of the active layer, such as at internal donor-acceptor interfaces. Here, we demonstrate that the addition of low molecular weight poly(3-hexylthiophene)s (low-MW P3HT) to the P3HT/fullerene active layer increases device performance up to 36% over an unmodified control device. Low MW P3HT chains ranging in size from 1.6 to 8.0 kg/mol are blended with 77.5 kg/mol P3HT chains and [6,6]-phenyl C₆₁ butyric acid methyl ester (PCBM) fullerenes while keeping P3HT/PCBM ratio constant. Optimal photovoltaic device performance increases are obtained for each additive when incorporated into the bulk heterojunction blend at loading levels that are dependent upon additive MW. Small-angle X-ray scattering and energy-filtered transmission electron microscopy imaging reveal that domain sizes are approximately invariant at low loading levels of the low-MW P3HT additive, and wide-angle X-ray scattering suggests that P3HT crystallinity is unaffected by these additives. These results suggest that oligomeric P3HTs compatibilize donor-acceptor interfaces at low loading levels but coarsen domain structures at higher loading levels and they are consistent with recent simulations results. Although results are specific to the P3HT/PCBM system, the notion that low molecular weight additives can enhance photovoltaic device performance generally provides a new opportunity for improving device performance and operating lifetimes.

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.

Chain conformations and phase behavior of conjugated polymers

Conjugated polymers may play an important role in various emerging optoelectronic applications because they combine the chemical versatility of organic molecules and the flexibility, stretchability and toughness of polymers with semiconducting properties. Nevertheless, in order to achieve the full potential of conjugated polymers, a clear description of how their structure, morphology, and macroscopic properties are interrelated is needed. We propose that the starting point for understanding conjugated polymers includes understanding chain conformations and phase behavior. Efforts to predict and measure the persistence length have significantly refined our intuition of the chain stiffness, and have led to predictions of nematic-to-isotropic transitions. Exploring mixing between conjugated polymers and small molecules or other polymers has demonstrated tremendous advancements in attaining the needed properties for various optoelectronic devices. Current efforts continue to refine our knowledge of chain conformations and phase behavior and the factors that influence these properties, thereby providing opportunities for the development of novel optoelectronic materials based on conjugated polymers.

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.

Petascale Simulations of the Morphology and the Molecular Interface of Bulk Heterojunctions

Understanding how additives interact and segregate within bulk heterojunction (BHJ) thin films is critical for exercising control over structure at multiple length scales and delivering improvements in photovoltaic performance. The morphological evolution of poly(3-hexylthiophene) (P3HT) and phenyl-C61-butyric acid methyl ester (PCBM) blends that are commensurate with the size of a BHJ thin film is examined using petascale coarse-grained molecular dynamics simulations. Comparisons between two-component and three-component systems containing short P3HT chains as additives undergoing thermal annealing demonstrate that the short chains alter the morphology in apparently useful ways: they efficiently migrate to the P3HT/PCBM interface, increasing the P3HT domain size and interfacial area. Simulation results agree with depth profiles determined from neutron reflectometry measurements that reveal PCBM enrichment near substrate and air interfaces but a decrease in that PCBM enrichment when a small amount of short P3HT chains are integrated into the BHJ blend. Atomistic simulations of the P3HT/PCBM blend interfaces show a nonmonotonic dependence of the interfacial thickness as a function of number of repeat units in the oligomeric P3HT additive, and the thiophene rings orient parallel to the interfacial plane as they approach the PCBM domain. Using the nanoscale geometries of the P3HT oligomers, LUMO and HOMO energy levels calculated by density functional theory are found to be invariant across the donor/acceptor interface. These connections between additives, processing, and morphology at all length scales are generally useful for efforts to improve device performance.

Peculiarity of Two Thermodynamically-Stable Morphologies and Their Impact on the Efficiency of Small Molecule Bulk Heterojunction Solar Cells

Structural characteristics of the active layers in organic photovoltaic (OPV) devices play a critical role in charge generation, separation and transport. Here we report on morphology and structural control of p-DTS(FBTTh₂)₂:PC₇₁BM films by means of thermal annealing and 1,8-diiodooctane (DIO) solvent additive processing, and correlate it to the device performance. By combining surface imaging with nanoscale depth-sensitive neutron reflectometry (NR) and X-ray diffraction, three-dimensional morphologies of the films are reconstituted with information extending length scales from nanometers to microns. DIO promotes the formation of a well-mixed donor-acceptor vertical phase morphology with a large population of small p-DTS(FBTTh₂)₂ nanocrystals arranged in an elongated domain network of the film, thereby enhancing the device performance. In contrast, films without DIO exhibit three-sublayer vertical phase morphology with phase separation in agglomerated domains. Our findings are supported by thermodynamic description based on the Flory-Huggins theory with quantitative evaluation of pairwise interaction parameters that explain the morphological changes resulting from thermal and solvent treatments. Our study reveals that vertical phase morphology of small-molecule based OPVs is significantly different from polymer-based systems. The significant enhancement of morphology and information obtained from theoretical modeling may aid in developing an optimized morphology to enhance device performance for OPVs.

Electrode materials, thermal annealing sequences, and lateral/vertical phase separation of polymer solar cells from multiscale molecular simulations

The nanomorphologies of the bulk heterojunction (BHJ) layer of polymer solar cells are extremely sensitive to the electrode materials and thermal annealing conditions. In this work, the correlations of electrode materials, thermal annealing sequences, and resultant BHJ nanomorphological details of P3HT:PCBM BHJ polymer solar cell are studied by a series of large-scale, coarse-grained (CG) molecular simulations of system comprised of PEDOT:PSS/P3HT:PCBM/Al layers. Simulations are performed for various configurations of electrode materials as well as processing temperature. The complex CG molecular data are characterized using a novel extension of our graph-based framework to quantify morphology and establish a link between morphology and processing conditions. Our analysis indicates that vertical phase segregation of P3HT:PCBM blend strongly depends on the electrode material and thermal annealing schedule. A thin P3HT-rich film is formed on the top, regardless of bottom electrode material, when the BHJ layer is exposed to the free surface during thermal annealing. In addition, preferential segregation of P3HT chains and PCBM molecules toward PEDOT:PSS and Al electrodes, respectively, is observed. Detailed morphology analysis indicated that, surprisingly, vertical phase segregation does not affect the connectivity of donor/acceptor domains with respective electrodes. However, the formation of P3HT/PCBM depletion zones next to the P3HT/PCBM-rich zones can be a potential bottleneck for electron/hole transport due to increase in transport pathway length. Analysis in terms of fraction of intra- and interchain charge transports revealed that processing schedule affects the average vertical orientation of polymer chains, which may be crucial for enhanced charge transport, nongeminate recombination, and charge collection. The present study establishes a more detailed link between processing and morphology by combining multiscale molecular simulation framework with an extensive morphology feature analysis, providing a quantitative means for process optimization.