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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Impact of Linker Engineering in Core‐Linked Dimeric Acceptors for High‐Performance Organic Solar Cells

Abstract The dimerization of small molecule acceptors (SMAs) is a promising strategy for enhancing the long‐term stability and power conversion efficiency (PCE) of organic solar cells (OSCs). However, the reported DSMAs are primarily limited to end‐linked molecular configurations, highlighting the need for further exploration of various dimer architectures. Herein, the development of two distinct core‐linked dimerized SMAs (DYF‐V and DYF‐E) are reported with tailored linker structures (vinylene and ethynyl, respectively), achieving high‐performance OSCs (PCE = 18.53%). Interestingly, a subtle change in the linker structures results in markedly different molecular properties and photovoltaic performances of the dimer acceptors. DYF‐E with an ethynyl linker exhibits more twisted backbone conformation and mitigated aggregation property compared to DYF‐V, inducing desirable blend morphologies with a polymer donor including high crystallinity, face‐on oriented packing structures, and well‐intermixed domains. Thus, the DYF‐E‐based OSCs exhibit a high PCE (17.02%), which significantly outperforms the DYF‐V‐based OSCs (PCE = 9.98%). Furthermore, the ternary OSCs based on DYF‐E achieve a higher PCE of 18.53%. Thus, this study highlights the significance of selecting an appropriate linker in core‐linked dimerized SMAs for producing high‐performance OSCs.

Oh, Shinbee↗
DOE OSTI2020

Precise Control of Phase Separation Enables 12% Efficiency in All Small Molecule Solar Cells

Abstract Compared to conjugated polymers, small‐molecule organic semiconductors present negligible batch‐to‐batch variations, but presently provide comparatively low power conversion efficiencies (PCEs) in small‐molecular organic solar cells (SM‐OSCs), mainly due to suboptimal nanomorphology. Achieving precise control of the nanomorphology remains challenging. Here, two new small‐molecular donors H13 and H14 , created by fluorine and chlorine substitution of the original donor molecule H11 , are presented that exhibit a similar or higher degree of crystallinity/aggregation and improved open‐circuit voltage with IDIC‐4F as acceptor. Due to kinetic and thermodynamic reasons, H13 ‐based blend films possess relatively unfavorable molecular packing and morphology. In contrast, annealed H14 ‐based blends exhibit favorable characteristics, i.e., the highest degree of aggregation with the smallest paracrystalline π–π distortions and a nanomorphology with relatively pure domains, all of which enable generating and collecting charges more efficiently. As a result, blends with H13 give a similar PCE (10.3%) as those made with H11 (10.4%), while annealed H14 ‐based SM‐OSCs have a significantly higher PCE (12.1%). Presently this represents the highest efficiency for SM‐OSCs using IDIC‐4F as acceptor. The results demonstrate that precise control of phase separation can be achieved by fine‐tuning the molecular structure and film formation conditions, improving PCE and providing guidance for morphology design.

Bin, Haijun↗
DOE OSTI2026

Achieving 20.1% Efficiency in Organic Solar Cells Through Interconnected Fibrillar Networks via Local Molecular Stacking

ABSTRACT The performance of organic solar cells (OSCs) is governed by how molecular packing evolves into interconnected networks that facilitate exciton dissociation and charge transport. Using an all‐small‐molecule blend DR3TSBDT:Y6 as a model system, we study how local molecular stacking evolves into performance‐relevant morphology during solvent vapor annealing (SVA) and subsequent thermal annealing (TA). SVA promotes end‐to‐end stacking of amorphous acceptors to form interconnected fibrils, while TA compacts inter‐fibril spacing without disrupting favorable local order. Such molecular‐to‐morphological refinements broaden light absorption, enhance charge transport, and markedly improve device efficiency. Extending this approach to additional blend systems (D18:Y6, D18:L8‐BO, and DR3TSBDT:L8‐BO) yields similar structural evolution and performance gains, with the D18:L8‐BO system achieving up to 20.10% PCE. Our study establishes control over local stacking in amorphous acceptors into fibrillar networks as a general and effective route to realize high‐performance OSCs.

Wu, Junying↗
DOE OSTI2022

Improving the performance of PM6 donor polymer by random ternary copolymerization of BDD and DTBT segments

Developing high-performance wide bandgap polymer donors to match the rapidly growing non-fullerene small molecule acceptors (NF-SMAs) is of great importance to further improve the photovoltaic performances of organic solar cells (OSCs). PM6 and D18 are two leading wide bandgap donor polymers, but their performances are highly sensitive to the molecular weights, which have distinct impact on the morphology and thereby the charge generation and recombination processes. Here, in this work, we reported the random ternary copolymerization of PM6 and D18 segments to develop random terpolymers with finely tuned photoelectronic properties and optimized blend morphology for high-performance OSCs. The resulting random terpolymers (PMD-5, PMD-10, PMD-15 and PMD-20) exhibited finely tuned absorptions, energy levels and blend morphology. The optimal morphology of PMD-15:L8-BO contributed to the fast exciton diffusion and dissociation, efficient charge extraction with suppressed recombination. Thus, the power conversion efficiency was improved from 17.22% of the control PM6 devices and 17.47% of the control D18 devices to 18.12% of PMD-15 based devices, which is the top performance of random terpolymers. Moreover, the PMD-15 exhibited much higher batch-to-batch reproducibility at a broad molecular weight range than that of PM6 and D18, showing promising for practical applications.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Correlation of Dimer-Linker-Induced Conformational Lock with Nonradiative Energy Loss in Organic Solar Cells

The efficiencies of dimer-based devices still lag those of their small molecule-based counterparts. This is primarily due to the considerable dihedrals in the dimer skeleton, which compromises the molecular packing, thus influencing the charge generation and nonradiative voltage loss (ΔV oc,nr ). Herein, we developed two dimeric acceptors with varied π-linkers to investigate the influence of linker-induced conformational lock on ΔV oc,nr . We find that the helically lapped O-shaped dimer delivers better intermolecular packing than the planar S-shaped one that incorporates a bulkier π-linker. However, its planar skeleton is instead more favorable for forming a compact and ordered stacking with the host acceptor in ternary blend. This possibly promotes exciton dissociation, thus reducing the nonradiative decay of excited states. Moreover, its longer exciton lifetime could offer additional charge-transfer channels. Finally, these contributions effectively minimize ΔV oc,nr to 0.195 eV, while delivering a high efficiency approaching 20% in the derived ternary device.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A Top-Down Strategy to Engineer ActiveLayer Morphology for Highly Efficient and Stable All-Polymer Solar Cells

A major challenge hindering the further development of all-polymer solar cells (all-PSCs) employing polymerized small-molecule acceptors is the relatively low fill factor (FF) due to the difficulty in controlling the active-layer morphology. The issues typically arise from oversized phase separation resulting from the thermodynamically unfavorable mixing between two macromolecular species, and disordered molecular orientation/packing of highly anisotropic polymer chains. Herein, a facile top-down controlling strategy to engineer the morphology of all-polymer blends is developed by leveraging the layer-by-layer (LBL) deposition. Optimal intermixing of polymer components can be achieved in the two-step process by tuning the bottom-layer polymer swelling during top-layer deposition. Consequently, both the molecular orientation/packing of the bottom layer and the molecular ordering of the top layer can be optimized with a suitable top-layer processing solvent. A favorable morphology with gradient vertical composition distribution for efficient charge transport and extraction is therefore realized, affording a high all-PSC efficiency of 17.0% with a FF of 76.1%. The derived devices also possess excellent long-term thermal stability and can retain >90% of their initial efficiencies after being annealed at 65 °C for 1300 h. In conclusion, these results validate the distinct advantages of employing an LBL processing protocol to fabricate high-performance all-PSCs.

14 SOLAR ENERGY↗
DOE OSTI2024

Identification and characterization of the low molecular mass ferredoxins involved in central metabolism in Heliomicrobium modesticaldum

The homodimeric Type I reaction center (RC) from Heliomicrobium modesticaldum lacks the PsaC subunit found in Photosystem I and instead uses the interpolypeptide [4Fe–4S] cluster F X as the terminal electron acceptor. Our goal was to identify which of the small mobile dicluster ferredoxins encoded by the H. modesticaldum genome are capable of accepting electrons from the heliobacterial RC (HbRC) and pyruvate:ferredoxin oxidoreductase (PFOR), a key metabolic enzyme. Analysis of the genome revealed seven candidates: HM1_1462 (PshB1), HM1_1461 (PshB2), HM1_2505 (Fdx3), HM1_0869 (FdxB), HM1_1043, HM1_0357, and HM1_2767. Heterologous expression in Escherichia coli and studies using time-resolved optical spectroscopy revealed that only PshB1, PshB2, and Fdx3 are capable of accepting electrons from the HbRC and PFOR. Modeling studies using AlphaFold show that only PshB1, PshB2, and Fdx3 should be capable of docking on PFOR at a positively charged patch that overlays a surface-proximal [4Fe–4S] cluster. Proteomic analysis of wild-type and gene deletion strains ΔpshB1, ΔpshB2, ΔpshB1pshB2, and Δfdx3 grown under nitrogen-replete conditions revealed that Fdx3 is undetectable in the wild-type, ΔpshB1, and Δfdx3 strains, but it is present in the ΔpshB2 and ΔpshB1pshB2 strains, implying that Fdx3 may substitute for PshB2. When grown under nitrogen-deplete conditions, Fdx3 is present in the wild-type and all deletion strains except for Δfdx3. None of the knockout strains demonstrated significant impairment during chemotrophic dark growth on pyruvate, photoheterotrophic light growth on pyruvate, or phototrophic growth on acetate+CO 2 , indicating a high degree of redundancy among these three electron transfer proteins. As a result, loss of both PshB1 and PshB2, but not FdxB, resulted in poor growth under N 2 -fixing conditions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Eliminating the Burn‐in Loss of Efficiency in Organic Solar Cells by Applying Dimer Acceptors as Supramolecular Stabilizers

Abstract The meta‐stable active layer morphology of organic solar cells (OSCs) is identified as the main cause of the rapid burn‐in loss of power conversion efficiency (PCE) during long‐term device operation. However, effective strategies to eliminate the associated loss mechanisms from the initial stage of device operation are still lacking, especially for high‐efficiency material systems. Herein, the introduction of molecularly engineered dimer acceptors with adjustable thermal transition properties into the active layer of OSCs to serve as supramolecular stabilizers for regulating the thermal transitions and optimizing the crystallization of the absorber composites is reported. By establishing intimate π‐π interactions with small‐molecule acceptors, these stabilizers can effectively reduce the trap‐state density (N t ) in the devices to achieve excellent PCEs over 19%. More importantly, the lowN t associated with an initially optimized morphology can be maintained under external stresses to significantly reduce the PCE burn‐in loss in devices. This research reveals a judicious approach to improving OPV stability by establishing a comprehensive correlation between material properties, active‐layer morphology, and device performance, for developing burn‐in‐free OSCs.

Chemistry↗
DOE OSTI2021

Small molecule dye for molecular imaging and photothermal therapy

Disclosed is a small molecule dye for use in imaging in the near-infrared window, namely between 1000 nm-1700 nm wavelength. The present dyes are also useful for photoacoustic imaging and photothermal therapy. The dyes have a structure of a D-A-D (donor-acceptor-donor) fluorescent compound core and side chains rendering the compounds water soluble and easily conjugated to hydrophilic polymers and/or targeting ligands. Further disclosed is compound, CH1055 that can be PEGylated, conjugated to a targeting ligand, or conjugated to taurine. Key steps utilized to assemble the core structure of the target included a cross-Suzuki coupling reaction, iron reduction and N-thionylaniline induced ring closure. Four carboxylic acid groups were introduced into the donor-acceptor-donor (D-A-D) type fluorescent compound to impart a certain aqueous solubility and to allow facile conjugation to targeting ligands.

Cheng, Zhen↗
DOE OSTI2022

Catalytic Chemical Recycling of Post-Consumer Polyethylene

Among commercial plastics, polyolefins are the most widely produced worldwide but have limited recyclability. Here, we report a chemical recycling route for the conversion of post-consumer high-density polyethylene (HDPE) into telechelic macromonomers suitable for circular reprocessing. Unsaturation was introduced into HDPE by catalytic dehydrogenation using an Ir-POCOP catalyst without an alkene acceptor. Cross-metathesis with 2-hydroxyethyl acrylate followed by hydrogenation transformed the partially unsaturated HDPE into telechelic macromonomers. The direct repolymerization of the macromonomers gave a brittle material due to the low overall weight-average molecular weight. Aminolysis of telechelic macromonomers with a small amount of diethanolamine increased the overall functionality. The resulting macromonomers were repolymerized through transesterification to generate a polymer with comparable mechanical properties to the starting post-consumer HDPE waste. Finally, depolymerization of the repolymerized material catalyzed by an organic base regenerated the telechelic macromonomers, thereby allowing waste polyethylene materials to enter a chemical recycling pathway.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A butterfly-shaped acceptor with rigid skeleton and unique assembly enables both efficient organic photovoltaics and high-speed organic photodetectors

ABSTRACT It remains challenging to design efficient bifunctional semiconductor materials in organic photovoltaic and photodetector devices. Here, we report a butterfly-shaped molecule, named WD-6, which exhibits low energy disorder and small reorganization energy due to its enhanced molecular rigidity and unique assembly with strong intermolecular interaction. The binary photovoltaic device based on PM6:WD-6 achieved an efficiency of 18.41%. Notably, an efficiency of 19.42% was achieved for the ternary device based on PM6:BTP-eC9:WD-6. Moreover, the photodetection device based on WD-6 demonstrated an ultrafast response speed (205 ns response time at λ of 820 nm) and a high cutoff frequency of −3 dB (2.45 MHz), surpassing the values of most commercial Si photodiodes. Based on these findings, we showcased an application of the WD-6-based photodetection device in high-speed optical communication. These results offer valuable insights into the design of organic semiconductor materials capable of simultaneously exhibiting high photovoltaic and photodetective performance.

Science & Technology - Other Topics↗
DOE OSTI2020

Electron‐Deficient and Quinoid Central Unit Engineering for Unfused Ring‐Based A 1 –D–A 2 –D–A 1 ‐Type Acceptor Enables High Performance Nonfullerene Polymer Solar Cells with High V oc and PCE Simultaneously

Abstract Here, a pair of A 1 –D–A 2 –D–A 1 unfused ring core‐based nonfullerene small molecule acceptors (NF‐SMAs), BO2FIDT‐4Cl and BT2FIDT‐4Cl is synthesized, which possess the same terminals (A 1 ) and indacenodithiophene unit (D), coupling with different fluorinated electron‐deficient central unit (difluorobenzoxadiazole or difluorobenzothiadiazole) (A 2 ). BT2FIDT‐4Cl exhibits a slightly smaller optical bandgap of 1.56 eV, upshifted highest occupied molecular orbital energy levels, much higher electron mobility, and slightly enhanced molecular packing order in neat thin films than that of BO2FIDT‐4Cl . The polymer solar cells (PSCs) based on BT2FIDT‐4Cl:PM7 yield the best power conversion efficiency (PCE) of 12.5% with a V oc of 0.97 V, which is higher than that of BO2FIDT‐4Cl ‐based devices (PCE of 10.4%). The results demonstrate that the subtle modification of A 2 unit would result in lower trap‐assisted recombination, more favorable morphology features, and more balanced electron and hole mobility in the PM7:BT2FIDT‐4Cl blend films. It is worth mentioning that the PCE of 12.5% is the highest value in nonfused ring NF‐SMA‐based binary PSCs with high V oc over 0.90 V. These results suggest that appropriate modulation of the quinoid electron‐deficient central unit is an effective approach to construct highly efficient unfused ring NF‐SMAs to boost PCE and V oc simultaneously.

Zhang, Chao↗
NASA NTRS1988

Second and third order nonlinear optical properties of conjugated molecules and polymers

Second- and third-order nonlinear optical properties of some newly synthesized organic molecules and polymers are reported. Powder second-harmonic-generation efficiencies of up to 200 times urea have been realized for asymmetric donor-acceptor acetylenes. Third harmonic generation chi(3)s have been determined for a series of small conjugated molecules in solution. THG chi(3)s have also been determined for a series of soluble conjugated copolymers prepared using ring-opening metathesis polymerization. The results are discussed in terms of relevant molecular and/or macroscopic structural features of these conjugated organic materials.

Perry, Joseph W.↗
DOE OSTI2021

Evolution of Chain Dynamics and Oxidation States with Increasing Chain Length for a Donor–Acceptor-Conjugated Oligomer Series

While it is known that the chain length strongly affects the properties of π-conjugated polymers, the effects of chain length on the molecular structure, chain conformation, and oxidation state properties in donor–acceptor-type conjugated structures remain unclear. This limits our understanding of how the polymer molecular weight impacts material properties. Here, a discrete and monodisperse oligomer series (n = 3, 5, 7, 9, 15, and 21) and polymers (nPB), composed of the donor 3,4-propylenedioxythiophene (ProDOT), the acceptor benzothiadiazole (BTD), and methylthio end-capping groups, are synthesized by C–H-activated cross-coupling. The molecular structure, molecular weight, and dispersity of each oligomer/polymer are thoroughly characterized by nuclear magnetic resonance spectroscopy, mass spectrometry, and gel permeation chromatography. This series reveals a rod-to-coil transition at n = 15 and coil formation at polymer length scales of ~28 units via solution small-angle neutron scattering characterization. The oxidation states are deciphered via cyclic voltammetry, differential pulse voltammetry, spectroelectrochemistry, and density functional theory calculations. Oligomers 3–9 undergo successive one-electron oxidation steps, while 15 and higher undergo multielectron oxidations per step in CH 2 Cl 2 –TBAPF6 at a Pt ultramicroelectrode. The electronic transition of each oxidation state (1+, 2+, 3+, etc.) is tracked by absorption spectroscopy, revealing a “bipolaron to di-polaron” transition at n = 7 at which shorter oligomers prefer bipolaron formation and longer oligomers prefer di-polaron formation in their dication states. Furthermore, oxidized 15 has a lower electronic transition energy compared to its polymer homologue, as shown by spectroelectrochemistry, revealing a synergy between the chain length and the oxidation state properties. This study proves that the convergence limit between small molecule and polymer behavior occurs at approximately 15 units and highlights the property transitions that occur as a function of chain length for a donor–acceptor class of conjugated organic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Formation and Evolution of Metallocene Single-Molecule Circuits with Direct Gold-π Links

Single molecule circuits with group 8 metallocenes are formed without additional linker groups in Scanning Tunnelling Microscope-based break junction (STMBJ) measurements at cryogenic and room temperature conditions with gold (Au) electrodes. We investigate the nature of this direct gold-π binding motif and its affect on molecular conductance and persistence characteristics during junction evolution. The measurement technique under cryogenic conditions tracks molecular plateaus through the full cycle of extension and compression. Analysis reveals that junction persistence when the metal electrodes are pushed together correlates with whether electrodes are locally sharp or blunt, suggesting distinct scenarios for metallocene junction formation and evolution. The top and bottom surfaces of the "barrel" shaped metallocenes present the electron-rich π system of cyclopentadienyl rings which interacts with the gold electrodes in two distinct ways. An undercoordinated gold atom on a sharp tip forms a donor-acceptor bond to a specific carbon atom in the ring. However, a small, flat patch on a dull tip can bind more strongly to the ring as a whole through Van der Waals interactions. Density functional theory (DFT) based calculations of model electrode structures provide an atomic-scale picture of these scenarios, demonstrating the role of these bonding motifs during junction evolution and showing that the conductance is relatively independent of tip atomic-scale structure. Furthermore, the non-specific interaction of the cyclopentadienyl rings with the electrodes enables extended conductance plateaus, a mechanism distinct from that identified for the more commonly studied, rod-shaped organic molecular wires.

25 ENERGY STORAGE↗
DOE OSTI2026

Synergistic Alignment of Low Aspect‐Ratio π‐Conjugated Molecules Enables Exceptional UV–vis–NIR Polarization Detection

Abstract Polarization detection enhances signal contrast and is widely utilized in diverse advanced applications. An ongoing challenge is the development of high‐performance polarization‐sensitive photodetectors based on optically anisotropic organic semiconductors, particularly in the near‐infrared (NIR) region. While uniaxially aligned π‐conjugated polymers with high aspect ratios exhibit strong linear dichroism and have shown promise, their limited NIR performance and heavy reliance on polymer material now represent critical limitations. Here, a breakthrough is reported in achieving giant linear dichroism and exceptional polarization detection with low aspect‐ratios (AR) non‐fullerene small‐molecule (NFSM) acceptors, extending polarization sensitivity from the UV–vis to the NIR range. An impressive dichroic ratio of 27.1 at 605 nm and 12.0 at 780 nm is demonstrated. The maximum polarization photocurrent ratio is 11.2 at 780 nm under parallel versus perpendicular polarized light. This unprecedented performance originates from synergistic molecular alignment, wherein NFSMs significantly enhance the uniaxial orientation of both the polymer matrix and the NFSMs themselves during self‐assembly and thermal annealing. Besides, such a linear‐polarization‐sensitive photodetectors (LPS‐PDs) are showcased in generating degree‐of‐linear‐polarization imaging. The work establishes NFSMs as a viable material system for next‐generation of organic LPS‐PDs and provides fundamental insights into structural origins of polarization sensitivity in low AR organic semiconductors.

Xue, Yingying↗
DOE OSTI2022

Enhancing exciton diffusion by reducing energy disorder in organic solar cells

A highly crystalline, highly emissive, and wide-bandgap polymer AC174 with an extremely small Stokes shift is designed and synthesized in water, and is used to reduce system energetic disorder and increase the exciton diffusion length of the classical PM6:Y6 blend system. AC174 is incompatible with PM6 and Y6, improves molecular packing, and reduces system energetic disorder. The long-range Förster resonance energy transfer between the donor and acceptor is enhanced, and the exciton diffusion constant and exciton lifetime are increased, leading to a longer exciton diffusion length and more efficient exciton dissociation and charge generation. The addition of AC174 simultaneously improves the open-circuit voltage, short-circuit current density (J SC ) and fill factor of PM6:Y6 devices; especially the highest internal quantum efficiency approaches 100%, and the highest J SC is 28.4 mA cm –2 . Ternary devices with 5% AC174 in the donors achieve a power conversion efficiency of 17.2%, higher than those of the parent binary devices based on PM6:Y6 (15.9%) and AC174:Y6 (3.24%).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Integrated linker-regulation and ring-fusion engineering for efficient additive-free non-fullerene organic solar cells

The rational molecular design and structural modification of quasi-two-dimensional fused perylene diimide (quasi-2D FPDI) acceptors have received growing attention for application in non-fullerene organic solar cells (NF-OSCs). Herein, we designed and synthesized two pairs of FPDI acceptors, one in the form of FPDI–π-bridge–FPDI with the π-bridge being either an axisymmetric thiophene (T) or a centrosymmetric thienothiophene (TT) unit, and the other being the corresponding ring-fusion counterpart. Additionally, four small molecule acceptors, namely T-FPDI, TT-FPDI, FT-FPDI and FTT-FPDI, were paired with a common PTB7-Th polymeric electron donor as active materials for a comparative study of the effects of linkers and ring fusion on their photovoltaic performances. The T-FPDI-based NF-OSC exhibited a decent power conversion efficiency (PCE) of 5.50%, while a higher PCE of 7.17% with a simultaneous enhancement in the open circuit voltage ( V oc ), the short-circuit current density ( J sc ) and the fill factor (FF) was achieved for the TT-FPDI-based solar cells. The solar cells based on the ring-fused FT-FPDI and FTT-FPDI acceptors displayed PCEs of 6.75% and 7.66%, respectively, both higher than those of the corresponding non-fused counterparts. Notably, the trade-off between the J sc and V oc , commonly observed in fullerene OSCs, is alleviated in these systems. It is also worth noting that the NF-OSCs based on these FPDI acceptors do not need any solvent additives. Overall, this successful molecular engineering based on novel quasi-2D FPDI building blocks may inspire the development of emergent electron acceptors for high performance additive-free NF-OSCs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗