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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 OSTI2025

Functional Design of Peptide Materials Based on Supramolecular Cohesion

Peptide materials offer a broad platform to design biomimetic soft matter, and filamentous networks that emulate those in extracellular matrices and the cytoskeleton are among the important targets. Given the vast sequence space, a combination of computational approaches and readily accessible experimental techniques is required to design peptide materials efficiently. Here, we report here on a strategy that utilizes this combination to predict supramolecular cohesion within filaments of peptide amphiphiles, a property recently linked to supramolecular dynamics and consequently bioactivity. Using established coarse-grained simulations on 10,000 randomly generated peptide sequences, we identified 3500 likely to self-assemble in water into nanoscale filaments. Atomistic simulations of small clusters were used to further analyze this subset of sequences and identify mathematical descriptors that are predictive of intermolecular cohesion, which was the main purpose of this work. We arbitrarily selected a small cohort of these sequences for chemical synthesis and verified their fiber morphology. With further characterization, we were able to link the latent heat associated with fiber to micelle transitions, an indicator of cohesion and potential supramolecular dynamicity within the filaments, to calculated hydrogen bond densities in the simulation clusters. Based on validation from in situ synchrotron X-ray scattering and differential scanning calorimetry, we conclude that the phase transitions can be easily observed by very simple polarized light microscopy experiments. We are encouraged by the methodology explored here as a relatively low-cost and fast way to design potential functions of peptide materials.

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

Diversifying hierarchical ionic assembly by docking cations to anions as salt bridges

Here, we expand the diversity of building blocks available for ionic assembly by introducing tertiary (3°) ammonium cations into anion complexes. We use proton transfer between 3° amines and organo-phosphoric acids to generate H-bonding cations (R 3 NH + ) and anions (RHPO 4 – ) that co-assemble with cyanostar macrocycles into assemblies with 2:2:2 stoichiometry. At the heart is a supramolecular dimer where phosphate anions form salt bridges by H-bonding with cations. Unlike conventional 4° ammonium cations, 3,000 commercial amines provide diversity for high-throughput screening of 72 combinations (9 nitrogen bases and 8 acids), producing 13 privileged partners for quantitative assembly. Yields depend on the solvent and sterics of salt bridge formation. Ten more nitrogen bases connect to fluorophores (pyrene), photocatalysts (quinoline), drugs (Cipralex, Zytiga), and ionic liquids (imidazole). The synthesis and examination of 82 new salts exemplify how acid-base chemistry can open a pipeline to a diversity of building blocks for exploring hierarchical ionic assembly.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Elucidating the speciation of extracted lanthanides by diglycolamides

Many studies over the past few decades have been devoted to addressing the application of diglycolamides (DGAs) for hydrometallurgical-based, f-element separations. Work to date has shown the molecular structure of a DGA derivative can have a significant impact on intra-lanthanide partitioning patterns. More recent studies have pushed towards probing the structure function relationship of the lanthanide-DGA complex to enable the design of more efficient lanthanide separation systems. Spectroscopic techniques, such as UV–Visible, Fourier Transformed Infrared Spectroscopy (FT-IR), Nuclear Magnetic Resonance (NMR), and Extended X-ray Absorption Fine Structure (EXAFS), provide information regarding the inner-sphere coordination of a given lanthanide-DGA complex. Scattering techniques, such as Dynamic Light Scattering (DLS), Small-Angle X-ray Scattering (SAXS), and Small-Angle Neutron Scattering (SANS), address nanoscale structures including aggregate sizes and morphology. Here, this review assesses the current state-of-knowledge regarding lanthanide-DGA hydrometallurgical (i.e., solvent extraction systems) interrogated using spectroscopic and scattering techniques to characterize the extracted Ln 3+ DGA species. Of particular interest to this review is the impact of varied diluents, inclusion and variation of phase modifiers, and DGA derivatization on system characteristics. While there has been extensive literature on the application of DGAs for f-element separations, the literature lacks a collective assessment of the speciation of Ln 3+ in the organic phase. This review provides new insights into the field of DGA separations, explicitly with an application to intra-lanthanide separations. Specifically, this review illustrates the importance of both the co-extraction anion (Cl - , NO 3 - , or ClO 4 - ) as it pertains to both the aggregate size and Ln 3+ distribution coefficient. It is evident the ability of the anion to disrupt the hydrogen bonding network limits both aggregate size and distribution coefficients according to the Hoffmeister series. This suggests the importance of the large, softer anions with a low charge-to-surface area ratio on encouraging hydrogen bond interactions. In addition, the co-extracted cation (H + vs Na + ) is important for mitigating transfer of Ln 3+ from the aqueous to the organic phase through extensive hydrogen bonding networks. These networks are responsible for forming supramolecular aggregates where a change in morphology is observed with increasing concentrations of H + and/or Ln 3+ in the organic phase.

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

A nitrogen- and carbonyl-rich conjugated small-molecule organic cathode for high-performance sodium-ion batteries

Organic-based cathode materials have attracted considerable attention for sustainable Na-ion batteries due to their great promise to overcome the issues arising from the insertion of large Na + into the rigid structures of conventional transition-metal-containing inorganic electrodes. The structural flexibility as a result of weak intermolecular interactions and simple electron- and ion-storage mechanisms found in organic compounds ensure facile and reversible transport of Na ions. In order to address the general drawbacks of small-molecule organic electrodes such as material dissolution in commonly used organic electrolytes and poor electronic conductivity, we report the use of a nitrogen- and carbonyl-rich highly extended π-conjugated small molecule, hexaazatrianthranylene (HATA) embedded quinone (HATAQ), as a cathode for sodium-ion batteries. The unique hydrogen bonds between highly functionalized conjugated HATAQ molecules allow supramolecular graphite-like 2D layered arrangements in the solid state which help facilitate the structural stability during long-term cycling and promote charge transfer. The compound delivers a capacity as high as 460 mA h g -1 at 500 mA g -1 and an excellent capacity retention of 99% (~138 mA h g -1 ) after 5000 cycles at an extremely high rate of 60 A g -1 . The reaction kinetics and redox mechanism of the material have been elucidated by several characterization techniques together with density functional theory (DFT) studies. The insights gained in this work could pave the way for ultra-high-performance small-molecule organic cathodes for sustainable energy storage.

25 ENERGY STORAGE↗
DOE OSTI2023

Guiding Principles for the Rational Design of Hybrid Materials: Use of DFT Methodology for Evaluating Non‐Covalent Interactions in a Uranyl Tetrahalide Model System

Abstract Together with the synthesis and experimental characterization of 14 hybrid materials containing [UO 2 X 4 ] 2− (X=Cl − and Br − ) and organic cations, we report on novel methods for determining correlation trends in their formation enthalpy (ΔH f ) and observed vibrational signatures. Δ H f values were analyzed through isothermal acid calorimetry and a Density Functional Theory+Thermodynamics (DFT+T) approach with results showing good agreement between theory and experiment. Three factors (packing efficiency, cation protonation enthalpy, and hydrogen bonding energy [ ]) were assessed as descriptors for trends in Δ H f . Results demonstrated a strong correlation between and Δ H f , highlighting the importance of hydrogen bonding networks in determining the relative stability of solid‐state hybrid materials. Lastly, we investigate how hydrogen bonding networks affect the vibrational characteristics of uranyl solid‐state materials using experimental Raman and IR spectroscopy and theoretical bond orders and find that hydrogen bonding can red‐shift U≡O stretching modes. Overall, the tightly integrated experimental and theoretical studies presented here bridge the trends in macroscopic thermodynamic energies and spectroscopic features with molecular‐level details of the geometry and electronic structure. This modeling framework forms a basis for exploring 3D hydrogen bonding as a tunable design feature in the pursuit of supramolecular materials by rational design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Guiding Principles for the Rational Design of Hybrid Materials: Use of DFT Methodology for Evaluating Non‐Covalent Interactions in a Uranyl Tetrahalide Model System

Abstract Together with the synthesis and experimental characterization of 14 hybrid materials containing [UO 2 X 4 ] 2− (X=Cl − and Br − ) and organic cations, we report on novel methods for determining correlation trends in their formation enthalpy (ΔH f ) and observed vibrational signatures. Δ H f values were analyzed through isothermal acid calorimetry and a Density Functional Theory+Thermodynamics (DFT+T) approach with results showing good agreement between theory and experiment. Three factors (packing efficiency, cation protonation enthalpy, and hydrogen bonding energy [ ]) were assessed as descriptors for trends in Δ H f . Results demonstrated a strong correlation between and Δ H f , highlighting the importance of hydrogen bonding networks in determining the relative stability of solid‐state hybrid materials. Lastly, we investigate how hydrogen bonding networks affect the vibrational characteristics of uranyl solid‐state materials using experimental Raman and IR spectroscopy and theoretical bond orders and find that hydrogen bonding can red‐shift U≡O stretching modes. Overall, the tightly integrated experimental and theoretical studies presented here bridge the trends in macroscopic thermodynamic energies and spectroscopic features with molecular‐level details of the geometry and electronic structure. This modeling framework forms a basis for exploring 3D hydrogen bonding as a tunable design feature in the pursuit of supramolecular materials by rational design.

36 MATERIALS SCIENCE↗
DOE OSTI2021

r 2 SCAN-D4: Dispersion corrected meta-generalized gradient approximation for general chemical applications

We combine a regularized variant of the strongly constrained and appropriately normed semilocal density functional with the latest generation semi-classical London dispersion correction. The resulting density functional approximation r 2 SCAN-D4 has the speed of generalized gradient approximations while approaching the accuracy of hybrid functionals for general chemical applications. We demonstrate its numerical robustness in real-life settings and benchmark molecular geometries, general main group and organo-metallic thermochemistry, and non-covalent interactions in supramolecular complexes and molecular crystals. Main group and transition metal bond lengths have errors of just 0.8%, which is competitive with hybrid functionals for main group molecules and outperforms them for transition metal complexes. The weighted mean absolute deviation (WTMAD2) on the large GMTKN55 database of chemical properties is exceptionally small at 7.5 kcal/mol. This also holds for metal organic reactions with an MAD of 3.3 kcal/mol. The versatile applicability to organic and metal–organic systems transfers to condensed systems, where lattice energies of molecular crystals are within the chemical accuracy (errors <1 kcal/mol).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

N -Terminal Octylated Peptoid Hydrogels as 3D-Printable Cell Scaffolds and Proteolytically Robust Cargo Depots

Supramolecular hydrogels that mimic the extracellular matrix (ECM) represent promising materials for tissue engineering and drug delivery. However, conventional hydrogels formed via the self-assembly of natural or synthetic building blocks often face a trade-off between biological functionality and biochemical stability, limiting their utility in long-term or protease-rich environments. Peptoids, a class of peptide-inspired, sequence-defined polymers, offer a compelling alternative due to their exceptional proteolytic resistance and bioactivity. Despite this potential, the development of supramolecular peptoid hydrogels has been hindered by the absence of backbone hydrogen bond donors, which limits long-range ordering necessary for efficient hydrogel formation. This work describes a short peptoid functionalized at the N-terminus with an octyl chain that readily self-assembles into hydrogels. Hydrophobic interactions among pendant octyl groups promote directional peptoid packing into highly ordered nanosheets, which interconnect to form a porous hydrogel network. These hydrogels exhibit tunable viscoelasticity, shear-thinning, and self-healing properties, enabling their use as inks for extrusion-based 3D printing. They support NIH-3T3 fibroblast adhesion, spreading, and proliferation, maintaining greater than 95% cell viability over 4 days. Moreover, the hydrogels retain their macroscopic integrity under protease-rich conditions, enabling sustained cargo release and uniform cellular uptake. Together, this study demonstrates a class of supramolecular peptoid hydrogelators that integrate biocompatibility, 3D printability, and proteolytic stability, providing a versatile platform for ECMmimetic scaffolds in regenerative medicine and long-term therapeutic delivery.

cargo delivery↗
DOE OSTI2024

Peptide programming of supramolecular vinylidene fluoride ferroelectric phases

Ferroelectric structures have spontaneous macroscopic polarization that can be inverted using external electric fields and have potential applications including information storage, energy transduction, ultralow-power nanoelectronics and biomedical devices. These functions would benefit from nanoscale control of ferroelectric structure, the ability to switch polarization with lower applied fields (low coercive field) and biocompatibility. Soft ferroelectrics based on poly(vinylidene fluoride) (PVDF) have a thermodynamically unstable ferroelectric phase in the homopolymer, complex semi-crystalline structures, and high coercive fields. Here, in this work, we report on ferroelectric materials formed by water-soluble molecules containing only six VDF repeating units covalently conjugated to a tetrapeptide, with the propensity to assemble into the β-sheet structures that are ubiquitous in proteins. This led to the discovery of ribbon-shaped ferroelectric supramolecular assemblies that are thermodynamically stable with their long axes parallel to both the preferred hydrogen-bonding direction of β-sheets and the bistable polar axes of VDF hexamers. Relative to a commonly used ferroelectric copolymer, the biomolecular assemblies exhibit a coercive field that is two orders of magnitude lower, as the result of supramolecular dynamics, and a similar level of remnant polarization, despite having a peptide content of 49 wt%. Furthermore, the Curie temperature of the assemblies is about 40 °C higher than that of a copolymer containing a similar amount of VDF. This supramolecular system was created using a biologically inspired strategy that is attractive in terms of sustainability and that could lead to new functions for soft ferroelectrics.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Motion of Molecules in Supramolecular Scaffolds Enhances Bone Regeneration

The regeneration of human tissues is a great scientific challenge and a critical factor to achieve a long healthspan and prevent disabilities due to injury or disease. Materials chemistry can contribute to this goal with the development of bioactive supramolecular systems that can signal cells for regeneration. Recent work in our laboratory using in vivo models of spinal cord injury and cartilage regeneration has demonstrated that the motion of bioactive molecules in supramolecular scaffolds enhances receptor signaling. We report here on a novel molecular strategy to control supramolecular motion in filamentous assemblies using bone regeneration as a functional target. The supramolecular assemblies are composed of monomers that arrange, by design, with either parallel or antiparallel β-sheets, and some of them contain a terminal peptide sequence that binds BMP-2. We found that parallel β-sheet supramolecular assemblies promote greater osteogenic differentiation of progenitor cells in vitro relative to antiparallel assemblies, as well as superior quality of newly regenerated bone in a rat model of spinal fusion. Furthermore, these assemblies drastically reduce the dangerous supraphysiological dose of BMP-2 used clinically for spinal fusion. Here, we attribute the enhanced bioactivity to the weaker nature of hydrogen bonds in parallel relative to antiparallel β-sheet assemblies, which in turn allows greater supramolecular motion and cell signaling of the growth factor-binding molecules.

Anatomy↗
DOE OSTI2020

Supramolecular Tuning Enables Selective Oxygen Reduction Catalyzed by Cobalt Porphyrins for Direct Electrosynthesis of Hydrogen Peroxide

Abstract We report a supramolecular strategy for promoting the selective reduction of O 2 for direct electrosynthesis of H 2 O 2 . We utilized cobalt tetraphenylporphyrin (Co‐TPP), an oxygen reduction reaction (ORR) catalyst with highly variable product selectivity, as a building block to assemble the permanently porous supramolecular cage Co‐PB‐1(6) bearing six Co‐TPP subunits connected through twenty‐four imine bonds. Reduction of these imine linkers to amines yields the more flexible cage Co‐rPB‐1(6). Both Co‐PB‐1(6) and Co‐rPB‐1(6) cages produce 90–100 % H 2 O 2 from electrochemical ORR catalysis in neutral pH water, whereas the Co‐TPP monomer gives a 50 % mixture of H 2 O 2 and H 2 O. Bimolecular pathways have been implicated in facilitating H 2 O formation, therefore, we attribute this high H 2 O 2 selectivity to site isolation of the discrete molecular units in each supramolecule. The ability to control reaction selectivity in supramolecular structures beyond traditional host–guest interactions offers new opportunities for designing such architectures for a broader range of catalytic applications.

Smith, Peter T.↗
DOE OSTI2020

Supramolecular Tuning Enables Selective Oxygen Reduction Catalyzed by Cobalt Porphyrins for Direct Electrosynthesis of Hydrogen Peroxide

Abstract We report a supramolecular strategy for promoting the selective reduction of O 2 for direct electrosynthesis of H 2 O 2 . We utilized cobalt tetraphenylporphyrin (Co‐TPP), an oxygen reduction reaction (ORR) catalyst with highly variable product selectivity, as a building block to assemble the permanently porous supramolecular cage Co‐PB‐1(6) bearing six Co‐TPP subunits connected through twenty‐four imine bonds. Reduction of these imine linkers to amines yields the more flexible cage Co‐rPB‐1(6). Both Co‐PB‐1(6) and Co‐rPB‐1(6) cages produce 90–100 % H 2 O 2 from electrochemical ORR catalysis in neutral pH water, whereas the Co‐TPP monomer gives a 50 % mixture of H 2 O 2 and H 2 O. Bimolecular pathways have been implicated in facilitating H 2 O formation, therefore, we attribute this high H 2 O 2 selectivity to site isolation of the discrete molecular units in each supramolecule. The ability to control reaction selectivity in supramolecular structures beyond traditional host–guest interactions offers new opportunities for designing such architectures for a broader range of catalytic applications.

Smith, Peter T.↗
DOE OSTI2023

Advanced supramolecular design for direct ink writing of soft materials

The exciting advancements in 3D-printing of soft materials are changing the landscape of materials development and fabrication. Among various 3D-printers that are designed for soft materials fabrication, the direct ink writing (DIW) system is particularly attractive for chemists and materials scientists due to the mild fabrication conditions, compatibility with a wide range of organic and inorganic materials, and the ease of multi-materials 3D-printing. Inks for DIW need to possess suitable viscoelastic properties to allow for smooth extrusion and be self-supportive after printing, but molecularly facilitating 3D printability to functional materials remains nontrivial. While supramolecular binding motifs have been increasingly used for 3D-printing, these inks are largely optimized empirically for DIW. Hence, this review aims to establish a clear connection between the molecular understanding of the supramolecularly bound motifs and their viscoelastic properties at bulk. Herein, extrudable (but not self-supportive) and 3D-printable (self-supportive) polymeric materials that utilize noncovalent interactions, including hydrogen bonding, host–guest inclusion, metal–ligand coordination, micro-crystallization, and van der Waals interaction, have been discussed in detail. In particular, the rheological distinctions between extrudable and 3D-printable inks have been discussed from a supramolecular design perspective. Examples shown in this review also highlight the exciting macroscale functions amplified from the molecular design. Challenges associated with the hierarchical control and characterization of supramolecularly designed DIW inks are also outlined. The perspective of utilizing supramolecular binding motifs in soft materials DIW printing has been discussed. Finally, this review serves to connect researchers across disciplines to develop innovative solutions that connect top-down 3D-printing and bottom-up supramolecular design to accelerate the development of 3D-print soft materials for a sustainable future.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Sequence Programmable Order–Disorder Transitions in Supramolecular Assembly of Peptide Nanofibers

Protein–protein interactions determine the assembly of complexes that are responsible for numerous key biological processes. The assembly of many natural protein complexes is mediated by post-translational structural changes and environmental stimuli. In this study, we show that incorporation of adjacent lysine residues results in the pH-tunable stability of peptide secondary structure and assembly, allowing for the incorporation of complementary order-inducing motifs. The strategic placement of cysteine pairs in the same peptide sequence results in redox-dependent disulfide staple formation, inducing a transition from random coil to β-sheet conformation and subsequent supramolecular nanofiber assembly from otherwise disordered peptide monomers. Spectroscopic, imaging, molecular dynamics, and kinetic studies highlight the critical role of sequence motif location, oligomerization, and the competitive interplay between intra- and interpeptide disulfide bonding in determining assembly outcomes. We extend this approach to demonstrate phosphorylation-dependent assembly from the design of the same parent peptide sequence, suggesting a general approach to the design of diverse stimulus-responsive peptide sequences for supramolecular assembly. Furthermore, these findings also provide a framework for investigating sequence-dependent pathways in amyloid fiber formation with potential implications for neurodegenerative disease research.

Disulfides↗
DOE OSTI2020

Supramolecular Energy Materials

Self-assembly is a bioinspired strategy to craft materials for renewable and clean energy technologies. In plants, the alignment and assembly of the light-harvesting protein machinery in the green leaf optimize the ability to efficiently convert light from the sun to form chemical bonds. In artificial systems, strategies based on self-assembly using noncovalent interactions offer the possibility to mimic this functional correlation among molecules to optimize photocatalysis, photovoltaics, and energy storage. Here, one of the long-term objectives of the field described here as supramolecular energy materials is to learn how to design soft materials containing light-harvesting assemblies and catalysts to generate fuels and useful chemicals. Supramolecular energy materials also hold great potential in the design of systems for photovoltaics in which intermolecular interactions in self-assembled structures, for example, in electron donor and acceptor phases, maximize charge transport and avoid exciton recombination. Possible pathways to integrate organic and inorganic structures by templating strategies and electrodeposition to create materials relevant to energy challenges including photoconductors and supercapacitors are also described. The final topic discussed is the synthesis of hybrid perovskites in which organic molecules are used to modify both structure and functions, which may include chemical stability, photovoltaics, and light emission.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Hierarchical Self-Assembly of Carbon Dots into High-Aspect-Ratio Nanowires

Here, we report a spontaneous and hierarchical self-assembly mechanism of carbon dots prepared from citric acid and urea into nanowire structures with large aspect ratios (>50). Scattering-type scanning near-field optical microscopy (s-SNOM) with broadly tunable mid-IR excitation was used to interrogate details of the self-assembly process by generating nanoscopic chemical maps of local wire morphology and composition. s-SNOM images capture the evolution of wire formation and the complex interplay between different chemical constituents directing assembly over the nano- to microscopic length scales. We propose that residual citrate promotes tautomerization of melamine surface functionalities to produce supramolecular shape synthons comprised of melamine-cyanurate adducts capable of forming long-range and highly directional hydrogen-bonding networks. This intrinsic, heterogeneity-driven self-assembly mechanism reflects synergistic combinations of high chemical specificity and long-range cooperativity that may be harnessed to reproducibly fabricate functional structures on arbitrary surfaces.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2025

Cryo-EM Visualization of Intermolecular π-Electron Interactions within π-Conjugated Peptidic Supramolecular Polymers

The self-assembly of “π-peptides” – molecules with π-electron cores substituted with two or more oligopeptide chains – brings organic electronic function into biologically relevant nanomaterials. π-Peptides assemble into fibrillar nanomaterials as driven by enthalpic peptide-based hydrogen bonding networks and pi-core-based quadrupolar interactions. A large body of spectroscopic, morphological and computational studies informs on the nature of the self-assembly process and the resulting nanostructures, but detailed structural information has remained elusive. Here, inspired by the recent use of cryogenic electron microscopy (cryo-EM) to provide high-resolution structures for synthetic peptide nanomaterials, we present here the use of cryo-EM to offer ca. 3 Å resolution of π-peptide nanomaterial assemblies, visualizing for the first time the nature of the intermolecular π-core electronic interactions responsible for energy transport through these supramolecular materials.

Group theory↗
DOE OSTI2026

Structural and compositional complexities of hierarchical self-assembly: A hypergraph approach

Programmable self-assembly enables the construction of complex molecular, supramolecular, and crystalline architectures from well-designed building blocks. In this work, we introduce a hypergraph-based formalism, Blocks & Bonds (B&B), which generalizes classical chemical graph theory by incorporating directed and multicolored interactions, internal symmetries, and hierarchical organization. Within this framework, we develop the Structure Code (SC), a compact and versatile language for describing self-assembled architectures. We define a Kolmogorov-style structural complexity as the total information content of SC, obtained through its tokenization and Shannon information assignment. Complementing this encoding-based measure, we introduce a much simpler quantity, the compositional complexity, which depends only on the number and cumulative usage of block and bond types in the construction set. A central result of this work is a strong empirical correlation between the token-based structural complexity and the compositional complexity across all examined systems. Owing to this agreement, the compositional complexity emerges as the most practical and broadly applicable measure: it is easy to compute, requires no explicit encoding, and yet closely tracks the actual information content of structurally diverse architectures. Applications to molecular systems (ethylene glycol and glucose), DNA-origami lattices, and crystalline assemblies show that B&B hypergraphs provide a unified, scalable, and information-efficient representation of structural organization, naturally capturing symmetry, modularity, and stereochemistry. This framework establishes a quantitative foundation for complexity-aware classification and inverse design of programmable matter.

36 MATERIALS SCIENCE↗