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At least 253 records · Page 14

Accelerated Self-Healing and Property Recovery in Brush Particle Solids Featuring Brush Dispersity

Brush particles, hybrid materials consisting of polymer chains tethered to particle surfaces, offer tunable properties that make them promising candidates for advanced functional materials. This study investigated the role of chain dispersity in the viscoelastic self-healing of poly (methyl acrylate) (PMA)-based brush particle solids. Increasing the molecular weight dispersity of grafted chains significantly enhanced both strain-to-fracture and toughness of brush particle solids, while the elastic modulus and glass transition temperature were independent of chain dispersity. Cut-and-adhere testing revealed a significant acceleration of the rate of toughness recovery in high-dispersity systems as compared to low-dispersity analogs for which toughness recovery markedly lagged the recovery of Young’s modulus. The results suggest that structure and property recovery in brush particle solids are sensitive to the dynamical heterogeneity of brush canopies and highlight the role of molecular weight dispersity as a design parameter to enable hybrid materials with advanced self-healing ability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Tunable Nanoscale Structure via Divalent Ion Identity in Charged-Neutral Polymer Blends

Charged-neutral polymer blends, wherein an ioncontaining polymer is blended with a neutral polymer, are potential candidates for battery electrolytes due to their improved ion transport properties and electrochemical stability. Though electrostatic interactions in charged polymer blends can theoretically stabilize ordered nanostructures analogous to those observed in neutral block copolymers, direct experimental evidence remains limited. Here, we investigate the effects of divalent cation identity on the nanoscale morphology of charged-neutral polymer blends composed of poly(ethylene oxide) (PEO) and Mg 2+ or Ca 2+ ioncontaining polymers, poly[3-(methylacryloxy)propylsulfonyl-1-(trifluoromethanesulfonylimide)] (P(Mg(MTFSI) 2 ) or P(Ca- (MTFSI) 2 ). By tuning the size of the divalent counterion, we are able to precisely tune the ion solvation between the free cation and PEO, which acts as a solvent in this system. Differential scanning calorimetry (DSC) and small-angle X-ray scattering (SAXS) measurements reveal that Mg 2+ and Ca 2+ ions induce distinct structural behavior. In both systems, the blends become more miscible as the concentration of ion-containing polymer is increased indicated by increased suppression of PEO crystallinity. At the highest concentrations of P(Mg(MTFSI) 2 ), the blends undergo microphase separation and generate nanostructures with shortranged ordering. In contrast, calcium ions, which are more readily solvated by PEO, produce more homogeneous blends characterized by a single glass-transition temperature and featureless SAXS data. The results demonstrate the novel experimental confirmation that charged-neutral polymer blends can undergo microphase separation and show that counterion identity can be exploited as a design parameter to control nanoscale morphology.

Ions↗

Colloidal Clusters and Networks Formed by Oppositely Charged Nanoparticles with Varying Stiffnesses

Colloidal clusters and gels are ubiquitous in science and technology. Particle softness has a strong effect on interparticle interactions; however, our understanding of the role of this factor in the formation of colloidal clusters and gels is only beginning to evolve. Here, we report the results of experimental and simulation studies of the impact of particle softness on the assembly of clusters and networks from mixtures of oppositely charged polymer nanoparticles (NPs). Experiments were performed below or above the polymer glass transition temperature, at which the interaction potential and adhesive forces between the NPs were significantly varied. Hard NPs assembled in fractal clusters that subsequently organized in a kinetically arrested colloidal gel, while soft NPs formed dense precipitating aggregates, due to the NP deformation and the decreased interparticle distance. Importantly, interactions of hard and soft NPs led to the formation of discrete precipitating NP aggregates at a relatively low volume fraction of soft NPs. A phenomenological model was developed for interactions of oppositely charged NPs with varying softnesses. Furthermore, the experimental results were in agreement with molecular dynamics simulations based on the model. This work provides insight on interparticle interactions before, during, and after the formation of hard–hard, hard–soft, and soft–soft contacts and has impact for numerous applications of reversible colloidal gels, including their use as inks for additive manufacturing.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Synergistic Evolution of Segmental Motion and Cooperative Relaxation within the Amorphous Phase of Organic Mixed Ionic-Electronic Conductors

Organic mixed ionic-electronic conductors (OMIECs) facilitate a variety of electrochemical processes and feature a heterogeneous microstructure composed of both crystalline and amorphous phases. However, structural evolution in amorphous regions during electrochemical doping remains poorly understood, limiting our understanding of mixed conduction mechanisms. Here, in this work, we develop operando chip calorimetry to probe amorphous phase evolution in poly­(3,4-ethylenedioxythiophene):poly­(styrenesulfonate) (PEDOT:PSS) under swelling and electrochemical (de)­doping. Our results reveal that amorphous regions providing ionic transport pathways and those within electronic transport channels undergo heterogeneous, yet synergistic, evolution during electrochemical modulation. The cooperative interplay between segmental motion and relaxation maintains ionic conductivity and intergrain electronic transport upon electrowetting and doping, while facilitating efficient ion hopping and adaptable chain conformations during dedoping. Such synergies are more pronounced in loose structures featuring a fibrillar morphology, which exhibit lower glass transition temperatures (T g ) and higher fragility (m). High-throughput robotic screening further establishes a strong correlation between elevated m/T g ratios and enhanced mixed conduction. These findings elucidate the role of the amorphous phase in the synthesis of OMIECs and underscore the potential of operando chip calorimetry in uncovering structure–property relationships in electroactive polymers.

amorphous phase↗

Recycling Epoxy by Vitrimerization: Influence of an Initial Thermoset Chemical Structure

Epoxy/anhydride cured thermosets are widely used in aerospace and wind energy structures. Recycling the enormous amounts of epoxy thermoset waste remains a global challenge. Vitrimerization, a practical, low-cost, eco-friendly and scalable method was developed for closed-loop recycling of the crosslinked epoxy by converting the permanent network into a vitrimer type dynamic network. Here we study the effect of virgin epoxy network properties on network reforming efficiency and the activation energy of the dynamic network by varying the epoxy/anhydride ratio. The results point out that the permanent network crosslink density and glass transition temperature have a more pronounced effect on vitrimerization efficiency by comparison with the concentration of free hydroxyl groups in the system. Furthermore, the result can be potentially used to better control vitrimerization efficiency in recycling epoxy thermoset polymers and tailor the vitrimerized products properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Melt Processing Pretreatment Effects on Enzymatic Depolymerization of Poly(ethylene terephthalate)

Poly(ethylene terephthalate) (PET) is a common thermoplastic material, used in a wide variety of applications (i.e., bottles, fabrics, packaging, electronics, and automotive components). Increasing demand for PET has precipitated a need for improved recycling technology, especially for single-use PET waste. Recently, enzymatic depolymerization has shown promise as an environmentally responsible alternative for PET chemical recycling that yields economically useful products (e.g., terephthalic acid, adipic acid, and ethylene glycol). However, the depolymerization system still suffers from low rates on crystalline PET substrates, and effects of realistic waste streams are not known. In our work, PET waste is pretreated using an ultra-high-speed twin-screw extruder system. PET substrates were modified by various processing pretreatments to allow enzymes better access to depolymerize substrate materials. The effect of varying throughput and mechanical shear on structural properties of the PET waste was analyzed using molecular weight and thermal characterizations. These pretreated samples exhibit modifications in molecular weight, glass transition temperature, crystallinity, and specific surface area. The unpurified leaf-branch compost cutinase enzyme produced from the fed-batch fermentation of Escherichia coli BL21(DE3) was used in enzymatic depolymerization, where a faster reaction was observed as crystallinity was decreased and the specific surface area was increased. The rate of terephthalic acid production was also significantly higher for samples processed at lower mechanical shear with higher throughputs. As a result, this work demonstrates the potential for tailoring pretreatments in pursuit of faster and more energy efficient PET recycling using enzymes, with facile adaptation to the industrial scale for the circular economy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Chemical Recycling of Polybutadiene Rubber with Tailored Depolymerization Enabled by Microencapsulated Metathesis Catalysts

The effective management of plastic waste streams to prevent plastic land and water pollution is a growing problem that is also one of the most important challenges in polymer science today. Polymer materials that are stable over their lifetime and can also be cheaply recycled or repurposed as desired could more easily be diverted from waste streams. However, this is difficult for most commodity plastics. It is especially difficult to conceive this with intractable, cross-linked polymers such as rubbers. In this work, we explore the utility of microencapsulated Grubbs’ catalysts for the in-situ depolymerization and reprocessing of polybutadiene (PB) rubber. Second-generation Hoveyda-Grubbs catalyst (HG2) contained within glassy thermoplastic microspheres can be dispersed in PB rubber below the microsphere’s glass transition temperature (T g ) without adverse depolymerization, evidenced by rubber with and without these microspheres obtaining similar shear storage moduli of ≈16 and ≈28 kPa, respectively. The thermoplastic’s T g can be used to tune the depolymerization temperature, via release of HG2 into the rubber matrix. For example, using poly(lactic acid) (PLA) vs polysulfone results in an 85 and 162 °C depolymerization temperature, respectively. Liquefaction of rubber to a mixture of small molecules and oligomers is demonstrated using a 0.01 mol % catalyst loading using PLA as the encapsulant. Furthermore, at that same catalyst loading, depolymerization occurs to a greater extent in comparison to two ex-situ approaches, including a conventional solvent-assisted method, where it occurs at roughly twice the extent at each given catalyst loading. In addition, depolymerization of the microsphere-loaded rubbers was demonstrated for samples stored under nitrogen for 23 days. Lastly, we show that the depolymerized products can be reprocessed back into solid rubber with a shear storage modulus of ≈32 kPa. Thus, we envision that this approach could be used to recycle and reuse cross-linked rubbers at the end of their product lifetime.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Not Cutting Corners: Bioderived Triggers Driving Oxidative Main Chain Scission of Poly(ethylene terephthalate)

About 20–34 billion poly(ethylene terephthalate) (PET) bottles from the beverage industry leak into aquatic ecosystems annually, necessitating the development of urgent strategies to treat waterborne plastic pollution. Inspired by the scalability of water disinfection infrastructure and protocols, we present a dual depolymerization approach relying on oxidation, followed by hydrolysis. Incorporating bioderived monounsaturated C18 diacid (C18:1-DA) counits at low dosages (2–5%) in the PET backbone overcomes the diffusional limitations of depolymerizing PET in the solid state by suppressing the glass transition temperature of the copolymer by 20 °C. Cryomilled C18:1-PET powder suspended in an oxidant-loaded alkaline slurry underwent bulk depolymerization to oligomers at 80–100 °C via oxidative scissions at the internally located unsaturations. In contrast, conventional PET undergoes only minor end-chain scission under mild alkaline conditions. These oligomers are suitable for low-energy repolymerization or facile solvolysis to monomers. A permanganate-periodate oxidant couple demonstrated successful oxidation through the bulk of the polymer, which subsequently was hydrolyzed to monomers. Furthermore, this model system serves as a proxy for ozonolysis, followed by mild hydrolysis to reduce the energetics of alkaline hydrolysis. This integrated oxidation–hydrolysis strategy paves the way for the industrial adoption of cleaner, advanced oxidation processes, such as ozonolysis for plastic pretreatment, further enabling commercialized chemical recycling of unsaturation-containing polyesters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Enhancing Biopolyester Backbone Rigidity with an Asymmetric Furanic Monomer

Biobased furanic polyesters can exhibit performance advantages over petroleum-derived polyesters, primarily due to their rigid furan-containing backbones. Herein, we develop two strategies to polymerize methyl 5-hydroxymethyl furanoate to poly(5-hydroxymethyl furanoate) (PHMF), a furan-based polyester with even greater backbone rigidity than poly(ethylene furanoate). Thermal, spectroscopic, and computational investigations of PHMF alongside analogous furan-based and phenyl-based polyesters suggest that the high furan content of PHMF leads to its high glass transition temperature, slow crystallization kinetics, and low amorphous mobility. Molecular dynamics simulations suggest that while the backbone of PHMF is exceptionally rigid, its amorphous phase is denser than its phenyl analog due to noncovalent interchain interactions. Together, these results highlight how asymmetric furan-based monomers can modulate key properties in biobased polyesters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Topology-Informed Design Rules for Deconstructable Thermoset Copolymer Networks

Existing models of thermoset deconstruction facilitated by incorporating cleavable comonomers rely on a mean-field reverse gel point paradigm, which predicts network dissolution once cleavable bonds reach a critical stoichiometric threshold, but does not account for where those bonds reside within the network architecture. Using reactive coarse-grained molecular dynamics simulations coupled with graph-theoretic analysis, we extend this stoichiometric picture to show that deconstructability is governed by the curing-imprinted network topology rather than stoichiometry alone. This topological organization is hierarchical: at the local scale, the elastic effectiveness of cross-link junctions determines which cross-links constitute the load-bearing scaffold; at the mesoscale, the cross-linking rate kinetically templates that scaffold into topologically modular communities─densely cross-linked clusters connected by sparse bridging strands that sustain network connectivity. Using betweenness centrality to identify nodes that disproportionately lie on intercommunity shortest paths, we demonstrate that effective deconstruction of the network into macromolecular fragments requires cleavable comonomers to intercept these high-centrality bridging strands. We further find that under uniform, disassortative comonomer incorporation, this topological requirement provides a mechanistic basis for extending the reverse gel point to incorporate network topology. We also show that modularity imposes a fundamental limit on fragment uniformity that persists even when the centrality requirement is met. Finally, we demonstrate that chain stiffness provides a nearly independent lever to suppress mechanically redundant cross-links and raise the glass transition temperature without significantly altering the deconstruction outcome. Together, these findings reframe the thermoset design space around network topology and provide actionable guidelines for engineering thermoset copolymers with predictable deconstructability and targeted thermomechanical performance.

coarse-grained molecular dynamics↗

Gamma Radiation Effects in Amorphous and Crystalline Polyaryletherketones

This work investigates the effect of gamma radiation on chain scission and crosslinking in polyaryletherketone (PAEK) thermoplastic filaments, namely, polyetheretherketone (PEEK) and polyetherketoneketone (PEKK) that is either semicrystalline (PEKK-c) or highly amorphous (PEKK-a). The PAEK thermoplastic filaments were exposed to total ionizing doses (TID) of gamma radiation from 1 to 8 MGy in the Gamma Irradiation Facility at Sandia National Laboratories. A combination of thermal and FT-IR spectral analysis of the irradiated specimens was used to study the chain scission and crosslinking behavior between PEEK, PEKK-c, and PEKK-a. Crystallinity decreased with increased TID and melt enthalpy decreased. Despite clear indications of changes to melt and crystallization behavior, any change to the glass-transition temperature was minor until a post-irradiation thermal annealing occurred, which caused an increase in crystallinity. Gamma radiation impacted PEKK-a more due to the lower degree of initial crystallinity, where a reduction in melt enthalpy, crystallinity, and crystallization kinetics was observed. Despite these effects, the ability to achieve a higher degree of crystallization (X c < 20%) by annealing was not affected. The results presented here provide important insight into the performance of a class of commercialized PEKK thermoplastics exposed to a harsh radiation environment.

Crystallinity↗

Sourcing thermotolerant poly(ethylene terephthalate) hydrolase scaffolds from natural diversity

Enzymatic deconstruction of poly(ethylene terephthalate) (PET) is under intense investigation, given the ability of hydrolase enzymes to depolymerize PET to its constituent monomers near the polymer glass transition temperature. To date, reported PET hydrolases have been sourced from a relatively narrow sequence space. Here, we identify additional PET-active biocatalysts from natural diversity by using bioinformatics and machine learning to mine 74 putative thermotolerant PET hydrolases. We successfully express, purify, and assay 51 enzymes from seven distinct phylogenetic groups; observing PET hydrolysis activity on amorphous PET film from 37 enzymes in reactions spanning pH from 4.5–9.0 and temperatures from 30–70 °C. We conduct PET hydrolysis time-course reactions with the best-performing enzymes, where we observe differences in substrate selectivity as function of PET morphology. We employed X-ray crystallography and AlphaFold to examine the enzyme architectures of all 74 candidates, revealing protein folds and accessory domains not previously associated with PET deconstruction. Overall, this study expands the number and diversity of thermotolerant scaffolds for enzymatic PET deconstruction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Attention-based functional-group coarse-graining: a deep learning framework for molecular prediction and design

Machine learning (ML) offers considerable promise for the design of new molecules and materials. In real-world applications, the design problem is often domain-specific, and suffers from insufficient data, particularly labeled data, for ML training. In this study, we report a data-efficient, deep-learning framework for molecular discovery that integrates a coarse-grained functional-group representation with a self-attention mechanism to capture intricate chemical interactions. Our approach exploits group-contribution concepts to create a graph-based intermediate representation of molecules, serving as a low-dimensional embedding that substantially reduces the data demands typically required for training. Using a self-attention mechanism to learn the subtle but highly relevant chemical context of functional groups, the method proposed here consistently outperforms existing approaches for predictions of multiple thermophysical properties. In a case study focused on adhesive polymer monomers, we train on a limited dataset comprising only 6,000 unlabeled and 600 labeled monomers. The resulting chemistry prediction model achieves over 92% accuracy in forecasting properties directly from SMILES strings, exceeding the performance of current state-of-the-art techniques. Furthermore, the latent molecular embedding is invertible, enabling the design pipeline to automatically generate new monomers from the learned chemical subspace. We illustrate this functionality by targeting several properties, including high and low glass transition temperatures (Tg), and demonstrate that our model can identify new candidates with values that surpass those in the training set. The ease with which the proposed framework navigates both chemical diversity and data scarcity offers a promising route to accelerate and broaden the search for functional materials.

Han, Ming [Univ. of Chicago, IL (United States)]↗

A free-standing lithium phosphorus oxynitride thin film electrolyte promotes uniformly dense lithium metal deposition with no external pressure

Lithium phosphorus oxynitride (LiPON) is an amorphous solid electrolyte that has been extensively studied over the last three decades. Despite the promise of pairing it with various electrode materials, LiPON’s rigidity and air sensitivity set limitations to understanding its intrinsic properties. We report a methodology to synthesize LiPON in a free-standing form that manifests remarkable flexibility and a Young’s modulus of ∼33 GPa. We use solid-state nuclear magnetic resonance and differential scanning calorimetry to quantitatively reveal the chemistry of the Li/LiPON interface and the presence of a well-defined LiPON glass-transition temperature of 207 °C. Combining interfacial stress and a gold seeding layer, our free-standing LiPON shows a uniformly dense deposition of lithium metal without the aid of external pressure. This free-standing LiPON film offers opportunities to study fundamental properties of LiPON for interface engineering for solid-state batteries.

25 ENERGY STORAGE↗

Dynamics at the crystal-melt interface in a supercooled chalcogenide liquid near the glass transition

Direct quantitative measurements of nanoscale dynamical processes associated with structural relaxation and crystallization near the glass transition are a major experimental challenge. These type of processes have been primarily treated as macroscopic phenomena within the framework of phenomenological models and bulk experiments. Here, we report x-ray photon correlation spectroscopy measurements of dynamics at the crystal-melt interface during the radiation induced formation of Se nano-crystallites in pure Se and in binary AsSe 4 glass-forming liquids near their glass transition temperature. We observe a heterogeneous dynamical behaviour where the intensity correlation functions g 2 (q, t) exhibits either a compressed or a stretched exponential decay, depending on the size of the Se nano-crystallites. The corresponding relaxation timescale for the AsSe 4 liquid increases as the temperature is raised, which can be attributed to changes in the chemical composition of the melt at the crystal-melt interface with the growth of the Se nano-crystallites.

36 MATERIALS SCIENCE↗

Design of closed-loop recycling production of a Diels–Alder polymer from a biomass-derived difuran as a functional additive for polyurethanes

Acetalization of biomass-derived 5-hydroxymethyl furfural (HMF) with pentaerythritol produced a difuran (HPH) monomer in the presence of an acid catalyst. A recyclable polymer was then synthesized by Diels–Alder reaction of bismaleimide and the HMF-derived difuran (HPH). A polyurethane, produced from the Diels–Alder polymer has a higher glass transition temperature than a polyurethane, produced from ethylene glycol. The polyurethane, containing Diels–Alder polymer also has a self-healing ability. The Diels–Alder polymer could be hydrolyzed in acidic acetate buffer at 60 °C to produce the monomers for recycling. Each produced monomer was separated by solvent extraction, and the extracted monomers were recovered in different solvent fractions, such as aqueous, ethyl acetate, and acetone fractions. Techno economic analysis was used to assess the minimum selling price ($\$14.1$ per kg) for the primary production of Diels–Alder polymer at a feed capacity of 400 tons per year. The economic viability of the primary recovery process for the most expensive recovered monomer, bismaleimide, was assessed by calculating the minimum selling price of the bismaleimide ($\$15.2$ per kg). In conclusion, a circular closed-loop recycling production process for the Diels–Alder polymer was developed and this approach can produce the Diels–Alder polymer at $8.2 per kg when the feed capacity was 40 ktons per year.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Design, synthesis, and characterization of vinyl-addition polynorbornenes with tunable thermal properties

Unfunctionalized vinyl-addition polynorbornene (VAPNB) possesses many outstanding properties such as high thermal, chemical, and oxidative stability. These features make VAPNB a promising candidate for many engineering applications. However, VAPNB has a small service window between its glass transition temperature (T g ) and decomposition temperature (T d ), and it cannot be readily processed in a melt state. In this work, we demonstrate that the service window of VAPNBs can be tailored through the use of norbornene monomers bearing alkyl, aryl, and aryl ether substituents. The vinyl addition homopolymerization and copolymerization of these functionalized norbornyl-based monomers yielded VAPNBs with high T' g s (>150 °C) and large service windows (T d –T g > 100 °C), which are comparable to other commercial engineering thermoplastics. To further establish the feasibility of melt processing, a functionalized VAPNB material with T g = 209 °C and a service window of 170 °C was successfully extruded and molded into bars. Subsequent characterization of the bars by dynamic mechanical analysis (DMA), nuclear magnetic resonance spectroscopy (NMR), and gel permeation chromatography (GPC) revealed only minor signs of polymer degradation. Furthermore, these studies suggest that substituted VAPNBs could be developed into a new class of engineering thermoplastics that is compatible with workhorse melt processing techniques such as extrusion and injection molding, as well as emerging techniques such as extrusion-based 3D printing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Covalently integrated silica nanoparticles in poly(ethylene glycol)-based acrylate resins: thermomechanical, swelling, and morphological behavior

Nanocomposites integrate functional nanofillers into viscoelastic matrices for electronics, lightweight structural materials, and tissue engineering. Herein, the effect of methacrylate-functionalized (MA-SiO 2 ) and vinyl-functionalized (V-SiO 2 ) silica nanoparticles on the thermal, mechanical, physical, and morphological characteristics of poly(ethylene glycol) (PEG) nanocomposites was investigated. The gel fraction of V-SiO 2 composites decreases upon addition of 3.8 wt% but increases with further addition (>7.4 wt%) until it reaches a plateau at 10.7 wt%. The MA-SiO 2 induced no significant changes in gel fraction and both V-SiO 2 and MA-SiO 2 nanoparticles had a negligible impact on the nanocomposite glass transition temperature and water absorption. The Young's modulus and ultimate compressive stress increased with increasing nanoparticle concentration for both nanoparticles. Due to the higher crosslink density, MA-SiO 2 composites reached a maximum mechanical stress at a concentration of 7.4 wt%, while V-SiO 2 composites reached a maximum at a concentration of 10.7 wt%. Scanning electron microscopy, transmission electron microscopy, and small-angle X-ray scattering revealed a bimodal size distribution for V-SiO 2 and a monomodal size distribution for MA-SiO 2 . Although aggregates were observed for both nanoparticle surface treatments, V-SiO 2 dispersion was poor while MA-SiO 2 were generally well-dispersed. Finally, these findings lay the framework for silica nanofillers in PEG-based nanocomposites for advanced manufacturing applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗