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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Role of solvation site segmental dynamics on ion transport in ethylene-oxide based side-chain polymer electrolytes

Ion conducting capability is often imparted to polymeric materials through short polyether side-chains, and yet the impact of this graft polymer architecture on ion solvation and conduction has not been fully explored. Here, we use a combination of impedance spectroscopy, vibrational spectroscopy, and atomistic molecular dynamics (MD) to compare the conductivity, ionic interactions, and polymer dynamics in a series of graft polyether electrolytes. We find that in poly[(oligo ethylene oxide)methyl ether methacrylate] (POEM), a widely used graft polymer electrolyte, the ionic conductivity drops more than an order of magnitude as the side-chain length is decreased from nine ethylene oxide (EO) units to three. This difference in conductivity is unexplained by differences in the calorimetric glass transition temperature (T g ), which varies only slightly with side-chain length. Furthermore, through vibrational spectroscopy and MD simulations we demonstrate that both linear and graft polyethers solvate Li⁺ ions effectively and dissociate them from large counterions, irrespective of side-chain length. Li⁺ ions do, however, show preferential solvation by EO units far from the methacrylate backbone. Similarly, EO units far from the backbone show enhanced segmental dynamics, while those near the immobile methacrylate group move substantially more slowly, as quantified by bond vector autocorrelation relaxation times. This heterogeneity in both ion solvation and local segmental relaxation explains variation in ion conductivity where material-averaged properties such as T g and number of free ions fail to do so. Importantly, the ionic conductivity is dictated primarily by the segmental mobility of the EO units which form effective solvation sites, rather than system-wide dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Simultaneously characterization of tumoral angiogenesis and vasculogenesis in stem cell-derived teratomas

Highlights: • CAM supports the growth and differentiation of embryonic stem cells into teratomas. • In teratomas, parenchymal Embryonic stem cell-derived endothelial cells form chimeric vessels with stromal endothelial cells. • CAM allows the simultaneously characterization of vasculogenesis and angiogenesis processes. Tumor neovascularization may occur via both angiogenic and vasculogenic events. In order to investigate the vessel formation during tumor growth, we developed a novel experimental model that takes into account the differentiative and tumorigenic properties of Embryonic Stem cells (ESCs). Leukemia Inhibitory Factor-deprived murine ESCs were grafted on the top of the chick embryo chorionallantoic membrane (CAM) in ovo. Cell grafts progressively grew, forming a vascularized mass within 10 days. At this stage, the grafts are formed by cells with differentiative features representative of all three germ layers, thus originating teratomas, a germinal cell tumor. In addition, ESC supports neovascular events by recruiting host capillaries from surrounding tissue that infiltrates the tumor mass. Moreover, immunofluorescence studies demonstrate that perfused active blood vessels within the tumor are of both avian and murine origin because of the simultaneous occurrence of angiogenic and vasculogenic events. In conclusion, the chick embryo ESC/CAM-derived teratoma model may represent a useful approach to investigate both vasculogenic and angiogenic events during tumor growth and for the study of natural and synthetic modulators of the two processes.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Neutron Reflectometry Reveals Diffusion in Contrast-Matched Brush Particle Bilayers

A material system for performing layer-spread experiments on brush particle bilayers is presented and used to determine the diffusion constant of brush particles in the melt state. Selective deuteration of the core and shell of organo-silica nanoparticles grafted with poly(methyl methacrylate) was used to match the scattering length density of the core and the polymer canopy layer. This subdued the scattering of particle cores (i.e., formfactor scattering) and enabled the analysis of the interdiffusion kinetics using neutron reflectivity. For low molecular grafts, i.e., grafts with a molecular weight below the entanglement limit, the interdiffusion kinetics revealed both a sub- and Fickian diffusion regime. The former was attributed to the local dynamics that was constrained by the slow-moving cores of neighboring brush particles that acted as long-lived physical cross-links. No transition to Fickian diffusion was observed for entangled systems, even at prolonged annealing times. This suggested a higher level of kinetic restraint in entangled brush particle melts as compared to, for example, star polymers with a comparable chain length for which Fickian diffusion has been reported under similar conditions.

Diffusion, Polymer Grafted Nanoparticles, Neutron ↗
DOE OSTI2025

Reversible Nanocomposite by Programming Amorphous Polymer Conformation Under Nanoconfinement

Nanoconfinements are utilized to program how polymers entangle and disentangle as chain clusters to engineer pseudo bonds with tunable strength, multivalency, and directionality. When amorphous polymers are grafted to nanoparticles that are one magnitude larger in size than individual polymers, programming grafted chain conformations can "synthesize" high-performance nanocomposites with moduli of ≈25GPa and a circular lifecycle without forming and/or breaking chemical bonds. These nanocomposites dissipate external stresses by disentangling and stretching grafted polymers up to ≈98% of their contour length, analogous to that of folded proteins; use both polymers and nanoparticles for load bearing; and exhibit a non-linear dependence on composition throughout the microscopic, nanoscopic, and single-particle levels.

Chen, Tiffany↗
DOE OSTI2025

In‐Scribe Silane Bonding for Mechanical Reinforcement of Perovskite Photovoltaic Modules

Despite the extraordinary rise in power conversion efficiency over the last decade, metal halide perovskite (MHP) photovoltaics remain more mechanically fragile than other PV technologies. In this work, the scribe area, created by the monolithic interconnection of thin-film solar cells, is used to extrinsically reinforce the mechanical robustness of packaged MHP solar modules. In contrast to the epoxy-based chemistries often leveraged in the MHP literature, silane-grafted polyolefin encapsulants are designed to form strong covalent bonds to oxide surfaces, specifically to glass and the transparent conductive oxide at the base of the scribe line. Pseudo-modules encapsulated with silane-grafted polyolefin are measured with more than an order-of-magnitude enhancement infracture energy from 0.27 ± 0.01 J·m −2 (no scribes) to 5.97 ± 0.42 J·m −2 (scribes perpendicular to delamination directioncovering ≈2.2% of the module area). The silane-grafted polyolefin retains strong adhesion even after undergoing an accelerated IEC 61215 thermal cycling test consisting of 250 cycles. We find that the in-scribe bonding allows perovskite modules to have adhesion strength comparable to commercial c-Si and CdTe technologies with only 5% reduction in the active module area. This manufacturing-compatible approach offers a practical solution to address the mechanical integrity challenges in MHP solar modules, regardless of cell architecture.

14 SOLAR ENERGY↗
DOE OSTI2022

Supported Lanthanum Borohydride Catalyzes CH Borylation Inside Zeolite Micropores

Abstract The zeolite‐supported lanthanide La(BH 4 ) x ‐HY 30 catalyzes C−H borylation of benzene with pinacolborane (HBpin), providing a complementary approach to precious, late transition metal‐catalyzed borylations. The reactive catalytic species are generated from La grafted at the Brønsted acid sites (BAS) in micropores of the zeolite, whereas silanoate‐ and aluminoate‐grafted sites are inactive under the reaction conditions. During typical catalytic borylations, conversion to phenyl pinacolborane (PhBpin) is zero‐order in HBpin concentration. A turnover number (TON) of 167 is accessed by capping external silanols, selectively grafting at BAS sites, and adding HBpin slowly to the reaction.

Li, Yuting↗
DOE OSTI2022

Supported Lanthanum Borohydride Catalyzes CH Borylation Inside Zeolite Micropores

Abstract The zeolite‐supported lanthanide La(BH 4 ) x ‐HY 30 catalyzes C−H borylation of benzene with pinacolborane (HBpin), providing a complementary approach to precious, late transition metal‐catalyzed borylations. The reactive catalytic species are generated from La grafted at the Brønsted acid sites (BAS) in micropores of the zeolite, whereas silanoate‐ and aluminoate‐grafted sites are inactive under the reaction conditions. During typical catalytic borylations, conversion to phenyl pinacolborane (PhBpin) is zero‐order in HBpin concentration. A turnover number (TON) of 167 is accessed by capping external silanols, selectively grafting at BAS sites, and adding HBpin slowly to the reaction.

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

Monitoring SEIRAS on a Graphitic Electrode for Surface-Sensitive Electrochemistry: Real-Time Electrografting

The ubiquity of graphitic materials in electrochemistry makes it highly desirable to probe their interfacial behavior under electrochemical control. Probing the dynamics of molecules at the electrode/electrolyte interface is possible through spectroelectrochemical approaches involving surface-enhanced infrared absorption spectroscopy (SEIRAS). Usually, this technique can only be done on plasmonic metals such as gold or carbon nanoribbons, but a more convenient substrate for carbon electrochemical studies is needed. Here, we expanded the scope of SEIRAS by introducing a robust hybrid graphene-on-gold substrate, where we monitored electrografting processes occurring at the graphene/electrolyte interface. These electrodes consist of graphene deposited onto a roughened gold-sputtered internal reflection element (IRE) for attenuated total reflectance (ATR) SEIRAS. The capabilities of the graphene-gold IRE were demonstrated by successfully monitoring the electrografting of 4-amino-2,2,6,6-tetramethyl-1-piperidine N -oxyl (4-amino-TEMPO) and 4-nitrobenzene diazonium (4-NBD) in real time. These grafts were characterized using cyclic voltammetry and ATR-SEIRAS, clearly showing the 1520 and 1350 cm –1 NO 2 stretches for 4-NBD and the 1240 cm –1 C–C, C–C–H, and N–Ȯ stretch for 4-amino-TEMPO. Successful grafts on graphene did not show the SEIRAS effect, while grafting on gold was not stable for TEMPO and had poorer resolution than on graphene-gold for 4-NBD, highlighting the uniqueness of our approach. The graphene-gold IRE is proficient at resolving the spectral responses of redox transformations, unambiguously demonstrating the real-time detection of surface processes on a graphitic electrode. This work provides ample future directions for real-time spectroelectrochemical investigations of carbon electrodes used for sensing, energy storage, electrocatalysis, and environmental applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Strategies toward the Synthesis of Advanced Functional Sorbent Performance for Uranium Uptake from Seawater

A polymer fiber-based adsorbent (AF1) composed of acrylonitrile and itaconic acid functional groups was synthesized by a radiation-induced graft polymerization technique onto hollow-gear shaped polyethylene (PE) fibers. Investigation of the optimum reaction parameters for the conversion of grafted cyano moieties into amidoxime groups was conducted by the reaction with hydroxylamine at different temperatures and periods in a variety of aqueous and organic solvents. The 13 C CP/MAS spectra of amidoximated AF1 adsorbent fibers from water–methanol and dimethyl sulfoxide (DMSO) revealed that both the cyclic imide dioxime and open-chain amidoxime were formed through the reaction. The conversion from amidoxime to imide dioxime was found to occur slowly and gradually with the increasing reaction time. The quicker diffusion of DMSO as compared to that of water–methanol, in the grafted trunk PE fiber, resulted in faster kinetics of the amidoximation reaction. The uranium adsorption capacity of the amidoximated AF1 samples was determined after (i) 24 h contact with sodium-based brine spiked with uranium and (ii) 56 days of exposure to filtered seawater (Sequim Bay, WA, USA) in flow-through columns. Finally, the uranium extraction performance of the adsorbents after exposure to filtered seawater was consistent with the laboratory screening results, and the amidoximated AF1 samples (in DMSO at 70 °C for 3 h) exhibited the highest 56 day uranium adsorption capacity (5.04 ± 0.15 g U/kg-ads) with faster adsorption kinetics compared to the pristine AF1 adsorbents.

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

Single-Walled Zeolitic Nanotube–Poly(oxazoline) Nanocomposites as Heterogeneous Catalysts for Acid–Base Cascade Reactions

Zeolites with a unique, 1-dimensional form factor were recently discovered − zeolite nanotubes (ZNTs). Here we describe the synthesis and characterization of NaH-ZNTpoly( oxazoline) composites targeting liquid-phase acid−base cascade catalysis. NaH-ZNT, a one-dimensional zeolite analogue with mesoporosity (3−4 nm) associated with nanotubes and inherent Brønsted acid sites associated with the microporous zeolite domains, is functionalized with poly(oxazoline)-based triblock copolymers with varying molecular weights (3−17 kDa). The composites are characterized using N2 sorption, STEM, FTIR, and elemental analysis, confirming successful grafting and preservation of the zeolite nanotube structure. The composites’ catalytic performance is evaluated through separate acid and base reactions, followed by a combined cascade of a deacetalization−Knoevenagel condensation for the synthesis of chalcone compounds. High initial reaction rates are demonstrated, but modest overall cascade product formation rates are observed, attributed to interactions between Brønsted acid sites and base amine groups that occur in the polymer-grafted systems. Physical mixtures of NaH-ZNT-SH and poly(oxazoline)s, lacking covalent linkages between ZNT and the polymer, support this supposition. This work demonstrates the potential of NaH-ZNT-poly(oxazoline) composites for liquid-phase cascade catalysis for synthesizing compounds of potential medicinal interest, highlighting the benefits of the grafting-to approach as well as the need for further optimization of the catalytic performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Topological Frustration as a New Parameter to Tune Morphology Revealed through Exploring the Continuum between A-B-C 3-Arm Star and Linear Triblock Polymers

Block polymers assemble into a variety of phase-separated morphologies based on volume fraction (φ) and interactions (χ) of the respective blocks. The arrangement of three different polymer blocks could either be a 3-arm star, with each block having one terminus attached to a common junction point or a linear A-B-C architecture. A versatile strategy is reported to synthesize a series of well-defined graft polymers that lie along the unexplored continuum between a 3-arm star and an A-B-C linear triblock polymer architecture. Using the technique of single-molecule insertion, precise control over the position of graft arm C along the B chain was achieved. A series of discrete graft polymers (PMMA-b-PS-g-PEO) with fixed φ and prescribed ω values that lie on the continuum between a 3-arm star (ω = 0) and linear triblock polymer (ω = 1) were synthesized. Morphological studies using small-angle X-ray scattering and conventional and energy-filtered transmission electron microscopy reveal the transition between lamellae, perforated lamellae, and cylindrical morphologies with systematic variation in the ω values, a trend attributed to the topological frustration and the associated χ values between the three blocks. Molecular dynamic simulations of coarse-grained models were found to predict phase diagrams that are consistent with the experimentally observed morphologies. Furthermore, our results suggest that changes in ω lead to topological frustration which is an important additional new design parameter that can be used to tune the morphology of multiblock polymers in addition to φ and χ.

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

Nanoparticle Diffusion in Miscible Polymer Nanocomposite Melts

X-ray photon correlation spectroscopy measurements were used to quantify the dynamics of bare and bimodal grafted silica nanoparticles mixed with PEO melts of different molecular weights. In dilute polymer nanocomposite (PNC) samples, we find diffusive NP behavior as described by the Stokes–Einstein relationship so long as the adsorbed PEO polymer layer is taken into account in determining both the effective NP size and its role on composite viscosity. The size of this bound layer was found to be approximately 2R g , where R g is the chain radius of gyration. We also expanded our system to investigate how the dynamics of grafted NPs differ from bare NPs with an adsorbed layer. We showed that the dynamics again can be determined by an effective NP radius at a scale smaller than the effective interparticle spacing; however, at larger length scales, the morphology and grafting parameters play a major role in the system dynamics. These results allow us to quantify NP ordering driven by polymer crystallization. It has previously been speculated that behavior is controlled by the relative ratio of time scale of crystal growth and the diffusive time scale of the NPs, a Peclet number. When the former time scale is longer, then the NPs are expected to be segregated into the interlamellar amorphous zones, while the NPs are too slow to be reorganized in the opposite case. We show here that this conjecture is quantitatively correct and the demarcation in behavior occurs for Pe = 1. Thus, we provide a way to estimate a critical spherulite growth rate for any semicrystalline PNC, at which a given NP can be ordered. Together, the results of this study permit us to tunably design PNCs through directed dispersion of NPs in a polymer matrix.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Mechanical Properties of Polyisoprene-Based Elastomer Composites

Herein we have explored the origins of mechanical reinforcement in elastomers filled with polymer-grafted nanoparticles (NPs). The brush chains are constructed from the same monomers as the polymer melt, although they have different microstructures (i.e., different amounts of trans and cis isomers). The NPs display a variety of morphologies depending on variations in the graft density of the polymers, with these morphologies hardly changing when the matrix (and the grafts) is cross-linked using dicumyl peroxide (DCP). NMR measurements show that the cross-link densities depend only on the DCP content and are independent of NP morphologies. We find that the elastic moduli of these materials are strongly dependent on the NP morphology but that the maximum reinforcement occurs when the NPs percolate, in a manner where the cores are exposed enough to have strong enthalpic interactions; these interactions could either be due to direct core–core van der Waals attractions or due to bridging interactions driven by polymers adsorbed on adjacent NPs. The nonlinear mechanical response of these materials is less sensitive to changes in NP morphology and loading. These results emphasize the important role of the exposed NP surface in determining the moduli of cross-linked elastomers. This last aspect is apparently less relevant for the corresponding uncross-linked melts filled with NPs.

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

Aqueous Carbon Capture Using Guanidinium-Functionalized Hollow Fiber Sorbent Contactors

As part of the growing suite of technologies aimed at combatting rising temperatures, negative emissions technologies have become a powerful tool in the global effort to minimize the consequences of human-induced climate change. Among these, carbon removal from aqueous sources, which contain much higher carbon concentrations than the atmosphere, remains largely unexplored. Indeed, developing robust and efficient carbon capture materials for usage in complex aqueous environments remains a significant challenge. Here, we explore the potential of functionalizing polyvinylidene fluoride (PVDF) hollow fiber contactors grafted with a guanidinium-derived polymer sorbent for carbon removal from aqueous sources, including saline waters. Computational screening against amine-based analogs is utilized to identify guanidinium as a promising motif for bicarbonate (HCO 3 – ) ions binding. To leverage this finding, synthesis of a guanidinium polymer and subsequent covalent grafting onto PVDF hollow fibers is employed to structured polymer–sorbent–grafted hollow fiber contactors. Our prototype achieves an initial HCO 3 – removal of 34% with an increase to 98% after four cycles. The functionalized fibers demonstrate aqueous stability over 13 adsorption/desorption cycles in model NaHCO 3 solutions where regeneration is facilitated by a mild pH swing. Importantly, the system maintains selective performance in the presence of competitive chloride ions over multiple cycles; carbon removal remained above 10% even at high (10:1) NaCl/NaHCO 3 ratios. These findings demonstrate the feasibility of sorbent-based aqueous carbon removal and highlight its potential as a promising approach for negative emissions.

carbon capture↗
DOE OSTI2020

Creation of discrete active site domains via mesoporous silica poly(styrene) composite materials for incompatible acid–base cascade reactions

This work highlights the design and synthesis of bifunctional mesoporous silicate – polymer composite dual acid–base supported cascade catalysts. Compartmentalization of the two incompatible active sites is sought by segregating acid sites on the silica surface, and base sites within polymer chains and/or polymer domains. The ability to isolate and segregate active sites via control of the mesoporous silica pore size and polymer molecular weight is probed with silica samples functionalized by a grafting-to process. Supplemental activator and reducing agent (SARA) atom transfer radical polymerization is used to synthesize random copolymers containing protected primary amines. Thiol–ene ‘click’ chemistry facilitates silica functionalization via a convergent approach, with the ene-functionalized polymer end group and silica-grafted thiols forming SBA/MCM-SH-poly(styrene-co-2-(4-vinylbenzyl)isoindoline-1,3-dione). Polymer deprotection and thiol oxidation produces primary amine/sulfonic acid containing composite catalysts. With the polymer supported Lewis base and silica grafted Brønsted acid, the two-step deacetalization – Knoevenagel condensation cascade is explored to assess the ability of these polymer/silica hybrids to segregate active sites, allowing both acid and base site accessibility. Six composite catalysts are synthesized and tested in individual and cascade reactions with kinetic results demonstrating that lower molecular weight SBA-15-P1 and MCM-41-P1 catalysts outperform (higher turnover frequencies and initial rates) their higher molecular weight analogues, as well as a polymer-free system containing molecular active sites dispersed on the silica surface. Higher molecular weight composite catalysts perform more poorly due to limited chain solubility, mass transfer limitations, and poor catalyst accessibility. In many cases, the polymer chains effectively thread into the mesopores, with higher molecular weight polymers leading to pore blockage and inhibited mass transfer.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Effect of surface modification on silica supported Ti catalysts for cyclohexene oxidation with vapor-phase hydrogen peroxide

Surface modification via grafting of organic moieties on a Lewis acid catalyst (silica supported Ti catalyst, Ti-SiO 2 ) alters the activation of H 2 O 2 in vapor-phase cyclohexene epoxidation. Grafting a fluorous group (1H,1H-perfluoro-octyl) suppresses activity of Ti-SiO 2 . Conversely, grafting either a nonpolar group (octyl) or a polar aprotic group (triethylene glycol monomethyl ether) enhances rates and shifts selectivity toward trans-1,2-cyclohexanediol.

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

Modulating thermal conductance at ligand/nanocrystal interfaces via oxygen-coordinated ligands

Here, the interfacial thermal conductance (h lig–NC ) between a cadmium selenide (CdSe) nanocrystal (NC) and three related organic ligands—olealdehyde, oleyl alcohol, and oleic acid—was investigated computationally. These ligands have the same carbon backbone but differ in the number and type of oxygen-coordinated headgroups (carbonyl and/or hydroxyl), leading to distinct bonding geometries involving monodentate and bidentate bonds. For a fully encapsulated NC, h lig–NC increases in the order of olealdehyde, oleic acid, and oleyl alcohol ligands. To isolate the contributions of h lig–NC from each headgroup type, the distinct bonding geometries were analyzed. Aldehyde and alcohol ligands, each featuring a single oxygen headgroup (carbonyl or hydroxyl), exhibit similar O–Cd separations and nearly identical h lig–NC per ligand at full surface coverage. However, the hydroxyl group in the alcohol ligand enables a higher ligand grafting density on the NC surface, resulting in a greater overall h lig–NC than the aldehyde-grafted NCs. In contrast, the oleic acid ligand forms multidentate bonds with the NC, leading to a shorter average O–Cd separation and a higher h lig–NC per ligand compared to monodentate bonds. Nevertheless, steric hindrance from the acid ligand's larger headgroup reduces its grafting density relative to alcohol ligands, ultimately resulting in a lower overall h lig–NC .

Wong, Kae-Lin [Zhejiang Univ., Hangzhou (China)] (↗
DOE OSTI2021

End-exclusion zones in strongly stretched, molten polymer brushes of arbitrary shape

Theories of strongly stretched polymer brushes, particularly the parabolic brush theory, are valuable for providing analytically tractable predictions for the thermodynamic behavior of surface-grafted polymers in a wide range of settings. Furthermore, the parabolic brush limit fails to describe polymers grafted to convex curved substrates, such as the surfaces of spherical nanoparticles or the interfaces of strongly segregated block copolymers. It has previously been shown that strongly stretched curved brushes require a boundary layer devoid of free chain ends, requiring modifications of the theoretical analysis. While this “end-exclusion zone” has been successfully incorporated into the descriptions of brushes grafted onto the outer surfaces of cylinders and spheres, the behavior of brushes on surfaces of arbitrary curvature has not yet been studied. We present a formulation of the strong-stretching theory for molten brushes on the surfaces of arbitrary curvature and identify four distinct regimes of interest for which brushes are predicted to possess end-exclusion zones, notably including regimes of positive mean curvature but negative Gaussian curvature. Through numerical solutions of the strong-stretching brush equations, we report predicted scaling of the size of the end-exclusion zone, the chain end distribution, the chain polarization, and the free energy of stretching with mean and Gaussian surface curvatures. Through these results, we present a comprehensive picture of how the brush geometry influences the end-exclusion zones and exact strong-stretching free energies, which can be applied, for example, to model the full spectrum of brush geometries encountered in block copolymer melt assembly.

36 MATERIALS SCIENCE↗