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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 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Multimorphic Materials: Spatially Tailoring Mechanical Properties via Selective Initiation of Interpenetrating Polymer Networks

Access to multimaterial polymers with spatially localized properties and robust interfaces is anticipated to enable new capabilities in soft robotics, such as smooth actuation for advanced medical and manufacturing technologies. Here, orthogonal initiation is used to create interpenetrating polymer networks (IPNs) with spatial control over morphology and mechanical properties. Base catalyzes the formation of a stiff and strong polyurethane, while blue LEDs initiate the formation of a soft and elastic polyacrylate. IPN morphology is controlled by when the LED is turned “on”, with large phase separation occurring for short time delays (≈1–2 min) and a mixed morphology for longer time delays (>5 min), which is supported by dynamic mechanical analysis, small angle X-ray scattering, and atomic force microscopy. Through tailoring morphology, tensile moduli and fracture toughness can be tuned across ≈1–2 orders of magnitude. Furthermore, a simple spring model is used to explain the observed mechanical behavior. Photopatterning produces “multimorphic” materials, where morphology is spatially localized with fine precision (<100 µm), while maintaining a uniform chemical composition throughout to mitigate interfacial failure. As a final demonstration, the fabrication of hinges represents a possible use case for multimorphic materials in soft robotics.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Directing Assembly of Mesoscale Multi‐Shell Morphologies of DNA Origami Crystals

Nature builds hierarchically ordered materials, such as seashells, wood, and bones, through spatially and temporally regulated growth. Mimicking such a level of control in synthetic systems remains challenging, particularly in achieving multiscale organizations with prescribed nanoscale arrangements and desired material morphologies. In this study, we introduce a DNA-based self-assembly strategy for constructing diverse multi-shell mesoscale morphologies from nanoscale lattices, enabling prescribed structural, and compositional 3D material patterns. Using DNA origami frames as modular monomers, we direct anisotropic epitaxial growth through addressable DNA frame binding motifs and encapsulate nanoparticles (NPs) in desired 3D patterns. Sequential monomer addition under thermodynamically favorable conditions enables shell growth through heterogeneous nucleation while minimizing unwanted homogeneous nucleation. Here, we demonstrate that DNA-encoded addressability enables epitaxial shell growth along specific lattice directions, yielding crystals with multilayered mesoscale organization, including tube-like (sushi roll) and plate-like (macaron) morphologies. Shell-specific NP configurations and compositions are achieved through addressable and differentiated placement of NPs within each shell, as validated by small-angle x-ray scattering and cross-sectional scanning transmission electron microscopy. We further demonstrate addressable NP release and reveal that shells modulate release kinetics. Together, these findings establish a platform for fabricating DNA origami crystals with programmable mesoscale morphologies, nanoscale structure, composition, and transport properties.

3D patterning↗
DOE OSTI2022

Restriction-In-Motion of Surface Ligands Enhances Photoluminescence of Quantum Dots - Experiment and Theory

Here the relationship between emission and ligand restriction of a series of ZnSe/ZnS quantum dots (QDs) encapsulated in nanoparticles is investigated systematically via experiments and quantum theory. The QDs have a ZnSe core and a ZnS shell, capped with hydrophobic ligands (triotylphosphine oxide/hexadecylamine), allowing them to be entrapped in a model biomembrane, bicelle, made of zwitterionic dipalmitoyl and dihexanoyl phosphatidylcholines and charged dipalmitoyl phosphatidylglycerol. Enhanced photoluminescence is observed upon encapsulation, depending on the QD-to-lipid ratio. Transmission electron microscopy and small-angle X-ray scattering confirm that QDs are preferably situated at the rim of bicellar discs. A simplified quantum dissipation heat-bath theory is proposed to correlate the enhancement with slower nonradiative processes caused by the restriction-in-motion (RIM) of the surface ligands. However, Fõrster resonance energy transfer due to QD aggregation counteracts the effect.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Monitoring Structural and Electronic Changes of Supported Metal Catalysts Using Combined X‐Ray Techniques

Supported metal nanoparticle catalysts have become increasingly crucial for many catalytic applications. However, long-term catalyst stability remains a problem due to catalyst deactivation caused by coke formation and sintering. The deposition of a thin overcoating via atomic layer deposition (ALD) onto metal-supported nanoparticles has shown to greatly inhibit catalyst deactivation. This work utilizes a model catalyst system comprised of Pt nanoparticles supported on Al 2 O 3 to demonstrate the effect of an atomically thin overcoating on supported metal nanoparticles. Continuous operando small-angle X-ray scattering (SAXS) and X-ray absorption near edge spectroscopy (XANES) monitor structural and electronic changes to the catalyst and overcoating during calcination. SAXS data fitting reveals the formation of nanopores in the overcoating at high temperatures, while XANES monitors the oxidation state of the Pt catalyst. Herein, the usefulness of combined X-ray techniques is demonstrated to characterize supported metal catalysts to further understanding of the synergistic effects of the ALD overcoating to aid in the design of new catalyst materials.

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

Ce IV 70 oxosulfate rings, frameworks, supramolecular assembly and redox activity

M IV molecular oxo-clusters (M=Zr, Hf, Ce, Th, U, Np, Pu) are prolific in bottoms-up material design, catalysis, and elucidating reaction pathways in nature and in synthesis. Here we introduce Ce 70 , a wheel-shaped oxo-cluster, [Ce IV 70 -(OH) 36 (O) 64 (SO 4 ) 60 (H 2 O) 10 ] 4- . Ce 70 crystallizes into intricate high pore volume frameworks with divalent transition metals and Ce-monomer linkers. Eight crystal-structures feature four framework types in which the Ce 70 -rings are linked as propellers, in offset-stacks, in a tartan pattern, and as isolated rings. In this work, small-angle X-ray scattering of Ce 70 dissolved in butylamine, with and without added cations (Ce IV , alkaline earths, Mn II ), shows the metals‘ differentiating roles in ring linking, leading to supramolecular assemblies. The large acidic pores and abundant terminal sulfates provide ion-exchange behavior, demonstrated with U IV and Nd III . Frameworks featuring Ce III/IV -monomer linkers demonstrate both oxidation and reduction. Furthermore, this study opens the door to mixed-metal, highly porous framework catalysts, and new clusters for metal-organic framework design.

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

Multi–Step Nucleation of a Crystalline Silicate Framework via a Structurally Precise Prenucleation Cluster

Hierarchical nucleation pathways are ubiquitous in the synthesis of minerals and materials. In the case of zeolites and metal–organic frameworks, pre-organized multi-ion “secondary building units” (SBUs) have been proposed as fundamental building blocks. However, detailing the progress of multi-step reaction mechanisms from monomeric species to stable crystals and defining the structures of the SBUs remains an unmet challenge. Furthermore, combining in situ nuclear magnetic resonance, small-angle X-ray scattering, and atomic force microscopy, we show that crystallization of the framework silicate, cyclosilicate hydrate, occurs through an assembly of cubic octameric Q 3 8 polyanions formed through cross-linking and polymerization of smaller silicate monomers and other oligomers. These Q 3 8 are stabilized by hydrogen bonds with surrounding H 2 O and tetramethylammonium ions (TMA + ). When Q 3 8 levels reach a threshold of ≈32 % of the total silicate species, nucleation occurs. Further growth proceeds through the incorporation of [(TMA) x (Q 3 8 )•n H 2 O] (x–8) clathrate complexes into step edges on the crystals.

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

Discharge Rate‐Driven Li 2 O 2 Growth Exhibits Unconventional Morphology Trends in Solid‐State Li‐O 2 Batteries

Solid-state lithium oxygen batteries (LOBs) are known for their enhanced safety, higher electrochemical stability, and improved energy density compared to liquid-state LOBs. However, the investigation of solid-state LOBs is limited with little understanding of their discharge and charge processes. In this work, a polymer-based solid-state LOB is used to investigate the effect of discharge rate on lithium peroxide (Li 2 O 2 ) formation, the oxygen evolution reaction (OER), and cycle performance. Notably, we observe a counterintuitive trend: Li 2 O 2 particle size increases with increasing discharge current density, in contrast to liquid systems. This behavior arises from inherent space charge layers that restrict Li⁺ transport under high current, and spatially heterogeneous active sites at the solid electrolyte–cathode interface, directly evidenced by small angle X-ray scattering (SAXS), which govern nucleation accessibility and promote site-selective Li 2 O 2 growth. Furthermore, higher current densities improve ORR and OER efficiency but accelerate anode degradation, while lower currents promote side reactions. These opposing effects result in a trade-off that defines an optimal discharge rate (0.1 mA cm -2 ) for maximizing cycle life. This study provides a new mechanistic perspective on discharge-driven processes in solid-state LOBs and offers practical guidelines for performance optimization in future high-energy battery systems.

Discharge current density↗
DOE OSTI2026

Tuning the Mechanical Properties of Crosslinked Copolymers via Sequence and Solvent‐Selective Swelling for Vat Photopolymerization

Block copolymers (BCPs) offer distinct advantages for vat photopolymerization by enabling mechanically programmable network structures through microphase-separated morphologies that can be kinetically trapped during curing, yielding properties unattainable in homogeneous resins. However, the respective roles of repeat-unit sequence and solvent environment, together with their interplay in directing network formation and mechanical performance, remain unclear. Here, we synthesize a series of CO 2 -based polycarbonate copolymers comprising a crosslinkable glassy poly(vinyl cyclohexene carbonate) (PVCHC, A block) and a non-crosslinkable soft poly(propylene carbonate) (PPC, B block). The polymer sequence is systematically varied (ABA, BAB, and statistical), and solvent choice controls block-selective swelling to jointly control gelation behavior, microphase morphology, and mechanical response through changes in the accessibility and local environment of photocrosslinkable vinyl groups during network formation, as revealed by photorheology and small angle x-ray scattering. By tuning polymer sequence and curing solvent, we transform nominally identical formulations from brittle to highly ductile materials, achieving a three-orders-of-magnitude range in toughness (0.003 to 9.1 MJ m −3 ). These results establish clear structure–processing–property relationships and identify polymer sequence and selective solvation as powerful strategies for programming both printability and performance of block copolymer resins for additive manufacturing.

additive manufacturing↗
DOE OSTI2020

Building [U IV 70 (OH) 36 (O) 64 ] 4– oxocluster frameworks with sulfate, transition metals, and U V

Uranium (IV) oxide clusters, colloids, and materials are designed and studied for 1) nuclear materials applications, 2) understanding environmental fate and transport of actinides, and 3) exploring the complex bonding behavior of open-shell f-elements. U IV -oxyhydroxsulfate clusters are particularly relevant in industrial processes and in nature. Recent studies have shown that counter-cations to these polynuclear anions differentiate rich structural topologies in the solid-state. Here we present nine different structures with wheel-shaped [U 70 (OH) 36 (O) 64 (SO 4 ) 60 ] 4- (U 70 ) linked into 1-dimensional and 2-dimensional frameworks with sulfate, divalent transition metals (Cr II , Fe II , Co II , Ni II ) and U V . Here, the small-angle X-ray scattering of these phases dissolved in butylamine reveals differing supramolecular assembly of U 70 clusters, controlled primarily by sulfates. However, observed trends in transition metal linking guide future design of U 70 -materials with different topologies. Finally, U 70 linking via U IV -O-U V -O-U IV bridges presents a rare example of mixed oxidation state uranium oxides without disorder.

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

Structure- and Interaction-Based Design of Anti-SARS-CoV-2 Aptamers

Aptamer selection against novel infections is a complicated and time-consuming approach. Synergy can be achieved by using computational methods together with experimental procedures. In this study, we aim to develop a reliable methodology for a rational aptamer in silico et vitro design. The new approach combines multiple steps: (1) Molecular design, based on screening in a DNA aptamer library and directed mutagenesis to fit the protein tertiary structure; (2) 3D molecular modeling of the target; (3) Molecular docking of an aptamer with the protein; (4) Molecular dynamics (MD) simulations of the complexes; (5) Quantum-mechanical (QM) evaluation of the interactions between aptamer and target with further analysis; (6) Experimental verification at each cycle for structure and binding affinity by using small-angle X-ray scattering, cytometry, and fluorescence polarization. By using a new iterative design procedure, structure- and interaction-based drug design (SIBDD), a highly specific aptamer to the receptor-binding domain of the SARS-CoV-2 spike protein, was developed and validated. The SIBDD approach enhances speed of the high-affinity aptamers development from scratch, using a target protein structure. The method could be used to improve existing aptamers for stronger binding. This approach brings to an advanced level the development of novel affinity probes, functional nucleic acids. It offers a blueprint for the straightforward design of targeting molecules for new pathogen agents and emerging variants.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

The Role of Alkalis in Orchestrating Uranyl-Peroxide Reactivity Leading to Direct Air Capture of Carbon Dioxide

Spectator ions have known and emerging roles in aqueous metal-cation chemistry, respectively directing solubility, speciation, and reactivity. Here, in this work, we isolate and structurally characterize the last two metastable members of the alkali uranyl triperoxide series, the Rb + and Cs + salts (Cs-U 1 and Rb-U 1 ). We document their rapid solution polymerization via small-angle X-ray scattering, which is compared to the more stable Li + , Na + and K + analogues. To understand the role of the alkalis, we also quantify alkali-hydroxide promoted peroxide deprotonation and decomposition, which generally exhibits increasing reactivity with increasing alkali size. Cs-U 1 , the most unstable of the uranyl triperoxide monomers, undergoes ambient direct air capture of CO 2 in the solid-state, converting to Cs 4 [U VI O 2 (CO 3 ) 3 ], evidenced by single-crystal X-ray diffraction, transmission electron microscopy, and Raman spectroscopy. We have attempted to benchmark the evolution of Cs-U 1 to uranyl tricarbonate, which involves a transient, unstable hygroscopic solid that contains predominantly pentavalent uranium, quantified by X-ray photoelectron spectroscopy. Powder X-ray diffraction suggests this intermediate state contains a hydrous derivative of CsU V O 3 , where the parent phase has been computationally predicted, but not yet synthesized.

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

Pertechnetate/perrhenate–capped Zr/Hf–Dihydroxide Dimers: Elucidating Zr–TcO 4 Co–Mobility in the Nuclear Fuel Cycle

Spent nuclear fuel contains heavy element fission products that must be separated for effective reprocessing for a safe and sustainable nuclear fuel cycle. 93 Zr and 99 Tc are high-yield fission products that co-transport in liquid-liquid extraction processes. Here we seek atomic-level information of this co-extraction process, as well as fundamental knowledge about Zr IV (and Hf IV ) aqueous speciation in the presence of topology-directing ligands such as pertechnetate (TcO 4 – ) and non-radioactive surrogate perrhenate (ReO 4 – ). In this context, we show that the flat tetrameric oxyhydroxyl-cluster [M IV 4 (OH) 8 (H 2 O) 16 ] 8+ (and related polymers) is dissociated by perrhenate/pertechnetate to yield isostructural dimers, M 2 (OH) 2 (XO 4 – ) 6 (H 2 O) 6 • 3H 2 O (M=Zr/Hf IV ; X=Re/Tc VII ), elucidated by single-crystal X-ray diffraction. We used these model compounds to understand the pervasive 93 Zr- 99 Tc coextraction with further speciation studies in water, nitric acid, and tetrabutylphosphate (TBP) -kerosene; where the latter two media are relevant to nuclear fuel reprocessing. SAXS (small angle X-ray scattering), compositional evaluation, and where experimentally feasible, ESI-MS (electrospray ionization mass spectrometry) showed that perrhenate/pertechnetate influence Zr/Hf IV -speciation in water. Here, in Zr-XO 4 solvent extraction studies to simulate fuel reprocessing, we provide evidence that TcO 4 – enhances extraction of Zr IV , and compositional analysis of the extracted metal-complexes (Zr-ReO 4 study) is consistent with the crystallized Zr IV 2 (OH) 2 (Re VII O 4 – ) 6 (H 2 O) 6 •dimer.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2025

Self‐Assembly Methods Induce Different Individual‐Polymer‐Block Solvation Responses

An understanding of block-specific responses to stimuli in self-assembled copolymers is essential for the effective design of responsive materials. Here, materials formed from different post-reaction processing methods of the same ROMP block copolymer exhibit different block-specific solvent responses, as characterized in situ by fluorescence lifetime imaging microscopy (FLIM). FLIM data were acquired by tagging the polar or nonpolar block separately with a covalently incorporated viscosity-sensitive fluorescent molecular rotor to measure the changing tightness or looseness of assembly upon changes in solvent composition. Rapid precipitation from an insoluble solvent to form a film results in tighter assembly and less difference in tightness/looseness between the two blocks. Further, it interrupts individual block-solvent response behavior. Both results indicate an apparent disruption of the core–shell assembly. This model from FLIM is further supported by differential scanning calorimetry (DSC) and small-angle X-ray scattering (SAXS) data from isolated solids, which show tighter long-range interactions and more long-range order in these kinetically trapped states. Here, the experiments develop FLIM as a method for pinpointing stimuli-responsive behaviors from different processing methods to individual blocks. Together these outcomes provide a future handle for tailoring solvent-triggered assembly/disassembly behavior.

López, Pía A. [University of California, Irvine, C↗
DOE OSTI2022

Controlling Rheology of Fluid Interfaces through Microblock Length of Sequence-Controlled Amphiphilic Copolymers

Previous studies have demonstrated that films of sequence-controlled amphiphilic copolymers display contact angles that depend on microblock size. This suggests that microblock length may provide a means of tuning surface and interfacial properties. In this work, the interfacial rheology of a series of sequence-controlled copolymers, prepared through the addition of bicyclo[4.2.0]oct-1(8)-ene-8-carboxamide (monomer A) and cyclohexene (monomer B) to generate sequences up to 24 monomeric units composed of (A m B n ) i microblocks, where m, n, and i range from 1 to 6. Interfacial rheometry is used to measure the mechanical properties of an air–water interface with these copolymers. As the microblock size increases, the interfacial storage modulus, G', increases, which may be due to an increase in the size of interfacial hydrophobic domains. Small-angle X-ray scattering shows that the copolymers have a similar conformation in solution, suggesting that any variations in the mechanics of the interface are due to assembly at the interface, and not on solution association or bulk rheological properties. This is the first study demonstrating that microblock size can be used to control interfacial rheology of amphiphilic copolymers. Here, the results provide a new strategy for controlling the dynamics of fluid interfaces through precision sequence-controlled polymers.

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

Nanostructure Scaling in Semi-Dilute Triblock Copolymer Gels

Here, there is a considerable body of work that describes the scaling of diblock copolymer micelle dimensions in dilute and semi-dilute solution based upon block degrees of polymerization and copolymer concentration. However, there is a lack of analogous information for semi-dilute ABA triblock copolymer gels, which consist of ABA triblock copolymer dissolved in midblock-selective (B-selective) solvent. The present study uses small angle X-ray scattering to extract micelle dimensions for numerous triblock copolymer gels that vary in copolymer identity (and hence block lengths) and copolymer concentration, as well as gels that contain various ratios of two unique triblock copolymers. Analysis of micelle structural data subsequently translates to universal scaling expressions for the micelle core radius – r A ≈ N A 0.53 N B -0.14 $\phi$ ABA 0.16 where N A and N B are the endblock and midblock degrees of polymerization, respectively, and $\phi$ ABA is the volume fraction of triblock copolymer in the gel – and for the intermicelle spacing – l AA ≈ N A 0.09 N B 0.29 $\phi$ ABA -0.35 . Each scaling expression describes the full collection of experimental data very well. Additionally, these scaling expressions are partially in line with expectations from semi-dilute diblock copolymer solution theory.

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

Dynamics of High Molecular Weight Cylindrical and Lamellar Block Copolymers with X‐ray Photon Correlation Spectroscopy

Here, the structure and dynamics of polystyrene (PS)-b-poly(ethylene oxide) block copolymers (BCPs) are studied. The BCPs exhibit microphase-separated cylindrical and lamellar morphologies. Structural dynamics are measured with X-ray photon correlation spectroscopy in the small-angle regime. Morphologies and domain sizes are evaluated using small-angle X-ray scattering (SAXS), scanning electron microscopy, and atomic force microscopy. Different solvent processing conditions are investigated. Grain sizes evaluated using SAXS are found to depend on processing only for the rubbery majority BCP. The structural relaxation times are examined as a function of PS volume fraction, temperature, morphology, and structural sizes. Well above the glass transition temperature (T g ) of PS, all samples exhibit stretched autocorrelation decays and diffusive dynamics. Near T g of PS, the dynamics of all samples are anomalous with compressed autocorrelation decays and hyperdiffusive dynamics. This transition occurs at 153 °C or 1.13 T g of PS. In the diffusive regime (at high temperature), structural relaxation times are dependent on the processing method. Near PS T g (at low temperature), structural relaxation times scale with the PS volume fraction. Structural relaxation times do not correlate with grain size, indicating that the out-of-equilibrium state of PS dominates the structural dynamics of these strongly phase-segregated BCPs.

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

Alignment frustration in block copolymer films with block copolymer grafted TiO 2 nanoparticles under soft-shear cold zone annealing

Block copolymers (BCPs) have received significant attention as promising candidates for sequestering nanoparticles and fabrication of aligned nanostructures with optimal optical or electrical properties. We investigate the influence of static and dynamic thermal field on the alignment of polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) BCP morphology with the loading of novel poly(methyl methacrylate-block-Polystyrene) (PMMA-b-PS)-grafted-TiO 2 nanoparticles (BCP-g-TiO 2 ). Observation of characteristics IR peaks for PMMA and PS in BCP-g-TiO 2 nanoparticles and Transmission Electron Microscopy (TEM) results of the outer coating of core nanoparticle, validate the grafting to approach in synthesizing BCP-g-TiO 2 . In this work, we report that under the sharp dynamic thermal field, at low loading of BCP-g-TiO 2 , there is good dispersion of nanoparticles in unidirectionally aligned BCP matrix in film interior probed by GISAXS, while, at high nanoparticle loading (~10 wt%), there is local frustration in the unidirectional alignment of the BCP matrix due to aggregation of BCP-g-TiO 2 nanoparticles. However, Grazing incidence small angle X-ray scattering (GISAXS) shows clearly that the BCP films remain largely locally ordered at the domain scale, despite these large perturbations to long-range ordering even at high loading level, while bringing in new TiO 2 functionality to the BCP films, such as UVO absorptivity or biofouling prevention, important to potential new applications of such membranes.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

Effect of network connectivity on the mechanical and transport properties of block copolymer gels

Establishing the independent tunability of transport and mechanical properties in polymer gels would significantly contribute to their implementation as transdermal drug delivery media, among other things. The work conducted herein uses facile changes in the formulation of physically crosslinked styrenic ABA/AB block copolymer organogels to alter their mechanical properties independently from the mass transport of an internally-loaded nanocarrier. Therefore, such independent tunability is made possible by altering the relative amounts of ABA triblock and AB diblock copolymers while holding total copolymer concentration fixed. Specifically, three series of gels each with a fixed total copolymer concentration (10, 20, or 30 wt%) comprised of varying triblock copolymer concentration are studied. Small angle x-ray scattering confirms that, at the nanoscale, only gel network connectivity changes within each series, while mechanical and release experiments show that increasing network connectivity leads to significant growth of gel moduli, but little change in nanocarrier release rate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗