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At least 631 records · Page 35

Microphase Separation of Randomly Linked Branched Polystyrene/Polylactic Acid for Formation of Cocontinuous Nanostructures

Cocontinuous polymeric nanomaterials have gained attention for their ability to preserve distinct properties of constituent microphases within a single material. Randomly linked copolymer networks have shown very wide stability windows for disordered cocontinuous phases (extending over ≈ 30 wt % in composition), but the reliance on a network architecture prevents subsequent solution- or melt-processing. Furthermore, the key factors contributing to cocontinuity have remained unclear. We recently found that randomly linked star copolymers (RSCs) can exhibit a cocontinuous window as wide as 25 wt % in the case of 4-arm stars, suggesting that while a network architecture is not essential for the formation of disordered cocontinuous phases, the presence of random elastic forces in such architectures may indeed facilitate their formation. In addition, the behavior was found to be highly sensitive to arm number, with 6-arm RSCs exhibiting almost no cocontinuous phase. These results raised a key mechanistic question regarding the contribution of random elastic forces, originating from strands that bridge between junctions, in stabilizing disordered cocontinuous phases. In the current study, we synthesized randomly linked branched copolymers (RBCs) of polystyrene (PS) and poly(D,L-lactic acid) (PLA), which represent an intermediate architecture between networks and stars. This approach allows for the introduction of elastic contributions from strands bridging between different junctions, while still maintaining the processability advantages of a non-network architecture. The cocontinuous regions of the PS/PLA RBCs, with varying polymer and linker functionalities (f p and f l , respectively), were characterized by small-angle X-ray scattering, gravimetry, and scanning electron microscopy. We found that the cocontinuous windows of RBCs typically expanded with increasing elastic contributions and exhibited reduced sensitivity to junction-functionality compared to RSCs. Notably, RBCs with f p = 1.50 and f l = 3, which had large molecular weights due to proximity to the gel point, achieved a cocontinuous window of ≈ 34 wt %, which is almost twice as wide as analogous 3-arm RSCs and comparable to randomly linked networks. Leveraging this robust cocontinuity and solution-processability, we fabricated a film of interconnected nanoporous PS.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Birth of the Hydrated Electron via Charge-Transfer-to-Solvent Excitation of Aqueous Iodide

A primary means to generate hydrated electrons in laboratory experiments is excitation to the charge-transfer-to-solvent (CTTS) state of a solute such as I – (aq), but this initial step in the genesis of e – (aq) has never been simulated directly using ab initio molecular dynamics. Here, we report the first such simulations, combining ground- and excited-state simulations of I – (aq) with a detailed analysis of fluctuations in the Coulomb potential experienced by the nascent solvated electron. What emerges is a two-step picture of the evolution of e – (aq) starting from the CTTS state: I – (aq) + hν → I –* (aq) → I • (aq) + e – (aq). Notably, the equilibrated ground state of e – (aq) evolves from I –* (aq) without any nonadiabatic transitions, simply as a result of solvent reorganization. The methodology used here should be applicable to other photochemical electron transfer processes in solution, an important class of problems directly relevant to photocatalysis and energy transfer.

Carter-Fenk, Kevin↗

Application of the FUN3D Unstructured-Grid Navier-Stokes Solver to the 4th AIAA Drag Prediction Workshop Cases

FUN3D Navier-Stokes solutions were computed for the 4th AIAA Drag Prediction Workshop grid convergence study, downwash study, and Reynolds number study on a set of node-based mixed-element grids. All of the baseline tetrahedral grids were generated with the VGRID (developmental) advancing-layer and advancing-front grid generation software package following the gridding guidelines developed for the workshop. With maximum grid sizes exceeding 100 million nodes, the grid convergence study was particularly challenging for the node-based unstructured grid generators and flow solvers. At the time of the workshop, the super-fine grid with 105 million nodes and 600 million elements was the largest grid known to have been generated using VGRID. FUN3D Version 11.0 has a completely new pre- and post-processing paradigm that has been incorporated directly into the solver and functions entirely in a parallel, distributed memory environment. This feature allowed for practical pre-processing and solution times on the largest unstructured-grid size requested for the workshop. For the constant-lift grid convergence case, the convergence of total drag is approximately second-order on the finest three grids. The variation in total drag between the finest two grids is only 2 counts. At the finest grid levels, only small variations in wing and tail pressure distributions are seen with grid refinement. Similarly, a small wing side-of-body separation also shows little variation at the finest grid levels. Overall, the FUN3D results compare well with the structured-grid code CFL3D. The FUN3D downwash study and Reynolds number study results compare well with the range of results shown in the workshop presentations.

Lee-Rausch, Elizabeth M.↗

Multi-grid domain decomposition approach for solution of Navier-Stokes equations in primitive variable form

The new multigrid (or adaptive) pseudospectral element method was carried out for the solution of incompressible flow in terms of primitive variable formulation. The desired features of the proposed method include the following: (1) the ability to treat complex geometry; (2) high resolution adapted in the interesting areas; (3) requires minimal working space; and (4) effective in a multiprocessing environment. The approach for flow problems, complex geometry or not, is to first divide the computational domain into a number of fine-grid and coarse-grid subdomains with the inter-overlapping area. Next, it is necessary to implement the Schwarz alternating procedure (SAP) to exchange the data among subdomains, where the coarse-grid correction is used to remove the high frequency error that occurs when the data interpolation from the fine-grid subdomain to the coarse-grid subdomain is conducted. The strategy behind the coarse-grid correction is to adopt the operator of the divergence of the velocity field, which intrinsically links the pressure equation, into this process. The solution of each subdomain can be efficiently solved by the direct (or iterative) eigenfunction expansion technique with the least storage requirement, i.e. O(N(exp 3)) in 3-D and O(N(exp 2)) in 2-D. Numerical results of both driven cavity and jet flow will be presented in the paper to account for the versatility of the proposed method.

Ku, Hwar-Ching↗

Traveling Molten Zone Refining Process Development for Innovative Fuel Cycle Solutions

This ARPA-E ONWARDS project successfully developed and demonstrated an innovative immiscibility zone refining process for separating actinides from active fission products in metallic nuclear fuel applications. The technology addresses a critical challenge in advanced nuclear fuel cycles by providing a high-throughput, low-waste alternative to conventional electrorefining.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Towards Thermomechanical Processing of Alloy 709: Progress in Defining High-Temperature Deformation-Recrystallization "Space"

The Advanced Reactor Technologies (ART) Program has established a multi-year plan to develop Alloy 709 advanced stainless steel, generate the data package and develop material-specific design parameters in qualifying it as a new structural material for Class A construction in the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code, Section III, Division 5, High Temperature Reactors (ASME 2025). In collaboration with material vendors, the Advanced Materials Development activities under ART have successfully scaled the Alloy 709 plate form production from a laboratory heat of 500 pounds to commercial heats totaling 133,000 pounds of Alloy 709 plate fabricated from three heats. The goal of the overall Alloy 709 development program is to establish the necessary microstructural and mechanical properties relationship for Alloy 709 to ultimately develop fabrication parameters for other product forms such as bars, pipes, and forgings using the available ART Alloy 709 materials. This study will enable its deployment in the industry as an advanced construction material for high-temperature components. The objective of this Alloy 709 development work in FY 2025 is to experimentally determine the high-temperature deformation-recrystallization response of the Alloy 709 heats and to experimentally generate true stress-true strain data for Alloy 709 using the available commercial heat plate materials. Integral to this work is the previous characterization of the as-rolled materials and the determination of an effective solution-annealing process, which was reported in Y. Wang et al., 2023, and the evaluation of the effect of controlled cooling on the resultant precipitation in these commercial heats. This report summarizes and builds on the results of the previous reports to assess the high-temperature deformation behavior as a function of deformation temperature, strain and strain rate using commercial Alloy 709 heat 58776-3RB fabricated by G. O. Carlson and heat 529900-02 fabricated by Allegheny Technologies Incorporated (ATI) Specialty Rolled Products.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Solid Solvation Assisted Electrical Doping Conserves High‐Performance in 500 nm Active Layer Organic Solar Cells

Abstract Organic solar cells (OSCs) process fascinating solution‐printing capability to achieve low‐cost and large‐scale manufacture. However, the rapid power conversion efficiency (PCE) decay with active layer thickness enlargement inhibits the implement of OSCs’ potential advantages. To overcome the bottlenecks of PCE decay in thick active layer OSCs, the electrical doping with componential selectivity in bulk heterojunction (BHJ) film is achieved by introducing a solid solvation additive. Benefiting from the higher exciton splitting efficiency together with the longer drift (L dr ) and diffusion (L diff ) lengths, an OSC with 100 nm BHJ film demonstrates a PCE increment from 16.44% to 18.24% with prolonged dark and illuminated storage stabilities. Applying the solid solvation assisted (SSA) doping method in the OSCs with 500 nm active layer, the PCE significantly increases by 31.9%, from the original value of 11.79% to 15.55%. It further improves to 15.84% in a ternary blend thick‐film device, which is the record value to the best of our knowledge. Besides, the SSA doping narrows the PCE gap between the 0.04 and 1 cm 2 devices. All improvements demonstrate the great potential of SSA doping for OSC commercial manufacture, since it optimizes the photovoltaic performance under all practical conditions of long‐term, thick‐film, and large‐area.

Chemistry↗

Zinc‐Imidazolate Films as an All‐Dry Resist Technology

Here, motivated by the drawbacks of solution phase processing, an all‐dry resist formation process is presented that utilizes amorphous zinc‐imidazolate (aZnMIm) films deposited by atomic/molecular layer deposition (ALD/MLD), patterned with electron beam lithography (EBL), and developed by novel low temperature (120 °C) gas phase etching using 1,1,1,5,5,5‐hexafluoroacetylacetone (hfacH) to achieve well‐resolved 22 nm lines with a pitch of 30 nm. The effects of electron beam irradiation on the chemical structure and hfacH etch resistance of aZnMIm films are investigated, and it is found that electron irradiation degrades the 2‐methylimidazolate ligands and transforms aZnMIm into a more dense material that is resistant to etching by hfacH and has a C:N:Zn ratio effectively identical to that of unmodified aZnMIm. These findings showcase the potential for aZnMIm films to function in a dry resist technology. Sensitivity, contrast, and critical dimensions of the patterns are determined to be 37 mC cm −2 , 0.87, and 29 nm, respectively, for aZnMIm deposited on silicon substrates and patterned at 30 keV. This work introduces a new direction for solvent‐free resist processing, offering the prospect of scalable, high‐resolution patterning techniques for advanced semiconductor fabrication processes.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

PFSA-Ionomer Dispersions to Thin-Films: Interplay Between Sidechain Chemistry and Dispersion Solvent

In fuel-cell catalyst layers (CLs), ionomers exists as nanoscale thin-films binding catalyst particles, wherein ionic and gaseous species transport to catalyst sites. To improve film function, ionomers have been designed based on the prototypical perfluorosulfonic acid (PFSA). Since CLs are fabricated through solution-based processing of inks, understanding how ink/dispersion solvent impacts ionomer interactions and function is important to guide future ionomer design. Herein, PFSA and its chemical derivatives are characterized from dispersion (in solvent) to thin film (cast on support) to investigate the impact of solvent water content on ionomer dispersion (structure, acidity) and resulting film properties. Dispersion characterization reveals that secondary aggregate structure depends on the sidechain chemistry, but all PFSA-based ionomers evolve similarly as dispersion becomes water-rich. The differences in aggregation alter ionomer adsorption and thin film morphology. Further, hydrophilic domain spacing and orientation are affected primarily by sidechain chemistry, and modulated by solvent composition. Thin-film conductivity correlates with hydration and nanodomain alignment, signifying the role of morphology in properties. Overall, this work provides insights into how chemistry can be used to coarse-tune structure–property relationships, while processing solvent is for fine-tuning of dispersion-film interplay for controlling CL-ionomer function, which can be translated to other chemistries and ink formulations.

25 ENERGY STORAGE↗

Seasonal and tidal variations in hydrologic inputs drive salt marsh porewater nitrate dynamics

Salt marshes remove terrestrially derived nutrients en route to coasts. While these systems play a critical role in improving water quality, we still have a limited understanding of the spatiotemporal variability of biogeochemically reactive solutes and processes within salt marshes. We implemented a high-frequency sampling system to monitor sub-hourly nitrate (NO$^{–}_{3}$) concentrations in salt marsh porewater at Elkhorn Slough in central California, USA. We instrumented three marsh positions along an elevation gradient subjected to different amounts of tidal inundation, which we predicted would lead to varied biogeochemical characteristics and hydrological interactions. At each marsh position, we continuously monitored porewater NO$^{–}_{3}$ concentrations at depths of 10, 30, and 50 cm and porewater levels measured at 70 cm depth over seven deployments of ~10 days each that spanned seasonal wet/dry periods common to Mediterranean climates. We quantified tidal event hysteresis between NO$^{–}_{3}$ and water level to understand how NO$^{–}_{3}$ concentrations and sources fluctuate across tidal cycles. In dry periods, the NO$^{–}_{3}$-porewater level relationship indicated that the NO$^{–}_{3}$ source was likely estuarine surface water that flooded the transect during high tides and the salt marsh was a NO$^{–}_{3}$ sink. In wet periods, the NO$^{–}_{3}$-porewater level relationship suggested the salt marsh was a source of NO$^{–}_{3}$. Finally, these findings suggest that tidal and seasonal hydrologic fluxes together control NO$^{–}_{3}$ porewater dynamics and export and influence ecological processes in coastal environments.

54 ENVIRONMENTAL SCIENCES↗

Prediction of local concentration fields in porous media with chemical reaction using a multi scale convolutional neural network

The study of solute transport in porous media is of interest in many chemical engineering systems. Some example applications include packed bed catalytic reactors, filtration devices, and batteries. The pore scale modeling of these systems is time consuming and may require large computing resources, for this reason computational fluid dynamics (CFD) simulations are not practical if a large number of simulations is required, like in multiscale modeling, where a model at a large scale calls for pore scale simulations. It has been shown that neural networks can be trained with a dataset of flow simulations and then predict fields orders of magnitude faster, and with less computational resources, in new domains. However, it is crucial to provide the neural network with an effective description of the domain and the undergoing operating conditions to be able to train models that generalize accurately in unseen samples. Therefore, research is needed to employ neural networks in new complex systems. The appropriate training of a network for predicting coupled flow and solute transport processes is an outstanding problem due to the complex interplay between geometry and operating conditions. In this work, we train a multi scale convolutional neural network (MSNet) with a diverse dataset of simulations of transport and chemical reaction in porous media to predict the local concentration fields in images of porous media. Our dataset contains a wide diversity of sphere pack arrangements under different operating conditions (Péclet and Reynolds numbers). Further, we train a robust model by employing different input descriptors that represent the medium and the different operating conditions of each system. Our trained model is able to provide nearly instantaneous predictions, compared to around twenty hours of the CFD workflow, with less than 3.5% error on new geometries and transport conditions. Thus the model could be easily integrated in a multiscale workflow where fast response is needed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

After the hurricane: Validating a resilience assessment methodology

With increasing utility grid outages in the United States, there is growing interest in assessing risk and developing mitigation strategies to reduce the impact of grid outages. Working with the U.S. Air Force, the U.S. Department of Energy's National Renewable Energy Laboratory (NREL) developed a replicable energy resilience assessment methodology and investment decision tool to: (1) identify and score hazards and vulnerabilities at the site level; (2) analyze risks to energy infrastructure; and (3) identify and prioritize energy resilience investments. This work improves on existing resilience assessment methodologies and tools by combining a bottom-up, all-hazards assessment methodology with top-down geographic information system mapping capabilities to provide an innovative, dynamic tool for identifying and prioritizing actionable solutions. This process combines probabilistic forecasting with an iterative approach for continuously updating and reassessing risks to address temporal dynamism. Relationships among systems are modeled and visualized to estimate the effectiveness of resilience actions across multiple interdependent systems and inform financial priorities through cost-difficulty-impact trade-offs. The approach is validated in a case study at Tyndall Air Force Base (AFB) in Florida, which experienced a Category 5 hurricane in 2018. The risks and mitigation strategies identified pre-hurricane are compared with post-hurricane, realized impacts. The assessment effectively identifies risks and actions to increase site energy resilience, but the methodology can be enhanced though greater consideration of the interdependencies between the energy system and related systems like transportation, communication, and food/water systems, which impact the recovery of the energy system and the base.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Size- and concentration-dependent Eu 2+ /Eu 3+ mixed luminescent characteristics of rare-earth-doped CaF 2 nanoparticles and their monolithic epoxy nanocomposites

CaF 2 is a promising luminescent host material for a wide range of applications, due to its high transparency, non-hygroscopy, low refractive index, low density, low backscattering efficiency, and abundance in nature. Here we report the photoluminescence (PL) and cathodoluminescence (CL) characteristics of rare-earth-doped CaF 2 nanoparticles and their composite monoliths with epoxy with visible emissions. The CaF 2 nanoparticles of ca. 36, 108 and 305 nm were prepared by a facile solution-mixing process and subsequent hydrothermal treatment. As the particle size decreases, the luminescence intensity increases for single-doped particles, while oppositely decreases for codoped particles because of energy transfer. Further, Eu 2+ - and Tb 3+ -codoped CaF 2 nanoparticles exhibit red emission, providing an efficient path for red emission through an energy transfer by Tb 3+ bridging without direct Eu 3+ doping. The effects of size and concentration are found to be pronounced in CL than PL, as the charge transfer between Eu 2+ and Eu 3+ reduces the concentration quenching in CL. The luminescence emission characteristics of epoxy/CaF 2 monoliths are different from those of particles due to the interactions with the epoxy molecules, and thus the energy transfer is hindered in PL while not in CL, enabling them for high-energy irradiation applications.

36 MATERIALS SCIENCE↗

Comparison of continuum and cross-core theories of dynamic strain aging

Dynamic strain aging (DSA) is the process of solute atoms segregating around dislocations on the timescale of loading. Continuum theories of DSA derived from elasticity theory have been shown to severely overpredict both the timescale and strengthening of DSA. Recently, cross-core theory was developed to reconcile this gap, invoking a special single-atomic-hop diffusion mechanism across the core of an extended dislocation. In this work, we show that the classical continuum theory expression for the rate of solute segregation is in error. After correcting this error, we show that continuum theory predictions match cross-core theory when the elevated diffusivity near the dislocation core is accounted for. Finally, our findings indicate that continuum theory is still a useful tool for studying dislocation-solute interactions.

36 MATERIALS SCIENCE↗

Butyltin Keggin Ion with a Rare Four-Coordinate Ca Center

Alkyltin clusters are exploited in nanolithography for the fabrication of microelectronics. The alkyltin Keggin family is unique among Keggin clusters across the periodic table; its members appear to favor the lower-symmetry β and γ isomers rather than the highly symmetrical α and ε isomers. Therefore, the alkyltin Keggin family may provide important fundamental information about the formation and isomerization of Keggin clusters. In this study, we have synthesized and structurally characterized a new butyltin Keggin cluster with a tetrahedral Ca 2+ center, fully formulated [(BuSn) 12 (CaO 4 )(OCH 3 ) 12 (O) 4 (OH) 8 ] 2+ (β-CaSn 12 ). The synthesis is a simple one-step process. Extensive solution characterization including electrospray ionization mass spectrometry, small-angle X-ray scattering, and multinuclear ( 1 H, 13 C, and 119 Sn) nuclear magnetic resonance shows β-CaSn 12 is essentially phase-pure and stable. This differs from the previously reported Na-centered analogues that always form a mixture of β and γ isomers, with facile interconversion. Therefore, this study has clarified prior confusion over complex spectroscopic and crystallographic characterization of the Na-centered analogues. Density functional theory calculations showed the following stability order: γ-CaSn 12 < γ-NaSn 12 < β-CaSn 12 < β-NaSn 12 . The β analogue is always more stable than the γ analogue, consistent with experiment. Notable outcomes of this study include a rare tetrahedral Ca coordination, a Na-free alkyltin cluster (important for microelectronics manufacturing), and a better understanding of Keggin families built of different metal cations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Atomic Edge-Guided Polyethylene Crystallization on Monolayer Two-Dimensional Materials

In this report we combine an advanced synthesis of two-dimensional (2D) materials (MoSe 2 ) having well-defined atomic edge configurations with ab initio and atomistic molecular dynamics (MD) simulations to study how atomic edges interact with polyethylene (HDPE) chains in a dilute solution assembly process. Our results reveal that Mo-terminated zigzag (Mo-ZZ) edges act as preferred nucleation sites and strongly interact with HDPE chains. The HDPE chains align in parallel with the Mo-ZZ edges and form arrays of lamellae that are perpendicular to the edges. Interestingly, atomic edge configurations are observed to dramatically change such interactions. The crystallization discrepancy at different edges was demonstrated on the same piece of MoSe 2 with different types of edges. The ab initio and MD simulations between n-alkane (n = 5 and 25), a segment of HDPE, and MoSe 2 suggest that the atomic structures of MoSe 2 can affect their interactions with n-alkane chains. Following the Mo-ZZ edge preferred nucleation principle, controlled long-range alignment of HDPE lamellae can be realized by creating multilayer MoSe 2 with parallel atomic steps. This research opens a pathway toward an atomic level understanding of polymer–2D nanomaterial interactions. It also bridges the gap between atomic-level and long-range mesoscopic structures and introduces a novel strategy for long-range structural control.

36 MATERIALS SCIENCE↗

NMR Studies of Block Copolymer-Based Supramolecules in Solution

Hierarchical assemblies from block copolymer (BCP)-based supramolecules have shown immense potential as programmable materials owing to their versatility for incorporating functional molecules and provide access to arrays of hierarchical structures. However, there remains a knowledge gap on the formation of the supramolecule in solution. Here, we applied NMR techniques to investigate the solution-phase behavior of the most studied supramolecular systems, polystyrene-block-poly(4-vinylpyridine)(3-pentadecylphenol) (PS-b-P4VP(PDP) r ). The results show that the supramolecule likely adopts a coil-comb conformation, despite the small molecule's (PDP) rapid exchange between the bonded and free states. The exchange rate (>10 4 s -1 ) exceeds the NMR time scale at the frequency of interest. The supramolecules form under dilute conditions (~2 vol %) and are attributed to the enthalpic gain of the hydrogen bonding between the PDP and 4VP. As the solute concentration increases (>10 vol %), the supramolecule forms micelle-like aggregates with PDP accumulated within the comb-block's pervaded volume based on analysis of the apparent molecular weight, viscosity, and chain dynamics. Overall, this work sheds light on the long-standing question regarding the evolution of the constituents in the BCP-based supramolecule in solution and provides valuable guidance toward their solution-based processing and morphological control.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Characterization of the ALSEP Process at Equilibrium: Speciation and Stoichiometry of the Extracted Complex

We have determined the identity of the complexes extracted into the ALSEP process solvent from solutions of nitric acid. The ALSEP process is a new solvent extraction separation designed to separate americium and curium from trivalent lanthanides in irradiated nuclear fuel. ALSEP employs a mixture of two extractants, 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester (HEH[EHP]) and N,N,N',N'-tetra(2-ethylhexyl)diglycolamide (TEHDGA) in n-dodecane, which makes it difficult to ascertain the nature of the extracted metal complexes. It is often asserted that the weak acid extractant HEH[EHP] does not participate in the extracted complex under ALSEP extraction conditions (2–4 M HNO 3 ). However, the analysis of the Am extraction equilibria, Nd absorption spectra, and Eu fluorescence emission spectra of metal-loaded organic phases argues for the participation of HEH[EHP] in the extracted complex despite the high acidity of the aqueous phases. The extracted complex was determined to contain fully protonated molecules of HEH[EHP] with an overall stoichiometry of M(TEHDGA) 2 (HEH[EHP]) 2 ·3NO 3 . Computations also demonstrate that replacing one TEHDGA molecule with one (HEH[EHP]) 2 dimer is likely energetically favorable compared to Eu(TEHDGA) 3 ·3NO 3 , whether the HEH[EHP] dimer is monodentate or bidentate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗