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At least 91 records · Page 5

Tuning Surface Stoichiometry of SOFC Electrodes at the Molecular and Nano-scale for Enhanced Performance and Durability

This project achieved the following objectives. Different cation segregation behaviors of different common SOFC cathodes, including La 0.6 Sr 0.4 Co0.2Fe 0.8 O 3-δ (LSCF), Sr 0.5 Sm 0.5 O 3-δ (SSC), and PrBa 0.5 Sr 0.5 Co 1.5 Fe 0.5 O5 +δ (PBSCF), were determined. We showed how oxygen partial pressure and gas impurities impact the stability of SOFC cathodes. We developed atomic layer deposition (ALD) coating techniques for electrodes and showed that by introducing different elements and different ALD oxidizers, electrode surface chemistry can be altered, resulting in enhanced oxygen reduction kinetics. In addition, we developed solution infiltration technique to enhance performance and durability of electrodes. Different infiltrates as well as different thermal treatment processes were screened to identify the optimal surface modification process that yields both low impedance and high durability. The modified cathode shows excellent stability and has a low area specific resistance (ASR) of only 0.2 Ωcm 2 at 600 °C after over 2000 hours of operation. Further, we developed ceramic anodes, SrFe(Co,Mo)O 3 (SFCM) and SrFe(Ni,Mo)O 3 (SFNM), and enhanced anode oxidation kinetics by solution infiltration or in situ catalyst exsolution from the ceramic anode surface. The modified anodes showed improved performance in full SOFCs, and the optimized anode modification shows high stability for over 400 hours at 550 °C. Moreover, the modified anode also demonstrates high durability in methane. This work provides fundamental understanding of electrode surface chemistry and demonstrates a simple, facile, cost-effective approach to enhance catalytic activity and durability of SOFC electrodes.

20 FOSSIL-FUELED POWER PLANTS↗

Microsphere LiMn 0.6 Fe 0.4 PO 4 /C cathode with unique rod-like secondary architecture for high energy lithium ion batteries

LiMn x Fe 1-x PO 4 /C is considered a promising next-generation cathode material with significant commercial potential, inheriting the safety of LiFePO 4 while offering higher energy densities. However, the extremely low conductivity and the Jahn-Teller effect induced by Mn 3+ limit its practical capacity and rate performance. Effective modifications can be achieved through particle nanonization and uniform carbon coating. Here, in this work, we synthesized microspherical LiMn 0.6 Fe 0.4 PO 4 /C cathode materials using a hydrothermal method combined with spray drying carbon coating. The cathode material exhibits a microsphere structure composed of aggregated nanorods with a uniform 3 nm carbon coating, showing good dispersibility, small specific surface area and high tap density. In-situ diffraction analysis showed that expanding the single-phase solid solution region during (de)lithiation can reduce the energy barrier for electron transport, improve the kinetics of the (dis)charge process, and enhance both cycling and rate performance. The initial capacity at 0.1C can reach 155 mAh/g, and the capacity remains at 133.5 mAh/g with a retention rate of 97.1 % after 300 cycles. The synergistic effect of particle nanonization and uniform carbon coating endows the LiMn x Fe 1-x PO 4 /C material with excellent electrochemical performance.

25 ENERGY STORAGE↗

Surface engineering of polymeric membranes with metal oxides for improved fouling resistance and superior oil-water separation

Rapid industrial growth has increased the need for efficient membranes to separate oil-water emulsions. Polyvinylidene fluoride (PVDF) membranes, although widely used due to their chemical inertness and favorable mechanical properties, suffer from fouling due to their intrinsic hydrophobicity. Modifying these membranes after fabrication offers a practical solution as it easily fits into existing large-scale manufacturing processes. Atomic layer deposition (ALD), an atomically-precise vapor phase surface modification technique, can create ultrathin metal oxide layers that greatly improve membrane hydrophilicity without significantly affecting the original pore size. However, PVDF's lack of reactive chemical moieties makes ALD challenging. Here, in this study, we present a simple alkali treatment that greatly enhances ALD nucleation and growth on PVDF membranes. This treatment imparts exceptional oil-water emulsion separation capabilities and antifouling behavior in PVDF membranes after just a few ALD cycles, surpassing the performance of PVDF membranes coated with hundreds of ALD cycles. This dramatic reduction in the number of ALD cycles required could enable cost-effective modification of commercial PVDF membranes at scale using spatial, roll-to-roll ALD. These modified membranes outperform reported modified PVDF membranes, with >99 % permeance recovery and <1 % irreversible loss of permeance and >98 % oil rejection from oil-water emulsions over 100 h continuous operation, making them promising for advanced water purification technologies.

Atomic layer deposition↗

Compositions and methods for the modification of imine covalent organic frameworks (COFs)

The present invention provides for a method for modifying a covalent organic framework (COF), the method comprising: contacting a COF comprising an imine group with a phenylacetylene in, or to form, a mixture, in a suitable reaction condition for converting the imine group into a quinoline group, and COF comprising a quinoline group. The present invention also provides for a superhydrophobic surface comprising a solid surface coated with or comprising the covalent organic framework (COF).

Li, Xinle↗

Surface Modification of Nickel-Rich Cathode Materials by Ionically Conductive Materials at Room Temperature

Nickel-rich cathode materials (LiNi x Mn y Co 1-x-y O 2 , NMC) are promising to push the limits of lithium-ion batteries to higher energy density. This approach is favored in practical applications including electric vehicles and aviation transportation. However, the instability of the NMC at charged state results in safety concerns and poor cycling stability. Surface coating is a practical and effective strategy to address this. Cubic Li7La3Zr2O12 (LLZO) is an ideal coating material regarding the low electron transfer rate and high Li+ conductivity. Thus, a LLZO coating layer can suppress the parasitic reactions in the electrode/electrolyte interface without deteriorating the lithium migration. However, high-temperature calcination seems to inevitably create the chemical couplings between NMC and LLZO, leading to the interdiffusion and degradation of NMC and LLZO crystal structures. This work presents a simple mechanochemical method to effectively coat LLZO on the NMC particle surface. Furthermore, the coated cathode demonstrates superior electrochemical performance compared with the pristine NMC cathode.

25 ENERGY STORAGE↗

Water-induced surface ordering facilitating the microcutting of ductile metals

Metal cutting is a crucial process in modern manufacturing. Enhancing the machinability of metals can significantly improve their production efficiency and surface integrity. Coating surface-active media (SAM) on the free surface of the metals before cutting is an easy method to improve machinability, which usually pertains to the category of the renowned Rehbinder effect. However, the existing SAM is usually hazardous and complex materials. Besides, the effect of SAM on the local structure of the metal surface remains unclear. In this study, water is employed as a simple yet often overlooked SAM in the microcutting of copper. Using water as SAM also allows the employment of X-ray absorption fine structure spectroscopy (XAFS) to study the local structure of copper with and without water coating. Results show that water coating on the free surface of copper can significantly reduce the cutting force and chip thickness, and improve the surface finish. Interestingly, removing the water coating enables the recovery of the cutting force, demonstrating a reversible effect. Based on the XAFS results and molecular dynamics simulation, a water-induced surface ordering mechanism is proposed to explain the findings from the microcutting experiments. This mechanism suggests that water molecules can induce surface ordering in copper, resulting in reduced surface energy and fracture toughness of copper, thus enhancing machinability. In conclusion, this work provides valuable insights into the comprehension of the Rehbinder effect and shows that picometer-scale modifications of the surface atom arrangement can considerably alter the deformation mode of metals, paving the way for the development of new manufacturing processes.

36 MATERIALS SCIENCE↗

Surface Regulating of a Double–Perovskite Electrode for Protonic Ceramic Fuel Cells to Enhance Oxygen Reduction Activity and Contaminants Poisoning Tolerance

Protonic ceramic fuel cells (PCFCs) are one of the most efficient energy conversion devices. However, the performance of current PCFCs is greatly limited by the sluggish oxygen reduction reaction (ORR) kinetics and the fast degradation of cathode due to contaminants poisoning (such as Cr species and steam). In this work, we report a surface regulating of a double perovskite PrBa 0.5 Sr 0.5 Co 1.5 Fe 0.5 O 5+δ (PBSCF) cathode by a Pr 0.9 Fe 0.7 Co 0.3 O 3 (PFC) catalyst coating to enhance the ORR activity and stability. When tested in direct contact with Cr in the air with 3% H 2 O at 650 °C, the polarization resistance (Rp) of the PFC-PBSCF electrode increases from $\approx$0.39 to 0.45 Ω cm 2 after 100 h operation; in contrast, the R p of a PBSCF electrode increases from 0.63 to 0.82 Ω cm 2 . Further, a PCFC with the PFC-PBSCF cathode demonstrates an excellent peak power density ($\approx$1.08 W cm -2 at 650 °C) and significantly enhanced durability (degradation rate of 0.03 % h -1 ), much better than those of the cells with a PBSCF cathode ($\approx$0.75 W cm -2 and degradation rate of 0.12 % h -1 ). Raman spectroscopy and density functional theory calculations indicate that the PFC catalyst coating diminishes the formation of Cr species, such as (Ba 1-x Sr x )CrO 4 , on the cathode surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Neodymium-iron-boron magnet with selective surface modification, and method of producing same

A bulk high performance permanent magnet comprising a neodymium-iron-boron core having an outer surface, and a coercivity-enhancing element residing on at least a portion of said outer surface, with an interior portion of said neodymium-iron-boron core not having said coercivity-enhancing element therein. Also described herein is a method for producing the high-coercivity bulk permanent magnet, the method comprising: (i) depositing a coercivity-enhancing element on at least a portion of an outer surface of a neodymium-iron-boron core substrate to form a coated permanent magnet; and (ii) subjecting the coated permanent magnet to a pulse thermal process that heats said outer surface to a substantially higher temperature than an interior portion of said neodymium-iron-boron core substrate, wherein said substantially higher temperature is at least 200° C. higher than said interior portion and is of sufficient magnitude to induce diffusion of said coercivity-enhancing element below said outer surface but outside of said interior portion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Surface-Modified Pd/CeO 2 Single-Atom Catalyst Shows Increased Activity for Suzuki Cross-Coupling

Single-atom catalysts (SACs) comprise catalytically active atoms dispersed on supports; they combine the high activity and site uniformity of homogeneous catalysts with the ease of separability of heterogeneous catalysts. However, SACs lack fine control over the active site, provided by ligands in homogeneous catalysts. In this work, we demonstrate that modification of the support with an organic monolayer is a viable approach to improving the catalytic performance. Here, the addition of catechol-type monolayers to a Pd/CeO 2 SAC increases its catalytic activity for Suzuki cross-coupling, a central reaction in the synthesis of fine chemicals and pharmaceuticals. Kinetic trials reveal that the coating reduces the activation energy from 49 ± 9 to 22 ± 5 kJ/mol and produces a 4-fold rate enhancement at 25 °C, an effect we attribute to π-π interactions between the reactant and the catechol coating. Further development of this approach could vastly increase the utility of SACs in organic synthesis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Vapor-phase grafting of functional silanes on atomic layer deposited Al 2 O 3

Fundamental studies are needed to advance our understanding of selective adsorption in aqueous environments and develop more effective sorbents and filters for water treatment. Vapor-phase grafting of functional silanes is an effective method to prepare well-defined surfaces to study selective adsorption. In this investigation, we perform vapor phase grafting of five different silane compounds on aluminum oxide (Al2O3) surfaces prepared by atomic layer deposition. These silane compounds have the general formula L3Si–C3H6–X where the ligand, L, controls the reactivity with the hydroxylated Al2O3 surface and the functional moiety, X, dictates the surface properties of the grafted layer. We study the grafting process using in situ Fourier transform infrared spectroscopy and ex situ x-ray photoelectron spectroscopy measurements, and we characterize the surfaces using scanning electron microscopy, atomic force microscopy, and water contact angle measurements. Here, we found that the structure and density of grafted aminosilanes are influenced by their chemical reactivity and steric constraints around the silicon atom as well as by the nature of the anchoring functional groups. Methyl substituted aminosilanes yielded more hydrophobic surfaces with a higher surface density at higher grafting temperatures. Thiol and nitrile terminated silanes were also studied and compared to the aminosilane terminated surfaces. Uniform monolayer coatings were observed for ethoxy-based silanes, but chlorosilanes exhibited nonuniform coatings as verified by atomic force microscopy measurements.

36 MATERIALS SCIENCE↗

Hierarchically structured MoO 2 /dopamine-derived carbon spheres as intercalation electrodes for lithium-ion batteries

A hydrogen peroxide initiated sol-gel process involving molybdenum transformation in the presence of dopamine (Dopa) hydrochloride excess produced the metastable precipitate composed of polydopamine (PDopa) spheres coated with Dopa preintercalated molybdenum oxide, (Dopa) x MoO y @PDopa. The hydrothermal treatment (HT) of the (Dopa) x MoO y @PDopa precursor resulted in the simultaneous carbonization of Dopa and molybdenum reduction generating MoO 2 nanoplatelets distributed and confined on the surface of the Dopa-derived carbon matrix (HT-MoO 2 /C). The consecutive annealing (An) of the HT-MoO 2 /C sample at 600 °C under Ar atmosphere led to the formation of MoO 2 with increased Mo oxidation state and improved structural stability (AnHT-MoO 2 /C). Annealing had also further facilitated interaction between the molybdenum-derived and Dopa-derived components resulting in the modification of the carbon matrix confirmed by Raman spectroscopy. Morphology of both materials is best described as Dopa-derived carbon spheres decorated with MoO 2 nanoplatelets. These integrated metal oxide and carbon structures were tested as electrodes for lithium-ion batteries in the potential window that corresponds to the intercalation mechanism of charge storage. The AnHT-MoO 2 /C electrode showed enhanced electrochemical activity, with an initial specific discharge capacity of 260 mAh/g and capacity retention of 67% after 50 cycles, compared to the HT-MoO 2 /C electrode which exhibited an initial specific discharge capacity of 235 mAh g –1 and capacity retention of 47% after 50 cycles. The rate capability experiments revealed that the capacity of 93 mAh/g and 120 mAh/g was delivered by the HT-MoO 2 /C and AnHT-MoO 2 /C electrodes, respectively, when the current density was increased to 100 mA/g. Here, the improved specific capacity, electrochemical stability, and rate capability achieved after annealing were attributed to higher crystallinity of MoO 2 , increased oxidation state of Mo, and formation of the tighter MoO 2 /carbon contact accompanied by the annealing assisted interaction between MoO 2 and Dopa-derived carbon.

25 ENERGY STORAGE↗

Interface chemistry informs about cathode and anode degradation during fast charging

Here, the aim of this study is to examine the development and makeup of the Solid Electrolyte Interphase (SEI) and Cathode Electrolyte Interphase (CEI) in lithium-ion batteries during rapid charging. Using X-ray photoelectron spectroscopy (XPS) and depth profiling, we investigate the chemical modifications occurring on the electrode surfaces during the initial formation and subsequent fast charge-discharge cycles. Our research shows that the anode's SEI initially comprises a thin layer rich in ketones, which then transforms into a thicker layer dominated by carbonaceous compounds during rapid charging cycles. Following assembly, lithium fluoride (LiF) quickly becomes a key element of the SEI, and its presence continues to grow substantially during the formation cycle, remaining the primary component throughout subsequent cycles. Initially, the cathode forms a thin oxide layer rich in ketones, with no noticeable carbonaceous CEI. The CEI primarily comprises LiF, which experiences an increase during the formation cycle and retains a thin layer of carbon coating after the initial rapid discharge. These findings show how the interphase layers impact the performance and stability of lithium-ion batteries, especially during fast charging for electric vertical take-off and landing (eVTOL) vehicles.

Fast charging↗

Potassium Prussian blue-coated Li-rich cathode with enhanced lithium ion storage property

With high specific capacity, the layered Li-rich Mn-based oxide (LRMO) is a promising candidate cathode material for Li-ion batteries. However, the irreversible release of Li-ions during the first charging process, instability of LRMO/electrolyte interface and relatively low ion conductivity of LRMO result in low initial Coulombic efficiency (ICE), poor cycle stability and rate performance, which prohibit its further application. Furthermore, interface engineering via additive coating is expected to effectively address these issues. Herein, we rely on potassium Prussian blue (KPB), a Li + acceptor with good ion conductivity, as a new coating material on LRMO particles. The KPB coating not only forms a protective layer on the surface of LRMO against electrolyte corrosion, but also functions as a host for Li + transport and accommodation, leading to enhanced ion conductivity and ICE of LRMO cathode. Consequently, 2 wt% KPB coated LRMO cathode achieved an initial discharge capacity of up to 281.7 mA h g -1 with an ICE of 85.69% compared to an ICE of 79.52% for the LRMO cathode without coating. The cycling and rate performance are also greatly improved as evidenced by the well maintained capacity of up to 176.8 mA h g -1 after 100 cycles at a current density of 0.5 C, compared to the limited capacity of only 135.3 mA h g -1 for the LRMO cathode without coating. Overall, this work pioneers the use of potassium Prussian blue as additive coating material to enhance performance of LRMO cathode, and we expect it to inspire the battery community with new strategies of material engineering/design toward practical application in high-energy lithium-ion batteries.

25 ENERGY STORAGE↗

High-Resolution Three-Dimensional Sculpting of Two-Dimensional Graphene Oxide by E-Beam Direct Write

On demand switchable additive/subtractive patterning of 2D nanomaterials is an essential capability for developing new concepts of functional nanomaterials and their device realizations. Traditionally, this is performed via a multi-step process using photoresist coating and patterning by conventional photo or electron beam lithography, which is followed by bulk dry/wet etch or deposition. This limits the range of functionalities and structural topologies that can be achieved, as well as increases the complexity, cost, and possibility of contamination which are significant barriers to device fabrication from highly sensitive 2D materials. Focused electron beam induced processing (FEBIP) enables a material chemistry/site-specific, high-resolution multi-mode atomic scale processing and provides unprecedented opportunities for direct-write, single-step surface patterning of 2D nanomaterials with an in-situ imaging capability. It allows for realizing a rapid multi-scale/multi-mode approach, ranging from an atomic scale manipulation (e.g., via targeted defect introduction as an active site) to a large-area surface modification on nano and micro scales, including patterned doping and material removal/deposition with 2D (in-plane)/3D (out-of-plane) control. In this work, we report on a new capability of FEBIP for nanoscale patterning of graphene oxide via removal of oxygenated carbon moieties with no use of reactive gas required for etching complemented by carbon atom deposition using focused electron beam. The mechanism of experimentally observed phenomena is explored using the density functional theory (DFT) calculations, revealing that interactions of e-beam liberated reactive oxygen radicals with carbon atoms on graphene basal plane lead to creation of atomic vacancies in the material. The reaction by-products are volatile carbon di-oxides, which are dissociated and volatilized from the graphene oxide surface functional groups by interactions with an energetic focused electron beam. Along with selective “subtractive” patterning of graphene oxide, the same electron beam with increased irradiation doses can deposit out-of-plane 3D carbon nanostructures on top of or around the 2D etched pattern, thus forming a hybrid 2D/3D nanocomposite with feature control down to a few nanometers. Furthermore, this in-operando dual nanofabrication capability of FEBIP is unmatched by any other nanopatterning techniques and opens a new design window for forming 2D/3D complex nanostructures and functional nanodevices.

36 MATERIALS SCIENCE↗

Tuning Surface, Phase, and Magnetization of Superparamagnetic Magnetite by Ionic Liquids: Single-Step Microwave-Assisted Synthesis

Achieving colloidal and chemical stability in ferrofluids by surface modification requires multiple steps, including purification, ex situ modification steps, and operation at high temperatures. In this study, a single-step microwave-assisted methodology is developed for iron oxide nanoparticle (IONP) synthesis utilizing a series of imidazolium-based ionic liquids (ILs) with chloride, bis(trifluoromethylsulfonyl)imide, and pyrrolide anions as the reaction media, thus eliminating the use of volatile organics while enabling rapid synthesis at 80 °C as well as in situ surface functionalization. The characterized surface functionality, hydrodynamic particle size, magnetization, and colloidal stability of the IONPs demonstrate a strong dependence on the IL structure, ion coordination strength, reactivity, and hydrophilicity. The IONPs present primarily a magnetite (Fe 3 O 4 ) phase with superparamagnetism with the highest saturation magnetization at 81 and 73 emu/g at 10 and 300 K, respectively. Depending on the IL coating, magnetization and exchange anisotropy decrease by 20 and 2–3 emu/g (at 35 wt % IL), respectively, but still represent the highest magnetization achieved for coated IONPs by a coprecipitation method. Further, the surface-functionalized superparamagnetic magnetite nanoparticles show good dispersibility and colloidal stability in water and dimethyl sulfoxide at 0.1 mg/mL concentration over the examined 3 month period. This study reports on the intermolecular and chemical interactions between the particle surface and the ILs under synthetic conditions as they relate to the magnetic and thermal properties of the resulting IONPs that are well suited for a variety of applications, including separation and catalysis.

36 MATERIALS SCIENCE↗

In-Silico Design of Next Generation Cellulose-Derived Packaging Materials (CRADA Final Report)

Developing sustainable solutions for single-use packaging is an important objective to combat the environmental crisis of plastics pollution. Most embodiments of cellulose-based packaging materials, including CellophaneTM, are completely biodegradable in both terrestrial and marine environments. However, petroleum-derived alternatives offer some performance advantages for metrics such as moisture barriers and mechanical properties. This project leverages molecular dynamics simulation to investigate how molecular modifications to cellulose-based polymer assemblies impact their material properties. An important performance criterion for the modified materials was to retain biodegradability; thus, modifications by naturally occurring, biodegradable additives were the focus of this study. Specifically, we developed models with xylan and lignin of varying monomeric compositions into the cellulose matrix. The mechanical properties were investigated by performing stress-strain simulations, and the water barrier and hydrophobicity were investigated by simulating the water contact angle. Our findings indicate that the incorporation of xylan into the cellulose matrix tends to increase the mechanical properties with an optimal loading of ~27 wt%. We also predict that orienting the nanoscale directionality of the xylan chains such that they are perpendicular to the cellulose fibrils will dramatically increase mechanical strength. In contrast, the incorporation of lignin tends to weaken the composite at all loadings investigated. Simulations of water contact angle predicted that coating polymers on the surface of the cellulose assembly creates a more hydrophobic surface than incorporating them throughout the matrix. Of the coatings investigated, lignin resulted in the most hydrophobic surface, followed by pectin and keratin, which both imparted modest increases in hydrophobicity. Future experimental work done by Futamura will focus on designing material prototypes to capitalize on the predictions of performance enhancement obtained from molecular modeling. While substantial progress was made by the simulations performed in this project, there still exists a vast parameter space that we were unable to investigate, including branching, functional group decoration, and degree of polymerization of polymer additives. However, the methods developed in this initial investigation will facilitate more rapid evaluation of the impact of molecular characteristics on the performance of biopolymer composite materials and thereby accelerate future materials discovery efforts in this area.

36 MATERIALS SCIENCE↗

Tailoring the Near-Surface Environment of Rh Single-Atom Catalysts for Selective CO 2 Hydrogenation

For this study, we used a combination of experimental spectroscopies, density functional theory calculations, and CO 2 hydrogenation studies to investigate the effects of modifying single-atom Rh 1 /TiO 2 catalysts with functionalized phosphonic acid monolayers. We found that the deposition of specific amine-functionalized ligands resulted in an ~8× increase in site-specific CO 2 reduction turnover frequency at 150 °C and a ~2× increase at 250 °C. On-stream stability also improved following ligand deposition. The effect of the modifier on reactivity was highly sensitive to the proximity of the amine functional group to the surface, which was controlled by adjusting the length of the phosphonic acid tail. Furthermore, deposition of alkyl phosphonic acids without an amine functional group resulted in blocked CO 2 adsorption and a near-complete loss of catalytic activity. Infrared spectroscopy studies suggested that the amine group provided binding sites for CO 2 that enabled hydrogenation when the amine was positioned near a Rh1 site. Phosphonic acid-modified catalysts also exhibited high selectivity to CO over the series product methane; the selectivity effect was traced to modification of the Rh1 sites to favor CO desorption. Phosphonic acid deposition resulted in 80–90% loss of accessible Rh1 sites, likely due to blocking by tail groups. However, even with the loss of sites, under low-temperature reaction conditions, the rates of CO 2 hydrogenation were improved with the coatings, indicating that the remaining sites are highly efficient. Organic functionalization of the supports for atomically dispersed catalysts offers the opportunity to precisely control the positioning of functional groups in the vicinity of a well-defined active site, potentially enabling an additional level of control over active site design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗