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At least 109 records · Page 6

A Theoretical Operational Model for Complex Experiments and its Invariance Theorems

We develop and systematize the Theoretical–Operational Model (TOM), a framework that treats preparation and measurement —including their operational residues— as intrinsic structures of physical theory. The central contribution is a principled geometric–algebraic organization of admissible operational deformations, formulated using quantum channels, renormalization-style flows, and information-geometric tools. Within this structure, operational residues and background processes are represented as effective morphisms attached to these operational components, whose invariants yield constraints on how theoretical parameters vary under specified classes of deformations. Illustrations drawn from muon–electron conversion, long-baseline neutrino oscillations, and quark–gluon-plasma phenomenology show how TOM maps operational effects into inferences about theoretical parameters, enables systematic cross-experimental comparisons, and stabilizes parameter estimation against defined deformation families. By embedding the operational layer—together with its residues—within a structured theoretical setting, TOM supports both theory testing and theory development, clarifying the conceptual relation between experimental realization and the physical quantities represented by the theory.

Pronskikh, Vitaly [Fermilab] (ORCID:00000002518174↗

Quasi‐2D Perovskite Crystalline Layers for Printable Direct Conversion X‐Ray Imaging

Abstract Polycrystalline perovskite film‐based X‐ray detector is an appealing technology for assembling large scale imager by printing methods. However, thick crystalline layer without trap and solvent residual is challenging to fabricate. Here, the authors report a solution method to produce high quality quasi‐2D perovskite crystalline layers and detectors that are suitable for X‐ray imaging. By introducing n ‐butylamine iodide into methylammonium lead iodide precursor and coating at elevated temperatures, compact and crystalline layers with exceptional uniformity are obtained on both rigid and flexible substrates. Photodiodes built with the quasi‐2D layers exhibit a low dark current and stable operation under constant electrical field over 96 h in dark, and over 15 h under X‐ray irradiation. The detector responds sensitively under X‐ray, delivering a high sensitivity of 1214 µC Gy air −1 cm −2 and a sensitivity gain is observed when operated under higher fields. Finally, high resolution images are demonstrated using a single pixel device that can resolve 80–200 µm features. This work paves the path for printable direct conversion X‐ray imager development.

36 MATERIALS SCIENCE↗

Use of a Pressurized Water Treatment to Prevent Cracking of Internal Gelation Sol-Gel Microspheres

Pressurized water treatments were investigated as a means to prevent cracking of internal gelation sol-gel microspheres upon drying and heating. A batch of gelled cerium oxide microspheres was prepared, split into two samples that were processed with and without a pressurized water treatment, and dried in air at room temperature. Thermal gravimetric analysis was used to compare the mass loss profiles between the two samples and to understand volatile emissions from cerium oxide microspheres during heat treatments up to 600 °C. Microspheres that were processed without a pressurized water treatment lost approximately 4.6 times more mass upon heating than microspheres that were subjected to a pressurized water treatment. Comparison of the cracking behavior of microspheres prepared with and without a pressurized water treatment indicated that microspheres subjected to a pressurized water treatment were virtually crack-free after heat treatments. Conversely, microspheres processed without a pressurized water treatment, which is typical of traditional washing processes, exhibited extensive cracking. Analysis of residues dried from pressurized water treatment effluents indicated that hexamethylenetetramine and urea, which are excess reactants from the internal gelation process, were removed from gelled microspheres during the pressurized water treatment step. Traditional processing methods for preparing internal gelation microspheres use specific feed solution and gelation parameters to reduce subsequent cracking upon drying and heating. Results from this study indicate that more aggressive gel-forming conditions may be used to produce crack-free microspheres, if a pressurized water treatment step is included after washing and before air-drying.

cerium oxide, internal gelation, microsphere, TRIS↗

The effect of lignin degradation products on the generation of pseudo-lignin during dilute acid pretreatment

Pseudo-lignin is an insoluble material that tends to deposit on acidic pretreated fiber surface and negatively impacts the biological conversion of biomass to valued added products. Employing a laboratory generated acidic hydrolysate solution from dilute acid pretreatment of bamboo residues, we sought to seek an improved understanding of pseudo-lignin formation from fragmented carbohydrates. In addition, we also performed experiments to investigate how lignin model compounds interact with carbohydrates en route to pseudo-lignin’s formation. The yields of pseudo-lignin generated from xylose (CXPL) were higher than those generated from glucose (CGPL). Gas chromatography-Mass spectrometry and Foloin-Ciocalteau analysis suggested that there were more aromatic compounds in hydrolyzate during CGPL’s formation. The presence of lignin phenolic model compounds had both a positive and negative effect upon quantitative yields of pseudo-lignin. Gel permeation chromatography and NMR analysis ( 31 P and 2D-HSQC NMR) of the pseudo-lignin samples generated in the presence and absence of 4-hydroxybenzoic acid (4-HA), employed as a lignin model compound, revealed drastic differences in molecular weight, changes in hydroxyl group content, and hydrocarbon bonds, suggesting significant differences in the pseudo-lignin reaction pathways when certain lignin model compounds are present. Finally, our findings demonstrate the effects of both hemicellulose carbohydrate makeup and lignin model compound impact on the formation of pseudo-lignin and its chemical properties, suggesting a potential way to minimize pseudo-lignin formation.

59 BASIC BIOLOGICAL SCIENCES↗

Techno-economic analysis of cellulosic ethanol conversion to fuel and chemicals

In this paper, we describe multiple scenarios investigated to assess the techno-economic results of producing fuels from corn stover-derived ethanol and the impact of co-producing higher-value, ethanol-derived n-butanol and 1,3-butadiene to improve economic feasibility. An alternative approach that produces only chemicals from the lignocellulosic-derived ethanol while producing fuels from the residual cell mass, unconverted sugars and lignin using hydrothermal liquefaction and hydrotreating also is described. Our results indicate that the hydrothermal liquefaction pathway has cost advantages relative to pathways that burn lignin from the corn stover conversion process to make ethanol when the associated ethanol stream is used to make only chemicals.

09 BIOMASS FUELS↗

Selective Bidentate Coordination Reconstructs Residual PbI 2 to Homogenize Interfacial Energetics in Perovskite Solar Cells

Spatially heterogeneous interfacial energetics, often originating from residual lead iodide (PbI 2 ), represent a fundamental bottleneck to both the efficiency and operational stability of perovskite photovoltaics. Conventional PbI 2 passivation strategies based on monodentate ligands or highly polar solvents either interact weakly with PbI 2 or undesirably perturb the underlying three-dimensional perovskite lattice. Here, we report a diammonium bidentate strategy that selectively reconstructs residual PbI 2 into corner-sharing PbI 6 octahedra while preserving the bulk perovskite. Enabled by dual-site coordination, a newly designed thiophene-based bidentate ligand (MeXT) stabilizes PbI 6 units during passivation and establishes spatially homogeneous interfacial energetics. Perovskite solar cells incorporating MeXT achieve 26.19% power conversion efficiency and retain over 80% of their initial efficiency after 1000 h of continuous 1-sun illumination at 75 °C. This dual-anchor coordination passivation strategy establishes a general design principle for selectively treating residual PbI 2 and creating electronically coherent and operationally stable interfaces in perovskite photovoltaics.

ligands↗

Catalytic Reduction of Esters over Zirconia-Supported Metal Catalysts

Esters are often produced as unwanted byproducts during the catalytic upgrading of ethanol to diesel fuel precursors through Guerbet coupling. Removal of esters from the product stream is important to prevent the loss of downstream catalyst activity from ester-derived carboxylic acids. In this work, we studied ester hydrogenolysis to the parent alcohols as a viable route for enhanced diesel fuel production. Specifically, we investigated the reduction of hexyl acetate in butanol over ZrO 2 -supported Ni, Co, Cu, Rh, Pd, and Pt catalysts, where Cu/ZrO 2 was the most selective catalyst for the hydrogenolysis of hexyl acetate into hexanol and ethanol. Thermodynamic analysis reveals that a 90% alcohol yield can be obtained at 200 °C, 30 bar, and a relatively high H 2 :hexyl acetate molar ratio of 480:1. Experimentally, an alcohol yield of 88% yield was obtained with a 10 wt % Cu/ZrO 2 catalyst at these conditions with a residence time of 5.4 h kg cat kmol gas –1 . Catalytic tests on the support revealed that ZrO 2 catalyzes the transesterification reaction between hexyl acetate and butanol. However, only the Cu sites can catalyze the hydrogenolysis of the esters into the final alcohols. We developed a kinetic model for our experimental results, which shows that the transesterification and hydrogenolysis reactions run at two different timescales, the former being 10 times faster than the latter. Data regression has been used to develop a model to predict the mole fraction distribution of ester hydrogenolysis products over a wide range of contact times. Cu/ZrO 2 loses half its catalytic activity after 80 h of time on stream. Modeling of deactivation data reveals that the ZrO 2 support conserves a residual activity due to external active sites, while active sites over the Cu surface deactivate at different rates. Furthermore, the catalytic conversion of esters into their parent alcohols is relevant to the production of surrogate liquid fuels since alcohols can be bimolecularly dehydrated to produce a blend of ethers with diesel fuel-like properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantifying Impacts of Biomass Pelletization on Fast Pyrolysis Using a Single-Particle Reactor, X-ray Computed Tomography, and Computational Modeling

The pore structure and density of lignocellulosic feedstocks dictate intraparticle transport phenomena and thereby play an important role in thermochemical conversion processes such as fast pyrolysis for biofuel and biochemical production. Variations in microstructure are inherent from different biomass species and can be introduced by preprocessing techniques such as cutting and pelletization. Morphological changes also occur during conversion and lead to vastly different pore structures and behavior during pyrolysis, which impact required conversion times and product distributions. The current work presents a comprehensive comparison of fast pyrolysis of neat and pelletized pine feedstocks, which includes single-particle experiments, modeling, and 3D imaging by X-ray computed tomography (XCT). The particle-scale model included anisotropic heat and mass transport in a shrinking particle with pyrolysis reactions based on the CRECK mechanism with boundary conditions informed by reactor-scale simulations of the single-particle reactor. The models were validated by measurements of the temperature and mass loss from single-particle pyrolysis experiments of neat and pelletized pine. Quantitative analysis of XCT geometries revealed that pyrolytic conversion yielded chars with increased porosity and permeability compared to the unpyrolyzed materials, along with decreased tortuosity and anisotropy. Pelletization of the pine feedstock resulted in a much denser, less permeable material, which converted slower and produced more residual char after pyrolysis compared to neat pine. The results from particle modeling revealed that accounting for the dynamic and anisotropic heat and mass transport caused by differences in pore structure is critical to achieving agreement with experimental results. Overall, this study highlights the dramatic differences in conversion behavior imparted by pelletization and the importance of capturing microstructural attributes in computational models to guide the design and optimization of pyrolysis processes for specific biomass feedstocks.

09 BIOMASS FUELS↗

Soil microbiome feedbacks during disturbance-driven forest ecosystem conversion

Abstract Disturbances cause rapid changes to forests, with different disturbance types and severities creating unique ecosystem trajectories that can impact the underlying soil microbiome. Pile burning—the combustion of logging residue on the forest floor—is a common fuel reduction practice that can have impacts on forest soils analogous to those following high-severity wildfire. Further, pile burning following clear-cut harvesting can create persistent openings dominated by nonwoody plants surrounded by dense regenerating conifer forest. A paired 60-year chronosequence of burn scar openings and surrounding regenerating forest after clear-cut harvesting provides a unique opportunity to assess whether belowground microbial processes mirror aboveground vegetation during disturbance-induced ecosystem shifts. Soil ectomycorrhizal fungal diversity was reduced the first decade after pile burning, which could explain poor tree seedling establishment and subsequent persistence of herbaceous species within the openings. Fine-scale changes in the soil microbiome mirrored aboveground shifts in vegetation, with short-term changes to microbial carbon cycling functions resembling a postfire microbiome (e.g. enrichment of aromatic degradation genes) and respiration in burn scars decoupled from substrate quantity and quality. Broadly, however, soil microbiome composition and function within burn scar soils converged with that of the surrounding regenerating forest six decades after the disturbances, indicating potential microbial resilience that was disconnected from aboveground vegetation shifts. This work begins to unravel the belowground microbial processes that underlie disturbance-induced ecosystem changes, which are increasing in frequency tied to climate change.

Nelson, Amelia R.↗

Opportunities for Utilization of Low-Cost Algae Resources: Techno-Economic Analysis Screening for Near-Term Deployment (Parts 1 and 2)

This report presents a comprehensive techno-economic analysis (TEA) for the production, collection, or procurement of several low-cost algae resources that may otherwise be considered "waste" biomass materials today, as well as the utilization of these materials through exemplary conversion processes to produce renewable fuels and chemicals. In contrast to conventional TEA models attributed to large-scale algae "farming" approaches, which may be able to produce substantially more biomass and thus fuels/products at a national scale in the future, this assessment focuses on understanding opportunities and costs for such "waste" algal biomass resources as may be available at considerably lower cost today. Economics for base case assumptions and a range of sensitivity scenarios are presented, employing conversion technologies that are simple and well understood, and thus may be deployed at smaller community scale in the near term, as a means to support and expand a nascent algae industry on the way to employing a larger commercial algae farm approach for commodity-scale production. Specifically, three algal biomass resources are considered in this assessment, as may be sourced from (1) municipal wastewater treatment (WWT) utilizing algae in place of more conventional technologies for nitrogen/phosphorus removal, (2) collection and removal of harmful algal bloom (HAB) biomass as proliferates in certain inland water bodies, and (3) procurement of residual biomass following commercial lipid extraction (EXT) operations performed at smaller scale by industry today focused on higher-value nutraceutical applications. These three resources are evaluated through two conversion pathways: (1) combined algal biomass processing (CAP) through a simple/low-complexity configuration, and (2) anaerobic digestion (AD). The CAP pathway produces liquid fuels and chemical coproducts (polymer for off-site upgrading to bioplastics), whereas the AD pathway produces biogas (specifically renewable natural gas [RNG]) and crop fertilizer coproducts. To streamline the discussion, this report is broken into two sections: Part 1 focuses on WWT-derived biomass, and Part 2 on HAB and EXT biomass.

09 BIOMASS FUELS↗

Decontamination Strategies to Increase Fuel and Product Conversion Yields of Municipal Solid Waste

Since the implementation of China’s Green Fence and National Sword policies, many areas lost a market for heavily contaminated municipal solid waste (MSW). Approximately 17.2 million tons of paper and 26.9 million tons of plastic were landfilled in the United States in 2018. This non-recyclable waste that would normally be landfilled can be converted into fuels and chemicals, but common contaminants that are present in non-recyclable waste can negatively affect low and high-temperature conversion yields. In addition, MSW is a heterogeneous feedstock whose composition can vary widely across geographical areas and socio-economic statuses. This presents a unique challenge for providing a consistent feedstock to biorefineries around the world. Techniques that are commonly used in other industries, in addition to pre-processing methods used for traditional biomass, can be used to increase conversion yields. Drawing on established techniques, as well as experimental decontamination strategies, non-recyclable MSW could represent a viable alternative to agricultural residues for biofuel production. Although many of the techniques explored in this chapter have been used extensively in other industries, the feedstock composition needs to be carefully considered when choosing prospective decontamination methods. It is likely that there is not a “one-size-fits-all” decontamination method for MSW. In conclusion, a pre-processing and decontamination plan will rely heavily on the composition of the individual waste stream.

09 BIOMASS FUELS↗

Deconstruction of Woody Biomass via Protic and Aprotic Ionic Liquid Pretreatment for Ethanol Production

Ionic liquids (ILs) have emerged as important solvents for conversion of lignocellulosic feedstocks to fuels and chemicals due to their ability to enable efficient biomass deconstruction and fractionation. Woody biomass derived from forest and agricultural residues has the potential to be used for production of biofuels and its removal from forests can help mitigate disastrous wildfires in fire-prone states like California. This study evaluated woody biomass types (pine, almond, walnut, and fir) from California as potential biofuel feedstocks. The feedstocks were pretreated with the ILs cholinium lysinate ([Ch][Lys]) and ethanolamine acetate ([EOA][OAc]), followed by enzymatic hydrolysis and fermentation of lignocellulosic sugars to produce ethanol. Under optimal conditions, [EOA][OAc] pretreatment and enzymatic hydrolysis generated glucose and xylose yields in the range of 24-82 and 14-80%, respectively, while glucose and xylose yields for the [Ch][Lys] ranged between 28-83 and 23-80%, respectively. Maximum fermentable sugar was released from almond wood, and the lowest amount was from pine and fir. Further, blends of feedstocks were also explored, and a blend with a mass ratio of 2/2/1 (almond/walnut/pine) resulted in maximum glucose and xylose (>90%) yields using [Ch][Lys]. Fermentation of this hydrolysate using a C5-utilizing strain of Saccharomyces cerevisiae resulted in a maximum ethanol concentration of 17.9 g/L for mixture biomass hydrolysate, corresponding to 60.8% fermentation efficiency. This study represents the first demonstration of the use of these ILs for pretreatment of woody biomass blends that resulted in a high overall conversion efficiency for ethanol production.

09 BIOMASS FUELS↗

Nonthermal hydrogen plasma-enabled ambient, fast lignin hydrogenolysis to valuable chemicals and bio-oils

The reduction of fossil fuel resources and the ongoing surge in global energy demand have captured the interest of researchers worldwide, prompting a focus on developing renewable energy sources. For this reason, biomass conversion has emerged as a crucial pathway for renewable fuel production. Lignin, constituting 10–35% of woody biomass, represents a significant and largely untapped sustainable feedstock. Despite the potential of lignin, a substantial portion of this lignocellulosic residue remains unused, with approximately 60% considered waste. This study addresses the challenge of underutilized lignin by introducing an innovative approach to its hydrogenolysis. Despite their potential, existing hydrogenolysis methods face obstacles such as complexity, high cost, and the need for high temperatures or pressures. Herein we report a noncatalytic nonthermal hydrogen plasma method for lignin hydrogenolysis, conducted under ambient temperature and pressure conditions. Our method proves to be highly effective in breaking lignin bonds, achieving complete conversion, and generating valuable gaseous and bio-oil products including methane and aromatic dimers and monomers obtained from guaiacyl and syringyl units within the lignin structure. Our results showed an increase in gaseous products, especially methane, and aromatic monomer yields, as well as a reduction in total bio-oil and biochar yields and lignin functional groups by increasing reaction time, input power, and H2 partial pressure. This research confirms the considerable promise of utilizing noncatalytic nonthermal hydrogen plasma-assisted hydrogenolysis as an effective technique for producing gaseous and liquid fuels from lignin.

Pishva, Parsa↗

Funneled Depolymerization of Ionic Liquid-Based Biorefinery “Heterogeneous” Lignin into Guaiacols over Reusable Palladium Catalyst

The efficient utilization of lignin, the direct source of renewable aromatics, into value-added renewable chemicals is an important step towards sustainable biorefinery practices. Nevertheless, owing to the random heterogeneous structure and limited solubility, lignin utilization has been primarily limited to burning for energy. The catalytic depolymerization of lignin has been proposed and demonstrated as a viable route to sustainable biorefinery, however, low yields and poor selectivity of products, high char formation, and limited to no recycling of transition-metal-based catalyst involved in lignin depolymerization demands attention to enable practical-scale lignocellulosic biorefineries. In this study, we demonstrate the catalytic depolymerization of ionic liquid-based biorefinery poplar lignin into guaiacols over a reusable zirconium phosphate supported palladium catalyst. The essence of the study lies in the high conversion (>80 %), minimum char formation (7–16 %), high yields of guaiacols (up to 200 mg / g of lignin), and catalyst reusability. In conclusion, both solid residue, liquid stream, and gaseous products were thoroughly characterized using ICP-OES, PXRD, CHN analysis, GC-MS, GPC, and 2D NMR to understand the hydrogenolysis pathway.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Biomass supply chain equipment for renewable fuels production: A review

The production of renewable fuels is a critical component of global strategies to reduce greenhouse gas (GHG) emissions. Moreover, the collection of raw materials for its production can provide added benefits such as reduction of wildfire risk, additional income for farmers, and decreased disposal costs. Although there is substantial literature on design and modeling of supply chains, the authors were unable to find a single reference with the information needed for the selection and cost estimation of each type of equipment involved in the supply chain. Therefore, the goal of this research is to gather information necessary for the construction and utilization of models that might drive the identification of a feasible supply chain to produce renewable fuels at a commercial scale. The primary objectives are to 1) understand the supply chain of critical feedstocks for renewable fuels production; 2) identify the equipment commercially available for collection and adequation of feedstock; and 3) consolidate information regarding equipment cost, energy consumption, and efficiency, as well as feedstock storage and transportation systems. This paper provides a compilation for five feedstock types studied for sustainable aviation fuel production: 1) agricultural residues and grasses, 2) forest residues, 3) urban wood waste, 4) oilseeds, 5) fats, oils & greases. All the technologies involved from the field to the gate of the preprocessing or conversion unit were reviewed. The information on fats, oils & greases supply chains and equipment purposely designed for forest thinning and pruning was very limited.

: Feedstock, Collection and Adequation, Renewable ↗

Combined hydrothermal liquefaction and catalytic hydrothermal gasification system and process for conversion of biomass feedstocks

A combined hydrothermal liquefaction (HTL) and catalytic hydrothermal gasification (CHG) system and process are described that convert various biomass-containing sources into separable bio-oils and aqueous effluents that contain residual organics. Bio-oils may be converted to useful bio-based fuels and other chemical feedstocks. Residual organics in HTL aqueous effluents may be gasified and converted into medium-BTU product gases and directly used for process heating or to provide energy.

09 BIOMASS FUELS↗

Nitrogen derived from Combined Algal Processing supports algae cultivation for biofuels

Algae biomass, a biofuel feedstock with potential to reduce global CO 2 emissions, is currently too expensive Nitrogen, a significant input and life cycle cost, requires research on recycling and additional sources to reduce costs. Integral to nitrogen recycling is the knowledge of actual nitrogen requirements in outdoor ponds, thus data from the Unified Field Studies of the Algae Testbed Public-Private Partnership was analyzed. The data showed that Nannochloropsis oceanica used 14–24 mg/L NH 4 + per harvest cycle for robust growth. Nitrogen recycled directly from the algae conversion process will likely be the primary source of nitrogen for algae cultivation. Harvested algae can be fractionated via Combined Algal Processing (CAP), where algae are pretreated, fermented, and the fuel feedstocks (e. g. ethanol, lipids) are removed leaving a nitrogen rich slurry. Chlorella vulgaris grew robustly in nitrogen-free media supplemented with CAP residues through 4 harvest cycles with no inhibition. The amount of nitrogen as free ammonium available for recycling directly without further processing was insufficient (~4% of total needed), thus the nitrogen fixing bacteria, Azotobacter vinelandii, was investigated as a means for increasing ammonium concentration in CAP residues. This organism was shown to be proficient at growth on sugars liberated from algae biomass during pretreatment and sustained algae growth using A. vinelandii supernatants was also demonstrated. Using Azotobacter to increase ammonium concentrations on-site using an inexpensive biological process to generate the necessary ammonium for outdoor algae cultivation improves sustainability of algae biofuels by avoiding the energy intensive steps of typical ammonium production and transport. Furthermore, these results show that byproducts of algae conversion begin to close nitrogen demand and, with further supplementation by diazotrophic bacteria or protein hydrolysis, may completely replace current energyintensive and costly industrial nitrogen sources offering a path to increased economic feasibility and improved life cycle analysis of algae-based biofuels.

09 BIOMASS FUELS↗

Surface-Controlled Conversion of Ammonia Borane from Boron Nitride

“One-pot regeneration”, which is simple regneneration method of ammonia borane (AB) using hydrazine and liquid ammonia, enables conversion of AB from hexagonal boron nitride (h-BN) after milling hydrogenation. Solution 11 B-NMR revealed the presence of AB after NH 3 /N 2 H 4 treatment of milled h-BN (BNH x ) although the yield of AB was less than 5%. The conversion mechanism was clarified as B-H bonds on the h-BN surface created by ball-milling under hydrogen pressure have an ability to form AB, which was confirmed by Thermogravimetry-Residual Gas Analysis (TG-RGA) and Infrared (IR) analysis. The reaction routes are also the same as regeneration route of polyborazylene because intermediates of AB such as (B(NH 2 ) 3 and hydrazine borane were found by solution 11 B-NMR after soaking BNH x in liquid NH 3 and hydrazine, respectively. Because of the fact that all reactions proceed on the h-BN surface and no reaction proceeds when neat h-BN is treated, breaking of B 3 N 3 ring structure and then creation of B-H bond is the key issue to increase conversion yield of AB.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗