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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Isolated Single Metal Atoms Supported on Silica for One Step Non-Oxidative Methane Upgrading to Hydrogen and Value-Added Hydrocarbons

Natural gas in the United States offers substantial economic opportunities due to its abundance but its transportation is challenging because its primary component, methane (CH 4 ), does not liquefy at ambient temperature and typical pressures. As a result, a significant portion of natural gas is either used for heat, flared in remote locations, or remains unutilized, presenting a lost economic opportunity and an environmental harm. Converting natural gas to larger hydrocarbons in an economically competitive manner would enable transportation of products and further boost the economy and reduce environmental footprint. Our research goal is to enable efficient non-oxidative methane conversion (NMC) via catalyst innovation to convert CH 4 in one-step to olefins and aromatics and hydrogen (H 2 ) co-product. The catalysts are made of supported single metal atoms and operated at medium-high temperatures. The single metal atoms achieve methane activation by heterogeneous surface dehydrogenation to generate a hydrocarbon pool and importantly limit coke formation. The integration of novel single atom catalysts in a short contact time microreactor enable unprecedented NMC performance that could lead to economically-feasible, distributed natural gas upgrading by advanced manufacturing and process intensification. Our innovated catalyst and reactor technology promise to tap into previously uneconomic natural gas resources, such as stranded, vented, and flared methane.

03 NATURAL GAS↗
DOE OSTI2025

Deactivation of Mo/H-ZSM-5 in Microwave-Assisted and Thermal-Driven Methane Dehydroaromatization

A better understanding of catalyst deactivation is needed to improve catalyst design and performance in microwave-enhanced methane dehydroaromatization (MDA). Here, this study investigates the deactivation of a molybdenum supported H-ZSM-5 zeolite (Mo/H-ZSM-5) catalyst in MDA under microwave-heated conditions, comparing its performance to that of the same catalyst under conventional heating. While the microwave-assisted (MW) process achieved higher benzene yields, the catalyst experienced faster deactivation due to the selective and rapid deposition of coke within the pores of the zeolite, as confirmed through Brunauer–Emmett–Teller (BET), X-ray diffraction (XRD), ammonia-temperature programmed desorption (NH 3 -TPD), thermal gravimetric analysis (TGA), temperature programmed oxidation (TPO), and X-ray photoelectron spectroscopy (XPS) analyses. The quantification of total coke content via TGA/TPO and surface carbon (XPS) revealed that nearly twice as much coke was deposited on the catalyst under MW conditions compared to that on the conventionally heated material, and the coke exhibited a more conductive and graphitic nature. The accelerated deactivation rates were attributed to the formation of hot spots in the MW system, leading to enhanced coupling with coke formed in situ during the reaction and resulting in increased Mo reduction. Observations indicated that the CO activation used to carburize the catalyst prior to the reaction is not advantageous in the MW heating environment. The presence of large amounts of Mo oxides at elevated temperatures (through hot spots) exposed to methane leads to instability under the reaction conditions. Optimizing the activation environment and improvement of the Mo dispersion within the pores are potential strategies to improve catalyst stability.

Mo/H-ZSM-5 zeolite↗
DOE OSTI2024

Graphitizable Pitch from Microwave Plasma Pyrolysis of Natural Gas

An innovative approach of microwave plasma was utilized to convert natural gas into tar, from which a highly graphitizable pitch was derived using fractional distillation. The natural gas-derived pitch (NGDP) was thoroughly characterized, and the graphitizability of the carbonized NGDP was assessed using polarized light microscopy. The NGDP and, for comparison, needle coke, petroleum coke, and shot coke were subjected to graphitization heat treatment (GR) at 2500 °C. Results indicate that the graphitizability of the NGDP exceeds those of all industrial standard cokes. The GR-NGDP showed the highest degree of graphitization and crystallite size among all samples.

03 NATURAL GAS↗
DOE OSTI2020

Role of ring-enlargement reactions in the formation of aromatic hydrocarbons

Ring-enlargement reactions can provide a fast route towards the formation of six-membered single-ring or polycyclic aromatic hydrocarbons (PAHs). To investigate the participation of the cyclopentadienyl (C 5 H 5 ) radical in ring-enlargement reactions in high-temperature environments, a mass-spectrometric study was conducted. Experimental access to the C 5 H 5 high-temperature chemistry was provided by two counterflow diffusion flames. Cyclopentene was chosen as a primary fuel given the large amount of resonantly stabilized cyclopentadienyl radicals produced by its decomposition and its high tendency to form PAHs. In a second experiment, methane was added to the fuel stream to promote methyl addition pathways and to assess the importance of ring-enlargement reactions for PAH growth. The experimental dataset includes mole fraction profiles of small intermediate hydrocarbons and of several larger species featuring up to four condensed aromatic rings. Results show that, while the addition of methane enhances the production of methylcyclopentadiene and benzene, the concentration of larger polycyclic hydrocarbons is reduced. The increase of benzene is probably attributable to the interaction between the methyl and the cyclopentadienyl radicals. However, the formation of larger aromatics seems to be dominated only by the cyclopentadienyl driven molecular-growth routes which are hampered by the addition of methane. Furthermore, in addition to the experimental work, two chemical mechanisms were tested and newly calculated reaction rates for cyclopentadiene reactions were included. In an attempt to assess the impact of cyclopentadienyl ring-enlargement chemistry on the mechanisms’ predictivity, pathways to form benzene, toluene, and ethylbenzene were investigated. Results show that the updated mechanism provides an improved agreement between the computed and measured aromatics concentrations. Nevertheless, a detailed study of the single reaction steps leading to toluene, styrene, and ethylbenzene would be certainly beneficial.

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

Effect of Mo precursors in Microwave-assisted Methane Dehydroaromatization over Mo/HZSM5 catalysts

Natural gas flaring occurs in remote shale regions due to limited pipeline takeaway capacity. The conversion of the associated natural gas into aromatics in modular microwave reactors is a viable alternative to monetize the wasted gas. Microwaves offer rapid, selective heating in compact reactor systems that can enable on-demand chemical production at the well-site. Mo-HZSM-5 catalysts are widely used for aromatic production, but the location and nature of the active sites are still under debate. This study focuses on the use of 6 different Mo precursors to elucidate insights into the Mo properties that are desirable for BTX production. The catalysts were characterized by different methods (XPS, TPR, Raman, etc) to determine differences in Mo catalytic properties that may affect performance and understand these differences through performance testing under microwave at 700C for methane dehydroaromatization. Metal precursors that enable a better distribution of Mo into the pores and over the surface lead to improved benzene yield, whereas those that limited Mo to primarily the surface suffer rapid deactivation and low benzene yields. Additionally, strong Lewis acidity that arises from the sodium containing precursor drastically shifts the product selectivity towards dehydrogenation, which produces more ethylene and carbon. This catalyst had the highest deactivation constant of all catalysts tested.

gas flaring reduction↗
DOE OSTI2021

Reaction paths of methane activation and oxidation of surface intermediates over NiO on Ceria-Zirconia catalysts studied by In-situ FTIR spectroscopy

Methane activation over NiO/Ce 0.82 Zr 0.18 O 2 catalysts synthesized by combustion synthesis is studied by in-situ IR spectroscopy and correlated to the properties and oxygen speciation of the catalyst. Through XRD, H 2 -TPR, and pyridine adsorption followed by FTIR spectroscopy, the reducibility and Lewis acidity of the catalysts are assessed. In-situ FTIR spectroscopy is used to monitor the methane activation on catalyst surfaces. Complex IR features of methane-derived surface species are observed and are attributed to the formation of surface alkyl/alkoxy, aldehyde, formate/carbonate, and aromatic species. A data analysis algorithm is developed to evaluate the evolution of different surface species over time. The formation of formate and carbonate species is driven by adsorbed surface oxygen, while less reactive oxygen species associated with NiO allow for the production of aromatics and alkoxy intermediates. Finally, by tuning the reducibility and Lewis acidity of the catalyst, the selectivity to alkoxy intermediates can be improved.

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

An experimental and kinetic modeling study of the pyrolysis of isoprene, a significant biogenic hydrocarbon in naturally occurring vegetation fires

Isoprene dominates the carbon flux emitted by vegetation and constitutes 40% of non-methane biogenic emissions worldwide. Despite pyrolysis experiments at temperatures above 1000 K showing a link between isoprene combustion and aromatic species formation, comprehensive mechanistic research on isoprene is scarce in the literature. Here, in this work, we carry out an experimental and theoretical study to build, for the first time, a chemical kinetic model describing isoprene pyrolysis. The formation of polycyclic aromatic hydrocarbon (PAH) precursor species, often observed in vegetation fire plumes, is partially explained by isoprene pyrolysis experiments and theoretical modeling. Molecular dynamics (MD) simulations unveil reaction pathways from allylic isoprenyl radicals to allene and cyclopentadiene (CPD) intermediates, two relevant species detected in the experiments. Rate constants for these identified pathways are calculated using variational transition state theory to update the kinetic model, which is validated against single-pulse shock tube (SPST), and jet-stirred reactor (JSR) experimental data in the temperature range of 850–1690 K. The kinetic model presents satisfactory agreement with the SPST experimental data, and a reaction pathway analysis shows that association of propargyl radicals results in benzene formation. The JSR pathway analysis also identifies the prominent reactions for CPD, benzene, styrene, and toluene formation. Our model does not reproduce the CPD experimental profiles, indicating that additional studies are necessary. Overall, our findings advance the understanding of isoprene pyrolysis and its related atmospheric pollutants in naturally occurring vegetation fires where smoldering and oxygen-deficient combustion processes are present.

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

Enhancing the Value of Wasted and Stranded Natural Gas Resources Through Conversion Into Aromatics Using Microwaves

Natural gas flaring results in the waste of significant amounts of valuable domestic energy resources while also producing undesirable environmental impacts. Transforming natural gas into value-added chemicals via direct nonoxidative reactions presents a compelling alternative to flaring. However, traditional thermal reactor systems face challenges due to thermodynamic limitations and poor catalyst stability. Microwave-assisted reactions offer a sustainable, on-demand approach for chemical production from natural gas, suitable for compact, flexible reactor systems at the well-site that can be powered by renewable energy. This method offers a novel, non-traditional approach in catalyst activation and product selectivity compared to a conventional thermal method, potentially leading to faster rates, higher selectivities, and higher conversion efficiencies. Despite these advantages, challenges exist, such as the low microwave-sensitivity of the state-of-the-art zeolite catalyst that is highly active for the methane dehydroaromatization reaction. This presentation will discuss recent research from the National Energy Technology Laboratory concerning microwave-assisted natural gas conversion directly into aromatics. It will address the difficulties with microwave heating of traditional thermochemical catalysts, and the application of Multiphysics modeling to understand temperature and field strength in the reactor, to enhance chemical conversion. The presentation will also cover how heating aids can mitigate heating challenges and transform microwave catalysis into a quasi-thermal kinetic problem. Additionally, catalyst activation and deactivation under microwave conditions will be examined, along with the future outlook and needs for microwave enhanced catalysis applications.

catalysis↗
DOE OSTI2023

Formation of hydrocarbons favored by high pressure at subduction zone conditions

Subduction zones enable carbon transport to the deep Earth. Inorganic and organic carbon in fluids released from the subducted slab are important in water-rock interactions. However, the potential role of reduced carbon species in fluids during subduction is still unclear. In particular, the pressure, temperature, and oxidation state conducive to the formation of fluid hydrocarbons are poorly understood. Here we focused on the role of pressure influencing the formation of hydrocarbons using diamond anvil cell experiments starting with 0.5 M Ca-acetate solutions over a broad range of pressures, from 1.6 to 4.6 GPa at temperatures of 300 and 350°C. Droplets of immiscible hydrocarbon fluid coexisting with aqueous carbonate or bicarbonate and crystals of calcite or aragonite were formed at peak pressure and temperature conditions in the experiments. Furthermore, greater quantities of hydrocarbons formed at higher pressure as revealed by measuring the in situ volume percent of the droplets. Measurement of the in situ Raman spectra of the co-existing aqueous solutions and analysis of the peak area ratios of acetate to HCO 3 – showed faster decrease at higher pressure, which indicated that the reactions forming hydrocarbons were accelerated by pressure. Compared to previous Na-acetate experiments at 300°C and 3.0 GPa, this study found hydrocarbons that were more methane-rich and had more propane and less isobutane. In experiments at 350°C, isobutane transformed to one or more aromatic hydrocarbons in an immiscible fluid. The air-dried aromatic hydrocarbons were measured using a UV laser, and show peaks of bitumen. Overall, our study supports the hypothesis that high pressures and high temperatures facilitate the possible occurrence of immiscible hydrocarbon fluids in the deep carbon cycle.

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

Zeolites interactions with microwaves during methane non-oxidative coupling

Microwave-zeolite interactions during direct non-oxidative reactions of methane were studied using three H-ZSM-5 zeolites with different concentrations of Bronsted acid sites. The formation of C 2 and aromatic hydrocarbons increased with increasing surface acidity. When compared to conventional heating, the microwave reaction produced less carbon with higher thermal stability. The increase in diffraction shifts and the decrease in its surface area of microwave-reacted zeolite suggested that the carbon started depositing inside the micropores rather than on the external surfaces. Inhomogeneous carbon deposits with filamentous carbon whiskers were observed under microwave compared to homogeneous spherical carbon deposits on the conventionally reacted sample. The dielectric properties and Raman analysis suggested that the graphitic nature and the thermal stability of deposited carbon increased with zeolite surface acidity under microwave. We believe that this is a very important study for designing microwave active zeolite-based catalysts with a low affinity towards carbon formation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Methane Activation on Cu Containing Zeolite Catalysts (Final Report)

In order to increase the value of the light alkane ethane found in shale gas, we investigated the transformation of ethane into ethylene and aromatic hydrocarbons using zinc-containing microporous catalysts. We investigated the kinetics of the reaction, and identified various active sites for the ethane dehydrogenation and aromatization. In addition, we investigated iron-containing zeolites, as catalysts for the addition of methyl groups to small olefins containing 2, 3 and 4 carbon molecules. We determined the reaction mechanism, the identity of the active site, and details of the reaction kinetics. We concluded that the use of iron zeolites is very promising to upgrade small olefins (2-4 carbon species) into larger olefins (4-7 carbon species) that are more valuable as fuels and as petrochemical products.

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

Investigating Kinetic Mechanisms of Soot Formation in Plasma Pyrolysis of Methane via Active Learning (Final Technical Report)

Plasma pyrolysis of methane is an effective route for zero-carbon hydrogen production. Yet, soot generated from pyrolysis of hydrocarbons is detrimental to the climate and human health. There is ample experimental and theoretical evidence that suggests polycyclic aromatic hydrocarbons (PAHs) are the molecular precursors to soot particles. The reaction pathways of PAH formation are intricately dependent on a multitude of process parameters, whose kinetic mechanisms are not well-understood in plasma pyrolysis. This project aims to leverage advances in the kinetic modeling of soot formation in combustion, as well as in surrogate modeling and active learning, to systematically investigate the effects of process parameter on the kinetics of PAH formation in plasma pyrolysis of methane. To this end, we propose to use the PAH formation kinetics model developed by the PPPL/PU group based on the well-established ABF and HACA mechanisms, coupled with low-temperature plasma models. We will develop an active learning (AL) framework based on Bayesian optimization to systematically and data-efficiently explore the complex and multivariable parameter space of plasma pyrolysis in order to quantify the effects of plasma and feed parameters on the ABF and HACA kinetic pathways. AL is the branch of machine learning concerned with systematically querying samples from a system (experimental or computational) to train a data-driven model that maps design parameters to a performance criterion. We will use the data generated via AL to perform global sensitivity analysis, combined with uncertainty quantification, to elucidate the impact of different reaction pathways on minimizing formation of soot precursors. This study will result in an improved understanding of kinetics of PAH formation in plasma pyrolysis and can pave the way for more advanced mechanistic studies (e.g., soot nucleation mechanisms). Additionally, the findings will be useful for establishing practical strategies for increasing the pyrolysis efficiency and producing high-grade carbon for synthesis of nanomaterials.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Olefin methylation over iron zeolites and the methanol to hydrocarbons reaction

The effect of olefin addition to a stream of dimethyl ether on the methanol homologation reaction is investigated using iron-substituted zeolites Fe-beta and Fe-ZSM-5. The reaction was investigated using plug-flow microreactors in the temperature range of 240–400 °C, at a total pressure of 0.239 MPa and a WHSV of 6.12 (g DME/ gcat -hr). For Fe-beta (Si/Fe= 9.2) catalysts, isobutene co-feeding almost doubles dimethyl ether (DME) consumption rate and shifts selectivity towards larger olefins with carbon numbers from 5 to 7. Addition of isobutene above 6.3%, however, resulted in a reduction of DME consumption rates, an effect assigned to the replacement of surface methoxy groups for adsorbed olefins in the zeolite pores. Below a temperature of 340 °C hydride-transfer rates are negligible; reaction rates are stable for over 5.5 h and the products consist almost exclusively of olefins and a small amount of methane. Above 360 °C the onset of catalytic hydride transfer processes is observed leading to fast catalyst deactivation rates and an increase in the concentration of aromatic species. Iron ZSM-5 (Si/Fe = 21.4) catalysts under similar reaction conditions consumes methanol faster than Fe-beta at approximately three times the TOF (on a per iron basis). The Fe-ZSM-5 catalyst was selective to a distribution of products (C5 to C8) as compared to Fe-beta which was selective to primarily C5 and C7. Co-feeding larger olefins (2-methyl-2-butene, 2,3-dimethyl-2-butene, 2,3,3-trimethyl-1-butene, and 2,4,4-trimethyl-2-pentene) at a 3.9% olefin concentration over Fe-beta changed selectivity towards cracking products (C4 compounds such as isobutene). As the size of the olefin increases, a reduction of DME consumption rate is also observed. Here these results show that co-feeding olefins with DME over Fe-zeolites is a promising route to increase methylation rates at relatively low temperatures producing larger branched olefins and that the product distribution is highly dependent on the zeolite pore size and structure of the olefin.

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

Alpha ketoacid decarboxylases: Diversity, structures, reaction mechanisms, and applications for biomanufacturing of platform chemicals and fuels

In living cells, alpha-ketoacid decarboxylases (KDCs, EC 4.1.1.-) are a class of enzymes that convert alpha-ketoacids into aldehydes through decarboxylation. These aldehydes serve as either drop-in chemicals or precursors for the biosynthesis of alcohols, carboxylic acids, esters, and alkanes. These compounds play crucial roles in cellular metabolism and fitness and the bioeconomy, facilitating the sustainable and renewable biomanufacturing of platform chemicals and fuels. This review explores the diversity and classification of KDCs, detailing their structures, mechanisms, and functions. We highlight recent advancements in repurposing KDCs to enhance their efficiency and robustness for biomanufacturing. Additionally, we present modular KDC-dependent metabolic pathways for the microbial biosynthesis of aldehydes, alcohols, carboxylic acids, esters, and alkanes. Lastly, we discuss recent developments in the modular cell engineering technology that can potentially be applied to harness the diversity of KDC-dependent pathways for biomanufacturing platform chemicals and fuels.

09 BIOMASS FUELS↗
DOE OSTI2020

Nickel/gallium modified HZSM-5 for ethane aromatization: Influence of metal function on reactivity and stability

Bimetallic catalysts often outperform their monometallic counterparts due to the synergistic effect. Here we reported that the Ni/Ga co-functionalized HZSM-5 catalyst, specifically with Ni 1 /Ga 1 stoichiometric ratio, shows significantly improved selectivity (above 80 %) and stability than the Ni/HZSM-5 catalyst and higher activity (with identical selectivity) than the Ga/HZSM-5 catalyst in ethane aromatization. According to the transient experiment, the Ga and Ni 1 Ga 1 /HZSM-5 catalysts show an induction period of a few minutes. However, for Ni/HZSM-5 and Ni 1 Ga 1/3 /HZSM-5, the induction period increased to >10 min and >30 min, respectively, where up to 100 % of ethane was converted into methane and coke through cracking/hydrogenolysis. Furthermore, based on the generalized power-law equation model, a modified model for deactivation kinetic was proposed. Consequently, the influence of the metal function on the kinetic parameters was discussed. We anticipate the formation of Ni 3 Ga intermetallic alloy and its synergy with the exchanged Ga δ+ to be responsible for optimal BTX formation.

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

Age and chemistry of dissolved organic carbon reveal enhanced leaching of ancient labile carbon at the permafrost thaw zone

Abstract. Climate change will alter the balance between frozen and thawed conditions in Arctic systems. Increased temperatures will make the extensive northern permafrost carbon stock vulnerable to decomposition and translocation. Production, cycling, and transport of dissolved organic carbon (DOC) are crucial processes for high-latitude ecosystem carbon loss that result in considerable export off the Arctic landscape. To identify where and under what conditions permafrost DOC is mobilized in an Arctic headwater catchment, we measured radiocarbon (14C) of DOC and assessed DOC composition with ultraviolet–visible spectroscopy (UV–Vis) of surface waters and shallow and deep subsurface porewaters from 17 drainages in the Barrow Environmental Observatory in Alaska. Samples were collected in July and September 2013 to assess changes in age and chemistry of DOC over time. DOC age was highly variable ranging from modern (19 ‰ Δ14C) to approximately 7000 BP (−583 ‰ Δ14C). DOC age increased with depth, over the summer as the active layer deepened, and with increasing drainage size. DOC quality indicators reflected a DOC source rich in high molecular-weight and aromatic compounds, characteristics consistent with vegetation-derived organic matter that had undergone little microbial processing, throughout the summer and a weak relationship with DOC age. In deep porewaters, DOC age was also correlated with several biogeochemical indicators (including dissolved methane concentration, δ13C, and the apparent fractionation factor), suggesting a coupling between carbon and redox biogeochemistry influencing methane production. In the drained thawed lake basins included in this study, DOC concentrations and contributions of vegetation-derived organic matter declined with increasing basin age. The weak relationship between DOC age and chemistry and consistency in DOC chemical indicators over the summer suggest a high lability of old DOC released by thawing permafrost.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Polystyrene Hydrogenolysis to High-Quality Lubricants Using Ni/SiO 2

Pyrolytic and light-activated oxidation processes are leading technologies for utilizing polystyrene (PS) wastes. These approaches exhibit poor selectivities, use complex reactors, and require solvents. Hydrogenolysis is effective for deconstructing polyolefins, but its application to PS feedstocks has been limited. Herein, we demonstrate Ni/SiO 2 catalysts to facilitate PS (M w ≈ 97 kDa) hydrogenolysis to produce lubricant base oils possessing group IV properties, achieving maximum yields of 70% within 6 h at 300 °C and 70 bar of H 2 . Gas, liquid, and oil product yields are stable across reaction conditions, whereas hydrogenation of the PS aromaticity and reduction of the molecular weight benefit from higher temperatures and H 2 pressures. Time-dependent experiments underscore the importance of elevated H 2 pressure, revealing that PS hydrogenolysis occurs sequentially, with aromatic ring hydrogenation preceding degradation of the C–C backbone. Kinetic measurements with 1,2-diphenylethane as a probe molecule demonstrate that ring hydrogenation pis 3 orders of magnitude faster than internal C–C bond cleavage over Ni/SiO 2 . Ni/SiO 2 proves to be effective in the hydrogenolysis of heavier PS polymers and rigid commercial PS products. Conversely, flexibility and foam PS feeds result in Ni/SiO 2 deactivation, attributed to performance additives. Unlike polyolefins, the process produces very little methane and other light hydrocarbons. Furthermore, these findings expand the applicability of hydrogenolysis to PS feedstocks, offering a versatile solution and broadening the range of high-value products from PS to include lubricant base oils.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗