Search NASA⌕ Search

SEARCH · Search NASA

Results for “Acid base chemistry”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

Critical review of functionalized silica sorbent strategies for selective extraction of rare earth elements from acid mine drainage

We report the ubiquitous and growing global reliance on rare earth elements (REEs) for modern technology and the need for reliable domestic sources underscore the rising trend in REE-related research. Adsorption-based methods for REE recovery from liquid waste sources are well-positioned to compete with those of solvent extraction, both because of their expected lower negative environmental impact and simpler process operations. Functionalized silica represents a rising category of low cost and stable sorbents for heavy metal and REE recovery. These materials have collectively achieved high capacity and/or high selective removal of REEs from ideal solutions and synthetic or real coal wastewater and other leachate source. These sorbents are competitive with conventional materials, such as ion exchange resins, activated carbon; and novel polymeric materials like ion-imprinted particles and metal organic frameworks (MOFs). This critical review first presents a data mining analysis for rare earth element recovery publications indexed in Web of science, highlighting changes in REE recovery research foci and confirming the sharply growing interest in functionalized silica sorbents. A detailed examination of sorbent formulation and operation strategies to selectively separate heavy (HREE), middle (MREE), and light (LREE) REEs from the aqueous sources is presented. Selectivity values for sorbents were largely calculated from available figure data and gauged the success of the associated strategies, primarily: (1) silane-grafted ligands, (2) impregnated ligands, and (3) bottom-up ligand/silica hybrids. These were often accompanied by successful co-strategies, especially bite angle control, site saturation, and selective REE elution. Recognizing the need to remove competing fouling metals to achieve purified REE “baskets,” we highlight techniques for eliminating these species from acid mine drainage (AMD) and suggest a novel adsorption-based process for purified REE extraction that could be adapted to different water systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Enhancing the capacitive performance of microporous materials with protic ionic liquids

Classical density functional theory (cDFT) is used to investigate the electrosorption of protic ionic liquids in porous electrodes within the framework of a coarse-grained model. The purpose of this study is to clarify the capacitive behavior of protic ionic liquids in confined geometry. Previous studies have indicated that thermodynamic properties (e.g., capacitance, phase behavior and ionic conductivity) are influenced by the composition of the acid-base system and show asymmetry between acid dominant versus base dominant compositions. Here, we find that the electric double layer capacitance can be significantly improved by using protic ionic liquids compared to its aprotic counterpart through optimization of the mixture composition (i.e., the ratio of acid to base). We demonstrate the influence of pore size and applied voltage on the capacitance performance of protic ionic liquids and provide insight into microscopic understanding of ion and solvent distributions inside micropores.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Binding and stability of MgO monomers on anatase TiO 2 (101)

In catalysis, MgO is often used to modify the acid-base properties of support oxides and to stabilize supported metal atoms and particles on oxides. In this study, we show how the sublimation of MgO powder can be used to deposit MgO monomers, hither on anatase TiO 2 (101). A combination of X-ray electron spectroscopy, high-resolution scanning tunneling microscopy, and density functional theory is employed to gain insight into the MgO monomer binding, electronic and vibrational properties, and thermal stability. In the most stable configuration, the Mg and O of the MgO monomer bind to two surface oxygens and one undercoordinated surface titanium, respectively. The additional binding weakens the Mg-O monomer bond and makes the Mg more ionic. The monomers are thermally stable up to 650 K, where the onset of diffusion into the TiO 2 bulk is observed. Finally, the monomeric MgO species on TiO 2 (101) represent an ideal, atomically precise system with modified acid-base properties and will be employed in our future catalytic studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Chemical insights into the multi-regime low-temperature oxidation of di-n-propyl ether: Jet-stirred reactor experiments and kinetic modeling

To further understand the combustion characteristics and the reaction pathways of acyclic ethers, in this work the oxidation of di-n-propyl ether (DPE) was investigated in a jet-stirred reactor (JSR) combined with a photoionization molecular-beam mass spectrometer. The experiments were carried out at near-atmospheric pressure (700 Torr) and over a temperature range of 425–850 K. Based on the experimental data and previous studies on ether oxidation, a new kinetic model was constructed and used to interpret the oxidation chemistry of DPE. In DPE oxidation, a high reactivity at low temperatures and two negative temperature coefficient (NTC) zones were observed. These behaviors are explained in this work by taking advantage of the obtained species information and the modeling analyses: the two NTC zones are caused by the competition of chain branching and termination reactions of the fuel itself and specific oxidation intermediates, respectively. Furthermore, the general requirements to have double-NTC behavior are discussed. A variety of crucial fuel-specific C 6 species, such as ketohydroperoxides and diones, were detected in the species pool of DPE oxidation. Their formation pathways are illuminated based on rate-of-production (ROP) analyses. Propanal was identified as the most abundant small molecule intermediate, and its related reactions have an important impact on the oxidation process of DPE. Both acetic acid and propionic acid were detected in high concentrations. A new formation pathway of propionic acid is proposed and incorporated into the kinetic model to achieve a more accurate prediction for propionic acid mole fractions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Control of Catalyst Isomers Using an N -Phenyl-Substituted RN(CH 2 CH 2 P i Pr 2 ) 2 Pincer Ligand in CO 2 Hydrogenation and Formic Acid Dehydrogenation

A novel pincer ligand, i Pr PN Ph P [PhN- (CH 2 CH 2 P i Pr 2 ) 2 ], which is an analogue of the versatile MACHO ligand, iPr PN H P [HN(CH 2 CH 2 P i Pr 2 ) 2 ], was synthesized and characterized. The ligand was coordinated to ruthenium, and a series of hydride-containing complexes were isolated and characterized by NMR and IR spectroscopies, as well as X-ray diffraction. Comparisons to previously published analogues ligated by iPr PN H P and iPr PN Me P [CH 3 N(CH 2 CH 2 P i Pr 2 ) 2 ] illustrate that there are large changes in the coordination chemistry that occur when the nitrogen substituent of the pincer ligand is altered. For example, ruthenium hydrides supported by the iPr PN Ph P ligand always form the syn isomer (where syn/anti refer to the relative orientation of the group on nitrogen and the hydride ligand on ruthenium), whereas complexes supported by iPr PN H P form the anti isomer and complexes supported by iPr PN Me P form a mixture of syn and anti isomers. We evaluated the impact of the nitrogen substituent of the pincer ligand in catalysis by comparing a series of iPr PN R P (R = H, Me, Ph)-ligated ruthenium hydride complexes as catalysts for formic acid dehydrogenation and carbon dioxide (CO 2 ) hydrogenation to formate. The iPr PN Ph P-ligated species is the most active for formic acid dehydrogenation, and mechanistic studies suggest that this is likely because there are kinetic advantages for catalysts that operate via the syn isomer. In CO 2 hydrogenation, the iPr PN Ph P-ligated species is again the most active under our optimal conditions, and we report some of the highest turnover frequencies for homogeneous catalysts. Experimental and theoretical insights into the turnover-limiting step of catalysis provide a basis for the observed trends in catalytic activity. Additionally, the stability of our complexes enabled us to detect a previously unobserved autocatalytic effect involving the base that is added to drive the reaction. Overall, by modifying the nitrogen substituent on the MACHO ligand, we have developed highly active catalysts for formic acid dehydrogenation and CO 2 hydrogenation and also provided a framework for future catalyst development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

System and method for forming activated carbon aerogels and performing 3D printing

Making a carbon aerogel involves 3-D printing an ink to make a printed part, removing the solvent from the printed part, and carbonizing the printed part (with the solvent removed) to make the aerogel. The ink is based on a solution of a resorcinol-formaldehyde resin (RF resin), water, and an organic thickener. Advantageously, the RF resin contains an acid catalyst, which tends to produce carbon aerogels with higher surface areas upon activation than those produced from methods involving an ink composition containing a base catalyzed resin.

36 MATERIALS SCIENCE↗

Association Kinetics for Perfluorinated n -Alkyl Radicals

Radical-radical reaction channels are important in the pyrolysis and oxidation chemistry of perfluoroalkyl substances (PFAS). In particular, unimolecular dissociation reactions within unbranched n-perfluoroalkyl chains, and their corresponding reverse barrierless association reactions, are expected to be significant contributors to the gas-phase thermal decomposition of families of species such as perfluorinated carboxylic acids and perfluorinated sulfonic acids. Unfortunately, experimental data for these reactions are scarce and uncertain. Furthermore, obtaining reliable theoretical predictions for such reactions is a laborious and computationally intensive task. Here, in this work, the chemical kinetics of the various association/decomposition reactions producing/decomposing the C 2 -C 4 series of unbranched n-perfluoroalkanes (C 2 F 6 , C 3 F 8 , and C 4 F 10 ) are examined using state-of-the-art ab initio transition-state-theory-based master-equation calculations. The variable-reaction-coordinate transition-state theory (VRC-TST) formalism is employed in computing the microcanonical and canonical rates for the association reactions. Reaction thermochemistry is obtained via composite quantum chemistry calculations and the laddering of error-canceling reaction schemes via a connectivity-based hierarchy approach employing ANL1/ANL0-style reference energies. Lennard-Jones collision model parameters for the considered systems were estimated by a direct dynamics approach, and collisional energy transfer parameters were obtained from analogies to systems of similar size and heavy-atom connectivity. A one-dimensional master equation approach was used to convert the microcanonical rate coefficients from the VRC-TST analysis into temperature- and pressure-dependent rate constants for the association reactions and the reverse dissociation reactions. The data are reported in standardized formats for usage in comprehensive chemical kinetic models for PFAS thermal destruction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ultrafiltration separation of Am(VI)-polyoxometalate from lanthanides

Partitioning of americium from lanthanides (Ln) present in used nuclear fuel plays a key role in the sustainable development of nuclear energy. This task is extremely challenging because thermodynamically stable Am(III) and Ln(III) ions have nearly identical ionic radii and coordination chemistry. Oxidization of Am(III) to Am(VI) produces AmO 2 2+ ions distinct with Ln(III) ions, which has the potential to facilitate separations in principle. However, the rapid reduction of Am(VI) back to Am(III) by radiolysis products and organic reagents required for the traditional separation protocols including solvent and solid extractions hampers practical redox-based separations. Herein, we report a nanoscale polyoxometalate (POM) cluster with a vacancy site compatible with the selective coordination of hexavalent actinides ( 238 U, 237 Np, 242 Pu and 243 Am) over trivalent lanthanides in nitric acid media. To our knowledge, this cluster is the most stable Am(VI) species in aqueous media observed so far. Ultrafiltration-based separation of nanoscale Am(VI)-POM clusters from hydrated lanthanide ions by commercially available, fine-pored membranes enables the development of a once-through americium/lanthanide separation strategy that is highly efficient and rapid, does not involve any organic components and requires minimal energy input.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Continuum Model to Define the Chemistry and Mass Transfer in a Bicarbonate Electrolyzer

Bicarbonate electrolyzers are devices designed to convert CO 2 captured from point sources or the atmosphere into chemicals and fuels without needing to first isolate pure CO 2 gas. In this work, we report here an experimentally validated model that quantifies the reaction chemistry and mass transfer processes within the catalyst layer and cation exchange membrane layer of a bicarbonate electrolyzer. Our results demonstrate that two distinct chemical microenvironments are key to forming CO at high rates: an acidic membrane layer that promotes in situ CO 2 formation and a basic catalyst layer that suppresses the hydrogen evolution reaction. We show that the rate of CO product formation can be increased by modulating the catalyst and membrane layer properties to increase the rate of in situ CO 2 generation and transport to the cathode. These insights serve to inform the design of bicarbonate and BPM-based CO 2 electrolyzers while demonstrating the value of modeling for resolving rate-determining processes in electrochemical systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ultrastable Carboxyl–Functionalized Pore–Space–Partitioned Metal–Organic Frameworks for Gas Separation

Isoreticular chemistry, which enables property optimization by changing compositions without changing topology, is a powerful synthetic strategy. One of the biggest challenges facing isoreticular chemistry is to extend it to ligands with strongly coordinating substituent groups such as unbound –COOH, because competitive interactions between such groups and metal ions can derail isoreticular chemistry. It is even more challenging to have an isoreticular series of carboxyl-functionalized MOFs capable of encompassing chemically disparate metal ions. Furthermore, with the simultaneous introduction of carboxyl functionalization and pore space partition, a family of carboxyl-functionalized materials is developed in diverse compositions from homometallic Cr 3+ and Ni 2+ to heterometallic Co 2+ /V 3+ , Ni 2+ /V 3+ , Co 2+ /In 3+ , Co 2+ /Ni 2+ . Cr-MOFs remain highly crystalline in boiling water. Unprecedentedly, one Cr-MOF can withstand the treatment cycle with 10m NaOH and 12m HCl, allowing reversible inter-conversion between unbound –COOH acid form and –COO – base form. These materials exhibit excellent sorption properties such as high uptake capacity for CO 2 (100.2 cm 3 g –1 ) and hydrocarbon gases (e.g., 142.1 cm 3 g –1 for C 2 H 2 , 110.5 cm 3 g –1 for C 2 H 4 ) at 1 bar and 298K, high benzene/cyclohexane selectivity (up to ≈40), and promising separation performance for gas mixtures such as C 2 H 2 /CO 2 and C 2 H 2 /C 2 H 4 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of stereochemistry on nanoscale assembly of ABA triblock copolymers with crystallizable blocks

We report on the nanoscale assembly of poly(lactic acid)-b-poly(ethylene oxide)-b-poly(lactic acid) (PLA-PEO-PLA) triblock copolymers in water, focusing on the effect of stereochemistry, where the PLA blocks are statistical copolymers of l-lactide and d-lactide with l/d ratios of 100/0, 95/5, 90/10, 85/15, 75/25, and 50/50. Small-angle neutron scattering (SANS) shows a nearly constant d-spacing as concentration varies in triblock systems with l/d ratios of 90/10 and 95/5, which we attribute to inhomogeneity in the structure of these gels, supported by previous USANS and confocal microscopy studies. The SANS data fit well to a core-shell ellipsoid form factor model with a hard-sphere structure factor. Polymeric micelles with l/d ratios from 75/25 to 85/15 displayed very high aggregation numbers, consistent with a strong interaction between PLA chains and the enhanced storage modulus observed in rheological studies of these systems. While the 90/10 and 95/5 samples showed lower aggregation numbers, their SANS profiles shows close spacing between micelles, which may promote a high fraction of intermicellar bridging chains, also consistent with a higher storage modulus. Overall, these results provide insight into the micellar assembly behavior of block copolymers with a crystallizable block, and indicate that tuning stereochemistry of PLA-based block copolymers is an effective means of modifying micellar properties for specific applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Comparing plant litter molecular diversity assessed from proximate analysis and 13 C NMR spectroscopy

Accurate representation of the chemical diversity of litter in ecosystem-scale models is critical for improving predictions of decomposition rates and stabilization of plant material into soil organic matter. In this contribution, we conducted a systematic review to evaluate how conventional characterization of plant litter quality using proximate analysis compares with molecular-scale characterization using 13 C NMR spectroscopy. Using a molecular mixing model, we converted chemical shift regions from NMR into fractions of carbon (C) in five organic compound classes that are major constituents of plant material: carbohydrates, proteins, lignins, lipids, and carbonylic compounds. We found positive correlations between the acid soluble fraction and carbohydrates, and between the acid insoluble fraction and lignins. However, the acid-soluble fraction underestimated carbohydrates, and the acid insoluble fraction overestimated lignins by 243%. We identified two sources of uncertainties: i) disparities between litter chemical composition based on hydrolysability and actual chemical composition obtained from NMR and ii) conversion factors to translate proximate fractions into organic constituents. Both uncertainties are critical, potentially leading to misinterpretations of decay rates in litter decomposition models. Consequently, we recommend including explicit substrate chemistry data in the next generation of litter decomposition models.

59 BASIC BIOLOGICAL SCIENCES↗

Highly stable and tunable peptoid/hemin enzymatic mimetics with natural peroxidase-like activities

Abstract Developing tunable and stable peroxidase mimetics with high catalytic efficiency provides a promising opportunity to improve and expand enzymatic catalysis in lignin depolymerization. A class of peptoid-based peroxidase mimetics with tunable catalytic activity and high stability is developed by constructing peptoids and hemins into self-assembled crystalline nanomaterials. By varying peptoid side chain chemistry to tailor the microenvironment of active sites, these self-assembled peptoid/hemin nanomaterials (Pep/hemin) exhibit highly modulable catalytic activities toward two lignin model substrates 2,2-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) and 3,3’,5,5’-tetramethylbenzidine. Among them, a Pep/hemin complex containing the pyridyl side chain showed the best catalytic efficiency ( V max / K m = 5.81 × 10 −3 s −1 ). These Pep/hemin catalysts are highly stable; kinetics studies suggest that they follow a peroxidase-like mechanism. Moreover, they exhibit a high efficacy on depolymerization of a biorefinery lignin. Because Pep/hemin catalysts are highly robust and tunable, we expect that they offer tremendous opportunities for lignin valorization to high value products.

59 BASIC BIOLOGICAL SCIENCES↗

Batch Extraction Studies to Evaluate Trace Element Behavior in PUREX Conditions

The multilab Intentional Forensics Venture is working to identify which stable elements (i.e., taggants) at trace concentrations relative to U would persist throughout the nuclear fuel cycle in a voluntary fuel tagging scheme. A taggant would provide the nuclear forensics community with a “barcode” to help identify nuclear materials found outside of regulatory control. A portion of this project was focused on reprocessing effects and determining which, if any, elements would coextract with U(VI) in standard Pu–U reduction extraction (PUREX) conditions. Elements with a propensity to coextract could, in theory, be used as taggants from a PUREX perspective. Although retention is not a performance requirement, the taggant signature would need to partition predictably from the U stream after the PUREX process to maintain forensic utility. This report documents results from several batch extraction studies with numerous trace elements from HNO 3 (1.5–5 M), with and without U(VI), into 30% tri-n-butyl phosphate (TBP) in kerosene. Extraction and back-extraction tests were used to evaluate nearly 60 elements in surrogate conditions for PUREX, and distribution coefficients (i.e., D-values) for most species were <0.1, indicating few species are likely to co-extract with U through PUREX. Additional studies are needed to optimize sample volumes and dilutions to dial in these low D-values. The D-values (D) were determined for several of the more promising elements, including Re and Se. Ultimately, we conclude that only a limited number of the ~ 60 elements investigated are extractable in the U stream of PUREX, based on measured D values, meaning most candidate elemental taggants would likely be lost at this stage of the nuclear fuel cycle, even when considering a range of acid concentrations.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Probing the Effects of Acid Electrolyte Anions on Electrocatalyst Activity and Selectivity for the Oxygen Reduction Reaction

The local microenvironment at the electrode-electrolyte interface plays an important role in electrocatalytic performance. Herein, we investigate the effect of acid electrolyte anion identity on the oxygen reduction reaction (ORR) activity and selectivity of smooth Ag and Pd catalyst thin films. Cyclic voltammetry in perchloric, nitric, sulfuric, phosphoric, hydrochloric, and hydrobromic acid, at pH1, reveals that Ag ORR activity trends as follows: HClO 4 >HNO 3 >H 2 SO 4 >H 3 PO 4 >HCl>>HBr, while Pd ORR activity trends as: HClO 4 >H 2 SO 4 >HNO 3 >H 3 PO 4 >HCl>>HBr. Moreover, rotating-ring-disk-electrode selectivity measurements demonstrate enhanced 4 e - selectivity on both Ag and Pd, by up to 35% H 2 O 2 and 10% H 2 O 2 respectively, in HNO 3 compared to in HClO 4 . Relating physics-based modeling and experimental results, we postulate that ORR performance depends greatly on anion-related phenomena in the double layer, for instance competitive adsorption and non-covalent interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Precisely doping the surface of tin-based electrocatalysts for improved CO 2 conversion to liquid chemicals

Doping tin catalysts with sulfur can improve the electrochemical CO 2 conversion into formate/formic acid, but the lack of composition-dependent activity trends hinders further catalyst development. Here, we precisely controlled the composition of sulfur-doped Sn catalysts to show that sulfur doping only improves CO 2 conversion over a very narrow composition range, achieving maximum activity at 1.4 at% S. In situ Raman spectroscopy indicted working catalysts were in a primarily metallic state (e.g. S-Sn), and we achieved some of the highest reported partial current densities in both H-cell and full-cell electrolyzer configurations. Density Functional Theory calculations predicted S atoms preferentially occupied the catalyst surface and improved CO 2 reduction by localizing charge density at the catalyst/intermediate interface, which stabilized the *OCOH intermediate and lowered the CO 2 conversion thermodynamic barrier. Our work quantifies the composition-dependent influence of S dopants on Sn-based CO 2 reduction catalysts and provides a pathway for maximizing their CO 2 conversion activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigations into Spin- and Unpolarized Secondary Electron-Induced Reactions in Self-Assembled Monolayers of Cysteine

Cysteine is the simplest thiolated, chiral amino acid and is often used as the anchor for studies of self-assembled monolayers (SAMs) of complex biomolecules such as peptides. Understanding the interaction of SAMs of cysteine with low-energy secondary electrons (SEs) produced by X-rays can further our understanding of radiation damage in biomolecules. In particular, if the electrons are polarized, chiral-selective chemistry could have bearing on the origin of homochirality in nature. In the present paper, we use synchrotron radiation-based X-ray photoelectron spectroscopy to determine the changes that occur in the bonding of self-assembled layers of cysteine on gold as a result of soft X-ray irradiation. To investigate the possibility of chiral selectivity resulting from the interaction of low-energy, spin-polarized SEs (SPSEs), measurements were conducted on cysteine adsorbed on a 3 nm-thick gold layer deposited on a CoPt thin-film multilayer with perpendicular magnetic anisotropy. Time-dependent measurements of the C 1s, N 1s, O 1s, S 2p, and Au 4f core levels are used to follow the changes in surface chemistry and determine reaction cross-sections as a function of SE exposure. Analysis of the data results in cross-sections in the range of 5-7 Mb and suggests possible reaction pathways. Changing the magnetization direction of the CoPt multilayer produces SPSEs with opposite polarity. Some evidence of spin-dependent reactions is indicated but is inconclusive. Possible reasons for the discrepancy are posited.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Revisiting the influence of Ni particle size on the hydrogenation of CO 2 to CH 4 over Ni/CeO 2

Nickel nanoparticles were supported on CeO 2 and evaluated in the hydrogenation of CO 2 to CH 4 at 538 K and 1 atm. Chemisorption of H 2 was used to estimate the average Ni particle size, which ranged from 1.3 to 17 nm. The apparent activation energy for CH 4 formation and turnover frequency for CO 2 conversion was independent of Ni particle size. The smallest Ni particles (1.3 nm) were less selective to CH 4 . Comparisons to alumina-supported Ni reveal the same performance as Ni/CeO 2 when normalized to active Ni atoms counted by H 2 chemisorption. A beneficial effect of ceria relative to alumina is the enhanced reducibility of Ni as evaluated by H 2 temperature-programmed reduction. The constancy of the turnover frequency on Ni particles suggests the acid-base and/or redox properties of the support do not play a significant role in the CO 2 methanation reaction under the conditions of study, which contrasts many earlier works.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗