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At least 325 records · Page 18

Developing V-Xanes Oxybarometry for Probing Materials Formed in Reducing Environments in the Early Solar Disk

Vanadium exhibits four oxidation states (V(sup 2+), V(sup 3+), V(sup 4+) and V(sup 5+)) that have been shown to preferentially partition between melt phases dependent on redox conditions, spanning oxygen fugacity across more than 10 log units. We are developing synchrotron-based x-ray absorption spectroscopy of low-fugacity standards for the determination of V oxidation state in highly reducing conditions relevant to the early solar nebula.

Butterworth, A. L.↗

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↗

In-situ anodic precipitation process for highly efficient separation of aluminum alloys

Electrorefining process has been widely used to separate and purify metals, but it is limited by deposition potential of the metal itself. Here we report in-situ anodic precipitation (IAP), a modified electrorefining process, to purify aluminium from contaminants that are more reactive. During IAP, the target metals that are more cathodic than aluminium are oxidized at the anode and forced to precipitate out in a low oxidation state. This strategy is fundamentally based on different solubilities of target metal chlorides in the NaAlCl4 molten salt rather than deposition potential of metals. The results suggest that IAP is able to efficiently and simply separate components of aluminum alloys with fast kinetics and high recovery yields, and it is also a valuable synthetic approach for metal chlorides in low oxidation states.

36 MATERIALS SCIENCE↗

In situ characterization of metastable Pb3O5 and Pb2O3 phases during thermal decomposition of PbO2 to PbO

Nonstoichiometric lead oxides play a key role in the formation and cycling of the positive electrodes in a lead acid battery. These phases have been linked to the underutilization of the positive active material but also play a key role in the battery’s cycle life, providing inter-particle adhesion and the connection to the underlying lead grid. Similar phases have previously been identified by mass loss or color change during thermal annealing of PbO2 to PbO, suggesting that at least two intermediate PbOx phases exist. Using multiple in situ analysis techniques (powder diffraction, x-ray absorption, x-ray photoelectron spectroscopy) and ex situ nuclear magnetic resonance measurements, the structural conversion and changes in the lead oxidation states were identified during this process. Isolation of the PbOx phases enabled confirmation of Pb3O5 and Pb2O3 by diffraction and the first 207Pb NMR measurement of these intermediates.

Kinnibrugh, Tiffany L.↗

Moessbauer Mineralogy on the Moon: The Lunar Regolith

A first-order requirement for spacecraft missions that land on solid planetary objects is instrumentation for mineralogical analyses. For purposes of providing diagnostic information about naturally-occurring materials, the element iron is particularly important because it is abundant and multivalent. Knowledge of the oxidation state of iron and its distribution among iron-bearing mineralogies tightly constrains the types of materials present and provides information about formation and modification (weathering) processes. Because Moessbauer spectroscopy is sensitive to both the valence of iron and its local chemical environment, the technique is unique in providing information about both the relative abundance of iron-bearing phases and oxidation state of the iron. The Moessbauer mineralogy of lunar regolith samples (primarily soils from the Apollo 16 and 17 missions to the Moon) were measured in the laboratory to demonstrate the strength of the technique for in situ mineralogical exploration of the Moon. The regolith samples were modeled as mixtures of five iron-bearing phases: olivine, pyroxene, glass, ilmenite, and metal. Based on differences in relative proportions of iron associated with these phases, volcanic ash regolith can be distinguished from impact-derived regolith, impact-derived soils of different geologic affinity (e.g., highlands, maria) can be distinguished on the basis of their constituent minerals, and soil maturity can be estimated. The total resonant absorption area of the Moessbauer spectrum can be used to estimate total FeO concentrations.

Morris, Richard V.↗

57 Fe nuclear resonance vibrational spectroscopic studies of tetranuclear iron clusters bearing terminal iron( III )–oxido/hydroxido moieties

57 Fe nuclear resonance vibrational spectroscopy (NRVS) has been applied to study a series of tetranuclear iron ([Fe 4 ]) clusters based on a multidentate ligand platform (L 3− ) anchored by a 1,3,5-triarylbenzene linker and pyrazolate or (tertbutylamino)pyrazolate ligand (PzNH t Bu − ). These clusters bear a terminal Fe(III)–O/OH moiety at the apical position and three additional iron centers forming the basal positions. The three basal irons are connected with the apical iron center via a μ 4 -oxido ligand. Detailed vibrational analysis via density functional theory calculations revealed that strong NRVS spectral features below 400 cm −1 can be used as an oxidation state marker for the overall [Fe 4 ] cluster core. The terminal Fe(III)–O/OH stretching frequencies, which were observed in the range of 500–700 cm −1 , can be strongly modulated (energy shifts of 20–40 cm −1 were observed) upon redox events at the three remote basal iron centers of the [Fe 4 ] cluster without the change of the terminal Fe(III) oxidation state and its coordination environment. Therefore, the current study provides a quantitative vibrational analysis of how the remote iron centers within the same iron cluster exert exquisite control of the chemical reactivities and thermodynamic properties of the specific iron site that is responsible for small molecule activation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Non-Equilibrium Actinide Radiation Chemistry and the Nuclear Fuel Cycle

Actinides are inherently unstable elements that frequently coexist with other radioisotopes, generating intense ionizing radiation fields that drive the formation of non equilibrium oxidation states. These transient species exert a profound mechanistic influence on the radiation response of actinide containing systems due to their unique redox chemistry. Despite their importance, they remain poorly understood, yet such insight is essential for advancing actinide science and accurately predicting radiation driven behavior. Actinide separations—critical for nuclear energy technologies, strategic deterrence, space exploration, and nuclear medicine—depend on precise control of actinide oxidation states to recover targeted elements from complex matrices such as used nuclear fuel. However, during these processes, actinides, their coordination complexes, and the separation media are all exposed to intense, multicomponent (alpha, beta, gamma, etc.) radiation fields that can alter process efficiency, selectivity, and chemical stability. Understanding, controlling, and mitigating radiation induced reactions is therefore key to innovating and optimizing next generation separation technologies. This seminar will provide an overview of the nuclear fuel cycle and non equilibrium actinide radiation chemistry in the context of recovering actinides from used nuclear fuel, with a particular emphasis on direct dissolution–based reprocessing strategies. We will explore time resolved electron pulse radiolysis and alpha and gamma dose accumulation studies, integrated with multiscale computational modeling, to elucidate the molecular level roles of radiation driven, non equilibrium actinide species in process performance and in the radiolytic stability of organic ligands used for actinide recovery. These insights offer new pathways for designing advanced separation methods and next generation solvent systems, with broad implications for the future of the nuclear fuel cycle.

37 - INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL C↗

Decoupling of particles and dissolved iron downstream of Greenlandic glacier outflows

Glaciers can be a significant and locally dominant source of iron (Fe), a biologically essential micronutrient, in high latitude coastal seas. The vast majority of this glacial Fe delivery is associated with particles, yet the speciation of the solid-phase Fe and specifically the relationships that govern exchange between particulate and dissolved Fe phases in these environments are poorly described. Here, in this work, we performed measurements of in situ dissolved Fe (dFe) along meltwater and particle plumes in three transects around Disko Bay and Ameralik Fjord (West Greenland). Measurements of dFe were combined with Fe K-edge X-ray absorption spectroscopy analysis of ~40 suspended sediment samples obtained from the same transects and from select depth profiles down to 300 m. We observed relatively constant dFe levels (4 to 10 nM for nearly all dFe measurements) across fjords with widely varying particulate Fe(II) contents (from 20 to 90% Fe(II)), indicating that dFe concentrations had little dependence on the oxidation state of Fe in the suspended sediment. Particulate Fe data were grouped by underlying bedrock geology, with suspended sediment consisting of 80-90% biotite-like Fe(II) in fjords with Precambrian shield geology and poorly-ordered Fe(III) particles (<20-30% Fe(II)) in one fjord with suspended sediments derived from tertiary basalts. Our characterization data indicated no significant change in the average Fe oxidation state and bonding environment of particles along the fjord transects, implying that Fe(II) in biotite-like coordination is not a readily labile Fe form on this spatial scale. Finally, our results suggest that dFe in these glacially-modified coastal waters is buffered at a relatively constant low nM concentration due to factors other than particle Fe mineralogy and that glacier-derived Fe phases are relatively inert on this spatial scale.

54 ENVIRONMENTAL SCIENCES↗

The chemical and physical properties of tetravalent lanthanides: Pr, Nd, Tb, and Dy

The fundamental redox chemistry and valence electronic structure of the lanthanides in molecular complexes and extended solids continues to be a fertile area of research. The contemporary understanding of the accessible oxidation states of the lanthanide elements and the variability in their electronic structure is the result of several paradigm shifts. While the lanthanide elements have already found widespread use in technical and consumer applications, the continued reevaluation of basic redox properties is a central chemical concern to establish a more complete description of periodic properties. This fundamental understanding of valence electronic structure as it is derived from oxidation state and coordination environment is essential for the continued development of lanthanides in quantum information science and quantum materials research. This review presents the chemical and physical properties of tetravalent lanthanide ions in extended solids and molecules with a focus on the elements apart from cerium: praseodymium, neodymium, terbium, and dysprosium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Non-Equilibrium Actinide Radiation Chemistry and the Nuclear Fuel Cycle

Invited John and Naomi Fackler Lectureship in Chemistry and English seminar at Valparaiso University, IN, USA. Actinides are inherently unstable elements that frequently coexist with other radioisotopes, generating intense ionizing radiation fields that drive the formation of non-equilibrium oxidation states. These transient species exert a profound mechanistic influence on the radiation response of actinide-containing systems due to their unique redox chemistry. Despite their importance, they remain poorly understood, yet such insight is essential for advancing actinide science and accurately predicting radiation-driven behavior. Actinide separations—critical for nuclear energy technologies, strategic deterrence, space exploration, and nuclear medicine—depend on precise control of actinide oxidation states to recover targeted elements from complex matrices such as used nuclear fuel. However, during these processes, actinides, their coordination complexes, and the separation media are all exposed to intense, multicomponent (alpha, beta, gamma, etc.) radiation fields that can alter process efficiency, selectivity, and chemical stability. Understanding, controlling, and mitigating radiation-induced reactions is therefore key to innovating and optimizing next-generation separation technologies. This seminar will provide an overview of the nuclear fuel cycle and non-equilibrium actinide radiation chemistry in the context of recovering actinides from used nuclear fuel, with a particular emphasis on direct-dissolution–based reprocessing strategies. We will explore time-resolved electron pulse radiolysis and gamma dose accumulation studies to elucidate the molecular-level roles of radiation-driven, non-equilibrium actinide species in process performance and in the radiolytic stability of organic ligands used for actinide recovery. These insights offer new pathways for designing advanced separation methods and next-generation solvent systems, with broad implications for the future of the nuclear fuel cycle.

37 - INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL C↗

Small-angle neutron scattering solution structures of NADPH-dependent sulfite reductase

Sulfite reductase (SiR), a dodecameric complex of flavoprotein reductase subunits (SiRFP) and hemoprotein oxidase subunits (SiRHP), reduces sulfur for biomass incorporation. Electron transfer within SiR requires intra- and inter-subunit interactions that are mediated by the relative position of each protein, governed by flexible domain movements. Using small-angle neutron scattering, we report the first solution structures of SiR heterodimers containing a single copy of each subunit. These structures show how the subunits bind and how both subunit binding and oxidation state impact SiRFP’s conformation. Neutron contrast matching experiments on selectively deuterated heterodimers allow us to define the contribution of each subunit to the solution scattering. SiRHP binding induces a change in the position of SiRFP’s flavodoxin-like domain relative to its ferredoxin-NADP + reductase domain while compacting SiRHP’s N-terminus. Reduction of SiRFP leads to a more open structure relative to its oxidized state, re-positioning SiRFP’s N-terminal flavodoxin-like domain towards the SiRHP binding position. These structures show, for the first time, how both SiRHP binding to, and reduction of, SiRFP positions SiRFP for electron transfer between the subunits.

59 BASIC BIOLOGICAL SCIENCES↗

Ligand effects on electronic structure and bonding in U(iii) coordination complexes: a combined MCD, EPR and computational study

The trivalent oxidation state of uranium has been shown to undergo unique reactivity, from its ability to activate a variety of small molecules to its role in the catalytic reduction of ethene to ethane amongst others. Central to this unique reactivity and ability to rationally design ligands for isotope separation is the underlying uranium electronic structure. While electronic structure studies of U(IV), U(V), and U(VI) have been extensive, by comparison, analogous studies of more reduced oxidation states such as U(III) remains underdeveloped. Herein we report a combined MCD and EPR spectroscopic approach along with density functional theory and multireference wavefunction calculations to elucidate the effects of ligand perturbation in three uranium(III) Tp* complexes. Overall, the experimental and computational insight suggests that the change in ligand environment across this series of U(III) complexes resulted in only minor perturbations in the uranium electronic structure. This combined approach was also used to redefine the electronic ground state of a U(III) complex with a redox non-innocent Bipy - ligand. Overall, these studies demonstrate the efficacy of the combined experimental and theoretical approach towards evaluating electronic structure and bonding in U(III) complexes and provide important insight into the challenges in altering ligand environments to modify bonding and reactivity in uranium coordination chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electronic Structure of Ru 2 6+ Complexes with Electron-Rich Anilinopyridinate Ligands

Diruthenium paddlewheel complexes supported by electron-rich anilinopyridinate (Xap) ligands were synthesized in the course of the first in-depth structural and spectroscopic interrogation of monocationic [Ru 2 (Xap) 4 Cl] + species in the Ru 2 6+ oxidation state. Despite paramagnetism of the compounds, 1 H NMR spectroscopy proved highly informative for determining the isomerism of the Ru 2 5+ and Ru 2 6+ compounds. While most compounds are found to have the polar (4,0) geometry, with all four Xap ligands in the same orientation, some synthetic procedures resulted in a mixture of (4,0) and (3,1) isomers, most notably in the case of the parent compound Ru 2 (ap) 4 Cl. The isomerism of this compound has been overlooked in previous reports. Electrochemical studies demonstrate that oxidation potentials can be tuned by the installation of electron donating groups to the ligands, increasing accessibility of the Ru 2 6+ oxidation state. The resulting Ru 2 6+ monocations were found to have the expected (π*) 2 ground state, and an in-depth study of the electronic transitions by Vis/NIR absorption and MCD spectroscopies with the aid of TD-DFT allowed for the assignment of the electronic spectra. Here, the empty δ* orbital is the major acceptor orbital for the most prominent electronic transitions. Both Ru 2 5+ and Ru 2 6+ compounds were studied by Ru K-edge X-ray absorption spectroscopy; however, the rising edge energy is insensitive to redox changes in the compounds due to the broad line shape observed for 4d transition metal K-edges. DFT calculations indicate the presence of ligand orbitals at the frontier level, suggesting that further oxidation beyond Ru 2 6+ will be ligand-centered rather than metal-centered.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modification of LiMn 2 O 4 surfaces by controlling the Acid–Base surface chemistry of atomic layer deposition

In this combined theoretical and experimental study, we report the effects of Al precursor selection on the growth chemistry, interfacial structure, and electrochemistry of Al 2 O 3 coatings on spinel LiMn 2 O 4 (LMO) surfaces by atomic layer deposition (ALD). Five Al precursors, exhibiting a range of Lewis acid-base properties, were used to establish trends in the ALD Al 2 O 3 growth chemistry on LMO powders in comparison to redox-inactive planar silicon substrates. We show that the Lewis acid-base properties of the Al precursor ligands can be used to tune both the Mn oxidation states and the Al 2 O 3 coverage on the LMO surface. Density functional theory calculations are used to examine the reaction mechanism of each precursor on LMO surfaces, elucidating a correlation between the Lewis acidity of the ligands and the decomposition thermochemistry. In-depth X-ray photoelectron spectroscopy and in situ Fourier transform infrared spectroscopy measurements support these theoretical predictions and further reveal how different Al precursors modify the atomic and electronic structure near the LMO surface during ALD. While the Mn oxidation state is strongly influenced by the Lewis acidity of the precursor ligand, the surface coverage and thickness of the Al 2 O 3 coating are a more representative descriptor of the electrochemical performance measured in coin cell experiments. Finally, we show how the ligand acid-base properties of ALD precursors can be used to rationally tailor atomic layer growth mechanisms, which may enable atomic level control over the structure of functionalized interfaces for various applications related to catalysis, semiconductors, and energy storage.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Revisiting Selenium Interactions with Pyrite: From Adsorption to Coprecipitation

Interactions of selenium (Se), a trace element bio-essential at low concentrations but highly toxic at high concentrations, with the most abundant sulfide mineral in the Earth's crust, namely pyrite, was investigated over a wide range of time scales. At the nanosecond scale, selenate Se(VI)O 4 2– adsorption onto the net pyrite surface is shown by ab-initio computations to proceed via the formation of a chemical bond between an oxyanion oxygen atom and a surface Fe atom, weakening the other Se-O bonds and reducing Se atom oxidation state. At the hour-to-day scale, adsorption and coprecipitation of selenate Se(VI)O 4 2– and selenite, Se(IV)O 3 2– , were investigated through wet chemical batch experiments at various pH values at different sulfide concentrations. Selenium removal from solution is slower and weaker for selenate than for selenite. After 24h, only 10% of selenate, against 60% of selenite (up to 100% in the presence of sulfide), is removed by the pyrite surface. Independently of its original oxidation state, adsorbed Se is completely reduced to elemental trigonal selenium via adsorption, precipitation or coprecipitation, as shown by XANES spectroscopy. Here, our EXAFS results, compared to published data on Se-rich pyrite, show a Se to S substitution within the pyrite structure. The reductive coprecipitation mechanism of selenium with pyrite represents valuable new insights for improving our understanding of modern and ancient biogeochemical cycles involving Se. In addition, several industries can benefit from direct applications of our findings, such as water treatment, green technologies and sustainable mining.

Adsorption↗

Unraveling the relationship between physicochemical properties of NiFeReOx catalysts and the correlated performance toward electrochemical oxygen evolution reaction

NiFeO x catalysts with single site Re dopants exhibit much higher active and stability toward electrochemical oxygen evolution reaction (OER) compared to traditional NiFeO x catalysts. Nevertheless, the relationship between physicochemical properties of NiFeReO x catalysts and the correlated performance toward OER is unclear, which hampers to enhance the OER performance further. Herein, we prepared a series of NiFeReO x catalysts with different physicochemical properties by treating them at different temperatures (up to 350 °C) and then evaluated their performance toward OER. Here, the results show that heat treatment can convert all metal oxidation states to higher values as well as specific surface areas, which are believed to favor real active site generation and OER activity enhancement. A decrease in activity is observed with the temperature increase at the low current range, and the smallest overpotential of 248 mV at 10 mA cm −2 is achieved with the pristine NiFeReO x catalyst. In contrast, the heat-treated samples possess smaller Tafel slopes and lower charge transfer resistance likely due to enhanced intrinsic activity (from higher oxidation states) and conductivity, which facilitate the reaction kinetics and surpass the pristine sample at a large current density. Additionally, the sample treated at 350 °C exhibits a higher activity at 1000 mA cm −2 (1.68 V vs. RHE compared to pristine sample of 1.92 V vs. RHE); however, it manifests a poorer stability compared to the pristine one due to the imbalance of reconstruction/transformations that occurred on the catalyst surface during OER operation. Our work unravels the relationship between physicochemical properties of NiFeReO x catalysts and the correlated OER performance and provides valuable insights for designing NiFeReO x catalysts with high activity and durability.

Catalyst reconstruction↗

Divergent Stabilities of Tetravalent Cerium, Uranium, and Neptunium Imidophosphorane Complexes**

Abstract The study of the redox chemistry of mid‐actinides (U−Pu) has historically relied on cerium as a model, due to the accessibility of trivalent and tetravalent oxidation states for these ions. Recently, dramatic shifts of lanthanide 4+/3+ non‐aqueous redox couples have been established within a homoleptic imidophosphorane ligand framework. Herein we extend the chemistry of the imidophosphorane ligand (NPC=[N=P t Bu(pyrr) 2 ] − ; pyrr=pyrrolidinyl) to tetrahomoleptic NPC complexes of neptunium and cerium ( 1‐M , 2‐M , M=Np, Ce) and present comparative structural, electrochemical, and theoretical studies of these complexes. Large cathodic shifts in the M 4+/3+ (M=Ce, U, Np) couples underpin the stabilization of higher metal oxidation states owing to the strongly donating nature of the NPC ligands, providing access to the U 5+/4+ , U 6+/5+ , and to an unprecedented, well‐behaved Np 5+/4+ redox couple. The differences in the chemical redox properties of the U vs . Ce and Np complexes are rationalized based on their redox potentials, degree of structural rearrangement upon reduction/oxidation, relative molecular orbital energies, and orbital composition analyses employing density functional theory.

Otte, Kaitlyn S.↗

Divergent Stabilities of Tetravalent Cerium, Uranium, and Neptunium Imidophosphorane Complexes

The study of the redox chemistry of mid-actinides (U–Pu) has historically relied on cerium as a model, due to the accessibility of trivalent and tetravalent oxidation states for these ions. Recently, dramatic shifts of lanthanide 4+/3+ non-aqueous redox couples have been established within a homoleptic imidophosphorane ligand framework. Herein we extend the chemistry of the imidophosphorane ligand (NPC=[N=P t Bu(pyrr) 2 ] – ; pyrr=pyrrolidinyl) to tetrahomoleptic NPC complexes of neptunium and cerium (1-M, 2-M, M=Np, Ce) and present comparative structural, electrochemical, and theoretical studies of these complexes. Large cathodic shifts in the M 4+/3+ (M=Ce, U, Np) couples underpin the stabilization of higher metal oxidation states owing to the strongly donating nature of the NPC ligands, providing access to the U 5+/4+ , U 6+/5+ , and to an unprecedented, well-behaved Np 5+/4+ redox couple. Furthermore, the differences in the chemical redox properties of the U vs. Ce and Np complexes are rationalized based on their redox potentials, degree of structural rearrangement upon reduction/oxidation, relative molecular orbital energies, and orbital composition analyses employing density functional theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗