Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “catalyst design”

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

Heterogeneous hydroformylation of alkenes by Rh-based catalysts

Heterogeneously catalyzed hydroformylation reactions avert the problems of separation in homogeneous reactions, reduce the discharge of phosphorus-containing wastes, and prevent the loss of precious metals. This review summarizes the developments of catalysts for heterogeneous hydroformylation in the last decade and proposes potential modification methods for future improvements. The hydroformylation properties of different reactants are compared in order to emphasize the fact that various olefins face unique challenges. The hydroformylation of ethylene requires the enhancement of catalytic activity and chemoselectivity, whereas that of propylene needs improvements in both chemoselectivity and regioselectivity. The hydroformylation of longer-chain olefins and styrene seeks further improvement in regioselectivity. The catalytic properties of activity, selectivity, and stability can be tuned through electronic effects (bimetallic effects, phosphine ligands, and single-atom catalysts), steric hindrance (encapsulation structures, diphosphine ligands, and local functional groups), and reaction condition optimization (temperature, pressure, and solvents). Furthermore, the understanding of these effects is critical in future catalyst design for heterogeneous hydroformylation reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Solvent absorption rate of perfluorosulphonic acid membranes towards understanding direct coating processes

Here we present a method for measurement of the rate of solvent absorption by perfluorosulfonic acid (PFSA) membranes using a force tensiometer. The method presented here can be used as a tool to understand solvent absorption and should provide a rationale for designing catalyst inks for direct coating processes since it is necessary to understand how the absorption rate – on a time scale of seconds to minutes – compares to the time scales of the coating process in order to minimize membrane swelling. This method allows for rapid screening of the absorption and swelling behavior of different solvents and mixtures. Using this method, the absorption of water/1-propanol mixtures were measured for three thicknesses of Nafion PFSA membrane – Nafion 1135, Nafion 115, and Nafion 117. We find that the absorption rate is dependent on the ratio of the solvents as well as the thickness of the membrane. The analysis indicates that the highest absorption rate occurs when the mass percentage of 1-propanol in the mixture is 50%, whereas the lowest rates are for pure water and 1-propanol. In addition, membrane distortion also occurs most quickly for the 50% 1-propanol mixture. Our results suggest that catalyst inks that are highly rich (=90%) in water or 1-propanol are likely best for direct coating as such formulations will minimize absorption and swelling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structure sensitivity of ammonia electro-oxidation on transition metal surfaces: A first-principles study

Ammonia electro-oxidation is a promising catalytic reaction for application in alkaline fuel cells. In this paper we study the trends in this reaction on the (1 0 0) facet of eight fcc transition metals: Au, Ag, Cu, Pt, Pd, Ni, Ir, and Rh. We calculate from first-principles (DFT-GGA-PW91) the energetics for two mechanisms: (i) the N + N mechanism and (ii) the Gerischer-Mauerer mechanism. The onset potentials for both mechanisms are provided for both (1 0 0) and (1 1 1) facets. We also calculate the activation energies for the N-N bond-making non-Faradaic events on Cu, Pt, Pd, Ni, Ir, and Rh. We discover that N* – which is considered a poison for Pt(1 1 1) – is a reactive intermediate on Pt(1 0 0), allowing for a facile dimerization to N2 on Pt(1 0 0) at high potentials. We draw similar analyses for the structure sensitivity on the other metals, and we conclude with some general principles to guide catalyst design for this reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An economic analysis of the role of materials, system engineering, and performance in electrochemical carbon dioxide conversion to formate

The development of technologies that utilize carbon dioxide is important to mitigating climate change. The electrochemical reduction of carbon dioxide is one technology that can utilize greenhouse gasses that would be otherwise be emitted to the atmosphere by producing chemicals and fuels from carbon dioxide and electricity. Significant progress has been made in the experimental performance of carbon dioxide reduction systems with novel catalyst designs, new materials, and systems engineering; however, no work has linked such changes in stack design and materials to capital costs for the stack itself. In this study, we present an analysis that accounts for and analyzes the impacts of alternative materials and system architectures on manufactured costs of carbon dioxide reduction stacks, thus providing a framework to understand exactly how these advances impact the at-scale capital costs of these systems. Specifically, we consider the impact that the addition of a catholyte buffer layer has on an electrolyzer reducing carbon dioxide to formate, finding that the cost of manufacturing this part only increases stack costs by about $30/m 2 at high manufacturing rates, while previous work finds that this part improves system performance. This work shows that the links between system performance, materials, and costs are nonlinear, and that achieving low-cost scalability requires optimization of not just performance parameters but also the use of low-cost and highly scalable materials. These results bridge experimental and techno-economic analysis of processes for carbon dioxide reduction, informing researchers by providing a quantifiable estimate of the impact of advances in electrochemical carbon dioxide reduction technology on manufactured stack capital costs.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Bimetallic NiCo boride nanoparticles confined in a MXene network enable efficient ambient ammonia electrosynthesis

Ambient electrocatalytic nitrogen fixation is an emerging technology for green ammonia synthesis, but the absence of optimized, stable and performant catalysts can render its practical application challenging. Herein, bimetallic NiCo boride nanoparticles confined in MXene are shown to accomplish high-performance nitrogen reduction electrolysis. Taking advantage of the synergistic effect in specific compositions with unique electronic d and p orbits and typical architecture of rich nanosized particles embedded in the interconnected conductive network, the synthesized MXene@NiCoB composite demonstrates extensive improvements in nitrogen molecule chemisorption, active area exposure and charge transport. As a result, optimal NH 3 yield rate of 38.7 μg h -1 mgcat. -1 and Faradaic efficiency of 6.92% are acquired in 0.1 M Na 2 SO 4 electrolyte. Moreover, the great catalytic performance can be almost entirely maintained in the cases of repeatedly-cycled and long-term electrolysis. Theoretical investigations reveal that the nitrogen reduction reaction on MXene@NiCoB catalyst proceeds according to the distal pathway, with a distinctly-reduced energy barrier relative to the Co 2 B counterpart. In conclusion, this work may inspire a new route towards the rational catalyst design for the nitrogen reduction reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electronic structure and oxophilicity optimization of mono-layer Pt for efficient electrocatalysis

The slow kinetics of the anodic hydrogen oxidation reaction (HOR) in alkaline medium is one of the limitations for anion exchange membrane fuel cells (AEMFCs). Hence, accurately regulate and understand catalytic interface structure are essential to solve this bottleneck and reveal the structure-activity relationship. In this work, a novel trimetal core-shell model with mono-layer Pt-shell is employed for hydrogen electrooxidation to avoid thermodynamic driven bulk/surface composition deviation. On account of the atomic radius discrepancies of 3d-transition metals M (M = Fe, Co and Cu), the electronic structure of mono-layer Pt is regulated by the strain-engineered Pd-M core and the electrocatalytic activity for HOR is tuned accordingly. Nevertheless, step-by-step electrochemical monitoring and surface-treatment experiments indicate that the oxophilicity optimization by low-valence M(OH) x species, rather than the hydrogen binding energy (HBE) optimization caused by strain engineering, influence the activity obviously. It is mainly derived from the enhanced adsorption of OH ad and accelerated desorption of the H ad . The trimetal core-shell model breathes new life into the low-Pt catalyst design for hydrogen electrooxidation reaction.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Electrocatalytic CO 2 Reduction to Fuels: Progress and Opportunities

The electrochemical reduction of CO 2 continues to be an appealing option for storing renewable energy in a chemical form. In this review, we assess progress in designing catalysts that convert CO 2 to high energy density products. We explain how reaction data can be reported to reflect the intrinsic properties of the catalyst. This analysis shows that limited advances have been made in improving the performance of Cu. We suggest that opportunities remain using bimetallic catalysts that are resistant to dealloying. While aqueous systems are instrumental to developing our understanding of this chemistry, gas-fed systems that operate at high current densities must be developed. Although obstacles remain for practical application of CO 2 reduction, advances in fundamental understanding made over the years give reason for optimism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Perovskite oxynitrides as tunable materials for electrocatalytic nitrogen reduction to ammonia

The electrocatalytic nitrogen reduction reaction (ENRR) to ammonia is a potentially sustainable alternative to the Haber-Bosch (HB) process, but low Faradaic efficiencies and rates hinder its implementation. Perovskite oxynitrides are a tunable class of materials with unique chemistry for ENRR. As a result, elucidating structure–property–mechanism relations for perovskite oxynitrides will aid ENRR catalyst design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Engineering bimetallic interfaces and revealing the mechanism for carbon dioxide electroreduction to C 3+ liquid chemicals

Reduction reaction of CO 2 (CO 2 RR) to liquid C 3+ chemicals is a net-zero-carbon process and can increase local resiliency to power outages and fuel consumption. The mechanism and the catalyst design rules of CO 2 RR-to-C 3+ are unknown. Engineering bimetallic interface (e.g., Pd/Au) to tune the intermediate adsorption is promising for promoting C 3+ formation. Our density functional theory (DFT) calculations find that *CH 2 could be the key intermediate and C 1 -CH 2 coupling could be the rate-limiting step to generate C 3+ . High CO surface coverages can promote the bimetallic interfacial sites, lower the energetics of the C 1 -CH 2 coupling step, and enhance the C 3+ formation. We further construct a volcano plot of C 1 -CH 2 kinetics as a function of the binding strength of key intermediate *CH 2 via engineering the d-band center of the interfacial site. Our findings could guide the rational design of bimetallic interfaces and their near-surface microenvironment for enhancing CO 2 RR-to-C 3+ .

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Synthetic and Mechanistic Implications of Chlorine Photoelimination in Nickel/Photoredox C(sp 3 )–H Cross-Coupling

In recent years, the development of light-driven reactions has contributed numerous advances in synthetic organic chemistry. A particularly active research area combines photoredox catalysis with nickel catalysis to accomplish otherwise inaccessible cross-coupling reactions. In these reactions, the photoredox catalyst absorbs light to generate an electronically excited charge-transfer state that can engage in electron or energy transfer with a substrate and the nickel catalyst. Our group questioned whether photoinduced activation of the nickel catalyst itself could also contribute new approaches to cross-coupling. Over the past 5 years, we have sought to advance this hypothesis for the development of a suite of mild and site-selective C(sp 3 )–H cross-coupling reactions with chloride-containing coupling partners via photoelimination of a Ni–Cl bond. On the basis of a report from the Nocera laboratory, we reasoned that photolysis of a Ni(III) aryl chloride species, generated by single-electron oxidation of a typical Ni(II) intermediate in cross-coupling, might allow for the catalytic generation of chlorine atoms. Combining this with the ability of Ni(II) to accept alkyl radicals, we hypothesized that photocatalytically generated chlorine atoms could mediate hydrogen atom transfer (HAT) with C(sp 3 )–H bonds to generate a substrate-derived alkyl radical that is captured by the Ni center in cross-coupling. A photoredox catalyst was envisioned to promote the necessary single-electron oxidation and reduction of the Ni catalyst to facilitate an overall redox-neutral process. Overall, this strategy would offer a visible-light-driven mechanism for chlorine radical formation enabled by the sequential capture of two photons. As an initial demonstration, we developed a Ni/photoredox-catalyzed α-oxy C(sp 3 )–H arylation of cyclic and acyclic ethers. This method was extended to a mild formylation of abundant and complex aryl chlorides through selective 2-functionalization of 1,3-dioxolane. Seeking to develop a suite of reactions that introduce carbon at all different oxidation states, we explored C(sp 3 )–H cross-coupling with trimethyl orthoformate, a common laboratory solvent. We found that trimethyl orthoformate serves as a source of methyl radical for a methylation reaction via β-scission from a tertiary radical generated upon chlorine-mediated HAT. Since chlorine radical is capable of abstracting unactivated C(sp 3 )–H bonds, our efforts have also been directed at cross-coupling with a range of feedstock chemicals, such as alkanes and toluenes, along with late-stage intermediates, using chloroformates as coupling partners. Overall, this platform enables access to valuable synthetic transformations with (hetero)aryl chlorides, which despite being the most ubiquitous and inexpensive aryl halide coupling partners, are rarely reactive in Ni/photoredox catalysis. Little is known about the photophysics and photochemistry of organometallic Ni complexes relevant to cross-coupling. We have conducted mechanistic investigations, including computational, spectroscopic, emission quenching, and stoichiometric oxidation studies, of Ni(II) aryl halide complexes common to Ni/photoredox reactions. These studies indicate that chlorine radical generation from excited Ni(III) is operative in the described C(sp 3 )–H functionalization methods. More generally, the studies illustrate that the photochemistry of cross-coupling catalysts cannot be ignored in metallaphotoredox reactions. We anticipate that further mechanistic understanding should facilitate catalyst design and lead to the development of new synthetic methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Engineering of a Coupled Nanocomposite as a High-Performance Protonic Ceramic Fuel Cell Cathode

The lack of high-performance cathode catalysts is a salient issue that bedeviled the commercialization of protonic ceramic fuel cells (PCFCs). Here, in this work, we report a remarkable electrocatalytic activity and stability enhancement of cathode electrodes by engineering a coupled nanocomposite. The as-prepared Pr 0.3 (Ba 0.5 Sr 0.5 ) 0.7 Co 0.8 Fe 0.2 O 3−δ nanocomposite possesses a bulk cubic phase on which homogeneous and intimate orthorhombic PrCo 0.5 Fe 0.5 O 3−δ nanoparticles are uniformly decorated. X-ray diffraction and Raman spectroscopy reveal the excellent thermal stability of the nanocomposite. It achieves a high peak power density of 1.02 W cm –2 based on protonic electrolytes at 600 °C. No noticeable structural degradation is observed over ∼210 h at 550 °C according to scanning electron microscopy analysis. This work demonstrates an effective strategy to boost the performance of perovskite oxides for PCFCs via nanocomposite engineering. It may apply to other catalyst designs and discoveries, such as for batteries, electrolyzers, and membrane reactors.

08 - HYDROGEN↗

Emerging Atomistic Modeling Methods for Heterogeneous Electrocatalysis

Heterogeneous electrocatalysis lies at the center of various technologies that could help enable a sustainable future. However, its complexity makes it challenging to accurately and efficiently model at an atomic level. Herein, we review emerging atomistic methods to simulate the electrocatalytic interface with special attention devoted to the components/effects that have been challenging to model, such as solvation, electrolyte ions, electrode potential, reaction kinetics, and pH. Additionally, we review relevant computational spectroscopy methods. Then, we showcase several examples of applying these methods to understand and design catalysts relevant to green hydrogen. We also offer experimental views on how to bridge the gap between theory and experiments. Finally, we provide some perspectives on opportunities to advance the field.

36 MATERIALS SCIENCE↗

Catalytic Upcycling of Polyolefins

The large production volumes of commodity polyolefins (specifically, polyethylene, polypropylene, polystyrene, and poly(vinyl chloride)), in conjunction with their low unit values and multitude of short-term uses, have resulted in a significant and pressing waste management challenge. Only a small fraction of these polyolefins is currently mechanically recycled, with the rest being incinerated, accumulating in landfills, or leaking into the natural environment. Since polyolefins are energy-rich materials, there is considerable interest in recouping some of their chemical value while simultaneously motivating more responsible end-of-life management. An emerging strategy is catalytic depolymerization, in which a portion of the C–C bonds in the polyolefin backbone is broken with the assistance of a catalyst and, in some cases, additional small molecule reagents. When the products are small molecules or materials with higher value in their own right, or as chemical feedstocks, the process is called upcycling. This review summarizes recent progress for four major catalytic upcycling strategies: hydrogenolysis, (hydro)cracking, tandem processes involving metathesis, and selective oxidation. Key considerations include macromolecular reaction mechanisms relative to small molecule mechanisms, catalyst design for macromolecular transformations, and the effect of process conditions on product selectivity. Metrics for describing polyolefin upcycling are critically evaluated, and an outlook for future advances is described.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Deciphering Distinct Overpotential-Dependent Pathways for Electrochemical CO 2 Reduction Catalyzed by an Iron–Terpyridine Complex

[Fe(tpyPY2Me)] 2+ ([Fe] 2+ ) is a homogeneous electrocatalyst for converting CO 2 into CO featuring low overpotentials of <100 mV, near-unity selectivity, and high activity with turnover frequencies faster than 100 000 s -1 . To identify the origins of its exceptional performance and inform future catalyst design, we report a combined computational and experimental study that establishes two distinct mechanistic pathways for electrochemical CO 2 reduction catalyzed by [Fe] 2+ as a function of applied overpotential. Electrochemical data shows the formation of two catalytic regimes at low (η TOF/2 of 160 mV) and high (η TOF/2 of 590 mV) overpotential plateaus. We propose that at low overpotentials [Fe] 2+ undergoes a two-electron reduction, two-proton-transfer mechanism (electrochemical-electrochemical-chemical-chemical, EECC), where turnover occurs through the dicationic iron complex, [Fe] 2+ . Computational analysis supports the importance of the singlet ground-state electronic structure for CO 2 binding and that the rate-limiting step is the second protonation in this low-overpotential regime. When more negative potentials are applied, an additional electron-transfer event occurs through either a stepwise or proton-coupled electron-transfer (PCET) pathway, enabling catalytic turnover from the monocationic iron complex ([Fe] + ) via an electrochemical-chemical-electrochemical-chemical (ECEC) mechanism. Comparison of experimental kinetic data obtained from variable controlled potential electrolysis (CPE) experiments with direct product detection with calculated rates obtained from the energetic span model supports the PCET pathway as the most likely mechanism. Moreover, we build upon this mechanistic understanding to propose the design of an improved ligand framework that is predicted to stabilize the key transition states identified in our study and explore their electronic structures using an energy decomposition analysis. Finally, taken together, this work highlights the value of synergistic computational/experimental approaches to decipher mechanisms of new electrocatalysts and direct the rational design of improved platforms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Predicting Bond Dissociation Energies and Bond Lengths of Coordinatively Unsaturated Vanadium–Ligand Bonds

Understanding the electronic structure of coordinatively unsaturated transition-metal compounds and predicting their physical properties are of great importance for catalyst design. Bond dissociation energy D e and bond length r e are two of the fundamental quantities for which good predictions are important for a successful design strategy. In the present work, recent experimentally measured bond energies and bond lengths of VX diatomic molecules (X = C, N, S) are used as a gauge to consider the utility of a number of electronic structure methods. Single-reference methods are one focus because of their efficiency and utility in practical calculations, and multireference configuration interaction (MRCISD) methods and a composite coupled cluster (CCC) method are a second focus because of their potential high accuracy. The comparison is especially challenging because of the large multireference M diagnostics of these molecules, in the range 0.15–0.19. For the single-reference methods, Kohn–Sham density functional theory (KS-DFT) has been tested with a variety of approximate exchange-correlation functionals. Of these, MOHLYP provides the bond dissociation energies in best agreement with experiments, and BLYP provides the bond lengths that are in best agreement with experiments; but by requiring good performance for both the D e and r e of the vanadium compounds, MOHLYP, MN12-L, MGGA_MS1, MGGA_MS0, O3LYP, and M06-L are the most highly recommended functionals. The CCC calculations include up to connected pentuple excitations for the valence electrons and up to connected quadruple excitations for the core–valence terms; this results in highly accurate dissociation energies and good bond lengths. In conclusion, averaged over the three molecules, the mean unsigned deviation of CCC bond energies from experimental ones is only 0.4 kcal/mol, demonstrating excellent convergence of theory and experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Altering Linear Scaling Relationships on Metal Catalysts via Ligand–Adsorbate Hydrogen Bonding

Linear scaling relationships for adsorption energies of related molecules provide a simple tool for the prediction of catalytic properties and also reveal inherent constraints in heterogeneous catalyst design. In an effort to predict materials that preferentially stabilize intermediates capable of forming hydrogen bonds (H-bonds) and thus reduce these constraints, scaling relations for thiolate-coated fcc (111) surfaces were developed. Here, we demonstrate how ligand–adsorbate H-bonds lead to the stabilization of certain adsorbates and how this affects the linear scaling of adsorption energies for similarly bound intermediates. For H-bonds that occur remote from the surface, ligand–adsorbate H-bond strength is independent of metal composition and instead depends only on the acidities of the H-bond-forming functional groups. As the distance of H-bond-accepting groups from the surface decreases and interactions with the metal strengthen, the effect of surface composition on H-bond strength increases while additional factors, such as conformational changes and steric hinderance, can offset the stabilizing effect of the ligands. In this work, these competing factors may influence both the slope and y-intercept of adsorption strength scaling. These findings aid the rational design of enhanced catalytic materials by enabling the screening of ligand- or spectator-modified materials that do not conform to the linear scaling relations of bare metal surfaces.

36 MATERIALS SCIENCE↗

Structure Sensitive Reaction Kinetics of Chiral Molecules on Intrinsically Chiral Surfaces

Enantiospecific heterogeneous catalysis utilizes chiral surfaces to resolve enantiomers via structure sensitive surface chemistry. The catalyst design challenge is the identification of chiral surface structures that maximize enantiospecificity. Herein, we develop data driven models for the enantiospecificity of tartaric acid reactions on chiral Cu(hkl) R&S surfaces. Measurements of enantiospecific rate constants were obtained by using curved Cu(hkl) R&S surfaces that enable kinetic measurements on hundreds of chiral surface orientations. One model uses feature vectors derived from generalized coordination numbers to capture the local structure around Cu atoms exposed by the Cu(hkl) R&S surfaces. The second model introduces the use of chiral cubic harmonic functions to capture the symmetry constraints of the face-centered cubic Cu structure. The model using 58 generalized coordination numbers has a fitting error similar to that of the model using only 5 cubic harmonic functions. The two models predict maxima in the enantiospecificity on surfaces with very similar surface orientations. The models developed in this work are applicable for any enantiospecific reaction happening on any chiral material with a cubic lattice structure, opening the way to understanding the surface structure sensitivity of the enantiospecific reaction kinetics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of Solvent on the Local Structure, Dynamics, and Vibrational Density of States in Sn-BEA Zeolite

Lewis acid zeolites are attractive catalysts for epoxidation and biomass valorization, as they are highly active and selective in the liquid phase and can operate at or near ambient conditions. While a rich experimental literature exists on liquid-phase Lewis acid zeolite catalysis, our understanding of the molecular organization and solvent dynamics in the vicinity of Lewis acid sites with differing metal site speciation remains limited. In this work, we investigate the molecular coordination and diffusion of two common solvents (methanol and water) around the closed and open Sn-BEA zeolite active sites using molecular dynamics simulations with a machine-learned interatomic potential trained on ab initio molecular dynamics trajectories. Molecular dynamics simulations reveal that introducing active sites significantly enhances local order in the first and second solvation shells compared to the pure silica case. For methanol, both closed and open active sites are singly coordinated, while more than two water molecules coordinate the open site. In contrast to methanol, we observed that water molecules dissociate, leading to the formation of additional Sn-OH and silanol groups away from the active site. The diffusion coefficients of water and methanol are functions of the solvent population in the pore. Here, our work provides insights into how active site speciation in Lewis acid zeolites affects solvent coordination, diffusion, and vibrational signature. This information is foundational for catalyst design and optimization of liquid-phase catalytic processes in zeolites. It also demonstrates the suitability of machine-learned interatomic potentials for modeling reactive systems, enabling sufficiently long trajectories for appropriate statistical averaging.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗