Search NASA⌕ Search

Engineering topics

Sacci, Robert L.

Publications and source records attributed to Sacci, Robert L..

18 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Direct Prelithiation of Silicon-Based Composite Electrodes via Island-like Thermal Evaporation

Irreversible losses of Li during solid electrolyte interface (SEI) conditioning is a key contributor to the lower specific capacities observed in silicon-containing Li-ion batteries. Herein, thermal evaporation of between 1 and 20 µm of Li onto Si-based composite anodes has been investigated as a prelithiation method to account for such losses. To account for mechanical strain caused by Li-Si alloying during the deposition, a stainless-steel mesh is applied to the electrodes before prelithiation to form “island-like” deposition on the electrode surface. The open circuit potential was also found to decrease as a function of increased Li evaporation, consistent with the potentials of electrochemically prepared LixSi alloys. Prelithiating to account for irreversible Li losses to SEI formation resulted in full cells with a 15.8% increase in initial coulombic efficiency and a 47.8% reduction in irreversible capacity loss after SEI formation cycling. Subsequent C/3 cycling showed up to a 62.9% increase in specific capacity in prelithiated cells. X-ray photoelectron spectroscopy (XPS) revealed differences in the SEI composition that was formed by electrochemical cycling and reactively formed in prelithiated cells upon exposure to Gen2 + 3% FEC electrolyte. The reactively formed SEI from the spontaneous reaction with lithiated silicon was carbonate-rich while the electrochemical SEI formation showed significantly more LiPFx species, which could play a role in overall cycling performance.

Musgrove, Amanda↗
DOE OSTI2024

Molecular structures of residual solvent in polyacrylonitrile based electrolytes: Implications for conductivity and stability

Lithium-ion batteries increasingly play significant roles in modern technologies; however, increased energy density also raises concerns about electrolyte safety. Traditional electrolytes that use volatile organic solvents face risks of thermal runaways and fires from electrode shorting. In response, polymer-based solid electrolytes have been developed for replacement. Polyacrylonitrile (PAN) is a promising fire-resistant component for electrolyte fabrication, but its limited solubility necessitates using low-volatility solvents, which are notoriously difficult to remove in subsequent drying processes. Here, we use femtosecond two-dimensional infrared spectroscopy to provide an in-depth understanding of how residual solvent from processing affects the molecular structures and dynamics within a polymer electrolyte. To this end, linear and nonlinear infrared spectroscopies are employed to interrogate the molecular interactions in PAN-based electrolytes containing various contents of N,N-dimethylformamide (DMF). We show that the amount of DMF within the PAN electrolyte affects the Li+ structure. Further, the coordination can proceed through the carbonyl group and/or the amide nitrogen to form antiparallel structures with the nitrile groups of PAN through dipole–dipole interactions. The free motion of DMF is drastically inhibited upon interaction with Li+ and PAN, which decreases the ionic conductivity and potentially affects the stability (resistance toward removal and chemical decomposition). These findings have implications for the design and processing of solid polymer electrolytes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Mechanisms of proton transport in aqueous acid solutions

The fundamental understanding of proton transport, specifically the Grotthuss-like mechanism, is critical for many technological applications. The present study presents a comprehensive analysis of proton transport in aqueous solutions of sulfuric and phosphoric acids using quasielastic neutron and light scattering, broadband dielectric spectroscopy, rheology, pulsed-field gradient-NMR measurements, and ab initio molecular dynamic simulations. Results show that in all systems, proton transport occurs through short “jumps” of ~0.5 Å that are faster than structural relaxation. However, proton hopping appears to be coupled to structural relaxation in aqueous solutions of sulfuric acid, while these processes are decoupled in phosphoric acid. Neutron scattering indicates that all protons have the same fast mobility in phosphoric acid systems, while at least one proton per sulfuric molecule remains slower than other protons. Analysis reveals correlated proton jumps, but these correlations suppress conductivity, suggesting that expected Grotthuss-like enhancement of conductivity is unlikely in bulk liquids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Effects of catholyte aging on high-nickel NMC cathodes in sulfide all-solid-state batteries

Sulfide solid-state electrolytes (SSEs) in all-solid-state batteries (SSBs) are recognized for their high ionic conductivity and inherent safety. The LiNi 0.8 Mn 0.1 Co 0.1 O 2 (NMC811) cathode offers a high thermodynamic potential of approximately 3.8 V vs. Li/Li + and a theoretical specific capacity of 200 mA h g −1 . However, the practical utilization of NMC811 in sulfide SSBs faces significant interfacial challenges. The oxidation instability of sulfide solid electrolytes against NMC811 and the formation of the cathode electrolyte interphase (CEI) during cycling lead to degradation and reduced cell performance. Volumetric changes in NMC during lithiation and de-lithiation can also cause detachment from sulfide electrolytes or internal particle cracking. Despite extensive galvanostatic cycling studies to address the issues, the calendar life of sulfide SSBs remains poorly understood. Here, we systematically studied the effects of four different catholytes on the calendar aging of LiNbO 3 (LNO)-coated NMC811, including Li 6 PS 5 Cl (LPSCl), Li 3 InCl 6 –Li 6 PS 5 Cl (LIC–LPSCl), Li 3 YCl 6 –Li 6 PS 5 Cl (LYC–LPSCl), and Li 10 GeP 2 S 12 (LGPS). Our results indicate that LPSCl provides optimal capacity retention when stored at high state-of-charge (SOC) at room temperature, but the LIC–LPSCl cathode shows significant capacity degradation and chemical incompatibility. We also established an effective electrochemical calendar aging testing protocol to simulate daily usage, enabling quick inference of the calendar life of SSBs. In conclusion, this new testing approach accelerates materials selection strategies for high-nickel NMC composite cathodes in sulfide SSBs.

25 ENERGY STORAGE↗
DOE OSTI2024

Elucidating the local structure of Li 1+ x Al x Ti 2– x (PO 4 ) 3 and Li 3 Al x Ti 2– x (PO 4 ) 3 ( x = 0, 0.3) via total scattering

Li 1+x Al x Ti 2–x (PO 4 ) 3 (LATP) and Li 3 Al x Ti 2–x (PO 4 ) 3 (x = 0, 0.3) are promising candidates in all-solid-state batteries due to their high room temperature conductivity of 10 –3 S cm –1 and air- and moisture-stability. They also exhibit unusual thermal expansion properties, with Li 1+x Al x Ti 2–x (PO 4 ) 3 showing near-zero thermal expansion along the a axis while Li 3 Al x Ti 2–x (PO 4 ) 3 exhibits polynomial positive thermal expansion along the a axis and polynomial negative thermal expansion along the c axis. A crucial component to understanding these properties is understanding the local structure. Total scattering is a powerful analytical technique as it provides information on the long-range, average structure as well as the local structure. Here, we report the first X-ray and neutron total scattering experiments performed on Li 1+x Al x Ti 2–x (PO 4 ) 3 and Li 3 Al x Ti 2–x (PO 4 ) 3 (x = 0, 0.3). We show that the PO 4 and TiO 6 polyhedra experience very little expansion of the P/Ti–O bonds up to 800 °C, nor is there much expansion when the Li content increases significantly. The minor thermal expansion of the nearest-neighbor bonds of the polyhedra is revealed to be the reason behind the unusual thermal expansion properties, causing the near-zero thermal expansion along a in Li 1+x Al x Ti 2–x (PO 4 ) 3 and moving as whole units in Li 3 Al x Ti 2–x (PO 4 ) 3 . The structural robustness of the framework is also the reason for the increased conductivity as Li content increases, as the framework remains undistorted as Li content increases, permitting Li-ion mobility as the number of charge carriers increases. Finally, this suggests that phosphate-based framework materials beyond LATP would also be a good material space to explore for new Li-ion (and other ion-) conducting materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Corrosion and Enhanced Hydrogen Evolution in Electrochemical Reduction of Ammonium Carbamate on Transition Metal Surfaces

Experiments and theory are combined to search for catalyst activity and stability descriptors for the direct reactive capture and conversion (RCC) of CO 2 in ammonia capture solutions using Cu, Ag, Au, Sn, and Ti electrodes. Two major phenomena emerge in RCC that are not predominant in the electrochemical CO 2 reduction (CO 2 R) reaction, namely, the rapid corrosion and restructuring of the catalyst in the presence of the CO 2 -ammonia adducts and the promotion of the competing hydrogen evolution reaction (HER). The prevalence of HER in RCC is correlated to the electrostatic attraction of the protonated amine to the electrode and the repulsion of the captured CO 2 , using the potential of zero charge (PZC). The stability of catalysts under RCC conditions is a function of the applied potential and cannot be readily predicted using binding energy descriptors commonly used in the prediction of CO 2 R activity. Finally, a direct correlation between calculated binding energies of CO 2 R intermediates, atomic oxygen, hydrogen, and ammonia and the activity and stability of transition metals for RCC cannot be found, highlighting the need for descriptors beyond those known for CO 2 R.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Reactive capture and electrochemical conversion of CO 2 with ionic liquids and deep eutectic solvents

Ionic liquids (ILs) and deep eutectic solvents (DESs) have tremendous potential for reactive capture and conversion (RCC) of CO 2 due to their wide electrochemical stability window, low volatility, and high CO 2 solubility. There is environmental and economic interest in the direct utilization of the captured CO 2 using electrified and modular processes that forgo the thermal- or pressure-swing regeneration steps to concentrate CO 2 , eliminating the need to compress, transport, or store the gas. The conventional electrochemical conversion of CO 2 with aqueous electrolytes presents limited CO 2 solubility and high energy requirement to achieve industrially relevant products. Additionally, aqueous systems have competitive hydrogen evolution. In the past decade, there has been significant progress toward the design of ILs and DESs, and their composites to separate CO 2 from dilute streams. In parallel, but not necessarily in synergy, there have been studies focused on a few select ILs and DESs for electrochemical reduction of CO 2 , often diluting them with aqueous or non-aqueous solvents. The resulting electrode–electrolyte interfaces present a complex speciation for RCC. In this review, we describe how the ILs and DESs are tuned for RCC and specifically address the CO 2 chemisorption and electroreduction mechanisms. Critical bulk and interfacial properties of ILs and DESs are discussed in the context of RCC, and the potential of these electrolytes are presented through a techno-economic evaluation.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Physicochemical control of solvation and molecular assembly of charged amphiphilic oligomers at air-aqueous interfaces

Hypothesis : Understanding the rules that control the assembly of nanostructured soft materials at interfaces is central to many applications. We hypothesize that electrolytes can be used to alter the hydration shell of amphiphilic oligomers at the air-aqueous interface of Langmuir films, thereby providing a means to control the formation of emergent nanostructures. Experiments : Three representative salts – (NaF, NaCl, NaSCN) were studied for mediating the self-assembly of oligodimethylsiloxane methylimidazolium (ODMS-MIM + ) amphiphiles in Langmuir films. The effects of the different salts on the nanostructure assembly of these films were probed using vibrational sum frequency generation (SFG) spectroscopy and Langmuir trough techniques. Experimental data were supported by atomistic molecular dynamic simulations. Findings : Langmuir trough surface pressure – area isotherms suggested a surprising effect on oligomer assembly, whereby the presence of anions affects the stability of the interfacial layer irrespective of their surface propensities. In contrast, SFG results implied a strong anion effect that parallels the surface activity of anions. These seemingly contradictory trends are explained by anion driven tail dehydration resulting in increasingly heterogeneous systems with entangled ODMS tails and appreciable anion penetration into the complex interfacial layer comprised of headgroups, tails, and interfacial water molecules. These findings provide physical and chemical insight for tuning a wide range of interfacial assemblies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Memory Effect on the Synthesis of Perovskite-Type Li-Ion Conductor Li x La 2/3– x /3 TiO 3 (LLTO)

The structural chemistry of the solid ion-conducting Li x La 2/3–x/3 TiO 3 (LLTO) is rich with various polymorphs related to atomic segregation. Here, we explored the LLTO reaction pathway from various structurally related precursors (La 2 LiO 3 H, Li 2 TiO 3 , and Li 4 Ti 5 O 12 ), focusing on the effects of LLTO-like structural motifs in precursors using a combination of experimental and computational techniques. Density functional theory (DFT) calculations revealed that the failure of syntheses to produce LLTO below 1300 °C is due to the presence of multiple competing low-energy phases that result in competitive byproduct formation. In all syntheses where T = 1300 °C, LLTO was the sole product; however, varying phase fractions of I4/mcm and P4/nbm polymorphs and double-perovskite P4/mmm can be obtained depending on the synthesis route. This is an unusual result as at 1300 °C, LLTO should only be the ideal cubic Pm-3m perovskite structure, yet there appears to be a memory effect from the different precursors resulting in the unique phase selectivity and stabilization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Cations Control Lipid Bilayer Memcapacitance Associated with Long-Term Potentiation

Phospholipid bilayers can be described as capacitors whose capacitance per unit area (specific capacitance, C m ) is determined by their thickness and dielectric constant–independent of applied voltage. It is also widely assumed that the C m of membranes can be treated as a “biological constant”. Recently, using droplet interface bilayers (DIBs), it was shown that zwitterionic phosphatidylcholine (PC) lipid bilayers can act as voltage-dependent, nonlinear memory capacitors, or memcapacitors. When exposed to an electrical “training” stimulation protocol, capacitive energy storage in lipid membranes was enhanced in the form of long-term potentiation (LTP), which enables biological learning and long-term memory. LTP was the result of membrane restructuring and the progressive asymmetric distribution of ions across the lipid bilayer during training, which is analogous, for example, to exponential capacitive energy harvesting from self-powered nanogenerators. Here, we describe how LTP could be produced from a membrane that is continuously pumped into a nonequilibrium steady state, altering its dielectric properties. During this time, the membrane undergoes static and dynamic changes that are fed back to the system’s potential energy, ultimately resulting in a membrane whose modified molecular structure supports long-term memory storage and LTP. Here, we also show that LTP is very sensitive to different salts (KCl, NaCl, LiCl, and TmCl 3 ), with LiCl and TmCl 3 having the most profound effect in depressing LTP, relative to KCl. This effect is related to how the different cations interact with the bilayer zwitterionic PC lipid headgroups primarily through electric-field-induced changes to the statistically averaged orientations of water dipoles at the bilayer headgroup interface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Single Ion Conducting Hairy Nanoparticle Additive to Improve Cycling Stability of Solid Polymer Electrolytes

The development of a solid electrolyte that can impede dendrite growth while still maintaining an appropriate level of conductivity is essential for improving performance of solid-state Li-ion battery. In this paper, we report the synthesis of single Li-ion conducting hairy nanoparticle (NP) materials that improved the cycling stability of lithium bis(trifluoromethanesulfonyl)imide (LiTFSI)-doped poly(ethylene oxide) (PEO) solid electrolyte without significant reduction in conductivity. To unveil mechanisms leading to improved cycling stability, several characterization techniques including broadband dielectric spectroscopy, differential scanning calorimetry, small angle X-ray scattering, transmission electron microscopy, and shear rheology were used to study properties of polymer composites (PC) with added hairy NPs. It was found that hairy NPs influenced the Li/electrolyte interface and improved mechanical properties of bulk composites, all of which contributed to homogenous Li plating and stripping. The improved performance has been found in composites with concentrations of 4.8 and 9.1 weight % of added hairy NPs, which enabled Li cycling stability at 0.2 mA cm–2 critical current density (>300 h) that was otherwise not possible in either PEO-LiTFSI alone or PEO-LiTFSI composites containing a polymer identical to that attached to hairy NPs. Based on the discovered ability of hairy NP to influence bulk and interfacial properties of solid electrolyte, their use as additives is expected to be equally effective in reducing dendrite formation in other electrolytes relevant for the design of solid-state battery.

25 ENERGY STORAGE↗
DOE OSTI2023

Tracking Molecular Transport Across Oil/Aqueous Interfaces: Insight into “Antagonistic” Binding in Solvent Extraction

Liquid/liquid (L/L) interfaces play a key, yet poorly understood, role in a range of complex chemical phenomena where time-evolving interfacial structures and transient supramolecular assemblies act as gatekeepers to function. Here, for this study, we employ surface-specific vibrational sum frequency generation combined with neutron and X-ray scattering methods to track the transport of dioctyl phosphoric acid (DOP) and di-(2-ethylhexyl) phosphoric acid (DEHPA) ligands used in solvent extraction at buried oil/aqueous interfaces away from equilibrium. Our results show evidence for a dynamic interfacial restructuring at low ligand concentrations in contrast to expectation. These time-varying interfaces arise from the transport of sparingly soluble interfacial ligands into the neighboring aqueous phase. These results support a proposed “antagonistic” role of ligand complexation in the aqueous phase that could serve as a holdback mechanism in kinetic liquid extractions. These findings provide new insights into interfacially controlled chemical transport at L/L interfaces and how these interfaces vary chemically, structurally, and temporally in a concentration-dependent manner and present potential avenues to design selective kinetic separations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Search for a Grotthuss mechanism through the observation of proton transfer

The transport of protons is critical in a variety of bio- and electro-chemical processes and technologies. The Grotthuss mechanism is considered to be the most efficient proton transport mechanism, generally implying a transfer of protons between ‘chains’ of host molecules via elementary reactions within the hydrogen bonds. Although Grotthuss proposed this concept more than 200 years ago, only indirect experimental evidence of the mechanism has been observed. Here we report the first experimental observation of proton transfer between the molecules in pure and 85% aqueous phosphoric acid. Employing dielectric spectroscopy, quasielastic neutron, and light scattering, and ab initio molecular dynamic simulations we determined that protons move by surprisingly short jumps of only ~0.5–0.7 Å, much smaller than the typical ion jump length in ionic liquids. Our analysis confirms the existence of correlations in these proton jumps. However, these correlations actually reduce the conductivity, in contrast to a desirable enhancement, as is usually assumed by a Grotthuss mechanism. Furthermore, our analysis suggests that the expected Grotthuss-like enhancement of conductivity cannot be realized in bulk liquids where ionic correlations always decrease conductivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

In Situ Measurement of Buried Electrolyte–Electrode Interfaces for Solid State Batteries with Nanometer Level Precision

Many technologies including high-energy solid-state batteries rely on high quality solid–solid interfaces. Solid–solid interfaces are particularly difficult to study as their nature requires the interface to be buried. Here, in this work, we demonstrate the use of a combination of neutron reflectometry and in situ electrochemistry to measure the interface between Li metal and the solid electrolyte LiPON across an 8 cm 2 area. Neutron reflectometry measurements confirm the interphase to be less than 7 nm thick. The neutron reflectometry data further emphasize that the interphase that forms is a chemical gradient consisting of a Li-rich layer that gradually decreases in Li content until it blends into pure LiPON. Experimental confirmation that we can make ideal solid–solid interphases less than 10 nm thick will help facilitate the adoption of high efficiency next generation solid state batteries. Further this combination of complementary techniques provides a more general methodology for studying buried solid–solid interfaces across applications.

25 ENERGY STORAGE↗
DOE OSTI2023

Halide Substitution Effects on Lithium-Ion Diffusion in Protonated Antiperovskites

Solid-state electrolytes (SSEs) for all-solid-state lithium-ion batteries are generating intense interest because these batteries can improve the safety and performance compared with devices fabricated with conventional, flammable liquid electrolytes. In these SSEs, it has been suggested that Li + ion diffusion in the grain boundaries is hindered and is a critical determinant of the overall ionic conductivity (σ). However, Li + ion diffusivities in the grain (D G ) and the grain boundary (D GB ) are difficult to determine experimentally, with few techniques capable of distinguishing the individual contributions. Here, we distinguished the D G and D GB for the protonated lithium antiperovskites (pLiAPs) SSEs: Li 2 OHCl, Li 2 OHBr, Li 2 OHF 0.1 Cl 0.9 , Li 2 OHF 0.1 Br 0.9 , and Li 2 OHCl 0.3 7Br 0.63 . The measurements were obtained directly from 7 Li pulsed-field gradient nuclear magnetic resonance (PFG-NMR) at 353 K. The 7 Li PFG-NMR echo profiles were composed of two primary components with additional secondary oscillatory components – the so-called NMR diffraction phenomenon. The length scale separating the two main components corresponds to a diffusion length of ~1.7 µm, which is thought to be the average grain size (by diameter). The short-range (≤ 1.7 µm) diffusion component associated with D G (≈10 -11 m 2 /s) varied minimally with halide substitution, while the long-range (≥ 1.7 µm) component D GB (≈10 -12 to 10 -15 m 2 /s) was highly sensitive to the substitution of halides and closely correlated with s. In addition, from the comparison of the ratio D GB /D G to D t (the Li + ion diffusion coefficient estimated from the rotational correlation time, t c ), it was determined that the contribution of D G to σ is negligible; 0.01 ~ 0.04 in the pLiAPs studied here. Finally, these insights provide fundamental understanding of the halide substitution effects on Li + ion grain versus grain boundary diffusion, and suggest that careful engineering of the grain boundaries at the microscopic level is necessary to achieve high-performance pLiAP SSEs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

A Membrane Contactor Enabling Energy-Efficient CO 2 Capture from Point Sources with Deep Eutectic Solvents

We demonstrate a scalable and energy-efficient hollow fiber membrane contactor (HFMC)-based process using a green solvent for CO 2 capture. This process uses a deep eutectic solvent (DES) in an HFMC to provide close interfacial interactions and contact between the DES and CO 2 . This approach overcomes disadvantages associated with direct absorption in DES and could potentially be applied to a variety of solvent-based CO 2 capture methods. Commercial low-cost polymer hollow fiber membranes (e.g., microporous polypropylene) were evaluated for CO 2 capture with reline, a prototypical DES. Single-gas measurements showed that the DES-based polypropylene HFMC can capture and separate CO 2 while rejecting N2. From a mixed gas containing 50 mol % N 2 and 50 mol % CO ν , the DES-based HFMC separated CO 2 with a purity of 96.9 mol %. The effect of several process parameters including solvent flow rate, pressure, and temperature on the CO 2 separation performance was studied. The flux of the recovered CO 2 was 67.43 mmole/m 2 /h at a feed pressure of 4 bar. In situ Fourier transform infrared (FTIR) measurements combined with density functional theory (DFT)-based molecular dynamics simulations revealed that reline absorbs CO 2 by physical absorption without forming a new chemical compound, and CO 2 separation by reline occurs via the pressure swing mechanism. This research provides fundamental insights about physical solvent-based separation processes and a pathway toward practical deployment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Direct Mechanochemical Synthesis, Phase Stability, and Electrochemical Performance of α-NaFeO 2

To better understand polymorph control in transition metal oxides, the mechanochemical synthesis of NaFeO 2 was explored. In this paper, we report the direct synthesis of α-NaFeO 2 through a mechanochemical process. By milling Na 2 O 2 and γ-Fe 2 O 3 for 5 h, α-NaFeO 2 was prepared without high-temperature annealing needed in other synthesis methods. While investigating the mechanochemical synthesis, it was observed that changing the starting precursors and mass of precursors affects the resulting NaFeO 2 structure. Density functional theory calculations on the phase stability of NaFeO 2 phases show that the α phase is stabilized over the β phase in oxidizing environments, which is provided by the oxygen-rich reaction between Na 2 O 2 and Fe 2 O 3 . This provides a possible route to understanding polymorph control in NaFeO 2 . Annealing the as-milled α-NaFeO 2 at 700 °C has resulted in increased crystallinity and structural changes that improved electrochemical performance in terms of capacity over the as-milled sample.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗