Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “monotonicity”

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 451 records · Page 25

Non-Isochronal Behavior of Charge Transport at Liquid–Liquid and Liquid–Glass Transition in Aprotic Ionic Liquids

A reversible, first-order transition separating two liquid phases of a single-component material is a fascinating yet poorly understood phenomenon. Here, we investigate the liquid–liquid transition (LLT) ability of two tetraalkylphosphonium ionic liquids (ILs), [P 666,14 ]Cl and [P 666,14 ][1,2,4-triazolide], using differential scanning calorimetry and dielectric spectroscopy. The latter technique also allowed us to study the LLT at elevated pressure. We found that cooling below 205 K transforms [P 666,14 ]Cl and [P 666,14 ][Trz] from one liquid state (liquid 1) to another (the self-assembled liquid 2), while the latter facilitates the charge transport decoupled from structural dynamics. In contrast to temperature, pressure was found to play an essential role in the self-organization of a liquid 2 phase, resulting in different time scales of charge transport for rapidly and slowly compressed samples. Furthermore, τ σ (P LL ) was found to be much shorter than τ σ (T LL , P=atm), which constitutes the first example of non-isochronal behavior of charge transport at LLT. In turn, dielectric studies through the liquid–glass transition revealed the non-monotonic behavior of τ σ at elevated pressure for [P 666,14 ]Cl, while for [P 666,14 ][Trz] τ σ (P g ) was almost constant. These results highlight the diversity of liquid–liquid transition features within the class of phosphonium ionic liquids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Interfacial Ice Density Fluctuations Inform Surface Ice-Philicity

The propensity of a surface to nucleate ice or bind to ice is governed by its ice-philicity─its relative preference for ice over liquid water. However, the relationship between the features of a surface and its ice-philicity is not well understood, and for surfaces with chemical or topographical heterogeneity, such as proteins, their ice-philicity is not even well-defined. In the analogous problem of surface hydrophobicity, it has been shown that hydrophobic surfaces display enhanced low water-density (vapor-like) fluctuations in their vicinity. To interrogate whether enhanced ice-like fluctuations are similarly observed near ice-philic surfaces, here we use molecular simulations and enhanced sampling techniques. Using a family of model surfaces for which the wetting coefficient, k , has previously been characterized, we show that the free energy of observing rare interfacial ice-density fluctuations decreases monotonically with increasing k . By utilizing this connection, we investigate a set of fcc systems and find that the (110) surface is more ice-philic than the (111) or (100) surfaces. By additionally analyzing the structure of interfacial ice, we find that all surfaces prefer to bind to the basal plane of ice, and the topographical complementarity of the (110) surface to the basal plane explains its higher ice-philicity. Using enhanced interfacial ice-like fluctuations as a measure of surface ice-philicity, we then characterize the ice-philicity of chemically heterogeneous and topologically complex systems. In particular, we study the spruce budworm antifreeze protein (sbwAFP), which binds to ice using a known ice-binding site (IBS) and resists engulfment using nonbinding sites of the protein (NBSs). We find that the IBS displays enhanced interfacial ice-density fluctuations and is therefore more ice-philic than the two NBSs studied. We also find the two NBSs are similarly ice-phobic. By establishing a connection between interfacial ice-like fluctuations and surface ice-philicity, our findings thus provide a way to characterize the ice-philicity of heterogeneous surfaces.

crystals↗

Insights into Rotational and Translational Dynamics in Mixtures of Ethylene Glycol and Choline Chloride Using Nuclear Magnetic Resonance Techniques

This work examines molecular dynamics and interactions in ethylene glycol–choline chloride (EG–ChCl) mixtures across 0–33 mol % ChCl, spanning the true eutectic region near 17–20 mol % and the commonly used 1:2 formulation. We combine pulsed-field-gradient (PFG) diffusion, fast-field-cycling (FFC) relaxometry, temperature-dependent 13 C T 1 , and nuclear Overhauser effect spectroscopy (NOESY) to disentangle local from macroscopic dynamics. PFG and FFC show that both translational and average rotational motions largely track the strong increase in viscosity with ChCl content, with ethylene glycol consistently diffusing faster than the choline cation and no global dynamical anomaly at the eutectic composition. More subtle, site-specific composition effects nevertheless emerge. The ratio of the diffusion coefficient of the hydroxyl group of choline to the diffusion coefficient of the methyl group of choline displays a shallow minimum in the 17–25 mol % region, indicating a modest change in how the hydroxyl-bearing end of choline samples the underlying translational motion relative to the methyl groups. 13 C T 1 analysis shows that rotational correlation times at 25 °C generally increase with ChCl, reflecting viscosity-coupled slowing, while the CH 2 –N α site exhibits a small but reproducible deviation from this monotonic trend near the eutectic. NOESY spectra at similar compositions reveal enhanced cross-relaxation between EG and choline protons, consistent with increased headgroup–solvent contact density rather than a wholesale structural rearrangement. Overall, our multitechnique study demonstrates that EG–ChCl dynamics are predominantly viscosity-dominated, with the eutectic region acting as a subtle dynamical crossover where specific choline segments become maximally coupled to the hydrogen-bond network. These insights refine the structure–dynamics picture of choline-chloride DESs and provide practical guidance for tuning composition in electrochemical, separation, and catalytic applications.

diffusion↗

Inverse Design of a Graphene-Based Quantum Transducer via Neuroevolution

Here we introduce an inverse design framework based on artificial neural networks, genetic algorithms, and tight-binding calculations, capable to optimize the very large configuration space of nanoelectronic devices. Our non-linear optimization procedure operates on trial Hamiltonians through superoperators controlling growth policies of regions of distinct doping. We demonstrate that our algorithm optimizes the doping of graphene-based three-terminal devices for valleytronics applications, monotonously converging to synthesizable devices with high merit functions in a few thousand evaluations (out of similar or equal to ≃ 2 3800 possible configurations). The best-performing device allowed for a terminal-specific separation of valley currents with similar or equal to ≃ 96% (≃ 94%) K(K') valley purity. Importantly, the devices found through our non-linear optimization procedure have both a higher merit function and higher robustness to defects than the ones obtained through geometry optimization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantifying Temperature Dependence of Electronic Band Gaps and Optical Properties in SnO 2 and SnO via First-Principles Simulations

Tin metal oxides SnO x ( x = 1, 2) have gained interest as gas-sensing materials. For their applications as high-temperature sensors, however, a better understanding of their temperature dependence sensing responses is needed. Here, we comparatively quantify the temperature-dependent electronic band gaps and optical properties of SnO 2 and SnO using first-principles calculations. Without considering the temperature effect, SnO 2 and SnO are predicted to have direct and indirect band gaps of 2.18 and 1.66 eV, respectively, at the PBE + U -GGA level that we employed. The temperature effect on the electronic and optical properties is captured by taking account of the electron–phonon interaction. Band gap renormalization with temperature is calculated via the Allen–Heine–Cardona theory. For both oxides, we find a monotonic decrease in the electronic band gap such that renormalization at zero point (0 K) is ~–0.17 and ~–0.52 eV at 1000 K. These results are also analyzed by employing an analytical equation that helps characterize the band gap shift with temperature. In addition, the optical properties at finite temperatures are simulated using the frozen-phonon method that combines electron–phonon coupling with the momentum matrix. As temperature increases, the optical property spectra are smoothed because of the smearing effect, which diminishes optical constants at shorter wavelengths. Our results are of interest for high-temperature functional materials in applications of optical detection.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Oxygen and Proton Transport in Flooded Graphene Pores with N-Dopants and Defects

Reactant transport is an important consideration in the design of ideal electrode structures. For the oxygen reduction reaction catalyzed by Pt/C in proton exchange membrane fuel cell cathodes, O 2 and H + delivery to Pt surfaces and H 2 O transport away are required. Some Pt nanoparticles may only be accessible via micropores that are too small for ionomer molecules to enter, possibly requiring flooding for H + transport. Here, to test if these “buried” Pt particles can play a role in activity through this proposed transport mechanism, we have performed atomic-scale simulations based on reactive force field molecular dynamics with an emphasis on confinement below 20 Å. Diffusion coefficients as a function of the molar concentration and local environment have been evaluated in water domains confined in two-dimensional graphene nanochannels of various channel heights representing a morphological model for micropores in proton exchange fuel cell cathodes. Our study shows that local atomic-scale structures can strongly modify H + , O 2 , and H 2 O transport rates in flooded micropores less than 20 Å in size. We find that there is a critical crossover in diffusion behavior around the 20 Å spacing with larger pores having bulk-like diffusion properties and confinement below 20 Å monotonically decreases diffusion rates. As pore size decreases, we observe locally dispersed water regions that ultimately strand reactants from long-distance transport. These findings suggest that flooded micropores may in fact be viable transport pathways for relevant reactants and products if the pore walls on opposite sides remain separated by ≥10 Å separation. Furthermore, the confinement effect is so strong that N-doping and C-vacancy defects in the C pore wall have only a minimal impact on diffusion rates and their effects are counterintuitively more apparent at larger spacings. These findings provide valuable insight regarding cathode performance and the role “stranded” catalyst particles may play in fuel cell cathodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Elucidating the Influence of Metal Surface Composition on Organic Adsorbate Binding Using Active Particle Dynamics

The adsorption strengths of organic compounds on metal surfaces are sensitive to the metal composition, and they play a central role in many catalytic reactions, helping to control the coverage of the reactant and altering the overall reaction rate. While adsorption energies are straightforward to measure and calculate in vacuum and gas-phase environments, adsorption energetics can be dramatically altered by the presence of solvent in liquid-phase reactions. However, the effects of metal composition on binding strengths in a liquid environment are less well understood, primarily due to the difficulty of accurate in situ measurements of organic binding on metal surfaces in the liquid phase. Here, we utilize the motion of active particles in water to probe the adsorption energies of an organic adsorbate (furfural) on a range of metal surfaces (pure Pd, pure Pt, and four PdAu alloy compositions) to elucidate the effect of metal composition. Janus particles with catalytic caps of particular metal compositions all exhibited active motion resulting from consumption of H 2 O 2 ; adsorbate binding was inferred through the decrease in the velocity of active motion and was modeled by a Langmuir adsorption isotherm. The measured adsorption affinities were used to extract the adsorption enthalpy of furfural on the different metals. The Pd surface was found to bind furfural more strongly than the Pt surface by some 10 kJ/mol. Furthermore, the adsorption of furfural on the alloys was found to increase monotonically in magnitude with Pd content. As a result, the data reported herein aid the development of accurate understanding of organic adsorption in the presence of solvent and the role of the metal surface in tuning adsorption strengths to optimize catalytic processes in the liquid phase.

36 MATERIALS SCIENCE↗

Temperature-Dependent Optical and Structural Properties of Chiral Two-Dimensional Hybrid Lead-Iodide Perovskites

Layered hybrid halide perovskites gain chirality via the incorporation of chiral organic cations in the spacer layer. These so-called chiral two-dimensional (2D) halide perovskites have attracted considerable interest recently for chiral optoelectronic, spintronic, and ferroelectric applications. However, the effect of temperature on these materials, especially how the structure changes with temperature and its impact on the chiral optoelectronic properties, remains an open question. Here, we study the effect of temperature change on chiral optoelectronic and structural properties through temperature-dependent circularly polarized photoluminescence (CPPL) microscopy and synchrotron powder X-ray diffraction as well as pair distribution function analysis to elucidate the intrinsic chiral optoelectronic and structural variations for R-, S-, and racemic-methylbenzylamine lead iodide. Here our results show that the temperature-induced band gap changes indicate a strong electron–phonon coupling compared to the thermal-induced lattice expansion in chiral 2D perovskites. From powder diffraction measurements, a monotonic lattice expansion is observed on heating with no structural phase transitions over 90–360 K detected for the three samples studied herein. Locally, a strongly anisotropic and even negative expansion in some components of the instantaneous Pb–I pair-distance distribution is suggestive of coupling between dynamical intralayer distortions and lattice expansion. This work provides insights into the fundamental understanding of the temperature effect on chiral optoelectronic and structural properties of chiral 2D perovskites, which can lead to new chiral materials design strategies for future chiral optoelectronic applications.

36 MATERIALS SCIENCE↗

Simultaneous Absorption and Desorption Isotherms of Various Hydrogen and Deuterium Mixtures between 20 and 120 °C Are Used to Determine the Activity Coefficients for Palladium-Hydride Solutions

A test bed was constructed to measure the absorption and desorption isotherms for palladium hydride using H 2 , D 2 , and various H 2 /D 2 mixtures for temperatures in the range 20 °C ≤ T ≤ 120 °C. The pressure–composition–temperature isotherms were measured. The pressures obtained with mixtures between each pure isotope were monotonic, yet nonlinear. This nonlinear dependence of total pressure with feed gas protium concentration reveals the mixed isotope hydride system behaves nonideally. A thermodynamic model was adapted from the literature, which accounts for the nonideal nature of the mixed-isotope system. The measured data were used as constraints in this model in order to calculate the protium mole fractions in the hydride phase and the protium activity coefficients for palladium hydride at various temperatures and protium concentrations in the system. Knowing the protium mole fraction and activity coefficients allows for a priori calculation of the isotopologue distribution in the gas phase and the isotope distribution in the hydride phase, given a palladium temperature and equilibrium pressure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Surface Transfer Doping in MoO 3– x /Hydrogenated Diamond Heterostructure

Surface transfer doping is proposed to be a potential solution for doping diamond, which is hard to dope for applications in high-power electronics. While MoO 3 is found to be an effective surface electron acceptor for hydrogen-terminated diamond with a negative electron affinity, the effects of commonly existing oxygen vacancies remain elusive. We have performed reactive molecular dynamics simulations to study the deposition of MoO 3–x on a hydrogenated diamond (111) surface and used first-principles calculations based on density functional theory to investigate the electronic structures and charge transfer mechanisms. We find that MoO 3–x is an effective surface electron acceptor and the spatial extent of doped holes in hydrogenated diamond is extended, promoting excellent transport properties. Charge transfer is found to monotonically decrease with the level of oxygen vacancy, providing guidance for engineering of the surface transfer doping process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Machine Learning-Accelerated First-Principles Molecular Dynamics Explains Anomalous Lattice Thermal Expansion in BaZr 0.78 Y 0.22 O 3-δ

Fuel cells are a vital clean energy technology that converts chemical energy directly into electricity with high efficiency, making them a cornerstone of a sustainable energy future. Herein we investigate the thermal and chemical lattice expansion behavior of hydrated BaZr 0.78 Y 0.22 O 3-δ using machine learning-accelerated ab initio molecular dynamics simulations. Here, our results reproduce the experimentally observed non-monotonic and anomalous temperature dependence of lattice expansion, which we attribute to the competing effects of thermal expansion and dehydration—two mechanisms that influence the lattice expansion in opposite directions. The importance of this work lies in its detailed demonstration of how advanced computational techniques can accurately capture complex environmental effects, providing a valuable framework for modeling similar phenomena in a variety of material systems and applications.

Proton conducting fuel cell↗

Complex pH-Dependent Interactions between Weak Polyelectrolyte Block Copolymer Micelles and Molecular Fluorophores

Amphiphilic block copolymers with weak polyelectrolyte blocks can assemble stimulus-responsive nanostructures and interfaces. Applications of these materials in drug delivery, biomimetics, and sensing largely rely on the well-understood swelling of polyelectrolyte chains upon deprotonation, often induced by changes in pH or ionic strength. This deprotonation can also tune interfacial interactions between the polyelectrolyte blocks and surrounding solution, an effect which is less studied than morphological swelling of polyelectrolytes but can be just as critical for intended function. Here, we investigate whether the pH-driven morphological response of polyelectrolyte-bearing nanostructures also affects the interactions of these nanostructures with molecules in solution, using micelles of a short-chain polybutadiene-block-poly(acrylic acid) (pBd–pAA) as a model system. Here we introduce a Förster resonance energy transfer (FRET) approach to probe interactions between micelles and fluorescent molecular solutes as a function of solution pH. As expected, the pAA corona of these pBd–pAA micelles increases in thickness monotonically as a function of pH. However, FRET efficiency, which provides a metric of the spatial proximity of fluorescently labeled micelles and freely diffusing fluorophores, exhibits complex nonmonotonic behavior as a function of pH, indicating that the average separation of micelles and acceptor fluorophores is not strictly correlated with micelle swelling. Dialysis experiments quantify the affinity of fluorophores for micelles as a function of pH, confirming that changes in FRET are driven almost entirely by the pH-dependent affinity of the pAA block for the investigated molecular fluorophores, not simply by a shape change of the pAA corona. This study provides key insights into the interfacial interactions between weak-polyelectrolyte-bearing nanostructures and molecular solutes, of importance for the development of their stimulus-responsive applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Simulations of Glass Transition and Mechanical Behavior of Off-Stoichiometric Crosslinked Polymers

Here, this work explores the influence of blend composition, network architecture, and hydrogen bonding on the material properties of crosslinked epoxy networks, focusing on the glass transition temperature (T g ) and Young’s modulus (Y). We used coarse-grained molecular dynamics simulations to simulate varying compositions of stiff and flexible components in epoxy monomer blends with varying excess of curative. We find that, without hydrogen bonding, networks of any composition show a monotonically increasing T g with decreasing excess curative, consistent with theory. In contrast, we find that when hydrogen bonding is introduced, the binary blend networks show significant enhancement in T g for lightly crosslinked systems. This result contributes to an explanation of the anomalous T g behavior observed experimentally in these systems. We further find that Y is generally enhanced by hydrogen bonds, especially below T g , demonstrating that hydrogen bonding has a significant influence on mechanical properties and can allow access to other desirable dynamic behavior, especially self-healing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Molecular Dynamics Study of the Effect of Grafting Density on Ion Diffusivity in a MARTINI Coarse-Grained Strong Polyelectrolyte Brush

Because surface-grafted polyelectrolyte brushes (PEBs) are responsive to external stimuli, such as electric fields and ionic strength, PEBs are attractive for applications ranging from drug delivery to separation technologies. Essential to PEB utilization is understanding how critical parameters like grafting density (σ) impact the PEB structure and the dynamics of the PEB and counterions. To study the effect of σ on PEB and the counterion structure and dynamics, we fine-tune a coarse-grained model that retains the chemical specificity of a strong polyelectrolyte, poly[(2-(methacryloyloxy)ethyl) trimethylammonium chloride] (PMETAC), using the MARTINI force field. Using “salt-free” conditions where the counterion concentration balances the charge on the brush, we build coarse-grained (CG) molecular dynamics simulations for MARTINI PMETAC brushes (N = 150 monomers; M W = 31.2 kg/mol) at experimentally relevant values of σ = 0.05, 0.10, 0.20, and 0.40 chains/nm 2 . Using 5 μs simulations, we investigate the effects of grafting density on the PEB structure, ion dissociation dynamics, polymer mobility, and counterion diffusivity. Results show that competition between electrostatic interactions, steric hindrance, and polymer mobility controls counterion diffusivity. Finally, the interplay of these factors leads to diffusivity that depends non-monotonically on σ, with counterion diffusivity peaking at an intermediate σ = 0.10 chains/nm 2 .

36 MATERIALS SCIENCE↗

Concentration-Driven Slowdown of Chain-Exchange Kinetics in Block Copolymer Micelle Solutions

Here, we investigate the dependence of chain-exchange kinetics on polymer concentration for spherical micelles prepared from a polystyrene-b-poly(ethylene-alt-propylene) (SEP) diblock copolymer ( M n = 75 kDa, Ð = 1.05, and f PS = 0.18) in the PEP-selective solvent squalane. Solutions with concentrations of 15 vol% or more adopt a body-centered-cubic (BCC) packing of micelles, or a dense liquid-like packing (LLP), as confirmed by small-angle X-ray scattering. Concurrently, the mean aggregation number of the micelles grows steadily from about 60 in dilute solution to nearly 200 by 50 vol%. Time-resolved small-angle neutron scattering (TR-SANS) analysis reveals a monotonic and substantial (i.e., more than four orders of magnitude) decrease in the rate of chain exchange as the polymer concentration increases from 1 to 50 vol%. The TR-SANS relaxation functions are analyzed, taking into account both changes in contrast (due to chain exchange) and evolution in the structure factor (due to refinement of micelle packing). The activation energy for chain pullout is extracted using an established model and can be expressed as a linear function of polymer concentration, indicating that, in addition to the enthalpic barrier for extracting the core block, the evolution of micelle characteristics with increasing concentration imposes further constraints on chain exchange. Consistent with a theory of Halperin, these results suggest that the dominant factor reflects steric penalties during core block pullout arising from a reduced interfacial area per chain and associated increased corona crowding, due to the increase in aggregation number. The rate of exchange is independent of whether the micelles adopt a BCC or LLP arrangement, confirming that the rate-limiting step is extraction of the core block.

chemical structure↗

Microscopic Origin of Twist-Dependent Electron Transfer Rate in Bilayer Graphene

Using molecular simulation and continuum dielectric theory, we consider how electrochemical kinetics are modulated by the twist angle in bilayer graphene electrodes. By establishing a connection between the twist angle and the screening length of charge carriers within the electrode, we investigate how tunable metallicity modifies the statistics of the electron transfer energy gap. Constant potential molecular simulations show that the activation free energy for electron transfer increases with screening length, leading to a non-monotonic dependence on the twist angle. Here, the twist angle alters the density of states, tuning the number of thermally accessible channels for electron transfer and the reorganization energy by affecting the stability of the vertically excited state through attenuated image charge interactions. Understanding these effects allows us to express the Marcus rate of interfacial electron transfer as a function of the twist angle in a manner consistent with experimental observations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Temperature-Dependent Phase Stable Hybrid Halide Perovskite Films by Chemical Vapor Deposition

Methylammonium lead iodide (MAPbI 3-x Cl x ) thin films were synthesized using chemical vapor deposition. Temperature-dependent grazing incidence synchrotron-based X-ray diffraction measurements confirm that the structure of MAP-bI 3-x Cl x , where Cl acts more like a dopant, remains throughout in the tetragonal phase in the temperature range of 20-300 K. Here these studies are further correlated with temperature-dependent photo-luminescence (PL) studies. The PL peak energy monotonically increases with temperature, suggestive of a single-phase behavior. Resistance measurements conducted as a function of temperature show an absence of inflection points, suggesting uniformity in its phase. Between 200 and 325 K, the resistance remains a constant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Assessing the Effects of Temperature and Oxygen Vacancy on Band Gap Renormalization in LaCrO 3-δ : First-Principles and Experimental Corroboration [plus supplemental information]

Understanding the temperature dependence of functional properties in high-temperature gas sensors is vital for applications in combustion environments. Temperature effect on the electronic structure due to electron-phonon coupling is a key property of interest as this influences other responses of sensors. In this work, we assess the impact of temperature on band gap renormalization of pristine and oxygen-vacant LaCrO 3–δ perovskite employing Allen–Heine–Cardona theory with first-principles simulations and corroborate with experimental observation. Antiferromagnetic cubic LaCrO 3 shows a direct ground-state band gap of 2.62 eV that is reduced by over 1 eV due to the presence of oxygen vacancies, which can form endothermically. We find excellent agreement in temperature-dependent band gap shift in LaCrO 3 between theory and an in-house experiment, proving that the theory can adequately predict renormalization on the band gap in a magnetic system. Band gaps in cubic LaCrO 3–δ are found to monotonically narrow by 1.13 eV in pristine and by around 0.62 eV in oxygen-vacant structures as temperature increases from 0 to 1500 K. The predicted band gap variations are rationalized using an analytical model. Furthermore, the experimental zero-temperature band gaps are extracted from the model fits that can provide useful insights on the simulated band gaps.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗