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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.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Addition of Short Polymer Chains Mechanically Reinforces Glassy Poly(2-vinylpyridine)–Silica Nanoparticle Nanocomposites

The addition of hard fillers to a polymer matrix is a well-known process for achieving mechanical reinforcement. With a decrease in the size of the fillers, the contribution from polymer–particle nanometer-sized interfaces become significant, and these interfaces affect the mechanical performance of polymer nanocomposites (PNCs) beyond the limits established for conventional composites. However, the molecular mechanisms underlying the improvement in the mechanical performance of glassy PNCs remain unresolved, necessitating a deeper understanding of the structure–property relationships in these intrinsically heterogeneous systems. In this effort, by using Brillouin light scattering (BLS) and dynamic mechanical analysis (DMA), we demonstrated that adding shorter chains to a PNC prepared with high molecular weight polymers significantly improved the mechanical properties of the PNC in the glassy state. The strongest enhancement of mechanical properties occurred at an optimum concentration of short chains. This is in contrast to behavior of the glass transition temperature of PNCs which shows a monotonic decrease with an increase in the concentration of shorter chains. Using experimental data and coarse-grained molecular dynamics (MD) simulations, we have identified the molecular mechanism leading to the observed non-monotonic changes in mechanical reinforcement. Here, this mechanism includes changes in the nanoscale organization at the interface, combined with chain stretching amplified by the addition of the short chains. Overall, our approach paves a simple, cost-effective pathway to fabricating glassy PNCs with significantly improved mechanical properties that will fill various practical needs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Surviving nanoscale interfacial stability in extreme thermal expansion contrast Zn(CN) 2 -epoxy resin matrix composites

Here, we report the remarkable stability at the nanoscale matrix-filler interface in a series of overall low coefficient of thermal expansion (CTE) zinc cyanide (ZC)/epoxy resin composites. These interfaces demonstrate the stability of highly contrasting materials. These composites are designed to optimize the properties of both materials: epoxy resins are valued for their high strength, superb chemical resistance, low dielectric properties, and adhesive abilities. ZC, a model flexible framework, exhibits negative thermal expansion (NTE) behavior and compensates for the epoxy resin’s detrimentally large thermal expansion values. Filled resins minimize the native 65 ppm/°C CTE values to 19 ppm/° C over a wide temperature range while maintaining linearity, yielding composites compatible with typical metal and ceramic substrates’—commonly bonded to the resin— 0–20 ppm/° C CTE values. Additionally, with significant intrinsic differences in the materials, we use wide-angle X-ray diffraction and atomic force microscopy to elucidate thermal movement. The ZC/epoxy interface is surprisingly resilient over 1,000 cycles between -55° C and 75° C, extremes typical to aerospace applications. Further, we show that the resin viscosity remains less than 21 Pa*s at up to 30 vol% ZC, an important consideration for workability. We also discuss settling distribution, glass transition temperature, flexural strength, and longevity. All results point favorably towards practical implementation in low thermal expansion application needs: filling the gap in component design.

42 ENGINEERING↗
DOE OSTI2021

Nanomechanical testing of freestanding polymer films: in situ tensile testing and Tg measurement

Abstract A method for small-scale testing and imaging of freestanding, microtomed polymer films using a push-to-pull device is presented. Central to this method was the development of a sample preparation technique which utilized solvents at cryogenic temperatures to transfer and deposit delicate thin films onto the microfabricated push-to-pull devices. The preparation of focused ion beam (FIB)-milled tensile specimens enabled quantitative in situ TEM tensile testing, but artifacts associated with ion and electron beam irradiation motivated the development of a FIB-free specimen preparation method. The FIB-free method was enabled by the design and fabrication of oversized strain-locking push-to-pull devices. An adaptation for push-to-pull devices to be compatible with an instrumented nanoindenter expanded the testing capabilities to include in situ heating. These innovations provided quantitative mechanical testing, postmortem TEM imaging, and the ability to measure the glass transition temperature, via dynamic mechanical analysis, of freestanding polymer films. Results for each of these mentioned characterization methods are presented and discussed in terms of polymer nanomechanics. Graphic Abstract

36 MATERIALS SCIENCE↗
DOE OSTI2022

Redesigned Hybrid Nylons with Optical Clarity and Chemical Recyclability

Aliphatic polyamides, or nylons, are typically highly crystalline and thermally robust polymers used in high-performance applications. Nylon 6, a high-ceiling-temperature (HCT) polyamide from e-caprolactam, lacks expedient chemical recyclability, while low-ceiling temperature (LCT) nylon 4 from pyrrolidone exhibits complete chemical recyclability, but it is thermally unstable and not melt-processable. Here, we introduce a hybrid nylon, nylon 4/6, based on a bicyclic lactam composed of both HCT ..epsilon..-caprolactam and LCT pyrrolidone motifs in a hybridized offspring structure. Hybrid nylon 4/6 overcomes trade-offs in (de)polymerizability and performance properties of the parent nylons, exhibiting both excellent polymerization and facile depolymerization characteristics. This stereoregular polyamide forms nanocrystalline domains, allowing optical clarity and high thermal stability, however, without displaying a melting transition before decomposition. Of a series of statistical copolymers comprising nylon 4/6 and nylon 4, a 50/50 copolymer achieves the greatest synergy in both reactivity and polymer properties of each homopolymer, offering an amorphous nylon with favorable properties, including optical clarity, a high glass transition temperature, melt processability, and full chemical recyclability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Reducing dielectric loss and enhancing electrical insulation for multilayer polymer films by nanoconfined ion transport under high poling electric fields

High temperature polar polymers have demonstrated potential for good thermal stability and high dielectric constant at the same time. However, polarization of contaminated impurity ions in polar polymers, even at the ppm level, can significantly increase the dielectric loss at high temperature and low frequencies. One effective strategy to mitigate this problem is to multilayer them with a high temperature nonpolar dielectric polymer to confine impurity ion transport at the nanometer scale. In this study, confined ion transport in high temperature polycarbonate (HTPC)/poly(vinylidene fluoride) (PVDF) multilayer films under high AC electric fields was studied using a direct analytical simulation method. Different from the ion transport under low fields, the ion diffusion model failed to describe the ion transport under high electric fields. An exponential ion distribution profile, which was observed for the DC poling situation, was employed to implement the direct analytical simulation. Confined impurity ion transport under high AC fields was quantitatively understood. As the AC field increased, the mobile ion concentration decreased whereas the diffusion coefficient increased. The decrease of mobile ion concentration was explained by the blockage of impurity ions by the HTPC layers. This knowledge helped in the determination of optimal conditions to polarize impurity ions from the PVDF layers into the HTPC layers. After cooling below the glass transition temperature of HTPC, polarized impurity ions were locked inside the HTPC layers. As a result, increased discharge efficiency and enhanced electrical insulation (i.e., increased dielectric breakdown strength) were achieved for the polarized multilayer films.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Pressure dependence of intermediate-range order and elastic properties of glassy Baltic amber

Amber is a unique example of a fragile glass that has been extensively aged below its glass transition temperature, thus reaching a state that is not accessible under normal experimental conditions. In this paper, we studied the medium-range order of Baltic amber by x-ray diffraction (XRD) at high pressures. The pressure dependences of the low-angle XRD intensity between 0 and 5 Å -1 were measured from 0 to 7.3 GPa by the energy-dispersive XRD. The first diffraction peak at 1.1 Å -1 and ambient pressure has a doublet structure consisting of the first sharp diffraction peak (FSDP) at 1.05 Å -1 and the second feature at 1.40 Å -1 . The peak position and the width of the FSDP increase as the pressure increases, while the intensity of the FSDP decreases. Below P 0 = 2.4 GPa, the rapid increase of the FSDP peak position was observed, while above P 0 , the gradual increase was observed. Below P 0 , voids and holes in a relatively low-density state are suppressed, whereas above P 0 , the suppression becomes mild. Such a change suggests the crossover from the low- to high-density state at P 0 . There is a close correlation between the pressure dependence of XRD and previously reported sound velocity results. The correlation between the mean-square fluctuation of the shear modulus on the nanometer scale and fragility in amber and other glass formers is also discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Computational investigation of water glasses using machine-learning potentials

The molecular origins of water’s anomalous properties have long been a subject of scientific inquiry. The liquid–liquid phase transition hypothesis, which posits the existence of distinct low-density and high-density liquid states separated by a first-order phase transition terminating at a critical point, has gained increasing experimental and computational support and offers a thermodynamically consistent framework for many of water’s anomalies. However, experimental challenges in avoiding crystallization near the postulated liquid–liquid critical point have focused attention to water’s canonical glassy states: low-density and high-density amorphous ice. Here, we use two Deep Potential machine-learning models, trained on the Strongly Constrained and Appropriately Normed density functional and the highly accurate Many-Body Polarizable potential, to conduct an investigation of water’s glassy phenomenology based on quantum mechanical calculations. Despite not being explicitly trained on amorphous ices, both models accurately capture the structure and transformation of the water glasses, including their interconversion along different thermodynamic paths. Isobaric quenching of liquid water at various pressures generates a continuum of intermediate amorphous ices and density fluctuations increase near the liquid–liquid critical pressure. The glass transition temperatures of the amorphous ices produced at different pressures exhibit two distinct branches, corresponding to low-density and high-density amorphous ice behaviors, consistent with experiment and the liquid–liquid transition hypothesis. Extrapolating transformation pressures from isothermal compressions to experimental compression rates brings our simulations into excellent agreement with data. Our findings demonstrate that machine-learning potentials trained on equilibrium phases can effectively model nonequilibrium glassy behavior and pave the way for studying long-timescale, out-of-equilibrium processes with quantum mechanical accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Large-scale reactive thermoset printing: Complex interactions between temperature evolution, viscosity, and cure shrinkage

Thermoset composites are strong candidates for large-scale material extrusion additive manufacturing (AM). However, uncured thermoset composites become unstable as print height increases. Here, chemical initiation of vinyl ester immediately before deposition was used to suppress collapse and enable large-scale thermoset printing. Structural stability was assessed by printing thin walls at various layer times and monitoring thermal gradients with an infrared camera. Stable printing was observed at a layer time of 4.50 min, approximately half the gel time of the material (8 min). Self-weight collapse occurred at short layer time (0.68 min), whereas warpage occurred at long layer time (6.50 min). Here, a new behavior was discovered at intermediate layer time (2.25 min) where the heat generated by the reaction causes new, un-gelled layers to flow. Forced convection eliminates this behavior, stabilizing the 2.25-min layer time print. These findings motivated development of a less exothermic material system, which was used to print a large-scale mold and demonstrate the value of this understanding. By presenting these challenges of large-scale reactive thermoset AM for the first time, this work motivates focused studies of the complex interplay between rheological, thermal, and chemical behaviors to improve the feasibility of large-scale thermoset AM. Tensile properties of the printed material were also measured. Longitudinal and transverse elastic moduli are 3.79 and 2.95 GPa, respectively, and corresponding tensile strengths are 36.11 and 18.83 MPa. The glass transition temperature is 93.13 °C.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Structures of glass-forming liquids by x-ray scattering: Glycerol, xylitol, and D-sorbitol

In this work, synchrotron X-ray scattering has been used to investigate three liquid polyalcohols of different sizes (glycerol, xylitol and D-sorbitol) from above the glass transition temperatures $T_g$ to below. We focus on two structural orders: the association of the polar OH groups by hydrogen bonds (HBs) and the packing of the non-polar hydrocarbon groups. We find that the two structural orders evolve very differently reflecting the different natures of bonding. Upon cooling from 400 K, the O$\cdots$O correlation at 2.8 Å increases significantly in all three systems, indicating more HBs, until kinetic arrest at $T_g$; the increase is well described by an equilibrium between bonded and non-bonded OH with ΔH = 9.1 kJ/mol and ΔS = 13.4 J/mol/K. When heated above $T_g$, glycerol loses the fewest HBs per OH, followed by xylitol and by D-sorbitol, in the same order the number of OH groups per molecule increases (3, 5, and 6). The pair correlation functions of all three liquids show exponentially damped density modulations of wavelength 4.5 Å, which are associated with the main scattering peak and with the intermolecular C$\cdots$C correlation. In this respect, glycerol is the most ordered with the most persistent density ripples, followed by D-sorbitol and by xylitol. Heating above $T_g$ causes faster damping of the density ripples with the rate of change being the slowest in xylitol, followed by glycerol and by D-sorbitol. Given the different dynamic fragility of the three liquids (glycerol being the strongest and D-sorbitol the most fragile), we relate our results to the current theories of the structural origin for the difference. We find that the fragility difference is better understood on the basis of the thermal stability of HB clusters than that of the structure associated with the main scattering peak.

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

Efficient and Photostable Organic Solar Cells Achieved by Alloyed Dimer Acceptors with Tailored Linker Structures

Abstract High power conversion efficiency (PCE) and long‐term stability are prerequisites for commercialization of organic solar cells (OSCs). Herein, two dimer acceptors (DYTVT and DYTCVT) are developed with different properties through linker engineering, and study their effects as alloy‐like acceptors on the photovoltaic performance and photostability of OSCs. These ternary OSCs effectively combine the advantages of both dimer acceptors. DYTVT, characterized by its high backbone planarity, ensures elevated electron mobility and high glass‐transition temperature (T g ), leading to efficient charge transport and enhanced photostability of OSCs. Conversely, DYTCVT, with its significant dipole moment and electrostatic potential, enhances compatibility of the alloy acceptors with donors and refines the blend morphology, facilitating efficient charge generation in OSCs. Consequently, D18:DYTVT:DYTCVT OSCs exhibit higher PCE (18.4%) compared to D18:MYT (monomer acceptor, PCE = 16.5%), D18:DYTVT (PCE = 17.4%), and D18:DYTCVT (PCE = 17.0%) OSCs. Furthermore, owing to higherT g of alloy acceptors (133 °C) than MYT (T g = 80 °C) and DYTCVT (T g = 120 °C), D18:DYTVT:DYTCVT OSCs have significantly higher photostability (t 80% lifetime = 4250 h under 1‐sun illumination) compared to D18:MYT (t 80% lifetime = 40 h) and D18:DYTCVT OSCs (t 80% lifetime = 2910 h).

Chemistry↗
DOE OSTI2022

Tethered Small-Molecule Acceptors Simultaneously Enhance the Efficiency and Stability of Polymer Solar Cells

For polymer solar cells (PSCs), the mixture of polymer donors and small-molecule acceptors (SMAs) is fine-tuned to realize a favorable kinetically trapped morphology and thus a commercially viable device efficiency. However, the thermodynamic relaxation of the mixed domains within the blend raises concerns related to the long-term operational stability of the devices, especially in the record-holding Y-series SMAs. Here, a new class of dimeric Y6-based SMAs tethered with differential flexible spacers is reported to regulate their aggregation and relaxation behavior. In their polymer blends with PM6, it is found that they favor an improved structural order relative to that of Y6 counterpart. Most importantly, the tethered SMAs show large glass transition temperatures to suppress the thermodynamic relaxation in mixed domains. For the high-performing dimeric blend, an unprecedented open circuit voltage of 0.87 V is realized with a conversion efficiency of 17.85%, while those of regular Y6-base devices only reach 0.84 V and 16.93%, respectively. Most importantly, the dimer-based device possesses substantially reduced burn-in efficiency loss, retaining more than 80% of the initial efficiency after operating at the maximum power point under continuous illumination for 700 h. In conclusion, the tethering approach provides a new direction to develop PSCs with high efficiency and excellent operating stability.

14 SOLAR ENERGY↗
DOE OSTI2026

Dynamic Diketoenamine Crosslinking Unlocks Vinyl Polymer Vitrimers From β ‐Triketone Chemistry

Covalent adaptable networks (CANs) offer a compelling strategy to unite the mechanical robustness of thermosets with the reprocessability of thermoplastics, yet achieving simultaneous durability, processability, and true recyclability remains challenging. We introduce diketoenamine (DKE) vitrimers derived from β-triketone methacrylate monomers and demonstrate how rational monomer design dictates network processability, viscoelasticity, and recyclability. By systematically varying the spacer length between the β-triketone (TK) moiety and the polymer backbone, we identify a key structure–property relationship that dictates vitrimer behavior. Networks bearing TK pendants minimally displaced from the backbone suppress creep but exhibit limited stress relaxation, whereas extended spacers yield lower glass transition temperatures, higher effective crosslink densities, and efficient stress dissipation, enabling optical transparency and reprocessability. Extending this platform to ultra-high molecular-weight prepolymers introduces physical entanglements as secondary crosslinks, further enhancing dimensional stability without compromising processability. Both mechanical and chemical recycling validate the closed-loop circularity of these materials. Furthermore, these results establish TK methacrylates as a versatile platform for designing high-performance vitrimers that integrate durability, reprocessability, and true closed-loop recyclability.

closed-loop recyclability↗
DOE OSTI2023

Regiospecific Incorporation of Acetylene Linker in High‐Electron Mobility Dimerized Acceptors for Organic Solar Cells with High Efficiency (18.8%) and Long 1‐Sun Lifetime (> 5000 h)

Abstract The commercialization of organic solar cells (OSCs) requires both high power conversion efficiency (PCE) and long‐term stability. However, the lifetime of the OSCs containing small‐molecule acceptors (SMA) should be significantly enhanced. In this study, a series of planarity‐controlled is developed, high electron mobility dimerized SMAs (DSMAs) and realize OSCs with high‐performance (PCE = 18.8%) and high‐stability ( t 80% lifetime = 5380 h under 1‐Sun illumination). An acetylene linker with a planar triple bond is designed for dimerization of SMA units to afford the high backbone planarity necessary to achieve high crystallinity and electron mobility. To further engineer the molecular conformation and electron mobility of the DSMAs, different regioisomers of a Y‐based SMA are dimerized to yield three regioisomerically distinct DSMAs, denoted as DYA‐I, DYA‐IO, and DYA‐O, respectively. It is found that the crystallinity, electron mobility, and glass transition temperature of the DSMAs gradually increase in the order of DYA‐O, DYA‐IO, and DYA‐I, which, in turn, enhance the PCE and device stability of the resulting OSCs; DYA‐O (PCE = 16.45% and t 80% lifetime = 3337 h) < DYA‐IO (PCE = 17.54% and t 80% lifetime = 4255 h) < DYA‐I (PCE = 18.83% and t 80% lifetime = 5380 h).

Chemistry↗
DOE OSTI2025

Synergistic Tuning of Microstructure and Morphology in Carbon Molecular Sieve Hollow Fibers for Propylene/Propane Separation

Abstract Asymmetric carbon molecular sieve (CMS) hollow fiber membranes with tunable micro‐ and macro‐structural morphologies for energy efficient propylene‐propane separation are reported here. A sub‐glass transition temperature (sub‐Tg) thermal oxidative crosslinking strategy enables simultaneous optimization of the intrinsic molecular sieving properties while also reducing the thickness of the CMS “skin” derived from the 6FDA : BPDA/DAM polyimide precursors. Such synergistic tuning of CMS microstructure and macroscopic morphology of CMS hollow fibers enables significantly increased propylene permeance (reaching 186.5 GPU) while maintaining an appealing propylene/propane selectivity of 13.3 for 50/50 propylene/propane mixed gas feeds. Our findings reveal a more refined and versatile tool than available with previous O 2 ‐doping pretreatments. The advanced approach here should be broadly useful to other polyimide precursors and diverse gas pairs.

Liu, Zhongyun [School of Chemical &amp, Biomolecul↗
DOE OSTI2024

Tailoring the Properties of Chemically Recyclable Polyethylene‐Like Multiblock Polymers by Modulating the Branch Structure

Abstract Developing plastics that fill the need of polyolefins yet are more easily recyclable is a critical need to address the plastic waste crisis. However, most efforts in this vein have focused on high‐density polyethylene (PE), while many different types of PE exist. To create broadly sustainable PE with modular properties, we present the synthesis, characterization, and demonstration of materials applications for chemically recyclable PE‐like multiblock polymers prepared from distinct hard and soft blocks using ruthenium‐catalyzed dehydrogenative polymerization. By altering the branching pattern within the soft blocks, a series of PE‐like multiblock polymers were synthesized with tunable glass transition temperatures ( T g ) while maintaining consistent high melting temperatures ( T m ). A clear U‐shape trend between T g and mechanical properties was found, showcasing their potential as sustainable materials with tailored properties spanning commercial linear low‐density polyethylene (LLDPE) and low‐density polyethylene (LDPE). These materials offer adjustable adhesive strength to metal and demonstrate chemical recyclability and selective depolymerization in mixed plastic streams, promoting circularity and separation.

Zhao, Yucheng↗
DOE OSTI2025

Cleavable Strand‐Fusing Cross‐Linkers as Additives for Chemically Deconstructable Thermosets with Preserved Thermomechanical Properties

Abstract Permanently cross‐linked polymer networks—thermosets—are often difficult to chemically deconstruct. The installation of cleavable bonds into the strands of thermosets using cleavable comonomers as additives can facilitate thermoset deconstruction without replacement of permanent cross‐links, but such monomers can lead to reduced thermomechanical properties and require high loadings to function effectively, motivating the design of new and optimal cleavable additives. Here, we introduce “strand‐fusing cross‐linkers” (SFCs), which fuse two network strands via a four‐way cleavable cross‐link. SFCs enable deconstruction of model polydicyclopentadiene (pDCPD) thermosets with as little as one‐fifth of the molar loading needed to achieve deconstruction using traditional cleavable comonomers. SFCs function under traditional oven curing as well as low‐energy frontal ring‐opening metathesis polymerization (FROMP) conditions and lead to improved thermomechanical properties, for example, glass transition temperatures, compared to prior cleavable comonomer designs. This work motivates the development of increasingly improved cleavable additives to enable thermoset deconstruction without compromising material performance.

Zhang, Shuyi [Department of Chemistry Massachusett↗
DOE OSTI2024

Synergistic Tuning of Microstructure and Morphology in Carbon Molecular Sieve Hollow Fibers for Propylene/Propane Separation

Abstract Asymmetric carbon molecular sieve (CMS) hollow fiber membranes with tunable micro‐ and macro‐structural morphologies for energy efficient propylene‐propane separation are reported here. A sub‐glass transition temperature (sub‐Tg) thermal oxidative crosslinking strategy enables simultaneous optimization of the intrinsic molecular sieving properties while also reducing the thickness of the CMS “skin” derived from the 6FDA : BPDA/DAM polyimide precursors. Such synergistic tuning of CMS microstructure and macroscopic morphology of CMS hollow fibers enables significantly increased propylene permeance (reaching 186.5 GPU) while maintaining an appealing propylene/propane selectivity of 13.3 for 50/50 propylene/propane mixed gas feeds. Our findings reveal a more refined and versatile tool than available with previous O 2 ‐doping pretreatments. The advanced approach here should be broadly useful to other polyimide precursors and diverse gas pairs.

Liu, Zhongyun↗
DOE OSTI2024

Tailoring the Properties of Chemically Recyclable Polyethylene‐Like Multiblock Polymers by Modulating the Branch Structure

Abstract Developing plastics that fill the need of polyolefins yet are more easily recyclable is a critical need to address the plastic waste crisis. However, most efforts in this vein have focused on high‐density polyethylene (PE), while many different types of PE exist. To create broadly sustainable PE with modular properties, we present the synthesis, characterization, and demonstration of materials applications for chemically recyclable PE‐like multiblock polymers prepared from distinct hard and soft blocks using ruthenium‐catalyzed dehydrogenative polymerization. By altering the branching pattern within the soft blocks, a series of PE‐like multiblock polymers were synthesized with tunable glass transition temperatures ( T g ) while maintaining consistent high melting temperatures ( T m ). A clear U‐shape trend between T g and mechanical properties was found, showcasing their potential as sustainable materials with tailored properties spanning commercial linear low‐density polyethylene (LLDPE) and low‐density polyethylene (LDPE). These materials offer adjustable adhesive strength to metal and demonstrate chemical recyclability and selective depolymerization in mixed plastic streams, promoting circularity and separation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗