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At least 379 records · Page 21

Influence of the air-cooled supercritical carbon dioxide recompression cycle design-point on molten salt power tower techno-economic performance

Here, this paper investigates the techno-economic performance of a molten salt power tower integrated with an air-cooled supercritical carbon dioxide recompression cycle. Prior research into the cycle design point showed trade-offs between efficiency, cost, and temperature difference across the heat input, resulting in trade-offs between the design-point generation of the molten salt power tower system and the cost of sensible-heat thermal energy storage. Prior research into cycle off-design showed that colder ambient temperature designs have higher efficiencies on cold days but lower efficiency and capacity degradation on hot days. We present a framework to evaluate how cycle design, cost, and corresponding off-design performance affect the techno-economic performance of the molten salt power tower system. We use a steady-state off-design cycle model assuming fixed shaft speeds, inventory control, and air-cooler fan power control and integrate the cycle model with the molten salt power tower model from the National Renewable Energy Laboratory's System Advisor Model. First, we present a surrogate model that uses a heuristic approach to correct the interpolation when the cycle reaches capacity limitations at ambient temperatures hotter than design. Next, we evaluate how the recompression cycle design-point ambient temperature, air-cooler approach temperature, air-cooler fan power, and recuperator conductance influence cycle and system design metrics. Finally, we complete annual simulations using an hourly "duck curve" pricing schedule and present annual performance metrics to evaluate the cumulative effects of the cycle design parameters and corresponding off-design performance on molten salt power tower techno-economics.

14 SOLAR ENERGY↗

Porous Organic Cages CC3 and CC2 as Adsorbents for the Separation of Carbon Dioxide from Nitrogen and Hydrogen

The selective capture of carbon dioxide over nitrogen and hydrogen is of great industrial interest in flue gas and hydrogen purification respectively. Microporous adsorbents are highly suitable materials to preferentially adsorb gases. Here, in particular, Porous organic cages (POCs) with tunable hierarchically ordered micropores, high surface area, and thermodynamic affinity for CO 2 make them appealing candidates for these applications. Herein, we demonstrate that two prototypical POCs denoted as CC3, and CC2 with limiting pore aperture of 3.6 Å can selectively separate CO 2 from N 2 , and H 2 . For CC3 adsorption selectivities as high as ~ 8 and ~20 for CO 2 /N 2 and CO 2 /H 2 respectively were observed. For CC2 adsorption selectivities as high as ~ 9 and ~35 for CO 2 /N 2 and CO 2 /H 2 respectively were observed. Interestingly, the adsorption selectivity of the studied gases correlated linearly with polarizability selectivity.

Carbon Dioxide↗

Synthesis and Evaluation of Cu@ZnO Core@Shell Nanowires for Use in the Carbon Dioxide Thermal Reduction Reaction

Copper-based core@shell nanomaterials are of interest for the catalytic hydrogenation of carbon dioxide toward value-added products. In this context, we have developed a facile, microwave-based procedure for the reliable and reproducible synthesis of Cu@ZnO core@shell nanowires. A systematic assessment of the effect of rationally varying various reaction conditions on this protocol was completed in order to better evaluate the growth process of these core–shell motifs. We determined that among different reaction parameters, it was the critical role of reaction time which enabled the quantitatively reliable growth of external shells with tunable thicknesses of up to 20 nm. As a demonstration of the material’s practical viability, catalytic testing was subsequently performed for the reverse water–gas shift reaction (CO 2 + H 2 → CO + H 2 O), with the evolution of the process followed with in situ X-ray diffraction and X-ray absorption spectroscopy in order to probe structural changes and gauge stability. These tests found the catalysts to be effective at converting CO 2 to CO, with notable stability detected in the shell layer and no observed alloying between copper and zinc. Furthermore, our studies support the idea that the Cu–ZnO and CuO x –ZnO interfaces are essential for the effective activation of CO 2 and H 2 .

36 MATERIALS SCIENCE↗

Selectivity of Electrochemical Ion Insertion into Manganese Dioxide Polymorphs

The ion insertion redox chemistry of manganese dioxide has diverse applications in energy storage, catalysis, and chemical separations. Unique properties derive from the assembly of Mn–O octahedra into polymorphic structures that can host protons and nonprotonic cations in interstitial sites. Despite many reports on individual ion-polymorph couples, much less is known about the selectivity of electrochemical ion insertion in MnO 2 . In this work, we use density functional theory to holistically compare the electrochemistry of A x MnO 2 (where A = H + , Li + , Na + , K + , Mg 2+ , Ca 2+ , Zn 2+ , Al 3+ ) in aqueous and nonaqueous electrolytes. We develop an efficient computational scheme demonstrating that Hubbard-U correction has a greater impact on calculating accurate redox energetics than choice of exchange-correlation functional. Using PBE+U, we find that for nonprotonic cations, ion selectivity depends on the oxygen coordination environments inside a polymorph. When H + is present, however, the driving force to form hydroxyl bonds is usually stronger. In aqueous electrolytes, only three ion-polymorph pairs are thermodynamically stable within water’s voltage stability window (Na + and K + in α-MnO 2 , and Li + in λ-MnO 2 ), with all other ion insertion being metastable. We find Al 3+ may insert into the δ, R, and λ polymorphs across the full 2-electron redox of MnO 2 at high voltage; however, electrolytes for multivalent ions must be designed to impede the formation of insoluble precipitates and facilitate cation desolvation. We also show that small ions coinsert with water in α-MnO 2 to achieve greater coordination by oxygen, while solvation energies and kinetic effects dictate water coinsertion in δ-MnO 2 . Finally, taken together, these findings explain reports of mixed ion insertion mechanisms in aqueous electrolytes and highlight promising design strategies for safe, high energy density electrochemical energy storage, desalination batteries, and electrocatalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Plastic Waste Product Captures Carbon Dioxide in Nanometer Pores

We discuss, plastic waste (PW) and increasing atmospheric carbon dioxide (CO 2 ) levels are among the top environmental concerns presently facing humankind. With an ambitious 2050 zero-CO 2 emissions goal, there is a demand for economical CO 2 capture routes. Here we show that the thermal treatment of PW in the presence of potassium acetate yields an effective carbon sorbent with pores width of 0.7–1.4 nm for CO 2 capture. The PW to carbon sorbent process works with single or mixed streams of polyolefin plastics. The CO 2 capacity of the sorbent at 25 °C is 17.0 ± 1.1 wt % (3.80 ± 0.25 mmol g –1 ) at 1 bar and 5.0 ± 0.6 wt % (1.13 ± 0.13 mmol g –1 ) at 0.15 bar, and it regenerates upon reaching 75 ± 5 °C. The CO 2 capture cost from flue gas via this technology is estimated to be <$21 ton –1 CO 2 , much lower than competing CO 2 capture technologies. Hence, this PW-derived carbon material should find utility in the capture of CO 2 from point sources of high CO 2 emissions while providing a use for otherwise deleterious PW.

01 COAL, LIGNITE, AND PEAT↗

Sequential Ammonia and Carbon Dioxide Adsorption on Pyrolyzed Biomass to Recover Waste Stream Nutrients

Untreated fecal waste in unsewered communities and reactive nitrogen (N) loading from wastewater and urine disposal are important environmental challenges. Through pyrolysis, untreated fecal waste can be converted into amine-rich carbon dioxide (CO 2 ) sorbents, the chemisorption of which tunes the surface chemistry toward ammonia (NH 3 ) uptake. We compared the N-loading potential within amine-rich pyrolyzed human solid waste through exposure to CO 2 followed by NH 3 with the N-loading potential on carboxyl-rich, pyrolyzed oxidized wood using sequential adsorption of isotopically labeled CO 2 and NH 3 . The total N content of pyrolyzed oxidized wood exposed once to NH3 was similar to native, pyrolyzed human solid waste (3.7% compared to 4.6%). However, sorption kinetics and spectroscopic evidence revealed distinct N forms between the two materials affecting subsequent CO 2 and NH 3 uptake. Tertiary amines comprised 70% of N in pyrolyzed waste, compared to only 53% in pyrolyzed oxidized wood. The high heat of adsorption of CO 2 on pyrolyzed human solid waste (50 kJ mol-1) at low concentrations (0.05 mmol CO 2 g -1 ) was indicative of CO 2 reactivity with tertiary amines, consistent with the formation of carbamic acid (Figure S1). Conversely, after exposure to NH 3 , pyrolyzed oxidized wood chemisorbed CO 2 at much higher concentrations (0.7 mmol CO 2 g-1), pointing to primary amines as the active functional moieties. Adsorption kinetics of pyrolyzed oxidized wood revealed continued, albeit diminishing NH 3 uptake with each consecutive CO 2 treatment, averaging 5.9 mmol NH 3 g -1 for the first NH 3 exposure event, and still 3.5 and 2.9 mmol NH 3 g -1 for the second and third. Penetration of 15 NH 3 and 13 CO 2 measured by NanoSIMS reached over 7 µm deep into both materials, explaining the large NH 3 capture. The significantly lower NH 3 adsorption compared to pyrolyzed oxidized wood may be a result of potassium (K) carbonate precipitation precluding a Lewis base interaction between NH 3 and chemisorbed CO 2 , suggested by a 2-fold increase in surface K concentrations after exposure of pyrolyzed human solid waste to CO 2 +NH 3 detected by XPS.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Titanium dioxide and table sugar enhance the leaching of silver out of nanosilver packaging

We manufactured laboratory-scale food packages containing 2.57 ± 0.18 × 10 –3 wt% silver nanoparticles (AgNPs) and used them to show that table sugar (sucrose) and microcrystalline titanium dioxide (μTiO 2 ) enhance Ag migration from these packages and into aqueous food simulants. Ag migration into purified water was detected but was below the limit of ICP-MS quantitation, giving a range of potential Ag migration between 0.059 and 0.082 ng cm –2 packaging surface area. Ag migration into 9 wt% aqueous sucrose solution was 0.547 ± 0.084 ng cm –2 and migration into 9 wt% sucrose solution containing 0.01 wt% μTiO 2 was 0.724 ± 0.032 ng cm –2 . Total Ag migration into a 0.01 wt% μTiO 2 aqueous dispersion without sucrose was between 0.122 and 0.162 ng cm –2 , with upper and lower limits defined by the detectability of Ag in the supernatant phase of the simulant. If the midpoint of this range is taken as a baseline, these results imply that, compared to purified water, Ag migration was increased by approximately 10.3 times when the water simulant contained μTiO 2 and sucrose at commercially-relevant concentrations. Notably, the Ag migrated into water containing both ingredients exceeded the total Ag migrated into either of the single-ingredient simulants, pointing to a potential cooperative relationship between sucrose and μTiO 2 that possibly derives from binding and redox interactions between these two ingredients. Sucrose and μTiO 2 also both reduced a portion of migrated Ag + back into AgNPs, and μTiO 2 particles efficiently captured (>25% by mass) migrated Ag on their surfaces. Similar effects on migration were observed with nanocrystalline TiO 2 . Furthermore, these experiments are the first to show that TiO 2 particles exert a strong influence on the quantity and form of Ag that could migrate from AgNP-enabled packaging, suggesting that food formulations and interactions between individual food components may be important to consider when evaluating the fate of nanoparticles in these consumer applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Defect-induced phonon-resonant scattering and its influence on thermal transport of irradiated thorium-dioxide

Thermal transport in proton irradiated thorium-dioxide (ThO 2 ) is investigated. Using a combination of experiments and first-principles computational framework, the role of lattice defects on thermal conductivity is analyzed. A resonant-phonon scattering mechanism beyond the traditionally considered Rayleigh scattering is found to significantly influence low-temperature thermal transport in the presence of irradiation-induced point defects. The existence of localized phonon modes associated with irradiation-induced defects is suggested by the inability of the first-principles based thermal conductivity model—which considers only three-phonon interactions and phonon-defects scattering using the Tamura formalism—to predict the experimental results, unless a resonant scattering mechanism is included. The emergence of additional peaks in the Raman spectra in the proximity of phonon-resonant frequency provides further evidence for the existence of localized modes. Coupled with a microstructure evolution model, this analysis enables more accurate analysis for contrasting the contributions of different phonon scattering mechanisms across all irradiation doses and temperatures.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

COVID-19 pandemic reveals persistent disparities in nitrogen dioxide pollution

We leverage the unparalleled changes in human activity during COVID-19 and the unmatched capabilities of the TROPOspheric Monitoring Instrument to understand how lockdowns impact ambient nitrogen dioxide (NO 2 ) pollution disparities in the United States. The least White communities experienced the largest NO 2 reductions during lockdowns; however, disparities between the least and most White communities are so large that the least White communities still faced higher NO 2 levels during lockdowns than the most White communities experienced prior to lockdowns, despite a ~50% reduction in passenger vehicle traffic. Similar findings hold for ethnic, income, and educational attainment population subgroups. Future strategies to reduce NO 2 disparities will need to target emissions from heavy-duty vehicles.

TROPOMI↗

Generation of the Thermal Scattering Law of Uranium Dioxide with Ab Initio Lattice Dynamics to Capture Crystal Binding Effects on Neutron Interactions

Scattering of thermal neutrons and Doppler broadening of epithermal neutron resonances in uranium and its compounds may be sensitive to crystal binding. The thermal scattering law (TSL) for uranium dioxide, which captures crystal binding effects, has been reevaluated for ENDF/B-VIII.0. Phonon spectra were generated using ab initio lattice dynamics for the paramagnetic phase and validated against experiment. Improved agreement with the Debye-Waller coefficient as a function of temperature is found relative to the spectrum used for the ENDF/B-VII.1 evaluation. The TSL was generated using the phonon expansion method within the NJOY nuclear data processing package and was found to be in reasonable agreement with inelastic neutron scattering measurements. The present evaluation predicts a reduction in the inelastic scattering cross section relative to ENDF/B-VII.1 and a total scattering cross section consistent with neutron transmission experiments

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Biochar as a carbon dioxide removal strategy in integrated long-run mitigation scenarios

Abstract Limiting global warming to under 2 °C would require stringent mitigation and likely additional carbon dioxide removal (CDR) to compensate for otherwise unabated emissions. Because of its technology readiness, relatively low cost, and potential co-benefits, the application of biochar to soils could be an effective CDR strategy. We use the Global Change Analysis Model, a global multisector model, to analyze biochar deployment in the context of energy system uses of biomass with CDR under different carbon price trajectories. We find that biochar can create an annual sink of up to 2.8 GtCO 2 per year, reducing global mean temperature increases by an additional 0.5%–1.8% across scenarios by 2100 for a given carbon price path. In our scenarios, biochar’s deployment is dependent on potential crop yield gains and application rates, and the competition for resources with other CDR measures. We find that biochar can serve as a competitive CDR strategy, especially at lower carbon prices when bioenergy with carbon capture and storage is not yet economical.

54 ENVIRONMENTAL SCIENCES↗

The impact of regional resources and technology availability on carbon dioxide removal potential in the United States

To achieve net zero carbon emissions by mid-century, the United States may need to rely on carbon dioxide removal (CDR) to offset emissions from difficult-to-decarbonize sectors and/or shortfalls in near-term mitigation efforts. CDR can be delivered using many approaches with different requirements for land, water, geologic carbon storage capacity, energy, and other resources. The availability of these resources varies by region in the U.S. suggesting that CDR deployment will be uneven across the country. Using the global change analysis model for the United States (GCAM-USA), we modeled six classes of CDR and explored their potential using four scenarios: a scenario where all the CDR pathways are available (Full Portfolio), a scenario with restricted carbon capture and storage (Low CCS), a scenario where the availability of bio-based CDR options is limited (Low Bio), and a scenario with constraints on enhanced rock weathering (ERW) capabilities (Low ERW). We find that by employing a diverse set of CDR approaches, the U.S. could remove between 1 and 1.9 GtCO 2 /yr by midcentury. In the Full Portfolio scenario, direct air carbon capture and storage (DACCS) predominates, delivering approximately 50% of CO 2 removal, with bioenergy with carbon capture and storage contributing 25%, and ERW delivering 11.5%. Texas and the agricultural Midwest lead in CDR deployment due to their abundant agricultural land and geological storage availability. In the Low CCS scenario, reliance on DACCS decreases, easing pressure on energy systems but increasing pressure on the land. In all cases CDR deployment was found to drive important impacts on energy, land, or materials supply chains (to supply ERW, for example) and these effects were generally more pronounced when fewer CDR technologies were available.

54 ENVIRONMENTAL SCIENCES↗

Cost of Using Laser Powder Bed Fusion to Fabricate a Molten Salt-to-Supercritial Carbon Dioxide Heat Exchanger for Concentrating Solar Power

Advances in manufacturing technologies and materials are crucial to the commercial deployment of energy technologies. We present the case of concentrating solar power (CSP) with molten salt (MS) thermal storage, where low-cost, high-efficiency heat exchangers (HXs) are needed to achieve cost competitiveness. Here, the materials required to tolerate the extreme operating conditions in CSP systems make it difficult or infeasible to produce them using conventional manufacturing processes. Although it is technically possible to produce HXs with adequate performance using additive manufacturing, specifically laser powder bed fusion (LPBF), here we assess whether doing so is cost-effective. We describe a process-based cost model (PBCM) to estimate the cost of fabricating a MS-to-supercritical carbon dioxide HX using LPBF. The PBCM is designed to identify modifications to designs, process choices, and manufacturing innovations that have the greatest effect on manufacturing cost. Our PBCM identified HX design and LPBF process modifications that reduced projected HX cost from $\$750$ per kilo-Watt thermal (kW-th) ($\$8$ /cm 3 ) to $\$350$ /kW-th ($\$6/$ cm 3 ) using currently available LPBF technology, and down to $\$220$ /kW-th ($\$4$ /cm 3 ) with improvements in LPBF technology that are likely to be achieved in the near term. The PBCM also informed a redesign of the HX design that reduced projected costs to $\$140$ –160/kW-th ($\$3$ /cm 3 ).

36 MATERIALS SCIENCE↗

Capturing the ground state of uranium dioxide from first principles: Crystal distortion, magnetic structure, and phonons

Uranium dioxide (UO 2 ) remains a formidable challenge for first-principles approaches due to the complex interplay among spin-orbit coupling, Mott physics, magnetic ordering, and crystal distortions. Here we use DFT+U to explore UO 2 at zero temperature, incorporating all the aforementioned phenomena. The technical challenge is to navigate the many metastable electronic states produced by DFT+U, which is accomplished using f-orbital occupation matrix control to search for the ground state. We restrict our search to the high-symmetry ferromagnetic phase, including spin-orbit coupling, which produces a previously unreported occupation matrix. This newfound occupation matrix is then used as an initialization to explore the broken symmetry phases. We find the oxygen cage distortion of the 3k antiferromagnetic state to be in excellent agreement with experiments, and both the spin-orbit coupling and the Hubbard U are critical ingredients. Further, we demonstrate that only select phonon modes have a strong dependence on the Hubbard U, whereas magnetic ordering has only a small influence overall. We perform measurements of the phonon dispersion curves using inelastic neutron scattering, and our calculations show good agreement when using reasonable values of U. The quantitative success of DFT+U warrants exploration of thermal transport and other observables within this level of theory.

36 MATERIALS SCIENCE↗

Abrupt permafrost thaw drives spatially heterogeneous soil moisture and carbon dioxide fluxes in upland tundra

Permafrost thaw causes the seasonally thawed active layer to deepen, causing the Arctic to shift toward carbon release as soil organic matter becomes susceptible to decomposition. Ground subsidence initiated by ice loss can cause these soils to collapse abruptly, rapidly shifting soil moisture as microtopography changes and also accelerating carbon and nutrient mobilization. The uncertainty of soil moisture trajectories during thaw makes it difficult to predict the role of abrupt thaw in suppressing or exacerbating carbon losses. Here, in this study, we investigated the role of shifting soil moisture conditions on carbon dioxide fluxes during a 13-year permafrost warming experiment that exhibited abrupt thaw. Warming deepened the active layer differentially across treatments, leading to variable rates of subsidence and formation of thermokarst depressions. In turn, differential subsidence caused a gradient of moisture conditions, with some plots becoming consistently inundated with water within thermokarst depressions and others exhibiting generally dry, but more variable soil moisture conditions outside of thermokarst depressions. Experimentally induced permafrost thaw initially drove increasing rates of growing season gross primary productivity (GPP), ecosystem respiration (R eco ), and net ecosystem exchange (NEE) (higher carbon uptake), but the formation of thermokarst depressions began to reverse this trend with a high level of spatial heterogeneity. Plots that subsided at the slowest rate stayed relatively dry and supported higher CO 2 fluxes throughout the 13-year experiment, while plots that subsided very rapidly into the center of a thermokarst feature became consistently wet and experienced a rapid decline in growing season GPP, R eco , and NEE (lower carbon uptake or carbon release). These findings indicate that Earth system models, which do not simulate subsidence and often predict drier active layer conditions, likely overestimate net growing season carbon uptake in abruptly thawing landscapes.

54 ENVIRONMENTAL SCIENCES↗

A Scalable Compact Additively Manufactured Molten Salt to Supercritical Carbon Dioxide Heat Exchanger for Solar Thermal Application

Design of an additively manufactured molten salt (MS) to supercritical carbon dioxide (sCO 2 ) primary heat exchanger (PHE) for solar thermal power generation is presented. The PHE is designed to handle temperatures up to 720 °C on the MS side and an internal pressure of 200 bar on the sCO 2 side. In the core, MS flows through a three-dimensional periodic lattice network, while sCO 2 flows within pin arrays. The design includes integrated sCO 2 headers located within the MS flow, allowing for a counterflow design of the PHE. The sCO 2 headers are configured to enable uniform flow distribution into each sCO 2 plate while withstanding an internal pressure of 200 bar and minimizing obstruction to the flow of MS around it. The structural integrity of the design is verified on additively manufactured (AM) 316 stainless steel sub-scale specimens. An experimentally validated, correlation-based sectional PHE core thermofluidic model is developed to study the impact of flow and geometrical parameters on the PHE performance, with varied parameters including the mass flowrate, surface roughness, and PHE dimensions. A process-based cost model is used to determine the impact of parameter variation on build cost. The model results show that a heat exchanger with a power density of 18.6 MW/m 3 (including sCO 2 header volume) and effectiveness of 0.88 can be achieved at a heat capacity rate ratio of 0.8. As a result, the impact of design and AM machine parameters on the cost of the PHE are assessed.

14 SOLAR ENERGY↗

Simulation of Methane Oxycombustion in Supercritical Carbon Dioxide

The Allam-Fetvedt Cycle (AFC) offers the potential for electricity generation with minimal or even negative carbon emissions by using oxycombustion in supercritical carbon dioxide (sCO2). Because of the extreme high temperatures and pressures encountered in these systems, simulation of oxycombustion requires use of a complex equation of state such as the modified Soave-Redlich-Kwong (SRK) equation, coupled with equally complex correlations for transport properties. The current work simulates a model combustor using both an ideal gas equation of state and the SRK equation of state. The model combustor features a jet of CH4 mixing with and reacting with O2 in the sCO2 ambient. Two jet configurations are considered: one of pure CH4, and one of CH4 mixed with sCO2. Comparison of results shows that key output properties such as combustor temperature and flow distribution are impacted by the choice of equations of state. Inspection of simulation results shows that mixing and reaction rates, as well as the uniformity of the flow, are impacted by the choice of equation of state. These results show that even though use of a complex equation of state greatly increases the computational costs of these simulations, it is critical to accurately capturing the physics of these systems.

computational fluid dynamics↗

Enhanced Carbon Dioxide Uptake in Drilled Hollow Core Fibers for Raman Spectroscopy

Fiber-based Raman spectroscopy enhances the Raman signal by maximizing the overlap of the optical field and the gas species. However, filling the hollow-core fiber (HCF) with gas requires time that is dependent on the fiber core diameter, fiber length, and pressure of the gas. At ambient pressure, the fiber gas uptake is driven by diffusion into the fiber ends, severely limiting the response time of the system. By laser drilling access holes to the core along the length of the fiber, the uptake time of the gas is reduced, improving the system response time. In this work, we study the carbon dioxide (CO 2 ) sensor dynamics based on Raman signal intensity generated in HCFs. The signal intensity versus gas concentration is characterized by controlling the CO 2 concentration in the surrounding environment of the fiber. Next, we characterize the gas uptake time in HCFs as a function of fiber length. Finally, we optimize the access hole configuration along the fiber, demonstrating reduced sensor uptake time by a factor of three.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗