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At least 523 records · Page 29

Determining the oxidation behavior of matrix graphite

This work presents the oxidation behavior of matrix graphite in air. Matrix graphite, graphite powder/flakes bonded by a small amount of non-graphitic carbon, surrounds coated fuel particles in order to form cylindrical fuel compacts (in prismatic core designs) or spheres (in pebble-bed reactor designs). This work focuses on oxidation tests conducted on two matrix graphite materials, one provided by Kairos Power and the other A3 matrix graphite. Some of the tests followed American Society for Testing and Materials (ASTM) oxidation testing standards using a vertical furnace system and others were performed in a thermogravimetric analyzer (TGA). It was determined that, at temperatures of 450 °C–700 °C, the oxidation rate of the Kairos matrix graphite follows the Arrhenius equation. In comparison with A3 matrix graphite, the Kairos matrix graphite shows better oxidation resistance at high temperatures (≥550 °C), but also a higher oxidation rate at low temperatures. Both the A3 matrix graphite and the Kairos matrix graphite materials may experience preferential oxidation of the partially graphitized binder. An oxygen penetration gradient was also observed when using the three characterization methods (i.e., optical microscope, x-ray tomography [XCT], and density profile by the lathe) enlisted in this research. In conclusion, the oxygen penetration depth increases with decreasing isothermal oxidation temperature, while the center of the oxidized samples (10% weight loss) remains almost untouched even at 500 °C.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Deformation band corrosion as a result of applied stress and cold-work in 304 stainless steel in simulated pressurized water reactor primary water conditions

Stainless steels like 304SS are commonly used in pressurized water reactor primary water environments due to their excellent resistance to stress corrosion cracking (SCC). However, SCC susceptibility has been observed in cold-worked 304SS. Cold-rolling introduces a high density of defects, such as deformation bands or dislocations, into the microstructure; applied stress, even if macroscopically below the yield stress, can result in regions with high localized stresses. Cold-worked and non-cold-worked samples were exposed to 360 °C simulated PWR primary water for 1500 h with and without active loading. Corrosion susceptibility of dislocations and deformation bands induced by cold-rolling and/or applied stress was studied using high-resolution (analytical) transmission electron microscopy. Deformation bands were generated in all specimens examined in the study. Penetrative oxidation was observed in some deformation bands in each specimen. The depth of penetrative deformation band oxidation frequently exceeded the depth of grain boundary oxidation in all specimens. However, deformation band oxides generally were narrowly confined to the deformation band plane. Highly Ni-rich regions were observed beyond all oxidation fronts. Surface oxides were thicker in the specimens exposed under active loading. In conclusion, the implications of these findings at surfaces for deformation bands intersecting stress corrosion crack paths are discussed.

EFTEM↗

Controlling dendrite propagation in solid-state batteries with engineered stress

Metal-dendrite penetration is a mode of electrolyte failure that threatens the viability of metal-anode-based solid-state batteries. Whether dendrites are driven by mechanical failure or electrochemical degradation of solid electrolytes remains an open question. If internal mechanical forces drive failure, superimposing a compressive load that counters internal stress may mitigate dendrite penetration. Here, we investigate this hypothesis by dynamically applying mechanical loads to growing dendrites in Li 6.6 La 3 Zr 1.6 Ta 0.4 O 12 solid electrolytes. Operando microscopy reveals marked deflection in the dendrite growth trajectory at the onset of compressive loading. For sufficient loading, this deflection averts cell failure. Using fracture mechanics, we quantify the impact of stack pressure and in-plane stresses on dendrite trajectory, chart the residual stresses required to prevent short-circuit failure, and propose design approaches to achieve such stresses. For the materials studied here, we show that dendrite propagation is dictated by electrolyte fracture, with electronic leakage playing a negligible role.

25 ENERGY STORAGE↗

The value of fusion energy to a decarbonized United States electric grid

Fusion could be a part of future decarbonized electricity systems, but it will need to compete with other technologies. In particular, pulsed tokamak plants have a unique operational mode, and evaluating which characteristics make them economically competitive can help select between design pathways. Using a capacity expansion and operations model, here we determined cost thresholds for pulsed tokamaks to reach a range of penetration levels in a future decarbonized US Eastern Interconnection. The required capital cost to reach a fusion capacity of 100 GW varied from $2,700 to $7,500 kW -1 , and the equilibrium penetration increases rapidly with decreasing cost. The value per unit power capacity depends on the variable operational cost and on the cost of its competition, particularly fission, much more than on the pulse cycle parameters. These findings can therefore provide initial cost targets for fusion more generally in the United States.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The Effect of Cell Geometry and Trigger Method on the Risks Associated with Thermal Runaway of Lithium-Ion Batteries

Consideration of thermal runaway heat output variability is paramount for the development of safe lithium-ion battery assemblies. This study utilizes data gathered from fractional thermal runaway calorimetry (FTRC) experiments to conduct a comparative analysis of thermal runaway heat output for three cell formats (18650, 21700, and 33600) as a function of trigger method (heaters, internal short-circuiting device, and nail penetration). The analysis is based on comparisons for the calculated total energy yield, fractional energy yield, heat rate, and heat flux. This study reveals that nail penetration tends to result in higher thermal runaway heat output for larger cells (21700 & 33600); these experiments also tended to result in higher fractions of the total energy being released through the cell body. The smaller cells (18650) did not appear to have significant variation in heat output as a function of trigger method. This finding suggests that, for this cell type, worst-case scenario heat output could be achievable in assembly level testing regardless of the utilized trigger method. This study also demonstrates successful translation of FTRC results, as recorded in the Battery Failure Databank, into meaningful analysis that breaks down the influence of specific conditions on thermal runaway heat output.

calorimetry↗

Proper orthogonal decomposition based reduced-order modeling of flux-Limited gray thermal radiation

Here, in this work, a proper orthogonal decomposition (POD) based reduced-order model (ROM) is developed to solve gray, flux-limited thermal radiation diffusion. We focus on the variable opacity radiation penetration benchmark posed by Olson, Auer, and Hall. The T -3 relationship for opacity in conjunction with high-temperature radiation penetrating an initially cold material produces a strong thermal radiation shock. This class of problems is particularly challenging for standard POD-based reduced-order modeling due to the nonlinearities presented by 1) the T 4 source term, and 2) flux-limited diffusion operator. To address these challenges and develop a cost competitive ROM, we employ a “hyper-reduction” technique through discrete empirical interpolation (DEIM) and allow for adaptive reduced-order projections through principal interval decomposition (PID). Performance of the proposed methodology is quantified by comparing the cost savings and accuracy relative to a full-order computation. Reference solutions and snapshot data are obtained through a full-order calculation performed by the University of Chicago maintained astrophysics code, FLASH. For consistency and potential extensibility, the developed ROM is also implemented in FLASH. We find that in the initialization regime, where the thermal radiation wave is initially created by the warming of the material, this class of problems is highly reducible and suitable for POD-based ROMs. However, the strong convective nature of the wave propagation regime is less reducible and more challenging to create an efficient ROM.

42 ENGINEERING↗

Enhancing membrane performance for CO 2 capture from flue gas with ultrahigh MW polyvinylamine

Membranes for post-combustion CO 2 capture are required to have a high CO 2 permeance due to the limited driving force. For facilitated transport membranes synthesized with polyvinylamine (PVAm), a defect-free selective layer of <200 nm is usually required to render sufficient permeance with high CO 2 /N 2 selectivity. In order to meet such a demand through the knife-coating process, the coating solution needs to have a high viscosity at a relatively low concentration to minimize its penetration into the substrate. The demand was met by synthesizing PVAm with an ultrahigh molecular weight (MW) via inverse emulsion polymerization (IEP) in this study. Compared to solution polymerization, IEP isolates the reaction in inverse micelles suspended in a continuous organic phase, which allows excellent dissipation of the heat generated by the reaction and reduces gel formation drastically. The polymerization parameters, including monomer concentration, initiator concentration, and reaction temperature, were investigated to obtain the optimal MW of PVAm for membrane performance. As compared to solution polymerization, IEP enhanced the MW of PVAm from 1.2 to 12.7 MDa, which minimized the penetration of the coating solution into the substrate and hence the extra mass transfer resistance. The effect of MW and degree of hydrolysis of PVAm on the membrane transport properties were studied. Furthermore, by employing PVAm with a MW of 12.7 MDa to strengthen the polymer matrix, the loading of piperazine glycinate in the membrane was increased up to 85 wt.%. In conclusion, the resultant membrane achieved a CO 2 permeance of 839 GPU and a CO 2 /N 2 selectivity of 161 at the typical flue gas temperature of 57°C.

20 FOSSIL-FUELED POWER PLANTS↗

Corrosion analysis of Al-Ce-Ni and Al-Cu-Ce cast alloys in dilute boric acid at room and elevated temperatures

Two Al-Ce-Ni cast alloys, and an Al-Cu-Ce cast alloy, as candidate wet storage materials for spent nuclear fuels, were tested in 0.23 wt% H 3 BO 3 solution to assess the alloy corrosion resistance. Electrochemical and gravimetric corrosion data suggest that the three Al alloys are unlikely to undergo any severe corrosion in dilute H 3 BO 3 at or below 50 °C. Post-exposure characterization of the three Al alloys, including scanning and transmission electron microscopy and electron dispersive spectroscopy, revealed a corrosion product layer, mostly Al 2 O 3 , on the exposed surface and local penetration of oxygen into the alloy matrix. The degree of oxide layer growth and oxygen penetration is greater at 80 °C than the temperature at/below 50 °C. The Al-Cu-Ce alloy is considered less corrosion resistant than the other two alloys studied.

Al-Ce alloy↗

The nanoscale distribution of copper and its influence on charge collection in CdTe solar cells

For decades, Cu has been the primary dopant in CdTe photovoltaic absorbers. Typically, Cu acceptor concentrations in these devices are on the order of 1 1014 cm-3, which has made it notoriously difficult to directly correlate nanoscale Cu distributions to the local charge transport properties of these devices. To measure and correlate these properties, measurement techniques require high sensitivity to elemental concentration, large penetration depth, and operando compatibility. Techniques such as secondary-ion mass spectroscopy and X-ray energy dispersive spectroscopy are widely adopted to measure Cu concentrations, but they are limited by penetration depth, sensitivity, or spatial resolution. Additionally, they lack the operando capabilities required to correlate one-to-one Cu concentrations to electrical performance. In this work, correlative X-ray microscopy is used to investigate the spatial distribution of Cu and its impact on charge collection through the depth and breadth of CdTe photovoltaic devices. Plan-view, nanoscale X-ray fluorescence maps clearly demonstrate the spatial segregation of copper around regions thought to be CdTe grain boundaries. Complementary cross-section imaging unveils the transition of the maximum charge-collection efficiency from the ZnTe-CdTe interface to the CdS-CdTe interface as a function of Cu incorporation. The copper concentration through the depth of the CdTe layer is characterized by slow and fast diffusion components, and cross-section charge-transport modeling shows that the experimentally obtained charge collection can be explained by the modeled acceptor distribution through the depth of the CdTe layer.

14 SOLAR ENERGY↗

Reserve and energy scarcity pricing in United States power markets: A comparative review of principles and practices

Here, errors in forecasting load and renewable-based generation in restructured power systems mean that independent system operators (ISOs) must procure sufficient operating reserves to keep the real-time operation of the system reliable and secure. But when procured reserves turn out to be insufficient in real-time due to the lack of resource capacity or ramp capability, operators often set higher prices for reserves and energy to encourage more supply, and to motivate consumers to decrease usage or shift it to other times. This procedure, which is called scarcity or shortage pricing, is a core feature of U.S. electricity markets. It is receiving increased attention from market designers and stakeholders because scarcity will become more important for spot price formation in the future with the increased penetration of zero-marginal cost renewables, and the shrinking role of fuel costs in setting prices. Scarcity pricing is implemented in various ways by different ISOs. These differences have practical implications for the level of prices and incentives for investment, operations, and demand modification. In this paper, general approaches and specific calculation procedures for reserve and energy scarcity pricing practices and calculations across the seven ISO-based U.S. power markets are reviewed and compared. A consistent terminology is used to facilitate the comparison. Current scarcity pricing practices are grouped into three approaches: (1) imposing an adder after the spot market is run; (2) including stepwise demand curves within market clearing procedures for non-contingency reserve products (e.g., the novel flexiramp product), which tends to yield longer right tails for energy scarcity premium curves; and (3) having stepwise demand curves for traditional contingency reserve products only, which results in shorter right tails in energy scarcity curves. A generic numerical example is presented to highlight the large practical differences among the reserve scarcity pricing approaches and specific implementations. To further investigate factors that contribute the most to demand curves differences among ISOs, a sensitivity analysis is performed. This analysis shows that the largest source of differences among the curves is the scarcity prices assumed in the case of severe scarcity, while the number of steps used and whether flexiramp is considered also yields important differences in scarcity prices. As renewable penetration increases, it will become increasingly crucial to employ administrative demand curves so that spot prices more effectively motivate supply and demand adjustments exactly when and where they are needed. This study shows that the different assumptions yield very different scarcity premiums for reserves and energy, and are likely to provide divergent incentives for resources to respond to shortages. It is concluded that to promote market efficiency, a reserve shortage demand curve should have at least three features: inclusion of the marginal value of reserve products at each shortage level, consideration of the magnitude and probability of supply contingencies, and avoidance of abrupt price discontinuities that can cause excessively volatile market outcomes.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Investigation of post-injection strategies for diesel engine Catalyst Heating Operation using a vapor-liquid-equilibrium-based spray model

Most multidimensional engine simulations spend much time solving for non-equilibrium spray dynamics (atomization, collision, vaporization). However, their accuracy is limited by significant grid dependency, and the need for extensive calibration. This is critical for modeling cold-start diesel fuel post injections, which occur at low temperatures and pressures, far from typical model validation ranges. At the same time, resolving micron-scale spray phenomena would render full Eulerian multiphase calculations prohibitive. In this study, an improved phase equilibrium based approach was implemented and assessed for simulating diesel catalyst heating operation strategies. A phase equilibrium solver based on the model by Yue and Reitz [1] was implemented: a fully multiphase CFD solver is employed with an engineering-size engine grid, and fuel injection is modeled using the standard Lagrangian parcels approach. Mass and energy from the liquid parcels are released to the Eulerian multiphase mixture according to an equilibrium-based liquid jet model. An improved phase equilibrium solver was developed to handle large real-gas mixtures such as those from accurate chemical kinetics mechanisms. The liquid-jet model was improved such that momentum transfer to the Eulerian solver better reproduces the physical spray jet structure. Validation of liquid/vapor penetration predictions showed that the model yields accurate results with very limited tuning and low sensitivity to the few calibration constants. In-cylinder simulations of diesel catalyst heating operation strategies showed that capturing spray structure is paramount when short, transient injection pulses and low temperatures are present. Furthermore, the EP model provides improved predictions of post-injection spray structure and ignitability, while conventional spray modeling does not capture the increase of liquid penetration during the expansion stroke. Finally, the only important EP model calibration constant, Cliq, does not affect momentum transfer, but it changes the local charge cooling distribution through the local energy transfer, which makes it candidate to additional research. The results confirm that non-equilibrium spray processes do not need to be resolved in engineering simulations of high-pressure diesel sprays.

42 ENGINEERING↗

Energy and mobility impacts of connected autonomous vehicles with co-optimization of speed and powertrain on mixed vehicle platoons

Intersections are known to be traffic bottlenecks where a significant amount of energy consumption could be caused due to deceleration/acceleration in the presence of red signals. With an increased level of connectivity and automation of intelligent transportation systems, connected autonomous vehicles (CAVs) are expected to be able to proactively adjust their driving strategies subject to constraints imposed by the predicted future traffic. As a result, many potential benefits can be achieved, such as improved energy efficiency, enhanced traffic safety, among many others. Notably, the way CAVs are controlled affects the following legacy vehicles (LVs) due to complex traffic dynamics. Here, we are particularly interested in studying the energy and mobility impact of CAVs with an improved traffic prediction method on mixed vehicle platoons at various market penetration rates. Leveraging traffic prediction, CAVs are controlled with co-optimization of their speed and gear position. Specifically, a traffic prediction framework in a rolling horizon fashion is employed based upon a modified Payne–Whitham (PW) model capable of handling mixed traffic consisting of CAVs and LVs. The prediction error of the modified PW model is reduced by 53.62% compared to that of the standard PW model under test scenarios. According to the predicted traffic conditions, speed and gear position of CAVs are co-optimized with the primary goal of minimizing energy consumption when driving on a signalized arterial. The energy benefits achieved by CAVs and the impact of CAVs on LVs behind are studied comprehensively for mixed vehicle platoons. The lead LV follows a real-world speed profile collected on TH-55 in Minnesota. Numerical results show that energy benefits achieved by the vehicle platoon range from 2% to 16%, and a 1% to 5% reduction in travel time for LVs behind CAVs is also observed, at different penetration rates of CAVs in various traffic scenarios. Furthermore, it is observed that CAVs using the proposed eco-driving approach appear to have a positive impact on the LVs behind in terms of energy consumption, regardless of the driving styles of the LVs ahead.

33 ADVANCED PROPULSION SYSTEMS↗

Pore-resolved investigation of turbulent open channel flow over a randomly packed permeable sediment bed

Pore-resolved direct numerical simulations are performed to investigate the interactions between streamflow turbulence and groundwater flow through a randomly packed porous sediment bed for three permeability Reynolds numbers, Re K = 2.56 , 5.17 and 8.94, representative of natural stream or river systems. Time–space averaging is used to quantify the Reynolds stress, form-induced stress, mean flow and shear penetration depths, and mixing length at the sediment–water interface (SWI). Here, the mean flow and shear penetration depths increase with Re K and are found to be nonlinear functions of non-dimensional permeability. The peaks and significant values of the Reynolds stresses, form-induced stresses, and pressure variations are shown to occur in the top layer of the bed, which is also confirmed by conducting simulations of just the top layer as roughness elements over an impermeable wall. The probability distribution functions (p.d.f.s) of normalized local bed stress are found to collapse for all Reynolds numbers, and their root-mean-square fluctuations are assumed to follow logarithmic correlations. The fluctuations in local bed stress and resultant drag and lift forces on sediment grains are mainly a result of the top layer; their p.d.f.s are symmetric with heavy tails, and can be well represented by a non-Gaussian model fit. The bed stress statistics and the pressure data at the SWI potentially can be used in providing better boundary conditions in modelling of incipient motion and reach-scale transport in the hyporheic zone.

turbulence simulation↗

Potential Adoption and Benefits of Co-Optimized Multimode Engines and Fuels for U.S. Light-Duty Vehicles

Exploring a diverse portfolio of technologies for decarbonization is crucial to understanding the potential impacts of different technological solutions and their associated environmental implications. Using high-octane, high-sensitivity biofuel blends in co-optimized multimode engines can increase engine efficiency and reduce vehicle emissions. Here, the multimode engine research focuses on the benefits of light-duty vehicle engines, which can operate in multiple modes depending on the vehicle's load. Low-temperature combustion can improve efficiency and reduce emissions (such as those from oxides of nitrogen and particulate matter) during low-load operation, while spark ignition performance is maintained in high-load operation. These advanced engines can be optimized to run on blends of biobased fuels. This analysis models scenarios for potential market adoption of co-optimized multimode vehicles fueled by three different bioblendstocks: ethanol, isopropanol, and isobutanol. An integrated modeling approach is used to forecast the energy and environmental impacts of the deployment of co-optimized multimode vehicles and fuels in the light-duty sector over the 2020-to-2050 time horizon. The multidisciplinary approach combines vehicle sales modeling, system dynamics modeling of the biorefining industry, and life cycle assessment to estimate the emissions and energy benefits. The models consider market forces such as consumer preferences for vehicle attributes, biofuel supply and demand dynamics subject to biorefinery capacity build-out and bioresource constraints, and forecasted changes to the U.S. bulk energy system over time. Market adoption of co-optimized vehicles is evaluated across a wide parameter space for incremental vehicle cost and engine efficiency improvement. This analysis reveals that the deployment of co-optimized multimode fuels and vehicles results in up to a 5% reduction in annual sector-wide life cycle greenhouse gas (GHG) emissions by 2050, relative to a business-as-usual scenario, but is also indicates environmental trade-offs, such as higher life cycle water-use. Emission benefits could potentially increase beyond 2050, as the new technologies penetrate the market and gain a foothold. Results also show that, under certain circumstances, vehicles with engines co-optimized for use with high-octane, high-sensitivity biofuel blends can be cost-competitive with conventional gasoline, while reducing GHG emissions. Our modeling results indicate that co-optimized multimode fuels and engines can be strategically leveraged in tandem with electrification to decarbonize the light-duty sector. Co-optimized vehicles could play a role in the early years of the time horizon, while electric vehicles (EVs) could become more competitive in the later years, highlighting the complementary benefits of these technologies for GHG reductions.

Oke, Doris↗

Microsized Pore Structure Determination in EPDM Rubbers Using High-Pressure 129 Xe NMR Techniques

Microsized pore parameters, such as pore size and distance between pores in a series of model EPDM rubbers, were determined in situ under the pressure of 500 psi using 129 Xe nuclear magnetic resonance (NMR) techniques: spin–lattice (T 1 ) and spin–spin (T 2 ) relaxation measurements, pulsed-field gradient (PFG) NMR, and two-dimensional exchange spectroscopy (2D EXSY). The T 1 /T 2 (>>1) ratio for the xenon confined in the pores is larger than that for nonconfined free xenon. This suggests that almost the entire pore surface interacts with xenon atoms like a closed pore. While these pores still connect each other through very narrow diffusion/exchange channels, it is possible to observe the echo decay in PFG-NMR and cross-peaks in 2D EXSY. The results show that both diffusion (D pore ≈ 2.1 × 10 –10 m 2 /s) and exchange (exchange rate, τ exch = a few tens of milliseconds) of xenon between a pore within the material and outer surface are prolonged. The exchange distances (l), which correspond to the xenon gas penetration depth, were estimated to be 70–100 μm based on the measured diffusion coefficients and exchange rate (1/τ exch ). NMR diffraction analysis reveals that pore size (a) and pore distance (b) are on the order of magnitude of micrometers and tens of micrometers, while the diffusion coefficients of xenon gas in the diffusion channels (D eff ) are about 10 –8 m 2 /s. Overall, this study suggests that the pores with a few micrometers connected through very narrow flowing channels with the length of several tens of micrometers are developed 70 to 100 μm below the rubber surface. Furthermore, the overall steady-state diffusion of xenon is slower, approximately 2 orders of magnitudes, than the diffusion in the channel between the pores. Finally, the pore and exchange distances correlated with the composition of rubbers showed that the properties of EPDM rubber as a high-pressure gas barrier could be improved by reducing the size of cracks and the depth of gas penetration by the addition of both carbon black and silica fillers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structure, Dynamics, and Hydrogen Transport in Amorphous Polymers: An Analysis of the Interplay between Free Volume Element Distribution and Local Segmental Dynamics from Molecular Dynamics Simulations

Polymers are attractive membrane materials owing to their mechanical robustness and relatively inexpensive fabrication. An important indicator of membrane performance are free volume elements (FVE): microporous void spaces created by the inefficient packing of bulky groups along the polymer chain. FVEs tend to degrade over time, as polymer chains reorganize irreversibly. While it is widely accepted that polymer flexibility has an impact on membrane transport properties, the molecular nature of this impact is still not well understood. By the establishment of a correlation between local chain dynamics and the distribution of free volume elements (FVEs), penetrant transport can be regulated more efficiently in amorphous polymer membranes. In this work, we implement all-atom molecular dynamics (MD) simulations to explore the relationship between chain dynamics and free volume in three polymers with different levels of backbone flexibility: polymethylpentene (PMP), polystyrene (PS), and HAB-6FDA thermally rearranged polymer (TRP). We construct these polymers at different temperatures and examine how temperature impacts the FVE distribution and segmental mobility. Our analysis shows that chain segments near FVEs have higher mobility compared with the atoms in the bulk; the extent of this difference increases with chain flexibility. Increasing the chain flexibility by increasing the temperature results in a broader FVE distribution. Rigid polymers such as TRP show the most robust FVE distribution and are not significantly affected by the temperature change. To capture penetrant diffusion through the polymer matrix, hydrogen is inserted and the diffusion is measured at different temperatures; hydrogen mobility is influenced by the FVE structure and overall mobility of polymer chains. Lastly, at low temperatures, hydrogen mobility is influenced by void distribution, while at high temperatures, polymer dynamics dictate hydrogen transport.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗