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NASA NTRS1986

Kinetics and mechanism of the IO + IO reaction

The flash photolysis-absorption technique has been used to measure the rate constant for the reaction IO + IO over the temperature range 250-373 K and pressure range 20-700 torr of N2. The rate constant for the overall reaction was found to be independent of pressure and equal to 1.73 x 10 to the -12th exp (1020 + or - 200)/T cu cm/molecule s. Branching ratios for the reaction channels forming 2I + O2, I2 + O2, and I2O2, were found to be pressure dependent, with the I2 channel accounting for less than 5 percent of the total reaction over the observed pressure range. A stable reaction product was observed between 230 and 300 nm which was formed on a long time scale compared to IO disappearance. The rate constant for the reaction I + O3 + yields to IO + O2 was measured at 298 K and found to be (9.5 + or - 1.5) x 10 to the -13th cu cm/molecule s.

Sander, S. P.↗

NASA NTRS1975

Proton transfer reactions from H3/+/ ions to N2, O2, and CO molecules

The rate constants for proton transfer from H3(+) ions to N2, O2, and CO have been measured as function of hydrogen-buffer-gas partial pressure. The rate constant for proton transfer from H3(+) to N2 shows a very large pressure dependence, increasing from 1.0 by 10 to the -9th power cu cm/s at low H2 partial pressures to 1.7 by 10 to the -9th power cu cm/s at high H2 partial pressures. The rate constants for proton transfer from H3(+) to O2 and CO are constant with partial pressure of H2. The roles of excess vibrational energy in H3(+) ions and of equilibrium between forward and back reactions are discussed. Back reaction is observed only for the reaction of H3(+) ions with O2, and an equilibrium constant of 2.0 (plus or minus 0.4) at 298 K has been determined. From these data, the proton affinity of O2 is deduced to be 0.47 (plus or minus 0.11) kcal/mole higher than that of H2.

Kim, J. K.↗

NASA NTRS1993

Rates of hydroxyl radical reactions with some HFCs

Relative rate constants for OH reactions with some HFCs have been determined at 298 K by a technique which measures the loss of HFC greater than OH. The following ratios were determine: k(152a)/k(CH4) = 5.2 +/- 0.5, k(CH4)/k(125) = 3.9 +/- 0.5, k(CH4)/k(134a) = 2.1 +/- 0.2, k(134a)/k(125) = 2.0 +/- 0.2, and k(C2H6)/k(152a) = 6.2 +/- 1.0. These results are in good agreement with literature values for the absolute rate constants except for HFC 134a, where a slower rate constant is indicated.

Demore, William B.↗

DOE OSTI2020

Formation of phenanthrene via H–assisted isomerization of 2–ethynylbiphenyl produced in the reaction of phenyl with phenylacetylene

Model chemistry G3(MP2,CC)//B3LYP/6–311G(d,p) calculations of the potential energy surface for the reaction of phenyl radical (C 6 H 5 ) with phenylacetylene (C 8 H 6 ) have been carried out and combined with Rice–Ramsperger–Kassel–Marcus/Master Equation calculations of temperature– and pressure–dependent rate constants. The results showed that the reaction can serve as a viable source for the formation of phenanthrene via an indirect route involving a primary reaction of phenyl addition to the ortho carbon in the ring of phenylacetylene and H elimination producing 2–ethynylbiphenyl followed by secondary H–assisted isomerization of 2–ethynylbiphenyl to phenanthrene. In the secondary reaction, the H atom adds to the α carbon of the ethynyl side chain, then a six–member ring closure takes place followed by aromatization via an H loss. The channel of H addition to the side chain of 2–ethynylbiphenyl appears to be much faster than H addition to the ortho carbon in the ethynyl–substituted ring leading back to the initial C 6 H 5 + C 8 H 6 reactants. Rate constants for the primary C 6 H 5 + C 8 H 6 ⇌2–ethynylbiphenyl (p1) + H and secondary p1 + H⇌phenanthrene (p2) + H reactions have been computed in the temperature range of 500–2500 K at pressures of 30 Torr, 1, 10, and 100 atm and fitted to modified Arrhenius expressions. Here, the suggested kinetic scheme and rate constants are proposed as a prototype for the modeling of the growth of polycyclic aromatic hydrocarbons via the phenyl addition–dehydrocyclization (PAC) mechanism involving an addition of a PAH radical to an ethynyl–substituted PAH molecule.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Conversion of acenaphthalene to phenalene via methylation: A theoretical study

Ab initio calculations of the C 13 H 10 and C 13 H 9 potential energy surfaces related to the reaction of 1-acenaphthyl and methyl radicals and secondary isomerization of C 13 H 9 primary radical products have been performed at the chemically accurate G3(MP2,CC)//B3LYP/6-311G** level of theory to unravel the mechanism of conversion of acenaphthalene to phenalene or phenalenyl radical + H. The computed energetics and molecular parameters were utilized in Rice-Ramsperger-Kassel-Marcus Master Equation (RRKM-ME) calculations of reaction rate constants and relative product yields. The 1-acenaphthyl + CH 3 reaction is predicted to proceed by a fast radical-radical recombination mechanism and to predominantly produce collisionally stabilized 1-methylacenaphthalene B1 or a C 13 H 9 benzylic radical A1 + H with exothermicities of 106.8 and 25.2 kcal/mol, respectively. The A1 + H channel is preferable at higher temperatures, whereas the stabilization of 1-methylacenaphthalene is favored at higher pressures. The radical A1 can nearly irreversibly interconvert to phenalenyl radical AP via a 22.7 kcal/mol exothermic isomerization process involving formal insertion of the CH 2 group into a C-C bond of the five-member ring leading to the expansion of this ring to a six-member ring. The rate constants for the H addition reaction to phenalenyl radical to form phenalene and the reverse H loss from phenalene were also computed and the strength of the weakest C-H bond in the CH 2 group of phenalene is evaluated as 62.2 kcal/mol. The analysis of the reaction kinetics allowed us to deduce a mechanism for the conversion of 1-acenaphthyl radical to phenalene or phenalenyl radical + H via methylation involving the formation of A1 via a well-skipping channel or stabilization and dissociation of (or H abstraction from) B1 followed by isomerization of A1 to phenalenyl AP, which can add an H atom producing phenalene. As a result, rate constants for the significant elementary reactions are fitted to modified Arrhenius expressions and are proposed for kinetic modeling of the expansion of a five-member ring on a zigzag edge of PAH to a six-member ring by methylation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

A framework for testing soil carbon dynamics post land-use transition in a multisector dynamics model

Soil carbon plays a crucial role in the global carbon cycle. Changes in land use can determine whether carbon is stored or is emitted into the atmosphere as carbon dioxide, which has broad implications for the human and Earth systems. These feedbacks to the carbon cycle and their socio-economic drivers are modelled by many global multisector dynamics models to project future possibilities for the human-Earth system. One notable model of this class is the Global Change Analysis Model (GCAM), which uses a simplified process to model soil organic carbon (SOC) content after land-use transition across 384 land units. While the current GCAM soil carbon framework is based on scientific principles, it has not been tested against experimental data. This work examines rates of SOC change from GCAM input data. Specifically, first order rate constants derived from model inputs were compared to values from two syntheses to assess GCAM’s accuracy. Welch’s t-tests and linear models were used to determine if rate constants were consistent across all tested geographical areas and land-use transition types. While we found that there was general agreement on the direction and magnitude (i.e., rate) of SOC change, the rate constant derived from GCAM and empirical values differed strongly in a subset of specific instances. These results indicate that GCAM’s current SOC dynamics during land use transition successfully capture broad patterns of change in this critical carbon pool, but should be interpreted with caution at finer spatial scales. One potential cause of these discrepancies is our highly aggregated variable, soil timescale, which could be made more granular to improve accuracy. When using economically rooted multisector dynamics models, such as GCAM, it is critical to understand such model limitations for representing specific Earth system processes.

carbon↗

DOE OSTI2021

High-Entropy Ceramic Coatings: Transformative New Materials for Environmentally-Compatible Thin-Film Insulators against High-T Molten Salts

An emerging new class of promising materials, High-Entropy Ceramics (HECs) or Compositionally-Complex Ceramics (CCCs), have been successfully fabricated in the last three years. This project evaluates HECs/CCCs in the concentrated solar power (CSP) context. In this project, we have identified a couple of simple, and key descriptors governing thermal conductivity in HECs. Size disorder among the cations was found to have a strong influence on the thermal conductivity across multiple systems and throughout a vast compositional space. Since identifying this, we have optimized previous compositions to achieve low thermal conductivities of $k$~$1-1.4Wm{-1}K{-1}$. We have further reduced our selection of promising compositions based on project guidelines and applied a theory that can potentially predict reactivity with molten salts to identify a small set of HECs that are suitable for further molten salt heat transfer media (HTM) stability testing. Many compositions reveal poor resistance to molten chloride salt after being exposed for 24 h compared to the reference structural alloy, Haynes 230. However, after 100 h, a few HECs/CCCs show strong parabolic rate constant effects and provide greater resistance to chloride salt compared to Haynes 230 alloy, which shows more linear kinetics. Postmortem characterization of the microstructure reveals the parabolic rate constant originates from a dense reaction layer form at the interface. This feature is absent in Haynes 230, which only shows grain boundary infiltration. The HECs/CCCs were also put in contact with the metal alloy under Ar for 800 h at 800°C and show negligible interaction. Lastly, parabolic rate constant HECs/CCCs also have low thermal conductivity $(<2 Wm^{-1} K^{-1})$ at 800°C. These specimens satisfy all project requirements and demonstrate their promising application in next-generation CSP.

14 SOLAR ENERGY↗

NASA NTRS1989

Airfoil stall penetration at constant pitch rate and high Reynolds number

The model wing consists of a set of fiberglass panels mounted on a steel spar that spans the 8 ft test section of the UTRC Large Subsonic Wind Tunnel. The first use of this system was to measure surface pressures and flow conditions for a series of constant pitch rate ramps and sinusoidal oscillations a Mach number range, a Reynolds number range, and a pitch angle range. It is concluded that an increased pitch rate causes stall events to be delayed, strengthening of the stall vortex, increase in vortex propagation, and increase in unsteady airloads. The Mach number range causes a supersonic zone near the leading edge, stall vortex to be weaker, and a reduction of unsteady airloads.

Lorber, Peter F.↗

DOE OSTI2022

Master equation study of hydrogen abstraction from HCHO by OH via a chemically activated intermediate

The abstraction reaction of hydrogen from formaldehyde by OH radical plays an important role in formaldehyde oxidation. The reaction involves a bimolecular association to form a chemically activated hydrogen-bonded reaction complex followed by a unimolecular reaction of the complex to generate the products. The reaction rate is usually considered to be pressure-independent by assuming equilibrium between the reactants and the complex. However, our nonequilibrium calculations based on the chemically significant eigenmode of the master equation, carried out with our recently developed TUMME program, indicate that the reaction complex makes the rate constant dependent on pressure at low temperatures (T < 200 K). The calculations include anharmonicity, variational effects, and multi-dimensional tunneling. We find that the reaction rate constant reaches a low-pressure limit at pressures below 10 Torr over the whole investigated temperature range (20–1800 K), which explains why the available low-temperature experiments, which are for pressures below 2 Torr, did not observe the pressure dependence. A new extension of the TUMME master-equation program is used to explore the time evolutions of the concentrations of the OH radical and the complex under pseudo-first-order conditions. The time-dependent evolution of the concentrations of the complex at a low temperature provide direct evidence for the stabilization of the reaction complex at high pressures, and it shows the negligible role of the stabilized reaction complex at low pressures. Finally, the picture that emerges is qualitatively consistent with our previous study of the reaction of methanol with OH in that the tunneling in the unimolecular step from the complex to the products affects the phenomenological reaction rate constants differently at high and low pressures and leads to a significant pressure effect.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1999

The Influence of Airmass Histories on Radical Species during POLARIS

The Goddard trajectory chemistry model was used with ER-2 aircraft data to test our current knowledge of radical photochemistry during the POLARIS (Polar Ozone Loss in the Arctic Region In Summer) campaign. The results of the trajectory chemistry model with and without trajectories are used to identify cases where steady state does not accurately describe the measurements. Over the entire mission, using trajectory chemistry reduces the variability in the modeled NO(x) comparisons to data by 25% with respect to the same model simulating steady state. Although the variability is reduced, NO(x)/NO(y) trajectory model results were found to be systematically low relative to the observations by 20-30% as seen in previous studies. Using new rate constants for reactions important in NO(y) partitioning improves the agreement of NO(x)/NO(y) with the observations but a 5-10% bias still exists. OH and HO2 individually are underpredicted by 15% of the standard steady state model and worsen with the new rate constants. Trajectory chemistry model results of OH/HO2 were systematically low by 10-20% but improve using the new rates constants because of the explicit dependence on NO. This suggests that our understanding of NO(x) is accurate to the 20% level and HO(x) chemistry is accurate to the 30% level in the lower stratosphere or better for the POLARIS regime. The behavior of the NO(x) and HO(x) comparisons to data using steady state versus trajectory chemistry and with updated rate coefficients is discussed in ten-ns of known chemical mechanisms and lifetimes.

Pierson, J. M.↗

NASA NTRS1984

Kinetics of the reaction Cl + NO2 + M

Using atomic chlorine resonance fluorescence at 140 nm to detect the decay of atomic chlorine in the presence of an excess of NO2, the rate constant for the reaction Cl + NO2 + M, where M is the total gas concentration, is measured over the temperature range 264 to 417 K and at a pressure 1 to 7 torr in a discharge flow system. The rate constants for M= He and M= N2 are measured and the results are summarized in a table. The systematic error of the rate constants is estimated to be about 15 percent. A static photolysis system coupled with an FTIR spectrophotometer is used to determine the branching ratio for the formation of two possible isomers. The ratio is concluded to be ClONO (greater than or equal 75 percent) and ClNO2 (less than or equal 25 percent) which is in agreement with the results of Niki et al. (1978).

Leu, M.-T.↗

DOE OSTI2026

Pressure-dependent kinetics of cyclopentene consumption

Recent experiments have uncovered deficiencies in the ability of current kinetic models for cyclopentane combustion to predict species profiles as a function of O2 concentration. One likely source of these discrepancies flows from the limited availability of relevant kinetic data for key functionalized intermediates, requiring the use of distant analogies to estimate their rates. This work fills this gap for cyclopentene, the most prominent C5 intermediate in low-temperature cyclopentane combustion. Ab initio transition-state-theory based master equation methods are used to calculate pressure-dependent rate constants across four potential energy surfaces (C5H8 + OH, C5H8 + HO2, C5H7, and C5H7 + O2). Potential energy surfaces are characterized at the CCSD(T)-F12/cc-pVDZ-F12//revDSD-PBEP86-D3BJ/def2-TZVPP level of theory. Pressure-dependent rate constants and branching fractions are determined via 1D master equation calculations. The results are used to analyze the competition for radicals between cyclopentene and cyclopentane in the intermediate temperature region, and to identify the dominant pathways flowing from these initiation channels. On the OH initiation surface, we find good agreement with recently published experimental rate constants at high temperature, and we elucidate the complex temperature dependence below 800 K, where 𝜋𝜋 addition becomes prominent. On the HO2 initiation surface, we find an interesting alternative route to bicyclic ether formation via well-skipping over the HO2 adduct well. On the cyclopentenyl radical surface, the major product is cyclopentadiene plus H. On the cyclopentenyl + O2 surface, we find that resonance stabilization largely prevents the allylic radical from undergoing oxidation, whereas the alkylic radical has a somewhat elevated propensity for oxidation pathways relative to cyclopentyl.

ab initio calculations↗

NASA NTRS1981

Rate of reaction of OH with HNO3

Measurements of the kinetics of the reaction of OH with HNO3, and mechanisms of HNO3 removal from the stratosphere, are reported. Bimolecular rate constants were determined at temperatures between 224 and 366 K by monitoring the concentrations of OH radicals produced by HNO3 photolysis and HNO3 according to their resonance fluorescence and 184.9-nm absorption, respectively. The rate constant measured at 298 K is found to be somewhat faster than previously accepted values, with a negative temperature dependence. Calculations of a one-dimensional transport-kinetic atmospheric model on the basis of the new rate constant indicate reductions in O3 depletion due to chlorofluoromethane release and NOx injection, of magnitudes dependent on the nature of the reaction products.

Wine, P. H.↗

DOE OSTI2022

An SECM-Based Spot Analysis for Redoxmer-Electrode Kinetics: Identifying Redox Asymmetries on Model Graphitic Carbon Interfaces

The fundamental process in non-aqueous redox flow battery (NRFB) operation revolves around electron transfer (ET) between a current collector electrode and redox-active organic molecules (redoxmers) in solution. Here, we present an approach utilizing scanning electrochemical microscopy (SECM) to evaluate interfacial ET kinetics between redoxmers and various electrode materials of interest at desired locations. This spot-analysis method relies on the measurement of heterogeneous electron transfer rate constants (k f or k b ) as a function of applied potential (E-E 0 '). As demonstrated by COMSOL simulations, this method enables the quantification of Butler-Volmer kinetic parameters, the standard heterogeneous rate constant, k 0 , and the transfer coefficient, α. Our method enabled the identification of inherent asymmetries in the ET kinetics arising during the reduction of ferrocene-based redoxmers, compared to their oxidation which displayed faster rate constants. Similar behavior was observed on a wide variety of carbon electrodes such as multi-layer graphene, highly ordered pyrolytic graphite, glassy carbon, and chemical vapor deposition-grown graphite films. However, aqueous systems and Pt do not exhibit such kinetic effects. Our analysis suggests that differential adsorption of the redoxmers is insufficient to account for our observations. Displaying a greater versatility than conventional electroanalytical methods, we demonstrate the operation of our spot analysis at concentrations up to 100 mM of redoxmer over graphite films. Looking forward, our method can be used to assess non-idealities in a variety of redoxmer/electrode/solvent systems with quantitative evaluation of kinetics for applications in redox-flow battery research.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Implementation of new mixture rules has a substantial impact on combustion predictions for H 2 and NH 3

Complex-forming reactions comprise a substantial fraction of all important combustion reactions and are central to combustion behavior. Despite being often called “pressure-dependent” reactions, their rate constants depend on not only the pressure but also the composition. While modern combustion codes allow arbitrarily high accuracy in treating pressure dependence, recent work has consistently demonstrated dramatic failures of essentially all available treatments of mixture dependence. In situations where mixture dependence is treated at all, it is inevitably treated through specification of pressure-dependent rate constants for a set of pure bath gases, which are then combined to estimate the rate constant in a mixture via a “mixture rule.” While there had been a generally unquestioning confidence in these mixture rules, they had, in reality, been scarcely tested until the last decade, when comparisons against master equation calculations revealed order-of-magnitude errors for important pressure-dependent reactions. New mixture rules, based on the reduced pressure, have recently been proposed and shown to reproduce master equation calculations for broad classes of complex-forming reactions very accurately. Here, in this work, we present an implementation of one such new mixture rule (“LMR-R”) in Cantera and then use it to enable simulations that use new high-accuracy ab initio data for individual bath gases (for the first time, since codes previously could not accommodate the complex bath gas dependence). Demonstrations focus on combustion of H 2 and NH 3 , where (1) high-accuracy ab initio data are available and (2) the impact is expected to be large due to the high fractions of efficient colliders (e.g., H 2 O and NH 3 ) in the burned and unburned gases. Indeed, we find the impact of this treatment to be substantial and may explain previous modeling difficulties for these important carbon-free fuels, particularly for NH 3 , whose extraordinarily high third-body efficiency (~20) is often omitted from kinetic models.

Ammonia↗

DOE OSTI2021

Role of a 3D Structure in Energy Transfer in Mixed-Ligand Metal–Organic Frameworks

We present a detailed investigation of the photophysical properties of mixed-ligand pyrene- and porphyrin-based metal–organic frameworks (MOFs) as a function of their 3D structure. Solvothermal reactions between metal salts (InCl 3 , Zr(acac) 4 , and ZrCl 4 ) and suitable ratios of 1,3,6,8-tetrakis(p-benzoic acid)pyrene (TBAPy) and meso-tetrakis- (4-carboxyphenyl)porphyrin (TCPP) were performed to prepare a series of mixed-ligand ROD-7, NU-901, and NU-1000 MOFs. Time-resolved and steady-state fluorescence measurements were conducted on the mixed-ligand MOFs to study their photophysics. Based on the results, we concluded that upon excitation of TBAPy linkers in the MOFs, singlet excitation energy migrates across TBAPy linkers until it finds a TCPP unit. TCPP acts as an energy trap and quenches the excitation. The efficiency of TBAPy-to-TBAPy energy transfer was found to be sensitive to the structural parameters of MOFs. Analysis of steady-state and time-resolved fluorescence data revealed that excitation energy transfer (EET) is most efficient in ROD-7, followed by NU-901 and NU-1000. We propose that topology that invokes the shorter interchromophoric distances between TBAPy linkers in ROD-7 is responsible for its higher EET efficiency. The distance dependence of the EET rate constant (kEET) was investigated to gain insight into the mechanistic aspects of energy transfer in MOFs. This study revealed that (a) energy transfer in MOFs deviates from the classical Förster model and (b) the geometrical arrangement of linkers influences the mechanism of EET in MOFs. A theoretical investigation was also performed to determine energy-transfer rate constants along different directions and assess the directionality of energy transfer in these MOFs. The magnitude of rate constants indicated that energy transfer in ROD-7 should be highly anisotropic along the stacking direction. Furthermore, these findings suggest that ROD-7 is a promising candidate to play the role of the light-harvesting and energy-transfer component in solar energy conversion devices, where directional energy transfer is required.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Mechanism and kinetics of the oxidation of 1,3-butadien-1-yl (n-C 4 H 5 ): a theoretical study

Here, ab initio CCSD(T)-F12/cc-pVTZ-f12//B3LYP/6-311G(d,p) calculations of the C 4 H 5 O 2 potential energy surface have been combined with Rice–Ramsperger–Kassel–Marcus Master Equation (RRKM-ME) calculations of temperature- and pressure-dependent rate constants and product branching ratios to unravel the mechanism and kinetics of the n-C 4 H 5 + O 2 reaction. The results indicate that the reaction is fast, with the total rate constant being in the range of 3.4–5.6 × 10 –11 cm 3 molecule –1 s –1 . The main products include 1-oxo-n-butadienyl + O and acrolein + HCO, with their cumulative yield exceeding 90% at temperatures above 1500 K. Two conformers of 1-oxo-n-butadienyl + O are formed via a simple mechanism of O 2 addition to the radical site of n-C 4 H 5 followed by the cleavage of the O–O bond proceeding via a van der Waals C 4 H 5 O∙∙∙O complex. Alternatively, the pathways leading to acrolein + HCO involve significant reorganization of the heavy-atom skeleton either via formal migration of one O atom to the opposite end of the molecule or its insertion into the C1–C2 bond. Not counting thermal stabilization of the initial peroxy adducts, which prevails at low temperatures and high pressures, all other products share a minor yield of under 5%. Rate constants for the significant reaction channels have been fitted to modified Arrhenius expressions and are proposed for kinetic modeling of the oxidation of aromatic molecules and 1,3-butadiene. As a secondary reaction, n-C 4 H 5 + O 2 can be a source for the formation of acrolein observed experimentally in oxidation of the phenyl radical at low combustion temperatures, whereas another significant (secondary) product of the C 6 H 5 + O 2 reaction, furan, could be formed through unimolecular decomposition of 1-oxo-n-butadienyl. Both the n-C 4 H 5 + O 2 reaction and unimolecular decomposition of its 1-oxo-n-butadienyl primary product are shown not to be a substantial source of ketene.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1992

The relative abundance of ethane to acetylene in the Jovian stratosphere

The inclusion of the results of laboratory kinetics studies on the reaction of C2H3 and H2 to yield C2H4, which is suggestive of an efficient chemical mechanism for the hydrogenation of C2H2 to C2H6, can be included in a comprehensive model of the Jupiter atmosphere hydrocarbon photochemistry to explain the observed altitude variation of the C2H6/C2H2 ratio. The sensitivity of these results to uncertainties in key low-temperature rate constants is demonstrated. These key reaction-rate constants decrease with falling temperature.

Allen, Mark↗