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At least 235 records · Page 13

Continental-scale integration of soil metagenomes and organic matter chemistry reveals ubiquitous microbial capacity for chemically-recalcitrant carbon decomposition

Soil organic matter (SOM) decomposition by microorganisms is a major uncertainty in predicting terrestrial carbon–atmosphere feedbacks, partly because we lack understanding of the microbial diversity involved in depolymerizing different carbon pools across environmental gradients. We address this gap using a continental-scale dataset pairing shotgun metagenomes with high-resolution SOM chemistry, assembling 0.76 Tbp of prokaryotic MAGs (828 genomes) and identifying 66,727 SOM molecules from 47 standardized U.S. soil cores selected using respiration rates from 106 soils. Integrating these datasets reveals widespread microbial potential for depolymerizing chemically-recalcitrant SOM previously considered stable. We uncover complementary metabolic specialization between genera affiliated with two abundant bacterial orders, Rhizobiales and Chthoniobacterales, and an archaeal order, Nitrososphaerales. This metabolic partitioning is consistent across soil depths and activity levels, suggesting coordinated decomposition of complex SOM through distinct but complementary biochemical strategies. The metabolic potential for depolymerization of chemically-recalcitrant compounds is supported by the abundance of these molecules across the soils, as indicated by Fourier-Transform Ion Cyclotron Resonance Mass Spectrometry (FTICR-MS), and by flux balance analysis of metabolic models. Our results show that a substantial portion of ostensibly stable SOM remains vulnerable to microbial decomposition, a mechanism not captured in current Earth System Models.

Song, Young C. [Pacific Northwest National Laborat↗

Unveiling the Mechanism of Mn Dissolution Through a Dynamic Cathode‐Electrolyte Interphase on LiMn2O4

Abstract Understanding the formation and evolution of the cathode‐electrolyte interphase (CEI), which forms at the interface between the cathode and electrolyte, is crucial for revealing degradation mechanisms in cathode materials, especially for developing strategies to stabilize the interphase in the strongly oxidizing conditions that evolve at high operating voltages in next‐generation Li‐ion batteries. However, The present understanding of the CEI is challenged by its complex and dynamic nature. In this work, near‐edge X‐ray absorption fine structure spectroscopy, electrochemical characterization, and reactive molecular dynamics simulations are combined to reveal a mechanism for CEI formation and evolution above model LiMn 2 O 4 (LMO) thin‐film electrodes in contact with conventional carbonate‐based electrolytes. It is found that Mn dissolution from LMO can be understood in terms of repetitive Mn 3 O 4 formation and dissolution behavior during cycling, which is closely connected to electrolyte decomposition and a key aspect of the CEI formation and growth. The behavior of the CEI in this model system offers detailed insight into the dynamic chemistry of the interphase, underscoring the important role of electrolyte composition and cathode surface structure in interphase degradation.

Ou, Wenhan↗

Climate warming and elevated CO 2 alter peatland soil carbon sources and stability

Peatlands are an important carbon (C) reservoir storing one-third of global soil organic carbon (SOC), but little is known about the fate of these C stocks under climate change. Here, we examine the impact of warming and elevated atmospheric CO 2 concentration (eCO 2 ) on the molecular composition of SOC to infer SOC sources (microbe-, plant- and fire-derived) and stability in a boreal peatland. We show that while warming alone decreased plant- and microbe-derived SOC due to enhanced decomposition, warming combined with eCO 2 increased plant-derived SOC compounds. We further observed increasing root-derived inputs (suberin) and declining leaf/needle-derived inputs (cutin) into SOC under warming and eCO 2 . The decline in SOC compounds with warming and gains from new root-derived C under eCO 2 , suggest that warming and eCO 2 may shift peatland C budget towards pools with faster turnover. Together, our results indicate that climate change may increase inputs and enhance decomposition of SOC potentially destabilising C storage in peatlands.

54 ENVIRONMENTAL SCIENCES↗

Stability of Calcium Ion Battery Electrolytes: Predictions from Ab Initio Molecular Dynamics Simulations

Multivalent batteries, such as magnesium-ion, calcium-ion, and zinc-ion batteries, have attracted significant attention as next-generation electrochemical energy storage devices to complement conventional lithium-ion batteries (LIBs). Among them, calcium-ion batteries (CIBs) are the least explored due to the difficult reversible Ca deposition-dissolution. In this work, we examined the stability of four different Ca salts with weakly coordinating anions and three different solvents commonly employed in existing battery technologies to identify suitable candidates for CIBs. By employing Born-Oppenheimer molecular dynamics (BOMD) simulations on salt-Ca and solvent-Ca interfaces, we find that the tetraglyme solvent and carborane salt are promising candidates for CIBs. Due to the strong reducing nature of the calcium surface, the other salts and solvents readily decompose. Further, we explain the microscopic mechanisms of salt/solvent decomposition on the Ca surface using time-dependent projected density of states, time-dependent charge-transfer plots, and climbing-image nudged elastic band calculations. Collectively, this work presents the first mechanistic assessment of the dynamical stability of candidate salts and solvents on a Ca surface using BOMD simulations, and provides a predictive path toward designing stable electrolytes for CIBs.

Born-Oppenheimer molecular dynamics↗

Seasonal Controls on Microbial Depolymerization and Oxidation of Organic Matter in Floodplain Soils

Floodplain soils are vast reservoirs of organic carbon often attributed to anaerobic conditions that impose metabolic constraints on organic matter degradation. What remains elusive is how such metabolic constraints respond to dynamic flooding and drainage cycles characteristic of floodplain soils. Here, in this work, we show that microbial depolymerization and respiration of organic compounds, two rate-limiting steps in decomposition, vary spatially and temporally with seasonal flooding of mountainous floodplain soils (Gothic, Colorado, USA). Combining metabolomics and -proteomics, we found a lower abundance of oxidative enzymes during flooding coincided with the accumulation of aromatic, high-molecular weight compounds, particularly in surface soils. In subsurface soils, we found that a lower oxidation state of carbon coincided with a greater abundance of chemically reduced, energetically less favorable low-molecular weight metabolites, irrespective of flooding condition. Our results suggest that seasonal flooding temporarily constrains oxidative depolymerization of larger, potentially plant-derived compounds in surface soils; in contrast, energetic constraints on microbial respiration persist in more reducing subsurface soils regardless of flooding. Our work underscores that the potential vulnerability of these distinct anaerobic carbon storage mechanisms to changing flooding dynamics should be considered, particularly as climate change shifts both the frequency and extent of flooding in floodplains globally.

54 ENVIRONMENTAL SCIENCES↗

Enabling Magnesium Anodes by Tuning the Electrode/Electrolyte Interfacial Structure

Here, a new deposition mechanism is presented in this study to achieve highly reversible plating and stripping of magnesium (Mg) anodes for Mg-ion batteries. It is known that the reduction of electrolyte anions such as bi s (trifluoromethanesulfonyl) imide (TFSI - ) causes Mg surface passivation, resulting in poor electrochemical performance for Mg-ion batteries. We reveal that the addition of sodium cations (Na + ) in Mg-ion electrolytes can fundamentally alter the interfacial chemistry and structure at the Mg anode surface. The molecular dynamics simulation suggests that Na + cations contribute to a significant population in the interfacial double layer so that TFSI - anions are excluded from the immediate interface adjacent to the Mg anode. As a result, the TFSI - decomposition is largely suppressed so does the formation of passivation layers at the Mg surface. This mechanism is supported by our electrochemical, microscopic, and spectroscopic analyses. The resultant Mg deposition demonstrates smooth surface morphology and lowered overpotential compared to the pure Mg(TFSI) 2 electrolyte.

25 ENERGY STORAGE↗

Photoelectron spectroscopy and computational investigations of the electronic structures and noncovalent interactions of cyclodextrin-closo-dodecaborate anion complexes x-CD·B12X122- (x = a, ß, y; X = H, F)

We report a joint negative ion photoelectron spectroscopy (NIPES) and computational study on the electronic structures and noncovalent interactions of a series of cyclodextrin-closo-dodecaborate dianion complexes, ?-CD·B12X122- (? = a, ß, ?; X = H, F). The measured vertical / adiabatic detachment energies (VDEs / ADEs) are 1.15/0.93, 3.55/3.20, 3.90/3.60, and 3.85/3.60 eV for B12H122- and its a-, ß-, ?-CD complexes, respectively; while the corresponding values are 1.90/1.70, 4.00/3.60, 4.33/3.95, and 4.30/3.85 eV for the X = F case. These results show that the inclusion of B12X122- into the CD cavities greatly increase the electronic stability of the dianions. The effect of electronic stabilization for ß-CD is roughly the same as for ?-CD, both being considerably stronger than that for a-CD. Density functional theory (DFT) based geometry optimization reveals that B12X122- are inserted into CDs increasingly deeper from a-CD to ?-CD. The calculated VDEs and ADEs agree with the experiments well, particularly, reproducing the electron binding energy (EBE) trends. The molecular orbital analyses indicate that the most loosely bound photodetached electrons origin from the guest B12X122- moieties. In addition to a shift of all signals to larger EBE, significant changes in the signal patterns are observed. At low EBE, this is due to the splitting of highly degenerate B12X122- orbitals, while at high EBE, photodetachment from CD oxygens contributes to the new bands. The guest B12X122- and host CD nocovalent, size-specific interaction based on the independent gradient model (IGM) and energy decomposition analysis (EDA), is dominated by electrostatic interactions. The analysis further unravels unambiguiously the existence of dihydrogen bonding and how it affects the total energy that stabilizes the host-guest complexes of CDs·B12H122- compared to the general hydrogen bonding interaction in CDs·B12F122-. This work clearly exhibits strong influences on the electronic structures of dodecaborates upon clustering with CDs, with both size (a-, ß-, ?-) and molecular (X = H or F) specificities, thus providing critical molecular-level information on the cyclodextrin-closo-dodecaborate interactions of interest to medical applications, e.g. Boron neutron capature therapy. The NIPES experiments done at PNNL were supported by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Bioscience (X.-B.W.) and was performed at the EMSL, a national scientific user facility sponsored by DOE’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. H.S. and Z.S. acknowledge the funding support of National Natural Science Foundation of China (Nos.11727810, 61720106009 and 21603074), the Science and Technology Commission of Shanghai Municipality (Nos. 19JC1412200), and the Program of Introducing Talents of Discipline to Universities 111 project (B12024). Z. L. thanks the China Scholarship Council (CSC) for financial support. We acknowledge the ECNU Multifunctional Platform for Innovation (001) and HPC Research Computing Team for providing computational and storage resources. J.W. acknowledges support from the Alexander von Humboldt foundation (Feodor Lynen Fellowship and Rückkehrerstipendium), a Freigeist fellowship of the Volkswagenfoundation and Prof. Vladimir A. Azov for helpful discussions.

Li, Zhipeng↗

Chiral population analysis: a real space visualization of X-ray circular dichroism

The microscopic understanding of probing and controlling molecular chirality is of considerable interest. Numerous spectroscopic techniques are capable of monitoring molecular asymmetry and its consequences, ranging from the infrared to the X-ray regime. Resonant X-rays have long been used to investigate local atomic sites within molecules thanks to the localized nature of core electronic transitions. These techniques can be used to determine the extent to which chirality is a local versus a delocalized property. However, how to systematically partition dichroic contributions from the point of view of electronic structure simulations remains an open question. Here, we introduce the concept of chiral population analysis that connects chirality to the atomic orbital picture. In analogy with Mulliken population analysis, which assigns charges to atomic orbitals, chiral populations allow the dichroic response to be distributed among the participating atomic orbitals. This decomposition can be further visualized in real space by representing it in terms of isosurface plots, providing an intuitive way to connect the dichroic response to its origins. Thus chiral population analysis can be particularly useful to assess the extent to which a given electronic transition is sensitive to chirality as a local or global feature of the molecular geometry.

36 MATERIALS SCIENCE↗

Computer Simulation of the far Infrared Collision Induced Absorption Spectra of Gaseous CO2

Far infrared collision induced absorption spectra of gaseous CO2 were computed using molecular dynamics simulations. The quadrupole and hexadecapole multipolar induction, through the trace, and the anisotropy of the molecular polarizability were found to be insufficient to represent properly the dipole induction mechanism. For a detailed analysis of the induction process the spectra obtained were decomposed into components resulting from different terms of the induced dipole. Based on this decomposition, all additional overlap contribution for each term was proposed. When spectra were recomputed including such overlap, good agreement between experiment and simulation was achieved over the temperature range at which measurements exist (233-400 K). The use of an anisotropic intermolecular potential was found to be of critical importance for obtaining the right shape of the far wings of the spectra.

Gruszka, Marcin↗

Machine learning approaches for structural and thermodynamic properties of a Lennard-Jones fluid

Predicting the functional properties of many molecular systems relies on understanding how atomistic interactions give rise to macroscale observables. However, current attempts to develop predictive models for the structural and thermodynamic properties of condensed-phase systems often rely on extensive parameter fitting to empirically selected functional forms whose effectiveness is limited to a narrow range of physical conditions. Here, we illustrate how these traditional fitting paradigms can be superseded using machine learning. Specifically, we use the results of molecular dynamics simulations to train machine learning protocols that are able to produce the radial distribution function, pressure, and internal energy of a Lennard-Jones fluid with increased accuracy in comparison to previous theoretical methods. The radial distribution function is determined using a variant of the segmented linear regression with the multivariate function decomposition approach developed by Craven et al. [J. Phys. Chem. Lett. 11, 4372 (2020)]. The pressure and internal energy are determined using expressions containing the learned radial distribution function and also a kernel ridge regression process that is trained directly on thermodynamic properties measured in simulation. The presented results suggest that the structural and thermodynamic properties of fluids may be determined more accurately through machine learning than through human-guided functional forms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reactions of Atomic Thorium and Uranium Cations with SF 6 Studied by Guided Ion Beam Tandem Mass Spectrometry

The fundamental chemistry of the thorium and uranium fluorides continues to be an area of interest because of the use of thorium and uranium fluoride compounds in nuclear fuel systems. Here, we study the reaction of thorium cations with sulfur hexafluoride for the first time and revisit the reaction of uranium cations with sulfur hexafluoride. By using guided ion beam tandem mass spectrometry, we explore the reaction pathways that become accessible well above thermal energies (E ~ 0.04 eV). Overall, we find that both Th + and U + react very efficiently with SF 6 , approaching the collision limit at both thermal and elevated energies. Here, the primary products observed at low energies include Th 1–3 + , UF 1–4 + , and SF 1–4 + , all of which are formed in barrierless, exothermic processes. SF 5 + was also observed, although the pressure dependence of this channel reveals that SF 5 + forms exothermically through secondary reactions, which the energy dependences suggest result from reactions between ThF 2 + and UF 3 + with SF 6 . At higher energies, both AnF 3 + products are observed to decay to AnF + + F 2 and both SF 4 + and SF 2 + exhibit cross sections with endothermic features. For both systems, the rise in SF 4 + can be attributed to a secondary collision between AnF + with SF 6 on the basis of the pressure dependence of the SF 4 + channel at higher energies and the rise in SF 2 + appears to result from the decomposition of SF 3 + to SF 2 + + F.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Descriptor-Based Analysis of Atomic Layer Deposition Mechanisms on Spinel LiMn 2 O 4 Lithium-Ion Battery Cathodes

Protective coatings have been shown to effectively suppress Mn ion dissolution from the spinel LiMn 2 O 4 lithium-ion battery cathode by stabilizing the surface against undesired side reactions with the electrolyte. In spite of extensive study, however, there remains a lack of atomic-scale understanding of how such coatings are deposited, and no molecular-level descriptor to predict trends in deposition mechanisms has been identified. We have recently shown that Al 2 O 3 coatings grown by atomic layer deposition (ALD) with alternating trimethylaluminum (TMA) and water exposures exhibit submonolayer growth because of precursor decomposition on the lithium manganate spinel (LMO) surface during early ALD pulses. In the present work, we elucidate the underlying mechanisms of this Al 2 O 3 ALD process using density functional theory (DFT) calculations and X-ray photoelectron spectroscopy (XPS) experiments, and we introduce a generalized descriptor-based framework to understand the resulting trends across a spectrum of surface structures and functionalities. We demonstrate that all decomposition products, including CH 3 -aluminum adducts and dissociated CH 3 groups, are Lewis bases and are coordinated to oxygen atoms on the LMO surface, leading to charge transfer to Lewis acidic Mn 3d states. Inert-transfer XPS supports these theoretical predictions, showing an increase in near-surface Mn 3+ content following TMA exposure and shifts in C is spectra consistent with C-O bond formation. We extend the DFT studies to various low- and high-index LMO surface facets, as a proxy for tuning the Lewis acid-base interactions between surface-bound CH 3 * and near-surface Mn ions. The thermochemistry for TMA reactions on these chemically distinct LMO surfaces demonstrates that ALD is structure-sensitive and that there is higher reactivity for TMA decomposition and Al 2 O 3 nucleation near LMO steps and defects. Motivated by the Lewis basic character of the decomposition products, we introduce the oxygen vacancy formation energy as a descriptor for decomposition energetics, and we demonstrate that all energetics are correlated to this quantity through the number of electrons that are transferred along the reaction coordinate. Finally, based on these findings, we hypothesize that improved electrochemical cycling with only 1-2 ALD cycles may be due to selective passivation of defect sites on the LMO surface that are more susceptible to Mn dissolution, and we suggest that similar descriptor-based analyses could be useful for the study of other ALD coatings on oxide substrates.

25 ENERGY STORAGE↗

The Effects of Polyolefin Structure and Source on Pyrolysis-Derived Plastic Oil Composition

Seven types of plastics were pyrolyzed in a fluidized bed reactor: post-consumer recycled (PCR) high-density polyethylene (HDPE), PCR polypropylene (PP), virgin resins of varying molecular weights of HDPE, virgin resins of low-density polyethylene (LDPE), linear low-density polyethylene (LLDPE), and (PP). Pyrolysis produced non-condensable gases (C1-C3), liquid phase products (C4-C40), and solids (C40+ and chars), with alkane, alkene, alkadiene, aromatic, and multi-cycloaromatics as the predominant compounds. Polymer structure had the greatest impact on product distribution, with minimal influence from molecular weight. Branches in polyethylene (PE) acted as thermal defects initiating degradation. Higher branch density in PE led to increased concentrations of aromatics, branched alkanes, and internal alkenes. PP and PE exhibited distinct degradation mechanisms, with PP requiring less energy for decomposition and yielding more oil. Here, pyrolysis oil from PCR HDPE and PCR PP contained a higher proportion of branched compounds. Additives in PCR plastics may promote isomerization during pyrolysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Genomes to Structure and Function Workshop Report 2022

The goal of the U.S. Department of Energy (DOE) Biological and Environmental Research (BER) Program is to achieve a predictive understanding of complex biological, earth, and environmental systems with the aim of advancing the nation’s energy and infrastructure security. (https://www.energy.gov/science/ ber/biological-and-environmental-research). To pursue this goal, collaborations among experts in diverse research areas that lead to multidisciplinary projects are indispensable. The roles of DOE’s User Facilities, which offer unique and powerful resources for such research projects, are evolving, and expectations for the facilities are increasing. To respond to Users’ needs, the Joint Genome Institute (JGI) and Environmental Molecular Sciences Laboratory (EMSL) initiated the Facilities Integrating Collaborations for User Science (FICUS) program in 2014. This collaboration has grown into a popular and successful program, advancing more than 100 multidisciplinary projects to date. Similarly, the new interFacility collaborations among the JGI, EMSL, and User resources for BER structural biology and imaging at the Basic Energy Science (BES) Program’s synchrotron and neutron facilities are becoming essential for cutting-edge transdisciplinary science. To further explore the need for the BER research community to combine genomic, functional, and structural approaches to advance their research, an organizing committee was formed to develop and jointly host a 3-part workshop. The committee’s members represented seven DOE National Laboratory User Facilities (Appendix 1 lists the members). The “Genomes to Structure and Function” virtual workshop (see Appendices 2–5) was composed of three sessions. The first session, titled “Molecular Structures” (October 27– 28, 2021), highlighted diverse integrative experimental and computational approaches correlating structural data with sequencing and functional information, as well as predicting protein structures to model complex biological systems. The second session, “Intracellular Organization, and Material Synthesis and Decomposition” (December 15–16, 2021), covered imaging methods for observing, quantifying, and manipulating biosystems. The third session, “Imaging the Rhizosphere and Cellular Organization” (January 26–27, 2022) emphasized advanced and non-invasive imaging techniques applied to plant root-microbe-soil interactions.

59 BASIC BIOLOGICAL SCIENCES↗

Colossal Strain Tuning of Ferroelectric Transitions in KNbO 3 Thin Films

Strong coupling between polarization ( P ) and strain (ɛ) in ferroelectric complex oxides offers unique opportunities to dramatically tune their properties. Here colossal strain tuning of ferroelectricity in epitaxial KNbO 3 thin films grown by sub‐oxide molecular beam epitaxy is demonstrated. While bulk KNbO 3 exhibits three ferroelectric transitions and a Curie temperature ( T c ) of ≈676 K, phase‐field modeling predicts that a biaxial strain of as little as −0.6% pushes its T c > 975 K, its decomposition temperature in air, and for −1.4% strain, to T c > 1325 K, its melting point. Furthermore, a strain of −1.5% can stabilize a single phase throughout the entire temperature range of its stability. A combination of temperature‐dependent second harmonic generation measurements, synchrotron‐based X‐ray reciprocal space mapping, ferroelectric measurements, and transmission electron microscopy reveal a single tetragonal phase from 10 K to 975 K, an enhancement of ≈46% in the tetragonal phase remanent polarization ( P r ), and a ≈200% enhancement in its optical second harmonic generation coefficients over bulk values. These properties in a lead‐free system, but with properties comparable or superior to lead‐based systems, make it an attractive candidate for applications ranging from high‐temperature ferroelectric memory to cryogenic temperature quantum computing.

36 MATERIALS SCIENCE↗

Initial decomposition mechanisms of 2,4,6-triamino-1,3,5-trinitrobenzene (TATB) and their kinetic isotope effect

2,4,6-triamino-1,3,5-trinitrobenzene (TATB) is an insensitive High Explosive (HE) that is widely studied to better understand the physical properties of safety and sensitivity of HE. A dominant initial decomposition mechanism of TATB is believed to be a dehydration reaction that forms mono- and di-furazans, although other mechanisms have been reported. In this work, seven initial decomposition mechanisms were modeled with ab initio simulations to calculate its free energy barriers, decomposition rates, and kinetic isotope effects. The energy barrier for mono-benzofurazan mechanisms was found to be high, >61 kcal/mol in the gas phase; however, the reaction energy can decrease significantly in a disordered condensed state. The predicted kinetic isotope effect ratio of the furazan mechanism was found to be k h /k d ≈ 1.41 at 60K, in agreement with the experiment. The NO 2 scission mechanism was found to be an entropy-driven mechanism because the free energy barrier decreased significantly with temperature, making it the most energetically favorable mechanism at high temperatures in the gas phase. So the results provide a better understanding of the atomistic decomposition mechanisms of TATB and may be useful for improving models of safety and sensitivity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Self-Assembled Solute Networks in Crowded Electrolyte Solutions and Nanoconfinement of Charged Redoxmer Molecules

Redoxmers are electrochemically active organic molecules storing charge and energy in electrolyte fluids circulating through redox flow batteries (RFBs). Such molecules typically have solvent-repelling cores and solvent-attracting pendant groups introduced to increase solubility in liquid electrolytes. These two features can facilitate nanoscale aggregation of the redoxmer molecules in crowded solutions. In some cases, this aggregation leads to the emergence of continuous networks of solute molecules in contact, and the solution becomes microscopically heterogeneous. In this study, we used small-angle X-ray scattering (SAXS) and molecular dynamics modeling to demonstrate formation of such networks and examine structural factors controlling this self-assembly. We also show that salt ions become excluded from these solute aggregates into small pockets of electrolytes, where these ions strongly associate. This confinement by exclusion is also likely to occur to charged redoxmer molecules in a “sea” of neutral precursors coexisting in the same solution. Here, we demonstrate that the decay lifetime of the confined charged molecules in such solutions can increase several fold compared to dilute solutions. We attribute this behavior to a “microreactor effect” on reverse reactions of the confined species during their decomposition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗