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At least 487 records · Page 27

Analysis of tumor-immune functional responses in a mathematical model of neoantigen cancer vaccines

Cancer neoantigen vaccines have emerged as a promising approach to stimulating the immune system to fight cancer. We propose a simple model including key elements of cancer-immune interactions and conduct a phase plane analysis to understand the immunological mechanisms of cancer neoantigen vaccines. Analytical results are obtained for two widely used functional forms that represent the killing rate of tumor cells by immune cells: the law of mass action (LMA) and the dePillis-Radunskaya Law (LPR). Using the LMA, our results reveal that a slowly growing tumor can escape the immune surveillance and that there is a unique periodic solution. The LPR offers richer dynamics, in which tumor elimination and uncontrolled tumor growth are both present. We show that tumor elimination requires sufficient number of initial activated T cells in relationship to the malignant cells, which lends support to using the neoantigen cancer vaccine as an adjuvant therapy after the primary tumor is surgically removed or treated using radiotherapy. We also derive a sufficient condition for uncontrolled tumor growth under the assumption of the LPR. Here, the juxtaposition of analyses with these two different choices for the killing rate function highlights their importance on model behavior and biological implications, by which we hope to spur further theoretical and experimental work to understand mechanisms underlying different functional forms for the killing rate.

60 APPLIED LIFE SCIENCES↗

Vapor-phase self-assembly for generating thermally stable single-atom catalysts

Preparation of thermally stable metal single-atom catalysts (SACs) is a challenge in heterogeneous catalysis, especially on conventional supports that provide a weak metal-support interaction. In this work, we report that a modified support MgAl 2 O 4 can stabilize Pt single atoms by a mechanism of vapor-phase self-assembly in a high-temperature treatment (800°C, air). The experimental results on the formation mechanism and the structure are validated by DFT and ab initio molecular dynamics simulations. We infer that stable triangular K 3 O 3 structures help stabilize Pt single atoms at high temperatures in oxidizing conditions, exhibiting excellent reactivity for methane oxidation. The obtained Pt/K/MgAl 2 O 4 SAC presents excellent stability in methane oxidation after steam treatment at elevated temperatures, whereas the Pt/MgAl 2 O 4 nanocatalyst suffers from rapid deactivation due to Pt nanoparticle growth. Now this work paves the way for preparing thermally stable and highly active SACs using conventional high-surface-area supports, despite the weak metal-support interaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A model to assess Zircaloy’s mechanical property changes following a transient beyond critical heat flux

Maintaining the integrity of nuclear fuel rods is essential for ensuring public health and safety in nuclear power generation. During reactor operation, this integrity is confirmed by demonstrating compliance with established regulatory acceptance criteria. For moderate-frequency events, such as limiting transients and anticipated operational occurrences (AOOs), the current fuel integrity criterion is based on preventing boiling transition. This criterion assumes that prevention of boiling transition will prevent excessive cladding heating and, thus, fuel failure during normal operations. While conservative, this approach places significant constraints on core design, fuel cycle economics, and a plant’s ability to perform major power uprates, leading to suboptimal fuel utilization and inefficient carbon-free energy production. A more efficient approach could be achieved by revising the failure criterion to a material-specific limit rather than strictly preventing the boiling transition, since boiling transition per se is not a cause of fuel cladding failure. Here, as a result, a new licensing framework based on material properties, termed time-at-temperature (t@T), is needed. This approach would allow for brief periods of post–critical heat flux operation during an AOO without compromising safety. Implementing the t@T licensing strategy requires a robust technical foundation in material properties, which must be established through comprehensive data collection on both unirradiated and irradiated fuel and cladding materials. This foundation would enable the development of a safety basis that ensures safe operation while providing greater flexibility and efficiency for reactor operation. This paper documents a thorough review of the available data to establish a baseline knowledge that can inform the development of cladding mechanical models, as well as identify experimental data gaps that need to be addressed in future research. Machine learning and data informatics were utilized to extract the importance of parameters on the t@T parameter. Industry tools were used to perform baseline analyses to define the relevant transient conditions for data analysis. The subsequent review successfully identified applicable experimental data, as well as sufficient data to evaluate changes in cladding mechanical properties following an AOO transient. Rather than developing new models, this work coupled existing irradiation annealing and recrystallization models to calculate changes in hardness, yield stress, and ultimate tensile stress following an AOO event. The findings from this review were summarized to highlight the experimental data needs required to fill remaining gaps and support the development of future t@T licensing methodologies.

Cladding performance↗

Thermal/Mechanical Durability of Polymer-Matrix Composites in Cryogenic Environments

In order to increase the reliability of the next generation of space transportation systems, the mechanical behavior of polymeric-matrix composite (PMC) materials at cryogenic temperatures must be investigated. This paper presents experimental data on the residual mechanical properties of a carbon fiber polymeric composite, IM7/PETI-5 as a function of temperature and aging. Tension modulus and strength were measured at room temperature, -196 C, and -269 C on five different specimens ply lay-ups. Specimens were preconditioned with one set of coupons being isothermally aged for 576 hours at -184 C, in an unloaded state. Another set of corresponding coupons were mounted in constant strain fixtures such that a constant uniaxial strain was applied to the specimens for 576 hours at -184 C. A third set was mechanically cycled in tension at -184 C. The measured properties indicated that temperature, aging, and loading mode can all have significant influence on performance. Moreover, this influence is a strong function of laminate stacking sequence. Thermal-stress calculations based on lamination theory predicted that the transverse tensile ply stresses could be quite high for cryogenic test temperatures. Microscopic examination of the surface morphology showed evidence of degradation along the exposed edges of the material because of aging at cryogenic temperatures. ________________

Gates, Thomas S.↗

The effect of material heterogeneity and random loading on the mechanics of fatigue crack growth

This paper reviews experimental work on the influence of variable amplitude or random loads on the mechanics and micromechanisms of fatigue crack growth. Implications are discussed in terms of the crack driving force, local plasticity, crack closure, crack blunting, and microstructure. Due to heterogeneity in the material's microstructure, the crack growth rate varies with crack tip position. Using the weakest link theory, an expression for crack growth rate is obtained as the expectation of a random variable. This expression is used to predict the crack growth rates for aluminum alloys, a titanium alloy, and a nickel steel in the mid-range region. It is observed, using the present theory, that the crack growth rate obeys the power law for small stress intensity factor range, and that the power is a function of a material constant.

Srivatsan, T. S.↗

Bone Formation Rate in Experimental Disuse Osteoporosis in Monkeys

Specific mechanisms underlying weightless and hypodynamic bone loss are obscure. A principal relationship which must be affected is the balance between bone formation and bone resorption rates. In order to better define the influence of those parameters on bone loss, and also to develop measurements in other species as a useful adjunct to human research, studies were undertaken with experimental monkeys. Tests were conducted with a total of 6 adult male monkeys, weighing 10-13 kg, and approximately 10-12 yrs. of age to evaluate specifically bone formation rate during the development of disuse osteoporosis and osteopenia. Three animals were restrained in a semi-recumbent position for six months; three animals served as normal caged controls. Food intake (Purina) was held relatively constant at 200g/day for each animal. Using a Norland Bone Mineral Analyzer, bone mineral losses of 3.5 to 6% were seen in the mid-shaft of the tibia and in the distal radius. Bone loss was confirmed radiographically, with observation of thinning of the proximal tibial cortex and trabeculae in the calcaneus. Bone formation rate was determined using standard Ca-47 kinetics under metabolic balance conditions. After six months of restraint, accretion was 7.2-13.2 mg Ca/kg/day, compared to 3.2-4.1 mg Ca/kg/day in caged controls and 3-8 mg Ca/kg/day in normal adult humans. Fecal and urine calcium was 25-40% higher in restrained animals than in controls. Dietary calcium absorption decreases during restraint, and calcium turnover increases, implying a rise in bone resorption rate concommitant with the observed rise in bone accretion rate. Further studies dealing specifically with bone resorption are underway to define this more fully.

Cann, Christopher↗

Health Monitoring of a Rotating Disk Using a Combined Analytical-Experimental Approach

Rotating disks undergo rigorous mechanical loading conditions that make them subject to a variety of failure mechanisms leading to structural deformities and cracking. During operation, periodic loading fluctuations and other related factors cause fractures and hidden internal cracks that can only be detected via noninvasive types of health monitoring and/or nondestructive evaluation. These evaluations go further to inspect material discontinuities and other irregularities that have grown to become critical defects that can lead to failure. Hence, the objectives of this work is to conduct a collective analytical and experimental study to present a well-rounded structural assessment of a rotating disk by means of a health monitoring approach and to appraise the capabilities of an in-house rotor spin system. The analyses utilized the finite element method to analyze the disk with and without an induced crack at different loading levels, such as rotational speeds starting at 3000 up to 10 000 rpm. A parallel experiment was conducted to spin the disk at the desired speeds in an attempt to correlate the experimental findings with the analytical results. The testing involved conducting spin experiments which, covered the rotor in both damaged and undamaged (i.e., notched and unnotched) states. Damaged disks had artificially induced through-thickness flaws represented in the web region ranging from 2.54 to 5.08 cm (1 to 2 in.) in length. This study aims to identify defects that are greater than 1.27 cm (0.5 in.), applying available means of structural health monitoring and nondestructive evaluation, and documenting failure mechanisms experienced by the rotor system under typical turbine engine operating conditions.

Abdul-Aziz, Ali↗

A thermodynamics-based damage model for the non-linear mechanical behavior of SiC/SiC ceramic matrix composites in irradiation and thermal environments

A damage model is developed and validated with experimental data for the non-linear mechanical behavior of SiC/SiC composite materials in nuclear applications. Cyclic thermal and mechanical loading associated with neutron irradiation effects of these composites leads to wide-spread and progressive micro-cracking that leads to loss of thermal conductivity and further enhancement of thermo-mechanical damage. A physics-based model of wide-spread micro-cracking is developed within the thermodynamic framework of continuum damage mechanics. Evolution equations for damage parameters that describe the growth of continuum damage are developed, where the material variables are obtained from experiments. The model novelty is in coupling mechanical, thermal, and irradiation damage through a consistent thermodynamic framework, including loss of thermal conductivity due to the evolution of mechanically induced micro-cracks. A number of thermo-mechanical experiments were conducted to confirm model assumptions. The model is shown to be validated with out-of-pile experiments, and then implemented using commercial finite element code COMSOL to the fuel cladding problem with normal and high radiation dose cases.

Materials Science↗

Dynamic nitrogen fixation in an aerobic endophyte of Populus

Biological nitrogen fixation by microbial diazotrophs can contribute significantly to nitrogen availability in non-nodulating plant species. In this study of molecular mechanisms and gene expression relating to biological nitrogen fixation, the aerobic nitrogen-fixing endophyte Burkholderia vietnamiensis, strain WPB, isolated from Populus trichocarpa served as a model for endophyte–poplar interactions. Nitrogen-fixing activity was observed to be dynamic on nitrogen-free medium with a subset of colonies growing to form robust, raised globular like structures. Secondary ion mass spectrometry (NanoSIMS) confirmed that N-fixation was uneven within the population. A fluorescent transcriptional reporter (GFP) revealed that the nitrogenase subunit nifH is not uniformly expressed across genetically identical colonies of WPB and that only ~11% of the population was actively expressing the nifH gene. Higher nifH gene expression was observed in clustered cells through monitoring individual bacterial cells using single-molecule fluorescence in situ hybridization. Through 15 N 2 enrichment, we identified key nitrogenous metabolites and proteins synthesized by WPB and employed targeted metabolomics in active and inactive populations. We cocultivated WPB Pnif-GFP with poplar within a RhizoChip, a synthetic soil habitat, which enabled direct imaging of microbial nifH expression within root epidermal cells. We observed that nifH expression is localized to the root elongation zone where the strain forms a unique physical interaction with the root cells. This work employed comprehensive experimentation to identify novel mechanisms regulating both biological nitrogen fixation and beneficial plant–endophyte interactions.

15 N-tracking metabolomics↗

Unraveling the multi-step crystallization mechanism of polytetrafluoroethylene, modified polytetrafluoroethylene, and their nanocomposites with boron nitride nanobarbs: Experimental insights and theoretical analysis

The non-isothermal crystallization behavior and kinetics of polytetrafluoroethylene (PTFE) composites with boron nitride nanobarb (BNNB), a new generation nanostructure with unique surface morphology and mechanical “barbs” have been analyzed, understanding these properties is essential for their high-end applications as thermal interface materials (TIM) for microwave, 5G and microelectronic devices. The analysis of the crystallization parameters includes crystallization onset, peak and end temperatures, crystallization half-life and overall crystallinity of PTFE, modified PTFE and their BNNB composites. The results were further analyzed using theoretical models such as the combined Avrami-Ozawa model. It was found that BNNB supports crystallization in the modified PTFE but shows minimal effect on the crystallization of PTFE. Due to the limitation of the classical theoretical models used above in fully characterizing the multi-step crystallization process of PTFE, an in-depth analysis using the model-free advanced isoconversional computation was used to characterize the PTFE crystallization based on the evolution of activation energy with fractional crystallinity and for the first time with temperature. Three kinetic regions were identified in the crystallization mechanism. Here, this study investigated the molecular organization and microstructural evolution of PTFE, modified PTFE and their composites during non-isothermal crystallization using advanced X-ray scattering measurements. An insight into the changes undergone by the material's microstructural units including crystallite size and morphology, lamellar thickness and lamellar interfacial layer thickness, and crystallographic phase dynamics during non-isothermal cooling from the melt, was provided here in this work. The effect of copolymer modification of PTFE and the inclusion of pristine and functionalized BNNB (a thermally conductive and electrically insulating ceramic) are both new investigations that provide valuable knowledge for the development of materials with strong matrix-nanofiller interaction and guidance for optimizing sintering and cooling cycles, two key steps in PTFE processing that largely affect the material microstructural features. Overall, the result of the three-part investigation demonstrates that BNNB supports crystallization in the modified PTFE up to 20 wt% concentration and at low and high cooling rates typically used in the industrial processing of PTFE.

36 MATERIALS SCIENCE↗

Simultaneous Pc 1 observations by the synchronous satellite ATS-1 and ground stations - Implications concerning IPDP generation mechanisms

Results are presented for an experimental study designed to examine the properties of Pc 1 activity observed simultaneously at ATS 1 and two Canadian ground stations. The Pc 1 activity is found to follow substorm expansion phase onsets and to occur most frequently at dusk. Dynamic spectra waves at both ground stations are that of IPDP (Intervals of Pulsations Diminishing by Period) type Pc 1. A previously proposed mechanism to explain IPDP generation, which required a rapid increase in the equatorial magnetic field to produce IPDP, is inconsistent with the dynamic spectra and magnetic field observations. Either purely azimuthal or a combination of azimuthal and radial inward drift of energetic resonant protons is an equally plausible mechanism to explain IPDP generation.

Bossen, M.↗

Defect‐Free Sound Insulator Using Single Metal‐Based Friction Stir Process Array

Metals are excellent conductors for phonon transportation such as vibration, sound, and heat. Generally, metal sound insulators require multimaterial structure or defects and unimetal sound insulators are challenging. Therefore, a design of a defect-free sound insulator made by single alloys with multiple friction stir processes (FSPs) is proposed. Periodic friction stir processing can induce superlattice-like local mechanical properties’ modifications. By experimental acoustic characterization, it is observed that FSP can introduce clear acoustic–elastic property contrast on an aluminum plate by the presence of stir zone and heat-affected zones. In numerical simulations, the signature FSP-induced property profile is periodically and parallelly arranged on a long aluminum plate. The transmission gap frequencies are present on the frequency spectrum with the sound propagation direction perpendicular to the FSP paths. Disorder offsets on FSP periodicity are further introduced. Anderson localization is found on a resonance frequency, which provides −11 dB sound reduction by an exponential decay. Due to the finite design length, the slight disorder can also enhance sound insulation in the periodic transmission gap frequency. In conclusion, with analysis and comparison with different configurations, the best performance in the models can achieve −30 dB sound insulation in the 350 mm-long aluminum alloy plate with 14 parallel FSPs.

36 MATERIALS SCIENCE↗

A Theoretical Investigation of Composite Overwrapped Pressure Vessel (COPV) Mechanics Applied to NASA Full Scale Tests

A theoretical investigation of the factors controlling the stress rupture life of the National Aeronautics and Space Agency's (NASA) composite overwrapped pressure vessels (COPVs) continues. Kevlar(TradeMark) fiber overwrapped tanks are of particular concern due to their long usage and the poorly understood stress rupture process in Kevlar(TradeMark) filaments. Existing long term data show that the rupture process is a function of stress, temperature and time. However, due to the presence of a load sharing liner, the manufacturing induced residual stresses and the complex mechanical response, the state of actual fiber stress in flight hardware and test articles is not clearly known. This paper is a companion to the experimental investigation reported in [1] and develops a theoretical framework necessary to design full-scale pathfinder experiments and accurately interpret the experimentally observed deformation and failure mechanisms leading up to static burst in COPVs. The fundamental mechanical response of COPVs is described using linear elasticity and thin shell theory and discussed in comparison to existing experimental observations. These comparisons reveal discrepancies between physical data and the current analytical results and suggest that the vessel's residual stress state and the spatial stress distribution as a function of pressure may be completely different from predictions based upon existing linear elastic analyses. The 3D elasticity of transversely isotropic spherical shells demonstrates that an overly compliant transverse stiffness relative to membrane stiffness can account for some of this by shifting a thin shell problem well into the realm of thick shell response. The use of calibration procedures are demonstrated as calibrated thin shell model results and finite element results are shown to be in good agreement with the experimental results. The successes reported here have lead to continuing work with full scale testing of larger NASA COPV hardware.

Greene, N.↗

Non-Genomic Origins of Proteins and Metabolism

It is proposed that evolution of inanimate matter to cells endowed with a nucleic acid- based coding of genetic information was preceded by an evolutionary phase, in which peptides not coded by nucleic acids were able to self-organize into networks capable of evolution towards increasing metabolic complexity. Recent findings that truly different, simple peptides (Keefe and Szostak, 2001) can perform the same function (such as ATP binding) provide experimental support for this mechanism of early protobiological evolution. The central concept underlying this mechanism is that the reproduction of cellular functions alone was sufficient for self-maintenance of protocells, and that self- replication of macromolecules was not required at this stage of evolution. The precise transfer of information between successive generations of the earliest protocells was unnecessary and, possibly, undesirable. The key requirement in the initial stage of protocellular evolution was an ability to rapidly explore a large number of protein sequences in order to discover a set of molecules capable of supporting self- maintenance and growth of protocells. Undoubtedly, the essential protocellular functions were carried out by molecules not nearly as efficient or as specific as contemporary proteins. Many, potentially unrelated sequences could have performed each of these functions at an evolutionarily acceptable level. As evolution progressed, however proteins must have performed their functions with increasing efficiency and specificity. This, in turn, put additional constraints on protein sequences and the fraction of proteins capable of performing their functions at the required level decreased. At some point, the likelihood of generating a sufficiently efficient set of proteins through a non-coded synthesis was so small that further evolution was not possible without storing information about the sequences of these proteins. Beyond this point, further evolution required coupling between proteins and informational polymers that is characteristic to all known forms of life. The emergence of such coupling must be postulated in any scenario of the origin of life, no matter whether it starts with RNA or proteins. To examine the evolutionary potential of non-genomic systems, a simple, computationally tractable model, which is still capable of capturing the essential features of the real system, has been studied computationally. Both constructive and destructive processes have been introduced into the model in a stochastic manner. Instead of assuming random reaction sets, only a suite of protobiologically plausible reactions has been considered. Peptides have been explicitly considered as protoenzymes and their catalytic efficiencies have been assigned on the basis of biochemical principles and experimental estimates. Simulations have been carried out using a novel approach (The Next Reaction Method) that is appropriate even for very low concentrations of reactants. Studies have focused on global autocatalytic processes and their diversity.

Pohorille, Andrew↗

Photoporomechanics: An Experimental Method to Visualize the Effective Stress Field in Fluid-Filled Granular Media

Effective stress governs the mechanical behavior of porous media. In this study, we use photoelasticimetry to visualize the evolving effective stress field in fluid-filled granular media in processes that couple fluid flow and mechanical deformation. We refer to this experimental method as photoporomechanics. We develop a fabrication process to produce millimeter-scale residual-stress-free photoelastic spheres with high geometric accuracy. We use color to quantify the forces acting on the particles over a wide range of forces, while using light intensity for a small range of forces. We then provide an application of photoporomechanics to illustrate the evolution of effective stress during one-dimensional consolidation: a process by which the stresses caused by a sudden load are gradually transmitted through a fluid-filled granular pack as the fluid drains and excess pore pressures dissipate. We report our technique provides a powerful experimental model system to study the grain-scale underpinning of coupled solid-fluid processes in granular media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Mechanical sensors for ultraheavy dark matter searches via long-range forces

Dark matter candidates with masses around the Planck scale are theoretically well-motivated, and it has been suggested that it might be possible to search for dark matter solely via gravitational interactions in this mass range. In this work, we explore the pathway towards searching for dark matter candidates with masses around the Planck scale using mechanical sensors while considering realistic experimental constraints, and develop analysis techniques needed to conduct such searches. These dark matter particles are expected to leave tracks as their signature in mechanical sensor arrays, and we show that we can effectively search for such tracks using statistical approaches to track-finding. We analyze a range of possible experimental setups and compute sensitivity projections for searches for ultraheavy dark matter coupling to the Standard Model via long-range forces. We find that while a search for Planck-scale dark matter purely via gravitational couplings would be exceedingly difficult, requiring ∼80 dB of quantum noise reduction with a 100 3 array of devices, there is a wide range of currently unexplored dark matter candidates which can be searched for with already existing or near-term experimental platforms.

Qin, Juehang [Rice Univ., Houston, TX (United Stat↗

A Theoretical Investigation of Composite Overwrapped Pressure Vessel (COPV) Mechanics Applied to NASA Full Scale Tests

A theoretical investigation of the factors controlling the stress rupture life of the National Aeronautics and Space Administration's (NASA) composite overwrapped pressure vessels (COPVs) continues. Kevlar (DuPont) fiber overwrapped tanks are of particular concern due to their long usage and the poorly understood stress rupture process in Kevlar filaments. Existing long term data show that the rupture process is a function of stress, temperature and time. However due to the presence of a load sharing liner, the manufacturing induced residual stresses and the complex mechanical response, the state of actual fiber stress in flight hardware and test articles is not clearly known. This paper is a companion to a previously reported experimental investigation and develops a theoretical framework necessary to design full-scale pathfinder experiments and accurately interpret the experimentally observed deformation and failure mechanisms leading up to static burst in COPVs. The fundamental mechanical response of COPVs is described using linear elasticity and thin shell theory and discussed in comparison to existing experimental observations. These comparisons reveal discrepancies between physical data and the current analytical results and suggest that the vessel s residual stress state and the spatial stress distribution as a function of pressure may be completely different from predictions based upon existing linear elastic analyses. The 3D elasticity of transversely isotropic spherical shells demonstrates that an overly compliant transverse stiffness relative to membrane stiffness can account for some of this by shifting a thin shell problem well into the realm of thick shell response. The use of calibration procedures are demonstrated as calibrated thin shell model results and finite element results are shown to be in good agreement with the experimental results. The successes reported here have lead to continuing work with full scale testing of larger NASA COPV hardware.

Thesken, John C.↗

Distinct Bimetallic Cooperativity Among Water Reduction Catalysts Containing [Co III Co III ], [Ni II Ni II ], and [Zn II Zn II ] Cores

We report three binuclear species [LCo III 2 (μ-Pz) 2 ](ClO 4 ) 3 (1), [LNi II 2 (CH 3 OH) 2 Cl 2 ]ClO 4 (2), and [LZn II 2 Cl 2 ]PF 6 (3) supported by the deprotonated form of the ligand 2,6-bis[bis(2-pyridylmethyl) amino-methyl]-4-methylphenol were synthesized, structurally characterized as solids and in solution, and had their electrochemical and spectroscopic behavior established. Species 1–3 had their water reduction ability studied aiming to interrogate the possible cooperative catalytic activity between two neighboring metal centers. Species 1 and 2 reduced H 2 O to H 2 effectively at an applied potential of -1.6 V Ag/AgCl , yielding turnover numbers of 2,820 and 2,290, respectively, after 30 minutes. Species 3 lacked activity and was used as a negative control to eliminate the possibility of ligand-based catalysis. Pre- and post-catalytic data gave evidence of the molecular nature of the process within the timeframe of the experiments. Species 1 showed structural, rather than electronic cooperativity, while species 2 displayed no obvious cooperativity. DFT methods complemented the experimental results determining plausible mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗