Monatomic Species Research Articles

Compactness property of the linearized Boltzmann collision operator for a multicomponent polyatomic gas

The linearized Boltzmann collision operator is fundamental in many studies of the Boltzmann equation and its main properties are of substantial importance. The decomposition into a sum of a positive multiplication operator, the collision frequency, and an integral operator is trivial. Compactness of the integral operator for monatomic single species is a classical result, while corresponding results for monatomic mixtures and polyatomic single species are more recently obtained. This work concerns the compactness of the operator for a multicomponent mixture of polyatomic species, where the polyatomicity is modeled by a discrete internal energy variable. With a probabilistic formulation of the collision operator as a starting point, compactness is obtained by proving that the integral operator is a sum of Hilbert-Schmidt integral operators and operators, which are uniform limits of Hilbert-Schmidt integral operators, under some assumptions on the collision kernel. The assumptions are essentially generalizations of the Grad's assumptions for monatomic single species. Self-adjointness of the linearized collision operator follows. Moreover, bounds on - including coercivity of - the collision frequency are obtained for a hard sphere like model. Then it follows that the linearized collision operator is a Fredholm operator, and its domain is also obtained.

Compactness Property of the Linearized Boltzmann Collision Operator for a Mixture of Monatomic and Polyatomic Species

The linearized Boltzmann collision operator has a central role in many important applications of the Boltzmann equation. Recently some important classical properties of the linearized collision operator for monatomic single species were extended to multicomponent monatomic gases and polyatomic single species. For multicomponent polyatomic gases, the case where the polyatomicity is modelled by a discrete internal energy variable was considered lately. Here we consider the corresponding case for a continuous internal energy variable. Compactness results, stating that the linearized operator can be decomposed into a sum of a positive multiplication operator, the collision frequency, and a compact operator, bringing e.g., self-adjointness, is extended from the classical result for monatomic single species, under reasonable assumptions on the collision kernel. With a probabilistic formulation of the collision operator as a starting point, the compactness property is shown by a decomposition, such that the terms are, or at least are uniform limits of, Hilbert–Schmidt integral operators and therefore are compact operators. Moreover, bounds on—including coercivity of—the collision frequency are obtained for hard sphere like, as well as hard potentials with cutoff like, models, from which Fredholmness of the linearized collision operator follows, as well as its domain.

Unraveling the high catalytic activity of single atom Mo-doped TiO2 toward NH3-SCR: Synergetic roles of Mo as acid sites and oxygen vacancies as oxidation sites

Herein, the single-atom Mo doped TiO2 catalysts with abundant oxygen vacancies (OVs) were fabricated to get a deep insight into the roles of Mo species and OVs for selectivity catalytic reduction (SCR) of NOx. The single-atom Mo doping largely enhances the catalytic activity of TiO2 even with the presence of 5 vol% H2O. Surface Mo species remarkably enhance the strength of Brønsted acid sites on TiO2, which further facilitates the adsorption and activation of NH3 to –NH2. Meanwhile, the in-situ generated OVs largely increase the concentration of monatomic species (O-), which facilitate the oxidation of NO to NO2, thus promoting the catalytic activity below 350 °C. Additionally, the surface polymeric Mo would lead to the side reaction at high-temperature range above 350 °C. This work gives a new insight into the effect of Mo species, and the synergistic role of Mo and OVs in the SCR reaction over Mo-based catalysts.

Diastereoselective Electrocatalytic Hydrogenation of Cyclic Ketones Using a Proton-Exchange Membrane Reactor: A Step toward the Electrification of Fine-Chemical Production

We report the diastereoselective electrocatalytic hydrogenation of cyclic ketones using a proton-exchange membrane (PEM) reactor. The adsorbed monatomic hydrogen species (Hads) generated from protons at the triple-phase boundary of the cathode were found to reduce cyclic ketones with high diastereoselectivity. As high as 94% cis-selectivity was realized under optimal conditions upon using a Rh catalyst. Operando infrared spectroscopy enabled the direct observation of the adsorbed ketone involved in the reaction. We also demonstrate 5 g scale electrolysis of 4-tert-butylcyclohexanone by coupling the hydrogenation process with water oxidation as an anodic reaction. This reaction successfully produced cis-4-tert-butylcyclohexanol, which is 52 times more expensive than the starting material, according to commercial prices, uses only electrical energy and water as the reagent, and, remarkably, does not require H2 gas. This study demonstrates the potential of PEM reactors as reliable, robust, and green systems for the electrochemical production of fine chemicals.

Rare-earth metal-N6 centers in porous carbon for electrocatalytic CO2 reduction.

Single-atom catalysts fabricated using rare earth elements have emerged for electrocatalytic carbon dioxide reduction, but they need to be studied systematically and intensively. Herein, density functional theory was employed to determine the electrocatalytic CO2 reduction activity of rare earth-N6 porous carbon (Re = Ce, Nd, Sm, Eu, Gd, Tb, Er, Tm, Yb, and Lu) single-atom catalysts. The results revealed that the binding energy of the rare-earth atoms to the N6C monolayers in the ten studied Re-N6C monatomic catalysts is much more negative than the cohesion energy of the bulk rare-earth metal, which makes rare-earth atoms stably dispersed in the N6C skeleton. CO is the primary chemical product of electrocatalytic CO2 reduction by Ce, Eu, and Lu. The primary product of the six monatomic species, i.e., Nd, Sm, Tb, Er, Tm, and Yb, is HCOOH. The dominant product of Gd is CH4. The limiting potentials of these catalysts are in the range of 0.31-0.786 V and their overpotentials are in the range of 0.06-0.707 V, all of which are relatively low, showing that they are potential and promising electrocatalysts for CO2 reduction. Subsequently, Eu-N6C was experimentally synthesized and used for electrocatalytic CO2 reduction to obtain CO products, and the overpotential showed good agreement with the theoretically calculated values.

Linearized Boltzmann Collision Operator: I. Polyatomic Molecules Modeled by a Discrete Internal Energy Variable and Multicomponent Mixtures

The linearized Boltzmann collision operator appears in many important applications of the Boltzmann equation. Therefore, knowing its main properties is of great interest. This work extends some classical results for the linearized Boltzmann collision operator for monatomic single species to the case of polyatomic single species, while also reviewing corresponding results for multicomponent mixtures of monatomic species. The polyatomicity is modeled by a discrete internal energy variable, that can take a finite number of (given) different values. Results concerning the linearized Boltzmann collision operator being a nonnegative symmetric operator with a finite-dimensional kernel are reviewed.A compactness result, saying that the linearized operator can be decomposed into a sum of a positive multiplication operator, the collision frequency, and a compact operator, bringing e.g., self-adjointness, is extended from the classical result for monatomic single species, under reasonable assumptions on the collision kernel. With a probabilistic formulation of the collision operator as a starting point, the compactness property is shown by a splitting, such that the terms can be shown to be, or be the uniform limit of, Hilbert-Schmidt integral operators and as such being compact operators. Moreover, bounds on - including coercivity of - the collision frequency are obtained for a hard sphere like model, from which Fredholmness of the linearized collision operator follows, as well as its domain.

Influence of Components Deposition Order on Silver Species Formation in Bimetallic Ag-Fe System Supported on Mordenite

In the present work, various experimental and theoretical methods were combined to study in detail the modifying effect of differences in the order of deposition of components on the state of silver in bimetallic iron–silver samples based on mordenite. In each of the silver-containing samples, the formation of large (≥2 nm in diameter) varieties of silver was observed, which differed from the varieties in the other samples, and in varying degrees. The formation of large Ag NPs on the outer surface of mordenite is explained by the redox interaction of Ag+-Fe2+ and the selectivity of ion exchange. The local surrounding of Ag in the studied samples is different: for AgMOR—monatomic species dominate, FeAgMOR—silver dimers and AgFeMOR—metal particles. In all investigated samples, the partially charged intra-channel Agnδ+ clusters (~0.7 nm in size) were formed due to partial Ag+ reduction and subsequent Ag0 agglomeration into the mordenite channel. Most of the silver in the bulk of the zeolite is represented in the cationic state attached to the mordenite framework by differently coordinated electrostatic forces, which can be Ag-O, Ag-Si or Ag-Al, with variations in interatomic distances and do not depend on the order of metal deposition. In addition, the arrangement of the cations in the side pockets means that the transport channels of mordenite are free, which is favorable for the application of the materials under study in catalysis and adsorption.

Understanding the characteristics of non-equilibrium alternating current gliding arc discharge in a variety of gas mixtures (air, N2, Ar, Ar/O2, and Ar/CH4) at elevated pressures (1–5 atm)

This work aims at clarifying the fundamental mechanisms of non-equilibrium alternating current gliding arc discharge (GAD) by investigating effects of gas compositions and pressures on the GAD characteristics with electrical and optical methods. Interestingly, the glow-to-spark transition was found by adding O2 or CH4 into the argon or modulating the power supply. This transition occurs attributed to the fact that the discharge mode is largely affected by the effective electron decay time (τ) as well as the feedback response of the power supply to the free electron density in the GAD. Short τ or low free electron density tends to result in the spark-type discharge. It further implies that the power supply characteristics is crucial for discharge mode control. The pressure effects on the GAD characteristics were found to vary with gas composition when the same alternating current power supply was used. In N2 or air, the emission intensity from the plasma column increases with pressure while the mean electric field strength (E) along the plasma column decreases with pressure. Differently, in Ar, the emission intensity and E do not change much with pressure. It can be explained by the different energy partition and transfer pathways between monatomic and molecular species. The molecular gases have vibrational excitation pathways to facilitate the electronic excitation and ionization that is different from the monatomic gas.

Computational and experimental insights into reactive forms of oxygen species on dynamic Ag surfaces under ethylene epoxidation conditions

The partial oxidation of ethylene to ethylene oxide (EO) proceeds over supported Ag particles. Adsorption of molecular oxygen upon Ag forms the reactive oxygen species responsible for both epoxidation and combustion reactions, however, the catalyst surface structure and the molecular structure and identity of the reactive oxygen species present remain debated despite past use of appropriate forms of in situ spectroscopy. Specifically, there is no consensus for the molecular origin of widely reported Raman features that appear on contact with only O2 or in reactant mixtures of C2H4 and O2 at pressures and temperatures relevant for the industrial process, in part, due to the lack of concerted ab initio studies that compute vibrational frequencies for oxygen-containing Ag surfaces. Here, we elucidate the molecular structure of the catalyst surface and reactive oxygen species by coordinating spectral deconvolution of transient and steady-state surface-enhanced Raman spectroscopy of Ag catalysts exposed to oxygen (2 – 101 kPa O2, 523 – 673 K) and mixtures of oxygen and ethylene (2 – 101 kPa O2, 0.5 – 9.8 kPa C2H4, 523 K) with ab initio thermodynamic modeling and vibrational frequency calculations. These comparisons suggest that during EO catalysis reconstructed surface oxides form and partially or completely encase metallic Ag particles. Raman features near 600 cm−1 that persist in O2 or cofed C2H4 represent O–Ag–O structural motifs that form only on surface oxides and high oxygen-coverage reconstructed AgxOy surfaces. We assign features centered near 810 – 840 cm−1 and at higher frequencies, which are ubiquitous throughout the literature, to dioxygen complexes partially embedded within an oxide-like overlayer that forms during exposure either to O2 or during steady-state epoxidations. Taken together our results implicate the presence of a combination of monatomic and diatomic surface oxygen species, which emerge with appreciable quantities of subsurface oxygen at temperatures and O2 pressures representative of EO catalysis.

Saturation loadings on 5A zeolite above and below the critical conditions: monatomic species data evaluation and modeling

Saturation loadings on 5A zeolite above and below the critical conditions: monatomic species data evaluation and modeling

Multi-species modeling in the particle-based ellipsoidal statistical Bhatnagar–Gross–Krook method for monatomic gas species

Multi-species modeling is implemented for the particle-based ellipsoidal statistical Bhatnagar–Gross–Krook method for monatomic species in the open-source plasma simulation suite PICLas. After a literature review on available multi-species extensions of the kinetic model equations and approaches for the determination of the transport coefficients, Brull's model is implemented for the former and Wilke's mixing rules and collision integrals for the latter. The implementation is verified with two simulation test cases: a supersonic Couette flow and the hypersonic flow around a 70° blunted cone. The simulation results are compared with the Direct Simulation Monte Carlo (DSMC) method, where good overall agreement can be achieved. However, the determination of the transport coefficients through collision integrals offers better agreement with the DSMC results at acceptable computational cost. For the last test case, a comparison of the computational efficiency is presented.

Dioxygen Activation Pathways over Cobalt Spinel Nanocubes—From Molecular Mechanism into Ab Initio Thermodynamics and 16O2/18O2 Exchange Microkinetics

A unified molecular, thermodynamic, and kinetic picture of dioxygen activation, surface diffusion, and reactivity over stoichiometric and defected cobalt spinel (100) termination was provided by combination of GGA–DFT+U modeling and experimental isotopic exchange investigations using Co3O4 nanocubes. Various diatomic (CoO5c–O2––CoO5c superoxo, CoO5c–O22––CoT2c peroxo, (O–Osurf)2– peroxo) and monatomic (O–CoT2c and O–CoO5c metal-oxo) reactive oxygen species were described in detail regarding their electronic and magnetic structure. The band alignment diagrams between the pDOS of dioxygen and the exposed cobalt cations were constructed and used to rationalize the revealed pronounced speciation of the surface oxygen, depending on the adsorption geometry (monodentate η1, bidentate η2, bridging μ), varying extent of oxygen reduction (one, two, four electrons), and the entailed complex spin relaxation. It was shown that surface cobalt cations work in tandem constituting dual CoO5c–CoO5c and CoO5c–CoT2c sites fo...

Saturation loadings on 13X (faujasite) zeolite above and below the critical conditions. Part III: Inorganic monatomic and diatomic species data evaluation and modeling

The saturation loadings for subcritical adsorption of inorganic monatomic and diatomic species on 13X zeolite are modeled using the modified Rackett model of Spencer and Danner (J Chem Eng Data 17:236–240, 1972) for the saturated liquid densities combined with crystallographic data for the 13X zeolite. A similar equation is derived for supercritical adsorption involving supercritical adsorbate densities and crystallographic data for the 13X zeolite. Adsorption data from the literature are first critically evaluated and then compared to the model. Log–log plots are used to determine whether each isotherm is near saturation; isotherms that exhibit a $${{\left( {\partial \ln q} \right)} \mathord{\left/ {\vphantom {{\left( {\partial \ln q} \right)} {\left( {\partial \ln p} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\partial \ln p} \right)}}$$ slope of zero at the maximum pressure point are assumed to be saturated. The highest loading is used from each isotherm that approaches saturation. Unsaturated isotherms are not considered further. The theoretical equation satisfactorily models the available experimental data for the data that are subcritical. However, a steric factor is required in the model for iodine. 80% of the data for helium, nitrogen and oxygen are in the supercritical region; this data reveals a linear decreasing trend with increasing reduced temperature Tr. For this data a new supercritical model is developed using the reduced critical adsorbate temperature, TCAR, and the slope of the decreasing linear plot against Tr. The physical phenomena causing this effect is considered to be increasing molecular vibration in the cavity reducing the total molecular loading with temperature rise.

Effect of defocusing on laser ablation plume observed by laser-induced fluorescence imaging spectroscopy

We used laser-induced fluorescence imaging with a varying beam focal point to observe ablation plumes from metal and oxide samples of gadolinium. The plumes expand vertically when the focal point is far from the sample surface. In contrast, the plume becomes hemispherical when the focal point is on the sample surface. In addition, the internal plume structure and the composition of the ablated atomic and ionic particles also vary significantly. The fluorescence intensity of a plume from a metal sample is greater than that from an oxide sample, which suggests that the number of monatomic species produced in each plume differs. For both the metal and oxide samples, the most intense fluorescence from atomic (ionic) species is observed with the beam focal point at 3–4 mm (2 mm) from the sample surface.

Effect of antimony on the reaction of nanocrystalline SnO2 with oxygen

Nanocrystalline antimony-doped ([Sb]/([Sb] + [Sn]) = 0–2 at %) SnO2 powders have been synthesized by coprecipitation from solution. The composition, crystal structure, and microstructural parameters of the powders, as well as the antimony distribution in them, have been studied by laser mass spectrometry, X-ray diffraction, low-temperature nitrogen adsorption measurements, and IR spectroscopy. The reaction of the synthesized materials with oxygen has been studied in situ by electrical conductance measurements. Oxygen chemisorption on the surface of unmodified SnO2 leads to predominant formation of the molecular species O2(ads) -. Increasing the Sb concentration in the SnO2‹Sb› samples increases the fraction of the monatomic species O2(ads) -, which can be explained in terms of a combination of crystal-chemical and electronic factors.

Degradation of carbon nanotubes by electron bombardment in radio-frequency glow discharge afterglows

A capacitively coupled radio-frequency afterglow is used to isolate the role of electron bombardment in the degradation process of muti-walled carbon nanotubes (MWNTs). MWNTs grown on a metal substrate act as a nanostructured anode that accelerate and focus electron bombardment, facilitated by the field enhancement effect. Tip-localized MWNT degradation has been observed in scanning electron microscope images showing the progression of the MWNT degradation process. This finding is confirmed by Raman spectra. GC-MS measurements indicate that the major products of MWNT degradation are short unsaturated hydrocarbons, identified as both propyne and 1,3-butadiyne vapours. This finding is corroborated by time-resolved optical emission spectroscopy during plasma oxidation of the degradation products. Analysis of the kinetics of plasma oxidation confirm that MWNT degradation produces species consistent with thermal evaporation, such as short carbon chains, C3–C4, but not monatomic or diatomic species, C1 and C2.

Influence of Partition Function and Interaction Potential on Transport Properties of Thermal Plasmas

This paper, divided into two parts, is devoted to the transport properties at local thermodynamic equilibrium: the first part shows the influences of partition functions through the plasma composition and the second part the influence of interaction potentials. In the first part, for complex chemical mixtures the determination of the partition functions of different species is considered: monatomic, diatomic and polyatomic. In the plasmas the monatomic species are important; we study thoroughly the partition functions of monatomic neutrals and ions. We introduce two cut-off criteria. We test the influence of the two criteria on the partition functions and consequently onto the plasma composition and transport properties. We applied the study to Ar–Cu mixtures. In the second part, an historic study shows that the collision integrals used in calculating the transport properties become more accurate leading to more reliable values of the transport coefficients: application to N2 plasma. Now we have to calculate transport properties of complex mixtures and in these cases, for numerous interactions, a lack of data means that model potentials have to be used to determine collision integrals. In this paper, we have used two potential models: the first, for neutral–neutral and ion–neutral interactions, is an improvement of the Lennard-Jones function and the second is developed, from Stockmayer potential, for polar gases. We compare, for the collision integrals, the results obtained by these two models with those determined with more accurate potentials: applications to CO2 plasma and H2–N2 mixtures.

Supercooled molecular liquids and the glassy phases of chemically bonded N, P, As, Si and Ge

Glassy phases which have insulating character exist for a variety of monatomic species. By contrast, until recently, it has been possible to make bulk metallic glasses (BMG) by vitrification only for multicomponent systems. After a relatively brief summary on supercooling of a few molecular liquids, we review some of the recently reported results on molecular assemblies of the series N, P, As and amorphous Si and Ge. Based on these results, we suggest that the transition metals with their directional bonding might be suitable candidates for the production of BMG by vitrification.

Internal state populations and velocity distributions of monatomic species ejected after the 1064 nm laser irradiation of barium

The plumes accompanying 1064 nm nanosecond pulsed laser ablation of barium in vacuum at three moderate incident laser fluences in the range of 5.3–10.8 J/cm2 have been studied using both wavelength and time resolved optical emission spectroscopy and time-of-flight laser-induced fluorescence. Neutral atoms and both singly and doubly charged monatomic cations in excited states up to near the corresponding ionization limits are identified in the optical emission spectra. The population distributions of low-lying (≤1.41 eV) “dark” states of Ba atoms measured by laser-induced fluorescence revel that the metastable D3J and D12 abundances in the plume are higher than predictions based on assuming a Boltzmann distribution. The D3J and D12 populations are seen, respectively, to decrease slightly and nearly no vary with raising fluence, which contrasts with the increasing trend that is observed in the ground-state Ba(S10) population. At all fluences, the time-of-flight distributions of the whole dark states and of various of the emitting levels are bimodal and well described by Maxwell–Boltzmann and shifted Maxwell–Boltzmann velocity functions, respectively, with different average translational temperatures ⟨T⟩ for each state. The ⟨T⟩ values for the dark states are insensitive to the fluence, while for all emitting species marked variations of ⟨T⟩ with fluence are found. These observations have been rationalized in terms of material ejection from the target being dominated by a phase explosion mechanism, which is the main contributor to the Ba(S10) population. Thermionic emission from the target surface can also release initial densities of free electrons and cations which, at the prevailing irradiances, will arguably interact with the incident laser radiation by inverse bremsstrahlung, leading to further excitation and ionization of the various plume species. Such a heating mechanism ensures that the energy injected to the plume will alter the propagation velocities of the primary inverse bremsstrahlung absorbers, i.e., cations, to a major extent than those of neutral atoms with increasing fluence. Electron-ion recombination occurring early in the plume expansion can lead to the generation of both neutral and ionic species in a manifold of long-lived Rydberg states, from which a radiative cascade will likely ensue. The distinct fluence dependences of the Ba(D3J) and Ba(D12) populations and velocity distributions show up the major complexity that distinguishes their populating mechanisms with respect to the remaining species.

An axisymmetric computational model of generalized hydrodynamic theory for rarefied multi-species gas flows

On the basis of the Eu’s generalized hydrodynamic (GH) theories for diatomic single species gas and monatomic multi-species gas, an axisymmetric GH computational model for multi-species gas containing monatomic and diatomic molecules is developed for the numerical simulation of hypersonic rarefied gas flows. The multi-species GH computational model includes monatomic and diatomic species of O 2 , N 2 , NO, O, N. The mass diffusion flux of the gas mixture is included in the GH constitutive relation. In addition, the physical relationship between the mass diffusion and heat fluxes is added to the evolution equation set. The multi-species GH theory includes the rotational nonequilibrium effect of diatomic molecules by introducing excess normal stress associated with the bulk viscosity. An efficient multi-species GH numerical solver for axisymmetric rarefied flows is then developed by adopting various numerical techniques, such as an adequate nonlinear equation solver for the GH constitutive relation, an accurate flux splitting scheme, multi-grid convergence acceleration and slip-wall boundary conditions. For validation, the proposed computational model is applied to hypersonic rarefied flows over a space shuttle nose, a sphere and a reentry body as well as 1D shock structure. By comparing the results of the multi-species GH model with those of the Navier–Stokes equation and the DSMC, the accuracy and physical consistency of the GH computational model are critically examined.