Three-body Recombination Reactions Research Articles

Py3BR: A software for computing atomic three-body recombination rates.

The three-body recombination reaction, or ternary association, is a termolecular reaction leading to a molecule after a three-body encounter that plays a vital role in many relevant scenarios in chemical physics. Here, we introduce the Python 3-Body Recombination program, which is dedicated to the computation of atomic three-body recombination rate coefficients. The software is based on a classical trajectory approach in hyperspherical coordinates after mapping the three-body problem as a single particle in a higher-dimensional space. This theoretical approach is fully general and applicable to any ion-atom-atom or atom-atom-atom three-body process. The predictive power of the methodology has been tested in several different experimental scenarios, reaching a good description of every system. The code structure is presented alongside examples and tests to ensure the software's capacity. In addition, the performance of the software after parallelization is shown.

High-pressure CO2 dissociation with nanosecond pulsed discharges

We investigate the conversion of CO2 into CO and O2 with nanosecond repetitively pulsed (NRP) discharges in a high-pressure batch reactor. Stable discharges are obtained at up to 12 bar. By-products are measured with gas chromatography. The energy efficiency is determined for a range of processing times, pulse energy, and fill pressures. It is only weakly sensitive to the plasma operating parameters, i.e the extent of CO2 conversion is almost linearly-dependent on the specific energy invested. A conversion rate as high as 14% is achieved with an energy efficiency of 23%. For long processing times, saturation in the yield and a drop in efficiency are observed, due to the increasing role of three-body recombination reactions, as described by zero-dimensional detailed kinetic modeling. The modeling reveals the presence of three-stage kinetics between NRP pulses, controlled by electron-impact CO2 dissociation, vibrational relaxation, and neutral elementary kinetics. Transport effects are shown to be important for CO2 conversion at high pressures. For fill pressures beyond 10 bar, CO2 may locally transit into supercritical states. The supercritical plasma kinetics may bypass atomic oxygen pathways and directly convert CO2 into O2. This work provides a detailed analysis of plasma-based high-pressure CO2 conversion, which is of great relevance to future large-scale sustainable carbon capture, utilization, and storage.

Dynamics of third order direct three-body recombination of heavy ions.

The direct three-body recombination reactions Cs+ + X- + R → CsX + R (X = F, I and R = Ar, Xe) are studied within the quasiclassical trajectory method using diabatic semiempirical potential energy surfaces, the encounters of the ions being non-central. The collision energies range between 1 and 10 eV (values typical for low temperature plasma), while the so-called delay parameter, which characterizes the delay in the arrival of the neutral atom R in relation to the time instant when the distance between the ions attains its minimum, is equal to 0 or 20%. The calculation results include the recombination excitation functions, the opacity functions, and the vibrational and rotational energy distributions of the recombination products. All the four reactions considered exhibit similar overall statistical dynamics, but each process has its own features. On the whole, for both the recombining pairs Cs+ + F- and Cs+ + I-, xenon is more effective than argon as an acceptor of excess energy from the ion pair. The rotational energy distributions of the salt molecules CsF and CsI are almost equilibrium, whereas the vibrational energy distributions are strongly non-equilibrium.

Plasma-Based CH4 Conversion into Higher Hydrocarbons and H2: Modeling to Reveal the Reaction Mechanisms of Different Plasma Sources.

Plasma is gaining interest for CH4 conversion into higher hydrocarbons and H2. However, the performance in terms of conversion and selectivity toward different hydrocarbons is different for different plasma types, and the underlying mechanisms are not yet fully understood. Therefore, we study here these mechanisms in different plasma sources, by means of a chemical kinetics model. The model is first validated by comparing the calculated conversions and hydrocarbon/H2 selectivities with experimental results in these different plasma types and over a wide range of specific energy input (SEI) values. Our model predicts that vibrational–translational nonequilibrium is negligible in all CH4 plasmas investigated, and instead, thermal conversion is important. Higher gas temperatures also lead to a more selective production of unsaturated hydrocarbons (mainly C2H2) due to neutral dissociation of CH4 and subsequent dehydrogenation processes, while three-body recombination reactions into saturated hydrocarbons (mainly C2H6, but also higher hydrocarbons) are dominant in low temperature plasmas.

Effects of non-equilibrium excitation on methane oxidation in a low-temperature RF discharge

The kinetic effects of non-equilibrium excitation by direct electron impact on low-temperature oxidation of CH4 were investigated by experiment and simulation. We focused on the vibrational-electronic-chemistry coupling of methane and oxygen molecules under conditions of immediate reduced electric field strengths of 30–100 Td in an RF dielectric barrier discharge. A detailed plasma chemistry mechanism governing the oxidation processes in an He/CH4/O2 combustible mixture was proposed and studied by including a set of electron impact reactions, dissociative recombination reactions, reactions involving vibrationally- and electronically- excited species, and important three-body recombination reactions. A linear increase in reactant consumption with an increase in plasma power was observed experimentally. This suggested the presence of decoupling between the molecular excitation by plasma and the low-temperature chemistry. However, CO formation showed a non-linear trend, with its formation increasing with lower energy inputs and decreasing at higher energy inputs. By modelling the chemical kinetic sensitivity and reaction pathways, we found that the formation of radicals via the chain propagation reactions CH4  +  O(1D)  →  CH3  +  OH, and O2(a1Δg)  +  H  →  O  +  OH was mainly accelerated by the electronically excited species O(1D) and O2(a1Δg). The numerical simulation also revealed that under conditions of incomplete relaxation, the vibrational species CH4(v) and O2(v) enhanced chain propagating reactions, such as CH4(v)  +  O  →  CH3  +  OH, CH4(v)  +  OH  →  CH3  +  H2O, O2(v)  +  H  →  O  +  OH, thus stimulating the production of active radicals and final products. Specifically, for an E/N value of 68.2 Td in a stoichiometric mixture (0.05 CH4/0.1 O2/0.85 He), O(1D), CH4(v13), and O2(v) were estimated to contribute to 12.7%, 3.6%, and 3.8% of the production of OH radicals respectively. The reaction channel CH4(v13)  +  OH  →  H2O  +  CH3 was estimated to be responsible for 1.6% of the H2O formation. These results highlight the strong roles of vibrational states in a complex plasma chemistry system and provide new insights into the roles of excited species in the low-temperature oxidation kinetics of methane.

Two-dimensional electron density visualization over plasma flare in vacuum breakdown process

Spatiotemporal evolution of plasma flares in a vacuum breakdown process was characterized by various optical techniques including Shack-Hartmann type laser wavefront sensors for two-dimensional electron density imaging, high-speed framing photography for speed determination of flare expansion, and optical emission spectroscopy for plasma composition assessment. The experimental results showed that the plasma flares with high electron densities of 1025 m−3 and gas temperature of 2 eV were initiated on the copper anode and expanded to the vacuum gap with a propagation speed of 6 × 103 m/s. Subsequently, the electron densities in the anode flare tips demonstrated a drastic decrease in a short time scale of 50 ns due to a three-body recombination reaction. The anode flare tips combined with the cathode plasma flares initiated on the copper cathode, and the conductive plasma channels containing flare-induced copper vapor were established in the interelectrode gap. In the final stage of the vacuum breakdown, the copper-vapor-contaminating plasmas were deconstructed and they transformed into the vacuum arc discharges.

Empirical values of branching ratios in the three-body recombination reaction for O(1S) and O2(0,0) airglow chemistry

The branching ratios ε and α in the three-body recombination reaction for O(1S) greenline and O2(0,0) atmospheric band airglow chemistry represent the fraction of O2 that branch into the b1∑g+ and c1∑u- electronic states, respectively. In the present work, the empirical values of these branching ratios have been deduced using a numerical optimization approach. They were obtained using the optimization scheme known as the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) with our MACD-00 model and simultaneous volume emission rate (VER) measurements of the O(1S) greenline and O2(0,0) atmospheric band emissions. The CMA-ES was employed as the optimization algorithm that would match the O(1S) and O2(0,0) VER profiles simulated by the MACD-00 model to observations made by OXYGEN/S35, S310.10, NASA Flight 4.339, ETON flights P229H and P230H, OASIS, SOAP/WINE, MULTIFOT, and WINDII. We found that most of the values deduced for ε were in the [0.1, 0.3] range, while most of the values of α were in the [0.01, 0.03] range. Excluding the outliers, the average branching ratio values involving the production of O2(b1∑g+) and O2(c1∑u-) were determined to be ε = 0.15 ± 0.02 and α = 0.018 ± 0.004, respectively. Overall, the simulations showed good agreement with the observations albeit with some discrepancies in the peak altitudes and shape of the profiles, possibly due to small perturbations in the observed VER profiles that are not considered in our simulations.

An analysis of the explosion limits of hydrogen/oxygen mixtures with nonlinear chain reactions.

The ignition boundary of hydrogen/oxygen mixtures is a Z-shaped curve in the pressure-temperature space, demonstrating the existence of three explosion limits. In this study, a general analysis governing all the three explosion limits in an isothermal environment is performed by considering both linear chain reactions (reactant-radical reactions) and nonlinear chain reactions (radical-radical reactions), in addition to the zeroth-order reactant-reactant reactions. For the nonlinear reactions, it is further shown that the linear-nonlinear coupling has the major influence, while the effect of nonlinear-nonlinear coupling is negligible. Phenomenologically, at low pressures, the competition between linear branching and linear termination as well as wall destruction determines the first and second explosion limits, while the nonlinear chain reactions are unimportant because of the small radical concentrations under these conditions. However, at higher pressures, both linear and nonlinear chain reactions are needed to accurately describe the third limit, which would be underpredicted by considering the linear chain reactions alone. For intermediate and high pressures, the dominant species are HO2 and H2O2, respectively. Mechanistically, the concentration of HO2 becomes higher at higher pressures due to the three-body recombination reaction, H + O2 + M → HO2 + M, such that the radical-radical reactions involving HO2 become important, while the reaction HO2 + HO2 → H2O2 + O2 renders HO2 nonessential at the third limit, with the H2O2 radical generated by the nonlinear chain reactions becoming the controlling species.

Error Analysis of Absolute Rate Coefficient Extrapolated Under Pseudo-First Order Conditions

Computer based simulations for the three-body recombination reaction of nitrogen (II) oxide with the hydroxyl radical have been used to estimate the error associated with the pseudo -first orderapproximation under different simulated conditions. For the absolute rate coefficients calculated by dividing the pseudo -first order constant by the concentration of the reactant in excess, the analysis of the relative error associated with working under pseudo -first order conditions shows that for a reactiants’ ratio higher than 10, the relative error is less than 5%.

Effects of water vapor dilution on the minimum ignition energy of methane, n-butane and n-decane at normal and reduced pressures

Water vapor dilution has great impact on fundamental combustion processes such as ignition, flame propagation and extinction. In the literature, there are many studies on how water vapor addition affects flame propagation and extinction limit. However, the influence of water vapor addition on ignition receives little attention. In this study, numerical simulations considering detailed chemical mechanisms are conducted for the ignition of methane, n-butane and n-decane/air/water vapor mixtures. The emphasis is spent on examining the effects of water vapor dilution on the ignition of these fuels at normal and reduced pressures. The minimum ignition energies (MIE) at different dilution ratios and initial pressures are obtained. It is found that at normal and reduced pressures, the MIE is proportional to the inverse of pressure and it increases exponentially with water vapor dilution ratio. A general correlation among the MIE, pressure and dilution ratio is proposed for each fuel. Furthermore, for stoichiometric methane/air/water vapor mixtures, the chemical and radiation effects of water vapor dilution are isolated and quantified. It is found that the three-body recombination reaction greatly increases the MIE and reduces the dilution limit.

Modeling plasma-assisted methane–air ignition using pre-calculated electron impact reaction rates

Development of practical combustion applications implementing plasma-assisted ignition technology for improved efficiency or fuel versatility will benefit from computationally-feasible models which include the plasma processes governing experimentally-observed combustion enhancement. A detailed chemical kinetic reaction mechanism for methane combustion with relevant plasma reactions has been compiled, including a set of electron impact cross sections for elastic and inelastic collisions with reactants, intermediate species, and products of methane combustion. In addition to electron impact reactions, the present mechanism includes reactions involving vibrationally- and electronically-excited species, dissociative recombination reactions, three-body recombination reactions, charge transfer reactions, and relaxation reactions, taken from the literature where available, and otherwise calculated using published correlations. While many past mechanisms have made assumptions limiting their use to specific regimes such as nanosecond discharges or microwave-enhanced flames, the present mechanism is generalized to include kinetics relating to both high- and low-energy excitation. The chemical kinetic mechanism is designed for use in a two-temperature chemical kinetics solver that tracks the electron temperature in addition to the gas temperature, as non-thermal plasma regimes characteristic to plasma-assisted combustion will typically have electron energies out of equilibrium with the energy of the heavier gas particles. Analysis considers the effects of initial temperature, mixture composition, electron concentration, and electric field strength on plasma ignition effectiveness. As commonly practiced, costly calculation of the Boltzmann equation at every time step is avoided by pre-calculating electron impact reaction rate coefficients using a Boltzmann equation solver. Here we evaluate the pre-calculated rates assumption, showing that ignition predictions depend on the gas composition at which the electron impact reaction rates are generated, but that induced errors are acceptable given the uncertainty in other model parameters such as impact cross sections. Finally, chemical kinetic sensitivity analysis highlights the importance of reactions governing free charge balance and nitrogen vibrational excitation when plasma effects on combustion enhancement are strong.

Dissociative electron attachment to CO2 produces molecular oxygen.

Until recently, it was widely regarded that only one reaction pathway led to the production of molecular oxygen in Earth's prebiotic primitive atmosphere: a three-body recombination reaction of two oxygen atoms and a third body that removes excess energy. However, an additional pathway has recently been observed that involves the photodissociation of CO2 on exposure to ultraviolet light. Here we demonstrate a further pathway to O2 production, again from CO2, but via dissociative electron attachment (DEA). Using anion-velocity image mapping, we provide experimental evidence for a channel of DEA to CO2 that produces O2(X(3)Σ(-)g) + C(-). This observed channel coexists in the same energy range as the competitive three-body dissociation of CO2 to give O + O + C(-). The abundance of low-energy electrons in interstellar space and the upper atmosphere of Earth suggests that the contributions of these pathways are significant and should be incorporated into atmospheric chemistry models.

Allowed energetic pathways for the three-body recombination reaction of nitrogen monoxide with the hydroxyl radical and their potential atmospheric implications

The OH initiated oxidation of nitric oxide (NO) is an important atmospheric reaction being, during the day time, the main channel that leads to the formation of HONO a reservoir species for both OH and odd nitrogen. This work reports ab initio study of the Potential Energy Surface (PES) of NO + OH using density functional theory calculations conducted at the B3LYP level of theory with a 6-311g (d,p) basis set. We confirmed experimental observations pointing out that the main channel for this reaction is the formation the HONO. From the addition of OH to NO both cis and trans isomers of HONO were found to be the formed as stable intermediate, both having a negative enthalpy of formation relative to the reactants, the cis isomer being more stable than the trans one. The ab initio calculations were extended to include the hydrogen extraction mechanism with its respective transition state to investigate the potential existence of a reaction channel leading to the formation of NO2 + H, that was found not to be of significant interest.

Alternative path for bridging the A = 5, 8 gap in neutron-rich nucleosynthesis scenarios

In neutron-rich nucleosynthesis scenarios the mass gaps A = 5, 8 are assumed to be bridged by the three-body electromagnetic recombination reaction 4He(αn, γ)9Be. However, an alternative path, the nuclear four-body neutron-recoil recombination reaction 4He(αnn, n)9Be, is also conceivable in neutron-rich environments. We estimate the rate of the alternative reaction and show that for temperatures of about 109 K it is comparable with the electromagnetic rate if the neutron density is of about 1030 neutrons per cm3. At higher neutron densities the nuclear process dominates.

Quantum-mechanical calculations on pressure and temperature dependence of three-body recombination reactions: application to ozone formation rates.

A quantum-mechanical model is designed for the calculation of termolecular association reaction rate coefficients in the low-pressure fall-off regime. The dynamics is set up within the energy transfer mechanism and the kinetic scheme is the steady-state approximation. We applied this model to the formation of ozone O + O2 + M --> O3 + M for M = Ar, making use of semiquantitative potential energy surfaces. The stabilization process is treated by means of the vibrational close-coupling infinite order sudden scattering theory. Major approximations include the neglect of the O3 vibrational bending mode and rovibrational couplings. We calculated individual isotope-specific rate constants and rate constant ratios over the temperature range 10-1000 K and the pressure fall-off region 10(-7)-10(2) bar. The present results show a qualitative and semiquantitative agreement with available experiments, particularly in the temperature region of atmospheric interest.

Effects of Vibrational Nonequilibrium on the Chemistry of Two-Temperature Nitrogen Plasmas

A new two-temperature chemical kinetics model for nitrogen plasmas is presented. The model is used together with the vibrationally-specific collisional-radiative model to study the effects of vibrational nonequilibrium distributions on the chemical composition of two-temperature atmospheric pressure nitrogen plasmas. It is found that over a wide range of conditions the vibrational levels follow Boltzmann distributions and that the vibrational temperature Tv is well approximated by gas temperature Tg at low electron number densities and by electron temperature Te at high electron number densities. This result suggests that simple kinetic models with two-temperature rate coefficients can be used to reliably model nonthermal plasmas. The calculation also yields a surprising result that, for a given constant gas temperature, the steady-state electron number density exhibits an S-shaped dependence on the electron temperature. This S-shaped behavior is caused by competing ionization, charge transfer reactions, two-body dissociative recombination, and three-body electron recombination reactions, and therefore is characteristic of molecular plasmas.

A WKB analysis of radical growth in the hydrogen-air mixing layer

The chain-branching process leading to ignition in the hydrogen-air mixing layer is studied by application of a novel WKB-like method with a four-step reduced scheme adopted for the chemistry description. Attention is restricted to initial free-stream temperatures above the crossover temperature corresponding to the second explosion limit of H2-O2 mixtures, thereby causing three-body recombination reactions to be negligible in the ignition process. It is shown that the initiation reactions, responsible for the early radical buildup, cease being important when the radical mass fractions reach values of the order of the ratio of the characteristic branching time to the characteristic initiation time, a very small quantity at temperatures of practical interest. The autocatalytic character of the chain-branching reactions causes the radical concentrations to grow exponentially with downstream distance in the process that follows. It is shown that, because of the effect of radical diffusion, the radical growth rate is uniform across the mixing layer in the first approximation, with an exponent given by that of a premixed branching explosion evaluated at the location where the effective Damkohler number based on the flow velocity is maximum. This exponent, as well as the leading-order representation of the radical profiles, are easily obtained by the imposition of a bounded, nonoscillatory behavior on the solution.

Absolute Fluorescence Yields from Electron Irradiated Gases: XeBr*

The techniques of pulse radiolysis and emission spectroscopy have been used to determine absolute total emission yields for the XeBr* exciplex. By application of known formation and quenching rate constants and mechanisms, individual fluorescence yields have been determined for the unquenched three-body ionic recombination reaction, Xe2+ + Br- + Xe → XeBr* + 2Xe, Go+ = 3.40 ± 0.18, and for the reaction of electronically excited xenon atoms with CF3Br, Xe* + CF3Br → XeBr* + CF3, Go* = 0.68 ± 0.10. These experimental yields are compared to the predictions of current theoretical models, which allow calculation of the efficiency for each ion-pair recombination event and excited state reaction to give the fluorescent XeBr* exciplex as 75% and 36%, respectively.

Absolute Fluorescence Yields from Electron-Irradiated Gases. 2. KrF* and XeF*

Absolute total fluorescence yields for the KrF*(B,C) and XeF*(B,C) states have been determined from pulse-electron-irradiated Kr/SF6 and Xe/SF6 gas mixtures. By application of established formation and quenching mechanisms and rate constants, the KrF* yield has been resolved into its two constituent components, corresponding to exciplex formation by excited-state reaction of Kr species and ionic recombination. The initial yield of electronically excited krypton atoms that can react with SF6, Kr* + SF6 → KrF* + products, was determined to be Go* = 0.70 ± 0.10, while the corresponding three-body ionic recombination reaction, Kr2+ + SF6- + Kr → KrF* + products, gave Go+ = 1.70 ± 0.10. Analogous studies of the XeF* emission showed that ionic recombination is essentially the only formation pathway, with a calculated initial fluorescence yield for the reaction Xe2+ + SF6- + Xe → XeF* + products of Go+ = 0.26 ± 0.02. The experimental values are compared to the predictions of current theoretical models, and the importance of alternative reaction pathways is discussed.

Theory of Structures of Hydrogen-Air Diffusion Flames

ABSTRACT The structure of the hydrogen-air counterflow diffusion flame is investigated by Damkohler-n umber asymptotics. Attention is restricted to flowfield strain times smaller than dissociation times but larger than the characteristic chemical time of three-body recombination reactions, thereby placing the system on the upper, vigorously burning branch of the characteristic S-curve of peak temperature as a function of strain time without equilibrium broadening. Under these conditions, it is shown that the reactants can coexist only within a thin reaction zone separating two radical-free equilibrium regions. First, the equations for the counterflow mixing layer in the two outer equilibrium regions are solved in the classical Burke-Schumann limit by the introduction of appropriate conserved scalars that account for variable transport coefficients and variable Schmidt numbers, different for different species. Then, the reaction zone is investigated with scaling that identifies the relevant reduced Damkohler number. While the solutions in the outer zones are peculiar to the counterflow configuration because of their convective-diffusive character, the reactive-diffusive nature of the reaction zone at leading order enables its structure in transformed coordinates to be expressed independently of the geometrical configuration. Matching the solutions from the inner reaction region with those from the outer equilibrium regions yields the first-order asymptotic solution to the problem, which compares favorably with results obtained by numerical integration of the full conservation equations with detailed chemistry and transport descriptions. In particular, the reason that the maximum radical concentration and temperature deficit vary linearly with the one-third power of the strain rate is explained.