Vibrational Kinetics Research Articles

A Global Enhanced Vibrational Kinetic Model for High-Pressure Hydrogen RF Discharges

A global enhanced vibrational kinetic model (GEVKM) is developed for multitemperature, chemically reacting hydrogen plasmas in inductively coupled cylindrical discharges for lowto high-pressure regimes. The species in a GEVKM are ground-state hydrogen atoms H and molecules H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , 14 vibrationally excited hydrogen molecules H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (v), v = 1 - 14, electronically excited hydrogen atoms H(2) and H(3), groundstate positive ions H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> , H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> , and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> , ground-state negative ions H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sup> , and electrons e. The GEVKM involves volume-averaged steady-state continuity equations for the plasma species, an electron energy equation, a total energy equation, a heat transfer equation to the chamber walls, and a comprehensive set of surface and volumetric chemical processes governing vibrational and ionization kinetics of hydrogen plasmas. The GEVKM is verified and validated by comparisons with previous numerical simulations and experimental measurements of a negative hydrogen ion source in the low-pressure (20-100 mtorr), low-absorbed-power-density (0.053-0.32 W/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) regime and of a microwave plasma reactor in the intermediate to high-pressure (1-100 torr), high-absorbed-power-density (8.26-22 W/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) regime. The GEVKM is applied to the simulation of a high-current negative hydrogen ion source (HCNHIS). The HCNHIS consists of a high-pressure (20-65 torr) radio-frequency discharge chamber in which the main production of high-lying vibrational states of the hydrogen molecules occurs, a bypass system, and a low-pressure (0.1-0.4 torr) negative hydrogen ion production region where negative ions are generated by the dissociative attachment of low-energy electrons to rovibrationally excited hydrogen molecules. The discharge pressure and negative hydrogen ion current predicted by the GEVKM compare well with the measurements in the HCNHIS.

LIF study of N2(A3, v = 0–10) vibrational kinetics under nitrogen streamer conditions

The evolution of individual v = 0–10 vibrational levels of N2(A3) metastable species produced by filamentary streamer discharge was investigated by the laser-induced fluorescence technique. Triggered single streamer filament was periodically produced in pure nitrogen at a pressure of 200 torr and metastable species were monitored during the streamer channel decay in the centre of the discharge gap. The observed dynamics of N2(A3) vibrational levels follow two very different scenarios: while higher (v > 6) vibronic levels decay exponentially in hundreds of nanoseconds, the populations of lower levels (v ≤ 6) definitely increase, first reaching a local maximum on a microsecond timescale and then decreasing afterwards. Population maxima of N2(A3, v ≤ 6) levels occur after the streamer onset with a certain delay, which decreases with increasing vibrational number. Interpretation of experimental observation based on a 0D kinetic model of the post-discharge period takes into account the most important processes redistributing populations between the N2(A3), N2 and N2 vibronic levels. The model reproduces experimental observations fairly well, including observed maxima delays occurring due to the collisional cascade, which transfers metastable species from higher even/odd vibrational levels towards v = 0/v = 1 terminal levels through the Δv = 2 vibrational relaxation mechanism. A calibration procedure based on the rate of energy-pooling processes was used to determine absolute populations of the v = 0 and 1 levels from LIF data, and the model results were utilized to place on an absolute scale all the higher (v > 1) measured vibronic levels. Vibrational distributions obtained from calibrated LIF data at selected instants show a reasonable qualitative agreement with model predictions. Population maxima exceeding 3 × 1014 cm−3 were fixed for v = 2 and 3 vibrational levels, while the lowest v = 0 level reaches only 8–9 × 1013 cm−3. Lastly, we show that the observed rate of the v = 2 level decay is not compatible with published rate constants for the v = 2 → v = 0 vibrational relaxation.

Numerical simulation of the two-dimensional structure of glow discharge in molecular nitrogen in light of vibrational kinetics

A two-dimensional computer model of glow discharge in molecular nitrogen in axisymmetric geometry is presented. The glow discharge structure is described within the diffusion-drift model, while the kinetic parameters of the model used are calculated from the solution to the kinetic Boltzmann equation. Calculations of the energy accumulated on the electronically and vibrationally excited levels of molecules and the effectiveness of electron energy conversion to the Joule heat are performed. In the context of state-to-state kinetics of anharmonic oscillators, populations of vibrational levels of molecular nitrogen are calculated.

Physical Parameters and Chemical Composition of a Nitrogen DC Discharge with Water Cathode

This paper reports the results of the experimental study and chemical composition modeling for a DC nitrogen discharge burning above water cathode in the pressure range of 0.1-1 bar and at discharge current of 40 mA. The gas temperature, vibrational temperatures, reduced electric field strength, cathode voltage drop, and emission intensities of some nitrogen bands were obtained from experiment. The modeling chemical composition of plasma was carried out on the basis of these data. At modeling, the combined solution of Boltzmann equation for electrons, equations of vibrational kinetics for ground states of N2 ,O 2 ,H 2 Oa nd NO molecules, equations of chemical kinetics and plasma conductivity equation were used. The calculations agree with the measured bands intensities for the second positive system of N2 and vibrational temperatures of N2ðC 3 PuÞ. In the frame of the model proposed, the data of other studies were explained. The second kind collision of electrons with N2 vibration excited states was shown to affect strongly the electron gas parameters. The electron av- erage energy and electron density are given. The difference between the properties of the discharges in N2 and air at the same conditions are discussed as well.

Vibrational non-equilibrium in the hydrogen–oxygen reaction. Comparison with experiment

A theoretical model is proposed for the chemical and vibrational kinetics of hydrogen oxidation based on consistent accounting of the vibrational non-equilibrium of the HO2 radical that forms as a result of the bimolecular recombination H+O2 → HO2. In the proposed model, the chain branching H+O2 = O+OH and inhibiting H+O2+M = HO2+M formal reactions are treated (in the terms of elementary processes) as a single multi-channel process of forming, intramolecular energy redistribution between modes, relaxation, and unimolecular decay of the comparatively long-lived vibrationally excited HO2 radical, which is able to react and exchange energy with the other components of the mixture. The model takes into account the vibrational non-equilibrium of the starting (primary) H2 and O2 molecules, as well as the most important molecular intermediates HO2, OH, O2(1Δ), and the main reaction product H2O. It is shown that the hydrogen–oxygen reaction proceeds in the absence of vibrational equilibrium, and the vibrationally excited HO2(v) radical acts as a key intermediate in a fundamentally important chain branching process and in the generation of electronically excited species O2(1Δ), O(1D), and OH(2Σ+). The calculated results are compared with the shock tube experimental data for strongly diluted H2–O2 mixtures at 1000 < T < 2500 K, 0.5 < p < 4 atm. It is demonstrated that this approach is promising from the standpoint of reconciling the predictions of the theoretical model with experimental data obtained by different authors for various compositions and conditions using different methods. For T < 1500 K, the nature of the hydrogen–oxygen reaction is especially non-equilibrium, and the vibrational non-equilibrium of the HO2 radical is the essence of this process. The quantitative estimation of the vibrational relaxation characteristic time of the HO2 radical in its collisions with H2 molecules has been obtained as a result of the comparison of different experimental data on induction time measurements with the relevant calculations.

Dimension reduction of non-equilibrium plasma kinetic models using principal component analysis

The chemical complexity of non-equilibrium plasmas poses a challenge for plasma modeling because of the computational load. This paper presents a dimension reduction method for such chemically complex plasmas based on principal component analysis (PCA). PCA is used to identify a low-dimensional manifold in chemical state space that is described by a small number of parameters: the principal components. Reduction is obtained since continuity equations only need to be solved for these principal components and not for all the species. Application of the presented method to a CO2 plasma model including state-to-state vibrational kinetics of CO2 and CO demonstrates the potential of the PCA method for dimension reduction. A manifold described by only two principal components is able to predict the CO2 to CO conversion at varying ionization degrees very accurately.

Absorption Dynamics of Nitric Oxide in Gas Mixtures Excited by Pulsed Discharge

Vibrational relaxation of NO molecules excited by a pulsed e-beam sustained discharge (EBSD) with the use of CO laser probing was studied. We developed numerical model of vibrational kinetics in ensemble of NO molecules due to comparing the experimental and calculated data on absorption dynamics of vibrational excited NO molecules.

Evaluation of the energy efficiency of CO2 conversion in microwave discharges using a reaction kinetics model

We use a zero-dimensional reaction kinetics model to simulate CO2 conversion in microwave discharges where the excitation of the vibrational levels plays a significant role in the dissociation kinetics. The model includes a description of the CO2 vibrational kinetics, taking into account state-specific VT and VV relaxation reactions and the effect of vibrational excitation on other chemical reactions. The model is used to simulate a general tubular microwave reactor, where a stream of CO2 flows through a plasma column generated by microwave radiation. We study the effects of the internal plasma parameters, namely the reduced electric field, electron density and the total specific energy input, on the CO2 conversion and its energy efficiency. We report the highest energy efficiency (up to 30%) for a specific energy input in the range 0.4–1.0 eV/molecule and a reduced electric field in the range 50–100 Td and for high values of the electron density (an ionization degree greater than 10−5). The energy efficiency is mainly limited by the VT relaxation which contributes dominantly to the vibrational energy losses and also contributes significantly to the heating of the reacting gas. The model analysis provides useful insight into the potential and limitations of CO2 conversion in microwave discharges.

Effect of updated relaxation rate constants on the H 2 O vibrational level populations and ro-vibrational spectra in the mesosphere and lower thermosphere

Abstract This paper discusses the formation mechanisms of infrared radiation in H2O ro-vibrational bands in the mesosphere and lower thermosphere (MLT). At these heights and above, the vibrational levels of the molecules involved in radiative transitions are not in local thermodynamic equilibrium (LTE) with the surrounding medium, and the biggest uncertainty source in modeling the IR radiation in molecular bands is associated with the corresponding vibrational kinetics model parameters. In this study, we re-analyze available experimental data of Barnes et al. (2004) and Zittel and Masturzo (1991) and update the rate constant of V–V exchange (k) corresponding to the second vibrational number v2 increase by two and the first (or the third) quantum number decrease by one. The estimated values of k for quenching by N2 and O2 are 1.7 × 10−12 and 1.3 × 10−12 cm3 s−1, respectively. These values are about four times larger than the values used in all earlier models of non-LTE populations of vibrational levels and IR radiation in ro-vibrational bands of H2O. We state that using the same k for all processes of vibrational–vibrational energy exchange does not correspond to laboratory experiments and can lead to offsets both in calculating the vibrational level populations and in H2O concentration retrievals from IR spectral radiance. We provide the estimates of these offsets as well as a list of spectral microwindows, in which H2O radiance is sensitive to uncertainty of k.

A chirped-pulse Fourier-transform microwave/pulsed uniform flow spectrometer. II. Performance and applications for reaction dynamics.

This second paper in a series of two reports on the performance of a new instrument for studying chemical reaction dynamics and kinetics at low temperatures. Our approach employs chirped-pulse Fourier-transform microwave (CP-FTMW) spectroscopy to probe photolysis and bimolecular reaction products that are thermalized in pulsed uniform flows. Here we detail the development and testing of a new K(a)-band CP-FTMW spectrometer in combination with the pulsed flow system described in Paper I [J. M. Oldham, C. Abeysekera, B. Joalland, L. N. Zack, K. Prozument, I. R. Sims, G. B. Park, R. W. Field, and A. G. Suits, J. Chem. Phys. 141, 154202 (2014)]. This combination delivers broadband spectra with MHz resolution and allows monitoring, on the μs timescale, of the appearance of transient reaction products. Two benchmark reactive systems are used to illustrate and characterize the performance of this new apparatus: the photodissociation of SO2 at 193 nm, for which the vibrational populations of the SO product are monitored, and the reaction between CN and C2H2, for which the HCCCN product is detected in its vibrational ground state. The results show that the combination of these two well-matched techniques, which we refer to as chirped-pulse in uniform flow, also provides insight into the vibrational and rotational relaxation kinetics of the nascent reaction products. Future directions are discussed, with an emphasis on exploring the low temperature chemistry of complex polyatomic systems.

Excited-state kinetics and radiation transport in low-temperature plasmas

An advanced self-consistent plasma physics model including non-equilibrium vibrational kinetics, a collisional radiative model for atomic species, a Boltzmann solver for the electron energy distribution function, a radiation transport module coupled to a steady inviscid flow solver and, has been applied to study non-equilibrium in high enthalpy flows for Jupiter’s atmosphere. Two systems have been considered, a hypersonic shock tube and nozzle expansion, emphasizing the role of radiation reabsorption on macroscopic and microscopic flow properties. Large differences are found between thin and thick plasma conditions not only for the distributions, but also for the macroscopic quantities. In particular, in the nozzle expansion case, the electron energy distribution functions are characterized by a rich structure induced by superelastic collisions between excited species and cold electrons.

Ionization Mechanism and Chemical Composition of an Argon DC Discharge with Water Cathode

This paper reports the results of the experimental study and chemical composition modeling for a DC argon discharge burning above water cathode in the pressure range of 0.1–1 bar and at discharge current of 40 mA. The gas temperature, reduced electric field strength, and emission intensities of some argon lines were obtained. On the base of these data, the modeling chemical composition of plasma was carried out. At modeling, the combined solution of Boltzmann equation for electrons, equations of vibrational kinetics for ground states of N2, O2, H2O and NO molecules, equations of chemical kinetics and plasma conductivity equation was used. The calculations agree well with the measured line intensities. It was shown that discharge burns in diffusion mode, at which the stepwise ionization rate of four lower excited states of argon is equal to the rate of charges diffusion losses.

N2, O2, NO state-to-state vibrational kinetics in hypersonic boundary layers: The problem of rescaling rate coefficients to uniform vibrational ladders

The NO formation in a hypersonic boundary layer is investigated by solving a numerical code that couples fluid dynamics and state-to-state vibrational kinetics. An N2/N/O2/O/NO mixture is considered to simulate the space vehicle Earth re-entry problem. Two new sets of state-to-state rate coefficients of the processes O+N2(v)↔NO(w)+N and N+O2(v)↔NO(w)+O are used, calculated in our research group by means of a molecular dynamics approach.Particular attention is payed to rescale the rates of different kinetic processes in order to have a unique vibrational scale for each molecular species (N2, O2, NO). This is not obvious because vibrational levels, obtained from asymptotics of three-body potential of different collisional systems, often do not match, particularly for high-lying vibrational states. The reactions involving NO affect the mass fractions, the molecular vibrational distributions and the heat flux in the boundary layer.

Chemical kinetics of low pressure high density hydrogen plasmas: application to negative ion sources for ITER

This paper presents a systematic kinetic characterization of a low pressure high power hydrogen plasma. The plasma physics is described with a global model coupled to a homogeneous kinetic model for hydrogen. This model involves reactions which describe the vibrational and electronic excited kinetics of H2, the positive and negative (H−) ion kinetics and the H chemistry. This enables the estimation of the particle density and the electron temperature and their evolutions as a function of power (1–100 kW) and pressure (0.3–4 Pa). These very specific plasma conditions involve physical phenomena not occurring in more usual plasmas, such as gas depletion. To account for this gas depletion, we incorporate in the global model both the H neutral heat equation to calculate the H temperature, and the gas pumping. Indeed, the gas depletion is mainly due to H atom heating leading to a higher pumping loss for H atoms. The consideration of the gas depletion allows us to obtain similar behaviors to the experiments when varying power and pressure. From an accurate analysis of the main formation and destruction pathways for each particle, the species kinetics is discussed and a simplified kinetic model that may be used to describe the non-equilibrium plasma in the negative source for ITER is proposed. Finally, the results point to strong coupling existing between the H atom wall recombination coefficient γH and the gas depletion. An increase of γH reduces the gas depletion, affecting the electron temperature and the electron density as well as the whole plasma kinetics.

Vibrational and chemical kinetics in plasma of CO containing gases

This paper discusses the experimental results pointing to the efficient channel of the CO vibrational to the C2 electron energy transfer. The radiation spectra of e3Π, C1Π, D1Σ states of C2 molecules were investigated and the relation of their kinetics to vibrational excitation of CO (X1Σ, v) molecules in the He-CO-O2 gas discharge plasma was discussed. The rate constant for VE- process CO (X1Σ, v≥ 25) + C2 → CO(X1Σ) + C2(D1Σu), was estimated, and kvE ~ 10−14 cm3/c.

State-to-state description of reacting air flows behind shock waves

In the present paper, non-equilibrium flows of the 5-component air mixture N2(i)/O2(i)/NO(i)/N/O behind shock waves are studied taking into account the state-to-state vibrational and chemical kinetics. Equations for the non-equilibrium kinetics including vibrational energy transitions, dissociation, recombination and Zeldovich reactions of NO formation are coupled to gas dynamic equations and solved numerically for different test cases of the re-entry conditions into the Earth atmosphere. Peculiarities of air parameters behind a shock wave formed in an initially vibrationally excited mixture are studied. Various models for state-dependent rates of kinetic processes are used for calculations and their applicability for prediction of flow parameters is discussed. The results obtained in the state-to-state approach are compared with those based on multi-temperature and one-temperature vibrational distributions and estimations for an accuracy of the simplified models are presented.

Vibrational-Chemical Kinetics in Mars Entry Problems

The paper deals with kinetic theory methods modelling of reacting gas flows near spacecrafts entering the Mars atmosphere. For mixtures containing CO2 molecules, the complete kinetic scheme including all vibrational energy transitions, dissociation, recombination and exchange chemical reactions is proposed. For the prediction of gas dynamic parameters and heat transfer to the surface of a spacecraft, a detailed approach taking into account state-to-state CO2 vibrational and chemical kinetics as well as multi-temperature approaches based on quasi-stationary vibrational distributions are used. A more accurate but complicated and time consuming state-to-state model is applied for the numerical simulation of a one-dimensional flow in a boundary layer near the entering body surface. More simple quasi- stationary three-temperature, two-temperature and one-temperature approaches are used for the numerical study of a 2-D viscous shock layer under entry conditions. The vibrational distributions near the surface are far from the local vibrational and chemical equilibrium and a noticeable difference is found between the values of CO2 vibrational-specific energies at the surface obtained by means of the state-to-state and quasi-stationary approaches. At the same time, for all considered approaches, the kinetic model for vibrational distributions and chemical reactions has a weak influence on the heat transfer to the non-catalytic vehicle surface.

Splitting of CO2 by vibrational excitation in non-equilibrium plasmas: a reaction kinetics model

We present a zero-dimensional kinetic model of CO2 splitting in non-equilibrium plasmas. The model includes a description of the CO2 vibrational kinetics (25 vibrational levels up to the dissociation limit of the molecule), taking into account state-specific VT and VV relaxation reactions and the effect of vibrational excitation on other chemical reactions. The model is applied to study the reaction kinetics of CO2 splitting in an atmospheric-pressure dielectric barrier discharge (DBD) and in a moderate-pressure microwave discharge. The model results are in qualitative agreement with published experimental works. We show that the CO2 conversion and its energy efficiency are very different in these two types of discharges, which reflects the important dissociation mechanisms involved. In the microwave discharge, excitation of the vibrational levels promotes efficient dissociation when the specific energy input is higher than a critical value (2.0 eV/molecule under the conditions examined). The calculated energy efficiency of the process has a maximum of 23%. In the DBD, vibrationally excited levels do not contribute significantly to the dissociation of CO2 and the calculated energy efficiency of the process is much lower (5%).

Effects of excluded volume and correlated molecular orientations on Förster resonance energy transfer in liquid water

Förster theory for the survival probability of excited chromophores is generalized to include the effects of excluded volume and orientation correlation in the molecular distribution. An analytical expression for survival probability was derived and written in terms of a few simple elementary functions. Because of the excluded volume, the survival probability exhibits exponential decay at early times and stretched exponential decay at later times. Experimental schemes to determine the size of the molecular excluded volume are suggested. With the present generalization of theory, we analyzed vibrational resonance energy transfer kinetics in neat water. Excluded volume effects prove to be important and slow down the kinetics at early times. The majority of intermolecular resonance energy transfer was found to occur with exponential kinetics, as opposed to the stretched exponential behavior predicted by Förster theory. Quantum yields of intra-molecular vibrational relaxation, intra-, and intermolecular energy transfer were calculated to be 0.413, 0.167, and 0.420, respectively.

Two-dimensional simulation of fast gas heating in an atmospheric pressure streamer discharge and humidity effects

Gas heating in an atmospheric-pressure streamer discharge was analysed by a two-dimensional streamer discharge simulation model describing internal molecular energy transfer. Our two-dimensional streamer simulation model incorporates concepts from the fast gas heating mechanism proposed by Popov (2011 J. Phys. D: Appl. Phys. 44 285201) and our self-developed state-to-state vibrational kinetics. In dry air, gas heating occurs mainly from electron-impact dissociation reactions of O2 molecules and from quenching processes of electronically excited N2(B 3Πg, C 3Πu) molecules and O(1D) atoms. In humid air, rapid vibration-to-translation transitions of H2O and the exothermicity of the OH formation reactions additionally increase the gas temperature. It is shown that gas heating during the discharge pulse increases with humidity.