Nonequilibrium Vibrational Distributions Research Articles

Energy distribution of fragments from H2 and H2 + dissociation by electron impact for the use in numerical models applied to negative ion sources

In negative hydrogen ion sources, the kinetic energy of the atoms is directly related to the negative ion yield at the caesiated converter, with a larger contribution from hot atoms. The energy distribution of hydrogen atoms is related to the formation process: either the kinetic energy release, resulting from dissociation of the hydrogen molecules or molecular ions, or the proton neutralization either in the volume or during reflection at walls. The interpretation of recent experimental measurements related to the translational energy distribution of atoms or positive ions could profit from accurate inclusion of the initial energy distribution in numerical models. In this work, we focus on the calculation of the kinetic energy release for the various dissociation channels due to electron impact on H2 and H2 +, in the Franck-Condon and delta approximation. Since in negative ion sources non-equilibrium vibrational distributions of H2 are found, the energy distribution of fragments is calculated for all vibrational levels. The inverse cumulative distribution functions related to the main dissociation processes are given, as well as the cumulative distributions for all dissociation channels by electron impact, for simple implementation in Monte Carlo numerical simulations. Finally, the application of the method to few cases of interest for negative ion sources is discussed.

Experimental and numerical studies on the thermal nonequilibrium behaviors of CO with Ar, He, and H2

The time-dependent rotational and vibrational temperatures were measured to study the shock-heated thermal nonequilibrium behaviors of CO with Ar, He, and H2 as collision partners. Three interference-free transition lines in the fundamental vibrational band of CO were applied to the fast, in situ, and state-specific measurements. Vibrational relaxation times of CO were summarized over a temperature range of 1110–2820 K behind reflected shocks. The measured rotational temperature instantaneously reached an equilibrium state behind shock waves. The measured vibrational temperature experienced a relaxation process before reaching the equilibrium state. The measured vibrational temperature time histories were compared with predictions based on the Landau–Teller model and the state-to-state approach. The state-to-state approach treats the vibrational energy levels of CO as pseudo-species and accurately describes the detailed thermal nonequilibrium processes behind shock waves. The datasets of state-specific inelastic rate coefficients of CO–Ar, CO–He, CO–CO, and CO–H2 collisions were calculated in this study using the mixed quantum-classical method and the semiclassical forced harmonic oscillator model. The predictions based on the state-to-state approach agreed well with the measured data and nonequilibrium (non-Boltzmann) vibrational distributions were found in the post-shock regions, while the Landau–Teller model predicted slower vibrational temperature time histories than the measured data. Modifications were applied to the Millikan–White vibrational relaxation data of the CO–Ar and CO–H2 systems to improve the performance of the Landau–Teller model. In addition, the thermal nonequilibrium processes behind incident shocks, the acceleration effects of H2O on the relaxation process of CO, and the characterization of vibrational temperature were highlighted.

State-resolved and two-temperature rate coefficients for CO+CO=CO2+C reaction

Several state-resolved and two-temperature models for the rate coefficients of reaction CO+CO=CO2+C are assessed, and a new simple state dependent model is proposed. Various models for the two-temperature non-equilibrium factor are considered: the theoretical alpha-model and the models based on averaging the state-resolved rate coefficients over the Boltzmann distribution. It is shown that for the Starik model, taking into account vibrational excitation of the partner CO molecule as well as the reaction product does not affect the two-temperature reaction rate coefficients. If the vibrational excitation of only one CO molecule is taken into account, the Starik model and that proposed in this work with the parameter U = ∞ yield identical results. However, our model is more general since it is capable to account for the preferential reaction mechanism from high vibrational states. Two-temperature rate coefficients provided by the a-model agree well with the averaged state-to-state ones, but the parameter α cannot be fixed in the entire temperature range and has to be chosen according to the specific ratio T/Tv. Thus, our computationally efficient state-specific model is recommended for state-to-state flow simulations; when being averaged with different non-equilibrium vibrational distributions, it can be used for modeling two-temperature flows.

Experimental study of recombining nitrogen plasmas: I. Vibronic population distributions and nonequilibrium molecular radiation

We present optical emission spectroscopy measurements in recombining nitrogen plasma flows at atmospheric pressure. An inductively coupled plasma torch is used to create an equilibrium plasma, which is then forced to recombine by flowing through a water-cooled tube. For certain conditions, the plasma is forced out of chemical equilibrium. The emission of and is studied to measure the nonequilibrium vibrational density distributions within these electronic states. These densities are found to be highly overpopulated in comparison with their corresponding equilibrium values, which is consistent with previous results in recombining flows. The measured densities are also compared with the predictions of a two-temperature model. This two-temperature model underpredicts the measured densities but is closer to the measured distributions than the equilibrium densities. The total measured radiation is approximately 100 000 times stronger than the corresponding equilibrium radiation. The 2-T model estimate of this radiation is much closer yet still underestimates by a factor of 10 the measured radiation. These data are intended as a new dataset to test the recombining plasma models used to simulate afterbody flows during atmospheric reentry.

Dissociative Electron Attachment From Vibrationally Excited Molecules in Nanosecond Repetitively Pulsed CO Discharges and Afterglows.

Non-equilibrium vibrational distributions and electron energy distributions of CO in nanosecond repetitively pulsed (NRP) discharges and afterglows have been determined from a coupled solution of the time dependent Boltzmann equation for the electron energy distribution function (eedf) of free electrons and the master equations for the vibrational distribution function (vdf) of CO and the electronic excited states of CO and O and C atoms. Emphasis is given to the role of dissociative electron attachment (DEA) from vibrationally excited states in affecting the eedf and vdf under extreme conditions, i.e., an optically thick plasma with quenching processes involving the electronic excited states, populated by a sequence of discharge pulses and corresponding afterglows. In particular, the quenching process of the a3Π electronic state of CO determines a pumping of vibrational quanta in the ground state, which in turn largely modifies the CO vdf promoting the activation of DEA process. DEA rate coefficients have been obtained by using a complete set of vibrational (v) dependent cross sections through the CO−(X2Π) channel and by using the experimental v = 0 cross section of Rapp and Briglia, which should include the contribution of other CO− resonant states. The importance of the last contribution has been also estimated by using a scaling law to extend the v = 0 cross section over all the vibrational ladder of CO. In particular, this mechanism becomes competitive with the other reactive channels for very short inter-pulse delay times, i.e., the tid = 1 μs, being less important for longer inter-pulse delay times, i.e., the tid = 25 μs.

Past and present aspects of Italian plasma chemistry

The linking between the initial activities of the Rome–Bari group to their present activities is discussed in different fields of plasma chemical-physics. Several topics are presented including (1) plasma catalysis, (2) the interaction of alumina particles with thermal plasmas and its linking with the thermodynamics and transport properties of plasmas, and (3) non-equilibrium vibrational kinetics coupled with the Boltzmann equation for the electron energy distribution functions (eedf) in aerospace and cold plasma applications. The old activities in plasma catalysis pointed out the importance of atomic species affecting catalytic reactions opening also to the possibility of non-equilibrium vibrational distributions on the chemisorbed ad-atoms. This last aspect is discussed also taking into account recent developments. The study of the interaction of alumina particles with thermal plasmas was rationalized assuming that the step controlling the reaction could be the heat transfer plasma-particle. The model used a simplified fluid dynamic approach with the insertion of accurate values of thermodynamic and transport properties of thermal plasmas. This kind of activity can be considered precursor on the intense work in the field with particular attention on the importance of electronic excited states in affecting thermodynamics and transport of plasmas. Moreover, the plasma-particle interactions can be recovered to a given extent in the modern aspects of hypersonics in the boundary layer of re-entering vehicles as well as in the nozzle flow expansion. In both cases, we underline the existence of vibrational distributions (vdf) far from the Boltzmann behaviour and rates presenting an anti-Arrhenius trend as a function of the inverse of gas temperature. Concerning the non-equilibrium vibrational kinetics, we discuss two case studies. The first one deals with the behaviour of cold nitrogen plasmas pointing out the role of superelastic vibrational and electronic collisions on vdf and eedf. In this case, we discuss also the same case study comparing the results obtained by a complete set of electron molecule cross-sections acting on the whole vibrational ladder with the corresponding ones which consider transitions starting and arriving to the vibrational ground state of the molecule. The last case study concerns the dissociation kinetics of CO2 in cold plasmas, a topic largely studied in the past to emphasize the role of vibrational excitation in CO2 destruction. Recent results obtained using a sophisticated model based on the coupling of Boltzmann equation for the eedf and a state-to-state vibrational kinetics of the asymmetric ladder of CO2 are reported. The interplay between dissociation process by direct electron impact collision and by heavy particle collisions with vibrationally excited CO2 molecules is discussed.

Multiquantum Transitions in Oxygen and Nitrogen Molecules in Hypersonic Nonequilibrium Flows

A computational fluid dynamics analysis was performed with state-to-state kinetics of oxygen and nitrogen for assessing the influence of vibrational excitation and dissociation on hypersonic flowfields in the range of Mach 7–20. Flows around an axisymmetric forebody geometry were considered by using multiquantum vibrational–translation and dissociation rate coefficients from an ab initio database. The nonequilibrium vibrational energy distributions were modeled by the master kinetic equation. Output quantities of interest included shock standoff distance, translational and vibrational temperatures, and population fractions in the quantum energy states. Both a two-temperature model and a state-to-state kinetics model were used to compare with existing experimental data. The objective of the study was to understand the energy exchange process of multiquantum transitions in the shock layer of a blunt body flow and to assess the maximum number of multiquantum jumps required in describing the nonequilibrium behavior. Multiquantum transitions caused an increase in population in upper energy states due to more efficient energy exchanges. The greater dissociation for the higher multiquantum jumps resulted in reduced shock standoff distance. At the higher Mach numbers, population depletion from the upper energy states demonstrated preferential dissociation. At high temperatures, results indicated that multiquantum transitions had a large influence on the macroscopic parameters of the gas flow behind the shock, especially on the temperature profiles as well as on vibrational population distributions in the upper energy states.

Non-equilibrium electron and vibrational distributions under nanosecond repetitively pulsed CO discharges and afterglows: II. the role of radiative and quenching processes

The non-equilibrium vibrational distributions and electron energy distributions of CO in nanosecond repetitively pulsed discharges and afterglows have been determined from a coupled solution of the time-dependent Boltzmann equation for the electron energy distribution function (eedf) of free electrons, the master equations for vibrational levels of CO and the electronic excited states of CO, O and C atoms. The optically thick plasma conditions have been investigated in a companion paper (part I), while in the present paper we also show the results obtained by allowing radiative emission processes (optically thin plasma) as well as electronic excited state collisional quenching processes. Two case studies, which differ for the duration of the afterglow following each pulse (1 μs and 25 μs case studies) are discussed, and each pulse is characterized by a time-dependent electric field profile in the range 0–20 ns. The results, which depend on the number of pulses considered in the discharge and the corresponding afterglow duration, show several peaks in the eedf due to super-elastic electronic collisions. On the other hand, the quenching process of the a3Π electronic state of CO determines the pumping of vibrational quanta in the v = 27 level, which in turn largely modifies the vibrational distribution function (vdf) of CO. As a consequence, the quenching of the a3Π state increases the reactivity of CO through the Boudouard reaction, and under given conditions, this channel can become more important than the dissociation rates by electron impact collisions.

Reprint of “The effect of site-specific spectral densities on the high-dimensional exciton-vibrational dynamics in the FMO complex”

The coupled exciton-vibrational dynamics of a three-site model of the FMO complex is investigated using the Multi-layer Multi-configuration Time-dependent Hartree (ML-MCTDH) approach. Emphasis is put on the effect of the spectral density on the exciton state populations as well as on the vibrational and vibronic non-equilibrium excitations. Models which use either a single or site-specific spectral densities are contrasted to a spectral density adapted from experiment. For the transfer efficiency, the total integrated Huang-Rhys factor is found to be more important than details of the spectral distributions. However, the latter are relevant for the obtained non-equilibrium vibrational and vibronic distributions and thus influence the actual pattern of population relaxation.

Nonequilibrium internal energy distributions during dissociation

In this work, we propose a model for nonequilibrium vibrational and rotational energy distributions in nitrogen using surprisal analysis. The model is constructed by using data from direct molecular simulations (DMSs) of rapidly heated nitrogen gas using an ab initio potential energy surface (PES). The surprisal-based model is able to capture the overpopulation of high internal energy levels during the excitation phase and also the depletion of high internal energy levels during the quasi-steady-state (QSS) dissociation phase. Due to strong coupling between internal energy and dissociation chemistry, such non-Boltzmann effects can influence the overall dissociation rate in the gas. Conditions representative of the flow behind strong shockwaves, relevant to hypersonic flight, are analyzed. The surprisal-based model captures important molecular-level nonequilibrium physics, yet the simple functional form leads to a continuum-level expression that now accounts for the underlying energy distributions and their coupling to dissociation.

Electron energy and vibrational distribution functions of carbon monoxide in nanosecond atmospheric discharges and microsecond afterglows

Nanopulse atmospheric carbon monoxide discharges and corresponding afterglows have been investigated in a wide range of applied reduced electric field (130 < E/N < 200 Td) and different pulse durations (2–50 ns). The results have been obtained by solving an appropriate Boltzmann equation for the electron energy distribution function (EEDF) coupled to the kinetics of vibrational and electronic excited states as well as to a simplified plasma chemistry for the different species formed during the activation of CO. The molar fraction of electronically excited states generated in the discharge is sufficient to create structures in the EEDF in the afterglow regime. On the other hand, only for long duration pulses (i.e. 50 ns), non-equilibrium vibrational distributions can be observed especially in the afterglow. The trend of the results for the case study E/N = 200 Td, $\unicode[STIX]{x1D70F}_{\text{pulse}}=2$ ns is qualitatively and quantitatively similar to the corresponding case for CO2 implying that the activation of CO2 by cold plasmas should take into account the kinetics of formed CO with the same accuracy as the CO2 itself.

The effect of site-specific spectral densities on the high-dimensional exciton-vibrational dynamics in the FMO complex

The coupled exciton-vibrational dynamics of a three-site model of the FMO complex is investigated using the Multi-layer Multi-configuration Time-dependent Hartree (ML-MCTDH) approach. Emphasis is put on the effect of the spectral density on the exciton state populations as well as on the vibrational and vibronic non-equilibrium excitations. Models which use either a single or site-specific spectral densities are contrasted to a spectral density adapted from experiment. For the transfer efficiency, the total integrated Huang-Rhys factor is found to be more important than details of the spectral distributions. However, the latter are relevant for the obtained non-equilibrium vibrational and vibronic distributions and thus influence the actual pattern of population relaxation.

Non-equilibrium vibrational and electron energy distribution functions in mtorr, high-electron-density nitrogen discharges and afterglows

Non-equilibrium vibrational distributions (vdf) and non-equilibrium electron energy distribution functions (eedf) in a nitrogen plasma at low pressure (mtorr) have been calculated by using a time-dependent plasma physics model coupled to the Boltzmann equation and heavy particle kinetics. Different case studies have been selected showing the non-equilibrium character of both vdf and eedf under discharge and post-discharge conditions in the presence of large concentrations of electrons. Particular attention is devoted to the electron-molecule resonant vibrational excitation cross sections acting in the whole vibrational ladder. The results in the post-discharge conditions show the interplay of superelastic vibrational and electronic collisions in forming structures in the eedf. The link between the present results in the mtorr afterglow regime with the existing eedf in the torr and atmospheric regimes is discussed.

Vibrational-Chemical Coupling in mixtures CO2/CO/O and CO2/CO/O2/O/C

The paper deals with modeling of vibration-chemical coupling in mixtures containing CO2 molecules. The temporal vibrational and chemical relaxation in the five-component and three-component space-homogeneous mixtures CO2/CO/O2/C/O and CO2/CO/O is studied taking into account vibrational energy transitions, dissociation, recombination and exchange chemical reactions. The vibrational-chemical coupling in considered mixtures is studied on the basis of three-temperature, two-temperature and one-temperature vibrational CO2 distributions. Governing equations for macroscopic mixture parameters in the three-temperature, two-temperature and one-temperature approximations are solved numerically for different initial conditions. Comparison of the results obtained in three approaches showed the in uence of non-equilibrium vibrational distributions on chemical reaction rates and on the temporal variation of the gas temperature, mixture composition and vibrational temperatures in two considered mixtures. The role of exchange chemical reactions in relaxation processes is also discussed in the paper.

Statistical dynamics of direct three-body recombination of heavy ions in the presence of argon and xenon atoms

Recombination of singly charged heavy Cs+ and Br– ions with stabilization with neutral Ar or Xe atoms was studied by the classic trajectory method in the range of ion collision energy and third body energy from 1 to 10 eV. The elementary reaction of recombination was studied on the potential energy surface (PES), which quantitatively reproduces the experimental results of collision-induced dissociation of CsBr molecules (the reverse of recombination). An analysis of the statistically reliable number of trajectories revealed a complex multifactor dynamics of recombination, which involves various mechanisms whose realization depends both on the mass and energy ratio of colliding particles and on the PES structure and spatial configurations of collision determined by impact parameters, orientation angles, etc. The molecules that formed as a result of recombination have nonequilibrium vibrational energy distributions and rotational energy distributions comparable to equilibrium.

Chemical reactions in non-equilibrium gas mixtures and mass action law breakdown

Strong deviation of chemical reaction rates from their equilibrium values in vibrationally non-equilibrium gas is shown. Performed analysis is based on a new approach for solving the generalized Boltzmann equation. It allows to overstep the limits of a traditional method, where the part of the collisional integral responsible for chemical reactions is assumed to be small (of the order of the Knudsen number). Another generalization consists in considering both the monomolecular and collisional reaction paths. The influence of non-equilibrium vibrational distributions, which are caused by the chemical reactions, on the chemical reactions themselves is studied. Strong correlation between parallel reactions (when one molecule reacts with a number of others) is shown. The situation when one reaction blocks another one is described. Such a behavior of the reaction rates means the mass action law breakdown.

Charge transmission through single molecules: Effects of nonequilibrium molecular vibrations and photoinduced transitions

A density matrix based description of charge transmission through a single molecule attached to two nano-electrodes is presented. By concentrating on a steady state situation the net current, electronic state populations and nonequilibrium vibrational distributions are computed. The dependence of these quantities on the applied voltage and on a cw-infrared as well as optical excitation is discussed. Effects are included of intra-molecular vibrational energy redistribution (IVR), of different charging states, and of an electron–hole pair generation in the leads. The considerations are valid for a sequential mechanism of charge transmission through the molecule. A possible current switch due to an infrared as well as an optical excitation is demonstrated and the crucial dependence of the switching mechanism on the strength of IVR is underlined. If the molecule attached to nano-electrodes is a part of an oligomer or supramolecular chromophore complex the current can be controlled by an external field induced Frenkel-exciton formation.

Optical field control of charge transmission through a molecular wire. II. Photoinduced removal of the Franck-Condon blockade

Charge transmission through a single molecule attached to two nanoelectrodes is discussed for the case of an additional optical excitation of electronic transitions in the neutral as well as the charged state. $I\text{\ensuremath{-}}V$ and current radiation field-strength characteristics are presented. For large values of nuclear rearrangement upon charging and in the low-voltage region, the current suppression known as the Franck-Condon blockade is completely removed. This suggests optical current switching via the opening of additional transmission channels and the formation of strongly nonequilibrium vibrational distributions. While the triggered current flow sensitively depends on the strength of intramolecular vibrational energy redistribution, it is rather robust with respect to molecular deexcitation caused by electron-hole pair formation in the leads.

Optical field control of charge transmission through a molecular wire. I. Generalized master equation description

A generalized master equation description of charge transmission through a single molecule that goes beyond a perturbative treatment of electron-vibrational coupling and accounts for nonequilibrium vibrational distributions is presented. By utilizing a projection superoperator formalism, exact expressions for the generalized master equation kernels that include intramolecular vibrational energy redistribution, excited electronic levels, as well as their optical excitation and de-excitation are derived. This enables one to study optical current switching in the case of weak electron-lead coupling and large reorganization energy upon charging. Additionally, it is possible to quantify the influence of intramolecular vibrational energy redistribution and excited state de-excitation on the current switching.

On the Coupling of Vibrational Relaxation with the Dissociation−Recombination Kinetics: From Dynamics to Aerospace Applications

A refined set of state-to-state dissociation cross sections for the process N + N2(v, j) → 3N has been obtained by the quasiclassical trajectory (QCT) method and used in a 1D code describing the expansion of a dissociation−recombination mixture through a converging−diverging nozzle. The relevant vibrational kinetics includes V−V and V−T energy transfers as well as dissociation−recombination processes. The results show strong nonequilibrium vibrational distributions and non-Arrhenius dissociation rates along the nozzle axis as a consequence of the recombination process.