Collisional Energy Exchange Research Articles

ENERGY RELAXATION OF HELIUM ATOMS IN ASTROPHYSICAL GASES

We report accurate parameters describing energy relaxation of He atoms in atomic gases, important for astrophysics and atmospheric science. Collisional energy exchange between helium atoms and atomic constituents of the interstellar gas, heliosphere, and upper planetary atmosphere has been investigated. Energy transfer rates, number of collisions required for thermalization, energy distributions of recoil atoms, and other major parameters of energy relaxation for fast He atoms in thermal H, He, and O gases have been computed in a broad interval of energies from 10 meV to 10 keV. This energy interval is important for astrophysical applications involving the energy deposition of energetic atoms and ions into atmospheres of planets and exoplanets, atmospheric evolution, and analysis of non-equilibrium processes in the interstellar gas and heliosphere. Angular- and energy-dependent cross sections, required for an accurate description of the momentum-energy transfer, are obtained using ab initio interaction potentials and quantum mechanical calculations for scattering processes. Calculation methods used include partial wave analysis for collisional energies below 2 keV and the eikonal approximation at energies higher than 100 eV, keeping a significant energy region of overlap, 0.1-2 keV, between these two methods for their mutual verification. The partial wave method and the eikonal approximation excellently match results obtained with each other as well as experimental data, providing reliable cross sections in the astrophysically important interval of energies from 10 meV to 10 keV. Analytical formulae, interpolating obtained energy- and angular-dependent cross sections, are presented to simplify potential applications of the reported database. Thermalization of fast He atoms in the interstellar gas and energy relaxation of hot He and O atoms in the upper atmosphere of Mars are considered as illustrative examples of potential applications of the new database.

Adding particle collisions to the formation of asteroids and Kuiper belt objects via streaming instabilities

Modelling the formation of super-km-sized planetesimals by gravitational collapse of regions overdense in small particles requires numerical algorithms capable of handling simultaneously hydrodynamics, particle dynamics and particle collisions. While the initial phases of radial contraction are dictated by drag forces and gravity, particle collisions become gradually more significant as filaments contract beyond Roche density. Here we present a new numerical algorithm for treating momentum and energy exchange in collisions between numerical superparticles representing a high number of physical particles. We adopt a Monte Carlo approach where superparticle pairs in a grid cell collide statistically on the physical collision time-scale. Collisions occur by enlarging particles until they touch and solving for the collision outcome, accounting for energy dissipation in inelastic collisions. We demonstrate that superparticle collisions can be consistently implemented at a modest computational cost. In protoplanetary disc turbulence driven by the streaming instability, we argue that the relative Keplerian shear velocity should be subtracted during the collision calculation. If it is not subtracted, density inhomogeneities are too rapidly diffused away, as bloated particles exaggerate collision speeds. Local particle densities reach several thousand times the mid-plane gas density. We find efficient formation of gravitationally bound clumps, with a range of masses corresponding to contracted radii from 100 to 400 km when applied to the asteroid belt and 150 to 730 km when applied to the Kuiper belt, extrapolated using a constant self-gravity parameter. The smaller planetesimals are not observed at low resolution, but the masses of the largest planetesimals are relatively independent of resolution and treatment of collisions.

Electron-vibrational energy exchange in collisions of Ar atoms in the 3 P 2 metastable state with N2(X 1S g + ) molecules

Rate constants for electron-vibrational energy exchange Ar(3P2) + N2(X1Σg+, ν = 0) → Ar(1S0) + N2(C3Πu, ν′), where ν′ = 0, 1, 2, were calculated. Calculations were performed taking into account the presence of a resonance in electron scattering by N2(X1Σg+). As a result, the interaction of Ar(3P2) with N2(X1Σg+, ν = 0) was characterized by attraction and, in the end, intersection of electron-vibrational potential surfaces correlating with Ar(3P2) + N2(X1Σg+, ν = 0) and Ar(1S0) + N2(C3Πu, ν′) at interparticle distances of 2.5–3.5 A. Exchange interaction at which electron-vibrational transitions in the region of intersection of electron-vibrational transitions in the region of intersection of electron-vibrational potential surfaces accompanied by spin exchange were induced was calculated by the asymptotic method. The rate constants determined at 300–600 K were on the order of 10−11−10−12 cm3/s and weakly increased as the temperature grew. Mainly the C3Πu, ν′ = 0 state of the N2 molecule was populated. The calculation results were in satisfactory agreement with the experimental data obtained at 300 K.

A statistical approach to energy loss during gas–liquid collisions

A novel theoretical approach to collisional energy exchange during a gas–liquid collision is outlined for the case of a light, fast incoming atom. The method differs from the usual ballistic models of energy exchange in that the energy loss is statistically inferred from the eventual response of the liquid surface to the collision, rather than by directly considering the mechanics of energy transfer into the surface. With this approach, we obtain simple, accurate formulas for the average collisional energy loss and trapping probability of the incoming atom. We also present a graphical method for determining the well depth of the gas–liquid potential.

Electronic energy exchange in high-temperature air

Kinetic processes with the participation of electronic states of atoms and molecules in air behind the shock wave front were analyzed. All metastable levels of molecular and atomic oxygen and nitrogen and nitrogen oxide molecules situated below the dissociation energy were analyzed. In high-temperature air, atom and molecule electronic states are formed in dissociation and recombination, electronic energy exchange in collisions of particles, and chemical exchange reactions. The formation of excited electronic states in the recombination of atoms and isoenergy vibrational energy transfer from highly excited vibrational levels into electronic energy is the fastest process. The quenching of metastable particles occurs in collisions between particles, dissociation and recombination, and chemical exchange reactions. A database on electronic energy exchange rate constants in high-temperature air is presented.

Electron-vibrational energy exchange in collisions of electronically excited N2(A 3Σ u + ) molecules with Zn(X 1 S) atoms

The interaction matrix between the N2 molecule in the X 1Σ g + and A 3Σ u + states and the Zn atom in the 1 S and 3 P states calculated earlier by the asymptotic method was used to find the rate constants for the electron-vibrational energy exchange N2(A 3Σ u + , v) + Zn(1 S) → N2(X 1Σ 8 + , v′) + Zn(3 P). The calculations were performed by the transition state method, and the probabilities of transitions between intersecting electron-vibrational terms of the system in motion along the reaction coordinate were determined by the Landau-Zener equation. The calculated electron excitation transfer constants between N2(A 3Σ u + , v = 1, 0) and Zn(1 S) over the temperature range 300–900 K were on the order of 10−11−10−12 cm3/s.

Theoretical study of the dynamics of hyperthermal collisions of Ar with a fluorinated alkanethiolate self-assembled monolayer

We present a classical-trajectory study of the dynamics of energy exchange in collisions between hyperthermal Ar (6-12 eV collision energy) and a fluorinated self-assembled monolayer (SAM). Product translational-energy, polar-angle, and azimuthal-angle distributions as a function of collision energy and incidence angle are presented to provide a detailed description of the gas/surface energy exchange dynamics. Our results indicate that while the properties of the scattered Ar atom at normal and 30 degrees incidence are notably similar and essentially independent of collision energy in the 6-12 eV range, the dynamics of energy exchange when Ar impinges at 60 degrees are remarkably different and depend on collision energy. This behavior is understood via analysis of the microscopic mechanism of the collisions. Three main collision mechanisms-direct collisions without surface penetration, direct collisions involving surface penetration, and surface-penetrating non-direct collisions-are found to govern the dynamics, and the ratio of these mechanisms determines the properties of the scattered Ar atom. Our study also reveals that the Ar atoms that penetrate the organic monolayer do not desorb following a direct-ejection mechanism proposed in recent studies of Xe collisions with a hydrogenated SAM. The vast amount of energy transferred to the surface found in the calculations lends support to recent experiments showing degradation of fluorinated surfaces in collisions with hyperthermal Ar.

70 years of Landau–Teller theory for collisional energy transfer. Semiclassical three-dimensional generalizations of the classical collinear model

This article, in historical retrospective, describes the development of the celebrated Landau-Teller (LT) model of 1936 for vibrational-translational energy exchange in collisions of an atom with a diatomic molecule. We discuss semiclassical generalizations of the classical LT model and generalizations of the collinear LT model to account for the effects of rotation of the diatom on the vibrational relaxation rate. The former is based on the recovery of the Landau semiclassical exponent from the classical LT encounter time, and the latter on the definition of a 1-D driving mode within the manifold of the translational and rotational degrees of freedom of the colliding partners. The utility of generalized LT models is illustrated by three case studies that exemplify weak and strong effects of the rotation as well as the efficiencies of different driving modes in the vibrational relaxation of highly asymmetric diatoms.

Turbulent ion heating in a plasma with two ion species

A description of ion heating by ion-acoustic turbulence in a plasma containing two ion species of different charge-to-mass ratio is presented. It is shown that, when collisions between ions of different species are ignored, only one of the ion species is heated substantially while the temperature of the other species approaches a constant value that differs insignificantly from the initial ion temperature. The only exception to this is a case in which the plasma parameters are in a particular relationship. For an example of a fully ionized HO plasma, it is shown that taking into account the collisional energy exchange between different ion species removes this restriction on the ion temperature.

Energy exchange in collisions of intrinsic localized modes.

Energy transfer process is examined numerically for the binary collision of intrinsic localized modes (ILMs) in the Fermi-Pasta-Ulam beta lattice. Unlike "solitons" in the integrable systems, ILMs exchange their energy in collision due to the discreteness effect. The mechanism of this energy exchange is examined in detail, and it is shown that the phase difference is the most dominant factor in the energy exchange process and, generally speaking, the ILM with advanced phase absorbs energy from the other. Heuristic model equations which describe the energy transfer of ILMs are proposed by considering the ILMs as interacting "particles." The results due to these equations agree qualitatively very well with those of the numerical simulations. In some cases, the relation between the phase difference of the ILMs and the transferred energy becomes singular, which may be regarded as one of the major mechanisms responsible for the generation of "chaotic breathers."

The dynamics of gas-surface energy exchange in collisions of Ar atoms with ω-functionalized self-assembled monolayers

Atomic-beam scattering experiments using n-alkanethiol and ω-functionalized alkanethiol self-assembled monolayers (SAMs) on gold are employed to explore the dynamics of gas-surface energy exchange in collisions with model organic surfaces. The studies are performed by directing a nearly monoenergetic beam of 80 kJ/mol Ar atoms onto a particular SAM at an incident angle of 30° with respect to the surface normal and recording the time-of-flight distributions for the atoms as they scatter from the surface at a final angle of 30°. Among the monolayers studied, long-chain CH3-terminated SAMs are found to be the most effective at dissipating the translational energy of impinging atoms. For alkanethiols with greater than seven total carbon atoms (HS(CH2)n>6CH3), we find that, for specular scattering conditions, over 80% of the incident energy is transferred to the surface and that over 60% of the impinging atoms approach thermal equilibrium with the surface before scattering back into the gas phase. In contrast to CH3-terminated monolayers, SAMs constructed from hydrogen-bonding alkanethiols: HS(CH2)11OH, HS(CH2)10COOH, and HS(CH2)11NH2, exhibit characteristics of more rigid collision partners. The Ar atoms transfer about 77% of their energy to these surfaces with only 43% of the atoms reaching thermal or near thermal equilibrium before recoiling. Further comparisons of mixed OH- and CH3-terminated SAMs and alkene-terminated SAMs suggest that intramonolayer hydrogen bonding of terminal functional groups may play an important role in determining the extent of energy transfer and thermalization.

The effect of hydrogen-bonding and terminal group structure on the dynamics of Ar collisions with self-assembled monolayers

Gas–surface scattering experiments are used to probe the dynamics of energy exchange in collisions of 80 kJ/mol Ar atoms with self-assembled monolayers (SAMs) composed of HS(CH 2) 11OH, HS(CH 2) 10COOH, HS(CH 2) 11CH 3, and HS(CH 2) 9CHCH 2 alkanethiols on gold. Strong similarities in scattering from the methyl and alkene-terminated SAMs indicate that end-group torsional motion and vibration of the terminal C–C bond play only a minor role in the gas–surface energy transfer dynamics. Both of the purely hydrocarbon monolayers proved to be highly effective at dissipating the Ar incident energy. In scattering experiments performed at a specular angle of 30°, over 60% of the incident Ar atoms reached thermal or near-thermal equilibrium before desorbing from the CH 3- and CH 2-terminated monolayers. For those atoms that do scatter directly from the surfaces after an impulsive collision, less than 13% of their incident energy is retained. In comparison, the OH- and COOH-terminated SAMs also yield nearly identical scattering results, but they appear to be much more rigid than the hydrocarbon monolayers. For the OH and COOH surfaces, only 43% of the atoms scatter at 30° off the surface normal after approaching thermal equilibrium and the atoms that scatter impulsively from the surface retain approximately 17% of their collision energy. Since these energy exchange characteristics do not appear to be the result of alterations in the structure or mass of the four monolayers, and the energy modes in the terminus of the monolayers have only minor influences on energy exchange, the differences in the scattering dynamics are attributed to the hydrogen-bonding nature of the COOH- and OH-terminated alkanethiol self-assembled monolayers.

Plasma temperature measurement of a low-pressure inductively coupled plasma using spectroscopic methods

Direct nebulization of an aqueous sample was successfully carried out in our laboratory in a lab-built low pressure-inductively coupled plasma (LP-ICP) using a double membrane desolvator (DMD). For the particular LP-ICP used, rotational temperatures of selected diatomic molecules and excitation temperatures of Fe II and Fe I were measured. The OH radical showed two rotational temperatures, low and high. The former were obtained in the range 800 to 1100 K, while the latter were obtained between 1850 and 2800 K. The molecular nitrogen ion consistently obtained the same temperatures as those of the high rotational temperatures of the OH radical. This result suggests that the high density of rotational states of these molecules, N+2 and OH radical, allows collisional energy exchange between molecular rotational and argon translational degrees of freedom in the plasma. An increase of plasma gas flow from 0.3 to 1.1 L min−1 produced a decrease of excitation temperatures of Fe II from 10400 to 9200 K. The excitation temperature of Fe I was measured to be about 6000 K. Noticeably, the excitation temperature of Fe ion was high, and even higher than that reported in an atmospheric ICP. This experiment provides proof that the mechanism of ionization and excitation was influenced mainly by the character of electrons in the low-pressure plasma.

Nonisothermal effects in the process of soot formation in ethylene pyrolysis behind shock waves

The nonisothermal nature of hydrocarbon pyrolysis explains the differences in the critical temperatures of soot formation in the experimental studies of these processes. When reaction heats are taken into account, the critical temperatures become close to 1600 K for all the systems studied. The estimated standard enthalpy of carbon atom formation in the composition of soot particles is δHf, z. ≈ 11 ±6 kJ/mol. A kinetic model is proposed for soot formation in ethylene pyrolysis that describes the experimental data. The calculated temperature of soot particles may differ substantially depending on the choice of a model for energy exchange in collisions.

Furnace atomization plasma emission spectrometry with He/Ar mixed gas plasmas

The influence of plasma gas composition on the operating and analytical characteristics of a furnace atomization plasma emission source (FAPES) is presented. He I and Ar I excitation temperatures increase 30% in the mixed gas plasmas whereas argon ion excitation temperatures decrease from 33 000 K to 26 000 K in the presence of He. Collisional exchange of internal energy between excited states of Ar and He accounts for these changes. Average analyte ionization temperatures (for Cr, Mn, Mg, Co, Fe, Cd and Zn), derived from the relative emission intensities of their ionic and atomic lines in a 40-MHz 50-W plasma, increase from 5270 K to 6740 K with the addition of Ar to He. Ionic line intensities increase from 10-fold (Mn) to 40-fold (Cd, Zn) with addition of Ar to the plasma while atomic line intensities increase only twofold. Limits of detection remain substantially unaltered for atomic transitions due to increased noise but are improved twofold (Cd) to 24-fold (Mn) for ionic transitions. The analytical advantages and disadvantages of mixed gas plasmas are discussed. The Ne I excitation temperature at 40 MHz and 50 W was determined to be 4330±80 K.

Rotationally specific rates of vibration–vibration energy exchange in collisions of NO(X 2Π1/2,v=3) with NO(X 2Π,v=0)

Infrared ultraviolet double resonance (IRUVDR) experiments have been performed to investigate the rotational specificity of the vibrational–vibrational (V–V) exchange process, NO(X 2Π1/2,v=3,Ji)+NO(v=0)→NO(X 2Π1/2,v=2,Jf)+NO(v=1), for which the vibrational energy discrepancy corresponds to 55.9 cm−1. Radiation from an optical parametric oscillator was used to excite NO molecules into a specific rotational level (Ji) in the X 2Π, Ω=12, v=3 state. Laser-induced fluorescence (LIF) spectra of the (0,2) band of the A 2Σ+–X 2Π1/2 system were then recorded at delays corresponding to a fraction of a collision. From the relative line intensities, rate coefficients were determined for transfer of the excited NO molecule from the level X 2Π1/2, v=3, Ji to different final rotational levels (Jf) in the X 2Π1/2, v=2 state. Results are reported for Ji=3.5, 4.5, 7.5, 10.5, and 15.5. The data show a significant, though not strong, propensity for J to decrease by one; i.e., for ΔJ=Jf−Ji=−1, especially for the higher Ji levels. This result is interpreted as arising from a combination of (a) the tendency to minimize the energy that has to be accommodated in the relative translation of the collision partners, and (b) the favoring of ΔJ=±1 changes when V–V intermolecular exchange occurs under the influence of dipole–dipole interactions.

A two‐fluid, MHD coronal model

We describe first results from a numerical two‐fluid MHD model of the global structure of the solar corona. The model is two‐fluid in the sense that it accounts for the collisional energy exchange between protons and electrons. As in our single‐fluid model, volumetric heat and momentum sources are required to produce high speed wind from coronal holes, low speed wind above streamers, and mass fluxes similar to the empirical solar wind. By specifying different proton and electron heating functions we obtain a high proton temperature in the coronal hole and a relatively low proton temperature above the streamer (in comparison with the electron temperature). This is consistent with inferences from SOHO/UltraViolet Coronagraph Spectrometer instrument (UVCS) [Kohl et al., 1997], and with the Ulysses/Solar Wind Observations Over the Poles of the Sun instrument (SWOOPS) proton and electron temperature measurements which we show from the fast latitude scan. The density in the coronal hole between 2 and 5 solar radii (2 and 5 RS) is similar to the density reported from SPARTAN 201‐01 measurements by Fisher and Guhathakurta [1994]. The proton mass flux scaled to 1 AU is 2.4 × 108 cm−2 s−1, which is consistent with Ulysses observations [Phillips et al., 1995]. Inside the closed field region, the density is sufficiently high so that the simulation gives equal proton and electron temperatures due to the high collision rate. In open field regions (in the coronal hole and above the streamer) the proton and electron temperatures differ by varying amounts. In the streamer the temperature and density are similar to those reported empirically by Li et al. [1998], and the plasma β is larger than unity everywhere above ∼ 1.5 RS, as it is in all other MHD coronal streamer models [e.g., Steinolfson et al., 1982; also G. A. Gary and D. Alexander, Constructing the coronal magnetic field, submitted to Solar Physics, 1998].

Jump length distribution in molecule-on-substrate diffusion

A kinetic theory is presented to describe the occurrence of long jumps of adsorbed molecules in a one-dimensional periodic potential. Under the assumption of collisional energy exchange with substrate excitations to be strong enough (≳kT), the jump length distribution is given by a simple analytic function of one parameter, the ratio of two characteristic times: the time of flight through a potential cell and the molecule–substrate relaxation time. It is strongly dependent on this ratio. The theory offers the possibility to understand the results of recent experiments.

The effect of electron‐neutral energy exchange on the fluid Farley‐Buneman instability threshold

The traditional equation for the linear instability threshold phase speed υph of Farley‐Buneman waves in terms of electron and ion temperatures is υph2 = (γeTe0 + γiTi0)/mi, with γe and/or γi taken to be identically unity or 5/3, depending on whether the electrons/ions are assumed to behave isothermally or adiabatically. A generalized fluid treatment of Farley‐Buneman waves, using Grad's 8‐moment method for the electrons with isothermal ions, has allowed us to investigate systematically the influence of two classes of electron thermal effects on the threshold phase speed not normally considered in fluid approaches. The first class is associated with the electron temperature dependence of the electron‐neutral momentum transfer collision frequency, which leads to coupling between momentum and heat flow (thermal force and thermoelectric effects). The second class is electron‐neutral collisional energy exchange and, in particular, the contribution of inelastic processes to electron energetics. A dispersion relation is presented in a form that makes manifest its consistency with earlier, less general treatments. From this dispersion relation an equation for υph2 is obtained, and in turn, an equation for an “effective γe” is presented. Our analysis of this equation leads to simple criteria that indicate when electron‐neutral collisional energy exchange becomes important, as well as when departures from isothermality become significant. While our formalism is valid for Farley‐Buneman waves in both the equatorial and auroral electrojets, our computed results focus on the auroral situation, allowing for background electron temperatures Te0 ranging from the neutral background to 1000 K.

Multiphoton excitation ionization of N_2 following collisional energy transfer with H_2O: a potential measure of molecular mixing

A multiphoton ionization excitation of N(2) following collisional energy exchange with optically excited H(2) O was demonstrated, and its potential for measuring H(2) O-N(2) mixing at the molecular level was evaluated. In this process, N(2) is sensitized by a collisional energy exchange with H(2)O molecules excited by a tunable KrF laser. The sensitized N(2) molecules are further excited and ionized by two additional photons of the same laser pulse. Independent images of sensitized N2(+) emission at 391.4 nm and by OH at 308 nm formed by the dissociation of excited H(2)O were obtained along a laser beam traversing slow dry-air and N(2) jets entering room air. Although effects of O(2) and N(2) collisional quenching were noted, such images can potentially be used to measure H(2)O-N(2) molecular mixing and the concentration of H(2)O independently. The detection of H(2)O nucleation by this technique suggests that imaging of H(2)O droplet evaporation or visualizing and monitoring H(2)O condensation may also be possible.