Collisional Energy Transfer Research Articles

Probing Nonadiabatic Effects in Low-Energy C(3 P j) + H2 Collisions.

Nonadiabatic effects are of fundamental interest in collision dynamics. In particular, inelastic collisions between open-shell atoms and molecules, such as the collisional excitation of C(3 P j) by H2, are governed by nonadiabatic and spin-orbit couplings that are the sole responsible of collisional energy transfer. Here, we study collisions between carbon in its ground state C(3 P j=0) and molecular hydrogen (H2) at low collision energies that result in spin-orbit excitation to C(3 P j=1) and C(3 P j=2). State-to-state integral cross sections are obtained experimentally from crossed-beam experiments with a source of almostpure beam of C(3 P j=0) and theoretically from highly accurate quantum calculations. We observe very good agreement between experimental and theoretical data that demonstrates our ability to model nonadiabatic dynamics. New rate coefficients at temperatures relevant to astrochemical modeling are also provided. They should lead to an increase of the abundance of atomic C(3 P) derived from the observations of interstellar clouds and a decrease of the efficiency of the cooling of the interstellar gas due to carbon atoms.

Atmospheric Oxidation Mechanism of Sabinene Initiated by the Hydroxyl Radicals

The atmospheric oxidation mechanism of sabinene initiated by the OH radical has been studied using quantum chemistry calculations at the CBS-QB3 level and reaction kinetic calculations using transition state theory and unimolecular rate theory coupled with collisional energy transfer. The oxidation is initiated by OH radical additions to the CH2═C< bond with a branching ratio of ∼(92-96)%, while all the hydrogen atom abstractions count for ∼(4-8)% of branching ratio, which was estimated by comparing the rate coefficients of the reactions of sabinene and sabinaketon with the OH radical. Addition of OH to the ═C< carbon forms radical adduct Ra, while addition of OH to the terminal CH2═ carbon forms radical adduct Rb, which would break the three-membered ring promptly and almost completely to radical Re. RRKM-ME calculations obtained fractional yields of 0.40, 0.09, and 0.51 for radicals syn-Ra, anti-Ra, and Re, respectively, at 298 K and 760 Torr. In the atmosphere, the syn/ anti-Ra radical would ultimately transform to sabinaketone in the presence of ppbv levels of NO, while in the transformation of the Re radical, both bimolecular reactions and unimolecular H-migrations could occur competitively for the peroxy radicals formed. The H-migrations in peroxy radicals result in the formation of unsaturated multifunctional compounds containing >C═O, -OH, and/or -OOH groups. Formation of sabinaketone from syn- and anti-Ra and formation of acetone from Re are predicted with yields of ∼0.37 and ∼0.38 in the presence of high NO, being larger than while in reasonable agreement with the experimental values of 0.19-0.23 and of 0.21-0.27, respectively.

Energy transfer in elastic collisions between electrons and trapped ions

Heating of trapped ion clouds by interactions with free electrons crossing the trapping potential was observed. A model describing such a process was proposed and discussed. The presented approach predicts two effects: pushing and heating of the ions' ensemble by electrons. The former was found to be too weak for observation; however, the latter was investigated experimentally. For comparison between experimental results and theoretical predictions, molecular dynamics simulations for various ion ensembles in various temperatures were performed to determine the dependence between ion cloud geometry and its temperature. A heating rate coefficient was defined and determined together with temperatures of ion clouds bombarded with electrons. Good correlation between the two quantities was found, which agrees with the proposed model.

Non-statistical intermolecular energy transfer from vibrationally excited benzene in a mixed nitrogen-benzene bath.

A chemical dynamics simulation was performed to model experiments [N. A. West et al., J. Chem. Phys. 145, 014308 (2016)] in which benzene molecules are vibrationally excited to 148.1 kcal/mol within a N2-benzene bath. A significant fraction of the benzene molecules are excited, resulting in heating of the bath, which is accurately represented by the simulation. The interesting finding from the simulations is the non-statistical collisional energy transfer from the vibrationally excited benzene C6H6 * molecules to the bath. The simulations find that at ∼10-7 s and 1 atm pressure there are four different final temperatures for C6H6 * and the bath. N2 vibration is not excited and remains at the original bath temperature of 300 K. Rotation and translation degrees of freedom of both N2 and C6H6 in the bath are excited to a final temperature of ∼340 K. Energy transfer from the excited C6H6 * molecules is more efficient to vibration of the C6H6 bath than its rotation and translation degrees of freedom, and the final vibrational temperature of the C6H6 bath is ∼453 K, if the average energy of each C6H6 vibration mode is assumed to be RT. There is no vibrational equilibration between C6H6 * and the C6H6 bath molecules. When the simulations are terminated, the vibrational temperatures of the C6H6 * and C6H6 bath molecules are ∼537 K and ∼453 K, respectively. An important question is the time scale for complete energy equilibration of the C6H6 * and N2 and C6H6 bath system. At 1 atm and 300 K, the experimental V-T (vibration-translation) relaxation time for N2 is ∼10-4 s. The simulation time was too short for equilibrium to be attained, and the time for complete equilibration of C6H6 * vibration with translation, rotation, and vibration of the bath was not determined.

Modelling spark-plug discharge in dry air

This work presents a novel numerical strategy for studying the electric discharge produced by a vehicular spark plug in dry air. For such a task an axial symmetric 2D domain is used. The starting gas mixture is formed by molecular nitrogen and oxygen (8:2 ratio). The mathematical model considers heat and species diffusion and convection jointly with a discrete sub-model for energy transfer in electronic, atomic and molecular collisions. Chemical reactions between species are also included. Solutions of source terms is accomplished in the frame of ZDPlaskin, a zero-dimensional plasma modelling tool. The used plasmo-chemical kinetics model includes 53 species and 430 processes. Experimental properties from an actual spark plug discharge are introduced to the simulation. Spatio-temporal evolution of species concentrations are obtained within this model. Gas temperature evolution and species distribution is discussed and compare with available values in literature.

Heterogeneity of hard skin layer in wrinkled PDMS surface fabricated by Ar ion-beam irradiation

The spatial distribution of binding states in the depth direction of a soft polydimethylsiloxane (PDMS) material was investigated in the hard skin layer formed by Ar ion-beam irradiation. The hard skin layer, typically considered silica-like and homogeneous, was heterogeneous, comprising a topmost layer and an intermediate layer. Impinging Ar ions transferred energy to the PDMS medium by collisional energy transfer, which was maximised at the surface and decreased gradually as the ions penetrated the PDMS. The decreasing energy transfer rate from the surface created a heterogeneous hard skin layer. X-ray photoelectron spectroscopic depth profiling showed the existence of the topmost and intermediate layers. In the topmost layer, scission and cross-linking occurred simultaneously; Si–O bonds showed the dissociated state of SiOx (x = 1.25–1.5). Under the topmost layer, the intermediate layer showed mostly cross-linking, with Si–O bonds showing silica-like binding states of SiOx (x = 1.75–2). The spatial distribution of carbon-related bonds such as C–Si and sp3 C–C also showed heterogeneity, yielding a gradient of bond distribution. A theoretical analysis of the collisional energy transfer rate and displacement per atom showed consistency with the XPS depth profiling results.

Evaluating mixture rules and combustion implications for multi-component pressure dependence of allyl + HO2 reactions

Many of the reactions important to combustion proceed through rovibrationally excited complexes, whose evolution depends on energy-transferring collisions with molecules in the surrounding mixture—yielding a strong dependence of rate constants on pressure and collisional energy transfer characteristics of the mixture. In nearly all realistic combustion environments, a substantial fraction of multiple species of distinct collisional energy transfer characteristics are present—thus requiring a “mixture rule” to interpolate kinetic data from individual single-component bath gases. While mixture effects for reactions proceeding through a single potential well to a single channel have been extensively investigated, mixture effects and mixture rules for multi-well and/or multi-channel reactions are significantly less characterized. The present study presents an investigation of the mixture effects, suitability of mixture rules for representing them, and their impacts on combustion predictions for the allyl + HO2 reaction system. The performance of different mixture rules for representing multi-component pressure dependence of rate constants for allyl + HO2 was evaluated through comparisons against master equation calculations for the mixture. The comparisons revealed that the classic linear mixture rule (LMR,P) yields deviations reaching a factor of two for typical combustion mixtures, whereas newly proposed mixture rules based on reduced pressure exhibit lower deviations of generally less ∼ 3%. Simulations of shock tube ignition delay times and jet-stirred reactor species profiles for C3H6 combustion suggest that mixture effects for allyl + HO2 on combustion predictions can be significant and may serve as a plausible explanation of the rate parameter adjustments employed in modeling studies to reproduce combustion measurements. Newly proposed mixture rules based on the reduced pressure are shown to accurately capture these mixture effects within combustion simulations.

Molecular dynamics investigation of energy transfer during gas-surface collisions

In this work, the energy transfer in gas-surface collisions is investigated using the molecular dynamics method. The numerical setup consists of a nitrogen molecule scattering from a graphite surface. The main focus is put on the energy redistribution between different molecular kinetic modes and the surface for the case of strong thermal non-equilibrium. The thermal non-equilibrium is defined as the state when either translational or rotational temperature of impinging molecules differs significantly from that of the surface. Accordingly, two different scenarios have been examined, including rotational and translational excitation of the initial molecular state. In contrast to the molecular beam method, the initial molecular velocities are sampled from the equilibrium Maxwellian distribution, ensuring isotropic incidence angles and energies. The obtained results are expressed in the form of energy transfer coefficients, which are used to quantify the normalized energy loss or gain in a specific mode. Furthermore, the velocity distributions of reflected molecules are analyzed and compared with some of the available wall kernels, providing further insight into the nature of the energy transfer dynamics and scattering process. Additionally, the numerical setup is tested against the available molecular beam experimental data and the obtained results were used to select a suitable numerical force field.

Scattering of CO with H2O: Statistical and classical alternatives to close-coupling calculations.

Energy transfer in inelastic atom-molecule and molecule-molecule collisions can be described theoretically using the quantum-mechanical close-coupling method. Unfortunately, for bimolecular collisions implying heavy colliders and/or for which the potential energy surface has a deep well, the resulting coupled equations become numerically intractable and approximate methods have to be employed. H2O-CO collisions provide an important example for which close-coupling calculations are not feasible. In this paper, we investigate the accuracy of three approximate methods (the coupled states method, the quasi-classical trajectory method, and the statistical adiabatic channel model) to describe inelastic collisions of H2O with CO. We perform scattering calculations on a recent 5D potential energy surface, and we compare the results of the three approximate methods to fully converged close-coupling calculations at energies below 300 cm-1 and at low values of the total angular momentum. We show that the statistical method provides an attractive alternative to fully quantum mechanical close-coupling calculations at low collision energies, while the quasi-classical method is more advantageous at high energies.

Chemical Dynamics Simulations and Scattering Experiments for O2 Collisions with Graphite

Energy transfer in collisions of O2 with a graphite surface was studied by chemical dynamics simulations. The simulations were performed for three collision energies Ei of 2.1, 7.4, and 15 kcal/mol, with the initial incident angle fixed at θi = 45°. Simulations were performed for each Ei at a surface temperature Tsurf = 300 K. For the higher surface temperature of 1177 K, a simulation was only performed for Ei = 15 kcal/mol. The following properties were determined and analyzed for the O2 + graphite collisions: (1) translational energy distributions of the scattered O2; (2) distribution of the final polar and azimuthal angle for the scattered O2; and (3) number of bounces of O2 on the surface before scattering. The average energy transferred to the graphite surface and that remaining in O2 translation, i.e., ⟨ΔEsurf⟩ and ⟨Ef⟩, exhibit a linear dependence with the initial translational energy. For the O2 + graphite scattering, the physisorption/desorption residence time distribution decays exponentially, with an increase in residence time with a decrease in Ei. The rate at which the distribution decreases shows a near-linear dependence with an increase in Ei. For higher collisional energies of 7.4 and 15 kcal/mol, O2 scattering from the surface follows a nearly quasi-trapping desorption process. However, for the lowest collision energy, it mostly follows conventional physisorption/desorption. For all of the scattering conditions considered experimentally, the relationship between the average final translational energy and average scattering angle for the O2 molecules found from the simulations is in excellent agreement with the experimental results. This experimental validation of precise simulation outcomes is important as it indicates that collisional energy-transfer predictions for this system can be reliably used in assessing interfacial energy flow in a variety of technological applications, including high-performance flight systems.

Kinetics of highly vibrationally excited O2(X) molecules in inductively-coupled oxygen plasmas

The high degree of vibrational excitation of O2 ground state molecules recently observed in inductively coupled plasma discharges is investigated experimentally in more detail and interpreted using a detailed self-consistent 0D global kinetic model for oxygen plasmas. Additional experimental results are presented and used to validate the model. The vibrational kinetics considers vibrational levels up to v = 41 and accounts for electron impact excitation and de-excitation (e-V), vibration-to-translation relaxation (V-T) in collisions with O2 molecules and O atoms, vibration-to-vibration energy exchanges (V-V), excitation of electronically excited states, dissociative electron attachment, and electron impact dissociation. Measurements were performed at pressures of 10–80 mTorr (1.33 and 10.67 Pa) and radio frequency (13.56 MHz) powers up to 500 W. The simulation results are compared with the absolute densities in each O2 vibrational level obtained by high sensitivity absorption spectroscopy measurements of the Schumann–Runge bands for O2(X, v = 4–18), O(3P) atom density measurements by two-photon absorption laser induced fluorescence (TALIF) calibrated against Xe, and laser photodetachment measurements of the O− negative ions. The highly excited O2(X, v) distribution exhibits a shape similar to a Treanor-Gordiets distribution, but its origin lies in electron impact e-V collisions and not in V-V up-pumping, in contrast to what happens in all other molecular gases known to date. The relaxation of vibrational quanta is mainly due to V-T energy-transfer collisions with O atoms and to electron impact dissociation of vibrationally excited molecules, e+O2(X, v)→O(3P)+O(3P).

Vibrational energy transfer and dissociation in O2-N2 collisions at hyperthermal temperatures.

Simulation of vibrational energy transfer and dissociation in O2-N2 collisions is conducted using the quasi-classical trajectory method on an ab initio potential energy surface. Vibrationally resolved rate coefficients are obtained in a high-temperature region between 8000 and 20 000 K by means of the cost-efficient classical trajectory propagation method. A system of master equations is constructed using the new dataset in order to simulate thermal and chemical nonequilibrium observed in shock flows. The O2 relaxation time derived from a solution of the master equations is in good agreement with the Millikan and White correlation at lower temperatures with an increasing discrepancy toward the translational temperature of 20 000 K. At the same time, the N2 master equation relaxation time is similar to that derived under the assumption of a two-state system. The effect of vibrational-vibrational energy transfer appears to be crucial for N2 relaxation and dissociation. Thermal equilibrium and quasi-steady state dissociation rate coefficients in O2-N2 heat bath are reported.

Perfluorooctyl bromide & indocyanine green co-loaded nanoliposomes for enhanced multimodal imaging-guided phototherapy

As a highly biocompatible NIR dye, indocyanine green (ICG) has been widely explored for cancer treatment due to its various energy level transition pathways upon NIR light excitation simultaneously, which leads to different theranostic effects (eg. Photoacoustic (PA) and fluorescence imaging (FL), photodynamic and photothermal therapy (PDT&PTT)). However, the theranostic efficiency of ICG is restricted intrinsically, owing to the competitive relationship of its co-existing imaging and therapeutic effect. Moreover, the extrinsic hypoxia nature of tumor further limits its therapeutic effect, especially for the oxygen-dependent PDT. Herein, perfluorooctyl bromide (PFOB), another biocompatible chemical, was integrated with ICG in a nanoliposome structure via a facile two-step emulsion method. Such an ICG&PFOB co-loaded nanoliposomes (LIP-PFOB-ICG) realized computed tomography (CT) contrast imaging in vivo, providing better anatomical information of tumor in comparison to ICG enabled PA and FL imaging. More importantly, LIP-PFOB-ICG inhibited MDA-MB-231 tumor growth completely via intravenous injection through enhanced PDT&PTT synergistic therapy due to the excellent oxygen carrying ability of PFOB, which effectively attenuated tumor hypoxia, improved the efficiency of collisional energy transfer between ICG and oxygen and reduced the expression of heat shock protein (HSP). As expected, the introduction of PFOB within nanoliposomes with ICG has augmented the theranostic effect of ICG comprehensively, which makes this simple biocompatible liposome-based nanoagent a potential candidate for clinical imaging guided phototherapy of cancer.

Collision Frequency for Energy Transfer in Unimolecular Reactions.

Pressure dependence of unimolecular reaction rates is governed by the energy transfer in collisions of reactants with bath gas molecules. Pressure-dependent rate constants can be theoretically determined by solving master equations for unimolecular reactions. In general, master equation formulations describe energy transfer processes using a collision frequency and a probability distribution model of the energy transferred per collision. The present study proposes a novel method for determining the collision frequency from the results of classical trajectory calculations. Classical trajectories for collisions of several polyatomic molecules (ethane, methane, tetrafluoromethane, and cyclohexane) with monatomic colliders (Ar, Kr, and Xe) were calculated on potential energy surfaces described by the third-order density-functional tight-binding method in combination with simple pairwise interaction potentials. Low-order (including non-integer-order) moments of the energy transferred in deactivating collisions were extracted from the trajectories and compared with those derived using some probability distribution models. The comparison demonstrates the inadequacy of the conventional Lennard-Jones collision model for representing the collision frequency and suggests a robust method for evaluating the collision frequency that is consistent with a given probability distribution model, such as the exponential-down model. The resulting collision frequencies for the exponential-down model are substantially higher than the Lennard-Jones collision frequencies and are close to the (hypothetical) capture rate constants for dispersion interactions. The practical adequacy of the exponential-down model is also briefly discussed.

Classical Trajectory Study of Collision Energy Transfer between Ne and C2H2 on a Full Dimensional Accurate Potential Energy Surface.

Collision energy transfer plays an important role in gas phase reaction kinetics and relaxation of excited molecules. However, empirical treatments are generally adopted for the collisional energy transfer in the master equation based approach. In this work, classical trajectory approach is employed to investigate the collision energy transfer dynamics in the C2H2-Ne system. The entire potential energy surface is described as the sum of the C2H2 potential and interaction potential between C2H2 and Ne. It is highlighted that both parts of the entire potential are highly accurate. In particular, the interaction potential is fit to ∼41 300 configurations determined at the level of CCSD(T)-F12a/cc-pCVTZ-F12 with the counterpoise correction. Collision energy transfer dynamics are then carried out on this benchmark potential and the widely used Lennard-Jones and Buckingham interaction potentials. Energy transfers and related probability densities at different collisional energies are reported and discussed.

On the enhancement of p-11B fusion reaction rate in laser-driven plasma by α → p collisional energy transfer

The possibility of triggering an avalanche reaction in laser-driven p-11B fusion by the effect of collisional energy transfer from α particles to protons has recently been debated, especially in connection to the high yield of α particles (4 × 108 per laser shot) achieved on engineered targets at the Prague Asterix Laser System (PALS), with a pulse of 500 J, 0.3 ns FWHM. We elucidate this controversial subject within the framework of a simple two-population model for protons, based on the binary collision theory in a plasma. We find an avalanche characteristic time of almost 1 μs for the 675 keV fusion cross section resonance in typical PALS plasma, upon idealized confinement conditions. This avalanche time is one order of magnitude higher than previously reported, meaning that no such process can substantially develop in plasma at the PALS on the 675 keV resonance, not even in the most optimistic confinement scenarios. Nevertheless, we put forward for further investigation that more realistic conditions for setting up the avalanche regime could rather be attained by suitably targeting the narrow 163 keV resonance in the fusion cross section, also in connection to recently proposed laser-driven magnetic trapping techniques.

Modeling of Vibration-Vibration Energy Transfer in the DSMC Method

Modeling of vibration-vibration (V-V) energy transfer in collisions of diatomic anharmonic oscillators is discussed, applicable for the direct simulation Monte Carlo method. An attempt is made to take into account the fast vibrational relaxation of nitrogen through V-V exchange with oxygen by increasing the vibration-translation relaxation rate by a constant factor. The results have shown that such an approach still significantly overpredicts the available relaxation times. Then, a new approach to account for V-V exchanges is proposed, which incorporates the calculation of near-resonant transitions according to a temperature-dependent probability calibrated with available experimental data. That approach was found to provide quantitative agreement with shock tube measurements of vibrational relaxation in mixtures. While targeting primarily high-temperature air flows, the approach is applicable to any flow where the VV energy transfer needs to be modeled. It provides the benefits of numerical efficiency, simplicity of implementation, and acceptable physical accuracy.

Dissociation channels, collisional energy transfer, and multichannel coupling effects in the thermal decomposition of CH3F.

The thermal unimolecular decomposition of CH3F has been studied with the aim of elucidating the multichannel character of the reaction. Experimentally, the temporal profiles of HF were recorded following the decomposition of CH3F in a shock tube. The profiles indicated that the yield of HF is close to unity at a pressure of ∼100 kPa (Ar bath) over the studied temperature range 1888-2279 K. The reaction channels were explored using quantum chemical calculations, which suggested that the decomposition of CH3F proceeds through direct C-H bond fission (CH3F → CH2F + H) or HF elimination (CH3F → 1CH2 + HF) reactions on the singlet potential energy surface. The rate constants were calculated by multichannel master equation analysis based on statistical reaction rate theory and classical trajectory calculations of the collisional energy transfer process. The analysis indicated that the two decomposition channels are competitive at the high-pressure limit but the 1CH2 + HF channel is dominant under the experimental conditions due to the multichannel coupling effect. The collision model dependency of the predicted rate constants and branching fractions has also been investigated, highlighting the importance of selecting the appropriate model for the collision frequency and energy transfer probability function.

Effect of energy dependence of the density of states on pressure-dependent rate constants.

The FE integral for the normalized Boltzmann-weighted number of unimolecular states above the threshold energy is the key quantity for computing the collision efficiency in the pressure-dependent unimolecular rate theory developed by Troe, who calls this the energy dependence factor of the density of states. By using the Whitten-Rabinovitch approximation and assuming that the Whitten-Rabinovitch a(E) function is independent of energy, FE can be approximated by an analytical formula; this approximate formula is widely used because of its convenience and computational efficiency. Here we test its validity by comparing the rate constants computed by using the approximate FE to the ones determined by using the numerically integrated FE. For small-sized molecules and for reactions with high threshold energies E0, the differences are negligible at all temperatures, but in other cases, the approximate formula tends to underestimate FE and thus overestimates the collision efficiency, and this leads to smaller pressure falloff. When a(E) at high energies differs appreciably from a(E0), we find that the underestimation of pressure-dependent rate constants by using the approximate formula can be greater than a factor of 5 at high temperatures. The physical insight we draw from this study is that, for reactions with threshold energies below about 30 kcal mol-1, the rate of collisional energy transfer can be appreciably slowed down by the increase in the density of states at higher energies, and this increases the falloff effect by which finite-pressure rate constants become lower than the high-pressure limit, especially at higher temperatures.

Probing resonant energy transfer in collisions of ammonia with Rydberg helium atoms by microwave spectroscopy.

We present the results of experiments demonstrating the spectroscopic detection of Förster resonance energy transfer from NH3 in the X1A1 ground electronic state to helium atoms in 1sns 3S1 Rydberg levels, where n = 37 and n = 40. For these values of n, the 1sns 3S1 → 1snp 3PJ transitions in helium lie close to resonance with the ground-state inversion transitions in NH3 and can be tuned through resonance using electric fields of less than 10 V/cm. In the experiments, energy transfer was detected by direct state-selective electric field ionization of the 3S1 and 3PJ Rydberg levels and by monitoring the population of the 3DJ levels following pulsed microwave transfer from the 3PJ levels. Detection by microwave spectroscopic methods represents a highly state selective, low-background approach to probing the collisional energy transfer process and the environment in which the atom-molecule interactions occur. The experimentally observed electric-field dependence of the resonant energy transfer process, probed both by direct electric field ionization and by microwave transfer, agrees well with the results of calculations performed using a simple theoretical model of the energy transfer process. For measurements performed in zero electric field with atoms prepared in the 1s40s 3S1 level, the transition from a regime in which a single energy transfer channel can be isolated for detection to one in which multiple collision channels begin to play a role has been identified as the NH3 density was increased.