A parametric study of electron energy distribution functions and rate and transport coefficients in nonequilibrium helium plasmas

Electron energy distribution functions in helium plasmas have been calculated by solving the Boltzmann equation at given values of reduced electric field, in the presence of superelastic and electron-electron collisions. Analytical expressions have been found connecting macroscopic coefficients to reduced electric field E/N, relative metastable concentration [He(2³S)]/N, and degree of ionization n_e/N.     

Impact of electron-electron interaction on the electron energy distribution function in molecular plasmas under rf field action

Calculations of the electron energy distribution and of relevant macroscopic quantities of collision-dominated, weakly ionized plasmas under rf field action have been performed with increasing degrees of ionization, and the impact of the electron-electron interaction on these quantities was determined. The investigations were performed for the gas plasmas in CO and H₂ as representatives of molecular plasmas The energy distribution and macroscopic quantities are obtained by solving the nonstationary Bolizmann equation for a given rf field and degree of ionization taking into accoung and additional Fokker-Planck term besides the collision integrals for the elastic and the main inelastic collision processes. In these molecular plasmas a remarkable impact of the electron-electron interaction connected with increasing Maxwellization is observed for degrees of ionization greater than 10.     

Comparison of reaction rates for ozone-alkene and ozone-alkane systems in the gas phase and in solution

Rate constants for ozone-alkene and ozone-alkane reactions in the gas phase and in solution are compared for 16 hydrocarbons. The gas-phase reactions proceed slower than the reactions in solution. The ratios of the rate constants in the liquid and gas phases differ for ozone-alkene (17) and ozone-alkane (2.4) reactions.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2391–2393, December, 1995.     

Coupling of radiation,excited states and electron energy distribution function in non equilibrium hydrogen plasmas

Some of the recent efforts in the state-to-state modeling of H/H₂-based plasma are considered, with particular concern to the aspects of self-consistent coupling between the chemical kinetics, electron kinetics and radiation. These aspects are first illustrated in the case of a 0-dimensional model considering both optically thin and optically thick cases in recombining and ionizing regimes. In the second part of the paper, a 1-dimensional extension of the model is applied to study a steady normal shock generated in an H₂/He plasma of interest in atmospheric entry problems. A radiation transfer equation is coupled to the model as well, to analyze the effect of radiation transfer on chemical kinetics and compare to the commonly used thin and thick plasma approximations. The most significant result is the influence of reabsorption on the concentration of excited states, which in turn creates additional structure on the electron energy distribution function through second kind collisions.     

A simple approach to treat anisotropic elastic collisions in Monte Carlo calculations of the electron energy distribution function in cold plasmas

A simplified method allowing one to treat anisotropic electron heavy species elastic scattering in MonteCarlo models of gas discharges with the proper value for collision frequency is proposed The method is applied to an electric discharge in a Ne · Xe/HCl mixture, and the results are compared with the solution of the two-term expansion of the Boltzmann equation under the same conditions. Methods for reduction of computational time in Monte Carlo codes and the use of the Monte Carlo flux method are also discussed.     

The study of electron energy distribution functions, Swarm parameters, and transition rates in N2+O2 plasma

Using the Boltzman equation electron energy distribution functions, swarm parameters (mean energy, characteristic energy, drift velocity and diffusion coefficient), and transition rates (one for vibrational and one for electronical excitation for each of the gases) for N₂+O₂ (80%+20%) mixture plasma have been calculated. The influence of the applied reduced electric field and the vibrational temperatures on these quantities is studied.     

On the mechanisms of spatial electron relaxation in nonisothermal plasmas

The impact of different collision processes of the electrons with the gas atoms on their spatial relaxation under the action of space-independent electric fields is analyzed in a weakly ionized, collision-dominated helium plasma. Based on the numerical solution of the one-dimensional inhomogeneous electron Boltzmann equation, the spatial evolution of the electron velocity distribution function and of the related macroscopic quantities is investigated for different models concerning the treatment of the elastic, exciting, and ionizing collision processes. The spatial relaxation into homogeneous states is initiated by a disturbance which is directly imposed on the electron velocity distribution as a boundary condition. At moderate and higher electric fields this disturbance excites spatially periodic structures in the distribution function which are damped out by special mechanisms inherent in the exciting and ionizing collision processes. With decreasing field strength the damping due to the energy loss in elastic collisions becomes more effective and causes at lower fields an aperiodic establishment into homogeneous states.     

A quantum theory of chemical processes and reaction rates based on diabatic electronic functions coupled in an external field

The method discussed in this work provides a theoretical framework where simple chemical reactions resemble any other standard quantum process, i.e., a transition in quantum state mediated by the electromagnetic field. In our approach, quantum states are represented as a superposition of electronic diabatic basis functions, whose amplitudes can be modulated by the field and by the external control of nuclear configurations. Using a one-dimensional three-state model system, we show how chemical structure and dynamics can be represented in terms of these control parameters, and propose an algorithm to compute the reaction probabilities. Our analysis of effective energy barriers generalizes previous ideas on structural similarity between reactant, and product, and transition states using the geometry of conventional reaction paths. In the present context, exceptions to empirical rules such as the Hammond postulate appear as effects induced by the environment that supplies the external field acting on the quantum system.     

Force-field parametrization based on radial and energy distribution functions

We propose a novel force-field-parametrization procedure that fits the parameters of potential functions in a manner that the pair distribution function (DF) of molecules derived from candidate parameters can reproduce the given target DF. Conventionally, approaches to minimize the difference between the candidate and target DFs employ radial DFs (RDF). RDF itself has been reported to be insufficient for uniquely identifying the parameters of a molecule. To overcome the weakness, we introduce energy DF (EDF) as a target DF, which describes the distribution of the pairwise energy of molecules. We found that the EDF responds more sensitively to a small perturbation in the pairwise potential parameters and provides better fitting accuracy compared to that of RDF. These findings provide valuable insights into a wide range of coarse graining methods, which determine parameters using information obtained from a higher-level calculation than that of the developed force field. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.     

Electron energy distribution functions and dissociation kinetics of HCl in non-equilibrium plasmas

Electron energy distribution functions (edf) have been calculated by numerically solving the Boltzmann equation coupled to a system of vibrational master equations which simulates both the vibrational relaxation due to e—V (electron—vibration), V—V (vibration—vibration) and V—T (vibration—translation) energy exchanges and the dissociation process. The calculated edf strongly depend on the vibrational nonequilibrium present in the gas phase, even though the atoms coming from the dissociation process tend to destroy the vibrational energy content of the molecules. Vibrationally excited molecules determine a joint vibro—electronic mechanism in the dissociation of HCl. This mechanism is the more efficient the smaller the gas temperature and pressure. Finally the contribution of a purely vibrational mechanism in the dissociation of HCl is presented and discussed.     

Bond functions and many-body effects of the helium trimer

A general scheme for efficient implementation of bond functions in homonuclear triatomics is suggested and applied to the linear and triangular configurations of the helium trimer. It is found that only one set of midbond functions of size 6s3p can provide nearly all of the benefits obtainable from larger sizes as well as 100% of the energy lowering obtained with ten sets of d-functions added at the atom centres. They also enhance the convergence properties of the many body terms at the Hartree-Fock and electron correlation levels. Correct dissociation limits and avoiding spurious minima of potential wells as well as other linear and triangular configurations are taken into account. Received: 5 November 1996 / Accepted: 7 April 1997     

Accuracy and convergence of free energy differences calculated from nonequilibrium switching processes

The molecular-dynamics-based calculation of accurate free energy differences for biomolecular systems is a challenging task. Accordingly, convergence and accuracy of established equilibrium methods has been subject of many studies, often focusing at small test systems. In contrast, the potential of more recently proposed nonequilibrium methods, derived from the Jarzynski and Crooks equalities, has not yet fully been explored. Here, we compare the performance of these methods by calculating free energy differences for test systems at different levels of complexity and varying extent of the involved perturbations. We consider the interconversion of ethane into methanol, the switching of a tryptophane-sidechain in a tripeptide, and the binding of two different ligands to the globular protein snurportin 1. On the basis of our results, we suggest and assess a new nonequilibrium free energy method, Crooks Gaussian Intersection (CGI), which combines the advantages of existing methods. CGI is highly parallelizable and, for the test systems considered here, is shown to outperform the other studied equilibrium and nonequilibrium methods.     

On the use of non-hydrogenic spectral line profiles for electron density diagnostics of inductively coupled plasmas

On the basis of the analysis of the results reported in several experimental papers, we draw attention to some experimental difficulties in electron number density determination from the shapes and shifts of non-hydrogenic spectral lines in atmospheric pressure inductively coupled plasmas. Some suggestions for further work are also given.     

Multi-element model for the simulation of inductively coupled plasmas: Effects of helium addition to the central gas stream

A model for an atmospheric pressure inductively coupled plasma (ICP) is developed which allows rather easy extension to a variable number of species and ionisation degrees. This encompasses an easy calculation of transport parameters for mixtures, ionisation and heat capacity. The ICP is modeled in an axisymmetric geometry, taking into account the gas streaming into a flowing ambient gas. A mixture of argon and helium is applied in the injector gas stream as it is often done in laser ablation ICP spectrometry. The results show a strong influence of the added helium on the center of the ICP, which is important for chemical analysis. The length of the central channel is significantly increased and the temperature inside is significantly higher than in the case of pure argon. This means that higher gas volume flow rates can be applied by addition of helium compared to the use of pure argon. This has the advantage that the gas velocity in the transport system towards the ICP can be increased, which allows shorter washout-times. Consequently, shorter measurement times can be achieved, e.g. for spatial mapping analyses in laser ablation ICP spectrometry. Furthermore, the higher temperature and the longer effective plasma length will increase the maximum size of droplets or particles injected into the ICP that are completely evaporated at the detection site. Thus, we expect an increase of the analytical performance of the ICP by helium addition to the injector gas.     

Two-Term and multi-term approximation of the nonstationary electron velocity distribution in an electric field in a gas

A very efficient, strict nonstationary multi-term approach has been developed as a generalization of the conventional and the strict nonstationary two-term approximations used for solving the nonstationary , electron Boltzmann equation. As a first application the temporal relaxation of electrons in a model plasma acted upon by a de electric field has been investigated. The results are compared with corresponding ones obtained by the conventional and the strict nonstationary two-term approach as well as with very accurate Monte Carlo simulations. Perfect agreement between nonstationary eight-term Boltzmann and Monte Carlo calculations is found.     

A simple line shape technique for electron number density diagnostics of helium and helium-seeded plasmas

The results of an experimental study of the He I 447.1 nm line and its forbidden component at high electron number density are presented and compared with profiles calculated using computer simulation method. Michelson interferometer at 632.8 nm was used to measure plasma electron number density in the range (1–7) × 10²³ m^− 3 while electron temperatures for the same experimental conditions in the range of 25 000 K to 35 000 K were determined using several spectroscopic techniques. The agreement of experimental overall line shape with computer simulation results is within 10% of what is well within theoretical and experimental uncertainty. This favorable comparison enabled the development of a simple approximate formula for the evaluation of electron number density from the measurement of wavelength separation between peaks of allowed and forbidden lines. This technique of plasma diagnostics is not sensitive to the presence of self-absorption of strong He I allowed line. The derivation of approximate formula with estimated accuracy of 15% was followed by detailed comparison with other experimental and theoretical data.     

Semi-classical generalized Langevin equation for equilibrium and nonequilibrium molecular dynamics simulation

Molecular dynamics (MD) simulation based on Langevin equation has been widely used in the study of structural, thermal properties of matter in different phases. Normally, the atomic dynamics are described by classical equations of motion and the effect of the environment is taken into account through the fluctuating and frictional forces. Generally, the nuclear quantum effects and their coupling to other degrees of freedom are difficult to include in an efficient way. This could be a serious limitation on its application to the study of dynamical properties of materials made from light elements, in the presence of external driving electrical or thermal fields. One example of such system is single molecule dynamics on metal surface, an important system that has received intense study in surface science. In this review, we summarize recent effort in extending the Langevin MD to include nuclear quantum effect and their coupling to flowing electrical current. We discuss its applications in the study of adsorbate dynamics on metal surface, current-induced dynamics in molecular junctions, and quantum thermal transport between different reservoirs.     

Chemical‐surface modification of polymers using atmospheric pressure nonequilibrium plasmas and comparisons with vacuum plasmas

We demonstrate that stable microwave‐coupled atmospheric pressure nonequilibrium plasmas (APNEPs) can be formed under a wide variety of gas and flow‐rate conditions. Furthermore, these plasmas can be effectively used to remove surface contamination and chemically modify polymer surfaces. These chemical changes, generally oxidation and crosslinking, enhance the surface properties of the materials such as surface energy. Comparisons between vacuum plasma and atmospheric plasma treatment strongly indicate that much of the vacuum‐plasma literature is pertinent to APNEP, thereby providing assistance with understanding the nature of APNEP‐induced reactions. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 40: 95–109, 2002     

Continuous medium theory for nonequilibrium solvation: II. Interaction energy between solute charge and reaction field and single-sphere model for spectral shift

On the basis of continuous medium theory, a model for evaluation of spectral shifts in solution has been developed in this work. The interaction energy between solute dipole and reaction field and the self-energy of the reaction field have been formulated through derivations. Applying the interaction energy expression together with the point dipole approximation to the case of spherical cavity produces new formulations of spectral shifts. The same expression of electrostatic free energy of the nonequilibrium state is achieved by integrating the change of the electrostatic free energy for a charging process. Moreover, generalized formulations evaluating spectral shifts have been established in the charge-potential notation, and the reduction of them to the point dipole case consistently leads to the same formulations of spectral shifts as those by interaction energy approach. Mutual supports provide convincing evidences for the reliability of the present results. In this work, attentions are particularly paid to the conclusion of zero self-energy of the reaction field, which is different from the previous theory. Reasoning and arguments are given on this point. From the present derivations, it is concluded that the spectral shifts of light absorption and emission were theoretically exaggerated in the past, in particular, by a factor of 2 for the spectral shift sum.     

Comparison of reaction pathways calculated by different algorithms for disilane and water trimer

There still exists some confusion in the literature concerning the definition of a minimum energy pathway and the coordinate system in which it is calculated. Here we compare steepest-descent and eigenvector-following pathways, both with and without a mass-weighted metric. The systems studied are disilane and the water trimer, and we employ various basis sets at the SCF level of theory. We find that paths calculated using eigenvector-following and steepestdescent are practically the same, at least in terms of the reaction mechanism.We find that for the mass-weighted metric the pathways are similar, although in principle they do not have to be identical. Finally, we verify that the geometrical symmetry selection rules hold for a pathway mediated by a recently discovered transition state of the disilane system.