Microscopic theory of gas-surface interaction

A kinetic theory for inelastic scattering, trapping and desorption of gas molecules by surfaces is described. The theory is valid if the time scale _l = 1/r introduced by the relaxation ratesr in the kinetic equations (which is of the order of the life time of vibrational states of adsorbates) is sufficiently large compared to the vibrational period ₀. For sufficiently large activation energies of the adsorbates another time constant _res, the residence time of adsorbed particles, can be determined from the theory. One thus may distinguish four different partly overlapping regimes defined by the time scalest _{I l} , ₀t_II, _l t_III and _rest_IV. Regime I is governed by the Schrödinger equation regime II by the kinetic equations. In the region where both regimes overlap the kinetic coefficients can be expressed in terms of microscopic quantities which have been calculated previously. The relevant quantities in the other regimes are introduced and discussed from a unified point of view thus providing a link between the regimes I and IV which have been treated in detail before.     

Current trends in the theories of gas-surface interaction

Studies on gas-surface dynamics have acquired considerable importance recently not only for their intrinsic scientific interest but also for their technological potential. This article first briefly describes various experimental techniques and a number of interesting recent observations resulting from these techniques. It then discusses certain important theoretical methodologies being extensively used nowadays. There arethree broad overlapping streams of theoretical works, viz classical, semi-classical and quantum-mechanical. There are alsothree basic problems in gas-surface interaction, viz (i) the interface presents a manybody problem; (ii) the solid surface is “rough”; (iii) the number of diffractive and inelastic channels is enormously large. The semi-classical approaches appear to dominate over the others in variety and quantity. But the sources of benchmark theoretical results are still the rigorous classical-trajectory and close-coupling quantum-mechanical calculations. The coming years are likely to witness not only increased numerical accuracy through refinements in semi-classical and quantum-mechanical approaches, but also certain special approximate methods designed to yield deeper physical insights into the nature of gas-surface interaction. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion. An erratum to this article is available at .     

Kinetic theory of rotating molecule interaction with a solid surface

A kinetic theory of interaction between molecules with rotational degrees of freedom and a solid surface for arbitrary ratios among the times of molecule rotation, flight through the region of surface forces, and relaxation of a molecular ensemble due to phonons has been developed. A kinetic equation for an ensemble of molecules residing in the field of surface forces has been derived from the equation for the one-particle distribution function of molecules by averaging it along the dynamical trajectories in the region of surface force action. A simple analytic expression for the probability of trapping a molecule with rotational degrees of freedom has been obtained. Experimental data on rotational cooling and rotational polarization of desorbed molecules are discussed. Zh. éksp. Teor. Fiz. 113, 1350–1363 (April 1998)     

Kinetic theory of the interaction in an electron current-electromagnetic wave system

The interaction between an electron beam and a retarded electromagnetic field with an accelerating electrostatic field (traveling wave tube with bunching) is considered. An exact steady-state solution of the kinetic equation is found for the case of a zero electrostatic field and an approximate solution is found for the case of a slowly varying electrostatic potential. A theory is constructed for the amplification of the electromagnetic wave; a critical value is indicated for the power of the amplified wave, above which stable amplification is possible. The dependence of the differential efficiency on the power of the amplified wave is calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 17–21, April, 1982.     

On the use of a Debye-Waller-type factor in gas-surface scattering theory

The status of the use of a Debye-Waller-type factor, in the theory of gas-surface inelastic (phonon) scattering to describe the attenuation of diffracted beams, is considered, and several conclusions are made; for example, it is concluded that the commonly-used Debye-Waller-type relation, which in the literature seems to be generally accepted as established, has no firm basis. In the context of such a relation, the role of the gas atom-solid interaction potential well is discussed; it is concluded that methods generally used in the literature for taking account of the presence of this well are arbitrary. No suggestions are made as to how the present situation may be improved.     

Laser-induced gas-surface interactions

Chemical reactions in homogeneous systems activated by laser radiation have been extensively investigated for more than a decade. The applications of lasers to promote gas-surface interactions have just been realized in recent years. The purpose of this paper is to examine the fundamental processes involved in laser-induced gas-surface chemical interactions. Specifically, the photon-enhanced adsorption, adsorbate-adsorbate and adsorbate-solid reactions, product formation and desorption processes are discussed in detail. The dynamic processes involved in photoexcitation of the electronic and vibrational states, the energy transfer and relaxation in competition with chemical interactions are considered. These include both single and multiple photon adsorption, and fundamental and overtone transitions in the excitation process, and inter- and intra-molecular energy transfer, and coupling with phonons, electron-hole pairs and surface plasmons in the energy relaxation process. Many current experimental and theoretical studies on the subject are reviewed and discussed with the goal of clarifying the relative importance of the surface interaction steps and relating the resulting concepts to the experimentally observed phenomena. Among the many gas-solid systems that have been investigated, there has been more extensive use of CO adsorbed on metals, and SF₆ and XeF₂ interactions with silicon as examples to illustrate the many facets of the electronically and vibrationally activated surface processes. Results on IR laser stimulated desorption of C₅H₅N and C₅D₅N molecules from various solid surfaces are also presented. It is clearly shown that rapid intermolecular energy exchange and molecule to surface energy transfer can have important effects on photodesorption cross sections and isotope selectivities. It is concluded that utilization of lasers in gas-surface studies not only can provide fundamental insight into the mechanism and dynamics involved in heterogeneous interactions, but also offer the possibility for technical innovation for practical applications.     

Kinetic theory of neutrinos

Some features of the relativistic kinetic theory of quantum systems are discussed. For a proper application to neutrinos in stellar collapse the particles' Fermi statistics must be fully taken into account. A number of transport coefficients appropriate to this context are considered. They include in particular generalizations of the well-known viscosity and heat conduction coefficients derived by Weinberg for cosmological neutrinos.     

Kinetic theory of dense fluids

A kinetic theory of dense fluids is presented in this series of papers. The theory is based on a kinetic equation for subsystems which represents a subset of equations structurally invariant to the sizes of the subsystem that includes the Boltzmann equation as an element at the low density limit. There exists a H-function for the kinetic equation and the equilibrium solution is uniquely given by the canonical distribution functions for the subsystems comprising the entire system. The cluster expansion is discussed for the N-body collision operator appearing in the kinetic equation. The kinetic parts of transport coefficients are obtained by means of a moment method and their density expansions are formally obtained. The Chapman-Enskog method is discussed in the subsequent paper.     

Kinetic theory of inhomogeneous diffusion

This paper theoretically investigates particle diffusion in a medium where the diffusivity depends on position. We exclusively consider continuous-time, continuous-space transport and our working tool is the linear kinetic theory pertinent to guest particles in a passive host medium (Lorentz’s picture of transport). The host medium may or may not thermalize the guest particles. It may be inhomogeneous in two ways: either particle scattering features depend on position in an explicit way (geometric inhomogeneity), or they depend on position through the medium’s local temperature (thermal inhomogeneity). When the inhomogeneity is geometric, it is found that Fick’s law is valid and the particle-current equation exhibits drift without current. When the inhomogeneity is thermal, current without drift is possible, but there is no generally valid pattern for the current equation. The consistency of our results with non-equilibrium thermodynamics is brought out. The results shed light on thermodiffusion (the Ludwig-Soret effect), which often combines inhomogeneities of both kinds. Finally, a limitation of the Lorentz picture of transport in accounting for thermodiffusion is outlined.     

Kinetic theory of hard spheres

Kinetic equations for the hard-sphere system are derived by diagrammatic techniques. A linear equation is obtained for the one-particle-one particle equilibrium time correlation function and a nonlinear equation for the one-particle distribution function in nonequilibrium. Both equations are nonlocal, noninstantaneous, and extremely complicated. They are valid for general density, since statistical correlations are taken into account systematically. This method derives several known and new results from a unified point of view. Simple approximations lead to the Boltzmann equation for low densities and to a modified form of the Enskog equation for higher densities.     

Kinetic theory of reacting systems

In this paper transport processes of reacting systems are investigated, based on the Boltzmann equations. The Boltzmann equations are solved by means of Grad's moment method to thirteen moments and some formal results are obtained for transport properties. It is shown that the rate coefficients are quadratic functions of hydrodynamic fluxes and are in the form

where

are the scalar moments associated with the reaction and q, J, Π are heat flux, material flux and traceless symmetric stress tensor. k⁽⁰⁾_i is the usual local equilibrium formula for reaction rate constant. Iterative solutions for the equations of change for

, q, J and Π are obtained from which transport coefficients are calculated for the reacting system. It is shown that the solutions, when specialized to nonreacting mixtures, lead to results for the transport coefficients which are exactly in agreement with the Chapman-Enskog theory results. The modifications of the transport coefficients due to reactions are obtained from the iterative solutions and the bracket integrals necessary for their calculations are explicitly given in an appendix.     

气体-表面相互作用中动量和能量分量间转化机制的分子动力学研究

气体分子与壁面之间的相互作用是影响稀薄气体流动状态的主要因素,但是由于其物理上的复杂性和微观性,这一过程的机理并没有得到充分揭示.本文利用分子束法对Ar分子在金属Pt表面的碰撞过程进行了分子动力学模拟,并探究了入射速度、角度和壁面粗糙度对动量、能量转化机制的影响.结果表明,当气体分子以5°的极角入射时,分子的法向速度分...     

Kinetic theory for supernova explosions

Coupled kinetic equations for the time evolution of baryons and neutrinos are introduced in order to present a new solution approach for the problem of type II supernova core collapse and explosion. A test-particle method is introduced in order to cast these kinetic equations into numerically tractable form.     

Kinetic theory of traveling wave gyro-peniotron

Using an equilibrium distribution function f_o=f_o(p, p, p_g), where R_g is the radial position of electron guiding center, this paper presents a kinetic theory of TW gyro-peniotron. The dispersion equation obtained in this paper can be used to describe both gyrotron and gyro-peniotron. The influence of beam position is discussed.     

Kinetic theory of photon density waves

A kinetic equation is obtained for the modulated intensity of multiply scattered light, which generalizes the known Bethe-Salpeter equation. An asymptotic solution is found in the P ₁ approximation, which takes into account the anisotropy of single scattering within the average cosine of the scattering angle. The parameters of the photon density wave are calculated from this solution. It is shown that the relative phase shift and modulation degree calculated for modulation frequencies exceeding several gigahertz noticeably differ from the values predicted by the radiation transfer equation.