Chemical kinetic modeling of hydrocarbon combustion

We review various methods of deriving expressions for quantum-mechanical quantities in the limit when hslash is small (in comparison with the relevant classical action functions). To start with we treat one-dimensional problems and discuss the derivation of WKB connection formulae (and their reversibility), reflection coefficients, phase shifts, bound state criteria and resonance formulae, employing first the complex method in which the classical turning points are avoided, and secondly the method of comparison equations with the aid of which uniform approximations are derived, which are valid right through the turningpoint regions. The special problems associated with radial equations are also considered. Next we examine semiclassical potential scattering, both for its own sake and also as an example of the three-stage approximation method which must generally be employed when dealing with eigenfunction expansions under semiclassical conditions, when they converge very slowly. Finally, we discuss the derivation of semiclassical expressions for Green functions and energy level densities in very general cases, employing Feynman's path-integral technique and emphasizing the limitations of the results obtained. Throughout the article we stress the fact that all the expressions obtained involve quantities characterizing the families of orbits in the corresponding purely classical problems, while the analytic forms of the quantal expressions depend on the topological properties of these families. This review was completed in February 1972.

https://iopscience.iop.org/article/10.1088/0034-4885/35/1/306/pdf

Semiclassical approximations in wave mechanics

Complex (dusty) plasmas: current status, open issues, perspectives

Ion mobility-mass spectrometry (IM-MS) is enhancing many areas of (bio)chemical analysis because it can separate ions both by their mass-to-charge ratio and differences in their cross-sectional area. IM-MS can be used for structural characterization, enhanced analysis of complex mixtures or to gain insights into conformational dynamics.
 Mass spectrometry is a vital tool for molecular characterization, and the allied technique of ion mobility is enhancing many areas of (bio)chemical analysis. Strong synergy arises between these two techniques because of their ability to ascertain complementary information about gas-phase ions. Ion mobility separates ions (from small molecules up to megadalton protein complexes) based on their differential mobility through a buffer gas. Ion mobility-mass spectrometry (IM-MS) can thus act as a tool to separate complex mixtures, to resolve ions that may be indistinguishable by mass spectrometry alone, or to determine structural information (for example rotationally averaged cross-sectional area), complementary to more traditional structural approaches. Finally, IM-MS can be used to gain insights into the conformational dynamics of a system, offering a unique means of characterizing flexibility and folding mechanisms. This Review critically describes how IM-MS has been used to enhance various areas of chemical and biophysical analysis.

/pdf/the-power-of-ion-mobility-mass-spectrometry-for-structural-1da43zeaym.pdf

The power of ion mobility-mass spectrometry for structural characterization and the study of conformational dynamics

A calculation of symmetric resonant charge exchange cross sections has been made for a selection of atoms in the velocity range where the impact parameter method is applicable. Cross sections for other atoms can be estimated by interpolating in terms of their ionization potentials. The results are in fair agreement with experiment. A similar calculation has been attempted for asymmetric nonresonant charge exchange processes. The approximations used are more restrictive in this calculation, the calculations being only semiquantitative in nature. The cross section of an asymmetric charge exchange process is determined in terms of the ΔE of the reaction and the ``average'' ionization potential of the two atoms. The results are qualitatively in agreement with experiment. A very brief discussion of approaches for extrapolating data to lower velocities, where the rectilinear orbit impact parameter method is not applicable, is given.

Charge exchange between gaseous ions and atoms.

Mobility of gaseous lons in weak electric fields

A rigorous formal kinetic theory of multicomponent polyatomic gas mixtures is derived. The methods are essentially a combination of those used by Chapman and Enskog for monatomic gases (as extended to multicomponent mixtures by Curtiss and Hirschfelder), and those used by Wang Chang and Uhlenbeck for a single polyatomic gas for the case where the equilibration between internal and translational degrees of freedom is easy. The calculations correspond to the first approximation in the classical Chapman—Enskog theory. Expressions are derived for the coefficients of shear viscosity, volume viscosity (which is proportional to a relaxation time), ordinary diffusion, translational and internal thermal conductivity, and thermal diffusion. Although the results are rather formal, a number of useful conclusions about the effects of inelastic collisions can be drawn without the necessity of detailed calculations. For instance, it is comparatively simple to show that inelastic collisions have very little effect on shear viscosity and ordinary diffusion, but probably seriously affect thermal conductivity and thermal diffusion. The Hirschfelder—Eucken formula for the thermal conductivity of polyatomic gas mixtures appears as a limiting case of the present formulas. A number of other conclusions and implications of the present formulas are also discussed.

Formal kinetic theory of transport phenomena in polyatomic gas mixtures

The repulsive and attractive screened Coulomb potentials may be used to represent interactions among charged particles in a gas. The classical Chapman‐Enskog collision integrals are calculated for these potentials over a wide range of reduced temperatures, equivalent to a wide range of electron densities and temperatures. At high temperatures the repulsive and attractive collision integrals are equal and agree with the earlier calculations of Kihara and Liboff. At lower temperatures the attractive collision integrals grow larger than the repulsive collision integrals as the temperature falls, and both grow apart from the previous results. It is shown that quantum effects are large in high‐density plasmas at all temperatures and in low‐density plasmas at very high temperatures.

Transport Coefficients of Ionized Gases

Ground state of hydrogen by the Rydberg-Kelein-Rees method

A study is made of the influence of inelastic processes on thermal diffusion in polyatomic gases, based on the Wang‐Chang—Uhlenbeck—deBoer treatment of the Boltzmann equation, in which it is assumed that the distribution function for molecular spins is isotropic. A generalized Stefan—Maxwell diffusion equation is obtained for multicomponent mixtures of polyatomic gases, carried to the second Chapman—Enskog approximation. The external form of this equation is the same as the well‐known result for monatomic gases, but contains higher‐order corrections for the binary diffusion coefficients (i.e., the composition dependence of these coefficients), and correction terms for the effect of inelastic collisions on the diffusion and thermal‐diffusion coefficients. Numerical calculations for several selected systems show that the effects of inelastic collisions on the thermal‐diffusion factor are not negligible and must be considered in any attempt to derive information on intermolecular forces from thermal‐diffusion measurements. However, inelastic effects are not capable by themselves of explaining the known anomalies in systems such as Ar–HCl and D2—HT.

E. A. Mason

Papers

Mobility of gaseous lons in weak electric fields

Formal kinetic theory of transport phenomena in polyatomic gas mixtures

Transport Coefficients of Ionized Gases

Ground state of hydrogen by the Rydberg-Kelein-Rees method

Thermal Diffusion in Polyatomic Gases: A Generalized Stefan—Maxwell Diffusion Equation