Chemical reactions cross-section

SCHEME 12.13 Competition between chemical reaction (cross-section i rxn) and spin exchange (cross-section of a reactive polarized radical r and a nitroxyl radical... 

Effects of Rotational Excitation on Chemical Reaction Cross-Section... 

R. A. Marcus, Chemical-reaction cross sections, quasiequilibrium, and generalized activated complexes, J. Chem. Phys. 45 2138 (1966). 

Y. S. M. Wu, A. Kuppermann, and B. Lepetit, Theoretical calculation of experimentally observable consequences of the geometric phase on chemical reaction cross sections, Chem. Phys. Lett. 186 319 (1991). 

E. F. Greene and A. Kuppermann, Chemical reaction cross sections and rate constants, J. Chem. Ed. 45, 361-369 (1968). 

A. Gelb and R.J. Suplinskas. Influence of the distorted wave approximation in calculations of chemical reaction cross sections Ar i HD. J. Chem. Phys.. 53. 2249-57 (1970). 

The relation between the chemical reaction cross section and the bimo-lecular reaction rate constant has been thoroughly discussed by Hirschfelder and Eliason (1959). Their results can be directly applied to the collisional quenching (or transfer). For a given collisional quenching cross section Qav.bv for the transition av - bv its corresponding detailed quenching constant /Cq(T)a ,j, is given by (Hirschfelder and Eliason, 1959 Lin et ai, 1971)... 

The majority of ionic species are formed by the removal (or the addition) of an electron from (or to) a stable atom or molecule. As a result, ionic species are highly reactive. Because the environment in which ionic species are created is often chemically complex, special techniques for the preparation and handling of such transients are required for reliable determination of ionization and appearance energies, energetic thresholds for chemical reactions, and unambiguous measurements of chemical reaction cross sections and rates. The general techniques of mass spectrometry form the basis for experimental methods that provide information on ion energetics and kinetics. 

Note that the angular dependence of the scattered products also needs to be included in the detailed study of chemical reaction cross-sections. The formalism is similar to that given further above for a general collision a summary is provided in Box 21.5. 

For the potential given by (5.3), it is easy to show that when b > bc the distance of closest approach is bc /21/2, whereas for b < b, the only thing preventing interpenetration is a repulsive core potential, which is not explicitly considered here. Equation (5.4) is actually the classical collision cross section for the problem. To translate this into a reaction cross section, we may assume that there is another critical separation r0 such that when r < rg chemical forces complete the reaction and no reaction takes place if r > rg. If rg is less than b /2m, then Eq. (5.4) is also the reaction cross section, since reaction definitely takes place if b < b. and it definitely does not take place if b > b.. According to this modification, the high-energy limit of the reaction cross section is nr2 rather than zero as given by (5.4). One therefore has... 

These ion molecule reactions show two characteristics which are of general importance for chemical considerations (I) their large reaction cross sections and (2) their energetics. The collision cross sections involved in ion molecule reactions were considered theoretically by Eyring et al.16 in 1936, and more recently by Field et al.17 and by Gioumousis and Stevenson.18 The dipole induced in a neutral molecule in the field of an ion of unit charge at a distance, r, is... 

The cross-section of a fusion reaction, as well as the rate constant of a-decay, decreases exponentially with decreasing kinetic energy of the nuclei relative motion. This strong dependence of the reaction cross-section on the energy leads to an unusual (from the point of view of the classic physical and chemical kinetics) dependence of the reaction rate constant on temperature... 

Harpoon reactions of alkaline metal atoms with halogen molecules in the gas phase seem to be the first instance of the observation of chemical electron transfer reactions at distances somewhat exceeding gas-kinetic diameters. Actually, as far back as 1932, Polanyi, while studying diffusion flames found for these reactions cross-sections of nR2, somewhat exceeding the gas-kinetic cross-sections [69]. Subsequently, more precise measurements which were carried out in the 1950s and 1960s with the help of the molecular beam method, confirmed the validity of this conclusion [70],... 

A theoretical determination of the rate constant for a chemical reaction requires a calculation of the reaction cross-section based on the dynamics of the collision process between the reactant molecules. We shall develop a general relation, based on classical dynamics, between reaction probabilities that can be extracted from the dynamics of the collision process and the phenomenological reaction cross-section introduced in Chapter 2. That is, we give a recipe for how to calculate the reaction cross-section in accord with the general definition in Eq. (2.7). 

In the DSMC technique, the probability that a chemical reaction occurs is the ratio of the reaction cross section to the elastic cross section. The most commonly applied chemistry model is the Total Collision Energy (TCE) form employed by Boyd based on a general model proposed by Bird. In this model, the probability of reaction, P, is obtained by integrating the microscopic equilibrium distribution function for the total collision energy, and equating it to a chemical rate coefficient, Kf. Specifically, the mathematical form of the probability is obtained from the following integral ... 

In order to evaluate DSMC chemistry models, we require experimental and/or detailed theoretical results. Data of interest that can be measured experimentally include reaction cross sections, and rate coefficients. The most useful type of theoretical data are generated by detailed analysis of the collision and reaction dynamics using potential surfaces obtained from high level quantum chemical methods. 

Chemical dynamics experiments in which OH product quantum state distributions and an absolute reaction cross section for reaction (1) could be measured were reported in 1984. Subsequent experiments revealed additional details about the reaction dynamics, including nascent OH( H) spin-orbit and A-doublet rotational fine structure state distributions, Oi P) product fine structure state distributions, and OH angular momentum polarization distributions,as well as differential cross sections. The experimental results indicate that depending on the reagent collision energy... 

From an analysis of 6000 meteors by radio echo techniques, Verniani concluded that the mean velocity was 34 km/s, and that their mean mass was 10" g. Verniani also found that the velocity distribution of the meteors shifted with meteor mass distribution. The physics of radar scatter from meteor trails extracts the ionization coefficient, Eq. (5), from the observed echo intensities and associated electron densities. More recent analysis of the ionization trails of meteors has indicated a slightly different expression than Eq. (6) for the ionization coefficient associated with faint, low velocity (< 35 km s ), radio meteors, namely (3 = 9.4 x 10" (u - 10) u , where v is in km s". The magnitude and velocity dependence of (3 remains a major puzzle. It must be noted that the calculations assume no chemical reactions in the trail this assumption is needed to make the calculations tractable and because many of the reaction cross sections are not known. Collision processes leading to ionization are discussed in Secs. 3.2.2 and 3.4. 

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