Reaction rate coefficient Langevin

Fig. 1.82. Relative reaction efficiencies fc/fcc for the conversion of CO to CO2 by PtnOm cluster of various compositions (fc is the measnred reaction rate coefficient and fee represents the Langevin ion-molecnle collision rate coefficient) [22]...

During the ion-dipole interaction, polarization of the neutral must also occur. The reaction rate coefficient may be considered to be composed of contributions from both the ion-dipole and the ion-induced dipole interactions. An estimate of the total rate coefficient may be made as the sum of the Langevin and the ion-dipole rate coefficients. 

Incorporation of this attractive potential into a simple collision model, which we shall not present here, allows the prediction of the reaction cross section and, ultimately, the reaction rate coefficient. The Langevin rate coefficient, as it is often known [21], is given by... 

The simulation of motion of the solvent as a Langevin-type Brownian motion is a most useful device to reduce computing time. Nevertheless, the essential features of the solvent cage are preserved. Allen was particularly interested in the reaction occurring in the low coupling limit, that is where the solvent does not interact with the particle which is transfered, B. However, when there is some interaction, the rate coefficient becomes diffusion-limited and can be described by a Kramers expression quite well (see Chap. 8, Sect. 2.4) [67]. 

Some of the initial work dealt with the formation of proton-bound dimers in simple amines. Those systems were chosen because the only reaction that occurs is clustering. A simple energy transfer mechanism was proposed by Moet-Ner and Field (1975), and RRKM calculations performed by Olmstead et al. (1977) and Jasinski et al. (1979) seemed to fit the data well. Later, phase space theory was applied (Bass et al. 1979). In applying phase space theory, it is usually assumed that the energy transfer mechanism of reaction (2 ) is valid and that the collisional rate coefficients kx and fc can be calculated from Langevin or ADO theory and equilibrium constants. 

Sunner et al. (1989) used a semiempirical treatment to theoretically evaluate the rate coefficients of hydride transfer reaction sec-C3H7 + iso-C4H10 — C3F18 + tert-C4Hg. Their kinetic scheme is based on a loose and excited chemically activated complex (C3H7 C4H10) formed at the Langevin rate. The complex can decompose back to reactants or form the products of the hydride transfer... 

Ion-Molecular Reactions, Ion-Molecular Polarization Collisions, and the Langevin Rate Coefficient... 

The typical valne of the rate coefficient for ion-molecular reactions is 10 cm /s, which is 10 times higher than the gas-kinetic value for neutral particles ko 10 cm /s. The preceding relations describe the interaction of a charge with an induced dipole. If an ion interacts with a molecnle having a permanent dipole moment /xd, the Langevin capture cross section becomes larger (Sn Bowers, 1973,1975) ... 

Most of the exothermic ion—molecular reactions have no activation energy (Talrose, 1952). Quantum-mechanical repulsion between molecules, which provides the activation barrier even in the exothermic reactions of nentrals, can be suppressed by the charge-dipole attraction in the case of ion-molecular reactions. Thus, rate coefficients of the reactions are very high and often correspond to the Langevin relations (2 8)-(2-50), sometimes partially hmitedby quantum-mechanical factors (Su Bowers, 1975 Virin et al., 1978). The efiect obviously can be apphed to both positive and negative ions. 

Note that /cl is independent of the kinetic energy of the reactants. For ion-molecule reactions without an energy barrier, and in the absence of a permanent dipole moment, the Langevin model gives reasonably good estimates of rate coefficients. For example, the rate coefficient for the reaction of Ar ions with H2 is predicted to be 1.5 x 10 cm mole-and the experimental value is reported to be... 

The case of N reaction with various isomers of dichloroethylene is of special interest. With the trans isomer which has no permanent dipole moment the rate coefficient is very dose to the Langevin value (1.810 cm s" ) at all temperatures. For the polar isomers the rate ooeffident is lower than the calculated capture rate but, at 300K, SIFT measurements shows that this is also true for reactions with Moreover the ratio of the experimental value of the rate coeffidents for N and H3 is very close to the ratio of the square roots of the readani... 

Gaucherel et al, 1986). The extrapolation of these experimental data down to OK yields respectively Langevin and half-Langevin value for the rate coefficient. Concerning the O2 reaction with methane and deuterated methane a very complete description of the... 

As shown by the present review experimental studies of ion-molecule reaction at extremely low temperatures have already provided several useful results for interstellar cloud chemistry. The rate coefficient values previously used in chemistry modeling have sometimes been confirmed as correct. This is the case for fast reactions with non-polar molecules which occur at near the Langevin rate at any temperatures. 

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