Langevin rate

The paper is arranged as follows. In Section 2, we discuss the Langevin(rate)... 

Equation (16) represents the locked-dipole capture rate constant. The first term, which at the same time is the high-temperature limit, denotes the well-known Langevin rate constant... 

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... 

Figure 22. Transition state rate estimates for ion-molecule encounter relative to Langevin rate...

Fig. 19. Rate constants for the reaction NJ(d) -I- Kr - N2 + Kr as a function of the vibrational quantum number v. Langevin rate constant = 8.1 x 10 " cm s (dashed line). The prediction is based on Franck ondon factors for energy-resonant transitions (solid line), whereas the dotted line is based on Franck-Condon factors assuming a relative shift of 0.02 A of the vibrational wave functions of and N2 (Kato eta/., 1997).

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

The numerical value of the Langevin rate coefficient for an electron-neutral collision is about 10 cm /s and also does not depend on temperature. 

Langevin Rate The Langevin rate is one of the most fundamental concepts which is indispensable in the discussion of ion kinetics (Langevin, 1905). ° In the laboratory discharge and in interstellar space an ion collides mostly with neutral molecules. If the polarizability of the neutral molecule is ot, the energy of interaction between the ion and the molecule (charge-induced dipole interaction) is... 

The experimental values of a and b can be found from the a(e) curve in the compilation by Kieffer. The value of k is typically 2 x ICT cm3/sec, that is, if we have 10 Vcm3 of electron density a molecule is ionized 0.2/sec. For a plasma with a pressure of 1 torr the ion production is on the order of 10 /cm3 sec, that is, 10ion pairs are produced per cm3 per second. Once ions are formed they react with neutrals with the large Langevin rate, that is 10" sec. 

Recombination Because of the long range Coulomb interaction, the electronic recombination usually occurs much faster than the Langevin rate. The typical value of the recombination rate constant is v.lo-T cm /sec. We can find electron recombination rates in Ref. 34 and 35. So, for an electron density of vloA cm, we find the recombination rate to be on the order of 10 7sec. At the Royal Society Meeting in London (March, 198 ), David Smith surprised us by announcing that the... 

If /C3 and can be taken as Langevin collision rate constants, then to the extent that t (= V3 ) can be taken from (7) (or other, more refined expressions) and p can be assumed constant (or otherwise approximated), one has a theory for three-body association reactions. If and/or deviate from Langevin rate constants, the factor p must absorb this effect also. Variations in third-body efficiency are commonly observed, although not generally very large ones. This establishes that k j) cannot be equal to /cl for the third-body collisions, i.e., either k ki ov p 1. 

A reaction requiring photoactivation is between Be+ and neutral molecular hydrogen gas, shown in Figure 18.24 [48]. This reaction does not proceed with the beryllium ion in its ground electronic state. But when laser-cooled Be" " ions are excited to the 7 3/2 state, reaction occurs with a rate comparable to the Langevin rate ... 

As can be seen from Eq. 2.14, classical theoiy predicts the capture cross section should vary inversely as the relative velocity of the coUiding pair and hence the Langevin rate constant, shonld be independent of the relative velocity and the temperature. Equation 2.15 predicts reasonably well the rate constants for ion-molecule reactions involving only ion-indnced dipole interactions. This indicates that a reaction occurs on every collision for many ion/molecule pairs there can be no activation energy for the reaction. The rate constant predicted is of the order of 1X 10 cm molecule s" . 

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. 

The ion induced-dipole potential and the corresponding Langevin rate expression have proven to be of great value in the interpretation of numerous studies of ion-molecule reaction kinetics (see chapters 2 and 3 by Canosa et al, and by Gerlich). For neutral reactions, a f/i potential, which can be taken to represent dispersion and/or dipole induced-dipole interactions, has provided a similarly important reference potential. The Gorin model, which is based on PST like assumptions for this potential, provides a simple expression for the capture rate ... 

X 10 sec at 350 K [20]. The experimental rate is significantly less than half the Langevin rate, which is the maximum anticipated for an efficient electron exchange during the lifetime of each ion-molecule encounter pair. The actual observed efficiency is 0.2 0.1. The branching fraction for a precursor with energy E is defined as... 

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... 

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