Capture rate coefficients

The cross-section for electron attachment shows an inverse dependence on electron velocity170, and for this reason there has been a marked inconsistency in the cross-sections obtained by different methods. Mahan and Young104 have reported a capture rate coefficient for thermal electrons of 2x 1014 l.mole-1.sec-1. This was obtained by a microwave technique in the presence of helium as a moderating gas. 

For a system having a Maxwell-Boltzmann energy distribution, current classical theories of ion-molecule interactions predict a collision or capture rate coefficient given by... 

In cases where neutral reactants already possess a permanent dipole moment, fiu, the capture rate coefficient is larger than ki. Su and Bowers have derived the expression... 

Numerically, the Langevin capture rate coefficient can be presented as... 

In this situation, molecular simulations such as BD as a type of numerical experiment are advantageous, as the situation can be easily controlled. Capture rate coefficients can be determined under predetermined conditions based on well-established mechanistic equations (e.g., molecular Brownian motion). This has been used recently to study the kinetics of radical entry, without the interference of competitive events such as radical desorption, propagation, and termination [38, 39]. 

At very low polymer volume fractions, the entry follows Smoluchowski kinetics Sm = 1), whereas for polymer volume fractions greater than 0.1% Smis increased (Figure 25.4). The BD simulations reveal an almost linear dependence of the radical capture rate coefficient on the polymer volume fraction in the dispersion, cf. Equation 25.26 ... 

Ion-molecule rate coefficients k can be viewed as the product of a reactton probability P by a capture rate coefficient k. This corresponds to a division of the potential... 

T3rpically, neglecting either the conservation of energy or angular momentum yields an overestimate in the capture rate coefficient of about 5 10%. Notably, however, the conservation of E and J can be much more significant when considering multiple transition states. 

The emphasis in this chapter is on bimolecular reactimis, i.e. reactions of the type A + B. Both the theoretical framework and the experimental techniques differ for reactions between an ion and a neutral molecule and between two neutral molecules, and they are discussed separately, in Sects. 3.3 and 3.4 respectively. In ion + neutral molecule reactions, the intermolecular forces are comparatively Imig range and theory concentrates on the calculation of the so-called capture rate coefficient. 

They showed that the ratio of the capture rate coefficient to the Langevin value, depends primarily on a reduced parameter, x, where... 

Maergoiz et al. [28-30] performed classical trajectory calculations for ion-dipole, ion-quadrupole and dipole-dipole collisions, deriving results for capture rate coefficients and expressing them in terms of two reduced parameters, the reduced temperature, d, closely related to the Tr parameter in the work of Chesnavich and co-workers, and the Massey parameter, which is equal to the ratio of the coUisional timescale to the rotational period of the neutral. 3> 1 corresponds to the adiabatic limit (see below). They gave parameterized expressions for k /ki, similar to those given by Su and Chesnavich [26], but extending the range of validity. 

While the results of trajectory calculations provide an accurate testing ground for more approximate theories, and, in the parameterised form developed by Su, Chesnavich and Bowers [25,26], a widely applied means of calculating capture rate coefficients for these more complex interactions, they provide less insight into reaction mechanisms and rate coefficient determinants than more analytic approaches. The simplest approach is provided by phase space theory (PST) which assumes an isotropic potential between the reactants [31]. The centrifugal term in the effective potential in (3.2) can be expressed in terms of the orbital angular momentum quantum number, , for the collision, so that the equation for Vejf (Rab) becomes ... 

Instead of seeking an analytical expression for the rate coefficient on the basis of classical expressions for the ion-molecule interaction potential, an alternative approach is to model the reaction process through a series of classical trajectory calculations. The details are somewhat complicated and so the interested reader should consult the original references. Importantly, the results of such trajectory calculations have been parameterized by Su and Chesnavich to give expressions which allow calculation of the rate coefficient [27], The resulting rate coefficient, termed the capture rate coefficient, heap, is given by... 

Finally, we turn to the capture rate coefficient, and begin by obtaining a value for Tr. 

Table 2.3 shows a comparison of the calculated and experimental rate coefficients for several other compounds. The comments made for the H3O+ reaction with acetone apply also to this larger group of reactions. Where supplied, the error margins for the experimental rate coefficients are about 20-30% of the mean value. In every reaction listed in Table 2.3, the capture rate coefficient lies within the stated error margins and in most cases is close to the quoted experimental mean value. From this comparison it seems fairly safe to assume that the calculated heap rate coefficient is likely to be every bit as reliable as any experimentally determined value and thus, as mentioned earlier, in the absence of an experimental rate coefficient, trajectory methods provide the best option for determining a reaction rate coefficient for subsequent use in analysing PTR-MS data. 

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