Weak-collision assumption

The significance of the thermodynamic parameters obtained in this way has been questioned in view of the assumption of a 1 1 collision complex, and the gross approximations involved in the calculation. The values are probably most meaningful for aliphatic solutes containing a single polar site, but even in such cases they are probably of limited significance. However, the weak nature of the interaction is usefully demonstrated by such techniques. 

Specified electron energy distribution function The EEDF is specified, normally assumed Maxwellian (Eq. 9). The electron energy balance (Eq. 31) is solved assuming an adiabatic condition for electron temperature at the wall. The Maxwellian assumption is very common in the literature [100, 125, 126, 130, 133, 135-137]. Measured EEDFs in ICPs, however, have a Maxwellian bulk (due to electron-electron collisions), and a depleted tail due to inelastic losses and escape of fast electrons to the walls. Thus a bi-Maxwellian distribution may be more appropriate [154]. A Maxwellian distribution is not expected to have a great effect on ion densities since the ionization rate is self-adjusted to balance the loss rate of ions to the walls and the latter depends only very weakly on the EEDF. The good agreement with experimental data [101, 130, 148, 152] is an indirect evidence that the Maxwellian EEDF is reasonable for obtaining species densities and their distributions. Other forms of... 

Since the introduction of the isolated binary collision model there has been considerable controversy over its applicability. A number of theoretical papers have challenged its basic assumptions and proposed corrections due to collective effects (usually within the weak coupling approximation of Section II.B), while others have supported and extended the model. In this section, we outline the development of the controversy over the binary collision approximation, which is not resolved even today. 

A ternary collision may be conveniently pictured as a very rapid succession of two binary collisions one to form the unstable product, and the second, occurring within a period of about 10 sec or less, to stabilize the product. It is immediately obvious that it is not possible to use the elastic-hard-sphere molecular model to represent ternary collisions since two such spheres would be in collision contact for zero time, the probability of a third molecule making contact with the colliding pair would be strictly zero. It is therefore necessary to assume a potential model involving forces which are exerted over an extended range. One such model is that of point centers having either inverse-power repulsive or inverse-power attractive central forces. This potential, shown in Fig. 2-If, is represented by U r) = K/r. For the sake of convenience, we shall make several additional assumptions first, at the interaction distances of interest the intermolecular forces are weak, that is, U(r) < kT second, when the reactants A and B approach each other, they form an unstable product molecule A B when their internuclear separations are in the range b third, the unstable product is in essential... 

However, later work showed that rather large deviations from experiment are obtained for reactions in which the reacting molecules are more complicated. This collision theory is evidently too simple and unlikely to be generally reliable. One weakness is the assumption that molecules are hard spheres, which implies that any collision with sufficient energy will lead to reaction if the molecules are more complicated, this is not the case. A more fundamental objection to the treatment is that when applied to forward and reverse reactions it cannot lead to an expression for the equilibrium constant that involves the correct thermodynamic parameters. More recent work has involved a similar approach but has treated molecular collisions in a more realistic and detailed way. 

This latest transformation is only valid with the assumption that the collision frequency oj(E) is only a weak function of E and hence can be treated as a constant. This assumption holds well if, for example, Lennard-Jones collision frequencies are used. 

However, one can not simply accept the Moore model in favor of BSH model since the latter is formulated on a more sound dynamical basis. The only weak point of the BSH model is the assumption that the three-dimensional collision can be reduced to a one-dimensional scattering problem in the direction of the gradient of the potential energy surface. This assumption can be probed by studying an alternative model that chooses a different mode as responsible for the vibrational deactivation. 

A rough approximation may be obtained by assuming that B depends on Q weakly B Q) B. This assumption is vaJid, for example, for impulsive collisions. 

In the derivations of this chapter, we have assumed a collision of an atom and a solid consisting of a finite number of atoms. The approach is easily extended to treating any number of atoms in the gas phase using classical mechanics. However, the derivation was based upon the assumption of a weak coupling between the gas-phase atom(s) and the solid. This assumption makes the simple Hartree trial function a good approximation. If reaction between the gas-phase atoms and the solid atoms can occur, this separability approximation obviously breaks down. Thus, if surface etching or laser evaporation or other processes in which the surface atoms are removed from the surface are considered, the... 

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