Gas-surface collisions

M. N. R. Ashfold, C. T. Rettner, eds. Dynamics of Gas-Surface Collisions. Cambridge Royal Soeiety of Chemistry, 1991. 

The vial heat transfer coefficient is the sum of heat transfer coefficients for three parallel heat transfer mechanisms (1) direct conduction between glass and shelf surface at the few points of actual physical contact, Kc (2) radiation heat exchange, Kr, which has contributions from the shelf above the vial array to the top of the vials, Krt, and from the shelf upon which the vial is resting, Krb and (3) conduction via gas-surface collisions between the gas and the two surfaces, shelf and vial bottom, Kg ... 

Net collisional uptake probability (ync]) is the net rate of uptake of the gas normalized to the rate of gas-surface collisions and since this is what is measured, is also often referred to as ymcas. 

Transport of the gas to the surface and the initial interaction. The first step in heterogeneous reactions involving the uptake and reaction of gases into the liquid phase is diffusion of the gas to the interface. At the interface, the gas molecule either bounces off or is taken up at the surface. These steps involve, then, gaseous diffusion, which is determined by the gas-phase diffusion coefficient (Dg) and the gas-surface collision frequency given by kinetic molecular theory. 

The physical and chemical processes occurring in a gas-liquid system are often treated in terms of a resistance model described in Box 5.2. As discussed there, the net uptake of gas (yIK.t) can be treated under some conditions in terms of conductances, T, normalized to the rate of gas-surface collisions. Individual conductances are associated with gas-phase diffusion to the surface (Tg), mass accommodation across the interface (a), solubility (rsol), and finally, reaction in the bulk aqueous phase (Tlxn). This leads to Eq. (QQ) ... 

We shall treat the individual processes in terms of the rate of transfer of gas across a surface of unit area per second. However, this rate will be expressed relative to the number of gas-surface collisions per second, given according to kinetic molecular theory by... 

In Eq. (PP), N is the gas concentration (molecules cm 3), um is the average molecular speed in the gas phase, R is the gas constant (J K 1 mol ), T the temperature (K), and M is the molecular weight (kg) of the gas. The normalized rates, i.e., divided by the rate of gas-surface collisions in Eq. (PP), will be referred to as conductances, T, for reasons that will become apparent shortly. However, the reader should keep in mind that these conductances just reflect the speeds of the individual processes. 

However, under many conditions the individual processes can be treated as if they are not coupled. In this case, an approximation that has found widespread use (e.g., see Schwartz and Freiberg, 1981 Schwartz, 1986 and Kolb et al., 1995, 1997), and that helps to assess the relative importance of each of the terms, is to treat the individual processes in terms of an electrical circuit (Fig. 5.16). Dimensionless conductances, T [where conductance = (resistance)-1], associated with each process reflect rates normalized to the rate of gas-surface collisions, and the corresponding resistances are given by 1 /r. The net, overall measured resistance, (ynct)-1, is then related to the individual resistances (see Problem 7) by... 

As already discussed, -ynul is a net probability normalized to the number of gas-surface collisions and is the parameter actually measured in experiments (and hence also often referred to as ymcas). In Eq. (QQ), each conductance represents one of the processes involved i.e., Tg involves the conductance for gas-phase diffusion, rran that for reaction in the aqueous phase, and rsol that for solubility and diffusion into the bulk. Each of the terms has been normalized and made unitless by dividing by the rate of gas-surface collisions, Eq. (PP), except for a, which by definition is already normalized to this parameter. 

Normalizing the rate of gas-surface collisions using Eq. (PP), one obtains... 

The first-order rate constant kr (s l) for the heterogeneous reaction is related to the rate of gas-surface collisions, 7S, and the fraction of those collisions that lead to uptake, yncl, since krNr = yl)CI/s. Since /s is also equal to A/Nt/V) um/A), then... 

A perturbation-trajectory method for determining the dynamics of gas-surface collision processes was tested on the collision and subsequent surface reactions of SiH2 on a Si(lll) surface233. The predictions of an exact classical trajectory calculation234 were confirmed the sticking probabilities were unity at all temperatures, and it was found that surface SiH2 can decompose by direct elimination of H2 or by successive dissociation of Si—H bonds. 

Incidentally we note that resonances do exist, however, in gas-surface collisions in which, as a consequence of the infinite mass of the solid, J is always zero resonances are indeed one major source of information on the gas-surface interaction (Hoinkes 1980 Barker and Auerbach 1984). Likewise, resonances are prominent features in electron-atom or electron-molecule collisions (Schulz 1973 Domcke 1991) the extremely light mass of the electron implies that only partial waves with very low angular momentum quantum numbers contribute to the cross section. 

Many chemisorptive interactions, however, are activated processes so that consideration of gas-surface collisions exclusively is insufficient to explain adsorption phenmnena. To fully appreciate the factors affecting adsorption equilibria, it is useful to examine the processes of adsorption in more detail. 

Theoretically, if reactions are able to proceed through either a Rideal-Eley step or a Langmuir-Hinshelwood step, the Langmuir-Hinshelwood route is much more preferred due to the extremely short time scale (picosecond) of a gas-surface collision. The kinetics of a Rideal-Eley step, however, can become important at extreme conditions. For example, the reactions involved during plasma processing of electronic materials... 

Studying the dynamics of hypervelocity gas/surface collisions under well-characterized conditions can provide insight into how a spacecraft s external surfaces will interact with the ionosphere/magnetosphere in orbit. 

Despite the variation in scattering results for the aforementioned prototypical systems, theoretical models have been successful in predicting the degree of energy and momentum transfer in gas/surface collisions. This will be discussed in the following section. 

Table 1. Linear momentum transfer in gas/surface collisions.

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