Gas phase termination

Since a radical is consumed and formed in reaction (3.3) and since R represents any radical chain carrier, it is written on both sides of this reaction step. Reaction (3.4) is a gas-phase termination step forming an intermediate stable molecule I, which can react further, much as M does. Reaction (3.5), which is not considered particularly important, is essentially a chain terminating step at high pressures. In step (5), R is generally an H radical and R02 is H02, a radical much less effective in reacting with stable (reactant) molecules. Thus reaction (3.5) is considered to be a third-order chain termination step. Reaction (3.6) is a surface termination step that forms minor intermediates (T) not crucial to the system. For example, tetraethyllead forms lead oxide particles during automotive combustion if these particles act as a surface sink for radicals, reaction (3.6) would represent the effect of tetraethyllead. The automotive cylinder wall would produce an effect similar to that of tetraethyllead. 

In this higher temperature regime and in atmospheric-pressure flames, the eventual fate of the radicals formed is dictated by recombination. The principal gas-phase termination steps are... 

The rest of the mechanism proposed by Tibbitt et al. " is also shown in Table 6. Two assumptions were introduced to simplify the mechanism. The first is that the extent of gas phase termination is very small and consequently, that essentially all of the radicals formed in the gas phase are adsorbed on the polymer surface. The second assumption is that the concentrations of adsorbed monomer and free radical are proportional to the gas phase concentrations of these species. These relationships are expressed by... 

At low pressures surface termination is predominant, and altering the size, shape and nature of the surface has a major effect. Addition of inert gas cuts down diffusion to the surface, decreasing the rate of surface termination. As the pressure increases diffusion to the surface decreases, and gas phase termination becomes increasingly important until it is predominant at high pressures. 

Gas phase terminations generally have very low, zero or negative activation energies, and their rate constants are governed by their pre-exponential factors. In contrast, surface terminations have a much wider range of activation energies. 

Standard mechanisms for chain reactions generally miss out the surface termination steps, but these should be included. Such terminations are written as first order in radical since diffusion to the surface or adsorption on the surface are rate determining, rather than the second order bimolecular step of recombination of the two radicals adsorbed on the surface. A complete mechanism will also include the need for a third body in any unimolecular initiation or propagation steps, and in any gas phase termination steps. 

Steps 7 and 8 are rate determining for surface termination, being diffusion of each type of radical to the surface or adsorption of each radical on to the surface, whichever is the slower process. The recombinations of adsorbed R and R by like-like and like-unlike radical recombinations are the fast steps in the surface termination process. Consequently surface termination consists of the two steps, 7 and 8, in contrast to the gas phase termination, which consists of the three steps, 4, 5 and 6. 

The reaction is now second order in contrast to 3/2 order when gas phase termination is dominant. 

The conclusion drawn from Worked Problem 6.14 is that changing the type of termination step from gas to surface alters the kinetics. This is because the order with respect to the radical differs between the second order recombination of the gas phase termination and surface termination where diffusion to the surface or adsorption on the surface is rate determining and first order. If, however, the rate-determining step in surface termination were bimolecular recombination on the surface, the order would not change between gas and surface termination. This is because both recombinations would now have the same order, i.e. 2 4[R ]2 and 2 7[R ]2, with the total rate of termination if both contributed being 2(k + 7)[R ]2. 

The third pressure limit, when it exists, occurs at even higher pressures. At the third limit, i.e. at pressures greater than at d, the reaction moves back into an explosive region which is in part thermal, and in part the result of some dramatic change in radical concentration. This results from another set of reactions coming into play so that gas phase termination can no longer cope with this new production of radicals. 

The important part of the mechanism applicable to pressures and temperatures along the major part of the second limit involves the competition between the branching cycle (l)-(3) and a gas-phase termination step... 

The ignition limit lies in the region of the p-T plane, corresponding to the second limit in classical closed vessels, and so we may surmise that the dominant features of the mechanism will be the competition between the branching cycle (1-3) and the gas-phase termination step producing HO2, step (5). A full steady-state analysis on the intermediates OH and O would introduce (out)flow terms for each species and a fairly complex polynomial in terms of fres- The full analysis appears in Chapter 4 of this volume. For now, we can note that the typical residence times of interest, 1 to 10 s,... 

The concentration of OH radicals as a function of time has been observed directly in a shock tube (see Chapter 6 for details of this technique) under conditions where the reaction between H2 and O2 proceeds smoothly (1100-2600°K, in the presence of excess argon) [28-30]. An induction period approximately 10 to 100 /isec long is followed by a rapid rise of the OH concentration to a maximum value and finally a slow approach to equilibrium. The rise of the OH concentration over its equilibrium value (a phenomenon also observed for H and O) results from a partial approach to equilibrium in the three propagation steps in the mechanism before a significant amount of termolecular reaction occurs in the gas phase termination step. A detailed analysis shows that this overshoot can occur only if there is a decrease in the number of moles in the overall reaction, since it is only in this case that the termolecular termination step may become rate limiting. 

---