Second-order point process collision

For second-order point processes such as hard-sphere collisions, the total number of particles remains unchanged. However, the number of particles with a specific phase-space vector will always increase or decrease. 

As pointed out previously, an upper limit is placed upon (C) by second-order recombination processes, so that the radical concentration cannot grow without limit. At pressures near the first explosion limit this restriction is unimportant. Thus if we assume that the reaction H -f- H -f M proceeds at every tenth triple collision (that is, A = 3 X 10 liters2/mole -sec) then the lifetime of an II atom at 750 K when M = 8 mm Hg and H = 0.8 mm Hg ( ) is about 0.2 sec [t = l/fc(M)(H)]. This is much slower than the rate of branching in the H2 + O2 system (see page 457). 

In the case of weak collisions, the moment changes in small steps AJ (1 — y)J < J, and the process is considered as diffusion in J-space. Formally, this means that the function /(z) of width [(1 — y2)d]i is narrow relative to P(J,J, x). At t To the latter may be expanded at the point J up to terms of second-order with respect to (/ — /). Then at the limit y -> 1, to — 0 with tj finite, the Feller equations turn into a Fokker-Planck equation... 

In most chemical reactions the rates are dominated by collisions of two species that may have the capability to react. Thus, most simple reactions are second-order. Other reactions are dominated by a loose bond-breaking step and thus are first-order. Most of these latter type reactions fall in the class of decomposition processes. Isomerization reactions are also found to be first-order. According to Lindemann s theory [1, 4] of first-order processes, first-order reactions occur as a result of a two-step process. This point will be discussed in a subsequent section. 

The second important point on which the CICR technique is based is the strict control of the average number of reactants deposited on the clusters. This is is achieved by using the pick-up technique originally developed by Scoles and coworkers [291]. It consists in capturing the reactants by sticky collisions between the clusters and a low-pressure gas. Of course, the number of particles trapped is not the same for every cluster, but the important point is that the capture process has known statistics, being a random Poisson process. Hence the probability distribution Pq (m ) of finding exactly q reactant molecule per cluster follows the Poisson law of order q ... 

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