Rate coefficients in the intermediate fall-off range

From the limiting low- and high-pressure rate constants ko and respectively, one immediately derives the pressure at which fall-off behavior is to be expected. The center of the fall-off curve, i.e., that bath-gas concentration [M]c at which the extrapolated limiting rate coefficients intersect, is given by rearranging Eq. (2.10) to 

The intermediate rate coefficient k switches from /cq to k when [M] increases from values much below [M] to values above [M]. As mentioned in Section 2, this switching function is very complicated and in fact has never been analyzed in full detail. Weak collision effects, rotational effects, and other factors do influence the switching function to some extent. Fortunately, however, according to our present knowledge, all these effects are small, and simple empirical expressions like Eq. (2.13) are useful in practice. 

We concentrate attention first on the broadening factor defined in Eq. (2.13), which defines the depression of the fall-off curve at the center relative to the Lindemann-Hinshelwood function. F ent can be expressed to good approximation by the three parameters and is defined 

Alternative expressions to Eqs. (5.6)-(5.9) have been proposed (Troe, 1983). 

Although the expressions in Eqs. (5.3)-(5.8) look somewhat complicated, they are in fact easy to evaluate. Using this procedure to evaluate F , the full fall-off curve is given to a first approximation by Eqs. (2.12) and (2.13). To a second approximation, needed particularly at high temperatures, one uses Eq. (2.12) with F(x) containing a scaling factor N defined by 

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