Bimolecular association of free radicals

Assuming that the long-range attraction between two free radicals can be described by the attractive part of the Lennard-Jones potential, V(r) = —4s(clrf, and applying equation (65), 

This cross-section can be inserted into equation (63), and the integral evaluated in terms of gamma functions. The rate coefficient is given by 

This equation predicts rate coefficients that are significantly greater than the SCT predictions from equations (59) and (60) because the effect of the attractive potential is to increase the reactive cross-section. For the combination of methyl radicals to form ethane, equation (60), with 

Applying a statistical factor of 1 /4 to both the SCT and the LJ predictions gives corrected rate coefficients of 8.3 x 10 and 2.5 X 10 cm molecule Sec respectively. The SCT prediction is now only 40% more than experiment, and the LJ prediction is a factor of 4 larger. It should not be concluded that SCT is better than LJ, because LJ includes attractive forces, and is more realistic. However, it is not clear that the — C/r attraction is correct, or for that matter what attraction should be used. Further discussion of this issue has been given by Johnston [22]. 

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