Cage combination rate constants, effect

As indicated by equation (2) above, the observed values for the rate constants of the second order self-termination of Scheme 1 free radicals (2k -obs) are the product 2kj) Fc(T). The RBM has provided the required values for F(,(T) and SW has given 2kj) so that the values of 2k obs can be predicted. The effective activation parameters for the k j/k competition and equations (3) and (4) offer the chemical model alternative for calculating 2k obs. The lower two curves of Figure 3 are the results of the two model calculations and simply reconfirm the equivalence of the RBM and chemical models shown in Figure 2. The important feature of Figure 3 is the pronounced curvature in the Eyring treatment of the predicted rate constants (2k obs). As mentioned at the outset, this is a result of the composite mechanism where neither diffusive separation nor cage combination is clearly rate dominant. 

Table III contains a summary of the parameters entering these calculations and shows the range of and T values. The cage combination of benzoyloxy-lb-butoxy and Jb-butoxy- -butoxy pairs, have significantly lower rate constants for combination than that for perfluoromethyl pairs. An additional observation, which was interesting to us, is that the product of k and t is nearly constant. In other words, the t required in D-10 is approximately a constant divided by Zkj for the pair undergoing reaction. A pair undergoing a slow combination reaction should thus have a larger effective cage radius. There is an intuitive basis for this to be a real feature of cage reactions.

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