Probability model theory of chain‐end activated polymer degradation. II. Second‐order radical termination

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Abstract
New analytical solutions are obtained for the kinetics of degradation when activation affects only the chain ends, and all chain ends have equal reactivity, using the following improvements in the models used. The initial polymer chains are distributed in size, following the radical‐combination type of distribution function (self‐convoluted exponential), rather than the chains being of equal size (homodisperse). The radical termination reaction is taken either kinetically of first order or second order. The latter case has not previously been solved exactly, because in the previous schemes of derivation it renders the differential equations nonlinear. Not unexpectedly, the results on the rates of decay of weight or molecular weight are very similar for first‐order and second‐order radical termination. The improvements in the model undoubtedly make these calculations more realistic than those previously available, but the results do not at all improve the fit of existing data on the rate of decay of the mean chain length with conversion in the degradation of polymethyl methacrylate. Probably this happens because the results are sensitive to the incursion of minor side reactions not yet taken into account.