橋かけ高分子の主鎖, 橋かけ両分子が同時切断する場合の理論式

抄録

In connection with the evaluation of polymer stability and chemical antioxidants it is a very urgent work to make clear the degradation mechanism of crosslinked polymers.
There have long been two extremely different opinions about the mechanism of scission of network chain polymers, especially about natural rubber vulcanizates. One is that only random chain scission of this vulcanizates occurs in the oxidation reaction from the experiments and theory by A. V. Tobolsky. Another is that only their crosslink scission occurs in the oxidation reaction from the experiments and theory by Berry and Watson.
The results of recent studies of crosslinked polymers including this vulcanizates show that both the scissions may occur at the some time in many cases.
So the authors have made an attempt to derive the general equations for both the scissions for the purpose of finding out the quantitative amounts of scission chains using the experimental results and judging the relative estimation of the scissions.
We have generalized the case where one cross-linkage is cut in the minimum model of perfect chain network, and the following equation has been derived for the vulcanizates in which both the scissions occur.
N_t/N₀=f_t/f₀={1-4kx/k+2x·Q(t)/M₀}·e^{-2x2/k+2x·Q(t)/M₀}+2kx/k+2x·Q(t)/M₀·e^{-4x2/k+2x·Q(t)/M₀}
(1)
The Eq. (1) in both the cases of k→0 and k→∞, conforms to that proposed by Tobolsky. Assuming the more practically probable mechanism in the scission of cross-linked polymer, the following Eq. (2) obtained by modification of Eq. (1) is derived.
N_t/N₀=f_t/f₀={1-8kx/k+2x·Q(t)/M₀}·e^{-2x2/k+2x·Q(t)/M₀}+6kx/k+2x·Q(t)/M₀·e^{-4x2/k+2x·Q(t)/M₀}-2kx/k+2x·Q(t)/M₀·e^{-8x2/k+2x·Q(t)/M₀}
(2)
The theoretical relation between Q(t)/M₀ and N_t/N₀ is shown and discussed.