Kinetics of a Self-Decelerating Polymerization

The presence of long-living radicals in the polymer network will cause the reaction to continue in the dark. In HDDA, the radicals persist for several months after irradiation if the sample is kept at room temperature and under vacuum even 

If we allow the samples to stand before extraction and determination of free monomer, we observe virtually no decrease of the radical concentration but the concentration of free monomer [M] decays in the dark in a self-decelerating 

If ordinary pseudo first-order kinetics were obeyed, log [M] vs. t should be linear here, however, the result is just opposite [M] vs. log t is almost linear over more than 4 decades of time. The first half-time is about 20 h and the next one 300 h. Physically, this would mean that the monomer molecules are distributed among traps and that the molecules from the shallowest traps escape and diffuse to a reactive radical site more quickly than the other ones. Further reaction will deepen the traps of the remaining molecules, so that the relaxation time of the system increases continuously. 

Many relaxation phenomena in polymeric glasses can be described in an empirical way using the Williams-Watts relaxation function t) in which a parameter p accounts for the width of the relaxation spectrum  

Stress relaxation , creep recovery , dielectric relaxation and volume recovery data have all been fitted with such a function. This purely empirical equation has also been connected with several kinds of models used for the description of polymeric glasses. 

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