Markovian approach to nonlinear polymer formation: Free-radical polymerization with chain transfer to polymer

✍ Scribed by Hidetaka Tobita

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 282 KB
• Volume: 36
• Category: Article
• ISSN: 0887-6266
• DOI: 10.1002/(sici)1099-0488(19980130)36:2<357::aid-polb14>3.0.co;2-g

✦ Synopsis

A Markovian model is proposed for nonrandom branching reactions, by using free-radical polymerization that involves chain transfer to polymer as an example. Free-radical polymerizations are kinetically controlled; therefore, each primary polymer molecule experiences different history of branched structure formation. By assuming that the primary chains with the identical birth time conform to the same chain connection probabilities, the nonlinear structural development can be viewed as a system in which the primary chains formed at different birth times are combined into nonlinear polymers in accordance with the first-order Markov chain statistics. An explicit formula for the weight-average chain length is derived in a matrix form. The onset of gelation is simply stated as a point at which the largest eigenvalue of the transition matrix X reaches unity, i.e., det( X 0 I) Å 0. This criterion for the onset of gelation can be considered as an extension of the Flory/Stockmayer theory to a nonequilibrium reaction system.