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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2002, 7(3), 241-252;

Kinetic Equations for Ultrasonic Scission of Polymers

Istanbul Technical University, Math. Dept., Maslak, 80626 Istanbul, Turkey
Published: 1 December 2002
PDF [463 KB, uploaded 1 April 2016]


When a long chain of polymer is sonicated it is known that it preferentially breaks at the middle and long chain radicals result. The termination step is especially important to control the degree of polymerisation Pn. In this paper, in the absence of the radical traps the nature of the phenomenological kinetic equations derived in [4] are studied. It has been found that for all possible values of the parameters, the only equilibrium point is linearly stable. But because of the nonlinear effects, stability of the equilibrium point depends on the parameter space. For some set of parameters and initial conditions, it has been observed that the solutions are asymptotically periodic. But large time behaviour of all these solutions are not realistic in the sense that functions representing nonnegative physical quantities assume negative values. A modified version of the kinetic equations whose solutions remain nonnegative in the time course is also proposed.
Keywords: Polymers; ultrasonic scission; nonlinear kinetic equations Polymers; ultrasonic scission; nonlinear kinetic equations
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Can, M. Kinetic Equations for Ultrasonic Scission of Polymers. Math. Comput. Appl. 2002, 7, 241-252.

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