Mathematical Problems in Engineering
Volume 5 (1999), Issue 2, Pages 139-160

A model of frontal polymerization using complex initiation

P. M. Goldfeder and V. A. Volpert

Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston 60208, IL, USA

Received 19 May 1998

Copyright © 1999 P. M. Goldfeder and V. A. Volpert. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Frontal polymerization is a process in which a spatially localized reaction zone propagates into a monomer, converting it into a polymer. In the simplest case of free-radical polymerization, a mixture of monomer and initiator is placed in a test tube. A reaction is then initiated at one end of the tube. Over time, a self-sustained thermal wave, in which chemical conversion occurs, is produced. This phenomenon is possible because of the highly exothermic nature of the polymerization reactions.

Though there are certain advantages to this polymerization process over the more traditional methods, one of the drawbacks is that conversion tends to be incomplete. One way to increase conversion is by using greater amounts of initiator. The disadvantage to using this method is that more initiator results in the production of more free radicals, leading to large numbers of undesirably short polymer chains. A second method is to use a mixture of unstable and stable initiators. In this paper we develop and study a mathematical model of the propagation of free-radical polymerization fronts using such a complex initiation. We compare the propagation velocity, maximum temperature and degree of conversion of fronts with a stable initiator, an unstable initiator and a mixture of the two. In addition, we examine how altering the stability of the stable initiator affects these quantities. We show that it is indeed the case that a mixture of unstable and stable initiators does have many advantages over using either type of initiator individually, in agreement with the existing experimental data.