The research project is devoted to theoretical investigations of frontal polymerization (FP) processes, in which a localized reaction zone propagates into a monomer converting it into a polymer. The project addresses both modeling of specific FP processes and the study of more general mathematical problems motivated by these modeling efforts. Specific modeling topics include the study of initiation of FP waves, their linear and nonlinear stability and fluid dynamical behavior. Asymptotic approaches are used to determine the structure of the polymerization wave and the composition of the product, as well as such experimentally measurable characteristics of the wave as its propagation velocity as a function of the kinetic and thermophysical parameters of the problem and the initial conditions. Topics of a more general mathematical nature are concerned with threshold phenomena in reaction diffusion systems, existence of time-periodic traveling waves of monotone parabolic systems, new kinds of integro-differential equations describing polymerization kinetics, and new forms of solutions of reaction diffusion systems, the so-called quasi-traveling wave solutions, the characteristics of which, including the propagation speed, vary slowly in time.
The importance of the proposed studies of frontal polymerization is twofold. First, it is a method to produce polymers which have become an integral part of human life. It bears strong similarities with another technological process occurring in a frontal regime, namely, self-propagating high-temperature synthesis which uses combustion waves to synthesize desired inorganic materials. Unlike the frontal polymerization process, the self-propagating high-temperature synthesis process is well-studied and is known to enjoy certain advantages over conventional technology, in which the mixture is placed in a furnace. These include (i) shorter synthesis times, (ii) less expense, since the internal chemical energy of the reactants is used rather than the external energy of the furnace, (iii) the use of simpler equipment, and (iv) purer products, since the high-temperature wave burns off volatile impurities. Similar benefits can be expected in polymer synthesis. Specifically, energy costs and waste solvent production can be reduced and unique materials obtained. However, before any advantages can be achieved and the frontal polymerization process becomes a competitive technology, a better understanding of the factors that affect frontal polymerization is necessary. Second, studies of specific models of frontal polymerization pose questions of a more general mathematical nature that are related to the behavior of solutions of general reaction/diffusion/convection systems. The study of these more general problems contributes to the understanding of specific frontal polymerization problems.
Date: June 18, 2001
