Mathematical modeling of polymerization waves

Frontal Polymerization is a process that converts monomers into polymers by means of a propagating spatially localized reaction front. In the simplest experimental setting, a mixture of monomer and initiator is placed into a test tube and upon initiation of the reaction at one end of the tube, a self-sustained wave develops and propagates through the tube. First we focus on Isothermal Frontal Polymerization (IFP) which occurs due to the coupling of mass diffusion of the species and the gel effect. Utilizing the free volume theory of Vrentas and Duda for describing the self-diffusive behavior in the gel, we mathematically model and study this IFP process. We determine, both numerically and analytically, characteristics of the process including the propagation velocity of the reaction zone and the structure of the wave. We also study the effect of inhibitors and show that they allow the front to propagate longer, before it breaks down due to reactions ahead of the front. Secondly, a mathematical model that describes exothermic thiol-ene frontal copolymerization is presented and studied, both numerically and analytically. In exothermic polymerization, the reaction is initiated by introducing a heat source to the monomer-initiator mixture. Exothermic wave propagation is due to heat diffusion and the heat release in the reactions. We determine the profiles of the temperature and concentrations of the reactants as well as the propagation velocity of the wave. We also discuss the conditions for existence of polymerization fronts. Finally, a nonisothermal gel effect model was formulated and studied. Here, a polymer test tube, containing its monomer-initiator mixture, is placed in a hot thermostatic bath. Typically, an isothermal front propagates from the wall of the tube towards the center, and an exothermic front propagates from the center of the tube moving radially towards the wall. An interesting scenario is also seen where an isothermal mode of propagation transitions to an exothermic mode of propagation. Frontal polymerization has applications associated with optical polymers that have gradients of refractive index and are of commercial importance.