Numerical modeling of self-propagating polymerization fronts: The role of kinetics on front stability

Abstract

Frontal propagation of a highly exothermic polymerization reaction in a liquid is studied with the goal of developing a mathematical model of the process. As a model case we consider monomers such as methacrylic acid and n-butyl acrylate with peroxide initiators, although the model is not limited to these reactants and can be applied to any system with the similar basic polymerization mechanism. A three-step reaction mechanism, including initiation, propagation and termination steps, as well as a more simple one-step mechanism, were considered. For the one-step mechanism the loss of stability of propagating front was observed as a sequence of period doubling bifurcations of the front velocity. It was shown that the one-step model cannot account for less than 100% conversion and product inhomogeneities as a result of front instability, therefore the three-step mechanism was exploited. The phenomenon of superadiabatic combustion temperature was observed beyond the Hopf bifurcation point for both kinetic schemes and supported by the experimental measurements. One- and two-dimensional numerical simulations were performed to observe various planar and nonplanar periodic modes, and the results for different kinetic schemes were compared. It was found that stability of the frontal mode for a one-step reaction mechanism does not differ for 1-D and 2-D cases. For the three-step reaction mechanism 2-D solutions turned out to be more stable with respect to the appearance of nonplanar periodic modes than corresponding 1-D solutions. Higher Zeldovich numbers (i.e., higher effective activation energies or lower initial temperatures) are necessary for the existence of planar and nonplanar periodic modes in the 2-D reactor with walls than in the 1-D case. (c) 1997 American Institute of Physics.

Frontal Polymerization

“…Solovyov et al performed two-dimensional numerical simulations using a standard three-step free-radical mechanism [92]. They calculated the Zeldovich number from the overall activation energy using the steady-state theory and determined the critical values for bifurcations to periodic modes and found that the complex kinetics stabilized the front.…”

On Step‐Function Reaction Kinetics Model in the Absence of Material Diffusion

“…The numerically determined behavior of the front for the step-function kinetics is qualitatively similar to that under the Arrhenius kinetics [7], [18], as it shows a similar hierarchy of dynamics and similar solution features, including those that result from the nonfrontal mode of polymerization. The same spectrum of system behaviors has also been demonstrated for the point-source kinetics [9]; however, all bulk (nonfrontal) reactions are ignored in this setting.…”

Thermal frontal polymerization with a thermally released redox catalyst

“…Such nonplanar modes of propagation have been the subject of much investigation. 40,[45][46][47][48][49][50][51] The complexity of the front increases with the value of the effective energy of activation. By reducing the number of propagating radicals, the transition metal reduces the contribution of the energy of activation for the termination step, which increases the effective activation energy.…”