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 a monomer and initiator is placed into a test tube. Upon reaction initiation at one end of the tube, a self-sustained thermal wave, in which chemical conversion occurs, develops and propagates through the tube. We develop a mathematical model of the frontal polymerization process and analytically determine the structure of the polymerization wave, the propagation velocity, maximum temperature, and degree of conversion of the monomer. Specifically, we examine their dependence on the kinetic parameters of the reaction, the initial temperature of the mixture, and the initial concentrations of the initiator and monomer. Our analytic results are in good quantitative agreement with both direct numerical simulations of the model and experimental data (on butyl acrylate polymerization), which are also presented in the paper.

We studied ascending fronts of acrylamide polymerization in dimethyl sulfoxide in which the reactants in solution are converted to a gel at a higher temperature than the solution. We have calculated the stability boundary (the critical viscosity at which convection occurs) as a function of the front velocity. We found that in a two-dimensional system the presence of walls does stabilize the front compared to an infinite plane, but the shape of the boundary is not affected. Experimental fronts exhibited antisymmetric convection for low viscosities and low front velocities, as predicted by our calculations. However, the experimentally determined boundary differed significantly from the calculated ones, the experimental fronts being more stable. The shapes of the boundaries differ, and we propose this is caused by the temperature dependence of the viscosity, which is not treated in our analysis.

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.

In this paper we show that ‘permeability’ of a heterogeneous structure with mass transport and thermodynamic properties varying across its thickness is a misleading concept leading to incorrect results and design decisions while two structural transmission rate equations are recommended for practical applications. The notion of structural identity of multi-layer films is introduced to explain the apparent failure of the ‘permeability’ concept. Structural identity of two or more films means the same material sequence in the structure relative to separated environments with constant relative thickness of each corresponding layer. Structurally identical films indeed have the same ‘permeability’, however the notion of identity is shown to contradict the practical goals of multi-layer film design. Engineering examples are provided to demonstrate potential misuses of the ‘permeability’ concept in practical multi-layer design decisions. Correct problem statements and calculation procedures are included. Some general limitations of transmission rate equations are also discussed. These include the role of boundary conditions, temperature and concentration dependence of permeant diffusivity and solubility in a polymer matrix, the presence of co-permeants, surface sorption effects, film thickness, homogeneity of polymer matrix for permeation purposes and correct utilization of available data for predicting gas transport properties of multilayer films.