Frontal copolymerization is a process in which a spatially localized reaction zone propagates into a mixture of two monomers, converting them into a copolymer. In the simplest case of free‐radical copolymerization, a mixture of monomers and initiator is placed into a test tube. Reaction is initiated at one end of the tube, and a self‐sustained thermal wave, in which chemical conversion occurs, develops and propagates through the tube. We develop a mathematical model of the frontal copolymerization process and analytically determine the structure of the polymerization wave, the propagation velocity, maximum temperature, and degree of conversion of the monomers. Specifically, we examine their dependence on reactivity ratios as well as other kinetic parameters, monomer feed composition, and exothermicity of the reactions. Our analytic results are in good quantitative agreement with both direct numerical simulations of the model and experimental data, which are also presented in the paper.Dependence of front velocity on monomer feed composition for different heat release parameters.imageDependence of front velocity on monomer feed composition for different heat release parameters.
Summary: A mathematical model of photopolymerization is presented for a stationary laser. Termination by radical combination and radical trapping is considered. Using simplifying assumptions, we derive analytical equations for the concentration of photoinitiator and monomer in the system. With these equations, we show that the light intensity and the initial amount of photoinitiator highly influence the polymerization process and determine the shape of the polymer that is formed. We also provide an analytic expression to determine the amount of polymer formed during dark reactions.Percent conversion of monomer as a function of time at z = 0 and r = 0 (Data from Table 1).imagePercent conversion of monomer as a function of time at z = 0 and r = 0 (Data from Table 1).
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