Solution of a field theory model of frontal photopolymerization

Frontal photopolymerization (FPP) provides a versatile method for the rapid fabrication of solid polymer network materials by exposing photosensitive molecules to light. Dimensional control of structures created by this process is crucial in applications ranging from microfluidics and coatings to dentistry, and the availability of a predictive mathematical model of FPP is needed to achieve such control. Previous work has relied on numerical solutions in validating the model against experiments because of the intractability of the governing nonlinear equations. The present paper provides solutions to these equations in the general case in which the optical attenuation decreases (photobleaching) or increases (photodarkening) with photopolymerization. These solutions are of mathematical and physical interest because they support traveling waves of polymerization that propagate logarithmically or linearly in time, depending on the evolution of optical attenuation of the photopolymerized material.