Exact Solution of a Field Theory Model of Frontal Photopolymerization

TL;DR

This paper derives exact solutions for a mathematical model of frontal photopolymerization, enabling precise control of polymer structures by understanding wave propagation under different optical attenuation scenarios.

Contribution

It provides the first exact solutions to the nonlinear kinetic equations governing FPP, accounting for photobleaching and photodarkening effects.

Findings

Supports traveling wave solutions of polymerization

Reveals logarithmic and linear propagation behaviors

Enhances predictive modeling of FPP processes

Abstract

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 this control. Previous work has relied on numerical solutions of the governing kinetic equations in validating the model against experiments because of the intractability of the governing nonlinear equations. The present paper provides exact solutions to these equations in the general case in which the optical attenuation decreases (photobleaching) or increases (photodarkening) with photopolymerization. These exact 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.