The polymerization rate is inhibited by air due to oxygen inhibition, which scavenges the radical species needed for cross-linking initialization. It is a noncontact, low-energy, and rapid process with capabilities of spatially specifying the reaction via photomasks (photolithography) ( Cabral et al., 2004 O'Brien and Bowman, 2006 Cramer et al., 2008 Dendukuri et al., 2008 Alvankarian and Majlis, 2015 Wohlers and Caffrey, 2016 Chen et al., 2017 Wu et al., 2018). Industrial applications include developing materials for applications such as thin films, coatings, printing, graphic work, dentistry, contact lenses, and electronics. The progress of light-responsive smart nanomaterials was recently review by Yang et al. Tissue engineering using scaffold-based procedures for chemical modification of polymers has been reported to improve its mechanical properties by cross-linking or polymerization with ultraviolet (UV) or visible light to produce gels or high-molecular-weight polymers ( Chen and Shi, 2014 Kotisch et al., 2017). Photoinitiated (photosensitized) polymerization and cross-linking provide advantageous means over thermal-initiated polymerization, including fast and controllable reaction rates, and spatial and temporal control over the formation of the material, without the need for high temperatures or harsh conditions ( Fouassier, 1995 Odian, 2006). Finally, various strategies for improved efficacy and curing depth are discussed.

Analytic formulas for the efficacy and curing depth are derived, for the first time, and utilized to analyze the measured pillar height in microfabrication. Efficacy is scaled by 0.5 at steady state. In conclusion, the curing depth has a non-linear dependence on the PS concentration, light intensity, and dose and a decreasing function of the oxygen inhibition effect. 5, defined by the radical producing rate ( k′) and the bimolecular termination rate ( k T). Efficacy is also an increasing function of the effective rate constant, K = k′/ k T 0. With oxygen inhibition effect, the efficacy temporal profile has an induction time defined by the oxygen depletion rate. For optically thick polymers (>100 um), light intensity is an increasing function of time due to PS depletion, which cannot be neglected. Higher intensity results in a faster depletion of PS and oxygen. The curing (or cross-link) depth is an increasing function of C 0 and light dose (time × intensity), but it is a decreasing function of the oxygen concentration, viscosity effect, and oxygen external supply rate. We show that photopolymerization efficacy is an increasing function of photosensitizer (PS) concentration ( C 0) and the light dose at transient state, but it is a decreasing function of the light intensity, scaled by 0.5 at steady state. Kinetic equations for a modeling system with type-I radical-mediated and type-II oxygen-mediated pathways are derived and numerically solved for the photopolymerization efficacy and curing depth, under the quasi-steady state assumption, and bimolecular termination.

4Department of Biomedical Imaging and Radiological Science, China Medical University, Taichung, Taiwan.

3Graduate Institute of Applied Science and Engineering, Fu Jen Catholic University, New Taipei City, Taiwan.

2Department of Life Science, Fu Jen Catholic University, New Taipei City, Taiwan.

Jui-Teng Lin 1 † Hsia-Wei Liu 2 † Kuo-Ti Chen 3 Da-Chuan Cheng 4 *

Intensity equation light