Modeling of Oxygen-Inhibited Free Radical Photopolymerization in a PDMS Microfluidic Device

Free-radical photopolymerization performed within PDMS microfluidic devices is now used for a variety of applications. We propose, through model and experiment, that atmospheric oxygen diffusing in through the porous PDMS is responsible for the presence, under UV light, of a thin, un-cross-linked film of oligomer abutting the walls of an all-PDMS device. After the advent of light exposure, an induction time τ i is required before the oxygen present in the oligomer is depleted, and cross-linking reactions can begin. A polymerized structure then grows from the center of the device outward, increasing sharply in height with time and leaving only a thin un-cross-linked film of thickness, δi,c, close to the walls where oxygen can penetrate. Under suitable simplification of the reaction−diffusion model developed, scaling relationships were obtained for τi (∼D a −1) and δi,c (∼D a −1/2) as a function of a Damköhler number, D a. The relationships were successfully verified by comparison with both the full solution and experimental data. The analysis shows that control over particle height can be obtained more easily by changing initiator concentration, irradiation intensity, or channel height rather than exposure time.