Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

# Modeling the Dynamic Concentration Profiles and Efficacy of Type-I and Type-II Photopolymerization

Version 1 : Received: 18 May 2018 / Approved: 31 May 2018 / Online: 31 May 2018 (11:25:02 CEST)
Version 2 : Received: 28 October 2018 / Approved: 30 October 2018 / Online: 30 October 2018 (07:18:35 CET)

How to cite: Lin, J.; Cheng, D.; Chen, K.; Liu, H. Modeling the Dynamic Concentration Profiles and Efficacy of Type-I and Type-II Photopolymerization. Preprints 2018, 2018050472. https://doi.org/10.20944/preprints201805.0472.v2. Lin, J.; Cheng, D.; Chen, K.; Liu, H. Modeling the Dynamic Concentration Profiles and Efficacy of Type-I and Type-II Photopolymerization. Preprints 2018, 2018050472. https://doi.org/10.20944/preprints201805.0472.v2.

## Abstract

The kinetics and efficacy profiles of photoinitiated polymerization are theoretically presented. For the same dose, lower light intensity achieves a higher steady-state-efficacy (SSE) in type-I; in contrast, type-II has an equal SSE. Higher light intensity has a faster rising efficacy, due to faster depletion of photoinitiator (PS) concentration. However, type-II process is also affected by the available oxygen. Higher light intensity produces more efficient singlet oxygen, resulting a higher transient efficacy, in which all intensities reach the same SSE when oxygen is completely depleted. With external oxygen, type-II efficacy increases with time, otherwise, it is governed only by the light dose, i.e., same dose achieves same efficacy. Moreover, type-II has an efficacy follows Bunsen Roscoe law (BRL), whereas type-I follows non-BRL. The measured type-I efficacy and gelation profile are analyzed by our analytic formulas. Schematics of the photocrosslinking stage defined by the availability of oxygen is developed, where both type-I and –II coexist until the oxygen is depleted. The overall efficacy may be enhanced by resupply of PS or oxygen during the light exposure. The roles of light dose and PS concentration on the efficacy of photoinitiated polymerization should be are governed a new concept of a volume efficacy (Ve), defined by the product of the crosslink (or gelation) depth (CD) and local [efficacy].

## Keywords

polymerization; modeling; kinetic; singlet oxygen; polymerization efficacy; crosslinking

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