Modeling of photobleaching for the photoinitiation of thick polymerization systems

We present a mathematical description of the spatial and temporal evolution of the light intensity gradient, initiator concentration gradient, and initiation rate profiles for photobleaching initiator systems. This article builds on the foundation provided by previous researchers' contributions by generalizing the governing differential equations to include the effects of absorption by the initiator fragments, absorption by the monomer, and diffusion of the initiator. Simulation results have confirmed that, at any given time, the initiation rate profile resembles a wave front that propagates through the sample. The simulation results suggest that there is an optimum initiator concentration for efficient photopolymerization of thick samples. As either the initiator concentration or molar absorptivity is increased, the initiation rate at the peak of the wave front increases, the breadth of the propagating front decreases, and the rate of spatial propagation through the sample decreases. In contrast, the maximum photoinitiation rate and rate of spatial propagation of the initiation front can be simultaneously increased with an increasing initiator quantum yield or a decreasing absorptivity of the monomer or photolysis products. Finally, on the basis of these studies, diffusion is expected to have negligible effects in most photobleaching systems.