Effects of optical attenuation and consumption of a photobleaching initiator on local initiation rates in photopolymerizations

For free-radical photopolymerization with a photobleaching initiator, we develop an unsteady one-dimensional model accounting for initiator consumption and optical attenuation and derive relationships for the spatial and temporal variation of the local initiator concentration and initiation rate. With increasing absorbance, the local initiation rate becomes increasingly nonuniform and assumes the form of a highly localized traveling wave propagating with speed φI₀/C_A,0 (where φ, I₀, and C_A,0 are the quantum yield of photoinitiator consumption, incident intensity, and initial photoinitiator concentration, respectively), independent of photoinitiator absorption coefficient. At high attenuation, the maximum photoinitiation rate (as a function of position) is asymptotically one-fourth the initial rate at the front of the layer. Qualitative effects of nonuniform initiation in free-radical photopolymerizations with simple and more complicated kinetics are discussed in terms of the model and results.