Effects of Kinetics and Optical Attenuation on the Completeness, Uniformity, and Dynamics of Monomer Conversion in Free-Radical Photopolymerizations

For free-radical photopolymerizations with a photobleaching initiator in an initially uniform layer illuminated from one direction, we incorporate nonuniform photoinitiation into a simple kinetic model to show how the degree of monomer conversion varies spatially and temporally with the incident light intensity ( I 0 ), the absorption coefficient (α A ) and initial concentration ( C A,0 ) of the photoinitiator, and the propagation ( k p ) and termination ( k t ) rate constants (taken to be independent of the degree of conversion). We show that the spatiotemporal variation of monomer conversion depends on two dimensionless parameters: the initial absorbance γ = α A C A,0 L, where L is the layer thickness, and β = k p [ fC A,0 /(φ α A I 0 k t )] 1/2, where φ is the quantum yield of photoinitiator consumption, and 0 ≤ f ≤ 2 is the number of primary radicals produced for each photoinitiator molecule consumed. For each value of γ, there is a minimum value of β beyond which a specified layer-averaged extent of monomer conversion is assured. As β decreases, so does the extent of monomer conversion, with the final degree of conversion being lowest near the optical “front” of the layer, where the light absorption and photoinitiation rates are initially highest. The extent of nonuniformity decreases with increasing β until β ≈ 2, beyond which monomer conversion is essentially complete regardless of the initial absorbance. The results are discussed in terms of the spatiotemporal distributions of the primary radical and radical chain concentrations.