Diffusion-Induced Nonuniformity of Photoinitiation in a Photobleaching Medium

Abstract

Absorption of incident light in photopolymerizations gives rise to instantaneous distributions of initiator concentration and initiation rate that are nonuniform along the beam path. Absent diffusion, however, the time-integrated production of primary radicals is uniform if the initial initiator concentration is uniform and all initiator is consumed, since each initiator molecule is photolyzed in place. Here, we consider the effects of diffusion of a photobleaching initiator for finite values of the ratio of the diffusive time scale l 2 /D to the reaction time scale 1/(φIoRA), where l and Io are the layer thickness and incident light intensity at the optical entrance, and D and RA are the diffusion coefficient and molar absorption coefficient of photoinitiator, respectively, whose quantum yield of consumption is φ. Compared to the limiting case in which diffusion is negligible, diffusion has the effect of shifting the instantaneous initiation rate profiles forward in the layer, where initiator is relatively depleted. On the other hand, for any nonzero initial absorbance, the overall (i.e., time-integrated) consumption of initiator becomes more nonuniform as the ratio of the rates of diffusion and reaction, expressed in the dimensionless ratio δ ) D/(l 2 φIoRA), increases. When diffusion is fast (large δ), the front-to-back difference in the time-integrated primary radical production varies quadratically with the initial concentration of initiator. Implications of the results for conversion of monomer and for chain-length distributions are discussed.

Controlling frontal photopolymerization with optical attenuation and mass diffusion

“…This is a consequence of diffusion replenishing the monomer near the transparent substrate where the intensity of radiation is the highest, both of which are factors that allow for an acceleration of the local conversion into polymer. Interestingly, these results differ from those of Terrones and Pearlstein [25], who show that in a perfectly photobleaching system, the mean conversion fraction is independent of the nondimensional diffusivity δ. In this case, the increase in the rate of polymerization that occurs due to the replenishment of the monomer near the transparent surface is exactly offset by the decrease in radiation intensity throughout the mixture due to this buildup of strongly absorbing molecules.…”

“…At one end of the spectrum are accurate physicochemical models accounting for each of the reaction steps (minimally photoinitiation, propagation, and termination) [19][20][21][22], nonuniform distributions of polymer chain length [23,24], generation and diffusion of thermal energy [15], mass transport [25], and intricate optical effects [26,27]. Such models, however, often suffer from an excessive number of parameters, some of which cannot be measured experimentally, and thus they offer limited insight and practical use.…”

“…The dashed line denotes a critical conversion fraction, φ c = 0.05, that can be used as an alternative definition of the solid-liquid interface. (b) Diffusion leads to a replenishment of the monomer near the transparent substrate located at z = 0, and this, in turn, increases the net production of polymer, which can be measured through the mean conversion fraction φ δ , defined in(25). (c) Front propagation kinetics, defined using the criteria φ(Z f (t),t) = φ c = 0.05, shows that FPP is accelerated due to mass diffusion.…”

Frontal Polymerization

“…The first is isothermal FP, which is discussed in Chapter 5. The second is photofrontal polymerization in which the front is driven by the continuous flux of radiation, usually UV light [1][2][3][4][5][6][7]. The last type is thermal FP, which we will henceforth refer to as frontal polymerization, and it results from the coupling of thermal transport and the Arrhenius dependence of the reaction rate of an exothermic polymerization.…”

Temperature controlled cationic photo-curing of a thick, dark composite

“…1,8,14,[16][17][18][19] However, the diffusion coefficient of these active centres is low, 16,18,20,21 which means that curing thick samples, if it is possible at all, takes a long time or requires a high temperature. What is more, coloured additives like pigment or bres, especially dark colours, further reduce the ability of light to penetrate the solution and the rate of production of active centres, and thus the maximum thickness of dark-coloured samples that can be cured is limited.…”