A Kinetic Model for Radical Trapping in Photopolymerization of Multifunctional Monomers

Abstract

An improved kinetic model is presented which accounts for radical trapping during the photopolymerization of multifunctional monomers such as diacrylates and dimethacrylates. Following earlier suggestions, the model assumes that trapping of radicals behaves as a unimolecular first-order reaction. The novel feature is that the trapping rate constant is presumed to increase exponentially with the inverse of the free volume; this treatment is qualitatively consistent with the free volume dependence previously proposed for the other rate constants. This improved model predicts the experimental reaction rate trends as well as previous models developed in the literature; more importantly, though, this improved model newly predicts, as no other model has, the following experimental trends in the trapped and active radical concentrations: (1) that the active radical concentration passes through a maximum while the trapped radical concentration increases monotonically; (2) that a higher light intensity leads to a lower fraction of trapped radicals at a given conversion of functional groups but to a higher trapped radical concentration at the end of the reaction. Moreover, unlike its antecedents, the improved model correctly predicts that the polymerization rate depends more on light intensity the higher the conversion and that higher light intensity can lead to a higher final conversion.

A Review on Modeling Cure Kinetics and Mechanisms of Photopolymerization

“…The models presented so far, and also models published, for instance, by Goodner et al [ 96 ], Lee et al [ 106 ], Buback et al [ 90 ], Dickey et al [ 93 , 107 ] and Long et al [ 87 ] assume that the termination is due to radical recombination, which is the most common assumption for termination [ 108 ]. However, Wen et al [ 109 ] state that a kinetic model that ignores radical trapping fails to predict two important aspects of experimental observations: Firstly, the concentration of trapped radicals increases monotonically with conversion, whereas the concentration of active radicals increases initially and then drops at high conversions [ 110 ]. Secondly, a higher light intensity leads to a lower fraction of trapped radicals at a given conversion but to a higher trapped radical concentration at the end of the reaction [ 110 ].…”

“…Secondly, a higher light intensity leads to a lower fraction of trapped radicals at a given conversion but to a higher trapped radical concentration at the end of the reaction [ 110 ]. In order to include radical trapping, Wen et al [ 109 ] extended the functional-group reaction scheme shown at the beginning of this section with the formation of trapped radicals like in Equation (39), in which are trapped (buried) radicals and is the rate constant for radical trapping (burying). Radical trapping is assumed to take place according to a unimolecular first-order reaction.…”

“…Radical trapping is assumed to take place according to a unimolecular first-order reaction. Consequently, the material balance equations proposed by Wen et al [ 109 ] include the trapped radical concentration and the active radical concentration , according to Equation (40), …”

“…In the proposed model, the propagation rate constant , the termination rate constant , as well as the rate constant for radical trapping , are simple functions of free volume following the model developed by Anseth and Bowman [ 38 , 101 ]. The model proposed by Wen et al [ 109 ] presumes that the rate constant for radical trapping increases with conversion as radical trapping occurs more and more often as the chain growth in the course of the polymerization proceeds. Therefore, the rate constant is modeled to increase exponentially with the inverse of the fractional free volume according to Equation (41), in which is the pre-exponential factor and the dimensionless activation volume that governs the rate at which radical trapping increases as a function of fractional free volume.…”

“…Therefore, the rate constant is modeled to increase exponentially with the inverse of the fractional free volume according to Equation (41), in which is the pre-exponential factor and the dimensionless activation volume that governs the rate at which radical trapping increases as a function of fractional free volume. Wen et al [ 109 ] compared their proposed model for predicting the reaction rate (with and without radical trapping) to photo-DSC experimental results during the polymerization of DEGDMA with 0.42 light intensity and 0.1 wt.% DMPA ( Figure 23 ). The markers on the dashed curve for the model considering radical trapping show (a) the onset of auto-acceleration, (b) reaction-diffusion becoming dominant for termination, (c) radical trapping becoming dominant for termination, and (d) the propagation reaction becoming reaction-diffusion controlled.…”