Kinetics of Free Radical Photopolymerization

3 Kinetics of Photoinitiated Reactions 4.3.1 Kinetics of Free Radical Photopolymerization 

Photoinitiated free radical polymerization proceeds via three main steps  

The initiation rate, V , depends on the radical yield per absorbed photon, O , and the number of photons absorbed per second in a unit volume, I. The latter quantity is a fraction of Iq, the number of photons per second per unit volume entering the process zone. 

In the chain propagation, mainly the monomer is consumed and the propagation rate depends on the monomer concentration, [M], and the concentration of polymeric radicals, [ ]. The quantity kp is the propagation rate constant. 

Chain termination occurs by combination or disproportionation of different polymer radicals. The termination rate, v is proportional to the polymer radical concentration, [ PJ, squared, with kt being the termination rate constant. Other possible chain termination processes are chain transfer and reaction of polymer radicals wifh inhibitors and radical trapping.  

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Complex Photopolymerization Systems. Kinetic modeling of free-radical photopolymerizations becomes more complicated as comonomers are added to the reaction system and as different polymerization methods are used to tailor the pol5uner properties. Although free-radical reaction mechanisms still hold true, rates of propagation and termination must be reconsidered to account for variables such as differences in double bond reactivities, reaction diffusion, and chain transfer. 

Free-radical photopolymerizations (see Chap. 10) of multifunctional acrylic monomers result in cross-linked polymeric networks. The kinetic picture of such polymerizations varies from ordinary linear polymerization because the diffusion of free radicals and functional groups becomes severely restricted. This causes growing polymer chains to rapidly cyclize and cross-link into clusters (microgels). The clusters become linked up into networks. Many free radicals become trapped, but terminations take place by combinations and by chain transferring. The cumulative chain length in such polymerizations can be calculated from the following equation [125] ... 

The vast majority of photopolymerizations used in industry are free-radical polymerizations, which have been studied extensively (for reviews, see references 1-5 as well as Photopolymerization, Free Radical (qv)). By far the most widely used classes of monomers for UV-initiated free-radical photopolymerizations are multiftinctional acrylates and methacrylates. Several investigations have demonstrated that free-radical polymerizations of these monomers exhibit imusual kinetic behavior, including immediate onset of autoacceleration, the formation of heterogeneous polymers (2,6-11), and the attainment of a maximum conversion... 

Polymers in Schemes 12 and 13 were the first examples of the preparation of pyridinium and iminopyridinium ylide polymers. One of the more recent contributions of Kondo and his colleagues [16] deals with the sensitization effect of l-ethoxycarbonyliminopyridinium ylide (IPYY) (Scheme 14) on the photopolymerization of vinyl monomers. Only acrylic monomers such as MMA and methyl acrylate (MA) were photoinitiated by IPYY, while vinylacetate (VA), acrylonitrile (AN), and styrene were unaffected by the initiator used. A free radical mechanism was confirmed by a kinetic study. The complex of IPYY and MMA was defined as an exciplex that served as a precursor of the initiating radical. This ylide is unique in being stabilized by the participation of a... 

Photoinitiated free radical polymerization is a typical chain reaction. Oster and Nang (8) and Ledwith (9) have described the kinetics and the mechanisms for such photopolymerization reactions. The rate of polymerization depends on the intensity of incident light (/ ), the quantum yield for production of radicals ( ), the molar extinction coefficient of the initiator at the wavelength employed ( ), the initiator concentration [5], and the path length (/) of the light through the sample. Assuming the usual radical termination processes at steady state, the rate of photopolymerization is often approximated by... 

It has been generally assumed that the polymer is formed by a free-radical chain which is initiated by H atoms or alkyl radicals. While this mechanism may be true for the mercury-photosensitized polymerization, recent results on the direct photopolymerization suggest that the two systems may be very similar and that a free-radical chain mechanism is not tenable for the latter case. It is probably most logical to examine this system by first studying the polymer that is formed, and then establishing the kinetics and mechanism of its formation. 

Bamford, who extensively investigated the kinetics of the thermal MMA polymerization with metal carbonyls and organic halides 6 3 7,5 3 8) recently advanced the following free radical mechanism for the photopolymerization of MMA with Mn2(CO)io and CCI4 33,34) ... 

The photopolymerization of methyl methacrylate using a quinoline-chlorine charge-transfer complex has been investigated. Bulk polymerization was found to follow normal free-radical kinetics, whereas in solution variable monomer exponents were observed depending on the nature of the solvent. The kinetic nonideality in solution was attributed to retardation and initiator termination via degradative chain-transfer involving solvent-modified initiating complexes and chain radicals. 

Photopolymerization systems, like thermally initiated systems, contain initiator, monomer, and other additives that impart desired properties (color, strength, flexibility, etc) (6). The reaction is initiated by active centers that are produced when light is absorbed by the photoinitiator. One important class of active centers includes free-radical species, which possess an impaired electron (5,7). The highly reactive free-radical active centers attack carbon-carbon double bonds in imsaturated monomers to form pol5nner chains. Although the kinetic treatment of photopoljnner systems is similar to that in thermal systems, significant differences arise in the description of the initiation step, which in turn affect the... 

Autoacceleration, where the rate of polymerization increases with conversion in isothermal conditions, is observed in both thermal- and photoinitiated free-radical polymerizations because the termination mechanisms are the same for both. As the chains grow longer, it becomes more difficult for the active centers to diffuse and imdergo bimolecular termination thus, termination frequency decreases and active centers at the chain ends can become trapped. In cases where termination is controlled by diffusion, the pseudo-steady-state assumption is no longer valid and chain length dependent termination (CLDT) may occur (67). As is discussed for chain cross-linking photopolymerizations below, more complicated kinetic treatments must then be considered, including unsteady-state kinetics. 

The systems are designed in order to improve the reaction rate of the mixture and the physical properties of the photopoljmier. The flexibility of the two photoinitiation schemes in one system allows for numerons possibilities in achieving greater control of viscosity, conversion, shrinkage, adhesion, and ultimate strength. The kinetics of hybrid photopolymerization systems are more difficult because two reactive systems (free-radical and cationic) mnst be resolved from one another. Cationic photopolymerization kinetics are more difficnlt to analyze than free-radical kinetics because the pseudo-steady-state assumption is often not valid for the cationic active center concentration, and the natnre and concentration of the cationic active centers is difficult to determine (p. 376 of Ref 33, see also Photopolymerization, Cationic). 

The features and detail of the IPN kinetics were also studied in other works [274-276]. The kinetics of thermally initiated cationic epoxy polymerization and free radical acrylate photopolymerization were investigated in [277]. It was found that the preexistence of one polymer has a significant effect on the polymerization of the second monomer. The reaction kinetics and phase separations were studied for sequential IPNs in [278]. The kinetics of IPN formation was studied for IPNs based on PDMS-cellulose acetate butyrate [279]. All these and other works [280-282] confirm the general regularities of the reaction kinetics and its connection with phase separation in forming systems. 

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