Propagation and Termination Rate Constants

Figure 4. Bulk polymerization of MM A at 22.5° C with AIBN Ri = 8.36 X 10 mol/L sec. Effect of conversion on propagation and termination rate constants (6).

The usual limitations (isothermal wall, radicals quasi-steady state, constant pressure) found in the lit -erature for similar models were released, and the importance of correctly evaluating the propagation and termination rate constants, kp and kt, was shown. 

Tabu 4-1 Representative Propagation and Termination Rate Constants... 

In the examples described above, the transition is shown from ideal (n = /2) to nonideal (n > /2) behavior. There are, however, systems for which ideal emulsion polymerization practically cannot be achieved. It is nevertheless possible to describe the kinetics of such systems quantitatively. Recently, Gerrens has obtained values of the propagation and termination rate constants at diflFerent temperatures for vinyltoluene and vinylxylene (28). The termination rate of polymer radicals of these monomers is so low that even at small rates of initiation in small particles, n is larger than /2. From measurements of the reaction rate before and after injection of additional initiator in the polymerizing system it was possible to calculate n both at the original and at the boosted initiation rate with the aid of Equation 5. Consistent results were obtained when the additional amount of initiator was varied. From these rate data, the termination rate constant was found to be 10 and 17 liters mole- sec. at 45° C. for vinyltoluene and vinylxylene, respectively. These values are to be compared with 10 for styrene (Table IV). 

Although several methods for the evaluation of oxidation initiation, propagation and termination rate constants and activation energies of these processes have been proposed (8,9). they did not provide the ground for samples comparison on routine basis and thus were of limiting practical value. 

In contrast, the typical polydispersity of polymers produced with Phillips catalysts varies from 6 to 20, and specialized catalyst treatments can provide polymers of PDI as low as 4.0 or as high as 100. Thus, 2 to 12 unique site types are required to reproduce the MW distribution from Phillips catalysts, because the catalyst contains a heterogeneous population of sites, differing widely in propagation and termination rate constants. Each site type generates polymer with its own characteristic MW, and consequently the polymer MW breadth reflects the heterogeneity of the site population. Differences in site reactivity no doubt derive from the... 

The photopolymerization steps can thus be divided into two main parts the photochemical event that leads to the first monomer radical, the classical chemical propagation and termination processes of the reaction. The rate of a radical polymerization is defined by Equation 10.5, where kp and kt are the propagation and termination rate constants and 7abs the amount of light absorbed. 

Equations (6.12) and (6.17)-(6.19) are based on the assumption that both the propagation and termination rate constants are independent of the size of the radical. This assumption facOitates the derivation of a kinetic expression, as shown... 

Fig. 4 Dependence of the propagation and termination rate constants on the degree of conversion of an acrylate resin...

One of the common features of all UV-curable systems is the rapidity at which the polymerization takes place under intense illumination, usually less than one second. Therefore it is difficult to accurately follow the kinetics of such ultrafast reactions, which is a prerequisite for a better understanding and control of the curing process. Moreover, evaluation of the kinetic parameters (rate of polymerization, kinetic chain length, propagation and termination rate constant) is essential in order to compare the reactivity of different photosensitive resins and assess the performance of novel photoinitiators and monomers. 

The data in Table 1 also illustrate the effect of the size of the counterion on the values of the propagation and termination rate constant (150,151). This table illustrates that the tetrakis pentafluorophenyl borate anion, which is 14 times more voluminous than the hexafluoroantimonate anion, results in a higher propagation rate constant and lower termination rate constant for the photopolymerization. These are the expected trends since the larger counterion will result in a more weakly associated ion pair. 

The propagation and termination rate constants have been determined for many systems (5,12,43-46). In most cases, the propagation rate constant is lower than that for a reaction carried out in the same conditions but without a template. The termination rate constant in the template polymerization is much lower in comparison with the blank reaction. Retarded termination may be caused by retarded segmental diffusion of the template-boimd radicals. This leads to the template increasing the overall rate of polymerization. Much experimental data from the literature confirm this, and it is sometimes called the kinetic template effect. 

The photoinitiated polymerization of a sterically hindered semi-fluorinated monomer, which is characterized by a hindered radical chain propagation site, was followed both in an isotropic and a highly ordered smectic liquid crystalline phase. The polymerization rate is slower in the smectic phase than in the isotropic phase, presumably a result of a decrease in both the propagation and termination rate constants. The decrease in the propagation rate results in a very slow persistent increase in polymer molecular weight after the initiating light source is removed. Polymerization firom the smectic phase of the monomer proceeds in a non-equilibrium matrix. 

FIGURE 10.5 Decreases in ( ) and k (O) for the bulk polymerization of styrene with an increase in conversion. Reprinted (adapted) with permission from Yamada B, Kageoka M, Otsu T. Dependence of propagation and termination rate constants on conversion for the radical polymerization of styrene in bulk as studied by ESR spectroscopy. Macromolecules 1991 24 5234— 5236. 1991 American Chemical Society. 

Yamada B, Kageoka M, Otsu T. Dependence of propagation and termination rate constants on conversion for the radical polymerization of styrene in bulk as studied by ESR spectroscopy. Macromolecules 1991 24 5234-5236. 

Kinetic analysis of the propagation and termination rate constants in the polymerization of MMA-EGDMA mixtures is more difficult than for MM A. An understanding of the polymerization depends on knowledge of the individual concentrations of C=C bonds that are (1) in monomer molecules and (2) attached to polymer molecules. This information may be obtainable for NMR spectra utilizing differences in the relaxation times of the two types of C=C environments. However, it is likely that the polymerization is heterogeneous with a non spatially random distribution of crosslinks. 

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