Polymerization kinetics termination, computational

Computational Aspects of Free Radical Polymerization Kinetics with Chain Length Dependent Termination... 

The first quantitative model, which appeared in 1971, also accounted for possible charge-transfer complex formation (45). Deviation from the terminal model for bulk polymerization was shown to be due to antepenultimate effects (46). Mote recent work with numerical computation and C-nmr spectroscopy data on SAN sequence distributions indicates that the penultimate model is the most appropriate for bulk SAN copolymerization (47,48). A kinetic model for azeotropic SAN copolymerization in toluene has been developed that successfully predicts conversion, rate, and average molecular weight for conversions up to 50% (49). 

Batch Reactors. One of the classic works in this area is by Gee and Melville (21), based on the PSSA for chain reaction with termination. Realistic mechanisms of termination, disproportionation, and combination, are treated with a variety of initiation kinetics, and analytical solutions are obtained. Liu and Amundson (37) solved the simultaneous differential equations for batch and transient stirred tank reactors by using digital computer without the PSSA. The degree of polymerization was limited to 100 the kinetic constants used were not typical and led to radical lifetimes of hours and to the conclusion that the PSSA is not accurate in the early stages of polymerization. In 1962 Liu and Amundson used the generating function approach and obtained a complex iterated integral which was later termed inconvenient for computation (37). The example treated was monomer termination. 

The kinetics of chain-reaction polymerization is illustrated in Fig. 3.28 for a free radical process. Analogous equations, except for termination, can be written for ionic polymerizations. Coordination reactions are more difficult to describe since they may involve solid surfaces, adsorption, and desorption. Even the crystallization of the macromolecule after polymerization may be able to influence the reaction kinetics. The rate expressions, as given in Appendix 7, Fig. A7.1, are easily written under the assumption that the chemical equations represent the actual reaction path. Most important is to derive an equation for the kinetic chain length, v, which is equal to the ratio of propagation to termination-reaction rates. This equation permits computation of the molar mass distribution (see also Sect. 1.3). The concentration of the active species is very small and usually not known. First one must, thus, ehminate [M ] from the rate expression, as shown in the figure. The boxed equation is the important equation for v. 

In this chapter two novel methods are presented which enable the direct and model independent determination of chain-length dependent termination rate coefficients. Both methods are based on single-pulse pulsed-laser polymerization. After a theoretical derivation, both kinetic approaches are validated by means of computer simulations. As will be demonstrated, these simulations prove that the essential assumptions needed to gain access to the chain-length dependent coefficients are valid and do not significantly undermine the accurate and reliable determination of the termination rate coefficients. 

PLP-SEC and (iii) single-pulse pulsed-laser polymerization coupled with online time-resolved electron-spin resonance spectroscopy (SP-PLP-EPR). The propagation rate coefficient for MCRs may be obtained via ft-PLP-SEC and SP-PLP-EPR. Termination rate coefficients kt , and kt are only accessible from SP-PLP-EPR," in which different types of radicals can simultaneously be traced as a function of time. Remaining kinetic coefficients can then be obtained via computer modeling. Table 1.5 collates kinetic coefficients for butyl acrylate polymerization as an example. 

It is thus seen that at 60°C, the equilibrium conversion of styrene is close to 100%. In the practical range (25-100°C) of temperatures used, similar computations show that [M]g is close to 0% for most other systems. However, experimental data of Figures 5.7 and 5.9 show that the terminal monomer conversion is close to 90%, which is far less than values predicted by Eq. (5.6.8). Thus, it is usually not necessary to incorporate reverse reactions in the kinetic mechanism for chain-reaction polymerization. 

---