Narrow Radical Chain-Length Distributions

The attractiveness and major advantage of using pulsed lasers in kinetic studies is a result of the short duration of the laser pulse (typically 10 to 20 ns). Opposed to more conventional methods such as rotating sector and spatially intermittent polymerization, the initiation period can now be considered to be instantaneous on the time scale of propagation. As a consequence, all radicals formed in one laser pulse are of approximately the same chain length at any moment in time, which greatly simplifies the kinetic scheme. It is this quality of laser-induced experiments that leads to the reliability of the PLP method to determine kp values (in conjunction with an accurate MWD determination). 

In this chapter, the above way of thinking is used in two novel kinetic analyses of single-pulse initiation experiments. It is shown that the kinetic scheme of such experiments can be presented so that the termination rate coefficient can be determined as a function of chain length in a (virtually) model free fashion. In other words, no a priori choice is made for (or restriction set to) the functional dependence of kt upon chain length, but rather, this functional form can be determined. Hence, the exact dependence of L upon chain length can be determined with these methods. In this respect, the kinetic analyses presented here are distinctly different from any other kinetic study employing laser initiation reported so far in literature. 

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A very simple, but at the same time very interesting experiment that might contribute to an enhanced understanding of this unknown relation might be a time-resolved echo pulsed-laser polymerization experiment (TR-ec/io-PLP). TR-ec/ o-PLP is very similar to the TR-SP-PLP experiment, but now a second laser pulse is applied very short after the first one. In practical situations, two synchronized lasers, as previously employed in a PLP study by Lyons et al. [62], could be used for this purpose. In principle, this should result in a radical chain-length distribution that contains two very narrow peaks and, hence, only three different termination reactions have to be distinguished (i) the termination between two radicals generated in pulse one, (ii) the termination between two radicals of pulse two and (Hi) a termination reaction between a radical from the first pulse and a radical from the second pulse. For the very same reasons extensively discussed above, it seems fair to apply the... 

The approach used in this thesis to study the chain-length dependence of termination reactions can be characterized as empirical and model-independent. The basic thought behind this study is that when using single-pulse pulsed-laser initiation, the radical chain-length distribution is so narrow that a monodispersity assumption for this radical population seems to be justified. In this line of thought, two novel kinetic analyses have been presented which should enable the direct model-independent measurement of these microscopic chain-length... 

These are identical for the limiting values for the batch reactor, except that they require only the assumption of perfect mixing. Thus, while polydispersi-ties of 2.0 and 1.5 for termination by disproportionation and combination respectively represent unattainable minima for batch polymerization, these same values represent feasible operation in a well-mixed CSTR. Thus, the CSTR will give a narrower dead polymer number chain length distribution since it is possible to maintain a constant reaction environment at steady state. The effect of residence time distribution on the polydispersity is negligible since the lifetime of a single radical is far less than the average residence time. Likewise, for a copolymerization in a CSTR at steady state, the constancy of... 

In each of these mechanisms, the reverse reaction dominates the equihbriimi and keeps the overall concentration of the propagating radical (P ) low, typically [Pn ]/[Pn— X] < 10-5. If tijis reversible radical trapping process occurs frequently, it minimizes the irreversible termination reactions but also means that the polymer chains all have an equal chance to grow, resulting in polymers with a narrow molecular weight distribution. It also follows that, unlike conventional free-radical polymerizations, the polymer chain length will increase steadily with the reaction time, similar to living anionic polymerizations. 

In the synthesis of such polymers the double bond can also be activated by use of an anionic or a cationic initiator. A characteristic of some of these latter materials is that they can have a very narrow distribution of chain lengths, in contrast to radical initiated polymers. 

Reversible addition-fragmentation chain transfer polymerization is a reversible deactivation radical polymerization and it represents one of the most versatile methods for providing living characteristics to radical polymerization and polymers of predictable chain length and narrow molecular weight distribution. 

The quantity Fi, the instantaneous copolymer composition, is analogous to x , the instantaneous number-average chain length in free-radical addition polymerization. Like x , it depends on the conditions in the reactor at a particular instant. It, too, is really an average, since not all the copolymer formed at a particular instant has exactly the same composition. However, the instantaneous distribution of compositions is normally much narrower than the instantaneous distribution of chain lengths, and because the fact that it is an average is not normally of great practical importance and cannot be controlled anyhow, the overbar is left off of Fj. 

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