Lifetimes of growing chains

The growth times for individual polymer molecules in coordination polymerization are generally much longer than in free-radical initiated 

To calculate the average lifetime (f) in systems where the catalyst species are unstable it is necessary to know at any specific time the polymerization rate, the active site concentration and the number average degree of polymerization of the polymer being formed, since 

When the catalyst centres are stable and the monomer concentration is kept constant during the polymerization, lifetimes can be calculated from the steady molecular weight and the slope of 1/P versus 1/t 

Values in the literature relate to olefin polymerization with heterogeneous titanium based catalysts where the necessary information has been acquired, and the data are given in Table 9. It would not appear to 

The precise experimental conditions for the measurements of chain lifetimes of polyethylene with the TiCl4/Al(i-Bu2 )H catalyst are not explicitly stated, but there is clear evidence for a steady increase in lifetime with polymerization time. For an average lifetime of 4 min after 40 min polymerization time, the instantaneous values were 4 min after 18 min polymerization and 10 min after 40 min polymerization. As the concentration of active centres remains almost steady after a sharp initial fall, the increase cannot be accounted for wholly by changes in the monomer/active sites ratio. The explanation may lie in a reduced rate of chain transfer with increase in conversion, as has been found for propene with a-TiClj/AlEt2 Cl [121]. In accord with this view average chain lifetimes of polypropene have been calculated to increase with conversion [123]. 

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Schildknecht classified the type of chain polymerization suitable for the various monomers shown in Table 3.7 [13]. In the various ionic methods of polymerization, the monomer must fit between the growing chain end and an ion complex [13]. Cationic polymerizations proceed very rapidly, with the lifetimes of growing chains less than 1 s in the case of isobutylene. Stereoregularity is obtained as monomers are fit between chain and counter ions when polymerized. 

Thus, in order to reproduce the effect of an experimentally existing activation barrier for the scission/recombination process, one may introduce into the MC simulation the notion of frequency , lo, with which, every so many MC steps, an attempt for scission and/or recombination is undertaken. Clearly, as uj is reduced to zero, the average lifetime of the chains, which is proportional by detailed balance to Tbreak) will grow to infinity until the limit of conventional dead polymers is reached. In a computer experiment Lo can be easily controlled and various transport properties such as mean-square displacements (MSQ) and diffusion constants, which essentially depend on Tbreak) can be studied. 

Fig. 36. Approximate values of the mean lifetime of the chains of polypropylene growing on the active centers of a catalytic system a-TiCla-AUCjHsls-n-heptane at 70° and 950 mm. Hg pcm,. (The calculations were performed assuming the number of conventional active centers C = 1 mol. per 100 mol. of ground a-TiCU sample A and x = 95hJ .)...

The mean lifetime of polypropylene chains growing on each active center can reach several minutes. 

In the absence of hydrogen and under normal polymerization conditions and at normal ethylene concentrations, it was found that with Mg/Ti catalysts the chain transfer to monomer predominates 128). This has recently been confirmed by Kashiwa 38) in the case of propylene polymerization with the TiCl4/EB/MgCl2 -AlEt3/EB catalytic system. As a consequence of the increased chain transfer rate, mean lifetimes of growing polymer chains produced with Mg/Ti are considerably shorter than those observed with unsupported catalysts. Kashiwa, for example, quoted a value of 2-3 sec for the lifetime of polypropylene growing chains obtained at 50 °C with the above mentioned catalysts, as compared with 4-10 min for those obtained at 60-70 °C with conventional catalysts. 

Therefore, one is dealing with a heterophasic reaction which could be controlled by typical kinetic factors such as a) formation and decay of active centers with time, b) presence of a multiplicity of active centers energetically, structurally and chemically different form one another and therefore having different kinetic constants. Moreover a role could also be played by true physical phenomena such as a) variety of growing chain lifetime depending on the different degree of active centers encapsulation in the polymeric matrix, and b) limitations to heat transfer and, above all, to mass transfer from the gas phase to the liquid phase, from liquid to polymer surface and from the polymer to the surface or to the interior of the catalyst. 

In recent reports (2-7), it has been shown that it is important to consider the effect of such laser operating parameters as pulse repetition rate on the polymerization kinetics. It was clearly demonstrated that pulsing the laser at narrow time intervals on the order of the lifetime of growing polymer radical chains resulted in a premature chain termination due to injection of small molecule "terminator" radicals into the system. In this paper we focus on the effect of pulse repetition rate on the polymerization of multifunctional acrylates, in particular 1,6-hexanediol diacrylate (HDODA) and trimethylolpropane triacrylate (TMPTA). 

One of the fascinating features of the ESR technique is that it allows direct observation of growing chain radicals in radical polymerization. But, it is usually difficult to do this under usual polymerization conditions, because the growing radicals have a very short lifetime and their concentrations are very low. Therefore, the use of ESR for the study of radical polymerization has had to be limited to solid-state polymerization. 

The mean lifetime x of radical R in conventional RP is the time from its initiation to its termination, typically 1 s. In CRDRP, x is the time of activity of growing chains between two dormant states. For NMP, x is given by eqn... 

Where the mean lifetimes of the growing chains are short, narrower MWD s are produced than in a batch or plug flow reactor but the minimum Dp is 1.5 or 2.0 according to the mechanism of termination. Dp independent of Up and... 

Radical polymerizations have three important reaction steps in common chain initiation, chain propagation, and chain termination. For the termination of chain radicals several mechanisms are possible. Since the lifetime of a radical is usually less than 1 s, radicals are continuously generated and terminated. Each propagating radical can add a finite number of monomers between its initiation and termination. If a divinyl monomer is in the monomer mixture, the reaction kinetics changes drastically. In this case, a dead polymer chain may grow again as a macroradical, when its pendant vinyl groups react with radicals, and the size of the macromolecule increases until it extends over the whole available volume. 

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