Living polymerization Poisson chain-length

In order to rationalize the disagreement between the model of Scheme 7.6 and observation, Polyakov developed a more computable chain/block length distribution model to treat the continuum from a living polymerization (Poisson distribution) to a terminating polymerization (Shulz-Flory distribution... 

The MWD of polymers prepared by living anionic polymerization is a good example [65]. According to the early theoretical work of Flory, an ideal living anionic polymerization is expected to yield a polymer with Poisson distribution of chain lengths [66] ... 

So far, the only living processes industrially available are anionic and cationic polymerization [50, 51], which generally suffer little or no termination. In these processes, the initiation step is very fast compared to the process time and, hence, all the chains start growing almost simultaneously. The degree of polymerization, DP, increases linearly with monomer conversion and is inversely proportional to the initiator concentration. At the same time, Poisson-like distributions of the polymer chain length are obtained with final polydispersity values dose to the ideal value of (1 -I- 1/DP). Finally, the polymer retains the ionic end groups till the end of the polymerization and the reaction is simply restarted by further addition of monomer. However, this kind of polymerization is often impractical from the industrial viewpoint, since the main requirements are high purity of all the reactants, very low temperatures, and the use of solvents. Moreover, it does not work with several widely used monomers, such as styrene. 

This is a Hory distribution or most probable distribution and much broader (D>1) than the Poisson distribution (D=l) resulting from batch polymerization. The increase in molecular weight polydispersity is due to the fact that the chains are living, and so are directly impacted by the RTD. Recall that the polydispersity of the RTD for a CSTR is 2. For long residence time, approaches 1 and D becomes 2. Thus, the number chain length distribution (NCLD) takes on the breadth characteristics of the RTD, due to the living nature of the polymer chains. For comparison, one should recall that the lifetime of a free radical is 1-10 s. This is insignificant in comparison with the RTD and so that RTD has little to no effect on D in free radical polymerization. 

The living polymerization of strained three- and four-membered monomers typically provides polymers with a narrow molar mass distribution, best described by the Poisson function [91], for which the dispersity indexes (D = DP jDP = M /M ) assume values in the range -1.25 > D > 1, depending on the polymer chain length (Equahon 1.24). As discussed earlier, the polymerization of these monomers is essentially irreversible. 

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