Living polymerization number-average degree

The number-average degree of polymerization for a living cationic polymerization is defined as the concentration of monomer consumed divided by the total concentration of all propagating chains (dormant and active)... 

The number-average degree of polymerization for a living anionic polymerization is the ratio of the concentration of reacted monomer to the concentration of living ends (Eq. 5-58). For the usual situation where all the initiator I is converted into propagating chain ends, Eq. 5-58 becomes... 

Although an appreciable amount of termination is found at elevated temperatures, rate constants can be calculated from the initial slope of the first-order time-conversion curve. The concentration of living ends is calculated from the linear plot of the number-average degree of polymerization vs. conversion.which still remains linear when termination occurs, since the total number of chains remains unaltered., provided nor intermolecular termination (grafting) nor transfer occurs. 

The lack of termination has many important consequences. First of all, one has to realize that living" polymers are not infinitely long. In any polymerization system the amount of the available monomer is finite, hence if n growing centers are formed in the initiation process — the number average degree of polymerization of the living" polymer is... 

Anionic polymerizations, when carried out in aprotic solvents, are characterized by the long lifetime of the carbanionic (or oxanionic) sites l2). When neither spontaneous transfer nor termination reactions are involved, the polymers obtained exhibit sharp molecular weight distributions, and their number average degree of polymerization is determined by the [Monomer]/[Initiator] molar ratio, provided initiation is fast as compared to propagation. However, the major advantage of these methods, as far as synthesis is concerned, is the socalled living character of the polymers 12) After completion of the polymerization the active sites retain their reactivity and can be used for functionalizations at the chain end. 

The inverse problem is even more important. With living polymerizations, the number of generated macromolecules is given by the number of growth centres, i. e. by the amount of initiator molecules. The value of [N] can also be measured by a suitable physical method (see Chap. 8 Sect. 2.1). Therefore the number average degree of polymerization can be easily calculated ... 

Fig. 9. Plot of the number average degree of polymerization, j, of a living oligomer or polymer vs. temperature at constant total amount of supplied monomer, Mo, and a constant I...

The number average degree of polymerization of a living polymer is shown as follows ... 

Figure 15-1. Change in the number average degree of polymerization Xn with extent of reaction (conversion) p for living polymerizations (LP), polymerizations with monofunctional termination (PM), and polycondensations (PC). The positions of the straight lines for LP and PM are dependent on the monomer/initiator ratio.

Under these assumptions, the expressions for rate of polymerization (J p), kinetic chain length (A, the average number of monomer units on a living chain) and instantaneous number average degree of polymerization (DP)," , the average number of monomer units on a dead polymer chain formed at an instant in time) are written as... 

Calculate the ultimate number average degree of polymerization for the anionic polymerization of styrene in benzene at 25°C initiated by butyl lithium. The initial concentration of styrene was 10 mol m" and that of butyl lithium was 0.5 mol m . Account for the observation that even though this is a living polymer system a poly disperse sample is produced. 

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