Polymers Formed by Monomer Addition without Termination

Polymers Formed by Monomer Addition without Termination.— Polymerization of cyclic monomers such as ethylene oxide, as was pointed out in Chapter II, may be induced by small amounts of substances capable of cleaving the ring with generation of a hydroxyl group, which may add another monomer, and so forth as indicated by the following scheme  

Other cyclic compounds such as the N-carboxyanhydrides of a-amino acids,and lactams may be polymerized similarly with regeneration of an amino group at each step. According to the mechanism postulated, the number of polymer molecules formed should equal the number of initiator molecules (e.g., ROH) introduced, and the average number of monomers per polymer molecule should equal the ratio of monomer consumed to initiator. 

The distinguishing feature of such a mechanism occurs in the fact that the growth of all polymer molecules proceeds simultaneously under conditions affording equal opportunities for all. (This will hold provided the addition of monomer to the initiator is not much slower than succeeding additions.) These circumstances are unique in providing conditions necessary for the formation of a remarkably narrow molecular weight distribution—much narrower than may be obtained by polymer fractionation, for example. Specifically, they are the conditions which lead to a Poisson distribution of the number and mole fraction, i.e.  

Weight fraction distributions according to Eq. (33) for three values 

The conditions essential for the formation of this exceptionally sharp distribution are the following (1) growth of each polymer molecule must proceed exclusively by consecutive addition of monomers to an active terminal group, (2) all of these active termini, one for each molecule, must be equally susceptible to reaction with monomer, and this condition must prevail throughout the polymerization, and (3) all active centers must be introduced at the outset of the polymerization and there must be no chain transfer or termination (or interchange). If new active centers are introduced over the course of the polymerization, a much broader distribution will be produced for the obvious reason that those introduced late in the process will enjoy a shorter period in which to grow. If the chains suffer transfer, or if termination occurs with constant replenishment of the active centers by one 

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