Polymerizations without Termination

5-3b-2 Termination by impurities and Deiiberateiy Added Transfer Agents 

Most anionic (as well as cationic) pol3mierizations are carried out in an inert atmosphere with rigorously cleaned reagents and glassware since trace impurities lead to termination [Hadji-christidis et al., 2000]. Moisture absorbed on the surface of glassware is usually removed by 

The hydroxide ion is usually not sufficiently nucleophilic to reinitiate polymerization and the kinetic chain is broken. Water has an especially negative effect on polymerization, since it is an active chain-transfer agent. For example, C,r,s is approximately 10 in the polymerization of styrene at 25° C with sodium naphthalene [Szwarc, 1960], and the presence of even smaU concentrations of water can greatly limit the polymer molecular weight and polymerization rate. The adventitious presence of other proton donors may not be as much of a problem. Ethanol has a transfer constant of about 10 . Its presence in smah amounts would not prevent the formation of high polymer because transfer would be slow, although the polymer would not be living. 

Living polymers are terminated by the deliberate addition of chain-transfer agent such as 

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Eigenzeit Transformation. This simple change of variable first proposed by Dostal and Mark (16) linearizes equations when a monomer appears in every term. The quantity Mdt is defined as a new variable dZ. It is widely used for stepwise polymerization without termination. It is mentioned to avoid confusion with the Z-transform. In one paper, both transformations were used in the same equation, and both were referred to in connection with the letter Z. 

Batch Polymerization. The case of stepwise polymerization without termination was originally treated by Dostal and Mark (16) by using the Eigenzeit transformation to linearize the equations, as discussed earlier. Gee and Melville (21) extended this by the same technique to a case where the propagation rate constant varied with molecular size, contrary to the usual assumption. In the case of stepwise polymerization without termination, batch reactions can give a very narrow (Poisson) distribution. Abraham (2) and Kilkson (35) both showed that the use of the Z-transform simplified the handling of this type of mechanism. 

The rate of polymerization follows the standard equation obtained for an equilibrium polymerization without termination and with rapid initiation (20) ... 

Polymerization without termination living polymers. If care is taken, all termination reactions can be avoided. Polymerization then proceeds until all monomer is used up or the reaction is quenched by addition of a deactivating agent. Under such conditions, the rate of monomer consumption is the sum of the rates of initiation and propagation ... 

The kinetics of THF polymerization are expressed in terms of the rate of reaction for an equilibrium polymerization without termination viz. 

The mechanism of initiation is based on an examination of reaction products in an early stage of the polymerization. After short-stopping the polymerization by addition of sodium methoxide/methanol solution, the main product subsequently identified by gas chromatography was C2H5OCH2CH2OCH2OCH3. The rate of polymerization is presumed to follow the standard eqn. (6) for an equilibrium polymerization without termination and with rapid initiation. It is acknowledged that there is an induction period (presumably due to reaction of catalyst with adventitious water, since rigorous drying reduced the induction time to only... 

In the case of addition polymerization without termination, the number fraction distribution function (the probability that a given chain has degree of polymerization N) is given by the Poisson distribution function ... 

Kinetics The rate of the cationic ring-opening polymerization of cyclic ethers may be expressed in different ways depending on the monomer and the reaction conditions. Polymerizations without termination can be described (Odian, 1991) by kinetic expressions similar to those used in living polymerizations of alkenes (see Chapter 8), e.g.. 

The Poisson distribution written in the bottom boxed equation of Fig. 3.31 approaches the binomial molar mass distribution for the case that p is small and the average kinetic chain length v = No/N is large, a condition approached for most hving polymers. It is an equation that can be calculated much more easily than the binomial distribution. Analyzing the Poisson distribution, one finds that polymerizations without termination lead to rather narrow molar mass distributions as discussed in Sect. 3.3 with Figs. 3.39 1. 

There are several forms of the rate law that describe the cationic ring-opening polymerization. For living or polymerizations without termination, (me can write... 

If new monomer is added to such a polymerization without termination and transfer reactions after achievement of equilibrium, both the yield and the molecular weight increase further. If, however, transfer reactions occur, the yield increases but the molecular weight does not necessarily increase. 

According to the mechanism, several kinetic schemes are possible for polymerizations without termination reactions. Whether the polymerizations are anionic or cationic is only incidental to the kinetic formalism. 

One of the limitations of anionic polymerization is the types of monomers which can be polymerized without termination and chain transfer. The most well-behaved systems are the vinyl monomers based on styrene and butadiene which are available primarily from petroleum feedstocks. Several years ago we began a search for anionically polymerizable monomers which would be available from renewable natural resources. One of the monomers uncovered (rediscovered) in this search was myrcene (4) 7-methyl-3-methylene-1,6-octadiene,... 

As with any living system, an irutiator is needed which will polymerize without termination or chain transfer. In addition, to obtain well-controlled polymer molecular weight and polydis-peisity, the initiation and quenching of the growing polymer must be controlled. The mechanism of olefin metathesis provides this potential and with an understanding of the mechanistic steps, each of the three requirements can be regulated... 

Polymerization without termination electron transfer initiation... 

Polymerization without termination molar mass distribution... 

Fig. 2.8 Weight-fraction Poisson distribution of chain lengths for various values of x in a polymerization without termination. For comparison, the broken line represents the most probable distribution of molar mass when x = 11 (after Flory).

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