Step polymerization molecular weight distribution

The preceding discussions of the kinetics and molecular weight distributions in the step-growth polymerization of AB monomers are clearly exemplified by the esterification reactions of such monomers as glycolic acid or co-hydroxydecanoic acid. Therefore one method for polyester synthesis is the following ... 

The molecular weight distribution for a polymer like that described above is remarkably narrow compared to free-radical polymerization or even to ionic polymerization in which transfer or termination occurs. The sharpness arises from the nearly simultaneous initiation of all chains and the fact that all active centers grow as long as monomer is present. The following steps outline a quantitative treatment of this effect ... 

The primary polymerization product ia these processes has a relatively wide molecular weight distribution, and a separate step is often used to narrow the polydispersity. Such a narrowkig step may consist of high vacuum stripping to remove volatile polymer chains, often followed by a solvent fractionation step (35,36), sometimes a solvent fractionation step alone (37,38), or a fractional precipitation from organic solvent (32). The molecular weight distribution can also be narrowed by depolymerization at elevated temperatures ia the presence of a depolymerization catalyst (217—220). 

A factor in addition to the RTD and temperature distribution that affects the molecular weight distribution (MWD) is the nature of the chemical reaciion. If the period during which the molecule is growing is short compared with the residence time in the reactor, the MWD in a batch reactor is broader than in a CSTR. This situation holds for many free radical and ionic polymerization processes where the reaction intermediates are very short hved. In cases where the growth period is the same as the residence time in the reactor, the MWD is narrower in batch than in CSTR. Polymerizations that have no termination step—for instance, polycondensations—are of this type. This topic is treated by Denbigh (J. Applied Chem., 1, 227 [1951]). 

The present section analyzes the above concepts in detail. There are many different mathematical methods for analyzing molecular weight distributions. The method of moments is particularly easy when applied to a living pol5mer polymerization. Equation (13.30) shows the propagation reaction, each step of which consumes one monomer molecule. Assume equal reactivity. Then for a batch polymerization. 

Failure to remove the alcohols generated in either of the equilibrium condensation steps will reduce the efficiency of the polymerization process. This effect can be explained by Le Chatelier s principle, which was discussed in Chapter 3. The volatile alcohols produced during polymerization act as a chemical stress on the product side of the reaction, which inhibits polymerization. Another implication of the equilibrium nature of this polymerization process is seen in the molecular weight distribution of the final polymer. All polyesters contain a few percent of low molecular weight oligomers, regardless of the polymerization process. 

It should be noted that the product of a step polymerization is a mixture of polymer molecules of different molecular weights. The molecular weight distribution is characterized by the number-average and weight-average degrees of polymerization, X and Xw> respectively, defined by... 

The molecular weight distributions in chain polymerizations are broader than in step polymerization. The ratio Xw/Xn can reach as high as 5-10 due to the autoaccelerative effect and as high as 20-50 due to chain transfer to polymer. 

Macromolecular engineering is the ultimate goal of the polymer chemist when he has a monomer or a family of monomers at his disposal. Once each step of the polymerization process is carefully controlled, every molecular parameter of the polymer is predictable molecular weight, tacticity, molecular weight distribution, nature of the end groups, microstructure, and composition, and block... 

Another very important visible light-initiated reaction of alkyl aluminum porphyrins is their 1,4-addition to alkyl methacrylates to produce ester enolate species [Eq. (4)]. This enolate then acts as the active species in the subsequent polymerization of the acrylate monomer. For example, Al(TPP)Me acts as a photocatalyst to produce polymethylmethacrylate with a narrow molecular weight distribution in a living polymerization process [Eq. (4)]. Visible light is essential for both the initiation step (addition of methylmethacrylate to Al(TPP)Me) and the propagation... 

The product of a polymerization is a mixture of polymer molecules of different molecular weights. For theoretical and practical reasons it is of interest to discuss the distribution of molecular weights in a polymerization. The molecular weight distribution (MWD) has been derived by Flory by a statistical approach based on the concept of equal reactivity of functional groups [Flory, 1953 Howard, 1961 Peebles, 1971]. The derivation that follows is essentially that of Flory and applies equally to A—B and stoichiometric A—A plus B—B types of step polymerizations. 

The molecular weight distribution in radical chain polymerizations is more complex than those in step polymerization. Radical chain polymerization involves several possible modes... 

Consider the situation where one polymer molecule is produced from each kinetic chain. This is the case for termination by disproportionation or chain transfer or a combination of the two, but without combination. The molecular weight distributions are derived in this case in exactly the same manner as for linear step polymerization (Sec. 2-7). Equations 2-86, 2-88, 2-89, 2-27, 2-96, and 2-97 describe the number-fraction, number, and weight-fraction... 

In polyolefins, the chain is propagated by an intermediate free-radical species or by an alkyl species adsorbed onto a solid. Both the free radical and the alkyl have the possibility of termination, and this creates the possibility of growth mistakes by chain transfer and chain-termination steps that create dead polymer before all reactants are consumed. The presence of termination steps produces a broader molecular-weight distribution than does ideal addition polymerization. 

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