Step-growth polymerization molar mass distribution

A step-growth polymerization (with or without elimination of low-molar-mass products) involves a series of monomer + monomer, monomer + oligomer, monomer or oligomer + macromolecule, and macromolecule + macromolecule reactions. The molar mass of the product grows gradually and the molar mass distribution becomes continuously wider. Functionalities of monomers and the molar ratio between coreactive sites are the main parameters for controlling the polymer structure. 

Synthetic polymers are produced by chain polymerization or step growth polymerization. Due to differences in the lifetime of activated species or the size and reactivity of the oligomers which are coupled in each reaction step, synthetic polymers are heterogeneous in molar mass. Copolymers are produced from more than one monomer species. In general, the different monomer species are differently incorporated in the polymer chain which causes distribution in chemical composition. Distributions in molar mass and chemical composition are also to be expected in polymers derived from homopolymers by incomplete chemical modifications, e.g. in partially hydrolyzed poly(vinyl acetate) [1]. 

These two reactions have largely different reaction paths and lead to different molar-mass distributions which are often rather broad and must be described using the techniques derived in Sect. 1.3. Step-growth polymerization is treated in the remaining part of this Sect. 3.1, chain-growth polymerization is covered in Sect. 3.2. 

Recently, typical step-reaction polymerizations, as in polyesters, polyethers, and polyamides, have been forced into chain-reaction mechanisms by designing complex chain ends that react fast with the monomer only. Under the proper conditions, the step reaction can be suppressed almost completely. Such chain-growth polycondensation may even yield living polymers with narrow molar-mass distribution. A link to the initial literature is given in the General References for this section. 

The statistical analysis of linear step polymerization (Section 2.2.5) can be extended to the prediction of molar mass distributions for polymers prepared by free-radical polymerization. However, the situation is more complex because the growth of an active centre can be terminated by Various different reactions and because the molar mass of the polymer formed decreases with time due to the different rates of decrease in [M]... 

As mentioned before, Hory laid out the basic relations for the size distribution of finite macromolecules as a function of the extent of reaction but for cases of practical importance, these distribution functions become quite complex. Macosko and Miller described a simple method for calculating average physical quantities, such as average molar masses, gel point, soluble fraction, and so on. This method is based on an elementary law of conditional probability and on the recursive nature of a step-growth polymerization. 

The molar mass values resulting from step-growth or ring-opening polymerization processes depend solely on the extent of reaction (p) and, since they follow a Flory distribution at any p, low mass oligomers should be absent for values of p close to unity. 

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