Molecular Weight Distribution in Linear Polymerization

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. 

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The molecular weight distribution in this type of nonlinear polymerization will be much narrower than for a linear polymerization. Molecules of sizes very much different from the average are less likely than in linear polymerization, since this would require having the statistically determined / branches making up a molecule all very long or all very short. The distribution functions for this polymerization have been derived statistically [Peebles, 1971 Schaefgen and Flory, 1948], and the results are given as... 

The Flory distribution is a random distribution useful in several modes of polymerization. This distribution results from addition polymerization reactions when the only significant processes that interrupt macromolecular growth are either or both of chain transfer (to any species but the polymer) or termination by disproportionation. Likewise, this molecular weight distribution describes linear condensation polymerization when equal reactivity is assumed for all ends only when the reaction involves an equilibrium between polymerization and depolymerization. The model describes the distribution with one parameter which is the number average molecular weight. The distribution equation is ... 

Molecular weight distribution in the above type of multichain step polymerization would be expected to be much narrower than for a linear polymerization. Consider, for example, polymerization of bifunctional monomer A—B with a small proportion of an /-functional substance Ay leading to... 

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