Molecular mass distribution in products of radical polymerizations

3 MOLECULAR MASS DISTRIBUTION IN PRODUCTS OF RADICAL POLYMERIZATIONS 

The basic kinetics of radical polymerizations were discussed in Sect. 1.2. This should now be extended to calculations of distribution. 

For radicals of a certain degree of polymerization in the stationary state, the generation rates are given as 

The calculations are simplified when the monomer and initiator concentrations are constant. To a first approximation, this condition may be regarded as fulfilled at low conversions. At any instant, macromolecules of various length are produced by termination. Let us first consider termination exclusively by disproportionation [49]. The fraction of chains with degree of polymerization P is a function of their generation rate, and this in turn is proportional to the decay rate of a radical of equal length. Thus, according to eqn. (199) the mole fraction of macromolecules, Xp, is 

The distribution (201) is called the most probable distribution. In this case, the number average degree of polymerization, P, is given by 

The ratio of radical concentrations is given by the relation [after substitution for their stationary concentration from eqn. (22)] 

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