Flory–Schulz distribution

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Flory–Schulz distribution

The Flory–Schulz distribution is a discrete probability distribution named after Paul Flory and Günter Victor Schulz that describes the relative ratios of polymers of different length that occur in an ideal step-growth polymerization process. The probability mass function (pmf) for the mass fraction of chains of length is:

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Flory–Schulz distribution
Probability mass function
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Parameters 0 < a < 1 (real)
Support k ∈ { 1, 2, 3, ... }
PMF
CDF
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Skewness
Excess kurtosis
MGF
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In this equation, k is the number of monomers in the chain,[1] and 0<a<1 is an empirically determined constant related to the fraction of unreacted monomer remaining.[2]

The form of this distribution implies is that shorter polymers are favored over longer ones — the chain length is geometrically distributed. Apart from polymerization processes, this distribution is also relevant to the Fischer–Tropsch process that is conceptually related, where it is known as Anderson-Schulz-Flory (ASF) distribution, in that lighter hydrocarbons are converted to heavier hydrocarbons that are desirable as a liquid fuel.

The pmf of this distribution is a solution of the following equation:

References

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