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 for the mass [fraction (chemistry)|mass fraction] of chains of length is:
In this equation, k is the number of monomers in the chain, and 0
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 '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: As a probability distribution, one can note that if X and Y are two independent and geometrically distributed random variables with parameter taking values in, thenThis in turn means that the Flory-Schulz distribution is a shifted version of the negative binomial distribution, with parameters and.