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The Flory–Schulz distribution is a discrete
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, 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:
:
probability distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon i ...
named after Paul Flory
Paul John Flory (June 19, 1910 – September 9, 1985) was an American chemist and Nobel laureate who was known for his work in the field of polymers, or macromolecules. He was a leading pioneer in understanding the behavior of polymers in solu ...
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
In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete density function. The probability mass ...
(pmf) for the mass fraction of chains of length is:
:.
In this equation, ''k'' is the number of monomers in the chain, and ''0
References