Flory-Schulz Distribution
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Flory%E2%80%93Schulz Distribution
Flory-Schulz distribution
Parameters 0 < a < 1 (real)
Support k ? { 1, 2, 3, ... }
PMF
CDF
Mean
Median
Mode
Variance
Skewness
Ex. kurtosis
MGF
CF
PGF

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 (chemistry) of chains of length is:

.


In this equation, k is the numer 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, 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:

Mass fraction according to Flory-Schulz distribution

References

  1. ^ Paul J. Flory, "Molecular Size Distribution in Linear Condensation Polymers1", Journal of the American Chemical Society (in German), 58 (10), pp. 1877-1885, doi:10.1021/ja01301a016, ISSN 0002-7863
  2. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "most probable distribution". doi:10.1351/goldbook.M04035

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Flory%E2%80%93Schulz_distribution
 



 



 
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