#jsDisabledContent { display:none; } My Account | Register | Help

# Flory–Schulz distribution

Article Id: WHEBN0037194611
Reproduction Date:

 Title: Flory–Schulz distribution Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Flory–Schulz distribution

 Parameters 0 < a < 1 (real) k ∈ { 1, 2, 3, ... } a^2 k (1-a)^{k-1} \, 1-(1-a)^k (1+ a k) \frac{2}{a}-1 \frac{W\left(\frac{(1-a)^{\frac{1}{a}} \log (1-a)}{2 a}\right)}{\log (1-a)}-\frac{1}{a} -\frac{1}{\log (1-a)} \frac{2-2 a}{a^2} \frac{2-a}{\sqrt{2-2 a}} \frac{(a-6) a+6}{2-2 a} \frac{a^2 e^t}{\left((a-1) e^t+1\right)^2} \frac{a^2 e^{i t}}{\left(1+(a-1) e^{i t}\right)^2} \frac{a^2 z}{((a-1) z+1)^2}

The Flory–Schulz distribution is a mathematical function named after Paul Flory and G. V. Schulz that describes the relative ratios of polymers of different length after a polymerization process, based on their relative probabilities of occurrence. The distribution can take the form of:

f_a(k) = a^2 k (1-a)^{k-1} \,

In this equation, k is a variable characterizing the chain length (e.g. number average molecular weight, degree of polymerization), and a is an empirically-determined constant.[1]

The form of this distribution implies is that shorter polymers are favored over longer ones. 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.

\left\{(a-1) (k+1) f(k)+k f(k+1)=0,f(0)=0,f(1)=a^2\right\}

## References

1. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "most probable distribution".
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.

Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.