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, 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:
Referencesedit
^Flory, Paul J. (October 1936). "Molecular Size Distribution in Linear Condensation Polymers". Journal of the American Chemical Society. 58 (10): 1877–1885. doi:10.1021/ja01301a016. ISSN 0002-7863.
flory, schulz, distribution, discrete, probability, distribution, named, after, paul, flory, günter, victor, schulz, that, describes, relative, ratios, polymers, different, length, that, occur, ideal, step, growth, polymerization, process, probability, mass, f. The Flory Schulz distribution is a discrete probability distribution named after Paul Flory and Gunter 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 k displaystyle k is Flory Schulz distributionProbability mass functionParameters0 lt a lt 1 real Supportk 1 2 3 PMFa 2 k 1 a k 1 displaystyle a 2 k 1 a k 1 CDF1 1 a k 1 a k displaystyle 1 1 a k 1 ak Mean2 a 1 displaystyle frac 2 a 1 MedianW 1 a 1 a log 1 a 2 a log 1 a 1 a displaystyle frac W left frac 1 a frac 1 a log 1 a 2a right log 1 a frac 1 a Mode 1 log 1 a displaystyle frac 1 log 1 a Variance2 2 a a 2 displaystyle frac 2 2a a 2 Skewness2 a 2 2 a displaystyle frac 2 a sqrt 2 2a Excess kurtosis a 6 a 6 2 2 a displaystyle frac a 6 a 6 2 2a MGFa 2 e t a 1 e t 1 2 displaystyle frac a 2 e t left a 1 e t 1 right 2 CFa 2 e i t 1 a 1 e i t 2 displaystyle frac a 2 e it left 1 a 1 e it right 2 PGFa 2 z a 1 z 1 2 displaystyle frac a 2 z a 1 z 1 2 w a k a 2 k 1 a k 1 displaystyle w a k a 2 k 1 a k 1 text In this equation k is the number of monomers in the chain 1 and 0 lt a lt 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 a 1 k 1 w a k k w a k 1 0 w a 0 0 w a 1 a 2 displaystyle left begin array l a 1 k 1 w a k kw a k 1 0 text 10pt w a 0 0 text w a 1 a 2 text end array right References edit Flory Paul J October 1936 Molecular Size Distribution in Linear Condensation Polymers Journal of the American Chemical Society 58 10 1877 1885 doi 10 1021 ja01301a016 ISSN 0002 7863 IUPAC Compendium of Chemical Terminology 2nd ed the Gold Book 1997 Online corrected version 2006 most probable distribution doi 10 1351 goldbook M04035 Retrieved from https en wikipedia org w index php title Flory Schulz distribution amp oldid 1189592546, wikipedia, wiki, book, books, library,