04035 IUPAC Gold Book - most probable distribution 10.1351/goldbook.M04035 M04035 current 1 A discrete distribution with the differential mass-distribution function of the form: \[f_{\rm{w}}(x) = a^{2}\ x\ (1- a)^{x- 1}\] where \(x\) is a parameter characterizing the chain length, such as relative molecular mass or degree of polymerization and \(a\) is a positive adjustable parameter. For large values of \(x\), the most probable distribution converges to the particular case of the Schulz–Zimm distribution with \(b=1\). In the literature, this distribution is sometimes referred to as the Flory distribution or the Schulz–Flory distribution. Schulz–Zimm distribution https://goldbook.iupac.org//terms/view/S05502 chain length https://goldbook.iupac.org//terms/view/C00956 degree of polymerization https://goldbook.iupac.org//terms/view/D01569 mass-distribution function https://goldbook.iupac.org//terms/view/M03716 relative molecular mass https://goldbook.iupac.org//terms/view/R05271 Purple Book, 1st ed., p. 56 (http://old.iupac.org/publications/books/author/metanomski.html) https://goldbook.iupac.org/terms/view/M04035/html https://goldbook.iupac.org/terms/view/M04035/json https://goldbook.iupac.org/terms/view/M04035/plain Citation: 'most probable distribution' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.M04035 The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) for individual terms. If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org . The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using. 2026-05-18T01:49:26+00:00