Term: Schulz–Zimm distribution
https://doi.org/10.1351/goldbook.S05502

Definition:
In an assembly of macromolecules, a continuous distribution with the differential mass-distribution function of the form: \[f_{\text{w}}(x)\ \text{d}x = \frac{a^{b\,+\,1}}{\varGamma\left(b\,+\,1\right)}\ x^{b}\ \text{e}^{-a\ x}\ \text{d}x\] where x is a parameter characterizing the chain length, such as relative molecular mass or degree of polymerization, a and b are positive adjustable parameters, and (Γ b + 1) is the gamma function of (b + 1).

Related Terms:
1) mass-distribution function (http://doi.org/10.1351/goldbook.M03716).
2) chain length (http://doi.org/10.1351/goldbook.C00956).
3) relative molecular mass (http://doi.org/10.1351/goldbook.R05271).
4) degree of polymerization (http://doi.org/10.1351/goldbook.D01569).

Source: Purple Book, 1st ed., p. 56 (http://old.iupac.org/publications/books/author/metanomski.html)

Citation: 'Schulz–Zimm distribution' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. https://doi.org/10.1351/goldbook.S05502

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