Term: root-mean-square end-to-end distance, \(\text{}^{1/2}\)
https://doi.org/10.1351/goldbook.R05405

Definition:
The square root of the mean-square end-to-end distance of a linear polymer chain averaged over all conformations of the chain. For a freely jointed chain consisting of N segments each of length L, it is given by: \[\text{}^{1/2} = \sqrt{N}\ L\] The subscript zero is used to indicate unperturbed dimensions, as in < r2 >0(1/2). If this term is used repeatedly, and if it is not confusing, the abbreviated name 'end-to-end distance' may be used.

Related Terms:
1) linear polymer (http://doi.org/10.1351/goldbook.L03556).

Source: Purple Book, 1st ed., p. 49 (http://old.iupac.org/publications/books/author/metanomski.html)

Citation: 'root-mean-square end-to-end distance, \(\text{<}r^{2}\text{>}^{1/2}\)' 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.R05405

License: 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.

Disclaimer: 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.