Title: equivalent freely jointed chain
Long Title: IUPAC Gold Book - equivalent freely jointed chain
DOI: 10.1351/goldbook.12203
Status: current

Definition
Hypothetical freely jointed chain with the same mean-square end-to-end distance and contour length as an actual linear chain having unperturbed dimensions.

Note
The number of links, \(m\), and their length, \(l^{\prime}\), are evaluated from the mean-square end-to-end distance, \(\lt\!r_{\rm{o}}^{2}\!\gt\), and contour length, \(r_{\rm{max}}\), of the actual chain using the equations in freely jointed chain and contour length, with \[m = \frac{r_{\max}^{2}}{\lt\!r_{\rm{o}}^{2}\!\gt} \quad {\rm{and}} \quad l^{\prime} = \frac{\lt\!r_{\rm{o}}^{2}\!\gt}{r_{\max}}\] For example, for polymethylene at room temperature, one freely jointed link is equivalent to about 10 actual \(\ce{C-C}\) skeletal bonds.

Related Term
- mean-square end-to-end distance: https://goldbook.iupac.org//terms/view/12197

Source
- PAC, 2015, 87, 71. 'Definitions of terms relating to individual macromolecules, macromolecular assemblies, polymer solutions, and amorphous bulk polymers (IUPAC Recommendations 2014)' on page 79 (https://doi.org/10.1515/pac-2013-0201)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/12203/html
- json: https://goldbook.iupac.org/terms/view/12203/json
- xml: https://goldbook.iupac.org/terms/view/12203/xml

Citation: Citation: 'equivalent freely jointed chain' 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.12203
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.
Collection: If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org .
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.
Accessed: 2026-04-20T08:31:19+00:00