{"term":{"id":"12201","title":"mean-square end-to-end distance of a freely rotating chain","longtitle":"IUPAC Gold Book - mean-square end-to-end distance of a freely rotating chain","doi":"10.1351\/goldbook.12201","code":"12201","status":"current","definitions":[{"id":1,"text":"Mean-square end-to-end distance of a linear freely rotating chain.","notes":{"1":"\\(\\lt\\!r_{\\rm{o,f}}^2\\!\\gt\\) of a hypothetical, sufficiently long, linear freely rotating chain of identical single skeletal bonds is given by the equation \\[\\lt\\!r_{\\rm{o,f}}^{2}\\!\\gt = nl^{2}\\frac{(1 + \\cos \\theta)}{(1 - \\cos \\theta)}\\] where \\(n\\) is the number of skeletal bonds of length \\(l\\) and valence-angle supplement \\(\\theta\\)."},"sources":["PAC, 2015, 87, 71. 'Definitions of terms relating to individual macromolecules, macromolecular assemblies, polymer solutions, and amorphous bulk polymers (IUPAC Recommendations 2014)' on page 77 (https:\/\/doi.org\/10.1515\/pac-2013-0201)"]}],"altoutputs":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/12201\/html","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/12201\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/12201\/plain"},"citation":"Citation: 'mean-square end-to-end distance of a freely rotating 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.12201","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":"2026-06-07T03:49:57+00:00"}}