{"term":{"id":"12191","title":"root-mean-square radius of gyration","longtitle":"IUPAC Gold Book - root-mean-square radius of gyration","doi":"10.1351\/goldbook.12191","code":"12191","status":"current","definitions":[{"id":1,"text":"For a flexible macromolecule composed of \\(n\\) mass elements, of masses \\(m_{i}\\), \\(i = 1, 2, \\ldots, n\\), located at statistical-mechanical mean-square distances \\(\\lt\\!s_{i}^{2}\\!\\gt\\) from the centre of mass, the root-mean-square radius of gyration is the square-root of the mass average of \\(\\lt\\!s_{i}^{2}\\!\\gt\\) over all mass elements, i.e., \\[\\lt\\!s^{2}\\!\\gt^{1\/2}\\;= \\left(\\sum\\limits_{i=1}^{n} m_{i} \\lt\\!s_{i}^{2}\\!\\gt\\!\/\\sum\\limits_{i=1}^{n} m_{i} \\right)^{1\/2}\\]","notes":{"1":"The mass elements are usually taken as the masses of the skeletal groups constituting the macromolecule, e.g., \\(\\ce{-CH2-}\\) in poly(methylene).","2":"\\(\\lt\\!s_{i}^{2}\\!\\gt\\) is the statistical mechanical average of \\(s_{i}^{2}\\) over all chain conformations.","3":"The radius of gyration is a parameter characterizing the size of a macromolecule as a time-averaged spherical domain in laboratory coordinates."},"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 75 (https:\/\/doi.org\/10.1515\/pac-2013-0201)"]}],"altoutputs":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/12191\/html","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/12191\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/12191\/plain"},"citation":"Citation: 'root-mean-square radius of gyration' 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.12191","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":"2026-04-18T08:19:47+00:00"}}