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radius of gyration, s

A parameter characterizing the size of a particle of any shape. For a rigid particle consisting of mass elements of mass m i, each located at a distance r i from the centre of mass, the radius of gyration, s, is defined as the square root of the mass-average of r i 2 for all the mass elements, i.e.
s = ∑ i m i r i 2 ∑ i m i
For a non-rigid particle, an average over all conformations is considered, i.e.
< s 2 > = < ∑ i m i r i 2 > ∑ i m i
The subscript zero is used to indicate unperturbed dimensions, as in < s 2 > 0 1 / 2.
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IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook.
Last update: 2014-02-24; version: 2.3.3.
DOI of this term: doi:10.1351/goldbook.R05121.
Original PDF version: http://www.iupac.org/goldbook/R05121.pdf. The PDF version is out of date and is provided for reference purposes only. For some entries, the PDF version may be unavailable.
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