Hydrodynamic radius

The hydrodynamic radius of a macromolecule or colloid particle is $R_{{{\rm {hyd}}}}$. The macromolecule or colloid particle is a collection of $N$ subparticles. This is done most commonly for polymers; the subparticles would then be the units of the polymer. $R_{{{\rm {hyd}}}}$ is defined by

${\frac {1}{R_{{{\rm {hyd}}}}}}\ {\stackrel {{\mathrm {def}}}{=}}\ {\frac {1}{N^{{2}}}}\left\langle \sum _{{i\neq j}}{\frac {1}{r_{{ij}}}}\right\rangle$

where $r_{ij}$ is the distance between subparticles $i$ and $j$, and where the angular brackets $\langle \ldots \rangle$ represent an ensemble average. ^[1] The theoretical hydrodynamic radius $R_{{{\rm {hyd}}}}$ was originally an estimate by John Gamble Kirkwood of the Stokes radius of a polymer, and some sources still use hydrodynamic radius as a synonym for the Stokes radius.

Note that in biophysics, hydrodynamic radius refers to the Stokes radius,^[2] or commonly to the apparent Stokes radius obtained from size exclusion chromatography.^[3]

The theoretical hydrodynamic radius $R_{{{\rm {hyd}}}}$ arises in the study of the dynamic properties of polymers moving in a solvent. It is often similar in magnitude to the radius of gyration.

^[4]

Notes

1. J. Des Cloizeaux and G. Jannink (1990). Polymers in Solution Their Modelling and Structure. Clarendon Press. ISBN 0-19-852036-0. Chapter 10, Section 7.4, pages 415-417.
2. Harding, Stephen (1999). "Chapter 7: Protein Hydrodynamics" (PDF). Protein: A comprehensive treatise. JAI Press Inc. pp. 271–305. ISBN 1-55938-672-X.
3. Goto, Yuji; Calciano, Linda; Fink, Anthony (1990). "Acid-induced unfolding of proteins". Proc. Natl. Acad. Sci. USA. 87: 573–577.
4. Gert R. Strobl (1996). The Physics of Polymers Concepts for Understanding Their Structures and Behavior. Springer-Verlag. ISBN 3-540-60768-4. Section 6.4 page 290.

References

Grosberg AY and Khokhlov AR. (1994) Statistical Physics of Macromolecules (translated by Atanov YA), AIP Press. ISBN 1-56396-071-0