Hydrodynamic radius

Not to be confused with Stokes 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

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

where $r_{ij}$ is the distance between subparticles $i$ and $j$, and where the angular brackets $\langle \ldots \rangle$ represent an ensemble average. 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, or commonly to the apparent Stokes radius obtained from size exclusion chromatography.

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.

References

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