Stabilizer code

The hydrodynamic radius of a macromolecule or colloid particle has two meanings. Some books use it as a synonym for the Stokes radius.

Others books define a theoretical hydrodynamic radius $R_{\rm {hyd}}$. They consider the macromolecule or colloid particle to be 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. The theoretical hydrodynamic radius $R_{\rm {hyd}}$ was originally an estimate by John Gamble Kirkwood of the Stokes radius of a polymer.

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