The hydrodynamic radius of a macromolecule or colloid particle has two meanings. Some books use it as a synonym for the Stokes radius. [1]

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. [2] 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.

## Notes

1. ^ 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.
2. ^ 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.

## References

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