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 $R_{\mathrm{h}\mathrm{y}\mathrm{d}}$. 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. $R_{\mathrm{h}\mathrm{y}\mathrm{d}}$ is defined by

$\frac{1}{R_{\mathrm{h}\mathrm{y}\mathrm{d}}}\stackrel{\mathrm{d}\mathrm{e}\mathrm{f}}{=}\frac{1}{N^2}⟨\sum _{i\ne j}\frac{1}{r_{ij}}⟩$

where $r_{ij}$ is the distance between subparticles $i$ and $j$, and where the angular brackets $⟨\dots ⟩$ represent an ensemble average. The theoretical hydrodynamic radius $R_{\mathrm{h}\mathrm{y}\mathrm{d}}$ was originally an estimate by John Gamble Kirkwood of the Stokes radius of a polymer.

The theoretical hydrodynamic radius $R_{\mathrm{h}\mathrm{y}\mathrm{d}}$ 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