Hydrodynamic radius

The hydrodynamic radius of a macromolecule or colloid particle has two meanings. Some books use it as a synonym for the Stokes radius. cite book | author = Gert R. Strobl
title= The Physics of Polymers Concepts for Understanding Their Structures and Behavior| publisher=Springer-Verlag | year=1996 | id = ISBN 3-540-60768-4 Section 6.4 page 290. ]

Others books define a theoretical hydrodynamic radius $R\_\{hyd\}$. 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. $R\_\{hyd\}$ is defined by

:$frac\{1\}\{R\_\{hyd\; stackrel\{mathrm\{def\{=\}\; frac\{1\}\{N^\{2\; langle\; sum\_\{i\; eq\; j\}\; frac\{1\}\{r\_\{ij\; angle$

where $r\_\{ij\}$ is the distance between subparticles $i$ and $j$, and where the angular brackets $langle\; ldots\; angle$ represent an ensemble average. cite book | author = J. Des Cloizeaux and G. Jannink
title= Polymers in Solution Their Modelling and Structure | publisher=Clarendon Press | year=1990 | id = ISBN 0-19-852-036-0 Chapter 10, Section 7.4, pages 415-417. ] The theoretical hydrodynamic radius $R\_\{hyd\}$ was originally an estimate by John G. Kirkwood of the Stokes radius of a polymer.

The theoretical hydrodynamic radius $R\_\{hyd\}$ 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

References

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