Hydrodynamic radius

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The hydrodynamic radius $R h y d$ of a collection of $N$ particles (typically belonging to a polymer) is defined as

$\frac{1}{R_{hyd}} \ \stackrel{\mathrm{def}}{=}\ \frac{1}{N^{2}} \langle \sum_{i \neq j} \frac{1}{r_{ij}} \rangle$

where $r i j$ is the distance between particles $i$ and $j$ , and where the angular brackets $\langle \ldots \rangle$ represent an ensemble average.

The hydrodynamic radius 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.