Hydrodynamic radius

The hydrodynamic radius of a macromolecule or colloid particle is ${\displaystyle R_{\rm {hyd}}}$. The macromolecule or colloid particle is a collection of ${\displaystyle N}$ subparticles. This is done most commonly for polymers; the subparticles would then be the units of the polymer. ${\displaystyle R_{\rm {hyd}}}$ is defined by

where ${\displaystyle r_{ij}}$ is the distance between subparticles ${\displaystyle i}$ and ${\displaystyle j}$, and where the angular brackets ${\displaystyle \langle \ldots \rangle }$ represent an ensemble average. The theoretical hydrodynamic radius ${\displaystyle R_{\rm {hyd}}}$ was originally an estimate by John Gamble Kirkwood of the Stokes radius of a polymer, and some sources still use hydrodynamic radius as a synonym for the Stokes radius.

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