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.
Other books define a theoretical hydrodynamic radius 
. They consider the macromolecule or colloid particle to be a collection of 
subparticles. This is done most commonly for polymers; the subparticles would then be the units of the polymer. is defined by
where 
is the distance between subparticles 
and 
, and where the angular brackets 
represent an ensemble average.
The theoretical hydrodynamic radius was originally an estimate by John Gamble Kirkwood of the Stokes radius of a polymer.
The theoretical 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.
