  Understanding the dynamics of soft colloids, such as star polymers,
dendrimers, and microgels, is of scientific and practical importance. It is
known that the excluded volume effect plays a key role in colloidal dynamics.
Here, we propose a condition of compressibility equivalence that provides a
simple method to experimentally evaluate the excluded volume of soft colloids
from a thermodynamic view. We apply this condition to survey the dynamics of a
series of star polymer dispersions. It is found that as the concentration
increases, the slowing of the long-time self-diffusivity of the star polymer,
normalized by the short-time self-diffusivity, can be mapped onto the
hard-sphere behavior. This phenomenon reveals the dynamic equivalence between
soft colloids and hard spheres, despite the apparent complexity of the
interparticle interaction of the soft colloids. The methods for measuring the
osmotic compressibility and the self-diffusivities of soft colloidal
dispersions are also presented.
