Hydrodynamic radius ($R_h$)

The hydrodynamic radius is the radius of a hypothetical no-slip sphere with the same translational diffusion coefficient as the dissolved species. In the dilute continuum regime the Stokes–Einstein relation giveswhere $k_B$ is the Boltzmann constant, $T$ the absolute temperature, $\eta$ the dynamic viscosity of the solvent, and $D$ the translational diffusion coefficient. This effective radius need not equal the radius of gyration or a geometric molecular radius. It is a useful descriptor for SEC molar mass calibration, rather than a complete specification of how every shape enters every pore.

Approximating a dilute polymer coil as a hydrodynamic object of size $R$ gives $D\sim k_{B}T/(\eta R)$. If a stipulated model uses the theta-chain end-to-end distance $R=2a\sqrt{N}$ as a literal solid-sphere radius, Stokes law gives $D=k_{B}T/(12\pi \eta a\sqrt{N})$. The scaling matches theta-solvent hydrodynamic coupling, but a permeable coil's hydrodynamic radius is not generally equal to its end-to-end distance.