Free-draining polymer friction (${\zeta }_N=N{\zeta }_0$)

With additive drag from $N$ identical monomers, ${\zeta }_N=N{\zeta }_0$ and centre-of-mass diffusion is $D_N=k_{B}T/(N{\zeta }_0)$. For monomer Stokes law ${\zeta }_0=6\pi \eta a$, this gives $D_N\propto N^{-1}$. The model neglects long-range hydrodynamic coupling and does not alone describe the long-time spatial diffusion of a strongly entangled chain.