Rouse model

An overdamped bead-spring model of polymer dynamics with local friction and no long-range hydrodynamic interaction. For an ideal unentangled chain of $N$ identical frictional units, the centre-of-mass diffusion coefficient is proportional to $N^{-1}$ and the longest internal relaxation time to $N^2$. A tagged segment has an intermediate-time mean-square displacement proportional to $t^{1/2}$ before ordinary whole-chain diffusion dominates. Entanglement adds constraints beyond this model.

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.