Dynamical eigenmodes of star and tadpole polymers

The dynamics of phantom bead–spring chains with the topology of a symmetric star with f arms and tadpoles (f = 3, a special case) is studied, in the overdamped limit. In the simplified case where the hydrodynamic radius of the central monomer is f times as heavy as the other beads, we determine their dynamical eigenmodes exactly, along the lines of the Rouse modes for linear bead–spring chains. These eigenmodes allow full analytical calculations of virtually any dynamical quantity. As examples we determine the radius of gyration, the mean square displacement of a tagged monomer, and, for star polymers, the autocorrelation function of the vector that spans from the center of the star to a bead on one of the arms.