Polymer chains tethered to impenetrable interfaces: Broadening of relaxation spectra

We investigate the dynamics of an ideal polymer chain which is tethered with one of its ends to an impenetrable interface. Due to the geometric restrictions the relaxation of modes perpendicular to the interface differs significantly from that of modes parallel to it. A superposition of both components leads to a marked broadening of the relaxation spectrum, which may find its signature in dielectric measurements. We obtain the relevant dynamical quantities for a polymer chain subject to geometric constraints by use of the Smoluchowski equation combined with a Rayleigh-Ritz variational scheme.