The anomalous diffusion of polymers in random media

We re-examine the problem of the diffusion of a Gaussian chain in a fixed array of obstacles using the projection operator formalism introduced by Loring @J. Chem. Phys. 88, 6631 ~1988!#. We show that in the limit of long wavelengths, the frequency-dependent monomer friction coefficient that is used in the calculation of the mean square displacement of the center of mass can be rewritten exactly in terms of the time correlation function of the total force on the chain. When the decay profile of the force correlation function is assumed to be exponential, and its dependence on the density of obstacles written in an approximate resummed form, the dynamics of the center of mass is found to be diffusive at long and short times, and subdiffusive ~anomalous! at intermediate times. Moreover, the diffusion coefficient D that describes the long-time behavior of the chain at high concentrations of small obstacles is found to vary with chain length N as N22, which is in qualitative agreement with the predictions of the reptation model. These results are obtained in the absence of any mechanism that might incorporate the notion of reptation directly into the calculations, in contrast to Loring's approach, which treats the monomer friction coefficient approximately using a decoupling of segmental motion into parallel and perpendicular components.