Stretched exponential relaxation in polymer dynamics

A model of connected longitudinal dipoles is proposed in partial explanation of stretched exponential decay profiles in relaxation phenomena involving polymers. The net dipole moment of the system lies along the end-to-end vector of the chain, which is initially constrained to have the value R. The constraint represents the effects of an applied perturbation. Projection operator techniques are then used to derive an exact equation for the evolution of R in the absence of the constraint. This equation is solved under a series of well-controlled approximations, and in the limit of long times R(t) is found to vary as a stretched exponential, with an exponent of 1/2. A memory term in the evolution equation for R is identified as the factor responsible for the observed decay.