CALCULATION OF MEAN-SQUARE-DISPLACEMENT FUNCTION FOR SLOW MOTION OF LONG-CHAIN MOLECULES AND ITS APPLICATION TO NEUTRON DIFFUSION

We calculate the mean-square-displacement function for the motion of a polymer chain in solution. The motion is described by means of coupled Langevin equations. The peculiar behavior in square root of time obtained by de Gennes is rederived here. It is shown, however, that it is restricted to a certain time interval which depends on the number of beads and rank of the beads at which the mean-square displacement is computed. Implications for a neutron-scattering experiment are discussed. It is also seen that for infinite polymers the influence of inertial effects is entirely negligible, thus showing that the Bueche and Rouse models are equivalent in this respect.