Polydispersity effects in polymer self-diffusion measured by small-angle neutron scattering

The small-angle neutron scattering (SANS) method for measuring the self-diffusion coefficient D has been analyzed for effects of polydispersity in degree of polymerization for the case of linear polymers diffusing by reptation. Polydispersities corresponding to M_w/M_n = 1.0?10 were considered. It is shown that in all cases a meaningful effective diffusion coefficient D_e can be obtained from the short time recovery of the SANS intensity. This quantity D_e ≤ 1.3 D(M_w), where D(M_w) is the diffusion coefficient of a monodisperse polymer having molecular weight M = M_w. The method relies on SANS intensities extrapolated to zero scattering angle; realistic extrapolation is shown to give rise to quite acceptable errors on the order of 0.05 D_e.