Quasielastic scattering of neutrons from freely jointed polymer chains in dilute solutions

Abstract

Starting with Kirkwood's Fokker–Planck equation for the polymer configuration-space distribution function and using the Zwanzig–Mori projection operator technique we have calculated the scattering law S ( q , w ) for a freely jointed model polymer chain in a dilute solution. When memory effects are neglected, the theory predicts a Lorentzian for S ( q , w ) with a halfwidth Ω ( q ) , which we have determined as a function of the momentum transfer q for all values of q . The results are compared with recent neutron scattering experiments on deuterated polytetrahydrofuran and polystyrene in dilute solution in CS 2 . It is found that the observed q dependence of Ω (q) is represented satisfactorily by the present theory with a bond length b of about 6.3 Å for polystyrene and 3.8 Å for polytetrahydrofuran, and a friction coefficient Ζ = 4ΠΗ0 b where Η 0 is the viscosity of the solvent.