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

Abstract

AbstractStarting 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 CS2. 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 = 4πη0b where η0 is the viscosity of the solvent.