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Quasielastic scattering by dilute polymer solutions A summary of this work was presented at the IUPAP International Conference on Statistical Physics, August 25—29, 1975
Akcasu, A. Ziya; Gurol, H.
Akcasu, A. Ziya; Gurol, H.
1996-09-30
Citation:Akcasu, Z.; Gurol, H. (1996)."Quasielastic scattering by dilute polymer solutions A summary of this work was presented at the IUPAP International Conference on Statistical Physics, August 25—29, 1975 ." Journal of Polymer Science Part B: Polymer Physics 34(13): 2117-2126. <http://hdl.handle.net/2027.42/38873>
Abstract: The scattering law S(k, w) for dilute polymer solutions is obtained from Kirkwood's diffusion equation via the projection operator technique. The width Ώ(Κ) of S(k, w) is obtained for all k without replacing the Oseen tensor by its average (as is done in the Rouse-Zimm model) using the “spring-bead” model ignoring memory effects. For small documentclass{article}pagestyle{empty}begin{document}$ left( {kasqrt N ll 1} right) $end{document} and large ( ka >> 1) values of k we find OHacgr; = 0.195 Κ 2 /Β aŋo, documentclass{article}pagestyle{empty}begin{document}$ sqrt N $end{document} and OHacgr; = Κ 2 /ΒΞ respectively, indicating that the width is governed mainly by the viscosity ŋo for small Κ values and by the friction coefficient Ξ for large Κ values. For intermediate Κ values which are of importance in neutron scattering we find that in the Rouse limit Ώ = Κ 4 a 2 /12ΒΞ. When the hydrodynamic effects are included, Ώ( Κ ) becomes 0.055 Κ 3 /Βeng;o. Using the Rouse-Zimm model, it is seen that the effect of pre-averaging the Oseen tensor is to underestimate the half-width Ώ( Κ ). The implications of the theoretical predictions for scattering experiments are discussed.