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First Cumulant for Chains with Constraints

Published online by Cambridge University Press:  26 February 2011

A. Z Akcasu ,
B Hammouda ,
W. H Stockmayer  and
G. Tanaka
A. Z Akcasu
Affiliation:
Dept. of Nuclear Engin., U. of Michigan, Ann Arbor, MI 48109
B Hammouda
Affiliation:
Research Reactor and Dept. of Physics, U. of Missouri, Columbia, MO 65211
W. H Stockmayer
Affiliation:
Dept. of Chemistry, Dartmouth College, Hanover, NH 03755
G. Tanaka
Affiliation:
The Clayton Foundation Labs., The Salk Inst., La Jolla, CA 92037
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Abstract

The Fixman-Kovac formulation of chain dynamics with constraints is used to calculate the first cumulant Q(q) of the dynamic scattering function. This general formalism is applied to the case of freely jointed chains. It is shown that the large q limit (q being the scattering wavenumber) of Q(q) for a chain of N bonds in the absence of hydrodynamic interaction is proportional to the ratio (2N+3)/3(N+l) representing the fraction of unconstrained degrees of freedom of the chain. The inclusion of hydrodynamic interaction seems to enhance the apparent segmental diffusion. The use of constrained chain dynamics has no appreciable effects, however, on the behavior of Q(q) in the small and intermediate q regions for long enough chains. This formalism can be used to interpret neutron (spin echo) scattering experiments from semiflexible polymers in solution.

Type
Articles
Information
MRS Online Proceedings Library (OPL) , Volume 79: Symposium F – Scattering, Deformation and Fracture in Polymers , 1986 , 187
Copyright
Copyright © Materials Research Society 1987

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References

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