First Cumulant for Chains with Constraints

Abstract

AbstractThe 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.