Dynamics of coarse-grained helical wormlike chains. III. First cumulant of the dynamic structure factor

Abstract

The dynamic structure factor S(k,t) as a function of the magnitude k of the scattering vector and time t and its first cumulant Ω(k) are evaluated in the Gaussian approximation on the basis of the coarse-grained helical wormlike chain model. In this approximation, S(k,t) and therefore Ω(k) may be expressed in terms of the solutions of the 1(1) eigenvalue problem previously obtained. It is then found that the eigenvalues in the j=0 branch of the 1(1) eigenvalue spectrum at small wave numbers make main contribution to Ω(k). The numerical results for typical flexible polymers show that the so-called “universal” plot of η0Ω(k)/kBTk3 against 〈S2〉1/2k depends on the kind of polymer, where η0 is the solvent viscosity, kB the Boltzmann constant, T the absolute temperature, and 〈S2〉 the mean-square radius of gyration. It is also shown that for semiflexible chains, the plot depends appreciably on the reduced total contour length. A comparison of theory with experiment is made with respect to Ω(k) and also the coefficient C introduced by Stockmayer and co-workers. It is then found that the theory may give a rather satisfactory explanation of experimental results for both flexible and semiflexible polymers despite the fact that the preaveraged Oseen tensor is used along with the Gaussian approximation.