Theory of dynamic depolarized light scattering from nonrigid polymer chains

Abstract

The depo1arized light scattering spectrum from a dynamic. continuous chain model of a macromolecule in ~olution is calculated. For vanishing chain "stiffness" the results reduce to those predicted by Ono and Okano for the Rouse-Zimm model. For intermediate degrees of stiffness the contribution of the longer wavelength modes to the spectrum is enhanced. 3254

Quantitative prediction of .alpha. in the scaling law for self-diffusion

“…Only the numerical coefficient differs between the two cases. Equation 19 gives B for the case that the second polymer is definitely at R. Averaging R over all space (with cutoff R > 2a0 due to the bead size), summing over the independent contributions of polymer chains 2, ..., N to the linear concentration dependence of B, and substitution in eq 3-7 give Ds = D0 exp(acu) (20) with…”

Dynamics of wormlike chains

“…Thus, for example <P,(t)-P*(0)> = e-Wt<P,(0).P*(0)) (4.5) The eigenvalue equation (eq 4.1) is easily solved and in fact corresponds to the slightly bendable rod model of Landau and Lifschitz18 and to the = 0 limit in the HH equation. 13 If we put the origin in the center of the molecule, (-L/2 < s < L/2), the eigenfunctions have even or odd parity and are given by cos (v,s) cosh (vis)…”

“…(12) Hashimoto, T.; Shibayama, M.; Kawai, H. Macromolecules 1983, 16, 1093. (13) Shibayama, M.; Hashimoto, T.; Kawai, H. Macromolecules, 1983, 16, 1434. (14) Hashimoto, T.; Suehiro, S.; Shibayama, M.; Saijo, K.; Kawai, H. Polym.…”

Dynamics of wormlike coils: amplitudes of normal bending modes

“…The Harris-Hearst theory uses a quadratic expression for the potential energy and the distribution function for the normal modes is a Gaussian. 4 As a result, the expression for the average of the square of a normal mode amplitude is <P/0)P;(0)> = kBT/Xj = L22aU/K)/Xj (19) where t / is the ratio of the bending to the stretching force constants, a = L/2P, and x¡ is a dimensionless eigenvalue, typically of magnitude greater than 1. This expression is proportional to a, as in the weakly bending rod case presented above, but contains only one power of the dimensionless eigenvalue in the denominator.…”