Dynamics of helical wormlike chains. XII. Dynamic depolarized light scattering

Abstract

Dynamic depolarized light scattering from dilute solutions of flexible chain polymers is studied on the basis of the discrete helical wormlike (HW) chain. A preliminary consideration leads to the conclusion that the spring-bead model with the Kuhn–Grün expression for the spring polarizability tensor is, in principle, inappropriate for the description of the depolarized scattering, so that the Ono–Okano theory is invalid for real chains. In the approximations that the orientational fluctuations of the subbodies composing the HW chain may be decoupled from their density fluctuation at very small magnitude of the scattering vector and that the former relax much faster than the latter, which are good enough under the condition of usual measurements, it is shown that the spectrum JΓ of the excess depolarized component of the scattered light may be written in terms of the same class of basic time-correlation functions with the ‘‘total angular momentum quantum number’’ L=2 and the number of ‘‘excited’’ subbodies n=1, as in the case of nuclear magnetic relaxation and fluorescence depolarization. Numerical evaluation of JΓ is carried out, taking atactic polystyrene (a-PS) and atactic poly(methyl methacrylate) as typical examples of flexible polymers. It is then found that for both polymers JΓ may be represented in terms of a small number of those eigenvalues λj2,k of the diffusion operator for the HW model with very small wave numbers k which belong to two branches specified by the superscript j, one corresponding to the low frequency modes and the other to the high frequency modes. For a-PS, this result is consistent with the experimental result obtained by Bauer, Brauman, and Pecora [Macromolecules 8, 443 (1975)] except that the present low frequency modes do not correspond to the Rouse–Zimm modes of the spring-bead model.