Theoretical Studies of the Use of the Double Extrapolation Method to Determine the Forward Scattering of Light by Spherical Colloidal Particles

Abstract

Abstract An application of the double extrapolation method (the Zimm-plot method) for the reduced intensity of light scattered by colloidal dispersions, instead of polymer solutions, is discussed theoretically on the basis of the Mie theory. The correction factor, F, required to recalculate the experimental value of the molecular weight, MR, to the true value, M (M=FMR), is equal to unity in the case of the Rayleigh scattering (α→0) and the Rayleigh-Gans-Debye (R-G-D) scattering (|m–1|→0, where m is the relative refractive index of the sphere to the medium). Usually, however, the value of F is not equal to unity, but is found to be given by an empirical equation F=1–0.155Q+bQ1.5, where Q is a quantity proportional to the reduced specific scattering intensity at θ→0. For the determination of the radius of gyration from the “initial slope,” the R-G-D equation is applicable even in cases where |m–1| is not small. In order to determine the true molecular weight from the molecular weight, Mτ, obtained from the specific turbidity at the infinite dilution, the factor Φ is needed (M=ΦMτ). The factor Φ is considered to be a product; that is, Φ=F\varphi, where the factor \varphi seems to be independent of the m value. The empirical equation obtained was \varphi=1+0.537α2.08