Theory of Scattering by an Inhomogeneous Solid Possessing Fluctuations in Density and Anisotropy

Abstract

The theory of Debye and Bueche for the scattering of light by an amorphous solid is extended to the case where fluctuations in anisotropy as well as density are considered. A generalized correlation function is defined, which gives the probability of a simultaneous occurrence of fluctuations in polarizability in two volume elements a distance r apart. The fluctuations are specified by the magnitudes of the polarizabilities and the directions of the optic axes. The correlation function is assumed to depend on r, on the angle between the axes of the fluctuations, and on the angle giving the position of the second element with respect to the optic axis of the first. The intensities of the horizontal and vertical components of the scattered light are expressed as integrals over the correlation function of explicit functions of r and the two angles. From the initial slopes and intercepts of the intensities plotted against sin2(θ/2) where θ is the scattering angle, one can obtain average values and average dimensions of the fluctuations, and a measure of the extent to which fluctuations in density and anisotropy are correlated. The theory is applicable to glasses, gels, and liquid crystals.

Thermodynamics of Systems Containing Flexible-Chain Polymers

“…These values are in good agreement with p calculated for the king model by means of the renormalization group method (Wilson and Kogut, 1974;Raker et al, 1976;Golner and Riedel, 1976;Ma shang-keng, 1976; le Guillou and Zimm-Justin, 1977).…”

“…Such fluctuations arise as a result of mutual orientation of anisotropic molecules, or of their aggregates, or owing to the internal stresses in solid matter. In this case, the polarizability of scattering elements is represented by a polarizability tensor and two corrclation functions (density correlation and orientation correlation) are introduced (Goldstein and Michalik, 1955;van Aartsen, 1972).…”

Multivariable structural characterization of semicrystalline polymer blends by small‐angle light scattering

“…2(c)]. For small scattering angles, the total scattering intensity is given by18, 39, 56, 57 In eq 6, ω η and ω δ are the correlation volumes for density and orientation fluctuations 18, 56, 57. For a two‐phase system of crystalline and amorphous polymer the mean‐square density (〈η〉) and orientation (〈δ〉) fluctuations are given by where the volume fraction crystallinity is ϕ c , the average crystalline polarizability is α c , and α a is the polarizability of the amorphous phase, assumed to be isotropic.…”

Theory of Light Scattering by an Isotropic System Composed of Anisotropic Units with Application to the Porod–Kratky Chain

“…Light scattering by polymer chains in solution has much in common with light scattering by an isotropic, inhomogeneous solid. 3 Concerning the latter problem Goldstein and Michalik 4 developed a very general theory, whose result might be usable for the present purpose. Unfortunately they introduced some simplifying assumptions: the axial symmetry of polarizability of each unit and an assumption about the orientational distribution between two units which together spoil complete generality.…”