Dynamic light scattering from dilute suspensions of thin discs and thin rods as limiting forms of cylinder, ellipsoid and ellipsoidal shell of revolution

Abstract

A previous formulation of the field correlation function G 1(τ) of light quasielastically scattered from suspensions of rigid rods undergoing anisotropic translational as well as rotational diffusion (T. Maeda and S. Fujime, Macromolecules 17 (1984) 1157) was extended to the cases of suspensions of cylinders (length L and radius R), ellipsoids and ellipsoidal shells of revolution ( x 2/ b 2 + y 2/ b 2 + z 2/ a 2= 1). The present formulation includes that for suspensions of rigid rods in the limit of KR ⪡ 1 or in the limit of b/ a ⪡ 1 and Kb ⪡ 1 (an extremely prolate ellipsoid), and also that for suspensions of discs in the limit of KL ⪡ 1 or in the limit of b/ a ⪢ 1 and Ka ⪡ 1 (an extremely oblate ellipsoid), where K is the length of the scattering vector. Explicit forms of G 1(τ), of the first cumulant Γ of G 1(τ) and of the dynamic form factors will be given, and numerical methods suitable for computation of dynamic form factors will be discussed. The present results can be applied to the analysis of experimental data for dilute suspensions of thin rods and thin discs. When the situation is favorable, our method can provide transport coefficients D 1, D 3, and Θ from dynamic light-scattering data only, where D 1 and D 3 are, respectively, the translational diffusion coefficients parallel with the x ( y) and z axes, and Θ the rotational diffusion coefficient around the x ( y) axis.