Determining the size distribution of core–shell spheres and other complex particles by laser diffraction

Abstract

The goal of this work is to determine the size distribution of hollow glass spheres by laser diffraction, an experiment which involves measuring angle-dependent scattering of light from particles dispersed in a liquid. The proprietary software supplied with commercial instruments is not strictly applicable to our two-layer, glass-shell, hollow-core spheres because it requires that the particles have spatially homogeneous properties. We therefore developed Fortran code to compute the scattering from core–shell spherical particles. The results show that the scattering from representative hollow glass particles diverges from homogeneous sphere scattering when the radius decreases from 10 to 3 μm. Additionally, scattering measurements on two core–shell hollow glass powders were analyzed using the exact core–shell optical model and homogeneous sphere approximations. In both cases, the size distribution determined using the exact core–shell model differs from that determined using the homogeneous-sphere approximation when the distribution covers radii smaller than about 10 μm, as expected. The size distribution based on the exact core–shell optical model was determined using a new algorithm. Although the basic equations used in the algorithm have been published previously, they are developed here in a different form, which can be implemented using Fortran and MatLab routines available commercially and in the public domain. This algorithm could be used to determine the size distribution of other kinds of particles, such as cylindrical rods, as long as their angle-dependent scattering could be computed.