Particle Sizing of Polydisperse Samples by Mie-Scattering
A procedure for the computation of size distributions of polydisperse systems from elastic light scattering data is presented. Precise solutions are obtained if the shapes of the particles are known, if the size can be expressed by a single parameter and if it is possible to calculate the shape factor Ф (h, m, R) for the particles, as it is the case for spheres and spheroids. The method is not restricted with respect to the range of the refractive index m. However, wrong estimates for this index lead to severe errors in the results. Approximate solutions can be found for different globular particles by an evaluation as a distribution of spheres. The range of applicability of the method depends on the experimental set-up, but is in most cases in the size range from 100 nanometers to several microns, i.e., it lies in the gap between X-ray or neutron small-angle scattering and Fraunhofer diffraction. The inverse scattering problem is solved with the modified Indirect Fourier Transform method representing the solution as a series of equidistant cubic B-splines. The regularization method incorporated in the procedure uses a stabilization parameter that can be determined directly from the data. The solution is nearly free from oscillations typical for ill-conditioned problems and it is largely independent of the actual number of splines. A series of simulated experiments is used to show the merits and limitations of the method.
KeywordsReal Space Full Line Nonspherical Particle Prolate Ellipsoid Polydisperse System
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