Fourier inversion of light scattering intensity data from coagulating dispersions

Abstract

The short range structure of aggregates, which are formed during the coagulation of monodisperse sols, is investigated by developing a rigorous approach to the analysis of light scattering data. The particle distribution function is determined by the Fourier transformation of scattered light intensity data measured over scattering angles in the range 28 to 150°. The direct inversion of the intensity data produces large oscillations in the particle distribution function owing to the truncation of the data set as characterised by the “cut-off” parameter β(∝ particle size and incident light wavelength). These oscillations are removed by including an exponential modification function in the kernel of the transform. The effect of both the “cut-off” function and the “damping” function are assessed by adopting a general analysis and then testing the transformation method on intensity data generated using the Smoluchowski–Benoit model to simulate light scattering from a coagulating system. The results of an experimental investigation of the coagulation of a 0.234 µm diameter polystyrene sol indicates the formation of close-packed aggregates with the average number of neighbours increasing only slightly faster than expected from the von Smoluchowski model of coagulation. The average number of nearest neighbours is considerably less than expected from the Smoluchowski–Benoit model assuming the particles to be hexagonally close-packed.