Theoretical Studies of Light Scattering by Polydispersed Colloidal Systems of Spherical Particles

In order to study the light scattering of polydispersed colloidal systems of spherical particles, a weight distribution function, W(α), of the relative particle radius α has been assumed to be a modified Gaussian function with three parameters: the most probable α-value, αm; the width of the distribution, 〈Δα〉, and the dissymmetry of the distribution, Δ. The values of Yθ, which is proportional to the specific scattering intensity, for θ=45°, 90° and 135°, and the dissymmetry factor, z=Y45⁄Y135 have then been computed. In principle, it should be possible to determine three parameters of the particle size distribution, αm, 〈Δα〉 and Δ, from the observed values of three independent quantities, Y45, Y90 and Y135. It has, however, been concluded that practically the method requires very precise experiments. If one is satisfied with a distribution function of two parameters, αm and 〈Δα〉, the values of these parameters can be determined from the experimentally-obtained Y90 and z values on the basis of a chart constructed theoretically. The value of αw, which is the cubic root of weight-averaged 〈α3〉, is equal to the α value obtained from the measured specific scattering intensity by assuming that the system is monodispersed when α is small. If α is not small, the value of αw can be obtained according to the empirical equation: αw⁄α90=1+k(z⁄z90−1) The error will be within about 5% if αw<1.5.