Theoretical Investigations on the Light Scattering of Colloidal Spheres. XI. Determination of Size Distribution Curves from Spectra of the Scattering Ratio or from Depolarization Spectra

Abstract

The theory of a method is developed by means of which size distributions in heterodisperse systems of colloidal and small microscopic spheres can be determined from spectra of the scattering ratio or depolarization. The method is applicable whenever the distribution is unimodal, positively skewed, and of the type most commonly found in emulsions. It makes use of the Mie‐scattering functions and encompasses α values up to 25.2 (diameters up to 3.3 μ if the vacuum wavelength is 5460.73 A) and the relative refractive indices m=1.05 (0.05) 1.30. The method yields the mean number or weight average diameter, modal diameter, half‐width, and ``half‐spread'' of a distribution and, in addition, the diameter of the smallest particles present in consequential numbers. For those instances where the assumed type of distribution does not apply, an extension of the theory is provided which is based upon a linear combination of two distribution functions of the same type. It allows one, in principle, to consider also negatively skewed and bimodal distributions. Use of the linear combination is indicated only when failure to obtain a satisfactory fit between theoretical and experimental spectra shows nonvalidity, in a particular system, of the simple one‐term distribution function.