Effect of dispersing agents on the angular dependence of light scattered from polystyrene sphere/water sols

The particles in nearly monodisperse sols of polystyrene in water need small amounts of adsorbed emulsifier to combat aggregation tendencies. These sols are used in the calibration of many different types of instrument including instruments capable of measuring angular light scattering functions. Using an IBM 360-40 computer with extended precision on all variables and on machine functions, a calculation has been made of the range of observable effects attributable to an adsorbed layer of emulsifier on the sol particles in water suspension. The calculation of the polarization ratio as a function of angle was based on the formal solution of Maxwell's equations by Aden and Kerker [A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951)]. Two model sols were treated for three different commonly used wavelengths of incident light 436 nm, 546 nm, and 632.8 nm. The calculation made use of constituent functions up to the eleventh order. The effect of an adsorbed layer on the light-scattering angular functions was negligible unless the adsorbed layer differed from the medium by about 5% with respect to refractive index. If the layer was not at least 1% of the radius of the particle in thickness there was no observable change in the angular position of the maxima and/or minima of the polarization ratio angular function. For layers thicker than 1% of the particle radius and having a refractive index different from both medium or particle, interesting new maxima and minima are predicted.