Small angle X-ray scattering by spherical particles of Polystyrene and Polyvinyltoluene

The high intensity, high resolution multiple reflection diffractometer has been applied to make accurate measurements of the small angle X-ray scattering of eight different Dow Chemical latexes with stated diameters 2.051, 1.305, 0.814, 0.557, 0.365, 0.264, 0.126, and 0.088 μm. Using thin dry samples, the measured intensities of diffraction extrema with orders higher than the third were found to agree well with the simple Rayleigh-Gans theory which neglects multiple scattering as well as interparticle interference. Orders below the fourth showed a distinct effect of interparticle interference. This effect could be demonstrated to vanish when a liquid solution sample was used instead of a dry one. Scattering curves of thick dry samples had strongly decreased contrast between maxima and minima, an effect which is known to be due to multiple scattering. The following particle diameters were determined from the measured scattering curves: 2.102±0.013 μm, 1.313±0.008 μm, 0.823±0.004 μm, 0.552±0.002 μm, 0.352±0.002 μm, 0.254±0.002 μm, 0.119±0.001 μm and 0.078±0.001 μm. The discrepancies between these and the stated sizes are larger for the smaller particles. It is believed that the X-ray measurements are more accurate than the stated sizes which are based on measurements in the electron microscope. Therefore, as secondary standards, the diameter obtained from the X-ray measurements should be used.