Small-Angle X-Ray Scattering Determination of Particle-Diameter Distributions in Polydisperse Suspensions of Spherical Particles

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Abstract
A scheme is developed for using small‐angle x‐ray‐scattering data to find the distribution of the particle diameters in dilute colloidalsuspensions of noninteracting spherical particles. No assumptions need to be made about the form of the distribution function. An investigation is made of the errors likely to be introduced in the numerical operations on the data. The method was tested on theoreticalscattering curves for which the calculations could be done both numerically and analytically. After these tests showed the feasibility of the calculation, diameter distributions were computed from the x‐ray small‐angle scattering data from some polydisperse colloidal samples composed of spherical particles. The results suggest that this technique may often be a useful procedure for analysis of small‐angle x‐ray‐scattering data.