A new method to estimate the size distribution of non-interacting colloidal particles from small-angle scattering data is presented. The method demonstrates that the distribution can be efficiently retrieved through features of the scattering data when plotted in the Porod representation, thus avoiding the standard fitting procedure of nonlinear least squares. The present approach is elaborated using log-normal and Weibull distributions. The method can differentiate whether the distribution actually follows the functionality of either of these two distributions, unlike the standard fitting procedure which requires a prior assumption of the functionality of the distribution. After validation with various simulated scattering profiles, the formalism is used to estimate the size distribution from experimental small-angle X-ray scattering data from two different dilute dispersions of silica. At present the method is limited to monomodal distributions of dilute spherical particles only.

中文翻译：

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从小角度散射数据估计非相互作用球形颗粒的尺寸分布和指纹识别

提出了一种从小角度散射数据估计非相互作用胶体颗粒尺寸分布的新方法。该方法表明，当在 Porod 表示中绘制时，可以通过散射数据的特征有效地检索分布，从而避免非线性最小二乘法的标准拟合程序。本方法使用对数正态分布和威布尔分布进行阐述。该方法可以区分分布是否实际遵循这两个分布中的任何一个的功能，这与需要预先假设分布功能的标准拟合程序不同。在使用各种模拟散射剖面进行验证后，该形式用于根据来自两种不同的二氧化硅稀释分散体的实验小角度 X 射线散射数据来估计尺寸分布。目前，该方法仅限于稀球形颗粒的单峰分布。