Practical analysis of diffuse scattering patterns of inhomogeneous liquids

A simple analytical model for the analysis of diffuse small-angle scattering data is proposed in this work to characterize the structure of colloidal suspensions of water mixtures of organic solvents and amphiphiles. A fractal structure factor term describing the low q region was incorporated in the analytical function, which includes a particle diameter variable within the power-law decay term of the scattering intensity as a function of the scattering vector. This decay was associated with not only scattering from either surface or mass fractals but could also model the signal decay within a fluid more accurately than the Ornstein–Zernike, Debye–Anderson–Brumberger, or Teubner and Strey analytical models. This low q region also displayed a Guinier component (curvature) arising from the form factor of the scattering objects, considered here as spheres. Patterns also displayed a broad Gaussian peak at higher q associated with the aggregation of micelles within the fluid responsible for the formation of the mass or surface fractals. Each term (power-law, Guinier, and Gaussian) contained a diameter term, which was then shared among all three functions. Parameter sharing stabilized the numerical fits of the model to the data and provided an accurate estimate of the average size of the scattering object or the inhomogeneity in the fluid. Examples of the use of the model in the study of the separation of water-soluble organic solvent contaminants from water are given and used for the purpose of developing strategies for the remediation of polluted groundwater.