Scattering from oriented objects analysed by the anisotropic Guinier–Porod model

Abstract

Small angle scattering is frequently applied to study the anisotropy in complex soft matter systems. One emerging application is to probe the multi-scale structure in food matrices; while few models are available to describe the anisotropic scattering pattern in a quantitative, yet simple manner. For this purpose, anisotropy is introduced to the Guinier–Porod model to study the scattering from non-spherical objects with a preferred orientation. This generalised anisotropic Guinier–Porod model can be adapted to approximate the sector scattering from both cylinders and ellipsoids (both prolate and oblate). In practice, it is applied to describe the anisotropic scattering from fibres in a meat analogue made of calcium caseinate. A good agreement is found between fitted dimensions of the fibres and those observed from the microscopy image. The effect of orientation distribution on the shape and intensity of the scattering pattern is further discussed and three means to obtain the orientation distribution of the symmetry axis are proposed. Given the model is straightforward and the fitting remains phenomenological, it provides a novel approach to extract information from complex food systems. • Anisotropy is introduced to the Guinier Porod model. • The model describes the small angle scattering from non-spherical objects with preferred orientation. • The model can study the anisotropic small angle scattering from fibres in a meat analogue.