Evaluation of Two-Dimensional Real-Space Correlations from Anisotropic Small-Angle Scattering Data

Small-angle scattering is a powerful way to investigate the molecular structure of soft and biological materials. Prior studies established diverse analysis methods for isotropic patterns. There was, however, no robust analysis method for 2D “anisotropic” scattering patterns. We developed a calculation procedure of converting 2D scattering patterns in reciprocal space into 2D correlations in real space. As a test system, we applied this method to nanoparticle-hydrogel composites under uniaxial deformation. We obtained 2D real-space information about affine and non-affine displacements of nanoparticles in the gel in ways not possible before. We expect that our method can be applied to a wide variety of anisotropic systems in different ways of deformations.