2D pair distribution function analysis of anisotropic small-angle scattering patterns from elongated nano-composite hydrogels.

Small angle scattering (SAS) on polymer nanocomposites under elongation or shear flow is an important experimental method to investigate the reinforcement effects of the mechanical properties by fillers. However, the anisotropic scattering patterns that appear in SAS are very complicated and difficult to interpret. A representative example is a four-spot scattering pattern observed in the case of polymer materials containing silica nanoparticles, the origin of which is still in debate because of the lack of quantitative analysis. The difficulties in the interpretation of anisotropic scattering patterns mainly arise from the abstract nature of the reciprocal space. Here, we focus on the 2D pair distribution function (PDF) directly evaluated from anisotropic scattering patterns. We applied this method to elongated poly(N,N-dimethylacrylamide) gels containing silica nanoparticles (PDAM-NP gel), which show a four-spot scattering pattern under elongation. From 2D PDFs, we obtained detailed and concrete structural information about the elongated PDAM-NP gel, such as affine and non-affine displacements of directly attached and homogeneously dispersed silica nanoparticles, respectively. We proposed that nanoparticles homogeneously dispersed in the perpendicular direction are not displaced due to the collision of the adsorbed polymer layer during elongation, while those in the parallel direction are displaced in an affine way. We assumed that this suppression of the lateral compression is the origin of the four-spot pattern in this study. These results strongly indicate that our 2D PDF analysis will provide deep insight into the internal structure of polymer nanocomposites hidden in the anisotropic scattering patterns.