Three-Dimensional Orientation of Nanofibrils in Axially Symmetric Systems Using Small-Angle X‑ray Scattering

The increased availability and brilliance of new X-ray facilities have in the recent years opened up the possibility to characterize the alignment of dispersed anisotropic nanoparticles in various microfluidic applications, from hydrodynamic self-assemblies to flows in complex geometries. In such applications, it is vital to study the alignment of the nanoparticles in the flow, as this in turn affects the final properties of the self-assembled superstructures or those of the flow itself. Small-angle X-ray scattering (SAXS) is a well-suited characterization technique for this but typically provides the alignment in a projected plane perpendicular to the beam direction. In this work, we demonstrate a simple method to reconstruct the full three-dimensional orientation distribution function from a SAXS experiment through the assumption that the azimuthal angle of the nanoparticles around the flow direction is distributed uniformly, an assumption that is valid for a large range of nanoparticle flow processes. For demonstration purposes, the experimental results from previous works on hydrodynamic self-assembly of cellulose nanofibrils (CNFs) into filaments have been revised, resulting in a small correction to the presented order parameters. The results are then directly compared with simple numerical models to describe the increased alignment of CNFs both in the flowing system and during the drying of the filament. The proposed reconstruction method will allow for further improvements of theoretical or numerical simulations and consequently open up new possibilities for optimizing assembly processes, which include flow alignment of elongated nanoparticles.