Random field reconstruction of three-phase polymer structures with anisotropy from 2D-small-angle scattering data†

In this paper we present a computational method to analyze 2-dimensional (2D) small-angle scattering data obtained from phase-separated soft materials and output three-dimensional (3D) real-space structures of the three types of domains/phases. Specifically, we use 2D small-angle X-ray scattering (SAXS) data obtained from hydrated Nafion^TM membranes and develop a workflow using random fields to build the 3D real-space structure comprised of amorphous hydrophilic domains, amorphous polymer domains, and crystalline polymer domains. We demonstrate the method works well by showing that the reconstructed 3D Nafion^TM structures have a computed scattering profile that matches the input experimental scattering profile. Though not demonstrated in this work, such reconstructions can be used for further analysis of domain shapes and sizes, as well as prediction of transport properties through the structure. Our method in this work extends capabilities beyond the previously published random field small angle scattering reconstruction method introduced by Berk [Phys. Rev. Lett. 1987, 58 (25), 2718–2721] that had been used to reconstruct structures from 1D small angle scattering data of two-phase systems. The method in this work can be used to generate isotropic, two-phase reconstructions, but can also handle 2D SAXS profiles from three-phase systems that have structural anisotropy resulting from material processing effects.