Theoretical synthesis of small-angle neutron scattering spectra with a smearing effect from monodisperse and polydisperse hard spherical colloids

Small-angle neutron scattering (SANS) is a powerful technique for microstructural characterization with several advantages, such as unique isotopic sensitivity, deep penetration capability, in situ characterization potential, and minimal radiation damage to samples. However, the intrinsically low neutron flux unavoidably necessitates certain compromises during measurements. These include a finite spread in wavelength, beam divergence, and the large footprint of the incident neutron beam, all of which lead to the so-called smearing effect. Consequently, the measured SANS spectra not only encode the microstructural information of the samples but are also influenced by the experimental conditions, thereby complicating the interpretation of the data. To facilitate the development of a machine learning-based approach for de-smearing measured SANS spectra, this study aims to establish a theoretical framework for synthesizing spectra both with and without the smearing effect. We focus on hard-sphere colloidal systems and consider system parameters such as the colloidal particle size, polydispersity, and volume fraction, and measurement conditions such as the neutron wavelength and its spread and beam divergence. The exemplary spectra presented herein also highlight the impact of the smearing effect under typical experimental conditions.