where the variable 𝜈 represents the local volume fraction of hard spheres, RHS is the hardsphere radius and G(2qRHS) is a dependent function on q, 𝜈 and RHS (ESI: Eq. S1). The variable 𝜈, referred as the local volume fraction, expresses the packing of the hard-spheres/particles at a distance of 2RHS. In the fitting procedure, 𝜈 is kept constant, and was estimated based on the total pore volume from the gas adsorption measurements (see below). The size distributions of hard sphere pore radii/sizes RHS were calculated from the fits to the SAXS data using the Monte Carlo method in McSAS.