“…In particular, the nanoparticle core has a low-density matrix, while the mixing area between the charged groups, localized at the nanoparticle surface, is characterized by high density. In other words, the delocalization of charged groups, i.e., the diffusion of sulfonate acids occurred upon mixing surface-near polymer chains on the microspheres during film formation. ,, In order to calculate the interfacial thickness according to Ruland’s theory for two-phase materials with diffuse boundaries, the electron-density variation of the pseudo-two-phase system along the normal, η( z ), is followed by a convolution product of a step function, g ( z ), and a Gaussian smoothing function, h ( z ) as follows: In this study, the background scattering arising from the thermal density fluctuation from the total scattered intensity was subtracted from the SAXS intensity, I ( q ), by assuming that the background scattering is given by a straight line, which is the intensity of the highest observed q values (0.09 Å –1 ). It should be noted here that this is purely an empirical procedure and that there is also a way to subtract a curved background scattering.…”