Small-angle scattering from polydisperse particles with a diffusive surface

Particles with a diffusive surface, characterized by a deviation from the Porod power-law asymptotic behavior in small-angle scattering towards an exponent below -4, are considered with respect to the polydispersity problem. The case of low diffusivity is emphasized, which allows the description of the scattering length density distribution within spherically isotropic particles in terms of a continuous profile. This significantly simplifies the analysis of the particle-size distribution function, as well as the change in the scattering invariants under contrast variation. The effect of the solvent scattering contribution on the apparent exponent value in power-law-type scattering and related restrictions in the analysis of the scattering curves are discussed. The principal features and possibilities of the developed approach are illustrated in the treatment of experimental small-angle neutron scattering data from liquid dispersions of detonation nanodiamond. The obtained scattering length density profile of the particles fits well with a transition of the diamond states of carbon inside the crystallites to graphite-like states at the surface, and it is possible to combine the diffusive properties of the surface with the experimental shift of the mean scattering length density of the particles compared with that of pure diamond. The moments of the particle-size distribution are derived and analyzed in terms of the lognormal approximation.