Multiple small-angle scattering—A review

Small-angle scattering (SAS) is a powerful experimental technique in condensed matter physics for studying structural features of inhomogeneities of colloidal dimensions. So far the technique has been largely exploited to study thin samples for which the single scattering approximation, for the radiation-matrix interaction, holds good. The single scattering approximation is invalid when the thickness of the sample exceeds the scattering mean free path. This situation calls for a guideline to analyse the scattering data having significant contribution from multiple scattering. Since multiple scattering broadens the scattering profile, the beam broadening nature of multiple scattering can also be exploited, by making the sample suitably thick, to study large size inhomogeneities which are otherwise inaccessible to a small-angle scattering set up because of its resolution constraints. The present article presents a review and extension of the theoretical basis for analysing multiple scattering data from the point of view of a recent formalism on multiple small-angle scattering. The formalism is valid for both monodisperse and polydisperse scattering media characterized by the presence of large size inhomogeneities in the matrix. It is shown that multiple scattering from a polydisperse sample can be described by a system of coupled integrodifferential equation. However, multiple scattering from a monodisperse sample can be described by a Fokker-Planck type of equation. These equations have been analysed with an emphasis laid on the nature of the structural information pertaining to the inhomogeneities which is extractable from the multiple scattering profile. When the linear dimension of inhomogeneities becomes comparable to the scattering mean free path of the radiation in the sample, the statistical nature of the medium becomes pronounced. The statistical nature of the medium modulates the scattering profile. The modulation effect could be broadening or narrowing of the profile depending upon the nature of the inhomogeneities and their population distribution. The limiting regimes of validity and the implications of various approximations, frequently used to analyse the scattering data, have been indicated.