Form factor of cylindrical superstructures composed of globular particles

Abstract

The scattering form factor arising fromNlinearly aligned particles, thereby forming a cylindrical superstructure and potentially contained within a cylindrical cage, has been derived. The principal features of the scattering curves are aq−1regime at mid-q(qis the magnitude of the scattering vector) due to the linear long-range order of the particles and, arising from the repetition of the building blocks, a correlation peak atq≃ 2π/D(Dbeing the center-to-center distance between the particles). In order to be able to describe real systems also, as they might arise in electrostatically assembled arrays, the effect of polydispersity of particle size and spacing has been evaluated. Finally, the model of aligned particles contained in a cylinder was applied to polyelectrolyte–surfactant complexes. It is shown that, provided thatNis sufficiently large, the scattering arising from aligned particles is clearly distinguishable from that of a homogeneous cylinder and therefore the presence of single particles within the complex can be demonstrated. The precise shape of the scattering curves then depends markedly on the contrast conditions between the contained particles, the cylindrical cage and the surrounding medium.