Form factor of cylindrical superstructures composed of globular particles

Abstract

The scattering form factor arising from N linearly 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 a q−1 regime at mid‐q (q is 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 at q≃ 2π/D (D being 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 that N is 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.

Structure and dynamics of polyelectrolyte surfactant mixtures under conditions of surfactant excess

“…A question that cannot be answered satisfactorily by SANS, is whether or not the micelles are attached to the PE. While at lower concentrations, the peak position is a reliable means to differentiate between free micelles and polymer surfactant mixtures with a pearl necklace structure, 19,65,66 this is not possible in more concentrated solutions such as those investigated here. At higher concentrations, the correlation FIG.…”

Structural control of polyelectrolyte/microemulsion droplet complexes (PEMECs) with different polyacrylates

“…The curves shown in Fig. 7A were described with cylindrical arrangements of 1.5, 3, 11 and 17 droplets per aggregate for M w s of the NaPA of 5.1, 15, 60 and 315 kDa, respectively 45. The model-results for the longest NaPA (315 kDa) are not reliable anymore but here a number of 16 droplets per aggregate can be obtained from the I (0) value of the scattering data.…”

“…SANS curves at z = 0.7 (Fig. 5A and further curves are shown in S6†) were described by a model of spheres arranged in a cylindrical domain as described in (ref. 45) (for further details also see the ESI†).…”

Effect of Polymer Architecture on the Phase Behavior and Structure of Polyelectrolyte/Microemulsion Complexes (PEMECs)

“…More analytical description of the scattering data was also made. As a first step, the data were described with a model of homogeneous cylinders, before a more sophisticated model of linearly arranged spheres 50 was attempted. However, both models showed substantial shortcomings in properly describing the scattering data (see SI F).…”