The indirect Fourier transformation (IFT) is the method of choice for the model-free evaluation of small-angle scattering data. Unfortunately, this technique is only useful for dilute solutions because, for higher concentrations, particle interactions can no longer be neglected. Thus an advanced technique was developed as a generalized version, the so-called generalized indirect Fourier transformation (GIFT). It is based on the simultaneous determination of the form factor, representing the intraparticle contributions, and the structure factor, describing the interparticle contributions. The former can be determined absolutely free from model assumptions, whereas the latter has to be calculated according to an adequate model. In this paper, various models for the structure factor are compared, e.g. the effective structure factor for polydisperse hard spheres, the averaged structure factor, the local monodisperse approximation and the decoupling approximation. Furthermore, the structure factor for polydisperse rodlike particles is presented. As the model-free evaluation of small-angle scattering data is an essential point of the GIFT technique, the use of a structure factor without any in¯uence of the form amplitude is advisable, at least during the ®rst evaluation procedure. Therefore, a series of simulations are performed to check the possibility of the representation of various structure factors (such as the effective structure factor for hard spheres or the structure factor for rod-like particles) by the less exact but much simpler averaged structure factor. In all the observed cases, it was possible to recover the exact form factor with a free determined parameter set for the structure factor. The resulting parameters of the averaged structure factor have to be understood as apparent model parameters and therefore have only limited physical relevance. Thus the GIFT represents a technique for the model independent evaluation of scattering data with a minimum of a priori information.
Suspensions of charged rod-like particles are investigated theoretically in a concentration regime where the mean distance between rods is comparable to their length, L. The structure of these systems is studied by Monte Carlo simulations and a perturbation theoretical scheme. Results for the pair distribution function g( 12) are obtained, which show the onset of angular correlations at the cross-over concentration c* = L-3. Above c* there is a tendency for local alignments of neighbouring rods, although the systems remain globally isotropic up to c = 4c*, which is the highest concentration investigated. As a consequence, the peak position k,,, of the structure factor ~( k ) scales as k,,,cl/* for c > c* in contrast to the c " ~ behaviour for c < c*, where the rods behave as spherical particles. The time-correlation function of quasielastic scattering experiments is derived from a dynamical mean field theory. From it the collective diffusion coefficient and the first cumulant are obtained. The influence of the interaction between rods and of the coupling of translational and rotational diffusion are discussed.
The electrical and optical properties of rodlike fd-virus particles (L = 880 nm, D = 9 nm) are investigated by magnetic and electric birefringence experiments and supplemented by electric field light-scattering measurements. In aqueous suspension the fd-virus particles are negatively charged and surrounded by diffuse counterion clouds. The examinations are performed at very low ionic strength (10"6 M). Under these conditions a liquid crystalline phase already occurs at fd-particle concentrations above 0.6 mg/mL. In magnetic fields the rodlike fd-virus is aligned parallel to the magnetic field due to its diamagnetic anisotropy. Almost complete particle alignment in magnetic fields is obtained for liquid crystalline samples, and the saturation value of the birefringence is determined. The application of electric fields results in a polarization of the counterion clouds and a statistical orientation of the dispersed particles. In low electric fields Kerr behavior is found, providing the electric anisotropy Aotet of a single rod. At higher electric fields the diffuse Debye cloud is partly stripped away and a complete particle orientation is hindered. Electric field light-scattering investigations yield quantitatively the decrease of the electric anisotropy Aoiei in high electric fields.
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