In this paper two kinds of Bragg reflections from oriented mesogenic crystals are considered. Bragg reflections behave differently for ...ABABA... and ...ABCABCA... layer stacking. We call them black and white reflections. Black reflections are characterized by the fact that they behave identical for the two kinds of stacking. Therefore, the message is the following: Black rods should not be used to identify the two kinds of stacking. By contrast, white reflections show a different behavior for ...ABABA... and ...ABCABCA... stacking and for the resulting hexagonal close-packed (hcp) and face-centered cubic (fcc) crystals. White reflections can be used to distinguish the two kinds of crystals. For an application of this method the crystals should be oriented. It will be shown that orienting by flow is possible in a Couette cell. Flow ordering occurs in all rotation cells which are often applied in rheology. The scattering presented is therefore closely related to rheology. Details and experimental results will be given in the paper.

Rheology is commonly used as a tool for analytics and quality control in latex technology. As soon as flow becomes essential for the structure measured in a scattering experiment we call it scattering from shear-ordered dispersions or rheologic scattering. In this paper it is shown that the structure of concentrated dispersions can with advantage be studied by scattering experiments. Theoretical and experimental aspects as well as examples of small-angle synchrotron x-ray and neutron scattering from colloidal dispersions, presented in the paper, are closely related to rheology.

In this paper, the ordering in concentrated charge stabilized colloidal dispersions is considered. Despite the impressive Bragg reflections obtained for shear ordered dispersions by light (LS), small-angle neutron (SANS), and small-angle X-ray scattering (SAXS), a number of open questions remain. Sheared dispersions are usually ordered in layers. For such systems, two questions arise: (1) What is the structure in a layer? (2) What is the stacking structure perpendicular to the layers? The second question requires a method to determine the structure perpendicular to the layers. Although originally interested only in structural aspects, we were forced to consider different methods. Two methods are treated both applicable to neutron and X-ray scattering from concentrated dispersions. One has been used by physicists and chemists for many years to determine the structure of crystals by sample rotation. In colloid science, we have used it previously in neutron and X-ray scattering. A second method is treated here which can be applied in small-angle scattering from a Couette cell. It gives the scattering intensity in a certain direction without sample rotation. Although very useful with the Couette cell, it cannot be found in any of the well-known references on colloid science. A theoretical explanation and experimental examples obtained by synchrotron X-ray scattering from a Couette cell are given in the paper.

In this contribution we investigate whether the structure of concentrated shear-ordered dispersions as determined by small angle synchrotron x-ray or neutron scattering can be rationalized in terms of viscoelastic flow behavior as in rheological investigations. Although so far scattering experiments have contributed little to the understanding of rheological systems we are convinced that rheological investigations will profit considerably from a better knowledge of the micro-structure of the dispersions. Sheared dispersions are usually ordered in layers. There are two kinds of ordering of interest: (a) The structure in a layer (b) The structure between the layers. One interesting point of mesogenic systems is their viscoelastic nature. There is strong evidence that the structure in a layer (a) can be treated as elastic or solid-like, whereas the structure (b) between the layers seems to be fluid-like. With scattering experiments one is in the excellent position that two experiments exist with which the two effects can be investigated separately: The solid-like microstructure (a) can be determined at perpendicular incidence. The fluid-like microstructure (b) is given by the scattering intensity along certain Bragg rods (3n+/-1-rods). In particular this second micro-structure may change in time by aging.

In this contribution small-angle scattering from layered systems is considered. When a colloidal dispersion is stirred it usually decomposes into layers. There are two important questions concerning these layers: What is the structure in a layer? What is the stacking structure between such layers? For concentrated colloidal dispersions both these questions can be investigated by small-angle scattering experiments. It will become apparent that the answer is also important for technical applications. Both a theoretical description as well as an experimental verification are given in the paper.

Although rheology as well as neutron and x-ray scattering studies of ordered dispersions have been performed no coherent picture is discussable. In this paper we report our synchrotron x-ray and neutron scattering data of concentrated, charge stabilized, monodisperse polymer colloids and compare them with rheological data. We found that the scattering data can be understood in terms of viscoelastic flow. When ordered by flow-, solid- and liquid-like behavior can be separated with two independent experiments: (a) The solid-like character can be seen at perpendicular incidence as Bragg reflections, (b) the liquid-like character becomes apparent by sample rotation as the intensity distribution along Bragg rods.

The present paper is concerned with the structure of dispersions made from charged polymer particles. First, the determination of important properties of single particles is discussed. It follows a typical phase diagram of charge stabilized dispersions. Their structure and possibilities to manipulate the structure are considered in the following sections. For the understanding of scattering experiments, as light scattering (LS), small angle neutron (SANS) and small angle synchrotron x-ray scattering (SAXS) the reciprocal lattice is of fundamental importance. A separate chapter, therefore, is dedicated to it.The application of shear has been found to be a particularly successful method for manipulating the structure of dispersions. It is possible to generate one-dimensional (1D) strings as well as plane (2D) layers which become (3D) crystals with time. The phenomena and structures generated by shear are in part surprising and at present not fully understood. (C) 2002 Elsevier Science B.V. All rights reserved.

The influence of shear on the Bragg scattering of concentrated colloidal dispersions made from charged particles is considered in this paper. First, the reciprocal space of a layered sample at rest and under the influence of a disordering torque is considered. Next, the commonly used Couette cell and our disk shear cell are compared in view of the Ewald construction. An introduction of alpha- and beta -rotation axes follows. The first experimental example is concerned with the neutron scattering from a layered colloidal sample at rest. As a second experimental example from the same sample the dependence of synchrotron X-ray scattering on the shear rate is considered. It turns out that the sample does not achieve a microcrystalline state as claimed previously but remains in an orientationally disordered layered state. Finally, the intensity distribution I(l) along the two types of Bragg rods as obtained with remarkable precision by synchrotron X-ray scattering is presented.

The present paper is concerned with the structure of colloidal dispersions consisting of charged polymer particles. The scattering of light, neutrons or X-rays from such latex dispersions is best described in the reciprocal lattice. Two quantities of central importance will be introduced: the particle form factor P(Q) and the interparticle structure factor S(Q). In the present treatment we show that the structure can be adequately accounted for by introducing a redefined symmetry adapted aggregate structure factor. According to the structure of interest these aggregate structure factors are one-dimensional (string-like), two-dimensional (layer-like) or three-dimensional (crystal-like). The description appears particularly suited to account for systems under sheared conditions. In the final section we present experimental neutron scattering results. A structural change is observed as a function of the shear rate γ°. The occurrence of the structural change and its relation to the 'self´ part of the previously introduced aggregate structure factor are considered.

In this paper we present small-angle neutron scattering (SANS) studies on liquidlike ordered binary colloidal suspensions. Using perfluorinated (sigma(PFA) = 162 nm) and polystyrene (sigma(PS) = 79 nm) particles, we prepared samples made of the same colloids as in the preceding paper. All system parameters of the mixtures were as before. Via neutron contrast variation we directly obtained all three partial intensities I(PFA-PFA)(Q), I(PFA-PS)(Q), and I(PS-PS)(Q) and partial structure factors S(PFA-PFA)(Q), S(PFA-PS)(Q), and SPS-PS(Q) The experimental results are compared with theoretical predictions for binary colloidal mixtures, based on the pure repulsive part of the DLVO potential. Within the hypernetted chain (HNC) closure an accurate agreement is achieved. The particle correlation in the mixtures is clarified by means of the partial distribution functions g(ij)(r) and the one-component effective pair potentials U(PFA-PFA)(eff)(r) and U(PS-PS)(eff)(r). From this we deduce for the examined suspensions a partial clustering or local demixing by attractive interaction contributions of depletion origin.

Electrostatically stabilized diluted suspensions of negatively-charged poly(p-bromostyrene) particles have been studied by ultra small angle X-ray scattering (USAXS) and simultaneous osmotic pressure measurements. We investigated the structure and the interparticle interactions as a function of the crystal stiffness controlled by the salinity. By adding monovalent salt (NaCl) or multivalent +1/−5 salt (polyd(T)5), we reduced electrostatic repulsions and finally induced fusion of the colloidal crystal. The osmotic pressure drops and the crystal melts when the salt concentration in the reservoir is higher than 2.10−4 M for NaCl. In the case of a multivalent co-ion, 3.10−3 M polyd(T)5 is enough to reduce the osmotic pressure to zero. Thus, an experimental determination of the pressure versus distance relation allows the detection of less than micromolar amounts of multicharged co-ions. Surprisingly, the Poisson–Boltzmann cell model remains valid even when only a few screening co-ions are present in each unit cell of the colloidal crystal. By calculating the mean square displacement of a particle inside the cage made of nearest neighbours from the eccentric Poisson–Boltzmann Cell model, we have verified that the Lindemann criterion for the crystal–liquid transition is satisfied when the crystal melts due to the addition of monovalent salt.

In this paper, scattering from Bragg rods is considered. For layered colloidal structures, the intensity along Bragg rods reflects the stacking order of the layers. It is described how the small angle neutron (SANS) scattering intensity can be used to characterize layered systems. Scattering examples are presented for colloidal layers at rest and under sheared (flowing) conditions.

Dynamic light scattering experiments are reported on crystal-like ordered colloidal suspensions composed of two types of electrostatically interacting particles having similar size and effective particle charge. The particles differ only in their refractive indices. We obtain the incoherent (self) intermediate scattering function of these mixtures by using only a trace concentration of one of the species and matching the refractive index of the suspending liquid medium to that of the other. Localization of the tracer particles about randomly located lattice sites of the colloidal crystal is manifested in the nonergodicity of the incoherent intermediate scattering functions. The latter, and the particle mean-squared displacements obtained from them, plateau to finite values at long times. In analogy to neutron scattering these plateau values of the incoherent intermediate scattering functions may be called the elastic incoherent structure factor.

In this and the following paper we present scattering studies on binary colloidal mixtures made of charge-stabilized polystyrene (PS) and perfluorinated (PFA) particles with diameters sigma=79 and 162 nm, respectively. Both colloidal species were mixed to well-defined compositions. The total concentration was about 9 vol % fraction. By using ultra-small-angle X-ray scattering, we directly obtained the partial scattering intensities of only the PFA particles in liquidlike ordered suspensions. Furthermore, after dividing intensities by the PFA particle form factor P(PFA)(Q), We got the partial structure factor S(PFA-PFA)(Q) Without any additional treatment. The experimental results are compared with theoretical predictions obtained from the pure repulsive DLVO potentials and the hypernetted chain (HNC) integral equation, as applied to charged colloidal mixtures. It is shown that all measured intensities and extracted structure factors are in good agreement with the theoretical results.

A study is reported on the final stage of sedimentation of colloidal particles using Brownian dynamics simulation. For mono- and bidisperse systems at two different densities confined between two walls there was pronounced layering and a wealth of different states of order which were strongly height dependent. Also, phase separation in the bidisperse models could occur. In each system the layers were investigated individually by defining planar observables and comparing them with a dynamic freezing criterion.

Kossel rings of colloidal dispersions obtained with colloids at rest and under flowing conditions are described. When flowing only Kossel rings of planes with a component in the direction of the flow do not vanish. Compared with the dispersion at rest the number of Kossel rings of the dispersions under flow is reduced. Experimental examples are presented.

Neutron diffraction from charge stabilized shear ordered colloidal dispersions at rest and under sheared conditions are presented. A newly designed shear cell is used to generate a linear shear profile. Hexagonal scattering patterns were observed both at rest and under sheared conditions. The stacking probability A is determined by measuring the intensity dependence of the Bragg spots as a function of the angle between the incoming neutron beam and the sample cell. The shear experiments are discussed in terms of a continuous distortion [W. Loose and B. J. Ackerson, J. Chem. Phys. 101, 7211 (1994)] at small shear rates, and shear melting at higher shear rates.