The isotropic-nematic interface of colloidal goethite in an external magnetic field.

Polarization microscopy was used to study the behavior around the isotropic-nematic interface of colloidal goethite dispersions in a magnetic field. It has been found before that the nematic phase is favored in an external field. In the case of goethite this was also observed; nematic droplets formed inside the isotropic phase and coalesced with the nematic phase. However, the behavior was found to be much richer because of the particle rotation around a certain critical field strength. The simultaneous occurrence of (parallel)nematic-(perpendicular)nematic phase separation under the influence of a magnetic field also plays a role here.

Experimental realization of biaxial liquid crystal phases in colloidal dispersions of boardlike particles.

Biaxial nematic and biaxial smectic phases were found in a colloidal model system of goethite (alpha-FeOOH) particles with a simple boardlike shape and short-range repulsive interaction. The macroscopic domains were oriented by a magnetic field and their structure was revealed by small angle x-ray scattering. In accordance with theoretical predictions, biaxiality appears in a system with particles that have a shape almost exactly in between rodlike and platelike. Our results suggest that biaxial phases can be readily obtained by a proper choice of the particle shape.

Influence of polydispersity on the phase behavior of colloidal goethite.

The effect of fractionation on the phase behavior of colloidal goethite dispersions with different polydispersities (17%, 35%, and 55% in length) has been studied by small angle x-ray scattering and transmission electron microscopy. All systems show at least nematic and smectic phases. The occurrence of the latter phase at such a high polydispersity is remarkable. It is shown that in the highly polydisperse systems strong fractionation occurs, which is able to reduce the local length polydispersity up to a factor of 2. A columnar phase was only found in the 35% and 55% polydisperse systems. It seems that the columnar phase accommodates the particles that do not fit into the smectic layers and, thus, reduces the length polydispersity within the smectic phase even further. The fact that a columnar phase was not found in the system of lowest polydispersity indicates that the smectic phase is the most stable phase at higher concentrations.

Influence of a magnetic field on the nematic phase of hard colloidal platelets.

We report on a study of the influence of a magnetic field on the nematic phase and the isotropic-to-nematic (IN) phase transition of hard colloidal gibbsite platelets. We find direct visual evidence of a shift of the IN transition to lower concentrations due to the magnetic field. The nematic phase readily aligns when contained between two parallel flat glass walls, with homeotropic orientation. This well-defined surface anchoring enables a measurement of the bend Frederiks transition, yielding the bend elastic constant of a nematic phase of hard disks as K(3) = 7 x 10(-14) N . By applying a rotating magnetic field on the nematic phase, we observe the bend-splay Frederiks transition, visible as a spatially periodic transient pattern with a wavelength that depends on sample thickness and field strength. Following a linear stability analysis we are able to account for this dependence in a qualitative way. Moreover, the rotating magnetic field enables us to render the nematic phase single domain, with well-defined director orientation.

Magnetic-field-induced orientational order in the isotropic phase of hard colloidal platelets.

The magnetic-field-induced orientational order in the isotropic phase of colloidal gibbsite [Al(OH)3] platelets is studied by means of optical birefringence and small-angle x-ray scattering (SAXS) techniques. The suspensions display field-induced ordering at moderate field strengths (a few Tesla), which increases with increasing particle concentration. The gibbsite particles align their normals perpendicular to the magnetic field and hence possess a negative anisotropy of their diamagnetic susceptibility Delta(chi). The results can be described following a simple, Onsager-like approach. A simplified model is derived that allows one to obtain the orientational distribution function directly from the scattering data. However, it leads to an underestimate of the diamagnetic susceptibility anisotropy Delta(chi). This accounts for the difference between the Delta(chi) values provided by the two experimental techniques (SAXS and magneto-optics). The order of magnitude Delta(chi) approximately 10(-22) J/T(2) lies in between that of goethite suspensions and that of suspensions of organic particles.

Nematic order of model goethite nanorods in a magnetic field.

We explore the nematic order of model goethite nanorods in an external magnetic field within Onsager-Parsons density functional theory. The goethite rods are represented by monodisperse, charged spherocylinders with a permanent magnetic moment along the rod main axis, forcing the particles to align parallel to the magnetic field at low field strength. The intrinsic diamagnetic susceptibility anisometry of the rods is negative, which leads to a preferred perpendicular orientation at higher field strength. It is shown that these competing effects may give rise to intricate phase behavior, including a pronounced stability of biaxial nematic order and the presence of reentrant phase transitions and demixing phenomena.

Preparation and properties of colloidal iron dispersions.

We systematically study the properties of dispersions of iron-based colloids synthesized in a broad size range by thermal decomposition of ironcarbonyl using different stabilizing surfactants. The synthesis results in stable dispersions of monodomain magnetic colloids. Our particles appear to consist of an amorphous Fe(0.75)C(0.25) alloy. Sizes of particles coated with modified polyisobutene or oleic acid can be easily controlled in the 2-10 nm range by varying the amounts of reactants. Extensive characterization with various techniques gives particle sizes that agree well with each other. In contrast to dispersions of small particles, which consist of single colloids, dynamic aggregates are present in dispersions of larger particles. On exposure to air, an oxide layer forms on the particle surface, consisting of a disordered Fe(III) oxide.

Phase equilibria in systems of hard disks with thickness polydispersity.

We study isotropic-nematic (I-N) phase equilibria in the Onsager (-Parsons) model for systems of hard colloidal disks allowing for arbitrary polydispersity in thickness. The phase behavior is investigated by analyzing the exact phase equilibrium equations for Gaussian orientational distribution functions. We observe a strong fractionation effect, with the thicker disks found preferentially in the isotropic phase. Due to this effect, the system may undergo an I-N density inversion indicating that the mass density of the isotropic phase becomes higher than that of the coexisting nematic phase. This phenomenon has been observed explicitly in experiment. We also encounter a divergence of the I-N coexistence region for Schulz-distributed parents with polydispersities larger than 46%. An implication of this phenomenon is that the system cannot become fully nematic at high densities but will continue to split off a small fraction of a dilute isotropic phase predominantly containing very thick species.

Biaxial versus uniaxial nematic stability in asymmetric rod-plate mixtures.

The isotropic-nematic phase behavior of a binary mixture of rodlike and platelike particles is studied within Onsager's second virial theory. The phase behavior is obtained from the numerically exact equilibrium orientational distribution functions for both uniaxial and biaxial nematic phases. Inspired by recent experimental work on these systems we concentrated on asymmetric mixtures in which the excluded volume between the plates v(pp)(ex) is larger than that between the rods v(rr)(ex). Starting from the symmetric case (v(pp)(ex)/v(rr)(ex)=1) and increasing the rod-plate excluded volume ratio we scrutinized the phase behavior, in particular focusing on the stability of the biaxial nematic phase. We observe that, at a certain asymmetry, the characteristic bicritical point is replaced by a two-phase region marking first order isotropic-biaxial transitions. Increasing the asymmetry even further leads to several demixing scenarios. First, there is a uniaxial-biaxial (N+-B) demixing scenario with an associated isotropic-uniaxial-biaxial (I-N+-B) triple equilibrium. Second, a uniaxial-uniaxial (N+-N-) demixing occurs in case of strongly asymmetric mixtures indicating that the biaxial nematic phase may become fully metastable. Since all predicted demixing scenarios lie in the experimentally accessible regime, there is a possibility of finding biaxial nematic structures in lyotropic colloidal rod-plate mixtures.

Destruction of long-range order recorded with in situ small-angle x-ray diffraction in drying colloidal crystals.

High-resolution synchrotron small-angle x-ray diffraction is applied to characterize the structure and long-range order in a sedimentary hard-sphere colloidal crystal before and during its drying. The principles of the technique and the influence of the coherence properties of the x-ray beam are discussed in detail. The capillary forces generated during the drying process are shown to destroy the long-range order and to break the crystal into smaller crystallites with slightly different orientations. The diffraction is shown to switch from the dynamic regime in the long-range-ordered crystal to nearly kinematic diffraction in the mosaic (short-range-ordered) crystal.

Liquid crystal phase transitions in suspensions of mineral colloids: new life from old roots.

A review is given of the field of mineral colloidal liquid crystals: liquid crystal phases formed by individual mineral particles within colloidal suspensions. Starting from their discovery in the 1920s, we discuss developments on the levels of both fundamentals and applications. We conclude by highlighting some promising results from recent years, which may point the way towards future developments.

Ageing in a system of polydisperse goethite boardlike particles showing rich phase behaviour.

Using microradian x-ray scattering and polarized light microscopy the rich liquid crystalline phase behaviour of a polydisperse system of chromium-modified goethite particles has been studied for five years. We observe that the particles stay highly mobile over years and the rich phase behaviour keeps developing in novel and even surprising ways. While in many other colloidal systems particle size polydispersity suppresses the formation of ordered phases, goethite particles form multiple coexisting ordered phases. The particle polydispersity problem is then solved by particle exchange between coexisting phases. One usually expects that a less ordered phase (e.g., nematic) is formed first while crystallization of the smectic and columnar crystals might take a longer time. For goethite particles we find the opposite, i.e. the nematic phase grows over years at the expense of a better ordered smectic phase. Moreover, SAXS patterns revealed peak splitting for both the smectic and the columnar phase, meaning that the system displays fractionated crystallization. We further discovered that the centred rectangular columnar phase spontaneously forms out of the simple rectangular columnar phase. The reverse transition is observed as well. We explain the ease of these martensitic transitions by showing how slight rotation and translation of the particles triggers the transition.

3D structure of nematic and columnar phases of hard colloidal platelets.

We present small angle x-ray scattering data of single-domain nematic and columnar liquid crystal phases in suspensions of sterically stabilized gibbsite platelets. The measurements are performed with different sample orientations to obtain information about the three-dimensional structure of the liquid crystalline phases. With the x-ray beam incident along the director of the nematic phase a strong correlation peak is observed corresponding to the side-to-side interparticle correlations, which suggests a columnar nematic structure. Upon sample rotation this side-to-side correlation peak of the nematic shifts to higher Q-values, suggesting the presence of strong fluctuations of small stacks of particles with different orientations, while the overall particle orientation is constant. In the hexagonal columnar phase, clear Bragg intercolumnar reflections are observed. Upon rotation, the Q-value of these reflections remains constant while their intensity monotonically decreases upon rotation. This indicates that the column orientation fluctuates together with the particle director in the columnar phase. This difference between the behaviour of the columnar and the nematic reflections upon sample rotation is used to assign the liquid crystal phase of a suspension consisting of larger platelets, where identification can be ambiguous due to resolution limitations.

Magnetic-field-induced nematic-nematic phase separation and droplet formation in colloidal goethite.

We demonstrate the suitability of polarization microscopy to study the recently discovered (parallel) nematic-(perpendicular) nematic phase separation. This novel type of phase transition is induced by applying an external magnetic field to a nematic liquid crystal of boardlike colloidal goethite and is due to an interplay between the intrinsic magnetic properties of goethite and the collective effect of liquid crystal formation. It is shown that the intense ochre colour of goethite does not preclude the use of polarization microscopy and interference colours, and that dichroism can give valuable qualitative information on the nature of the phases, their anchoring and their sedimentation and order parameter profiles. We also apply these techniques to study 'nematic-nematic tactoids': nematic droplets sedimenting within a nematic medium with mutually perpendicular orientations.

Evidence of the hexagonal columnar liquid-crystal phase of hard colloidal platelets by high-resolution SAXS.

We report Small-Angle X-ray Scattering (SAXS) measurements of the columnar phase of hard colloidal gibbsite platelets. We have been able to create large oriented domains of the columnar phase both perpendicular and parallel to the sample wall, varying the volume fraction of platelets and adding non-adsorbing polymer to the dispersion. In conjunction with the increased resolution of the SAXS setup, this allowed a detailed analysis of the columnar phase, providing unambiguous evidence for the hexagonal nature of the phase.

Observation of a hexatic columnar liquid crystal of polydisperse colloidal disks.

We report the observation of a new type of columnar liquid crystal phase, which is formed by thin hard colloidal disks in a dense suspension. High-resolution small-angle x-ray diffraction reveals a combination of long-range bond-orientational order and short-range translational order between the columns, the hallmark of the hexatic phase. Our results imply that geometric frustration related to the size polydispersity of the particles destroys long-range translational order and therefore promotes the formation of this novel phase.

Bragg rods and multiple X-ray scattering in random-stacking colloidal crystals.

Synchrotron small-angle x-ray diffraction images of random-stacking-induced Bragg scattering rods are obtained in a wide range of wave vectors from a single colloidal crystal. The results reveal a strong multiple scattering effect, which leads to new features in the diffraction pattern-secondary Bragg rods. We argue that dynamic x-ray diffraction is rather common for high-quality colloidal photonic crystals and should be taken into account.

Direct observation of dipolar chains in iron ferrofluids by cryogenic electron microscopy.

A key issue in research on ferrofluids (dispersions of magnetic colloids) is the effect of dipolar interactions on their structure and phase behaviour, which is not only important for practical applications but gives fundamental insight in dipolar fluids in general. In 1970, de Gennes and Pincus predicted a Van der Waals-like phase diagram and the presence of linear chains of particles in ferrofluids in zero magnetic field. Despite many experimental studies, no direct evidence of the existence of linear chains of dipoles has been reported in the absence of magnetic field, although simulations clearly show the presence of chain-like structures. Here, we show in situ linear dipolar structures in ferrofluids in zero field, visualized on the particle level by electron cryo-microscopy on thin, vitrified films of organic dispersions of monodisperse metallic iron particles. On systematically increasing the particle size, we find an abrupt transition from separate particles to randomly oriented linear aggregates and branched chains or networks. When vitrified in a permanent magnetic field, these chains align and form thick elongated structures, indicating lateral attraction between parallel dipole chains. These findings show that the experimental model used is well suited to study the structural properties of dipolar particle systems.

High-resolution small-angle x-ray diffraction study of long-range order in hard-sphere colloidal crystals.

The long-range order parameters in single crystals of hard colloidal spheres grown in sediments of colloid-polymer mixtures are determined using synchrotron small-angle x-ray diffraction with a resolution of 10(-6) of the wave vector. The interplanar positional order derived from the width of lattice reflections extends over at least 500 lattice planes. The lattice planes are orientationally correlated within approximately 0.1 degrees throughout the crystals, whereas the stacking of hexagonal planes remains random.