Phase separation in mixed suspensions of bacteria and nonadsorbing polymers.

The shapes of bacteria can vary widely; they may, for instance, be spherical, rod-like, string-like, or curved. In general, bacilli are highly anisotropic. For research and (bio)technological purposes, it can be useful to concentrate bacteria, which is possible by adding nonadsorbing polymers. The induced phase separation originates from a polymer-mediated depletion interaction, first understood by Asakura and Oosawa. Here, it is shown that free volume theory (FVT) can semi-quantitatively describe the phase transitions observed when adding sodium polystyrene sulfonate polymers to E. coli bacteria [Schwarz-Linek et al., Soft Matter 6, 4540 (2010)] at high ionic strength. The E. coli bacteria are described as short, hard spherocylinders. FVT predicts that the phase transitions of the mixtures result from a fluid-ABC crystal solid phase coexistence of a hard spherocylinder-polymer mixture.

Convectively Assembled Monolayers of Colloidal Cubes: Evidence of Optimal Packings.

We employ a system of cubic colloids with rounded corners to study the close-packed monolayers that form via convective assembly. We show that by controlled solvent evaporation large densely packed monolayers of colloidal cubes are obtained. Using scanning electron microscopy and particle-tracking algorithms, we investigate the local order in detail and show that the obtained monolayers possess their predicted close-packed optimal packings, the Λ0-lattice and the Λ1-lattice, as well as the simple square-lattice and disordered packings. We further show that shape details of the cube corners are important for the final packing symmetry, where the frequency of the Λ1-lattice increases with decreasing roundness of the corners, whereas the frequency of the Λ0-lattice is unaffected. The formation of both optimal packings is found to be a consequence of the out-of-equilibrium formation process, which leads to small shifts in rows of cubes, thereby transforming the Λ1-lattice into the Λ0-lattice.

Entropic patchiness drives multi-phase coexistence in discotic colloid-depletant mixtures.

Entropy-driven equilibrium phase behaviour of hard particle dispersions can be understood from excluded volume arguments only. While monodisperse hard spheres only exhibit a fluid-solid phase transition, anisotropic hard particles such as rods, discs, cuboids or boards exhibit various multi-phase equilibria. Ordering of such anisotropic particles increases the free volume entropy by reducing the excluded volume between them. The addition of depletants gives rise to an entropic patchiness represented by orientation-dependent attractions resulting in non-trivial phase behaviour. We show that free volume theory is a simple, generic and tractable framework that enables to incorporate these effects and rationalise various experimental findings. Plate-shaped particles constitute the main building blocks of clays, asphaltenes and chromonic liquid crystals that find widespread use in the food, cosmetics and oil industry. We demonstrate that mixtures of platelets and ideal depletants exhibit a strikingly rich phase behaviour containing several types of three-phase coexistence areas and even a quadruple region with four coexisting phases.

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.

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 effects on tactoids of plate-like colloids.

We investigate the effect of a magnetic field on the shape and director field of nematic droplets in dispersions of sterically stabilized and charge-stabilized colloidal gibbsite platelets with a negative diamagnetic anisotropy. Depending on the magnetic field strength and tactoid size, we observe with polarized light microscopy several interesting structures, with different shapes and director fields both with and without defects. In particular, our findings provide the first experimental evidence for the existence of the split-core defect structure predicted ten years ago by Mkaddem and Gartland [Phys. Rev. E 62, 6694 (2000)]. The split-core structure is a metastable director-field configuration that can be stabilized by a sufficiently strong externally applied magnetic field but only if the diamagnetic anisotropy of the particles is negative. To account for our observations, we present a calculation of the stability regions of different shapes and director-field structures as a function of tactoid size, anchoring conditions, surface tension, elastic constants, and magnetic field strength. By fitting the experimental data to the theoretically predicted structures, we are able to extract values for the splay elastic constant, interfacial tension, and anchoring strength. Remarkably, we find significant differences between the two systems studied: for sterically stabilized gibbsite in bromotoluene the anchoring strength is one order of magnitude larger than that of aqueous gibbsite, with the latter exhibiting weak and the former strong anchoring of the director field to the interface. The splay elastic constants that we obtain are in agreement with earlier experiments, simulations, and theory, while the interfacial tension and anchoring strength are considerably larger than what was found in earlier experiments.

Tactoids of plate-like particles: size, shape, and director field.

We studied, by means of polarized light microscopy, the shape and director field of nematic tactoids as a function of their size in dispersions of colloidal gibbsite platelets in polar and apolar solvents. Because of the homeotropic anchoring of the platelets to the interface, we found large tactoids to be spherical with a radial director field, whereas small tactoids turn out to have an oblate shape and a homogeneous director field, in accordance with theoretical predictions. The transition from a radial to a homogeneous director field seems to proceed via two different routes depending in our case on the solvent. In one route, the what presumably is a hedgehog point defect in the center of the tactoid transforms into a ring defect with a radius that presumably goes to infinity with decreasing drop size. In the other route, the hedgehog defect is displaced from the center to the edge of the tactoid, where it becomes virtual again going to infinity with decreasing drop size. Furthermore, quantitative analysis of the tactoid properties provides us with useful information on the ratio of the splay elastic constant and the anchoring strength and the ratio of the anchoring strength and the surface tension.

Thermal fluctuation forces and wetting layers in colloid-polymer mixtures: derivation of an interface potential.

We discuss wetting layers in phase-separated colloid-polymer mixtures adsorbed at a vertical wall, observed in recent laser scanning confocal microscopy experiments. Matching of colloid and solvent dielectric properties renders van der Waals forces negligible and provides a system governed by short-range forces and thermal fluctuations on which the subtle predictions of renormalization group (RG) theory for wetting can be tested. The width w of the fluid-fluid ("liquid-gas") interface bounding the wetting layer scales with the square root of the wetting layer thickness l, in qualitative agreement with RG theory for short-range complete wetting in three dimensions. The measured wetting layer thickness l as a function of the height h above the horizontal plane of bulk phase separation is compared with two distinct theoretical predictions. A simple heuristic interface potential V(l), first proposed in a previous report, is now fully derived, and confronted here with the interface potential based on the linear RG theory. The heuristic approach does not capture fully the RG treatment. While fundamental differences exist between the two approaches, the resulting predictions for l(h) are almost identical. However, the theory does not follow the precise shape of the experimental curve of l(h).

Experimental observation of fractionated crystallization in polydisperse platelike colloids.

We have discovered that the long-term aging of the hexagonal columnar liquid-crystal phase of polydisperse gibbsite platelets leads to fractionated crystallization, that is, to the formation of coexisting columnar crystals with different periods. This process was revealed by microradian X-ray diffraction demonstrating the splitting of the Bragg intercolumnar reflections into sequences of sharper reflections. The fractionated crystallization was observed in a number of samples of sterically stabilized as well as charge-stabilized polydisperse gibbsite platelets.

Liquid crystal phase transitions in systems of colloidal platelets with bimodal shape distribution.

We have studied a system of polydisperse, charged colloidal gibbsite platelets with a bimodal distribution in the particle aspect ratio. We observe a density inversion of the coexisting isotropic and nematic phases as well as a three-phase equilibrium involving a lower density nematic phase, an isotropic phase of intermediate density, and a higher density columnar phase. To relate these phenomena to the bimodality of the shape distribution, we have calculated the liquid crystal phase behavior of binary mixtures of thick and thin hard platelets for various thickness ratios. The predictions are based on the Onsager-Parsons theory for the isotropic-nematic (I-N) transition combined with a modified Lennard-Jones-Devonshire cell theory for the columnar (C) state. For sufficiently large thickness ratios, the phase diagram features an I-N density inversion and triphasic I-N-C equilibrium, in agreement with experiment. The density inversion can be attributed to a marked shape fractionation among the coexisting phases with the thick species accumulating in the isotropic phase. At high concentrations, the theory predicts a coexistence between two columnar phases with distinctly different concentrations. In experiment, however, the demixing transition is pre-empted by a transition to a kinetically arrested, glassy state with structural features resembling a columnar phase.

Devitrification of the glassy state in suspensions of charged platelets.

Colloidal suspensions of charged gibbsite platelets at salt concentrations of 10(-2) M and below and with a sufficiently high particle concentration form a kinetically arrested, glassy state. We study the evolution of the glassy state in suspensions of three different gibbsite systems. Despite differences in size and polydispersity, we observe small, iridescent grains of the hexagonal columnar phase, for all these systems after periods of months to years. The connections between this devitrification phenomenon and the structure of the glassy state are discussed.

Statistics of fluctuating colloidal fluid-fluid interfaces.

Fluctuations of the interface between coexisting colloidal fluid phases have been measured with confocal microscopy. Due to a very low surface tension, the thermal motions of the interface are so slow that a record can be made of the positions of the interface. The theory of the interfacial height fluctuations is developed. For a host of correlation functions, the experimental data are compared with the theoretical expressions. The agreement between theory and experiment is remarkably good.

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.

Fluctuation forces and wetting layers in colloid-polymer mixtures.

We present confocal microscopy experiments on the wetting of phase-separated colloid-polymer mixtures. We observe that an unusually thick wetting layer of the colloid-rich phase forms at the walls of the glass container that holds the mixture. Because of the ultralow interfacial tension between the colloid-rich and the polymer-rich phases, the thermally activated roughness of the interfaces becomes very big and measurable. We observe that close to the critical point the roughness of the interface between the wetting layer and the polymer-rich phase decreases with decreasing layer thickness: large excursions of the interface are confined in the wetting layer. The measured relationship between the roughness and the thickness of the wetting layer is in qualitative agreement with the predictions of renormalization group theory for short-range forces and complete wetting.

Orientation dependent Stokes drag in a colloidal liquid crystal.

Stokes drag on the (sub)micrometre scale plays a key role in phenomena ranging from Brownian motion to the rheology of particulate suspensions. We report the first measurement of the direction dependent Stokes drag in a nematic liquid crystal of colloidal rods, where the viscous forces are of equal importance to the elastic forces. By tracking a sedimenting sphere with combined fluorescence confocal microscopy and polarization microscopy we find that the Stokes drag for motion along the director is two times larger than for motion perpendicular to the director. This brings the unique viscoelastic properties of a colloidal liquid crystal into focus.

Gelation versus liquid crystal phase transitions in suspensions of plate-like particles.

Gelation is a common effect in aqueous suspensions of charged colloidal clay platelets at concentrations as low as 1 wt%. However, in systems of charged gibbsite [Al(OH)3] platelets, gelation can be delayed to concentrations as high as 50 wt% depending on the ionic strength. We investigated the phase behaviour of this system approaching the state of gelation in the delicate region between attractive and repulsive states that originate from competition between Coulomb repulsion and van der Waals attraction. As a function of the ionic strength, isotropic-nematic, nematic-columnar and isotropic-columnar phase separations were observed. Moreover, compression by gravitational forces allowed us to observe phase separation that is arrested by gelation in the homogeneous suspensions.

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.

Drop formation by thermal fluctuations at an ultralow surface tension.

We present experimental evidence that drop breakup is caused by thermal noise in a system with a surface tension that is more than 10(6) times smaller than that of water. We observe that at very small scales classical hydrodynamics breaks down and the characteristic signatures of pinch-off due to thermal noise are observed. Surprisingly, the noise makes the drop size distribution more uniform, by suppressing the formation of satellite droplets of the smallest sizes. The crossover between deterministic hydrodynamic motion and stochastic thermally driven motion has repercussions for our understanding of small-scale hydrodynamics, important in many problems such as micro- or nanofluidics and interfacial singularities.

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.

Crystallization in settling mixtures of colloidal spheres and plates.

The behavior of mixtures of silica spheres and smaller silica-coated gibbsite plates is studied by means of confocal microscopy. Addition of plates slows down the crystallization of the settling spheres. Liquidlike microphases of the plates are found in the sediments of the spheres. It is argued that this is due to simultaneous sedimentation of the plates and spheres as well as depletion interaction between both species. Typical length scales in the sediments, derived from Fourier transforms of the confocal images, suggest there are still specific interactions present.