Observation of a hexatic columnar liquid crystal of polydisperse colloidal disks

Sedimentation path theory for mass-polydisperse colloidal systems

Both polydispersity and the presence of a gravitational field are inherent to essentially any colloidal experiment. While several theoretical works have focused on the effect of polydispersity on the bulk phase behavior of a colloidal system, little is known about the effect of a gravitational field on a polydisperse colloidal suspension. We extend here the sedimentation path theory to study sedimentation-diffusion-equilibrium of a mass-polydisperse colloidal system: the particles possess different buoyant masses but they are otherwise identical. The model helps to understand the interplay between gravity and polydispersity on sedimentation experiments. Since the theory can be applied to any parent distribution of buoyant masses, it can also be used to study the sedimentation of monodisperse colloidal systems. We find that mass-polydispersity has a strong influence in colloidal systems near density matching for which the bare density of the colloidal particles equals the solvent density. To illustrate the theory, we study crystallization in sedimentation-diffusion-equilibrium of a suspension of mass-polydisperse hard spheres.

Angular structure factor of the hexatic-B liquid crystals: bridging theory and experiment

We report results of X-ray scattering studies of the angular structure factor of liquid crystal hexatic-B films. According to the sixfold rotational symmetry of the hexatic-B phase, its characteristic scattering splits into six reflections. The shape of the radial and angular cross-sections of these reflections and their temperature evolution are analyzed. We find that over a wide temperature range of the hexatic-B phase existence the angular profiles of the in-plane X-ray scattering are well fitted by the Voigt function, which is a convolution of the Gaussian and Lorentzian functions. This result is supported by the known theoretical considerations of the hexatic structure factor below the smectic-hexatic phase transition temperature. Similar predictions for the angular shape of the hexatic peak in the vicinity of the smectic-hexatic phase transition temperature follow from the multicritical scaling theory of the hexatic-B phase in three dimensions. We find that the specific shape of the hexatic structure factor can be explained by the interplay of two distinct contributions to the free energy of the system, a liquid-like density term and a coupling term between the bond-orientational order and short-range density fluctuations.

Hierarchical self-assembly of 3D lattices from polydisperse anisometric colloids

Colloids are mainly divided into two types defined by size. Micron-scale colloids are widely used as model systems to study phase transitions, while nanoparticles have physicochemical properties unique to their size. Here we study a promising yet underexplored third type: anisometric colloids, which integrate micrometer and nanometer dimensions into the same particle. We show that our prototypical system of anisometric silver plates with a high polydispersity assemble, unexpectedly, into an ordered, three-dimensional lattice. Real-time imaging and interaction modeling elucidate the crucial role of anisometry, which directs hierarchical assembly into secondary building blocks-columns-which are sufficiently monodisperse for further ordering. Ionic strength and plate tip morphology control the shape of the columns, and therefore the final lattice structures (hexagonal versus honeycomb). Our joint experiment-modeling study demonstrates potentials of encoding unconventional assembly in anisometric colloids, which can likely introduce properties and phase behaviors inaccessible to micron- or nanometer-scale colloids.

Direct Liquid to Crystal Transition in a Quasi-Two-Dimensional Colloidal Membrane

Using synchrotron-based small-angle X-ray scattering, we study rigid fd viruses assembled into isolated monolayers from mixtures with a nonabsorbing polymer, which acts as an osmotic agent. As the polymer concentration increases, we observe a direct liquid to crystal transition, without an intermediate hexatic phase, in contrast with many other similar systems, such as concentrated DNA phases or packings of surfactant micelles. We tentatively attribute this effect to the difference in stiffness. The liquid phase can be well described by a hard-disk fluid, while we model the crystalline one as a hexagonal harmonic lattice and we evaluate its elastic constants.

Role of length polydispersity in the phase behavior of freely rotating hard-rectangle fluids

We use the density-functional formalism, in particular the scaled-particle theory, applied to a length-polydisperse hard-rectangle fluid to study its phase behavior as a function of the mean particle aspect ratio κ_{0} and polydispersity Δ_{0}. The numerical solutions of the coexistence equations are calculated by transforming the original problem with infinite degrees of freedoms to a finite set of equations for the amplitudes of the Fourier expansion of the moments of the density profiles. We divide the study into two parts. The first one is devoted to the calculation of the phase diagrams in the packing fraction η_{0}-κ_{0} plane for a fixed Δ_{0} and selecting parent distribution functions with exponential (the Schulz distribution) or Gaussian decays. In the second part we study the phase behavior in the η_{0}-Δ_{0} plane for fixed κ_{0} while Δ_{0} is changed. We characterize in detail the orientational ordering of particles and the fractionation of different species between the coexisting phases. Also we study the character (second vs first order) of the isotropic-nematic phase transition as a function of polydispersity. We particularly focus on the stability of the tetratic phase as a function of κ_{0} and Δ_{0}. The isotropic-nematic transition becomes strongly of first order when polydispersity is increased: The coexistence gap widens and the location of the tricritical point moves to higher values of κ_{0} while the tetratic phase is slightly destabilized with respect to the nematic one. The results obtained here can be tested in experiments on shaken monolayers of granular rods.

Observation of the Chiral and Achiral Hexatic Phases of Self-assembled Micellar polymers

We report the discovery of a thermodynamically stable line hexatic (N + 6) phase in a three-dimensional (3D) system made up of self-assembled polymer-like micelles of amphiphilic molecules. The experimentally observed phase transition sequence nematic (N)  N + 6  two-dimensional hexagonal (2D-H) is in good agreement with the theoretical predictions. Further, the present study also brings to light the effect of chirality on the N + 6 phase. In the chiral N + 6 phase the bond-orientational order within each "polymer" bundle is found to be twisted about an axis parallel to the average polymer direction. This structure is consistent with the theoretically envisaged Moiré state, thereby providing the first experimental demonstration of the Moiré structure. In addition to confirming the predictions of fundamental theories of two-dimensional melting, these results are relevant in a variety of situations in chemistry, physics and biology, where parallel packing of polymer-like objects are encountered.

Grain-boundary-induced melting in quenched polycrystalline monolayers

Melting in two dimensions can successfully be explained with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario which describes the formation of the high-symmetry phase with the thermal activation of topological defects within an (ideally) infinite monodomain. With all state variables being well defined, it should hold also as freezing scenario where oppositely charged topological defects annihilate. The Kibble-Zurek mechanism, on the other hand, shows that spontaneous symmetry breaking alongside a continuous phase transition cannot support an infinite monodomain but leads to polycrystallinity. For any nonzero cooling rate, critical fluctuations will be frozen out in the vicinity of the transition temperature. This leads to domains with different director of the broken symmetry, separated by a defect structure, e.g., grain boundaries in crystalline systems. After instantaneously quenching a colloidal monolayer from a polycrystalline to the isotropic fluid state, we show that such grain boundaries increase the probability for the formation of dislocations. In addition, we determine the temporal decay of defect core energies during the first few Brownian times after the quench. Despite the fact that the KTHNY scenario describes a continuous phase transition and phase equilibrium does not exist, melting in polycrystalline samples starts at grain boundaries similar to first-order phase transitions.

In Situ Synthesis of Catalytic Active Au Nanoparticles onto Gibbsite-Polydopamine Core-Shell Nanoplates

We report a facile method to synthesize anisotropic platelike gibbsite-polymer core-shell particles. Dopamine is self-polymerized on the surface of gibbsite nanoplates and forms a homogeneous layer on it. Transmission electron microscopy characterization of the resulting latexes demonstrates the formation of well-defined platelike core-shell particles. Reaction time and ultrasonification are found to be important factors to control the thickness of the polymer shell and avoid aggregation. Good control over the platelike morphology and 100% encapsulation efficiency have been achieved via this novel route. The resulting well-defined gibbsite-polydamine (G-PDA) core-shell nanoplates show excellent colloidal stability and can form opal-like columnar crystal with iridescent Bragg reflection after modest centrifugation. In addition, G-PDA core-shell nanoplates can serve both as reductant and stabilizer for the generation of Au nanoparticles (NPs) in situ. Au NPs with tunable size have been formed on the G-PDA particle surface, which show efficient catalytic activity for the reduction of 4-nitrophenol and Rhodamine B (RhB) in the presence of borohydride. Such nanocatalysts can be easily deposited on silicon substrate by spin-coating due to the large contact area of platelike G-PDA particles and the strong adhesive behavior of the PDA layer. The substrate-deposited nanocatalyst can be easily recycled which show excellent reusability for the reduction of RhB.

Specific heat in two-dimensional melting

We report the specific heat cN around the melting transition(s) of micrometer-sized superparamagnetic particles confined in two dimensions, calculated from fluctuations of positions and internal energy, and corresponding Monte Carlo simulations. Since colloidal systems provide single particle resolution, they offer the unique possibility to compare the experimental temperatures of the peak position of cN(T) and symmetry breaking, respectively. While order parameter correlation functions confirm the Kosterlitz-Thouless-Halperin-Nelson-Young melting scenario where translational and orientational order symmetries are broken at different temperatures with an intermediate so called hexatic phase, we observe a single peak of the specific heat within the hexatic phase, with excellent agreement between experiment and simulation. Thus, the peak is not associated with broken symmetries but can be explained with the total defect density, which correlates with the maximum increase of isolated dislocations. The absence of a latent heat strongly supports the continuous character of both transitions.

Influence of particle size and tunable interactions on isotropic-nematic transition of block copolymer single crystal platelet suspensions

We have studied the influence of the particle size and the tunable lateral interactions on the isotropic-nematic (I-N) phase transition of a plate-like colloidal system. The particles are single crystals of a block copolymer PS-b-PLLA (BCSC) prepared using a self-seeding procedure. These lozenge shape crystals have a uniform thickness and a narrowly distributed lateral size. The equilibrium phase behavior and I-N phase transition have been characterized using crossed polarizers at the room temperature. A nematic phase exists for all systems with size ranging from 700 to 4000 nm. For smaller crystals (<1200 nm), the I-N phase transition follows a process of slow sedimentation and subsequent macroscopic phase separation, resulting in a highly oriented nematic phase with a sharp I-N interface. For larger crystals (≥1200 nm), the I-N phase transition follows a process of nucleation and subsequent sedimentation, resulting in a random orientation of crystals in the nematic phase and a rough I-N interface. The I-N transition occurs at a very low volume fraction (<0.2%) for all systems, which is at least one order of magnitude lower than the theoretical prediction (2-7%). However, addition of a small amount of ethanol into the solution, the I-N transition can be significantly suppressed. These results demonstrate the existence of a lateral attraction between crystals, which is due to the polar attraction between the uncovered PLLA crystalline domains. Polar ethanol molecules can adsorb to the PLLA crystalline surface and screen the attraction. The attraction exhibits highly orientation-dependent. To further demonstrate this highly directional attraction, we have prepared two composite single crystal suspensions with PLLA homopolymer, which have a much wider open angle for the polar attraction. Indeed, the resulting liquid crystalline phases show much less horizontal ordering.

Electrostatically driven interactions between hybrid DNA-carbon nanotubes

Single-stranded DNA is able to wrap around single-wall carbon nanotubes (CNT) and form stable DNA-CNT hybrids that are highly soluble in solution. Here we report quantitative measurements and analysis of the interactions between DNA-CNT hybrids at low salts. Condensation of DNA-CNT hybrids by neutral osmolytes leads to liquid crystalline phases, and varying the osmotic pressure modulates the interhybrid distance that is determined by x-ray diffraction. Thus obtained force-distance dependencies of DNA-CNT hybrids show a remarkable resemblance to that of double-stranded DNA with differences that can be largely accounted for by their different diameters. This establishes their common physical nature of electrostatically driven interactions. Quantitative modeling further reveals the roles of hydration in mediating the interhybrid forces within the last nanometer of surface separation. This study also suggests the utility of osmotic pressure to control DNA-CNT assemblies at subnanometer precision.

Aspect-ratio-dependent phase transitions and concentration fluctuations in aqueous colloidal dispersions of charged platelike particles

Phase transitions of aqueous colloidal dispersions of charged platelike particles of niobate nanosheets were investigated as a function of the aspect ratio (r(asp)) and particle volume concentration (φ(p)) by means of small-angle neutron scattering and small-angle x-ray scattering. The results elucidated the following three pieces of evidence: (1) the macroscopic phase separation of the dispersions into an isotropic phase and a liquid crystalline (LC) phase under the conditions of (a) varying r(asp) (1.3×10(-4) ≤ r(asp) ≤ 2.5×10(-3)) at a constant φ(p) = 0.01 and (b) varying φ(p) (0.01 ≤ φ(p) ≤ 0.025) at a constant r(asp) = 2.5×10(-3), a mechanism of which is proposed in the text, where r(asp) ≡ d/ ̅L, with d and ̅L being thickness and the average lateral size of the plates, respectively; (2) the r(asp)-induced phase transition of the LC phase from a nematic phase to a highly periodic layered phase, the line shapes of the scattering peaks of which were examined by Caillé's analysis, upon increasing r(asp) under the condition (a); (3) the LC phase having remarkable concentration fluctuations of the particles which are totally unexpected for the conventional lyotropic molecular LC but which are anticipated to be general for the platelike colloidal particles.

Effect of polydispersity and soft interactions on the nematic versus smectic phase stability in platelet suspensions

We theoretically discuss, using density-functional theory, the phase stability of nematic and smectic ordering in a suspension of platelets of the same thickness but with a high polydispersity in diameter, and study the influence of polydispersity on this stability. The platelets are assumed to interact like hard objects, but additional soft attractive and repulsive interactions, meant to represent the effect of depletion interactions due to the addition of nonabsorbing polymer, or of screened Coulomb interactions between charged platelets in an aqueous solvent, respectively, are also considered. The aspect (diameter-to-thickness) ratio is taken to be very high, in order to model solutions of mineral platelets recently explored experimentally. In this regime a high degree of orientational ordering occurs; therefore, the model platelets can be taken as completely parallel and are amenable to analysis via a fundamental-measure theory. Our focus is on the nematic versus smectic phase interplay, since a high degree of polydispersity in diameter suppresses the formation of the columnar phase. When interactions are purely hard, the theory predicts a continuous nematic-to-smectic transition, regardless of the degree of diameter polydispersity. However, polydispersity enhances the stability of the smectic phase against the nematic phase. Predictions for the case where an additional soft interaction is added are obtained using mean-field perturbation theory. In the case of the one-component fluid, the transition remains continuous for repulsive forces, and the smectic phase becomes more stable as the range of the interaction is decreased. The opposite behavior with respect to the range is observed for attractive forces, and in fact the transition becomes of first order below a tricritical point. Also, for attractive interactions, nematic demixing appears, with an associated critical point. When platelet polydispersity is introduced the tricritical temperature shifts to very high values.

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.

Large-scale and highly oriented liquid crystal phase in suspensions of polystyrene-block-poly(L-lactide) single crystals

A large number of lozenge-shaped and sandwiched polystyrene-block-poly(L-lactide) (PS-b-PLLA) single crystals were prepared by the self-seeding technique. The single crystals were nearly monodispersed in both thickness and diameter. They are well-dispersed because of the steric stabilization offered by tethered PS in p-xylene, which is a good solvent for PS. The suspensions were observed to separate into a transparent upper phase and a turbid lower phase. The lower phase showed uniform iridescent stripes extending over the whole tube between crossed polarizers. The birefringence demonstrates the liquid crystal order, and the uniform stripes reveal that the phase is a well-oriented single domain. The phase-transition concentration is rather low. Polarizing light microscopy (PLM) images show Schlieren texture and thread-like texture. Small-angle X-ray scattering (SAXS) results showed that the single crystals in the liquid crystal phase oriented horizontally with a vertical repeat distance of about 70 nm. Additionally, the possible structure of the liquid crystal phase is being discussed. The novel disclike colloidal particle might be useful for anisotropic photonic materials.

Lyotropic hexagonal columnar liquid crystals of large colloidal gibbsite platelets

We report the formation of hexagonal columnar liquid crystal phases in suspensions of large (570 nm diameter), sterically stabilized, colloidal gibbsite platelets in organic solvent. In thin cells these systems display strong iridescence originating from hexagonally arranged columns that are predominantly aligned perpendicularly to the cell walls. Small angle X-ray scattering and polarization microscopy indicate the presence of orientational fluctuations in the hexagonal columnar liquid crystal phase. The presence of decoupling of the average platelet orientation and the column axis as well as column undulations leading to a decrease of the effective column diameter are discussed. The fact that these phenomena are particularly pronounced in the vertical direction and are enhanced toward the bottom part of the system points to the role of gravitational compaction on the structure.

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 Crystalline Behavior and Related Properties of Colloidal Systems of Inorganic Oxide Nanosheets

Inorganic layered crystals exemplified by clay minerals can be exfoliated in solvents to form colloidal dispersions of extremely thin inorganic layers that are called nanosheets. The obtained “nanosheet colloids” form lyotropic liquid crystals because of the highly anisotropic shape of the nanosheets. This system is a rare example of liquid crystals consisting of inorganic crystalline mesogens. Nanosheet colloids of photocatalytically active semiconducting oxides can exhibit unusual photoresponses that are not observed for organic liquid crystals. This review summarizes experimental work on the phase behavior of the nanosheet colloids as well as photochemical reactions observed in the clay and semiconducting nanosheets system.

Supramolecular helical fluid columns from self-assembly of homomeric dipeptides

Herein, we demonstrate that with the widespread theme of residue patterning and stereochemical restraints of self-complimenting proteinogenic amino acids, a new and rich class of homomeric dipeptides exhibiting two-dimensional fluid aggregates with hierarchical ordering can be obtained. In particular, a simple way of achieving a class of functional dipeptides, wherein the first and the second residues chosen are L-/D-alanines and L-/D-leucines, has been accomplished. The supramolecules synthesized can be regarded as intermediates between polycatenars and taper-shaped amphiphiles because they possess two lipophilic segments interlinked by a peptide unit (spacer). Two pairs of enantiomers and their respective diastereomers derived from these amino acids are evidenced to self-organize into a helical columnar phase through hydrogen bonding by means of FTIR, UV/Vis, and chiroptical circular dichroism (CD) spectral analyses as well as by optical, calorimetric, electrical switching, and X-ray studies. The CD and X-ray studies have revealed that the form chirality (handedness) and the magnitude of out-of-plane fluctuations of the lattice planes of the fluid supramolecular columnar structures are solely directed by the stereochemistry encoded in the spacer. Of special significance, the less frequently found oblique helical columnar phase formed by a pair of enantiomers derived from L-/D-alanines, unlike those derived from other amino acids, exhibit ferroelectric behavior; the measured spontaneous polarization is as high as 440 nC cm(-2). Besides, all these supramolecules form stable organogels in ethanol and the CD and SEM studies on a representative gel suggest the presence of helical structures.

Hexagonal order in crystalline and columnar phases of hard rods

We report a study of colloidal suspensions of highly monodisperse semiflexible chiral rodlike viruses, denoted fd, in the range of high concentrations. Small angle x-ray scattering experiments reveal the existence of two hexagonal phases: the first one is crystalline and the second one is hexatic columnar, as shown by its short-range positional order. The suspension of rodlike viruses is the first experimental system showing the whole phase sequence with increasing particle concentration theoretically predicted for systems of hard rods, ranging from the chiral nematic via the smectic to columnar and crystalline phases.

Synthesis and characterization of (Mo72Fe30)-coated large hexagonal gibbsite gamma-Al(OH)3 platelets

The polyoxometalates or POMs (clusters comprising at least two metal and many oxygen atoms) have recently gained significant interest owing to their versatile architecture and especially their catalytic activities. Due to their high catalytic activity but low surface area, there is always a demand for making high surface area POMs. This work demonstrates the attachment of the anionic (Mo72Fe30) POMs to gibbsite nanoplatelets with a residual positive charge to form large surface area composites. The resulting composite reported here has been characterized using cryo-TEM imaging, EDX/STEM (elemental) analysis, ATR-IR spectroscopy, SAXS, electrophoretic mobility determination and XRD. The composite reported here could find application in catalysis.

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.

Fast formation of opal-like columnar colloidal crystals

We demonstrate that highly polydisperse colloidal gibbsite platelets easily form an opal-like columnar crystal with striking iridescent Bragg reflections. The formation process can be accelerated by orders of magnitude under a centrifugation force of 900 g without arresting the system in a disordered glassy phase. Using transmission electron microscopy and small-angle X-ray scattering techniques, we find that the forced sedimentation is accompanied by particle size fractionation, leading to inversion of the iridescent colors. The relatively easy self-organization of the polydisperse colloidal particles into opal-like crystals may be explained on the basis of the observed particle fractionation and possibly also on hexatic-like ordering.

Polydispersity-induced macrophase separation in diblock copolymer melts

The effect of A-block polydispersity on the phase behavior of AB-diblock copolymer melts is examined using a complete self-consistent field theory treatment that allows for fractionation of the parent molecular-weight distribution. In addition to observing the established shift in phase boundaries, we find the emergence of significant two-phase coexistence regions causing, for instance, the disappearance of the complex phase window. Furthermore, we find evidence that polydispersity relieves packing frustration, which will reduce the tendency for long-range order.

Anisotropy of building blocks and their assembly into complex structures

A revolution in novel nanoparticles and colloidal building blocks has been enabled by recent breakthroughs in particle synthesis. These new particles are poised to become the 'atoms' and 'molecules' of tomorrow's materials if they can be successfully assembled into useful structures. Here, we discuss the recent progress made in the synthesis of nanocrystals and colloidal particles and draw analogies between these new particulate building blocks and better-studied molecules and supramolecular objects. We argue for a conceptual framework for these new building blocks based on anisotropy attributes and discuss the prognosis for future progress in exploiting anisotropy for materials design and assembly.

Phase behavior of aqueous suspensions of Mg(2)Al layered double hydroxide: the competition among nematic ordering, sedimentation, and gelation

Birefringence observations and rheological measurements were used to monitor the phase behavior of Mg/Al (the molar ratio of Mg(2+) to Al(3+) being 2:1) layered double hydroxide (LDH) suspensions. The suspensions of concentration lower than 16% (w/w) appear isotropic (I) between crossed polarizers. In contrast, the suspensions of concentration between 16% and 30% (w/w) showed an isotropic (I)-nematic (N) biphasic coexistence. Detailed observations led us to divide the suspensions in the gap into three groups according to their behaviors: the suspensions with concentration between 16% and 25% (w/w) experienced an I-N phase transition and particle sedimentation simultaneously, while the suspensions of 25% to 27% (w/w) showed I-N transition after particle sedimentation, and in the suspension of 30% (w/w), a critical sol-gel transition appeared with an I-N transition. Above 33% (w/w), the gel network hindered a complete I-N separation in the suspensions. Upon raising the NaCl concentration, the liquid crystalline phase transition and the sol-gel transition shifted to higher particle concentrations. The facts demonstrate that the phase behavior of aqueous LDH suspensions is controlled by the competition among liquid crystal phase transition, sedimentation, and gelation.

Frank's constant in the hexatic phase

Using videomicroscopy data of a two-dimensional colloidal system the bond-order correlation function G{6} is calculated and used to determine both the orientational correlation length xi{6} in the liquid phase and the modulus of orientational stiffness, Frank's constant F{A}, in the hexatic phase. The latter is an anisotropic fluid phase between the crystalline and the isotropic liquid phase. F{A} is found to be finite within the hexatic phase, takes the value 72/pi at the hexatic<-->isotropic liquid phase transition, and diverges at the hexatic<-->crystal transition as predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young theory. This is a quantitative test of the mechanism of breaking the orientational symmetry by disclination unbinding.

Structure of Electrorheological Fluids under an Electric Field and a Shear Flow: Experiment and Computer Simulation

It is known that macroscopic properties of colloidal suspensions are often determined by the microstructure of the particles in the suspensions, depending on the interparticle, Brownian, and hydrodynamic (if any) forces. We take electrorheological (ER) fluids as an example. By using a computer simulation and an experimental approach, we investigate the structure of ER fluids subjected to both an electric field and a shear flow. The microstructure evolution from random structure, to chains, and then to stable lamellar patterns, observed in the experiments, agrees very well with that obtained in the simulations. It is shown that the formation of such lamellar patterns originates from the difference between the dipole moment induced in the particles suspended in the ER fluids without shear and the one with shear. The results on the relaxation process of structural formation and the internal structure of layers are also presented. Thus, it seems possible to achieve various structures and hence desired macroscopic properties of colloidal suspensions by adjusting external fields and, simultaneously, a shear flow.

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.

Shape-induced frustration of hexagonal order in polyhedral colloids

The effect of a nonspherical particle shape and shape polydispersity on the structure of densely packed hard colloidal particles was studied in real space by confocal microscopy. We show that the first layer at the wall of concentrated size-monodisperse but shape-polydisperse polyhedral colloids exhibits significant deviations from a hexagonal lattice. These deviations are identified as bond-orientational fluctuations which lead to percolating "mismatch lines." While the shape-induced geometrical frustration of the hexagonal symmetry suppresses translational order, bond-orientational order is clearly retained, indicating a hexaticlike structure of the polyhedral colloids.