Liquid crystal formation in suspensions of hard rodlike colloidal particles: direct observation of particle arrangement and self-ordering behavior

On the lattice ground state of densely packed hard ellipses

Among lattice configurations of densely packed hard ellipses, Monte Carlo simulations are used to identify the so-called parallel and diagonal lattices as the two favorable states. The free energies of these two states are computed for several system sizes employing the Einstein crystal method. An accurate calculation of the free energy difference between the two states reveals the parallel lattice as the state with the lowest free energy. The origin of the entropic difference between the two states is further elucidated by assessing the roles of the translational and rotational degrees of freedom.

Elastic response of colloidal smectic liquid crystals: Insights from microscopic theory

Elongated colloidal rods at sufficient packing conditions are known to form stable lamellar or smectic phases. Using a simplified volume-exclusion model, we propose a generic equation of state for hard-rod smectics that is robust against simulation results and is independent of the rod aspect ratio. We then extend our theory by exploring the elastic properties of a hard-rod smectic, including the layer compressibility (B) and bending modulus (K_{1}). By introducing weak backbone flexibility we are able to compare our predictions with experimental results on smectics of filamentous virus rods (fd) and find quantitative agreement between the smectic layer spacing, the out-of-plane fluctuation strength, as well as the smectic penetration length λ=sqrt[K_{1}/B]. We demonstrate that the layer bending modulus is dominated by director splay and depends sensitively on lamellar out-of-plane fluctuations that we account for on the single-rod level. We find that the ratio between the smectic penetration length and the lamellar spacing is about two orders of magnitude smaller than typical values reported for thermotropic smectics. We attribute this to the fact that colloidal smectics are considerably softer in terms of layer compression than their thermotropic counterparts while the cost of layer bending is of comparable magnitude.

Splay-bend nematic phases of bent colloidal silica rods induced by polydispersity

Liquid crystal (LC) phases are in between solids and liquids with properties of both. Nematic LCs composed of rod-like molecules or particles exhibit long-range orientational order, yielding characteristic birefringence, but they lack positional order, allowing them to flow like a liquid. This combination of properties as well as their sensitivity to external fields make nematic LCs fundamental for optical applications e.g. liquid crystal displays (LCDs). When rod-like particles become bent, spontaneous bend deformations arise in the LC, leading to geometric frustration which can be resolved by complementary twist or splay deformations forming intriguing twist-bend (NTB) and splay-bend (NSB) nematic phases. Here, we show experimentally that the elusive NSB phases can be stabilized in systems of polydisperse micron-sized bent silica rods. Our results open avenues for the realization of NTB and NSB phases of colloidal and molecular LCs.

Machine-learning effective many-body potentials for anisotropic particles using orientation-dependent symmetry functions

Spherically-symmetric atom-centered descriptors of atomic environments have been widely used for constructing potential or free energy surfaces of atomistic and colloidal systems and to characterize local structures using machine learning techniques. However, when particle shapes are non-spherical, as in the case of rods and ellipsoids, standard spherically-symmetric structure functions alone produce imprecise descriptions of local environments. In order to account for the effects of orientation, we introduce two- and three-body orientation-dependent particle-centered descriptors for systems composed of rod-like particles. To demonstrate the suitability of the proposed functions, we use an efficient feature selection scheme and simple linear regression to construct coarse-grained many-body interaction potentials for computationally-efficient simulations of model systems consisting of colloidal particles with anisotropic shape: mixtures of colloidal rods and nonadsorbing polymer, hard rods enclosed by an elastic microgel shell, and ligand-stabilized nanorods. We validate the machine-learning (ML) effective many-body potentials based on orientation-dependent symmetry functions by using them in direct coexistence simulations to map out the phase behavior of colloidal rods and non-adsorbing polymer. We find good agreement with results obtained from simulations of the true binary mixture, demonstrating that the effective interactions are well-described by the orientation-dependent ML potentials.

Topological fine structure of smectic grain boundaries and tetratic disclination lines within three-dimensional smectic liquid crystals

Observing and characterizing the complex ordering phenomena of liquid crystals subjected to external constraints constitutes an ongoing challenge for chemists and physicists alike. To elucidate the delicate balance appearing when the intrinsic positional order of smectic liquid crystals comes into play, we perform Monte-Carlo simulations of rod-like particles in a range of cavities with a cylindrical symmetry. Based on recent insights into the topology of smectic orientational grain boundaries in two dimensions, we analyze the emerging three-dimensional defect structures from the perspective of tetratic symmetry. Using an appropriate three-dimensional tetratic order parameter constructed from the Steinhardt order parameters, we show that those grain boundaries can be interpreted as a pair of tetratic disclination lines that are located on the edges of the nematic domain boundary. Thereby, we shed light on the fine structure of grain boundaries in three-dimensional confined smectics.

Numerical Studies on Electrostatic Interaction Forces and the Free Energy between Parallel Colloidal Rods of Finite Size in Skewed Configurations

Formulas for interaction forces F(s) and the free energy G(s) between two parallel charged prismatic rods of various scaled values of d, ψ_s, and L in skewed configurations are obtained, where s is the lengthwise positional difference between the front-end faces of the respective rods, and d is the minimal distance between the opposing faces of the rods, ψ_s is the electric surface potential, L is the length of the rods. To obtain the free-energy function G(s), (i) 3D spatial distributions of the electric potential ψ around two rods were determined by numerically solving the nonlinear Poisson-Boltzmann equation with a finite element method, (ii) with the ψ distributions so determined, the lengthwise interaction electrostatic Maxwell stress tangential to the midplane between the rods was calculated to obtain the (discrete) s dependence of the stress, and (iii) by introducing two different fitting functions, the discrete s dependence was transformed into a continuous force function, F(s), which was then lengthwise integrated to derive G(s). It was found that the curves of G(s) linearly decreased with increasing s between 1 and L + 1 due to a localization of the stress. Although natural, it is of interest that the values of G(0) calculated for rods of various values of d, ψ_s, and L were in good agreement with those of the interaction free energy obtained in our preceding work by the widthwise integration of repulsive electrostatic forces normal to the midplane between the parallel rods in nonskewed configurations.

Size Tuned Synthesis of FeOOH Nanorods toward Self-Assembled Nanoarchitectonics

Various studies were performed to fabricate self-assembling nanoobjects out of noble metals, but a few efforts were made for engineering iron-based nanorods toward sell-assembling blocks. In this regard β-FeOOH nanorods were fabricated in various sizes to achieve iron-based rod nanoblocks with self-assembling potential. Hydrolysis of ferric ions in various concentrations was successfully developed as a novel approach to control the growth of β-FeOOH crystals and tuning the length of rods in the nano range, below 100 nm. It was found that the concentration of ferric ion has no effect on the widths of nanorods, but the length was affected. By increasing the concentration of ferric ions, an increase in the length of nanorods and an increase of aspect ratio occurred. All sizes of the resulting FeOOH nanorods exhibited mesoporous feature, but interestingly the hysteresis loops were different due to different pore patterns. In fact, pores on the larger particles were more uniform in size and shape. Nanorods of small length did not make suitable interactions toward ordered phase formation, but rods with the mean length of about 90 nm or longer, at a certain concentration, were able to form nematic phases. The large (∼+40 mV) zeta-potential of nanorods prevents formation of dense arrays, and just bundle-like structures were observed. These findings highlight the importance of size, surface charge, and concentration of nanoobjects in the formation of 3D structures. The developed technique in the fabrication of β-FeOOH nanorods provides pure structures that are free from any size-controlling agent. These pure structures are suitable for further functionalization or coating. Self-assembling nanoobjects is a developing field in nanotechnology, and therefore studies can help our understanding over the assembling process.

Nacre Is a Liquid-Crystal Thermometer of the Oceans

Nacre, or mother of pearl, is a biomaterial with a layered structure. In a recent geological study, researchers found that the width of the nacre layers depends on the formation temperature, which is determined by the ocean water temperature. A linear dependence of layer width with respect to temperature is understandable within the transient liquid-crystalline nature of incipient nacre. Thus, developing nacre is a liquid-crystal thermometer recording its formation temperature. A more complete understanding of nacre formation is of interest not only for biology and geology, in terms of biomineralization and paleoclimatology, but also for materials science: for reproducing nacre or fabricating synthetic analogues and also potentially for developing new classes of layered materials with layer spacings tunable by pH and temperature.

Numerical Studies on Electrical Interaction Forces and Free Energy between Colloidal Plates of Finite Size

By solving the nonlinear Poisson-Boltzmann (PB) equation with a finite element method (FEM), three-dimensional (3D) spatial distributions of the electric potential (ψ, scaled) in electrolyte solutions having two charged parallel finite plates (including cubes and prismatic rods) are determined for various separations (d, scaled by the Debye length, κ^-1), surface potentials (ψ_s), and plate dimensions (length × width × thickness, each scaled by κ^-1). The total interaction force between two plates, F, is the sum of the electrostatic double-layer (EDL) repulsion (the osmotic pressure, F_osm) and the Maxwell electrostatic stress (F_es). The EDL repulsion is estimated using the distribution of ψ not only between the facing surfaces of two parallel plates but also around the other extremities of the plates. The Maxwell stress (F_es) is localized near the extremities to act as a repulsive force on the midplane between the two plates. The ratio F_es/F is 0.07-0.5, depending on d, ψ_s, and dimensions. It is found that, with increasing dimensions, the total F values per unit area calculated for finite plates, F̃, decreasingly approach the exact ones for parallel infinite plates, F̃^inf; for example, at d = 1 and ψ_s = 5, the ratio F̃/F̃^inf is 2.83 for plates with dimensions of 1 × 1 × 1 and 1.18 for plates of 10 × 10 × 1. The repulsions arising from the extremities cannot be neglected for plates with dimensions <10 × 10 × 1. Furthermore, the total interaction forces (F) are calculated at a series of discrete d values, respectively, for parallel plates. We introduce a force fitting function, F_f(d), with parameters that can be determined so that F_f(d) fits well to the calculated serial F values. By integrating the F_f(d), we obtain the interaction free energy, G(d), for finite parallel plates that consists of two Γ functions.

Short and Soft: Multidomain Organization, Tunable Dynamics, and Jamming in Suspensions of Grafted Colloidal Cylinders with a Small Aspect Ratio

The yet virtually unexplored class of soft colloidal rods with a small aspect ratio is investigated and shown to exhibit a very rich phase and dynamic behavior, spanning from liquid to nearly melt state. Instead of the nematic order, these short and soft nanocylinders alter their organization with increasing concentration from isotropic liquid with random orientation to small domains with preferred local orientation and eventually a multidomain arrangement with a local orientational order. The latter gives rise to a kinetically suppressed state akin to structural glass with detectable terminal relaxation, which, on further increasing concentration, reveals features of hexagonally packed order as in ordered block copolymers. The respective dynamic response comprises four regimes, all above the overlapping concentration of 0.02 g/mL:(I) from 0.03 to 0.1 g/mol, the system undergoes a liquid-to-solidlike transition with a structural relaxation time that grows by 4 orders of magnitude. (II) From 0.1 to 0.2 g/mL, a dramatic slowing-down is observed and is accompanied by an evolution from isotropic to a multidomain structure. (III) Between 0.2 and 0.6 g/mol, the suspensions exhibit signatures of shell interpenetration and jamming, with the colloidal plateau modulus depending linearly on concentration. (IV) At 0.74 g/mL, in the densely jammed state, the viscoelastic signature of hexagonally packed cylinders from microphase-separated block copolymers is detected. These properties set short and soft nanocylinders apart from long colloidal rods (with a large aspect ratio) and provide insights for fundamentally understanding the physics in this intermediate soft colloidal regime and for tailoring the flow properties of nonspherical soft colloids.

Anisotropic Hollow Microgels That Can Adapt Their Size, Shape, and Softness

The development of soft anisotropic building blocks is of great interest for various applications in soft matter. Furthermore, such systems would be important model systems for ordering phenomena in fundamental soft matter science. In this work, we address the challenge of creating hollow and anisotropically shaped thermoresponsive microgels, polymeric networks with a solvent filled cavity in their center that are swollen in a good solvent. Sacrificial elliptical hematite silica particles were utilized as a template for the synthesis of a cross-linked N-isopropylacrylamide (NIPAm) shell. By varying the amount of NIPAm, two anisotropic microgels were synthesized with either a thin or thick microgel shell. We characterized these precursor core-shell and the resulting hollow microgels using a combination of light, X-ray, and neutron scattering. New form factor models, accounting for the cavity, the polymer distribution and the anisotropy, have been developed for fitting the scattering data. With such models, we demonstrated the existence of the cavity and simultaneously the anisotropic character of the microgels. Furthermore, we show that the thickness of the shell has a major influence on the shape and the cavity dimension of the microgel after etching of the sacrificial core. Finally, the effect of temperature is investigated, showing that changes in size, softness, and aspect ratio are triggered by temperature.

Preparation of colloidal molecules with temperature-tunable interactions from oppositely charged microgel spheres

The self-assembly of small colloidal clusters, so-called colloidal molecules, into crystalline materials has proven extremely challenging, the outcome often being glassy, amorphous states where positions and orientations are locked. In this paper, a new type of colloidal molecule is therefore prepared, assembled from poly(N-isopropylacrylamide) (PNIPAM)-based microgels that due to their well documented softness and temperature-response allow for greater defect tolerance compared to hard spheres and for convenient in situ tuning of size, volume fraction and inter-particle interactions with temperature. The microgels (B) are assembled by electrostatic adsorption onto oppositely charged, smaller-sized microgels (A), where the relative size of the two determines the valency (n) of the resulting core-satellite ABn-type colloidal molecules. Following assembly, a microfluidic deterministic lateral displacement (DLD) device is used to effectively isolate AB4-type colloidal molecules of tetrahedral geometry that possess a repulsive-to-attractive transition on crossing the microgels' volume phase transition temperature (VPTT). These soft, temperature-responsive colloidal molecules constitute highly promising building blocks for the preparation of new materials with emergent properties, and their optical wavelength-size makes them especially interesting for optical applications.

Relaxation in two-dimensional suspensions of rods as driven by Brownian diffusion

Relaxation in a two-dimensional suspensions containing rods was studied by using dynamic Monte Carlo simulations. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The initial state was produced by using a random sequential adsorption model. During the relaxation, the rods underwent translational and rotational Brownian motions. The simulations were run at different values of number density ρ (the number of rods per unit area) and of the initial orientation order parameter S_{i}. The rods were assumed to have core-shell structures. The evolutions of both the connectivity and the order parameter have revealed different relaxation behavior.

Biaxial, Twist-bend, and Splay-bend Nematic Phases of Banana-shaped Particles Revealed by Lifting the "Smectic Blanket"

We perform an extensive computational study on the phase behavior of hard banana-shaped particles, and show that biaxial, twist-bend, and splay-bend nematic phases are metastable with respect to a smectic phase for a system of hard bent spherocylinders. However, if the smectic phase is destabilized-either by polydispersity in the particle length or by curvature in the particle shape-stable biaxial, twist-bend, and splay-bend nematic phases are obtained. This provides a unified and consistent picture on the subtle role of particle shape on the phase behavior of bent rods.

Phase behavior of hard C_{2h}-symmetric particle systems

Using Monte Carlo numerical simulation, this work sketches the phase diagram of systems of certain hard C_{2h}-symmetric particles, formed by gluing two aligned and displaced hard spherocylinders with a cylindrical-length-to-diameter ratio realistically, if viewed not only from the lyotropic colloidal liquid-crystal side but also from the thermotropic low-molecular-mass liquid-crystal side, equal to 5, as a function of the displacement. Several distinctive phases are observed, such as a nonperiodic smectic-B-like phase, a nonperiodic smectic-H-like phase, a smectic-C phase, and a short-layer-spacing uniaxial smectic-A phase but no biaxial nematic phase.

Sedimentation of a suspension of rods: Monte Carlo simulation of a continuous two-dimensional problem

The sedimentation of a two-dimensional suspension containing rods was studied by means of Monte Carlo (MC) simulations. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The initial state before sedimentation was produced using a model of random sequential adsorption. During such sedimentation, the rods undergo translational and rotational Brownian motions. The MC simulations were run at different initial number densities (the numbers of rods per unit area), ρ_{i}, and sedimentation rates, u. For sediment films, the spatial distributions of the rods, the order parameters, and the electrical conductivities were examined. Different types of sedimentation-driven self-assembly and anisotropy of the electrical conductivity were revealed inside the sediment films. This anisotropy can be finely regulated by changes in the values of ρ_{i} and u.

Anisotropic Colloids: From Non-Templated to Patchy Templated Synthesis

Self-assembly of colloidal particles is an important and challenging way to generate novel colloidal superstructures for new materials. Recent progress on syntheses of anisotropic colloids highlights opportunities for such self-assembly, particularly in defining new non-cubic superstructures. Both non-templated and templated synthesis play an important role in preparing anisotropic colloidal particles. In this article, we briefly summarize recent progress in anisotropic colloids by non-templated and conventional templated synthesis, and introduce a conceptual strategy of "patchy templated synthesis" that differs from the conventional approach. We illustrate this strategy with recent examples emanating from colloidal rings, and discuss the future opportunities with this strategy for the synthesis of other anisotropic colloids.

Phase behaviour in complementary DNA-coated gold nanoparticles and fd-viruses mixtures: a numerical study

A new gel-forming colloidal system based on a binary mixture of fd-viruses and gold nanoparticles functionalized with complementary DNA single strands has been recently introduced. Upon quenching below the DNA melt temperature, such a system results in a highly porous gel state, that may be developed in a new functional material of tunable porosity. In order to shed light on the gelation mechanism, we introduce a model closely mimicking the experimental one and we explore via Monte Carlo simulations its equilibrium phase diagram. Specifically, we model the system as a binary mixture of hard rods and hard spheres mutually interacting via a short-range square-well attractive potential. In the experimental conditions, we find evidence of a phase separation occurring either via nucleation-and-growth or via spinodal decomposition. The spinodal decomposition leads to the formation of small clusters of bonded rods and spheres whose further diffusion and aggregation leads to the formation of a percolating network in the system. Our results are consistent with the hypothesis that the mixture of DNA-coated fd-viruses and gold nanoparticles undergoes a non-equilibrium gelation via an arrested spinodal decomposition mechanism.

Anisotropic responsive microgels with tuneable shape and interactions

Highly monodisperse polystyrene/poly(N-isopropylmethacrylamide) (PS-PNIPMAM) core-shell composite microgels were synthesized and further nanoengineered in either ellipsoidal, faceted or bowl-shaped particles. Beside their anisotropy in shape, the microgel design enables an exquisite control of the particle conformation, size and interactions from swollen and hydrophilic to collapsed and hydrophobic using temperature as an external control variable. The post-processing procedures and the characterization of the different particles are first presented. Their potential as model systems for the investigation of the effects of anisotropic shape and interactions on the phase behavior is further demonstrated. Finally, the self-assembly of bowl-shaped composite microgel particles is discussed, where the temperature and an external AC electric field are employed to control the interactions from repulsive to attractive and from soft repulsive to dipolar, respectively.

Orientation-Dependent London-van der Waals Interaction Energy between Macroscopic Bodies

The aim of this work is to derive formulas for numerical calculations of the orientation-dependent London-van der Waals (vdW) interaction energy (V(A)) between two rectangular bodies with arbitrary dimensions, arranged at arbitrary relative angles (θ) and separations in twisted and coplanar rotational modes. The formulation is made using a simple volume-element-integration method in the framework of the microscopic approach, in which V(A) is the sum of the local vdW energy (Vp) between body 1 and each thin plate constituting body 2. Examples of the calculation results are the following: (1) The θ values that give maximal and minimal values of V(A) depend on their shapes and relative positions. (2) As the bodies come close to each other, the variations of V(A) with θ and thus vdW dispersion torques generated are drastically intensified. (3) Upon increasing the length of crossing rods in twisted configurations, the V(A) values become constant beyond a critical length (depending on θ and separation), where the length effect on V(A) disappears. (4) The distribution curves of Vp show that the region in body 2 which interacts effectively with body 1 (i.e., the effective interaction region) is more sharply localized in the vicinity of the surface (closest to body 1) as the separation is decreased.

Synthesis of iron oxide rods coated with polymer brushes and control of their assembly in thin films

We investigated the surface-initiated atom transfer radical polymerization (SI-ATRP) of methyl methacrylate (MMA) using monodisperse rod-type particles of iron oxide, β-FeOOH. The slow hydrolysis of iron(III) chloride yielded monodisperse β-FeOOH rods with an average length-to-width ratio, L/W, of 6 (L = 210 nm and W = 35 nm on average). The surfaces of the β-FeOOH rods were modified with a triethoxysilane derivative as an ATRP-initiating site, namely, (2-bromo-2-methyl)propionyloxypropyl triethoxysilane. The SI-ATRP of MMA, mediated by a copper complex, was performed using the initiator-coated β-FeOOH rods in the presence of a "sacrificial" free initiator. Well-defined poly(methyl methacrylate) (PMMA) brushes with molecular weights of up to 700,000 could be grafted on the β-FeOOH rods with a surface density as high as 0.3 chains/nm(2). The resultant polymer-brush-afforded hybrid rods exhibited high dispersibility in various solvents for PMMA without forming aggregates. Thin films were prepared by dip-coating from a suspension of the hybrid rods, and the rods were oriented in a specific direction in the films. The arrangement of the rods could be controlled by varying the chain length of the polymer brush and the withdrawal speed during the dip-coating process.

Synthesis of multivalent silica nanoparticles combining both enthalpic and entropic patchiness

Silica particles with a controlled number of entropic patches, i.e. dimples, are synthesized through the growth of the silica core of binary multipods that have been produced by a seeded-growth emulsion polymerization reaction. Transmission electron microscopy studies indicate that the silica surface conforms to the shape of the polystyrene (PS) nodules of the multipods while growing, allowing good control of the final shape of the dimpled silica particles. The PS nodules are also used as protecting masks to regioselectively graft amino groups, as revealed by the adsorption of gold markers. After dissolution of the PS nodules, some polymer chains remain grafted onto the silica surface, forming organic bumps. These residues are also selectively functionalized, leading to silica particles with both entropic and enthalpic patches.

Soft epitaxy of nanocrystal superlattices

Epitaxial heterostructures with precise registry between crystal layers play a key role in electronics and optoelectronics. In a close analogy, performance of nanocrystal (NC) based devices depends on the perfection of interfaces formed between NC layers. Here we systematically study the epitaxial growth of NC layers for the first time to enable the fabrication of coherent NC layers. NC epitaxy reveals an exceptional strain tolerance. It follows a universal island size scaling behaviour and shows a strain-driven transition from layer-by-layer to Stranski-Krastanov growth with non-trivial island height statistics. Kinetic bottlenecks play an important role in NC epitaxy, especially in the transition from sub-monolayer to multilayer coverage and the epitaxy of NCs with anisotropic shape. These findings provide a foundation for the rational design of epitaxial structures in a fundamentally and practically important size regime between atomic and microscopic systems.

Shape-induced separation of nanospheres and aligned nanorods

We studied the phase separation and spatial arrangement of gold nanorods and nanospheres after evaporative self-assembly from aqueous suspension. Depending on the position relative to the contact line of the drying droplet, spheres and rods separate into various liquid-crystalline phases. Nanorods exhibit a strong preference for side-by-side alignment, giving rise to smectic phases; spheres in solution are forced out of these regions and form close-packed arrays. We discuss this self-separation into nanorod- and sphere-rich phases in terms of various interactions, including electrostatic, van der Waals, and deplection interactions forces. The experimental results are compared to quantitative calculations of the colloidal interaction energies. We also describe and discuss the role of the surfactant on the different crystal facets of the nanorods on the assembly process.

Biaxial mesophase behavior of amphiphilic anisometric colloids: a simulation study

The phase behavior of amphiphilic anisometric particles is explored using Monte Carlo simulations. The particles are composed of two incompatible laterally attached units: a spherocylinder and a spheroplatelet. A liquid crystalline phase polymorphism is obtained including biaxial nematic, (quasi long range biaxial) calamitic smectic-A, biaxial lamellar and columnar phases. The simulation results demonstrate intriguing phase transitions such as nematic-nematic, discotic nematic to (quasi long range biaxial) calamitic smectic-A, biaxial nematic to uniaxial calamitic smectic-A, and isotropic or discotic nematic to biaxial lamellar phases that possess nematic ordering within the layers. These findings are rationalized in terms of molecular geometry and amphiphilicity of different molecular units. The molecular model can be used as a tool for the prediction of the complex phase behavior that is relevant to liquid crystalline colloids.

Formation of the smectic-B crystal from a simple monatomic liquid

We report a molecular dynamics simulation demonstrating that the smectic-B crystalline phase (Cry-B), commonly observed in mesogenic systems of anisotropic molecules, can be formed by a system of identical particles interacting via a spherically symmetric potential. The Cry-B phase forms as a result of a first-order transition from an isotropic liquid phase upon isochoric cooling at appropriate number density. Its structure, determined by the design of the pair potential, corresponds to the Cry-B structure formed by elongated particles with the aspect ratio 1.8. The diffraction pattern and the real-space structure inspection demonstrate dominance of the ABC-type of axial layer stacking. This result opens a general possibility of producing smectic phases using isotropic interparticle interaction both in simulations and in colloidal systems.

Collective stringlike motion of semiflexible filamentous particles in columnar liquid crystalline phases

We study, by means of Brownian dynamics simulations, heterogeneous dynamics in a dense columnar phase of monodisperse hard filamentous particles, and find that in a background of barely moving particles, some particles occasionally engage in a fast coherent string-type motion similar to what is observed in glassy states of isometric particles. This fast motion is triggered by the exchange of particles between two or more columns at different positions in the columns, which leads to sudden displacement of particles between these positions. The distribution of particle displacements shows a pronounced peak at one particle length. We perform our simulations with particles of different persistence lengths and find that for more flexible particles, the number of jump events increases. As the number of particles in the columns increases with system size for a given linear fraction of particles in the columns, the peak in the distribution becomes wider and, for sufficiently large systems, the peak disappears completely. This is associated with the increase in the magnitude of fluctuations in the motion of particles as the system size increases. Our simulation results explain recent experimental observations on single-particle motion in dense columnar phases in aqueous dispersions of filamentous virus particles.

Spontaneous formation of stringlike clusters and smectic sheets for colloidal rods confined in thin wedgelike gaps

Monodispersed colloidal rods of β-FeOOH with sizes ranging from 270 to 580 nm in length and 50 to 80 nm in width were synthesized. Narrow wedgelike gaps (0 to 700 nm in height) were formed around the inner bottom edge of the suspension glass cells. Optical microscopic observations revealed the formation of stringlike clusters of the rods and smectic sheets (by spontaneous side-by-side clustering of the strings) in the isotropic phase of the rod suspensions confined in narrow gaps; the electrolyte (HCl) concentrations of the suspensions are 5-40 mM, at which inter-rod interactions are attractive. The strings exhibit different colors that were used to investigate the structures of the strings with the help of interference color theory for thin films. The results are as follows. (1) The rods, lying flat on the gap bottom, are connected side-by-side and stacked upward to form stringlike clusters with different thicknesses depending on the gap height. (2) The stacking numbers (N(sr)) of the rods are estimated to be 1-5. With N(sr) increasing from 2 to 5, the volume fractions (ϕ) of the rods in the strings increased typically from 0.25-0.3 to 0.35-0.42 to reach limiting values (close to the ϕ values of the rods in the bulk smectic phase). (3) Unexpected low-ϕ strings are found in regions with an intermediate height in the gaps. These behaviors of ϕ may be caused by thermal fluctuations of the strings.

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.

Ordered two-dimensional superstructures of colloidal octapod-shaped nanocrystals on flat substrates

We studied crystal structures in a monolayer consisting of anisotropic branched colloidal (nano)octapods. Experimentally, octapods were observed to form a monolayer on a substrate with a square-lattice crystal structure by drop-casting and fast evaporation of solvent. The experimental results were analyzed by Monte Carlo simulations using a hard octapod model consisting of four interpenetrating spherocylinders. We confirmed by means of free-energy calculations that crystal structures with a (binary-lattice) square morphology are indeed thermodynamically stable at high densities. The effect of the pod length-to-diameter ratio on the crystal structures was also considered and we used this to constructed the phase diagram for these hard octapods. In addition to the (binary-lattice) square crystal phase, a rhombic crystal and a hexagonal plastic-crystal (rotator) phase were obtained. Our phase diagram may prove instrumental in guiding future experimental studies.

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.

Studies of liquid crystalline self-assembly of GdF₃ nanoplates by in-plane, out-of-plane SAXS

Directed self-assembly of colloidal nanocrystals into ordered superlattices enables the preparation of novel metamaterials with diverse functionalities. Structural control and precise characterization of these superlattices allow the interactions between individual nanocrystal building blocks and the origin of their collective properties to be understood. Here, we report the directed liquid interfacial assembly of gadolinium trifluoride (GdF(3)) nanoplates into liquid crystalline assemblies displaying long-range orientational and positional order. The macroscopic orientation of superlattices is controlled by changing the subphases upon which liquid interfacial assembly occurs. The assembled structures are characterized by a combination of transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS) measurements performed on a laboratory diffractometer. By doping GdF(3) nanoplates with europium (Eu(3+)), luminescent phosphorescent superlattices with controlled structure are produced and enable detailed structural and optical characterization.

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.

Spectroscopic ellipsometry study on refractive index spectra of colloidal β-FeOOH nanorods with their self-assembled thin films

We prepared monodisperse colloidal β-FeOOH (square prismatic crystalline) nanorods. Self-assembled dry thin films of the rods were formed on quartz substrates by evaporating drops of repulsive-rod suspensions. Using spectroscopic ellipsometry, the complex refractive index spectra of the β-FeOOH nanorod films were deduced, which are further corrected on the basis of absorption spectra measured for β-FeOOH nanorod suspensions, with aid of the Kramers-Krönig relation and an optical two-phase mixing model. Simultaneously, in this correction process, the rod volume fraction in the films and the complex mean refractive index spectra of purely the rod were extracted together. The real part of the refractive index spectra of the β-FeOOH rod, n'(c)(λ), shows a maximal value of 2.365 (aver.) at 410 nm (λ(m)) (hence a normal dispersion at λ > λ(m) and an anomalous dispersion at λ < λ(m)). At λ = 589.3 nm (λ(D) for "sodium light"), the n'(c)(λ) value is consistent with refractive indices predicted by Gladstone-Dale's and Anderson's refractivity formulas with the density of the β-FeOOH rod, 3.638 ± 0.104 g/cm(3), measured in this work.

Mesophase behaviour of polyhedral particles

Translational and orientational excluded-volume fields encoded in particles with anisotropic shapes can lead to purely entropy-driven assembly of morphologies with specific order and symmetry. To elucidate this complex correlation, we carried out detailed Monte Carlo simulations of six convex space-filling polyhedrons, namely, truncated octahedrons, rhombic dodecahedrons, hexagonal prisms, cubes, gyrobifastigiums and triangular prisms. Simulations predict the formation of various new liquid-crystalline and plastic-crystalline phases at intermediate volume fractions. By correlating these findings with particle anisotropy and rotational symmetry, simple guidelines for predicting phase behaviour of polyhedral particles are proposed: high rotational symmetry is in general conducive to mesophase formation, with low anisotropy favouring plastic-solid behaviour and intermediate anisotropy (or high uniaxial anisotropy) favouring liquid-crystalline behaviour. It is also found that dynamical disorder is crucial in defining mesophase behaviour, and that the apparent kinetic barrier for the liquid-mesophase transition is much lower for liquid crystals (orientational order) than for plastic solids (translational order).

Computer simulations of the growth of synthetic peptide fibres

We present a coarse-grained computer model designed to study the growth of fibres in a synthetic self-assembling peptide system. The system consists of two 28 residue α-helical sequences, denoted AB and CD, in which the interactions between the half peptides, A, B, C and D, may be tuned individually to promote different types of growth behaviour. In the model, AB and CD are represented by double ended rods, with interaction sites distributed along their lengths. Monte Carlo simulations are performed to follow fibre growth. It is found that lateral and longitudinal growth of the fibre are governed by different mechanisms--the former is diffusion limited with a very small activation energy for the addition of units, whereas the latter occurs via a process of secondary nucleation at the fibre ends. As a result, longitudinal growth generally proceeds more slowly than lateral growth. Furthermore, it is shown that the aspect ratio of the growing fibre may be controlled by adjusting the temperature and the relative strengths of the interactions. The predictions of the model are discussed in the context of published data from real peptide systems.

Formation of one-dimensional capped ZnO nanoparticle assemblies at the air/water interface

The self-assembling behavior and microscopic structure of zinc oxide nanoparticle Langmuir-Blodgett monolayer films were investigated for the case of zinc oxide nanoparticles coated with a hydrophobic layer of dodecanethiol. Evolution of nanoparticle film structure as a function of surface pressure (π) at the air-water interface was monitored in situ using Brewster's angle microscopy, where it was determined that π = 16 mN/m produced near-defect-free monolayer films. Transmission electron micrographs of drop-cast and Langmuir-Schaefer deposited films of the dodecanethiol-coated zinc oxide nanoparticles revealed that the nanoparticle preparation method yielded a microscopic structure that consisted of one-dimensional rodlike assemblies of nanoparticles with typical dimensions of 25 × 400 nm, encased in the organic dodecanethiol layer. These nanoparticle-containing rodlike micelles were aligned into ordered arrangements of parallel rods using the Langmuir-Blodgett technique.

Glassy dynamics, spinodal fluctuations, and the kinetic limit of nucleation in suspensions of colloidal hard rods

Using simulations we identify three dynamic regimes in supersaturated isotropic fluid states of short hard rods: (i) for moderate supersaturations, we observe nucleation of multilayered crystalline clusters; (ii) at higher supersaturation, we find nucleation of small crystallites which arrange into long-lived locally favored structures that get kinetically arrested; and (iii) at even higher supersaturation, the dynamic arrest is due to the conventional cage-trapping glass transition. For longer rods we find that the formation of the (stable) smectic phase out of a supersaturated isotropic state is strongly suppressed by an isotropic-nematic spinodal instability that causes huge spinodal-like orientation fluctuations with nematic clusters diverging in size. Our results show that glassy dynamics and spinodal instabilities set kinetic limits to nucleation in highly supersaturated hard-rod fluids.