Isotropic-nematic phase transition of nonaqueous suspensions of natural clay rods

A novel model system for studying the behavior of hard colloidal rods is presented, consisting of sterically stabilized particles of natural sepiolite clay. Electron microscopy and scattering results confirmed that the organophilic clay particles were individual, rigid rods when dispersed in organic solvents. With a length-to-diameter ratio of approximately 27, the particles showed nematic ordering for volume fractions phi > 0.06. Polarizing microscopy revealed that the phase separation process involved nucleation, growth, and coalescence of nematic domains. The phase volumes and particle concentrations in the coexisting phases were determined. The dependence of these quantities on the total concentration of the suspension agrees well with Onsager's [Ann. N. Y. Acad. Sci. 51, 627 (1949)] isotropic-nematic phase transition theory extended to bidisperse and polydisperse rod systems, and with previous experimental results for rigid rodlike particles. Particle size distributions were obtained by analyzing transmission electron microscopy images. A significant fractionation with respect to rod length (but not diameter) was observed in the coexisting isotropic and nematic phases. The relative polydispersity of both daughter phases was distinctly smaller than that of the parent suspension. The phase behavior of these daughter fractions agrees well with the predictions for hard spherocylinders of corresponding aspect ratios. An isotropic-nematic-nematic phase equilibrium was seen to develop in phase separated samples after 1 month standing and is ascribed to the effect of polydispersity and possibly gravity. The second nematic phase appearing is dominated by very long rods.     

Formation of nematic liquid crystals of sterically stabilized layered double hydroxide platelets

Colloidal platelets of hydrotalcite, a layered double hydroxide, have been prepared by coprecipitation at pH 11-12 of magnesium nitrate and aluminum nitrate at two different magnesium to aluminum ratios. Changing the temperature and ionic strength during hydrothermal treatment, the platelets were tailored to different sizes and aspect ratios. Amino-modified polyisobutylene molecules were grafted onto the platelets following a convenient new route involving freeze-drying. Organic dispersions in toluene were prepared of the particles with the largest size and highest aspect ratio. The colloidal dispersions prepared in this way showed isotropic-nematic phase transitions above a limiting concentration in a matter of days. The number density at the transition and the width of the biphasic region were determined and compared to theory. The orientation of the platelets in nematic droplets (tactoids) and at the isotropic-nematic interface were analyzed by polarization microscopy. It was observed that sedimentation induces a nematic layer in samples that are below the limiting concentration for isotropic-nematic phase separation. No nematic phase was observed in the initial aqueous suspensions of the ungrafted particles.     

Anomalous columnar order of charged colloidal platelets

Monte Carlo computer simulations are carried out for a model system of like-charged colloidal platelets in the isothermal-isobaric ensemble (NpT). The aim is to elucidate the role of electrostatic interactions on the structure of synthetic clay systems at high particle densities. Short-range repulsions between particles are described by a suitable hard-core model representing a discotic particle. This potential is supplemented with an electrostatic potential based on a Yukawa model for the screened Coulombic potential between infinitely thin disklike macro-ions. The particle aspect-ratio and electrostatic parameters were chosen to mimic an aqueous dispersion of thin, like-charged, rigid colloidal platelets at finite salt concentration. An examination of the fluid phase diagram reveals a marked shift in the isotropic-nematic transition compared to the hard cut-sphere reference system. Several statistical functions, such as the pair correlation function for the center-of-mass coordinates and structure factor, are obtained to characterize the structural organization of the platelets phases. At low salinity and high osmotic pressure we observe anomalous hexagonal columnar structures characterized by interpenetrating columns with a typical intercolumnar distance corresponding to about half of that of a regular columnar phase. Increasing the ionic strength leads to the formation of glassy, disordered structures consisting of compact clusters of platelets stacked into finite-sized columns. These so-called "nematic columnar" structures have been recently observed in systems of charge-stabilized gibbsite platelets. Our findings are corroborated by an analysis of the static structure factor from a simple density functional theory.     

Phase behavior of hard colloidal platelets using free energy calculations

We investigate the phase behavior of a model for colloidal hard platelets and rigid discotic molecules: oblate hard spherocylinders (OHSC). We perform free energy calculations using Monte Carlo simulations to map out the phase diagram as a function of the aspect ratio L∕D of the particles. The phase diagram displays a stable isotropic phase, a nematic liquid crystal phase for L∕D≤0.12, a columnar phase for L∕D?0.3, a tilted crystal phase for L?0.45, and an aligned crystal phase for L∕D?0.45. We compare the results to the known phase diagram of hard cut spheres. Thin cut spheres are almost cylinder-shaped, while the interactions between real discotic mesogens and colloidal platelets are more consistent with the toroidal rims of the OHSC. Since the shapes of the OHSC and the cut spheres are otherwise similar, the phase diagrams of the two types of particles are quite akin. However, the tilted crystal phase for OHSC, which is of a crystal type that is frequently found in experiments on disklike molecules, has not been found for hard cut spheres. Furthermore, although we have found a cubatic phase, it was shown to be definitely unstable, whereas the stability of the cubatic phase of cut spheres is still disputed. Finally, we also show that the phase boundaries differ significantly from those for cut spheres. These are remarkable consequences of a subtle change in particle shape, which show that for a detailed comparison with the phase behavior of experimental particles, the OHSC should be used as a model particle.     

Dichroism in dye-doped colloidal liquid crystals

Nematic liquid crystals were obtained in sterically stabilized suspensions of rodlike particles of sepiolite clay, with an average length up to 900 nm and aspect ratio up to 40. In agreement with computer simulations for hard spherocylinders, the isotropic-nematic transition shifted to lower volume fractions with increasing aspect ratio. However, the coexistence gap was broadened noticeably due to particle polydispersity. The sepiolite crystal structure includes channels filled with zeolitic water, which can be replaced by indigo dye molecules. The indigo molecules are constrained inside the zeolitic channels to be aligned along the long axes of the rods. As a result, the colloidal nematic phase showed a marked dichroism, with an order parameter up to 0.5 for magnetically aligned samples, similar to typical values for dye-doped thermotropic liquid crystals.     

Phase behavior of colloidal hard tetragonal parallelepipeds (cuboids): a Monte Carlo simulation study

The impact of particle geometry on the phase behavior of hard colloidal tetragonal parallelepipeds (TPs) was studied by using Monte Carlo simulations in continuum space. TPs or "cuboids" of aspect ratios varying from 0.25 to 8 were simulated by approximating their shapes with multisite objects, i.e., via rigid clusters of hard spheres. Using equation of state curves, order parameters, radial distribution functions, particle distribution functions along three directions, and visual analysis of configurations, an approximate phase diagram for the TPs was mapped out as a function of aspect ratio (r) and volume fraction. For r > 3 and intermediate concentrations, the behavior of the TPs was similar to that of spherocylinders, exhibiting similar liquid crystalline mesophases (e.g., nematic and smectic phases). For r = 1, a cubatic phase occurs with orientational order along the three axes but with little translational order. For 1 < r < 4, the TPs exhibit a cubatic-like mesophase with a high degree of order along three axes where the major axes of the particles are not all aligned in the same direction. For r < 1, the TPs exhibit a smectic-like phase where the particles have rotational freedom in each layer but form stacks with tetratic order. The equation of state for perfect hard cubes (r = 1) was also simulated and found to be consistent with that of the rounded-edge r = 1 TPs, except for its lack of discontinuity at the cubatic-solid transition.     

Bifurcational analysis of the isotropic-nematic phase transition of rigid rod polymers subjected to biaxial stretching flow

A bifurcational analysis is performed on Doi's equation of nematodynamics that describes the non-equlibrium isotropic-nematic phase transition of rigid rod polymers in the presence of steady biaxial stretching flow. The symmetry of the flow and of the governing order parameter equations are shown to be the source of a rich bifurcation, symmetry breaking, and multistability behavior involving two physically equivalent biaxial nematic phases, one uniaxial nematic phase and one uniaxial paranematic phase. According to the relative intensity of the nematic ordering field and stretching rate, the uniaxial isotropic-biaxial nematic transition may be continuous (2nd order), discontinuous (1st order), or it may exhibit a tricritical non-equilibrium phase transition point. The solutions to the Doi equations of nematodynamics are found to be consistent with those of Khokhlov and Semenov [Macromolecules 15 , 1272 (1982)], which are based on a version of the Onsager theory of isotropic-nematic phase transitions. The present simulations provide a useful guide for orientation control in biaxial stretching flows.     

Dispersion control and nematic ordering of Ni/Al layered double hydroxide suspensions

In this paper, we report the preparation of aqueous suspensions of Ni/Al layered double hydroxide (LDH) nanoparticles by a non-steady co-precipitation followed by peptization. By choosing suitable peptization temperature and time, well-dispersed suspensions were obtained. Meanwhile, the particle size, shape and size polydispersity can be efficiently controlled. Nematic ordering is observed in colloidal Ni/Al LDH suspensions and confirmed by birefringence observations and SAXS measurements. Furthermore, we showed that the sol-gel transition takes place after a liquid crystalline phase transition in concentrated Ni/Al LDH suspensions. The absence of isotropic-nematic phase separation can be attributed to the fact that the nematic phase droplets are too small to settle to the bottom of the cuvette.     

Phase separations in liquid crystal-colloid mixtures

We present a mean-field theory to describe phase separations in mixtures of a nematic liquid crystal and a colloidal particle. The theory takes into account an orientational ordering of liquid crystals and a crystalline ordering of colloidal particles. We calculate phase diagrams on the temperature-concentration plane, depending on interactions between a liquid crystal and a colloidal surface and a coupling between nematic and crystalline ordering. We find various phase separation processes, such as a nematic-crystal phase separation and nematic-isotropic-crystal triple point. Inside binodal curves, we find new unstable and metastable regions which are important in phase ordering dynamics. We also find a stable nematic-crystalline (NC) phase, where colloidal particles dispersed in a nematic phase can form a crystalline structure. The coexistence between two NC phases with different concentrations can be appear though the coupling between nematic and crystalline ordering.     

Ordering of anisotropic polarizable polymer chains on the full many-body level

We study the effect of dielectric anisotropy of polymers on their equilibrium ordering within mean-field theory, but with a formalism that takes into account the full n-body nature of van der Waals (vdW) forces. Dielectric anisotropy within polymers is to be expected as the electronic properties of the polymer will typically be different along the polymer than across its cross section. It is therefore physically intuitive that larger charge fluctuations can be induced along the chain than perpendicular to it. We show that this dielectric anisotropy leads to n-body interactions which can induce an isotropic-nematic transition. The two body and three body components of the full vdW interaction are extracted and it is shown how the two body term behaves like the phenomenological self-aligning-pairwise nematic interaction. At the three body interaction level we see that the nematic phase that is energetically favorable is discotic, however, on the full n-body interaction level we find that the normal axial nematic phase is always the stable ordered phase. The n-body nature of our approach also shows that the key parameter driving the nematic-isotropic transition is the bare persistence length of the polymer chain.     

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

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

Gravity-induced liquid crystal phase transitions of colloidal platelets

The influence of gravity on a suspension of sterically stabilized colloidal gibbsite platelets is studied. An initially isotropic-nematic biphasic sample of such a suspension develops a columnar phase on the bottom on prolonged standing. This phenomenon is described using a simple osmotic compression model. We performed Monte Carlo simulations of cut spheres with aspect ratio L/D=1/15 and took data from the literature to supply the equations of state required for the model. We find that the model describes the observed three-phase equilibrium quite well.     

Phase behavior of colloidal hard perfect tetragonal parallelepipeds

The phase behavior of suspensions of colloidal hard tetragonal parallelepipeds ("TPs") (also known as rectangular nanorods or nanobars) was studied by using Monte Carlo simulations to gain a detailed understanding of the effect of flat-faceted particles on inducing regular local packing and long range structural order. A TP particle has orthogonal sides with lengths a, b, and c, such that a=b and its aspect ratio is r=c/a. The phase diagram for such perfect TPs was mapped out for particle aspect ratios ranging from 0.125 to 5.0. Equation of state curves, order parameters, particle distribution functions, and snapshots were used to analyze the resulting phases. Given the athermal nature of the systems studied, it is the interplay of purely entropic forces that drives phase transitions amongst the structures observed that include crystal, columnar, smectic, parquet, and isotropic phases. In the parquet phase that occurs for 0.54相似文献   

Computer simulation studies of anisotropic systems XXIX. Quadrupolar Gay-Berne discs and chemically induced liquid crystal phases

Liquid crystal phases can be induced chemically by mixing compounds whose specific interactions are such that the transition temperature for the induced phase is higher than the melting points of the two compounds. A particularly dramatic example of such behaviour is the creation of a columnar nematic and a hexagonal columnar phase on mixing discotic multiynes with 2,4,7-trinitrofluorenone. Although the intense colour of the mixture indicates a strong charge-transfer band, it is uncertain as to whether the charge-transfer interaction between unlike molecules is enough to stabilize the induced liquid crystal phases. An alternative explanation for the formation of such phases involves an electrostatic quadrupolar interaction between the components,whose quadrupole moments differ in sign. This interaction weakens the face-to-face attraction for like particles while strengthening it for unlike particles. We have explored this possible explanation for chemically induced liquid crystal phases in discotic systems by modelling the basic interaction between discs with a Gay-Berne potential, to which is added a point quadrupolar interaction. We have determined the phase behaviour of the pure systems and their binary mixtures with constant pressure Monte Carlo simulations. It would seem that the quadrupolar interaction can account for many of the features of chemically induced liquid crystals.     

Columnar and interdigitated structures from apolar discotic mesogens with radial dipoles: a Monte Carlo study

We have simulated, using a Monte Carlo method, a system of apolar Gay-Berne discotic particles without dipoles and with two or three dipoles symmetrically embedded in the disc. The dipoleless system can form nematic and hexagonal columnar mesophases. Adding two in-plane antiparallel radial dipoles has the effect of destabilizing the columnar ordering, in favour of a fully interdigitated arrangement of the molecular stacks, with strong correlations in the plane perpendicular to the director and large biaxiality. No columnar phase is observed for the systems with three planar radial dipoles with threefold symmetry up to very low temperatures. Finally, on decreasing the strength of the three dipoles, a columnar non-interdigitated phase is observed.     

Measurement of density distributions for colloidal beta-FeOOH rods in suspensions exhibiting phase separation: the role of long-range forces in smectic ordering

We prepared monodisperse colloidal beta-FeOOH rods with length-to-width ratios L/W of 3.6-7.0 (L=210-330 nm and W=40-58 nm). Density gradients of the rods occurred in the suspensions by gravity, inducing a phase separation. The denser phase showed smectic (Sm) liquid crystalline structures exhibiting iridescent colors in a wide range of pH from 1.2 (at which the rods interact attractively) to 4.7 (repulsively). The lower density phase was disordered, but frequently emitted diffuse colors locally (at pH>2.6), implying the occurrence of short-range order. The nematic phase was not observed in the beta-FeOOH systems, being consistent with theoretical predictions. The particle density distributions were measured over the whole region of the suspensions (separated into two phases) at various pH values using a rapid freezing method. A phase diagram was determined thereby, where the critical (minimal) packing fraction of the particles for the Sm phase showed a nonlinear decrease from 0.43 to 0.12 with increasing pH. Rod-rod spacings in the Sm phase estimated experimentally at various pH were well explained using Derjaguin-Landau-Verwey-Overbeek (DLVO) type pair potentials. It is suggested that Sm ordering can be induced by attractive minima at pH<2.2, while driven by soft repulsions at pH>2.6. The former Sm ordering is expected to be the condensation-type phase transition and the latter the disorder-order transition.     

Isotropic-nematic spinodals of rigid long thin rodlike colloids by event-driven Brownian dynamics simulations

The isotropic-nematic spinodals of solutions of rigid spherocylindrical colloids with various shape anisotropies L/D in a wide range from 10 to 60 are investigated by means of Brownian dynamics simulations. To make these simulations feasible, we developed a new event-driven algorithm that takes the excluded volume interactions between particles into account as instantaneous collisions, but neglects the hydrodynamic interactions. This algorithm is applied to dense systems of highly elongated rods and proves to be efficient. The calculated isotropic-nematic spinodals lie between the previously established binodals in the phase diagram and extrapolate for infinitely long rods to Onsager's [Ann. N. Y. Acad. Sci. 51, 627 (1949)] theoretical predictions. Moreover, we investigate the shear induced shifts of the spinodals, qualitatively confirming the theoretical prediction of the critical shear rate at which the two spinodals merge and the isotropic-nematic phase transition ceases to exist.     

Video microscopy of colloidal suspensions and colloidal crystals

Colloidal suspensions are simple model systems for the study of phase transitions. Video microscopy is capable of directly imaging the structure and dynamics of colloidal suspensions in different phases. Recent results related to crystallization, glasses, and 2D systems complement and extend previous theoretical and experimental studies. Moreover, new techniques allow the details of interactions between individual colloidal particles to be carefully measured. Understanding these details will be crucial for designing novel colloidal phases and new materials, and for manipulating colloidal suspensions for industrial uses.     

Simulation studies of self-assembly of end-tethered nanorods in solution and role of rod aspect ratio and tether length

We present temperature versus concentration phase diagrams for "shape amphiphiles" comprised of tethered moderate and low aspect ratio rods. Simulations of moderate aspect ratio rods (first reported by Horsch et al. [Phys. Rev. Lett. 95, 056105 (2005)]) predict their self-assembly into spherical micelles with bcc order, long micelles with nematic order, a racemic mixture of hexagonally ordered chiral cylinders, two perforated phases: one with tetragonal order and one with hexagonal order, and a smectic C lamellar phase. In contrast, we predict here that small aspect ratio tethered rods self-assemble into bcc ordered spherical micelles, hexagonally ordered cylinders, and a smectic C lamellar phase. We compare and contrast the phases obtained for the two aspect ratios and examine in further detail several unusual phases. Our simulations also reveal that for moderate aspect ratio rods there is a tendency toward phases with decreasing interfacial curvature with decreasing coil size, including a double gyroid phase. In addition, we investigate the role of tether length on the assembled structures. Our results are applicable to short rod-coil block copolymers and rodlike nanoparticles with polymer tethers, and to colloidal building blocks comprised of a flexible string of colloids tethered to a rigid string of colloids, with the interactions scaled appropriately.     

Nematic-nematic demixing in polydisperse thermotropic liquid crystals

We consider the effects of polydispersity on isotropic-nematic phase equilibria in thermotropic liquid crystals, using a Maier-Saupe theory [Z. Naturforsch. A 13A, 564 (1958)] with factorized interactions. A sufficient spread (approximately 50%) in the interaction strengths of the particles leads to phase separation into two or more nematic phases, which can in addition coexist with an isotropic phase. The isotropic-nematic coexistence region widens dramatically as polydispersity is increased, leading to reentrant isotropic-nematic phase separation in some regions of the phase diagram. We show that similar phenomena will occur also for nonfactorized interactions as long as the interaction strength between any two particle species is lower than the mean of the intraspecies interactions.