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.     

Computer simulation studies of anisotropic systems. XXII. An equimolar mixture of rods and discs: A biaxial nematic?

In principle, binary mixtures of rod-like and disc-like particles should exhibit a biaxial nematic phase, but in practice phase separation into two uniaxial nematic phases prevents this. Here, we report the results of a computer simulation study of an equimolar mixture of rods and discs in which phase separation is not allowed. The particles are confined to the sites of a simple cubic lattice in which each rod is surrounded by six discs and vice versa. Neighbouring particles interact such that they prefer to align with their respective symmetry axes orthogonal to each other. In contrast, the interaction between next nearest neighbours, which are either rods or discs, is such that their symmetry axes tend to be parallel. Monte Carlo simulations of this model mixture show that an orientationally ordered phase exists at low temperatures. This nematic phase has overall uniaxial symmetry and the particles have a negative second rank orientational order parameter, indicating that they tend to align at right angles to the director. The two interpenetrating sub-lattices containing either rods or discs, however, exhibit a biaxial nematic phase. The results of the simulation are found to be in reasonable agreement with the predictions of a molecular field theory for this model mixture. We have also investigated the behaviour of this mixture when the rods and discs are allowed to exchange between their lattice sites. The mixture is found to separate into two uniaxial nematic phases composed essentially of either rods or discs, as expected.     

Nematic and crystalline ordering in the lattice model of hard rods with a mean field interaction

A lattice model of long hard rods with a nearest neighbour attraction proportional to the length of overlap is considered. It is shown, that in the van der Waals approximation the model exhibits non only the isotropic and nematic phases obtained with the approximative treatment of the hard rod interaction but also a crystalline phase.     

Sol/gel and isotropic/nematic transitions in aqueous suspensions of natural nontronite clay. Influence of particle anisotropy. 1. Features of the i/n transition

The phase behavior of a natural nontronite clay was studied for size-selected particles by combining osmotic pressure measurements, visual observations under polarized light, and rheological experiments. In parallel, the positional and orientational correlations of the particles were analyzed by small-angle X-ray scattering. Aqueous suspensions of nontronite exhibit a true isotropic/nematic (I/N) transition that occurs before the sol/gel transition, for ionic strengths below 10(-3) M/L. In this region of the phase diagrams, the system appears to be purely repulsive. The I/N transition shifts toward lower volume fractions for increasing particle anisotropy, and its position in the phase diagram agrees well with the theoretical predictions for platelets. SAXS measurements reveal the presence of characteristic interparticular distances in the isotropic, nematic, and gel phases. The swelling law (separation distance vs swelling law) exhibits two regimes. For high volume fractions, the swelling law is one-dimensional as in layered systems and reveals the presence of isolated platelets. At lower volume fraction, distances scale as phi(-1/3), indicating isotropic volumic swelling. Finally, the experimental osmotic pressure curves can be satisfactorily reproduced by considering the interparticle distances between two charged planes whose effective charge is around 10% of the structural charge.     

Effect of quenched size polydispersity on the fluid-solid transition in charged colloidal suspensions

We study the effect of quenched size polydispersity on the phase behavior of charged colloidal suspensions using free-energy calculations in Monte Carlo simulations. The colloids are assumed to interact with a hard-core repulsive Yukawa (screened-Coulomb) interaction with constant surface potential, so that the particles are polydisperse both in size and charge. In addition, we take the size distribution to be fixed in both the fluid and crystal phase (no size fractionation is allowed). We study the fluid-solid transition for various screening lengths and surface potentials, finding that upon increasing the size polydispersity the freezing transition shifts toward higher packing fractions and the density discontinuity between the two coexisting phases diminishes. Our results provide support for a terminal polydispersity above which the freezing transition disappears.     

Isotropic–nematic phase separation and demixing in mixtures of spherical nanoparticles with length‐polydisperse nanorods

An extension of Onsager theory is developed to simulate isotropic–nematic phase separation in a mixture of spheres with length‐polydisperse system of rods. This work is motivated by recent experimental data on nanorod liquid crystals. Prior theoretical investigations indicate that both polydispersity and the presence of spheres should increase the biphasic–nematic phase transition, that is, the nematic cloud point. Results indicate that the phase diagrams undergo drastic changes depending upon both particle geometry and rod length polydispersity. The key geometric factor is the ratio between the sphere diameter and the rod diameter. In general, length fractionation is enhanced by the addition of spheres, which may be experimentally advantageous for separating short nanorods from a polydisperse population. Simulation results also indicate that the nematic cloud and shadow curves may cross one another because of the scarcity of spheres in the shadow phase. In general, these results do indicate that the nematic cloud point increases as a function of sphere loading; however, in certain areas of phase space, this relationship is nonmonotonic such that the nematic cloud point may actually decrease with the addition of spheres. This work has application to a wide range of nanoparticle systems, including mixtures of spherical nanoparticles with nanorods or nanotubes. Additionally, a number of nonspherical particles and structures may behave as spheres, including crumpled graphene and tightly coiled polymers. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Structure formation and fractionation in systems of polydisperse attractive rods

Fractionation effects and the formation of structured domains are investigated in polydisperse systems of attractive spherocylinders with the help of Monte Carlo simulations. For sufficiently high attractive interaction strength and pressure, the large rods in the system aggregate and form a highly ordered hexatic monolayer that coexists with an isotropic fluid of smaller rods. Fractionation diminishes with decreasing interaction strength but is still observed for hard rod systems, in which the large rods form a nematic droplet rather than a monolayer. Results for polydisperse systems are accompanied by phase diagrams for monodisperse systems of attractive spherocylinders. Here, the phase behavior is shown as a function of rod length and pressure.     

Phase behavior and interfacial properties of nonadditive mixtures of Onsager rods

Within a second virial theory, we study bulk phase diagrams as well as the free planar isotropic-nematic interface of binary mixtures of nonadditive thin and thick hard rods. For species of the same type, the excluded volume is determined only by the dimensions of the particles, whereas for dissimilar ones it is taken to be larger or smaller than that, giving rise to a nonadditivity that can be positive or negative. We argue that such a nonadditivity can result from modeling of soft interactions as effective hard-core interactions. The nonadditivity enhances or reduces the fractionation at isotropic-nematic (IN) coexistence and may induce or suppress a demixing of the high-density nematic phase into two nematic phases of different composition (N(1) and N(2)), depending on whether the nonadditivity is positive or negative. The interfacial tension between coexisting isotropic and nematic phases shows an increase with increasing fractionation at the IN interface, and complete wetting of the IN(2) interface by the N(1) phase upon approach of the triple-point coexistence. In all explored cases bulk and interfacial properties of the nonadditive mixtures exhibit a striking and quite unexpected similarity with the properties of additive mixtures of different diameter ratio.     

Isotropic-nematic interfacial tension of hard and soft rods: application of advanced grand canonical biased-sampling techniques

Coexistence between the isotropic and the nematic phase in suspensions of rods is studied using grand canonical Monte Carlo simulations with a bias on the nematic order parameter. The biasing scheme makes it possible to estimate the interfacial tension gamma(IN) in systems of hard and soft rods. For hard rods with LD=15, we obtain gammaIN approximately 1.4kBT/L2, with L the rod length, D the rod diameter, T the temperature, and kB the Boltzmann constant. This estimate is in good agreement with theoretical predictions, and the order of magnitude is consistent with experiments.     

Cubatic phase for tetrapods

We investigate the phase behavior of tetrapods, hard nonconvex bodies formed by four rods connected under tetrahedral angles. We predict that, depending on the relative lengths of the rods these particles can form a uniaxial nematic phase, and more surprisingly they can exhibit a cubatic phase, a special case of the biaxial nematic phase. These predictions may be experimentally testable, as experimental realizations of tetrapods have recently become available.     

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.     

Smectic ordering in athermal systems of rodlike triblock copolymers

The phase behavior of the system of parallel rigid triblock copolymers is examined using the second virial density functional theory. The triblock particle consists of two identical infinitely thin hard rods of finite lengths on the opposite ends of one central hard cylinder with nonzero length and diameter. Stability analyses and free energy calculations show that the system of parallel particles can form not only uniform nematic and smectic A phases but also a smectic C phase. The stability and structure of the tilted structure are controlled by only the diameter and the length of the central cylinder segment. Interestingly, the diameter affects only the layer tilting and the periodicity, but not the packing fraction of the nematic to smectic-C transition. For all values of cylinder length the usual smectic A and smectic C transitions compete with each other and no nematic-columnar transition is observed. At low and high cylinder lengths the smectic A phase is stabilized first, while the smectic C is the most stable for intermediate length values.     

Effect of particle geometry on phase transitions in two-dimensional liquid crystals

Using a version of density-functional theory which combines Onsager approximation and fundamental-measure theory for spatially nonuniform phases, we have studied the phase diagram of freely rotating hard rectangles and hard discorectangles. We find profound differences in the phase behavior of these models, which can be attributed to their different packing properties. Interestingly, bimodal orientational distribution functions are found in the nematic phase of hard rectangles, which cause a certain degree of biaxial order, albeit metastable with respect to spatially ordered phases. This feature is absent in discorectangles, which always show unimodal behavior. This result may be relevant in the light of recent experimental results which have confirmed the existence of biaxial phases. We expect that some perturbation of the particle shapes (either a certain degree of polydispersity or even bimodal dispersity in the aspect ratios) may actually destabilize spatially ordered phases thereby stabilizing the biaxial phase.     

Free isotropic-nematic interfaces in fluids of charged platelike colloids

Bulk properties and free interfaces of mixtures of charged platelike colloids and salt are studied within the density-functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model. The charges of the particles are concentrated in their center. The density functional is derived by functional integration of an extension of the Debye-Hückel pair distribution function with respect to the interaction potential. For sufficiently small macroion charges, the bulk phase diagrams exhibit one isotropic and one nematic phase separated by a first-order phase transition. With increasing platelet charge, the isotropic and nematic binodals are shifted to higher densities. The Donnan potential between the coexisting isotropic and nematic phases is inferred from bulk structure calculations. Nonmonotonic density and nematic order parameter profiles are found at a free interface interpolating between the coexisting isotropic and nematic bulk phases. Moreover, electrically charged layers form at the free interface leading to monotonically varying electrostatic potential profiles. Both the widths of the free interfaces and the bulk correlation lengths are approximately given by the Debye length. For fixed salt density, the interfacial tension decreases upon increasing the macroion charge.     

Rigid rod molecules as liquid crystal thermosets. II. Rigid rod esters

Nine rigid rod ester monomers endcapped with maleimide, nadimide, and methylnadimide groups were prepared and studied by DSC and hot stage polarized light microscopy. All of the monomers showed thermotropic nematic liquid crystalline phases and could be thermally crosslinked in the nematic phase. The nematic texture was maintained in the crosslinked solid state. The nematic phase range was enlarged by B-staging the monomeric compounds. Heating the monomers for a short period of time in the nematic phase lowered the crystal to nematic transition temperatures and increased the nematic to isotropic transition temperatures. A nonequilibrium phase diagram was proposed to explain the melting behavior of these reactive liquid crystal thermoset materials.     

Depletion induced isotropic-isotropic phase separation in suspensions of rod-like colloids

When non-adsorbing polymers are added to an isotropic suspension of rod-like colloids, the colloids effectively attract each other via depletion forces. We performed Monte Carlo simulations to study the phase diagram of such rod-polymer mixture. The colloidal rods were modeled as hard spherocylinders; the polymers were described as spheres of the same diameter as the rods. The polymers may overlap with no energy cost, while the overlap of polymers and rods is forbidden. Large amounts of depletant cause phase separation of the mixture. We estimated the phase boundaries of isotropic-isotropic coexistence both in the bulk and in confinement. To determine the phase boundaries we applied the grand canonical ensemble using successive umbrella sampling [J. Chem. Phys. 120, 10925 (2004)], and we performed a finite size scaling analysis to estimate the location of the critical point. The results are compared with predictions of the free volume theory developed by Lekkerkerker and Stroobants [Nuovo Cimento D 16, 949 (1994)]. We also give estimates for the interfacial tension between the coexisting isotropic phases and analyze its power-law behavior on the approach of the critical point.     

Phase coexistence in polydisperse athermal polymer-colloidal mixture

A theoretical scheme developed earlier [Y. V. Kalyuzhnyi et al., Chem. Phys. Lett. 443, 243 (2007)] is used to calculate the full phase diagram of polydisperse athermal polymer-colloidal mixture with polydispersity in both colloidal and polymeric components. In the limiting case of bidisperse polymer-colloidal mixture, theoretical results are compared against computer simulation results. We present the cloud and shadow curves, critical binodals, and distribution functions of the coexisting phases and discuss the effects of polydispersity on their behavior. According to our analysis polydispersity extends the region of the phase instability, shifting the critical point to the lower values of the pressure and density. For the high values of the pressure polydispersity causes strong fractionation effects, with the large size colloidal particles preferring the low-density shadow phase and long chain length polymeric particles preferring the high-density shadow phase.     

Depletion interaction mediated by polydisperse rods

The interaction between a colloidal hard sphere of radius R and a wall or between two spheres in a dilute suspension of infinitely thin rods of length L is calculated numerically. The method allows the study of depletion potentials for any value of LR and, consequently, the influence of rod length polydispersity can be investigated. It was observed that both the depth and the range of the potential increase drastically if the relative standard deviation sigma of the length distribution is larger than 0.25, while the potential is virtually indistinguishable from that caused by monodisperse rods, if sigma < or similar to 0.1.     

Isotropic-nematic transition of hard rods immersed in random sphere matrices

Using replica density functional theory and Monte Carlo computer simulations we investigate a system of annealed hard spherocylinders adsorbed in a matrix of quenched hard spheres. Theoretical predictions for the partition coefficient, defined as the ratio of density of rods in the matrix and that in a reservoir, agree well with simulation results. Theory predicts the isotropic-nematic transition to remain first order upon increasing sphere packing fraction, and to shift towards lower rod densities. This scenario is consistent with our simulation results that clearly show a jump in the nematic order parameter upon increasing the rod density at constant matrix packing fraction, corresponding to the isotropic-nematic transition, even for sphere matrix packing fractions < or approximately equal to 0.3.