Active microrheology of colloidal suspensions of hard cuboids

By performing dynamic Monte Carlo simulations, we investigate the microrheology of isotropic suspensions of hard-core colloidal cuboids. In particular, we infer the local viscoelastic behavior of these fluids by studying the dynamics of a probe spherical particle that is incorporated in the host phase and is dragged by an external force. This technique, known as active microrheology, allows one to characterize the microscopic response of soft materials upon application of a constant force, whose intensity spans here three orders of magnitude. By tuning the geometry of cuboids from oblate to prolate as well as the system density, we observe different responses that are quantified by measuring the effective friction perceived by the probe particle. The resulting friction coefficient exhibits a linear regime at forces that are much weaker and larger than the thermal forces, whereas a nonlinear, force-thinning regime is observed at intermediate force intensities.

Self-assembly of freely-rotating polydisperse cuboids: unveiling the boundaries of the biaxial nematic phase

Colloidal cuboids have the potential to self-assemble into biaxial liquid crystal phases, which exhibit two independent optical axes. Over the last few decades, several theoretical works have predicted the existence of a wide region of the phase diagram where the biaxial nematic phase would be stable, but imposed rather strong constraints on the particle rotational degrees of freedom. In this work, we use molecular simulation to investigate the impact of size dispersity on the phase behaviour of freely-rotating hard cuboids, here modelled as self-dual-shaped nanoboards. This peculiar anisotropy, exactly in between the oblate and prolate geometry, has been proposed as the most appropriate to promote phase biaxiality. We observe that size dispersity radically changes the phase behaviour of monodisperse systems and leads to the formation of an elusive biaxial nematic phase, being found in a large region of the packing fraction vs. polydispersity phase diagram. Although our results confirm the tendencies reported in past experimental observations on colloidal dispersions of slightly prolate goethite particles, they cannot reproduce the direct isotropic-to-biaxial nematic phase transition observed in these experiments.

A simulation study on the phase behavior of hard rhombic platelets

Using Monte Carlo simulations, we investigate the phase behavior of hard rhombic platelets as a function of the thickness of the platelets, T. The phase diagram displays a columnar phase and a crystal phase in which the platelets are stacked in columns that are arranged in a two-dimensional lattice. We find that the shape of the platelets determines the symmetry of the two-dimensional lattice, i.e., rhombic platelets form an oblique columnar phase and a simple monoclinic crystal phase. For sufficiently thick platelets, i.e., for a thickness-to-length ratio T/L>0.17, we find only an isotropic fluid, an oblique columnar phase, and a monoclinic crystal phase. Surprisingly, for an intermediate plate thickness, 0.083<T/L<0.17, we also find a region in between the isotropic (or nematic) phase and the columnar phase, where the smectic phase is stable. For sufficiently thin platelets, T/L<0.13, the phase diagram displays a nematic phase. With the exception of the smectic phase, our results resemble the phase behavior of discotic particles. Our results may guide the synthesis and future experiments on rhombic nanoplatelets.

Hard Competition: Stabilizing the Elusive Biaxial Nematic Phase in Suspensions of Colloidal Particles with Extreme Lengths

We use computer simulations to study the existence and stability of a biaxial nematic N_{b} phase in systems of hard polyhedral cuboids, triangular prisms, and rhombic platelets, characterized by a long (L), medium (M), and short (S) particle axis. For all three shape families, we find stable N_{b} states provided the shape is not only close to the so-called dual shape with M=sqrt[LS] but also sufficiently anisotropic with L/S>9,11,14,23 for rhombi, (two types of) triangular prisms, and cuboids, respectively, corresponding to anisotropies not considered before. Surprisingly, a direct isotropic-N_{b} transition does not occur in these systems due to a destabilization of N_{b} by a smectic (for cuboids and prisms) or a columnar (for platelets) phase at small L/S or by an intervening uniaxial nematic phase at large L/S. Our results are confirmed by a density functional theory provided the third virial coefficient is included and a continuous rather than a discrete (Zwanzig) set of particle orientations is taken into account.

Phase behaviour of hard board-like particles

We examine the phase behaviour of colloidal suspensions of hard board-like particles (HBPs) as a function of their shape anisotropy, and observe a fascinating spectrum of nematic, smectic, and columnar liquid-crystalline phases, whose formation is entirely driven by excluded volume effects. We map out the phase diagram of short and long HBPs by gradually modifying their shape from prolate to oblate and investigate the long-range order of the resulting morphologies along the phase directors and perpendicularly to them. The intrinsic biaxial nature of these particles promotes the formation of translationally ordered biaxial phases, but does not show solid evidence that it would, per se, promote the formation of the biaxial nematic phase. Our simulations shed light on the controversial existence of the discotic smectic phase, whose layers are as thick as the minor particle dimension, which is stable in a relatively large portion of our phase diagrams. Additionally, we modify the Onsager theory to describe the isotropic-nematic phase transition of freely rotating biaxial particles as a function of the particle width, and find a relatively strong first-order signature, in excellent agreement with our simulations. In an attempt to shed light on the elusive formation of the biaxial nematic phase, we apply this theory to predict the uniaxial-biaxial nematic phase transition and confirm, again in agreement with simulations, the prevailing stability of the translationally ordered smectic phase over the orientationally ordered biaxial nematic phase.

The Landau-de Gennes free energy expansion of a melt of V-shaped polymer molecules

The phase behavior of a monodisperse melt of polymer molecules consisting of two rod-like segments joined at an angle α has been inspected within the Landau theory of phase transitions. The interactions between monomer units were assumed to be of the Maier-Saupe form. The Landau-de Gennes expansion of the free energy of the melt has been obtained up to the sixth order in powers of the nematic order parameter, the coefficients of this expansion have been calculated from the microscopic model of polymer molecule. The phase diagram contains the regions of stability of isotropic, prolate uniaxial, oblate uniaxial, and biaxial nematic phases. The isotropic-uniaxial nematic and uniaxial-biaxial nematic transitions are of the first and second order, respectively. We found two Landau points in the phase diagram at which continuous transition from biaxial nematic state to isotropic phase occurs.

Phase behaviour and correlations of parallel hard squares: from highly confined to bulk systems

We study a fluid of two-dimensional parallel hard squares in bulk and under confinement in channels, with the aim of evaluating the performance of fundamental-measure theory (FMT). To this purpose, we first analyse the phase behaviour of the bulk system using FMT and Percus-Yevick (PY) theory, and compare the results with molecular dynamics and Monte Carlo simulations. In a second step, we study the confined system and check the results against those obtained from the transfer matrix method and from our own Monte Carlo simulations. Squares are confined to channels with parallel walls at angles of 0° or 45° relative to the diagonals of the parallel hard squares, respectively, which allows for an assessment of the effect of the external-potential symmetry on the fluid structural properties. In general FMT overestimates bulk correlations, predicting the existence of a columnar phase (absent in simulations) prior to crystallization. The equation of state predicted by FMT compares well with simulations, although the PY approach with the virial route is better in some range of packing fractions. The FMT is highly accurate for the structure and correlations of the confined fluid due to the dimensional crossover property fulfilled by the theory. Both density profiles and equations of state of the confined system are accurately predicted by the theory. The highly non-uniform pair correlations inside the channel are also very well described by FMT.

Orientational ordering of confined hard rods: the effect of shape anisotropy on surface ordering and capillary nematization

We examine the ordering properties of rectangular hard rods with length L and diameter D at a single planar wall and between two parallel hard walls using the second virial density-functional theory. The theory is implemented in the three-state Zwanzig approximation, where only three mutually perpendicular directions are allowed for the orientations of hard rods. The effect of varying shape anisotropy is examined at L/D=10,15,and20. In contact with a single hard wall, the density profiles show planar ordering, damped oscillatory behavior, and a wall-induced surface ordering transition below the coexisting isotropic density of a bulk isotropic-nematic (I-N) phase transition. Upon approaching the coexisting isotropic density, the thickness of the nematic film diverges logarithmically, i.e., the nematic wetting is complete for any shape anisotropy. In the case of confinement between two parallel hard walls, it is found that the continuous surface ordering transition depends strongly on the distance between confining walls H for H<L, while it depends weakly on H for H>L. The minimal density at which a surface ordering transition can be realized is located at around H∼2D for all studied shape anisotropies due to the strong interference effect between the two hard walls. The first-order I-N phase transition of the bulk system becomes a surface ordered isotropic I_{B} to capillary nematic N_{B} phase transition in the slit pore. This first-order I_{B}-N_{B} transition weakens with decreasing pore width and terminates in a critical point for all studied shape anisotropies.

Effect of shape biaxiality on the phase behavior of colloidal liquid-crystal monolayers

We extend our previous work on monolayers of uniaxial particles [J. Chem. Phys., 2014, 140, 204906] to study the effect of particle biaxiality on the phase behavior of liquid-crystal monolayers. Particles are modelled as board-like hard bodies with three different edge lengths σ1 ≥ σ2 ≥ σ3, and the restricted-orientation approximation (Zwanzig model) is used. A density-functional formalism based on the fundamental-measure theory is used to calculate phase diagrams for a wide range of values with the largest aspect ratio κ1 = σ1/σ3 ∈ [1,100]. We find that particle biaxiality in general destabilizes the biaxial nematic phase already present in monolayers of uniaxial particles. While plate-like particles exhibit strong biaxial ordering, rod-like ones with κ1 > 21.34 exhibit reentrant uniaxial and biaxial phases. As particle geometry is changed from uniaxial- to increasingly biaxial-rod-like, the region of biaxiality is reduced, eventually ending in a critical-end point. For κ1 > 60, a density gap opens up in which the biaxial nematic phase is stable for any particle biaxiality. Regions of the phase diagram, where packing-fraction inversion occurs (i.e. packing fraction is a decreasing function of density), are found. Our results are compared with the recent experimental studies on nematic phases of magnetic nanorods.

Self-assembly of biaxial discorectangular lead carbonate nanosheets into stacked ribbons studied by SAXS and HAADF-STEM tomographic tilt series

The self-assembling behaviour of 2.6 nm thin PbCO3 nanoplatelets with discorectangular shape and uniform width and thickness occurring after their formation in nonionic water-in-oil microemulsions has been investigated using synchrotron small angle X-ray scattering (SAXS) and (scanning) transmission electron microscopy ((S)TEM). The presence of attractive depletion forces originating from the ubiquitous microemulsion droplets triggers a new type of superstructure at low particle concentration. Instead of the universally observed formation of face-to-face assembled lamellar mesostructures, the nanosheets self-organise into extended ribbon structures, whereby each on top lying sheet is displaced by a constant shift in the length and width directions leading to a so far unprecedented staggered zigzag-type stack assembly with restricted height. This type of stacking gives rise to a complex interference pattern in the isotropic small angle scattering of the stacked ribbon assemblies (SRAs) in reverse micellar solution. Different to the, for lamellar-structured nanosheets typical, diffraction peaks at multiples of the wave vector corresponding to one particular repeat distance, the scattering peaks measured in this study are asymmetric, displaying a shoulder on their low wave vector side. The asymmetric shape of the observed face-to-face correlation peaks indicates that the SRAs do not extend in one direction only. Their scattering behaviour is analysed by expanding the Kratky-Porod structure factor for stacking plates into three dimensions. High-angle annular dark-field (HAADF)-STEM tilt series have complementary been acquired to retrieve three-dimensional structural information on the SRAs in the dry state and to confirm the model used for the refinement of the SAXS data.

Hard-body models of bulk liquid crystals

Hard models for particle interactions have played a crucial role in the understanding of the structure of condensed matter. In particular, they help to explain the formation of oriented phases in liquids made of anisotropic molecules or colloidal particles and continue to be of great interest in the formulation of theories for liquids in bulk, near interfaces and in biophysical environments. Hard models of anisotropic particles give rise to complex phase diagrams, including uniaxial and biaxial nematic phases, discotic phases and spatially ordered phases such as smectic, columnar or crystal. Also, their mixtures exhibit additional interesting behaviours where demixing competes with orientational order. Here we review the different models of hard particles used in the theory of bulk anisotropic liquids, leaving aside interfacial properties and discuss the associated theoretical approaches and computer simulations, focusing on applications in equilibrium situations. The latter include one-component bulk fluids, mixtures and polydisperse fluids, both in two and three dimensions, and emphasis is put on liquid-crystal phase transitions and complex phase behaviour in general.

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.

Model of hard spheroplatelets near a hard wall

A system of hard spheroplatelets near an impenetrable wall is studied in the low-density Onsager approximation. Spheroplatelets have optimal shape between rods and plates, and the direct transition from the isotropic to biaxial nematic phase is present. A simple local approximation for the one-particle distribution function is used. Analytical results for the surface tension and the entropy contributions are derived. The density and the order-parameter profiles near the wall are calculated. The preferred orientation of the short molecule axes is perpendicular to the wall. Biaxiality close to the wall can appear only if the phase is biaxial in the bulk.

Supramolecular nature of the nematic-nematic phase transitions of hard boardlike molecules

The phase behavior of hard boardlike biaxial particles of relative dimensions close to the clamitic to discotic crossover is explored by means of Monte Carlo molecular simulations. Transitions between two distinct biaxial nematic phases as well as transitions from a biaxial nematic to a uniaxial Sm-A phase are obtained. The formation of anisotropic supramolecular assemblies is demonstrated and is quantified by means of rotationally invariant pair correlation functions.

Depletion-induced biaxial nematic states of boardlike particles

With the aim of investigating the stability conditions of biaxial nematic liquid crystals, we study the effect of adding a non-adsorbing ideal depletant on the phase behavior of colloidal hard boardlike particles. We take into account the presence of the depletant by introducing an effective depletion attraction between a pair of boardlike particles. At fixed depletant fugacity, the stable liquid-crystal phase is determined through a mean-field theory with restricted orientations. Interestingly, we predict that for slightly elongated boardlike particles a critical depletant density exists, where the system undergoes a direct transition from an isotropic liquid to a biaxial nematic phase. As a consequence, by tuning the depletant density, an easy experimental control parameter, one can stabilize states of high biaxial nematic order even when these states are unstable for pure systems of boardlike particles.

Polydispersity stabilizes biaxial nematic liquid crystals

Inspired by the observations of a remarkably stable biaxial nematic phase [van den Pol et al., Phys. Rev. Lett. 103, 258301 (2009)], we investigate the effect of size polydispersity on the phase behavior of a suspension of boardlike particles. By means of Onsager theory within the restricted orientation (Zwanzig) model we show that polydispersity induces a novel topology in the phase diagram, with two Landau tetracritical points in between which oblate uniaxial nematic order is favored over the expected prolate order. Additionally, this phenomenon causes the opening of a huge stable biaxiality regime in between uniaxial nematic and smectic states.