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

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.

Dynamics of hard colloidal cuboids in nematic liquid crystals

We perform dynamic Monte Carlo simulations to investigate the equilibrium dynamics of hard board-like colloidal particles in oblate and prolate nematic liquid crystals. In particular, we characterize the particles' diffusion along the nematic director and perpendicularly to it, and observe a structural relaxation decay that strongly depends on the particle anisotropy. To assess the Gaussianity of their dynamics and eventual occurrence of collective motion, we calculate two- and four-point correlation functions that incorporate the instantaneous values of the diffusion coefficients parallel and perpendicular to the nematic director. Our simulation results highlight the occurrence of Fickian and Gaussian dynamics at short and long times, locate the minimum diffusivity at the self-dual shape, the particle geometry that would preferentially stabilise biaxial nematics, and exclude the existence of dynamically correlated particles.

Biaxial nematics of hard cuboids in an external field

By computer simulation, we model the phase behaviour of colloidal suspensions of board-like particles under the effect of an external field and assess the still disputed occurrence of the biaxial nematic (NB) liquid crystal phase. The external field promotes the rearrangement of the initial isotropic (I) or uniaxial nematic (NU) phase and the formation of the NB phase. In particular, very weak field strengths are sufficient to spark a direct I-NB or NU-NB phase transition at the self-dual shape, where prolate and oblate particle geometries fuse into one. By contrast, forming the NB phase at any other geometry requires stronger fields and thus reduces the energy efficiency of the phase transformation. Our simulation results show that self-dual shaped board-like particles with moderate anisotropy are able to form NB liquid crystals under the effect of a surprisingly weak external stimulus and suggest a path to exploit low-energy uniaxial-to-biaxial order switching.

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.

A molecular theory of nematic-nematic phase transitions in mesogenic dimers

We study theoretically the molecular origins of the fascinating, and still debated, nematic-nematic phase transition exhibited by symmetric, statistically achiral, mesogenic dimers. A simple molecular model that mimics the key features and symmetry (C2V) of this class of mesogens is presented. In the mean-field approximation, the model yields up to three positionally disordered phases, one isotropic and two nematic. The low temperature nematic phase (NX) has a local two-fold symmetry axis, which is also a direction of molecular polar ordering and is tightly twisted about a macroscopic phase axis. The onset of polar ordering generates spontaneous chiral symmetry breaking and the formation of chiral domains of opposite handedness, manifested primarily by the twisting of the polar director. Within these domains the statistical balance between the enantiomer conformations is slightly shifted and the principal axes of the ordering tensors of the molecular segments twist at constant tilt angles with the helical axis. Key experimental results on the NX phase of liquid crystalline dimers are discussed in the light of the theoretical predictions of the model, which are also contrasted with the predictions of the twist-bend nematic model.

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.

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.