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.

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.

Using simulations of hard rods in smectic-A states, we find stringlike clusters of up to 10 interlayer rods exhibiting dynamic cooperativity. We also find non-gaussian diffusion and heterogeneous dynamics due to the equilibrium periodic smectic density profiles, which give rise to permanent barriers for layer-to-layer diffusion. This relaxation behavior is surprisingly similar to that of nonequilibrium supercooled liquids, although there the particles are trapped in transient (instead of permanent) cages.

We report on the diffusion of purely repulsive and freely rotating colloidal rods in the isotropic, nematic, and smectic liquid crystal phases to probe the agreement between Brownian and Monte Carlo dynamics under the most general conditions. By properly rescaling the Monte Carlo time step, being related to any elementary move via the corresponding self-diffusion coefficient, with the acceptance rate of simultaneous trial displacements and rotations, we demonstrate the existence of a unique Monte Carlo time scale that allows for a direct comparison between Monte Carlo and Brownian dynamics simulations. To estimate the validity of our theoretical approach, we compare the mean square displacement of rods, their orientational autocorrelation function, and the self-intermediate scattering function, as obtained from Brownian dynamics and Monte Carlo simulations. The agreement between the results of these two approaches, even under the condition of heterogeneous dynamics generally observed in liquid crystalline phases, is excellent.