We investigate the phase behavior of colloidal suspensions of board-like particles under the effect of an external field and assess the still disputed occurrence of the biaxial nematic (N B ) liquid crystal phase. The external field promotes the rearrangement of the initial isotropic (I) or uniaxial nematic (N U ) phase and the formation of the N B phase. In particular, very weak field strengths are sufficient to spark a direct I-N B or N U -N B phase transition at the self-dual shape, where prolate and oblate particle geometries fuse into one. By contrast, forming the N B 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 N B liquid crystals under the effect of a surprisingly weak external stimulus and suggest a path to exploit low-energy uniaxial-to-biaxial order switching.It is well established that anisotropic colloidal particles can self-assemble into a plethora of fascinating liquid crystal (LC) phases in a solvent. Onsager showed that mere excluded volume effects can force hard-core particles to align along a common director at sufficiently large concentrations [1]. The resulting LC phases found at the thermodynamic equilibrium and their structural properties strongly depend on the particle geometry. In particular, prolate particles tend to orient along their major axis, while oblate particles along their minor axis. Although this tendency is regularly observed in systems of uniaxial particles, such as disks, whose orientation is determined by a single unit vector, it is less predictable for biaxial particles, such as cuboids, whose orientation is fully determined by two unit vectors. For instance, slightly oblate hard board-like particles (HBPs) have been shown to orient along their major axis and thus form prolate (rather than oblate) smectic LC phases [2]. This unusual arrangement was observed in suspensions of HBPs with length-to-thickness ratio L * ≡ L/T = 12 and width-tothickness ratio W * ≡ W/T ≈ √ L * , a geometry where oblate and prolate shapes fuse into one.Such an exclusive particle architecture, referred to as self-dual shape, was predicted to favour the formation of the biaxial nematic (N B ) phase in systems of HBPs with rounded [3] or square [4] corners. Nevertheless, these theoretical predictions were made within the context of the Zwanzig model, which does not allow free rotations of particles and restricts their orientations to only six. Computer simulations that explored the phase behavior of freely rotating HBPs highlighted the challenge of observing stable N B phases, even when an element of sizedispersity is incorporated [5]. The very recent and insightful simulation study by the Dijkstra's group showed that monodisperse HBPs, with a geometry close or equal to the self-dual shape, are able to stabilise the N B phase * Electronic address: alessandro.patti@manchester.ac.uk only if their anisotropy is signif...

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 behaviour 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 characterise 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 non-linear, force-thinning regime is observed at intermediate force intensities.

Polydisperse colloidal cuboids display a very rich self-assembling behaviour, which includes stable biaxial nematic liquid crystal phases.

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 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 employ 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 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 the elusive biaxial nematic phase, being found in an 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