A simulation study on the phase behavior of hard rhombic platelets

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.

Equation of state of hard lenses: A combined virial series and simulation approach

We provide highly accurate equation-of-state data for the isotropic phase of hard lenses obtained by means of cluster Monte Carlo simulations. This data is analyzed using a virial approach considering coefficients up to the order eight and Carnahan-Starling type closure relations for the virial series. The comparison with previously investigated systems consisting of hard, oblate ellipsoids of revolution allows insights into the detailed influence of the particle geometry. We propose a generalized Carnahan-Starling approach as a heuristic equation of state for the isotropic phase of hard lenses that in first approximation shows the same dependence on the excess part of the excluded volume as identified for oblate, hard lenses of revolution.

Reexamining equations of state of oblate hard ellipsoids of revolution: Numerical simulation utilizing a cluster Monte Carlo algorithm and comparison to virial theory

We provide highly accurate equation-of-state data determined by means of cluster Monte Carlo simulations for the isotropic phase of oblate hard ellipsoids of revolution. Both equation-of-state data and phase boundaries of the isotropic phase are obtained from relatively large ensembles with typically 1000 particles. The comparison of simulation data with a virial approach gives evidence for the importance of high-order so-far-unknown virial coefficients and therewith many-particle interactions in dense, isotropic systems of anisotropic particles. While a virial approach with a rescaled Carnahan-Starling correction for the unknown, higher-order virial coefficients reproduces the simulation data of moderately anisotropic particles with high accuracy, we suggest for highly anisotropic shapes a simple, heuristic equation of state as a suitable approach.

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.

Orientational ordering and layering of hard plates in narrow slitlike pores

We examine the ordering behavior of hard platelike particles in a very narrow, slitlike pore using the Parsons-Lee density functional theory and the restricted orientation approximation. We observe that the plates are orientationally ordered and align perpendicularly (face-on) to the walls at low densities, a first-order layering transition occurs between uniaxial nematic structures having n and n+1 layers at intermediate densities, and even a phase transition between a monolayer with parallel (edge-on) orientational order and n layers with a perpendicular one can be detected at high densities. In addition to this, the edge-on monolayer is usually biaxial nematic, and a uniaxial-biaxial nematic phase transition can be also seen at very high densities.

Biaxial, Twist-bend, and Splay-bend Nematic Phases of Banana-shaped Particles Revealed by Lifting the "Smectic Blanket"

We perform an extensive computational study on the phase behavior of hard banana-shaped particles, and show that biaxial, twist-bend, and splay-bend nematic phases are metastable with respect to a smectic phase for a system of hard bent spherocylinders. However, if the smectic phase is destabilized-either by polydispersity in the particle length or by curvature in the particle shape-stable biaxial, twist-bend, and splay-bend nematic phases are obtained. This provides a unified and consistent picture on the subtle role of particle shape on the phase behavior of bent rods.

Revealing a Vacancy Analog of the Crowdion Interstitial in Simple Cubic Crystals

Vacancies in simple cubic crystals of hard cubes are known to delocalize over one-dimensional chains of several lattice sites. Here, we use computer simulations to examine the structure and dynamics of vacancies in simple cubic crystals formed by hard cubes, right rhombic prisms (slanted cubes), truncated cubes, and particles interacting via a soft isotropic pair potential. We show that these vacancies form a vacancy analog of the crowdion interstitial, generating a strain field which follows a soliton solution of the sine-Gordon equation, and diffusing via a persistent random walk. Surprisingly, we find that the structure of these "voidions" is not significantly affected by changes in density, vacancy concentration, and even particle interaction. We explain this structure quantitatively using a one-dimensional model that includes the free-energy barrier particles have to overcome to slide between lattice sites and the effective pair interaction along this line. We argue that voidions are a robust phenomenon in systems of repulsive particles forming simple cubic crystals.

Isotropic, nematic, and lamellar phases in colloidal suspensions of nanosheets

The phase diagram of colloidal suspensions of electrically charged nanosheets, such as clays, despite their many industrial uses, is not yet understood either experimentally or theoretically. When the nanosheet diameter is very large (∼100 nm to 1 µm), it is quite challenging to distinguish the lamellar liquid-crystalline phase from a nematic phase with strong stacking local order, often called "columnar" nematic. We show here that newly upgraded small-angle X-ray scattering beamlines at synchrotron radiation facilities provide high-resolution measurements which allow us to identify both phases unambiguously, provided that single domains can be obtained. We investigated dilute aqueous suspensions of synthetic Sb₃P₂O₁₄^3- nanosheets that self-organize into two distinct liquid-crystalline phases, sometimes coexisting in the same sample. Close examination of their X-ray reflection profiles in the directions perpendicular to the director demonstrates that these two mesophases are a columnar nematic and a lamellar phase. In the latter, the domain size reaches up to ∼20 µm, which means that each layer is made of >600 nanosheets. Because the lamellar phase was only rarely predicted in suspensions of charged disks, our results show that these systems should be revisited by theory or simulations. The unexpected stability of the lamellar phase also suggests that the rims and faces of Sb₃P₂O₁₄^3- nanosheets may have different properties, giving them a patchy particle character.

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.