A two-dimensional nematic phase of magnetic nanorods

Effect of combined roundness and polydispersity on the phase behavior of hard-rectangle fluids

We introduce a model for a fluid of polydisperse rounded hard rectangles where the length and width of the rectangular core are fixed, while the roundness is taken into account by the convex envelope of a disk displaced along the perimeter of the core. The diameter of the disk has a continuous polydispersity described by a Schulz distribution function. We implemented the scaled particle theory for this model with the aim of studying: (i) the effect of roundness on the phase behavior of the one-component hard-rectangle fluid and (ii) how polydispersity affects phase transitions between isotropic, nematic, and tetratic phases. We found that roundness greatly affects the tetratic phase, whose region of stability in the phase diagram strongly decreases as the roundness parameter is increased. Also, the interval of aspect ratios where the tetratic-nematic and isotropic-nematic phase transitions are of first order considerably reduces with roundness, both transitions becoming weaker. Polydispersity induces strong fractionation between the coexisting phases, with the nematic phase enriched in particles of lower roundness. Finally, for high enough polydispersity and certain mean aspect ratios, the isotropic-to-nematic transition can change from second (for the one-component fluid) to first order. We also found a packing-fraction inversion phenomenon for large polydispersities: the coexisting isotropic phase has a higher packing fraction than the nematic.

Generalized van der Waals theory for phase behavior of two-dimensional nematic liquid crystals: Phase ordering and the equation of state

Liquid crystalline ordering of anisotropic particles in two dimensions is important in many physical and biological systems and their phase behavior is still a topic of interest. A generalized van der Waals theory is formulated, accounting for repulsive excluded volume and attractive van der Waals and Maier-Saupe interactions, for rectangles confined to two dimensions. The phase ordering transitions and equation of state are analyzed as a function of the model parameters (aspect ratioL/B and isotropic and anisotropic interaction parameters χ and ν). Different phase transitions are observed: continuous isotropic-nematic (high L/B and ν), first-order isotropic-nematic (intermediate L/B and small ν), and continuous isotropic-tetratic (small L/B and ν) followed by a continuous tetratic-nematic transition at higher densities. Increasing L/B decreases the pressure, and this effect is more pronounced in the nematic than in the isotropic phase. Increasing both interaction parameters decreases pressure and can lead to phase separation.

Liquid crystals of hard rectangles on flat and cylindrical manifolds

The self-assembly of rectangular particles on flat and curved substrates was investigated using density functional theory and simulations.

Role of length polydispersity in the phase behavior of freely rotating hard-rectangle fluids

We use the density-functional formalism, in particular the scaled-particle theory, applied to a length-polydisperse hard-rectangle fluid to study its phase behavior as a function of the mean particle aspect ratio κ_{0} and polydispersity Δ_{0}. The numerical solutions of the coexistence equations are calculated by transforming the original problem with infinite degrees of freedoms to a finite set of equations for the amplitudes of the Fourier expansion of the moments of the density profiles. We divide the study into two parts. The first one is devoted to the calculation of the phase diagrams in the packing fraction η_{0}-κ_{0} plane for a fixed Δ_{0} and selecting parent distribution functions with exponential (the Schulz distribution) or Gaussian decays. In the second part we study the phase behavior in the η_{0}-Δ_{0} plane for fixed κ_{0} while Δ_{0} is changed. We characterize in detail the orientational ordering of particles and the fractionation of different species between the coexisting phases. Also we study the character (second vs first order) of the isotropic-nematic phase transition as a function of polydispersity. We particularly focus on the stability of the tetratic phase as a function of κ_{0} and Δ_{0}. The isotropic-nematic transition becomes strongly of first order when polydispersity is increased: The coexistence gap widens and the location of the tricritical point moves to higher values of κ_{0} while the tetratic phase is slightly destabilized with respect to the nematic one. The results obtained here can be tested in experiments on shaken monolayers of granular rods.

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.