Phase behavior of colloidal hard perfect tetragonal parallelepipeds

Abstract

The phase behavior of suspensions of colloidal hard tetragonal parallelepipeds ("TPs") (also known as rectangular nanorods or nanobars) was studied by using Monte Carlo simulations to gain a detailed understanding of the effect of flat-faceted particles on inducing regular local packing and long range structural order. A TP particle has orthogonal sides with lengths a, b, and c, such that a=b and its aspect ratio is r=c/a. The phase diagram for such perfect TPs was mapped out for particle aspect ratios ranging from 0.125 to 5.0. Equation of state curves, order parameters, particle distribution functions, and snapshots were used to analyze the resulting phases. Given the athermal nature of the systems studied, it is the interplay of purely entropic forces that drives phase transitions amongst the structures observed that include crystal, columnar, smectic, parquet, and isotropic phases. In the parquet phase that occurs for 0.54<r< or =3.2, for example, the particles possess some translational entropy (mobility) but reduced orientational entropy; particles arrange in stacks oriented perpendicular to one another, so that all particle axes are aligned along three common directors. Multicanonical-type simulations were used to study in more detail the isotropic-parquet phase transition. Both similarities and differences were identified between the results for these perfect TPs and those unveiled in our previous study of approximate (polybead) TPs.

Mesophase behaviour of polyhedral particles

“…In contrast to earlier conjectures [11][12][13] , we now find clear evidence of layering in the cubatic phase (also observed in [32]) which becomes visible in our redefined particle distribution functions (see details in SI). While the finite size of our system prevents us from ascertaining the range of such a positional order, the appreciable D values observed at these densities indicates that the system has liquid-like behaviour and there is sufficient translational disorder for layers to rearrange dynamically.…”

“…These ordered assemblies have distinctive electronic, optical, and dynamical properties 4,5 and are highly desirable for fabrication of advanced electronic, photonic, and rheological devices 6,7 . Although numerous theoretical [8][9][10][11][12][13] and experimental 14,15 studies on mesophase behaviour of particles with anisotropic shapes have been reported, a roadmap marking out the most probable mesophases that could be formed by constituent particles with particular geometrical features is still incomplete. Exploring such relations will translate into a deeper understanding of the phase behaviour of colloidal systems with different particle shapes; e.g., Jiao et al 16 reported that unlike ellipsoids, convex superballs can be optimally packed in dense Bravais lattices because they are less symmetric but more isotropic than the former.…”

Biaxial nematic phases in fluids of hard board-like particles

“…A recent simulation work [33] analysed the full phase diagram of board-like particles with square cross section, σ 1 = σ 2 and 0.125 < σ 3 /σ 1 < 0.5. The first condition is not compatible with the formation of the the biaxial-nematic phase.…”

Statistical Theory of Biaxial Nematic and Cholesteric Phases

“…The parameters F (2) 20 and F (2) 22 are zero in the uniaxial phase and nonzero in the biaxial phase. In the limit of the perfect uniaxial order ( F were computed in the Monte Carlo simulations of hard tetragonal parallelepipeds [58] in order to identify the cubatic (parquet) phase.…”