Phase behavior of hard cylinders

Abstract

Using isobaric Monte Carlo simulations, we map out the entire phase diagram of a system of hard cylindrical particles of length (L) and diameter (D) using an improved algorithm to identify the overlap condition between two cylinders. Both the prolate L/D > 1 and the oblate L/D < 1 phase diagrams are reported with no solution of continuity. In the prolate L/D > 1 case, we find intermediate nematic N and smectic SmA phases in addition to a low density isotropic I and a high density crystal X phase with I–N-SmA and I-SmA-X triple points. An apparent columnar phase C is shown to be metastable, as in the case of spherocylinders. In the oblate L/D < 1 case, we find stable intermediate cubatic (Cub), nematic (N), and columnar (C) phases with I–N-Cub, N-Cub-C, and I-Cub-C triple points. Comparison with previous numerical and analytical studies is discussed. The present study, accounting for the explicit cylindrical shape, paves the way to more sophisticated models with important biological applications, such as viruses and nucleosomes.

Complex Smectic Phases in Polymer-Grafted Shape-Uniform Cellulose Nano-Crystals

“…From Figure , note that polymer grafting, provided dense enough, proves as an efficient means to stabilize Smectic order at low material content, given that the Smectic phase forms at ϕ ≈ 0.3 corresponding to a much lower CNC packing fraction of about ϕ rods ≈ 0.1. The transition toward Smectic order thus occurs at values that are way below the typical benchmark range ϕ = 0.45–0.5 reported for hard (sphero)cylinders. , Another discrepancy between our model and rigid cylinders is that the onset of Nematic ordering seems rather insensitive to the degree of polymer grafting, whereas one would expect the critical packing fraction to systematically increase with ρ g as the rods get fatter, and their effective aspect ratio is reduced by the grafted polymers.…”

“…Since the CNC interactions are purely repulsive, the observed tilt is likely stabilized by subtle excluded-volume effects imparted by the noncircular CNC cross-section and further compounded by weak twisting. Comparing our scenario with the emergence of a Smectic A phase in systems of rigid hard (sphero)cylinders, we find that the Sm-C phase appears at a slightly larger packing fraction than ϕ ≈ 0.45–0.55 reported for cylinders. , The discrepancy could be due to the backbone fluctuations and noncircular cross section of our CNCs which cause their shape to deviate from mere rigid cylinders with a prescribed aspect ratio.…”

“…With even higher grafting at 75% occupation (ρ g = 0.75), the anisotropy of the rods decreases enough to fully destabilize the Nematic order and induce a direct transition to a tilted Sm-I phase with an in-plane rectangular order, see the following Section. Monte Carlo simulations for hard (sphero)cylinders. , report direct transitions from isotropic to Smectic A-type order if the aspect ratio drops below 3. Translating this to our case, we may naively associate a lower bound effective aspect ratio L / D ≈ 1.5 for densely grafted CNCs if the polymers are taken to be fully stretched and closely packed together.…”

Equation of State of Charged Rod Dispersions

“…If the length ( L ) to diameter ( D ) ratio is larger than about 4 (see, for instance, ref ), hard rods can form liquid crystalline phases at low concentrations, as was already predicted by Onsager . The use of liquid crystals in device applications such as displays has gained enormous interest over the past 50 years, − and responsive liquid crystals are a recent topic of development. − Another reason for the increased interest into molecular and colloidal liquid crystals is the wealth of different possible phases with orientational order and/or partial positional order which appear. ,− Industrial applications are, for instance, the wet spinning of ultrastrong fibers and the increased interest in applying cellulose nanocrystals (CNC). − Understanding solutions of rodlike macromolecules is also of biological interest: think of the dense packing of rodlike DNA molecules in virus heads , or in the organization of cells. , Micro-organisms sometimes assume a spherocylinder shape, such as Escherichia coli, Campylobacter fetus, Salmonella typhimurium, and Mycobacterium tuberculosis bacteria. Assuming rodlike morphologies is considered to be a tool to gain a competitive advantage. , …”

“… 6 − 8 Another reason for the increased interest into molecular and colloidal liquid crystals is the wealth of different possible phases with orientational order and/or partial positional order which appear. 1 , 9 − 14 Industrial applications are, for instance, the wet spinning of ultrastrong fibers 15 and the increased interest in applying cellulose nanocrystals (CNC). 16 − 19 Understanding solutions of rodlike macromolecules is also of biological interest: think of the dense packing of rodlike DNA molecules in virus heads 20 , 21 or in the organization of cells.…”