Quoting Daan Frenkel from his 1999 review paper: ‘the idea of entropy-driven phase transitions is an old one. employed computer simulations on various hard-particle systems, such as ellipsoids, spherocylinders and disks, to provide evidence for the entropy-driven formation of not only the nematic phase but also the smectic and the columnar phases . Upon increasing the density of the system, the alignment of the rods along a common director becomes favourable at the expense of orientational entropy, but this loss is more than compensated by a gain in translational entropy. In 1949, Onsager showed in his seminal work that a system of infinitely thin hard rods exhibits a purely entropy-driven phase transition from an isotropic to a nematic phase at sufficiently high densities . Further classification is possible based on the symmetry of the positional order. In the case of biaxial particles, LC phases can be further divided into (i) prolate uniaxial (often denoted with a subscript ), (ii) oblate uniaxial (subscript ) and (iii) biaxial phases (subscript ), depending on whether the long-range orientational order of the system is associated to (i) the long, (ii) short or (iii) both particle axes. particles form columns that are arranged on a 2D lattice. the particles are arranged in smectic layers and finally, columnar ( Col) phases feature a 2D positional order, i.e. the particles are on average aligned along a common direction smectic ( Sm) phases have an additional 1D positional order, i.e. Nematic phases ( N) display only long-range orientational order, i.e. The different phases can be distinguished on the basis of the microscopic arrangement of the particles. Examples range from organic rods, such as tobacco mosaic viruses, fd-viruses, DNA, to inorganic materials, such as ferric oxyhydroxide rods, boehmite rods, vanadium pentoxide rods and silica rods . Moderately dense suspensions of anisotropic colloids can self-assemble into liquid crystal phases, exhibiting long-range orientational order but no, or only partial, positional order . Such a system-size effect depends both on particle shape and the competing phases, and appears to be more pronounced for less anisotropic particles. In particular, we observe that the characteristic layering of the stable smectic or crystal phase disappears when the dimension of the simulation box along the direction of the layers is too small. We show that the phases observed in previous simulation studies are mere artefacts due to either finite-size effects or simulation boxes that are incommensurate with the stable thermodynamic phase. We perform computer simulations of hard particles with different shapes: spherocylinders, top-shaped rods, cuboidal particles, and crooked rods. Here, we investigate whether or not a phase can exist in a purely entropy-driven single-component system. In contrast to the formation of the nematic and smectic phases for which it is well understood that it can be driven by entropy, the stabilisation mechanism of a prolate columnar phase ( ), observed for example in fd-virus suspensions, is still unclear.

Colloidal rod-like particles self-assemble into a variety of liquid crystal phases.

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