Two-dimensional liquid crystals: New symmetries and demixing transitions
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
The liquid-crystal biaxial nematic phase has been extensively studied
theoretically and through simulations since the '70. However, its occurrence
has only been confirmed recently. Extensive effort has been devoted
to formulate different models with the aim of predicting the type of
particle interactions and the degree of polydispersity necessary to stabilize
the biaxial phase, whose fast response times to external fields can be exploited
with advantage in the fabrication of electronic devices, such as liquid
crystal (LC) screens. The nano-technology industry is heading towards an
increasing reduction in the size of electronic components, a reduction that
in some cases is realised over one spatial direction, resulting in
an effective two dimensional system. Here we are interested in the study
of LC phase transitions when the constituent particles are strongly confined between two parallel planes. Specifically we are looking for the two-dimensional analogue of the biaxial and cubatic symmetries: the tetratic symmetry. With this aim, we formulate simple models for confined hard cylinders, which can be considered as two-dimensional hard rectangles when the confinement is extreme, and show the presence of tetratic order in the nematic phase. The stability of this phase is studied by means of a density-functional theory that includes second and third virial coefficients. Additionally, MC simulations of the hard rectangle fluid have been carried out to confirm stability. Also, a bifurcation analysis of the functional and the minimization of the corresponding Onsager version allowed us to locate the occurrence of non-uniform phases in the phase diagram. Finally, binary mixtures of hard rectangles, exhibiting different demixing scenarios, are considered. Interestingly, in contrast with one-component fluids, where the isotropic-nematic transitions in 2D and 3D have a different nature,phase behaviour in mixtures is essentially independent of dimensionality, implying that the same entropic mechanism operates in 2D and 3D. Experiments on vibrating granular rods have found phases with nematic, smectic and tetratic correlations
depending on the shape of the grains. Our results, obtained from equilibrium
statistical mechanics, show the same connection between particle shapes and
symmetries of the stable phases. From this we can draw the appealing conclusion
that the maximization of configurational entropy of the grains plays an important role in the presence of stationary steady-states in externally-excited granular fluids exhibiting LC symmetries.