Anisotropic translational diffusion in the nematic phase: Dynamical signature of the coupling between orientational and translational order in the energy landscape

We study the behaviour of Smectic-A (SmA) liquid crystals with a modified Landau-de Gennes (mLdG) model. The director and orientational order of SmA are described by a tensor-order parameter $\mathbf{Q}$, and the positional order is described by a real scalar $u$, which represents the deviation from the average concentration of liquid crystal molecules. Firstly, we prove the existence and regularity of the global minimiser of the mLdG free energy. Then, we analytically prove ...

Computer simulations are presented of the isotropic-to-nematic transition in a liquid crystal confined between two parallel plates a distance H apart. The plates are neutral and do not impose any anchoring on the particles. Depending on the shape of the pair potential acting between the particles, we find that the transition either changes from first-order to continuous at a critical film thickness H=Hx, or that the transition remains first-order irrespective of H. This demon...

Liquid crystals establish a nearly unique combination of thermodynamic, hydrodynamic, and topological behavior. This poses a challenge to their theoretical understanding and modeling. The arena where these effects come together is the mesoscopic (micron) scale. It is then important to develop models aimed at capturing this variety of dynamics. We have generalized the particle-based multiparticle collision dynamics (MPCD) method to model the dynamics of nematic liquid crystals...

We summarise some recent results on solution landscapes for two-dimensional (2D) problems in the Landau--de Gennes theory for nematic liquid crystals. We study energy-minimizing and non energy-minimizing solutions of the Euler--Lagrange equations associated with a reduced Landau-de Gennes free energy on 2D domains with Dirichlet tangent boundary conditions. We review results on the multiplicity and regularity of solutions in distinguished asymptotic limits, using variational ...

A significant deviation from the Debye model of rotational diffusion in the dynamics of orientational degrees of freedom in an equimolar mixture of ellipsoids of revolution and spheres is found to begin precisely at a temperature at which the average inherent structure energy of the system starts falling with drop in temperature. We argue that this onset temperature corresponds to the emergence of the alpha-process as a distinct mode of orientational relaxation. Equally impor...

Deviations of molecular shapes from spherical symmetry may give rise to a variety of novel phenomena, including their dynamic behavior. It has recently been predicted [Mazza \textit{et al}. Phys. Rev. Lett. \textbf{105}, 227802 (2010)] that liquid crystals in the reentrant nematic phases may show unexpectedly high rates of translational displacements. Using broadband dielectric spectroscopy and a single-component thermotropic liquid crystal we explore molecular dynamics in th...

Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits stable isotropic, nematic, smectic A, columnar, plastic crystalline and orientationally ordered crystalline phases. As far as the dynamics is concerned, the translational density is a conserved order parameter while the orientational ordering ...

Hard models for particle interactions have played a crucial role in the understanding of the structure of condensed matter. In particular, they help to explain the formation of oriented phases in liquids made of anisotropic molecules or colloidal particles, and continue to be of great interest in the formulation of theories for liquids in bulk, near interfaces and in biophysical environments. Hard models of anisotropic particles give rise to complex phase diagrams, including ...

Since a rigorous microscopic treatment of a nematic fluid system based on a pairwise interaction potential is immensely complex we had introduced a simple mean field potential which was a modification of the Maier-Saupe potential in a previous paper. Building up on that here we have modified that potential to take into account the various aspects of a smectic A-nematic phase transition. In particular we have studied the dependence of the phase transition on the coupling coeff...

Using computer simulations, we studied the diffusion and structural relaxation in equilibrium smectic liquid crystal bulk phases of parallel hard spherocylinders. These systems exhibit a non-Gaussian layer-to-layer diffusion due to the presence of periodic barriers and transient cages, and show remarkable similarities with the behavior of out-of-equilibrium supercooled liquids. We detect a very slow inter-layer relaxation dynamics over the whole density range of the stable sm...