Abstract:
Scaled particle theory for a binary mixture of hard discorectangles and for a binary mixture of hard rectangles is used to predict possible liquid-crystal demixing scenarios in two dimensions. Through a bifurcation analysis from the isotropic phase, it is shown that isotropic-nematic demixing is possible in two-dimensional liquid-crystal mixtures composed of hard convex bodies. This bifurcation analysis is tested against exact calculations of the phase diagrams in the framework of the restricted-orientation two-dimensional model (Zwanzig model). Phase diagrams of a binary mixture of hard discorectangles are calculated through the parametrization of the orientational distribution functions. The results show not only isotropic-nematic, but also nematic-nematic demixing ending in a critical point, as well as an isotropic-nematic-nematic triple point for a mixture of hard disks and hard discorectangles.

Abstract:
liquid crystals have been very fruitful systems to study equilibrium phase transitions. recently, they have become an important system to study dynamics of first-order phase transitions. the moving nonequilibrium nematic-isotropic interface is a model system to study growth of stable states into metastable states and displays a myriad of dynamical instabilities that, far from equilibrium, drive the system to a scenario of spatio-temporal chaos. we present a mean-field theory for the time evolution of a planar nonequilibrium nematic-isotropic interface for pure liquid crystals using a time dependent ginzburg-landau equation, which is one of the simplest approaches to dissipative dynamics. we obtain a theoretical expression for the growth kinetics of the nematic phase into a metastable isotropic phase and compare it with our experimental results. in a directional solidification arrangement we study instabilities of the nematic-isotropic interface of the liquid crystal 8cb doped with water and hexachloroethane. the observed instabilities are similar to cellular instabilities that appear during growth of crystal-melt interfaces of binary mixtures. we then compare our results with known theories of morphological instabilities during crystal growth.

Abstract:
Liquid crystals have been very fruitful systems to study equilibrium phase transitions. Recently, they have become an important system to study dynamics of first-order phase transitions. The moving nonequilibrium nematic-isotropic interface is a model system to study growth of stable states into metastable states and displays a myriad of dynamical instabilities that, far from equilibrium, drive the system to a scenario of spatio-temporal chaos. We present a mean-field theory for the time evolution of a planar nonequilibrium nematic-isotropic interface for pure liquid crystals using a time dependent Ginzburg-Landau equation, which is one of the simplest approaches to dissipative dynamics. We obtain a theoretical expression for the growth kinetics of the nematic phase into a metastable isotropic phase and compare it with our experimental results. In a directional solidification arrangement we study instabilities of the nematic-isotropic interface of the liquid crystal 8CB doped with water and hexachloroethane. The observed instabilities are similar to cellular instabilities that appear during growth of crystal-melt interfaces of binary mixtures. We then compare our results with known theories of morphological instabilities during crystal growth.

Abstract:
We present the first calculations of the pressure tensor profile in the vicinity of the planar interface between isotropic liquid and nematic liquid crystal, using Onsager's density functional theory and computer simulation. When the liquid crystal director is aligned parallel to the interface, the situation of lowest free energy, there is a large tension on the nematic side of the interface and a small compressive region on the isotropic side. By contrast, for perpendicular alignment, the tension is on the isotropic side. There is excellent agreement between theory and simulation both in the forms of the pressure tensor profiles, and the values of the surface tension.

Abstract:
We use an infinite-range Maier-Saupe model, with two sets of local quadrupolar variables and restricted orientations, to investigate the global phase diagram of a coupled system of two nematic subsystems. The free energy and the equations of state are exactly calculated by standard techniques of statistical mechanics. The nematic-isotropic transition temperature of system A increases with both the interaction energy among mesogens of system B, and the two-subsystem coupling $J$. This enhancement of the nematic phase is manifested in a global phase diagram in terms of the interaction parameters and the temperature $T$. We make some comments on the connections of these results with experimental findings for a system of diluted ferroelectric nanoparticles embedded in a nematic liquid-crystalline environment.

Abstract:
With the aim of investigating the stability conditions of biaxial nematic liquid crystals, we study the effect of adding a non-adsorbing ideal depletant on the phase behavior of colloidal hard boardlike particles. We take into account the presence of the depletant by introducing an effective depletion attraction between a pair of boardlike particles. At fixed depletant fugacity, the stable liquid crystal phase is determined through a mean-field theory with restricted orientations. Interestingly, we predict that for slightly elongated boardlike particles a critical depletant density exists, where the system undergoes a direct transition from an isotropic liquid to a biaxial nematic phase. As a consequence, by tuning the depletant density, an easy experimental control parameter, one can stabilize states of high biaxial nematic order even when these states are unstable for pure systems of boardlike particles.

Abstract:
The influence of the shape anisotropy of magnetic particles on the isotropic-nematic phase transition was studied in ferronematics based on the nematic liquid crystal 4-(trans-4-n-hexylcyclohexyl)-isothiocyanato-benzene (6CHBT). The liquid crystal was doped with spherical or rod-like magnetic particles of different size and volume concentrations. The phase transition from isotropic to nematic phase was observed by polarizing microscope as well as by capacitance measurements. The influence of the concentration and the shape anisotropy of the magnetic particles on the isotropic-nematic phase transition in liquid crystal is demonstrated. The results are in a good agreement with recent theoretical predictions.

Abstract:
Isotropic-genesis nematic elastomers (IGNEs) are liquid crystalline polymers (LCPs) that have been randomly, permanently cross-linked in the high-temperature state so as to form an equilibrium random solid. Thus, instead of being free to diffuse throughout the entire volume, as they would be in the liquid state, the constituent LCPs in an IGNE are mobile only over a finite length-scale controlled by the density of cross-links. We address the effects that such network-induced localization have on the liquid-crystalline characteristics of an IGNE, as probed via measurements made at high temperatures. In contrast with the case of uncross-linked LCPs, for IGNEs these characteristics are determined not only by thermal fluctuations but also by the quenched disorder associated with the cross-link constraints. To study IGNEs, we consider a microscopic model of dimer nematogens in which the dimers interact via orientation-dependent excluded volume forces. The dimers are, furthermore, randomly, permanently cross-linked via short Hookean springs, the statistics of which we model by means of a Deam-Edwards type of distribution. We show that at length-scales larger than the size of the nematogens this approach leads to a recently proposed phenomenological Landau theory of IGNEs [Lu et al., Phys. Rev. Lett. 108, 257803 (2012)], and hence predicts a regime of short-ranged oscillatory spatial correlations in the nematic alignment, of both thermal and glassy types. In addition, we consider two alternative microscopic models of IGNEs: (i) a wormlike chain model of IGNEs that are formed via the cross-linking of side-chain LCPs; and (ii) a jointed chain model of IGNEs that are formed via the cross-linking of main-chain LCPs. At large length-scales, both of these models give rise to liquid-crystalline characteristics that are qualitatively in line with those predicted by the dimer-and-springs model.

Abstract:
We analyze the experimental observation of metastable anisotropy resistance orientation at half filled quantum Hall fluids by means of a model of a quantum nematic liquid in an explicit symmetry breaking potential. We interpret the observed ``rotation'' of the anisotropy axis as a process of nucleation of nematic domains and compute the nucleation rate within this model. By comparing with experiment, we are able to predict the critical radius of nematic bubbles, $R_c\sim 2.6 \mu m $. Each domain contains about $10^4$ electrons.

Abstract:
We have employed the Density Functional Theory formalism to investigate the nematic-isotropic capillary transitions of a nematogen confined by walls that favor antagonist orientations to the liquid crystal molecules (hybrid cell). We analyse the behavior of the capillary transition as a function of the fluid-substrate interactions and the pore width. In addition to the usual capillary transition between isotropic-like to nematic-like states, we find that this transition can be suppressed when one substrate is wet by the isotropic phase and the other by the nematic phase. Under this condition the system presents interface-like states which allow to continuously transform the nematic-like phase to the isotropic-like phase without undergoing a phase transition. Two different mechanisms for the disappearance of the capillary transition are identified. When the director of the nematic-like state is homogeneously planar-anchored with respect to the substrates, the capillary transition ends up in a critical point. This scenario is analogous to the observed in Ising models when confined in slit pores with opposing surface fields which have critical wetting transitions. When the nematic-like state has a linearly distorted director field, the capillary transition continuously transforms in a transition between two nematic-like states.