Uniaxial-biaxial Nematic Phase Transition Research Articles

Orientational ordering and layering of hard plates in narrow slitlike pores

We examine the ordering behavior of hard platelike particles in a very narrow, slitlike pore using the Parsons-Lee density functional theory and the restricted orientation approximation. We observe that the plates are orientationally ordered and align perpendicularly (face-on) to the walls at low densities, a first-order layering transition occurs between uniaxial nematic structures having n and n+1 layers at intermediate densities, and even a phase transition between a monolayer with parallel (edge-on) orientational order and n layers with a perpendicular one can be detected at high densities. In addition to this, the edge-on monolayer is usually biaxial nematic, and a uniaxial-biaxial nematic phase transition can be also seen at very high densities.

Hierarchy of orientational phases and axial anisotropies in the gauge theoretical description of generalized nematic liquid crystals.

The paradigm of spontaneous symmetry breaking encompasses the breaking of the rotational symmetries O(3) of isotropic space to a discrete subgroup, i.e., a three-dimensional point group. The subgroups form a rich hierarchy and allow for many different phases of matter with orientational order. Such spontaneous symmetry breaking occurs in nematic liquid crystals, and a highlight of such anisotropic liquids is the uniaxial and biaxial nematics. Generalizing the familiar uniaxial and biaxial nematics to phases characterized by an arbitrary point-group symmetry, referred to as generalized nematics, leads to a large hierarchy of phases and possible orientational phase transitions. We discuss how a particular class of nematic phase transitions related to axial point groups can be efficiently captured within a recently proposed gauge theoretical formulation of generalized nematics [K. Liu, J. Nissinen, R.-J. Slager, K. Wu, and J. Zaanen, Phys. Rev. X 6, 041025 (2016)2160-330810.1103/PhysRevX.6.041025]. These transitions can be introduced in the model by considering anisotropic couplings that do not break any additional symmetries. By and large this generalizes the well-known uniaxial-biaxial nematic phase transition to any arbitrary axial point group in three dimensions. We find in particular that the generalized axial transitions are distinguished by two types of phase diagrams with intermediate vestigial orientational phases and that the window of the vestigial phase is intimately related to the amount of symmetry of the defining point group due to inherently growing fluctuations of the order parameter. This might explain the stability of the observed uniaxial-biaxial phases as compared to the yet to be observed other possible forms of generalized nematic order with higher point-group symmetries.

External magnetic field-dependent tricritical points of uniaxial-to-biaxial nematic transition

External magnetic field-dependent behavior of tricritical points of uniaxial–biaxial nematic phase transition in a mixture of prolate and oblate molecules has been studied using the Landau phenomenological theory. Topological classification of phase diagrams in the field-temperature coordinates is performed using a sixth-order term in order parameter tensor. For both prolate and oblate molecules, the tricritical order parameters corresponding to the uniaxial–biaxial increase with the intensity of the external magnetic field. Field-induced paranematic phase has only been reported for prolate molecules, but for oblate molecules, field-induced splitting of the order parameter has been reported.

Phase behaviour of liquid-crystal monolayers of rod-like and plate-like particles.

Orientational and positional ordering properties of liquid crystal monolayers are examined by means of Fundamental-Measure Density Functional Theory. Particles forming the monolayer are modeled as hard parallelepipeds of square section of size σ and length L. Their shapes are controlled by the aspect ratio κ = L/σ (>1 for prolate and <1 for oblate shapes). The particle centers of mass are restricted to a flat surface and three possible and mutually perpendicular orientations (in-plane and along the layer normal) of their uniaxial axes are allowed. We find that the structure of the monolayer depends strongly on particle shape and density. In the case of rod-like shapes, particles align along the layer normal in order to achieve the lowest possible occupied area per particle. This phase is a uniaxial nematic even at very low densities. In contrast, for plate-like particles, the lowest occupied area can be achieved by random in-plane ordering in the monolayer, i.e., planar nematic ordering takes place even at vanishing densities. It is found that the random in-plane ordering is not favorable at higher densities and the system undergoes an in-plane ordering transition forming a biaxial nematic phase or crystallizes. For certain values of the aspect ratio, the uniaxial-biaxial nematic phase transition is observed for both rod-like and plate-like shapes. The stability region of the biaxial nematic phase enhances with decreasing aspect ratios for plate-like particles, while the rod-like particles exhibit a reentrant phenomenon, i.e., a sequence of uniaxial-biaxial-uniaxial nematic ordering with increasing density if the aspect ratio is larger than 21.34. In addition to this, packing fraction inversion is observed with increasing surface pressure due to the alignment along the layers normal. At very high densities the nematic phase destabilizes to a nonuniform phases (columnar, smectic, or crystalline phases) for both shapes.

Infrared Spectra and Magnetic Properties of a Biaxial Nematic Bent-Core Liquid Crystal: Study of Conformations and Local Ordering in A131

Density functional theory (DFT) has been employed in a detailed conformational study of a bent-core mesogen (A131), in order to shed light on its uniaxial-biaxial nematic phase transition, questioned recently in the literature. Two distinct computed structural groups, namely the Banana-shaped (BS) and the Hockey Stick-shaped (HSS) forms, were found to give different theoretical infrared spectra and magnetic susceptibility tensors, suitable to potentially distinguish between the two nematic phases. GIAO-DFT chemical shielding tensors (CSTs) of the aromatic carbons, found in agreement with those experimentally measured by the 2D-NMR SUPER technique, were used to provide new structural and local orientational order parameters of A131.

Conformational Study of a Bent-Core Liquid Crystal: 13C NMR and DFT Computation Approach

A detailed conformational study is carried out by means of density functional theory (DFT) on a bent-core mesogen (A131) in order to shed light on its uniaxial-biaxial nematic phase transition. The most probable conformational states for this V-shaped core are found, from the potential energy surface (PES) of a five-ring model of A131, to fall into two distinct structural groups, namely, the banana-shaped and the hockey-stick-shaped forms. The chemical shielding tensors (CSTs) of the aromatic carbons, for the four prevalent conformers, have been calculated using the GIAO-DFT approach. The derived CSTs are found to compare well with the chemical shift anisotropy (CSA) tensors measured by the 2D-NMR SUPER technique. The CSA tensors are then used to aid the assignment of the aromatic carbon peaks, and the observed (13)C chemical shifts from its nematic phases are revisited to provide new structural and local orientational order parameters. In light of the conformational states found from the in vacuo DFT calculations, the "average" configuration shapes of the A131 molecule are found to be different in the nematic phases based on their new local order parameters S and D of the aromatic rings.

Temperature dependence of refractive indices near uniaxial–biaxial nematic phase transition

The uniaxial discotic ( N D ) and calamitic ( N C ) nematic phases are characterized by an order parameter which is a second-rank, symmetric, traceless tensor with two different eigenvalues and three in the biaxial nematic ( N B ) phase. The optical dielectric tensor may be chosen as the microscopic order parameter. The optical characterization of these uniaxial and biaxial nematic phases requires the measurements of two and three refractive indices, respectively. These optical parameters were determined near the reentrant isotropic ( I RE ) – N D – N B – N C –isotropic ( I ) phase transitions in a lyotropic mixture of potassium laurate, decanol and D 2O. The dynamic of micellar configuration of the uniaxial and biaxial nematic phases is discussed as a consequence of our refractive index data.

On the Uniaxial-Biaxial Nematic Phase Transition in Liquid-Crystalline Polymers and Elastomers

We study how the uniaxial-biaxial nematic phase transition changes its nature when going from a low molecular weight liquid crystal to a liquid-crystalline elastomer or polymer (the latter above the Maxwell frequency) and find a qualitative change due to the presence of a coupling to the strain field in these materials. While this phase transition can be of second-order in low-molecular-weight materials, as is also experimentally observed, we show bere that the order of this phase transition is changed generically to no phase transition at all or to a first-order phase transition in mean-field approximation. We analyze the influence of an external mechanical stress field above the uniaxial-biaxial nematic phase transition and find that either biaxial nematie order is induced, which is linear or quadratic in the stress intensity, or no response to an external stress results at all, depending on the relative orientation of the applied shear with respect to the director of the uniaxial nematic phase.

Nonuniversal Critical Behavior at the Uniaxial-Biaxial Nematic Phase Transition in a Lyotropic Mixture

Measurements of the order-parameter critical exponent $\ensuremath{\beta}$ at the uniaxial-biaxial nematic phase transition in a lyotropic mixture are reported. They reveal a strong dependence of $\ensuremath{\beta}$ on the concentration of the mixture compounds with two distinct intervals of values separated by a discontinuity. This nonuniversal behavior is interpreted as the result of three different contributions, which express the micellar biaxiality and the distribution of the micellar population with respect to biaxiality and volume.

Improved analysis of the Landau theory of the uniaxial-biaxial nematic phase transition

A phenomenological theory is developed for uniaxial and biaxial nematic phases, based on a two component tensor order parameter. Phase diagrams are plotted and investigated in the plane of two thermodynamic parameters. Anomalies in thermal properties are studied in the vicinity of an isolated four-phase critical point. The temperature dependences of the order parameter and the thermodynamic quantities are also calculated theoretically for the first time.