Two-state model for nematic liquid crystals made of bent-core molecules

Two-state model for the SmAP_{R} phase with randomized layer polarization exhibited by some compounds with bent-core molecules

One of the unusual liquid crystalline phases exhibited by some compounds with bent-core (BC) molecules is designated as SmAP_{R}, in which transverse polarization (P) of smectic layers with upright molecules has a random orientational distribution. Most of such compounds undergo a transition to the SmAP_{A} phase with antiferroelectric order of adjacent layers as the temperature is lowered. Second harmonic studies have shown that the medium consists of polarized domains with only a few hundred molecules, the number increasing at lower temperatures. This is in contrast to the random orientations of entire layers predicted by a few phenomenological models which have been proposed for the SmAP_{R} phase. In this paper we show that the two-state model, developed earlier by us to describe modulated phases found in compounds with BC molecules, can successfully account for all the experimental results on the SmAP_{R} phase. It is proposed that polarized domains which are made of ground state conformers, with a large bend of the aromatic cores, nucleate as circular disks in a first order transition from the isotropic phase. Excited state conformers (with a smaller bend) freely rotate about their long axes and surround the disks. The polarization in the disk has a spontaneous splay distortion which generates a texture with an expelled center of a partial disclination. The interdisk electrostatic energy is lower than the thermal energy and the disks are subject to significant rotational fluctuations, resulting in the uniaxial symmetry of the medium. Calculated equilibrium properties of the medium as functions of temperature and electric field reflect the trends seen in experiments. The model overestimates properties such as the radius of the disks as the transition to a lower temperature uniform phase is approached, and physical arguments are given to show that interlayer interactions ignored in the model become important in that regime, and should be included for an improved description of the medium.

Quantum-dots-dispersed bent-core nematic liquid crystal and cybotactic clusters: Experimental and theoretical insights

We study a quantum-dots (QDs) dispersed bent-core nematic liquid crystalline system in planar geometry and present experimental measurements of the birefringence (Δn), order parameter (S), dielectric dispersion, absorption spectra, and optical textures with attention to variations with temperature. A bent-core liquid crystal (LC) 14-2M-CH_{3} is used as the host material and CdSe/ZnS core-shell type QDs are used as the dopant. The nematic (N) phase of the pristine (undoped) LC 14-2M-CH_{3} contains cybotactic clusters, which are retained by its QDs incorporated LC nanocomposite. Our experimental findings support: (i) reduced orientational order parameter of the QDs dispersed LC system compared to its pristine counterpart at fixed temperatures, (ii) reduced cybotactic cluster sizes due to the incorporation of QDs, and (iii) increased activation energies related to reduced cluster sizes. We complement the experiments with a novel Landau-de Gennes-type free energy for a doped bent-core LC system that qualitatively captures the doping-induced reduced order parameter and its dependence on the properties of the QDs and its variation with temperature.

Some geometrical aspects of packing of bent-core molecules in the triclinic smectic-C_{g} liquid crystals and simple models of the modulated SmC_{gmod} phase

Organic compounds with bent-core (BC) molecules usually form the layered smectic liquid crystals with tilted molecules and polarization (P) which lies in the plane of the layer. A few such compounds have been found in which P itself tilts out of the plane of the layer, and the medium with general tilt (SmC_{g}) of the molecules has the low chiral triclinic symmetry. We discuss the geometric constraints of molecular packing in this structure to show that projecting groups attached to one of the arms of the BC molecules favors the formation of the SmC_{g} phase. We also extend our model for the modulated phases exhibited by BC molecules to show that the stripe structure made of bilayers shown by a few BC compounds, which is a signature of SmC_{g} layers, is preferentially formed by rotation of the BC molecules about their long axes, rather than about the layer normal. The theoretical results based on the unified model which describes all the modulated phases exhibited by the BC molecules broadly reflect experimental trends.

A two-state model for the modulated B7 liquid crystalline phase exhibited by bent-core molecules

Liquid crystals (LC) made of bent-core (BC) organic molecules have been intensively studied over the past two decades. The B₇ LC consists of smectic layers in which tilted molecules have an in-plane polar packing, the polarization vector ( P ) having a splay distortion forming stripes of tens of nanometers in width, and undulated layers giving rise to 2D rectangular or oblique lattices. The prevailing phenomenological theory attributes this structure to a strong coupling between molecular tilt in the layers and div P . Based on our recent studies on other phases exhibited by BC molecules, we propose a new model in which the physical origin of the stripes arises from a minority (~10%) of the BC molecules having less bent excited state (ES) conformers which can freely rotate about their long axes, and aggregate to form smectic C type walls, in which the tilt angle is relatively small. The more bent ground state (GS) conformers with polar packing in turn form the splayed structure between such walls to lower the free energy. The mismatch in the layer spacing between the domains with ES and GS conformers generates the structures in the B₇ phase described above. The model predicts a weak first order transition from B₇ to the uniform B₂ phase as the temperature is lowered, as experimentally observed in some compounds. We show that the observed slow increase of the stripe width in the LC to micrometer dimensions in free standing films can be attributed to changes in the physical parameters by chemical degradation and absorption of ions by the exposed polarized layers. We also describe different possible structures of the undulated layers, including a stacking of racemic pairs of SmC_aP_F layers within the stripes. Some possible methods of testing the model are also indicated.

Simple model for the stripe phase in compounds with bent-core molecules which exhibit a lower-temperature ferroelectric smectic-A phase

Bent-core (BC) molecules usually exhibit polar packing in smectic layers in which the long or bow axes tilt with respect to the layer normal. In many compounds, the tilt angle goes to zero, and typically the polarization (P) of neighboring layers has an antiferroelectric order (SmAP_{AF}). A careful molecular engineering has led to the discovery of the ferroelectric SmAP_{F} phase in a few BC compounds. Detailed experimental studies [Zhu et al., J. Am. Chem. Soc. 134, 9681 (2012)10.1021/ja3009314] have shown that one of the compounds undergoes a weak first order transition to a striped phase (SmAP_{Fmod}), in which the repolarization switching occurs at a threshold electric field, the latter increasing with temperature. The main optical birefringence of the SmAP_{Fmod} phase increases rapidly with the field at lower temperatures of its range. A small (<10%) fraction of the BC molecules can be expected to have less bent conformations in excited states (ESs), and we argue that the ES conformers rotate freely about the bow axes, and aggregate to form regions without any polar order to gain rotational entropy. In turn, a favorable divP term leads to the formation of stripes in the polarized regions made of ground state conformers. Based on this physical picture, we develop a simple phenomenological model to reproduce all the experimental trends qualitatively. In sample cells with insulating layers neighboring stripes prefer to have an antiparallel orientation of the mean P direction. The dielectric constant of the stripe phase increases with a dc bias electric field, a trend which is opposite to that in other ferroelectric liquid crystals.

One-dimensional theoretical analysis of coupling and confinement effects on the cybotactic clusters of bent-core nematic liquid crystals

The bent-core liquid crystals (LCs) are highly regarded as the next-generation materials for electro-optic devices. The nematic (N) phase of these LCs possesses highly ordered smecticlike cybotactic clusters which are promising for electro-optic applications. We have studied a one-dimensional Landau-de Gennes model of spatially inhomogeneous order parameters for the N phase of bent-core LCs. We investigate the effects of spatial confinement and coupling (between these clusters and the surrounding LC molecules modeled by a coupling parameter γ) on the order parameters. The coupling is found to increase the cluster order parameter significantly, suggesting enhancement in cluster formation, and also predicts a transition to a phase with weak nematiclike ordering above the nematic supercooling temperature.

Microscale Structures Arising from Nanoscale Inhomogeneities in Nematics Made of Bent-Shaped Molecules

Nanoscale structures in fluid media normally require techniques such as freeze fracture electron microscopy and atomic force microscopy for their visualization. As demonstrated in the present study, the surface modification due to nanoscale clusters occurring intrinsically in nematics made of bent-shaped molecules with either rigid or flexible cores leads to microscale structures, which are visible in an optical microscope. The underlying physical mechanism proposed here involves a quasiperiodic change in anchoring conditions on untreated glass plates for the medium made of islands of clusters surrounded by unclustered molecules. The resulting pattern of stripes outlines the director-normal field around line defects in the well-known schlieren texture. The instability, which is seen over most of the nematic range, with increasing visibility under continued cooling of the sample, sets the nematics made of bent-shaped molecules apart from the classical nematics of rod-shaped molecules.