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We present a generalized approach to compute the shape and internal structure of two-dimensional nematic domains. By using conformal mappings, we are able to compute the director field for a given domain shape that we choose from a rich class, which includes drops with large and small aspect ratios, and sharp domain tips as well as smooth ones. Results are assembled in a phase diagram that for given domain size, surface tension, anchoring strength, and elastic constant shows the transitions from a homogeneous to a bipolar director field, from circular to elongated droplets, and from sharp to smooth domain tips. We find a previously unaccounted regime, where the drop is nearly circular, the director field bipolar and the tip rounded. We also find that bicircular director fields, with foci that lie outside the domain, provide a remarkably accurate description of the optimal director field for a large range of values of the various shape parameters.
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We consider a mathematical model that describes the flow of a Nematic Liquid Crystal (NLC) film placed on a flat substrate, across which a spatially-varying electric potential is applied. Due to their polar nature, NLC molecules interact with the (nonuniform) electric field generated, leading to instability of a flat film. Implementation of the long wave scaling leads to a partial differential equation that predicts the subsequent time evolution of the thin film. This equation is coupled to a boundary value problem that describes the interaction between the local molecular orientation of the NLC (the director field) and the electric potential. We investigate numerically the behavior of an initially flat film for a range of film heights and surface anchoring conditions.
Instabilities in thin elastic sheets, such as wrinkles, are of broad interest both from a fundamental viewpoint and also because of their potential for engineering applications. Nematic liquid crystal elastomers offer a new form of control of these instabilities through direct coupling between microscopic degrees of freedom, resulting from orientational ordering of rod-like molecules, and macroscopic strain. By a standard method of dimensional reduction, we construct a plate theory for thin sheets of nematic elastomer. We then apply this theory to the study of the formation of wrinkles due to compression of a thin sheet of nematic liquid crystal elastomer atop an elastic or fluid substrate. We find the scaling of the wrinkle wavelength in terms of material parameters and the applied compression. The wavelength of the wrinkles is found to be non-monotonic in the compressive strain owing to the presence of the nematic. Finally, due to soft modes, the critical stress for the appearance of wrinkles can be much higher than in an isotropic elastomer and depends nontrivially on the manner in which the elastomer was prepared.
We report a dynamic light scattering study of the fluctuation modes in a thermotropic liquid crystalline mixture of monomer and dimer compounds that exhibits the twist-bend nematic ($mathrm{N_{TB}}$) phase. The results reveal a spectrum of overdamped fluctuations that includes two nonhydrodynamic and one hydrodynamic mode in the $mathrm{N_{TB}}$ phase, and a single nonhydrodynamic plus two hydrodynamic modes (the usual nematic optic axis or director fluctuations) in the higher temperature, uniaxial nematic phase. The properties of these fluctuations and the conditions for their observation are comprehensively explained by a Landau-deGennes expansion of the free energy density in terms of heliconical director and helical polarization fields that characterize the $mathrm{N_{TB}}$ structure, with the latter serving as the primary order parameter. A coarse-graining approximation simplifies the theoretical analysis, and enables us to demonstrate quantitative agreement between the calculated and experimentally determined temperature dependence of the mode relaxation rates.
We study the flow behaviour of a twist-bend nematic $(N_{TB})$ liquid crystal. It shows three distinct shear stress ($sigma$) responses in a certain range of temperatures and shear rates ($dot{gamma}$). In Region-I, $sigmasimsqrt{dot{gamma}}$, in region-II, the stress shows a plateau, characterised by a power law $sigmasim{dot{gamma}}^{alpha}$, where $alphasim0.1-0.4$ and in region-III, $sigmasimdot{gamma}$. With increasing shear rate, $sigma$ changes continuously from region-I to II, whereas it changes discontinuously with a hysteresis from region-II to III. In the plateau (region-II), we observe a dynamic stress fluctuations, exhibiting regular, periodic and quasiperiodic oscillations under the application of steady shear. The observed spatiotemporal dynamics in our experiments are close to those were predicted theoretically in sheared nematogenic fluids.
This work investigates how a thermal diode can be designed from a nematic liquid crystal confined inside a cylindrical capillary. In the case of homeotropic anchoring, a defect structure called escaped radial disclination arises. The asymmetry of such structure causes thermal rectification rates up to 3.5% at room temperature, comparable to thermal diodes made from carbon nanotubes. Sensitivity of the system with respect the heat power supply, the geometry of the capillary tube and the molecular anchoring angle is also discussed.
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