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Register a new userThe limits of flexoelectricity in liquid crystals
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The flexoelectric conversion of mechanical to electrical energy in nematic liquid crystals is investigated using continuum theory. Since the electrical energy produced cannot exceed the mechanical energy supplied, and vice-versa, upper bounds are imposed on the magnitudes of the flexoelectric coefficients in terms of the elastic and dielectric coefficients. For conventional values of the elastic and dielectric coefficients, it is shown that the flexoelectric coefficients may not be larger than a few tens of pC/m. This has important consequences for the future use of such flexoelectric materials in devices and the related energetics of distorted equilibrium structures.
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We present in this paper a detailed analysis of the flexoelectric instability of a planar nematic layer in the presence of an alternating electric field (frequency $omega$), which leads to stripe patterns (flexodomains) in the plane of the layer. This equilibrium transition is governed by the free energy of the nematic which describes the elasticity with respects to the orientational degrees of freedom supplemented by an electric part. Surprisingly the limit $omega to 0$ is highly singular. In distinct contrast to the dc-case, where the patterns are stationary and time-independent, they appear at finite, small $omega$ periodically in time as sudden bursts. Flexodomains are in competition with the intensively studied electro-hydrodynamic instability in nematics, which presents a non-equilibrium dissipative transition. It will be demonstrated that $omega$ is a very convenient control parameter to tune between flexodomains and convection patterns, which are clearly distinguished by the orientation of their stripes.
Previous theoretical studies of calamitic (i.e., rod-like) ionic liquid crystals (ILCs) based on an effective one-species model led to indications of a novel smectic-A phase with a layer spacing being much larger than the length of the mesogenic (i.e., liquid-crystal forming) ions. In order to rule out the possibility that this wide smectic-A phase is merely an artifact caused by the one-species approximation, we investigate an extension which accounts explicitly for cations and anions in ILCs. Our present findings, obtained by grand canonical Monte Carlo simulations, show that the phase transitions between the isotropic and the smectic-A phases of the cation-anion system are in qualitative agreement with the effective one-species model used in the preceding studies. In particular, for ILCs with mesogenes (i.e., liquid-crystal forming species) carrying charged sites at their tips, the wide smectic-A phase forms, at low temperatures and within an intermediate density range, in between the isotropic and a hexagonal crystal phase. We find that in the ordinary smectic-A phase the spatial distribution of the counterions of the mesogens is approximately uniform, whereas in the wide smectic-A phase the small counterions accumulate in between the smectic layers. Due to this phenomenology the wide smectic-A phase could be interesting for applications which hinge on the presence of conductivity channels for mobile ions.
We review and compare recent work on the properties of fluctuating interfaces between nematic and isotropic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial tension, which is anisotropic at small wavelengths (stiff director regime) and becomes isotropic at large wavelengths (flexible director regime). After determining the elastic constants in the nematic phase, theory and simulation can be compared quantitatively. We obtain good agreement for the stiff director regime. The crossover to the flexible director regime is expected at wavelengths of the order of several thousand particle diameters, which was not accessible to our simulations.
Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local $C_{infty v}$-symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals ($D_{infty h}$) in that it contains terms violating the ${bf{n}}to -{bf{n}}$ symmetry. First we show that these $mathcal{Z}_2$-odd terms induce a general splay instability of a uniform polarized state in a range of parameters. Next we use the general Poisson-bracket formalism to derive the hydrodynamic equations of the system in the polarized state. The structure of the linear hydrodynamic modes confirms the existence of the splay instability.
We study the topology of smectic defects in two and three dimensions. We give a topological classification of smectic point defects and disclination lines in three dimensions. In addition we describe the combination rules for smectic point defects in two and three dimensions, showing how the broken translational symmetry of the smectic confers a path dependence on the result of defect addition.
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