Open Access Kent State (OAKS)

We have developed a fully nonlocal model to describe the dynamic behavior of nematic liquid-crystal elastomers. The free energy, incorporating both elastic and nematic contributions, is a function of the material displacement vector and the orientational order parameter tensor. The free energy cost of spatial variations of these order parameters is taken into account through nonlocal interactions rather than through the use of gradient expansions. We also give an expression for the Rayleigh dissipation function. The equations of motion for displacement and orientational order are obtained from the free energy and the dissipation function by the use of a Lagrangian approach. We examine the free energy and the equations of motion in the limit of long-wavelength and small-amplitude variations of the displacement and the orientational order parameter. We compare our results with those in the literature. If the scalar order parameter is held fixed, we recover the usual viscoelastic theory for nematic liquid crystals.

Using a range of optical techniques, we have probed the nature of orientational order in a thermotropic bent-core liquid crystal, which features a shape-persistent molecular architecture designed to promote a biaxial nematic phase. In the upper range of the nematic phase (enantiotropic regime), dynamic light scattering reveals strong fluctuations attributable to the biaxial order parameter, in addition to the usual uniaxial director modes. Assuming a Landau-type expansion of the orientational free energy, we estimate the correlation length associated with these fluctuations to be similar to 100 nm. At lower temperatures, and mainly in the monotropic regime of the nematic, we observe by optical conoscopy an apparently biaxial texture, which develops when the sample temperature is changed but then relaxes back to a uniaxial state over time scales much longer than observed in the light scattering measurements. A combination of fluorescence confocal polarizing microscopy and coherent anti-Stokes Raman scattering confirms that the conoscopic texture arises from a flow-induced reorientation of the molecules, associated with a large thermal expansion coefficient of the material, rather than from the spontaneous development of a macroscopic secondary optical axis. We discuss a model to account for the observed behavior at both high and low temperatures based on the temperature-dependent formation of nanoscale, biaxially ordered complexes among the bent-core molecules within a macroscopically uniaxial phase.

Liquid crystals are a class of industrially important materials whose optical properties make them useful particularly in display technology. Optical imaging of these materials provides information about their structure and physical properties. Coherent anti-Stokes Raman scattering (CARS) microscopy is used to provide three-dimensional chemical maps of liquid crystalline samples without the use of external labels. CARS is an optical imaging technique that derives contrast from Raman-active molecular vibrations in the sample. Compared to many other three-dimensional imaging techniques, CARS offers more rapid chemical characterization without the use of external dyes or contrast agents. The use of CARS to image chemical and orientational order in liquid crystals is demonstrated using several examples, and the limitations and benefits are discussed.

Molecular shape is an important factor in determining the material properties of thermotropic liquid crystals (LCs). We synthesized and investigated several LC compounds formed by asymmetrically bent molecules with a rigid four-ring core in the shape of the letter 'L'. We measured the temperature dependencies of dielectric permittivities, birefringence, splay K-1 and bend K-3 elastic constants, splay viscosity eta(splay) and flow viscosities eta(parallel to) and eta(perpendicular to). The bend-splay anisotropy delta K-31 - K-3 - K-1 is negative, similar to the case of nematic LCs formed by symmetrically bent molecules of V-shape. The dielectric anisotropy Delta epsilon and birefringence are positive in the entire nematic range. The splay viscosity eta(splay) and the flow viscosities eta(parallel to) and eta(perpendicular to) are smaller than the viscosities measured for the symmetric V-shaped bent-core materials at similar temperatures. The ratio Gamma = eta(splay)/eta(parallel to,perpendicular to) is in the range 5-4 that is typical for rod-like LCs. The reported L-shaped bent-core nematic LCs combine the useful features of bent-core LCs (such as a negative delta K-31, suitable for formulation of broad-range blue phases) with the relatively low viscosities, a property typical for rod-like LCs and beneficial for electro-optic switching applications.

The distance of closest approach of hard particles is a key parameter of their interaction and plays an important role in the resulting phase behavior. For nonspherical particles, the distance of closest approach depends on orientation, and its calculation is surprisingly difficult. Although overlap criteria have been developed for use in computer simulations [ Vieillard-Baron J. Chem. Phys. 56 4729 (1972); Perram and Wertheim J. Comput. Phys. 58 409 (1985)], no analytic solutions have been obtained for the distance of closest approach of ellipsoids in three dimensions, or, until now, for ellipses in two dimensions. We have derived an analytic expression for the distance of closest approach of the centers of two arbitrary hard ellipses as a function of their orientation relative to the line joining their centers. We describe our method for solving this problem, illustrate our result, and discuss its usefulness in modeling and simulating systems of anisometric particles such as liquid crystals.

The distance of closest approach of hard particles is a key parameter of their interaction and plays an important role in the resulting phase behavior. For nonspherical particles, the distance of closest approach depends on orientation, and its calculation is surprisingly difficult. Although overlap criteria have been developed for use in computer simulations [ Vieillard-Baron J. Chem. Phys. 56 4729 (1972); Perram and Wertheim J. Comput. Phys. 58 409 (1985)], no analytic solutions have been obtained for the distance of closest approach of ellipsoids in three dimensions, or, until now, for ellipses in two dimensions. We have derived an analytic expression for the distance of closest approach of the centers of two arbitrary hard ellipses as a function of their orientation relative to the line joining their centers. We describe our method for solving this problem, illustrate our result, and discuss its usefulness in modeling and simulating systems of anisometric particles such as liquid crystals.

Deuteron quadrupole-perturbed NMR is used to study the perturbation of orientational order in a smectic-A liquid crystal (octylcyanobiphenyl or 8CB) caused by photoinduced trans-to-cis isomerization of a photosensitive dopant (diheptylazobenzene or 7AB). The time and temperature dependences of the orientational order were independently studied for 8CB, 7AB, and their mixtures. Upon UV irradiation that causes trans-to-cis isomerization of 7AB, the orientational order parameter of the smectic-A phase is reduced. Relaxation in the dark exponentially restores the equilibrium value of the order parameter. The characteristic time for this process closely matches the lifetimes of the 7AB excited state. While in the 8CB smectic-A matrix, the cis-isomerized 7AB molecules retain a uniaxial orientational order with the director oriented along the normal to the smectic layers. The highly bent 7AB cis molecules act as a disorienting factor, decreasing the orientational order in the layers and causing a small increase in layer spacing. This disorder-induced increase in layer spacing is much smaller than the actual increase as observed by in situ x-ray experiments on UV-irradiated mixtures of 8CB:7AB. Concomitant with the experimental observation that only a fraction of 7AB molecules are converted to the cis state, this work provides indirect evidence for a nanophase segregation with the 7AB cis-isomers arranged within the interlayer space, thus significantly increasing the smectic layer spacing.

A biaxial nematic phase had been predicted with D2h symmetry, wherein the mesogen’s long and short transverse axes are simultaneously aligned along the two orthogonal, primary and secondary directors, n and m, respectively. The unique low-angle x-ray diffraction patterns in the nematic phases exhibited by three rigid bent-core mesogens clearly reveal their biaxiality. The results of x-ray diffraction can be readily reproduced by ab initio calculations that explicitly include the bent-core shape in the form factor and assume short-range positional correlations.

The nematic (N) to lamellar (Lα) phase transition in binary mixtures of cesium-perfluoro-octanoate (CsPFO) and water has been studied by high-resolution synchrotron x-ray scattering at 46.6 weight % CsPFO. The longitudinal correlation length ξ∥ and the susceptibility σ associated with the lamellar phase fluctuations in the N phase, measured over three decades of reduced temperature, diverge with critical exponents ν∥=0.86±0.04 and γ=1.37±0.11, respectively. These results show that the N to Lα phase transition is quantitatively similar to the N to smectic-A phase transition of thermotropic liquid crystals with a wider nematic range.