Theory of chiral modulations and fluctuations in smectic-A liquid crystals under an electric field

Electroclinic effect in chiral smectic-A liquid crystal elastomers

Chiral smectic-A liquid crystal elastomers are rubbery materials composed of a lamellar arrangement of liquid crystalline mesogens. It has been shown experimentally that these materials shear when subjected to an electric field due to the electrically induced tilt of the director. Experiments have also shown that shearing a chiral smectic-A elastomer gives rise to a polarization. Roughly, the shear force tilts the directors which, in turn, induce electric dipoles. This paper builds on previous works and models the electromechanical response of smectic-A elastomers using free energy contributions that are associated with the lamellar structure, the relative tilt between the director and the layer normal, and the coupling between the director and the electric field. To illustrate the merit of the proposed model, two cases are considered-a deformation induced polarization and an electrically induced deformation. The predictions according to these two models qualitatively agree with experimental findings. Finally, a cylinder composed of helical smectic layers is also considered. It is shown that the electromechanical response varies as a function of the helix angle.

de Vries behavior of the electroclinic effect in the smectic-A* phase near a biaxiality-induced smectic-A*-smectic-C* tricritical point

Using a generalized Landau theory involving orientational, layering, tilt, and biaxial order parameters we analyze the smectic-A* and smectic-C* (Sm-A*-Sm-C*) transitions, showing that a combination of small orientational order and large layering order leads to Sm-A*-Sm-C* transitions that are either continuous and close to tricriticality or first order. The model predicts that in such systems the increase in birefringence upon entry to the Sm-C* phase will be especially rapid. It also predicts that the change in layer spacing at the Sm-A*-Sm-C* transition will be proportional to the orientational order. These are two hallmarks of Sm-A*-Sm-C* transitions in de Vries materials. We analyze the electroclinic effect in the Sm-A* phase and show that as a result of the zero-field Sm-A*-Sm-C* transition being either continuous and close to tricriticality or first order (i.e., for systems with a combination of weak orientational order and strong layering order), the electroclinic response of the tilt will be unusually strong. Additionally, we investigate the associated electrically induced change in birefringence and layer spacing, demonstrating de Vries behavior for each, i.e., an unusually large increase in birefringence and an unusually small layer contraction. Both the induced changes in birefringence and layer spacing are shown to scale quadratically with the induced tilt angle.

Self-assembled patterns and strain-induced instabilities for modulated systems

The self-assembled domain patterns of modulated systems are characteristic of a wide variety of chemical and physical systems, and are the result of competing interactions. From a technological point of view, there is considerable interest in these domain patterns, as they form suitable templates for the fabrication of nanostructures. We have analyzed the domains and instabilities that form in modulated systems, and show that a large variety of patterns--based on long-lived metastable or glassy states--may be formed as a compromise between the required equilibrium modulation period and the strain present in the system. The strain results from topologically constrained trajectories in phase space, that effectively preclude the equilibrium configuration.

Shape selection in chiral self-assembly

Many biological and synthetic materials self-assemble into helical or twisted aggregates. The shape is determined by a complex interplay between elastic forces and the orientation and chirality of the constituent molecules. We study this interplay through Monte Carlo simulations, with an accelerated algorithm motivated by the growth of an aggregate out of solution. The simulations show that the curvature changes smoothly from cylindrical to saddlelike as the elastic moduli are varied. Remarkably, aggregates of either handedness form from molecules of a single handedness, depending on the molecular orientation.

X-ray Evidence for a “Super”-Secondary Structure in Silk Fibers

X-ray studies on degummed B. mori silk fibers and on hydrogels prepared under a variety of conditions reveal moderately small angle reflections. These reflections are often highly oriented and are correlated to silk II lattice reflections. A superstructure can explain these features. Silk fibroin hydrogels were monitored as they dried to form the silk II structure. The silk II wide angle and moderately small angle patterns obtained from dried hydrogels and silk fibers are identical. The "superstructure" reflections at moderately small angle (3-7 nm) were first to appear, followed by the "intersheet" spacing, and then the remainder of the silk II wide angle scattering pattern. Thus, any superstructure hypothesized for the hydrogels (and for Silk II in fibers) must be both stable in a highly hydrated environment and must convert to silk II with little large scale diffusion. A folded structure, similar to amyloids and cross-beta-sheets but with much longer beta-strand stems, is proposed for silk II in fibers.

Simulations of helix unwinding in ferroelectric liquid crystals

In bulk ferroelectric liquid crystals, the molecular director twists in a helix. In narrow cells, this helix can be unwound by an applied electric field or by boundary effects. To describe helix unwinding as a function of both electric field and boundary effects, we develop a mesoscale simulation model based on a continuum free energy discretized on a two-dimensional lattice. In these simulations, we determine both the director profile across the cell and the net electrostatic polarization. By varying the cell size, we show how boundary effects shift the critical field for helix unwinding and lower the saturation polarization. Our results are consistent with experimental data.