Theory of self-assembled smectic-A "crenellated disks"

Smectic-A monolayers self-assembled in aqueous solutions of chiral fd viruses and a polymer depletant have been shown to exhibit a variety of structures including large, flat disks and twisted ribbons. The virus particles twist near the edge of the structure in a direction determined by the chirality of the viruses. When fd viruses and their mutants of opposite chirality are mixed together in nearly equal amounts unusual structures referred to as "crenellated disks" can appear. These disks are achiral overall but the twist at the edge alternates between left- and right-handedness. To minimize the mismatch where the two regions of opposing twist meet, the "crenellated" structure exhibits cusps rising out of the plane of the monolayer. We use a phenomenological elastic theory previously applied to flat disks and twisted ribbons to analyze an analytic model proposed to describe the "crenellated" structure . When compared with flat, circular disks, we find that the model "crenellated disks" are stable or at least metastable in a wide region of the phase diagram spanned by the Gaussian curvature modulus and the edge energy modulus, with a large energy barrier separating the two structures. The director pattern and geometric parameters of the "crenellated disks" are found to be in qualitative agreement with experimental observations.Comment: 8 pages, 6 figure

Piezoelectricity of Cholesteric Elastomers

We consider theoretically the properties of piezoelectricity in cholesteric elastomers. We deduce using symmetry considerations the piezoelectric contributions to the free energy in the context of a coarse-grained description of the material. In contrast to previous work we find that compressions or elongations of the material along the pitch axis do not produce a piezoelectric response, in agreement with fundamental symmetry considerations. Rather only suitable shear strains or local rotations produce a polarization. We propose some molecular mechanisms to explain these effects.Comment: 11 pages, 1 Postscript figure; Late

Surface extrapolation length and director structures in confined nematics

We report the results of Monte Carlo simulations of the Lebwohl--Lasher model of nematic liquid crystals confined to cylindrical cavities with homeotropic anchoring. We show that the ratio of the bulk to surface couplings is not in general equal to the corresponding parameter K/W used in elastic theory (where K is the Frank elastic constant in the one constant approximation and W is the surface anchoring strength). By measuring the temperature dependence of K/W (which is equivalent to the surface extrapolation length) we are able to reconcile the results of our simulations as well as others with the predictions of elastic theory. We find that the rate at which we cool the system from the isotropic to nematic phase plays a crucial role in the development of the final director structure, because of a large free energy barrier separating different director structures as well as the temperature dependence of $K/W$. With a suitably fast cooling rate we are able to keep the system out of a metastable planar state and form an escaped radial structure for large enough systems.Comment: 6 pages, 5 figure