Structural Landscapes in Geometrically Frustrated Smectics

A phenomenological free energy model is proposed to describe the behavior of smectic liquid crystals, an intermediate phase that exhibits orientational order and layering at the molecular scale. Advantageous properties render the functional amenable to numerical simulation. The model is applied to a number of scenarios involving geometric frustration, leading to emergent structures such as focal conic domains and oily streaks and enabling detailed elucidation of the very rich energy landscapes that arise in these problems.

Figure 1

Applying a bend deformation to a smectic liquid crystal. (a) Bifurcation diagram. (b)–(e) Stable stationary solutions for different values of ${\theta }_0$. The visualization displays the density variation $\delta \rho$.

Figure 2

Focal conic domains under tilted boundary conditions. Example solutions with (a) single- and (b) double-screw dislocation defects at ${\theta }_c=\pi /12$. (c) Stable stationary solutions for different values of ${\theta }_c$. Here, zero isosurfaces of the density variation $\delta \rho$ are displayed to visualize the layer structure of the smectic. Among the three solutions shown for ${\theta }_c=\pi /12$, the FCD solution possesses the lowest energy value, while the double-screw dislocation solution has the highest value.

Figure 3

Oily streaks. (a)–(c) Candidate structures proposed in Michel et al. [42] consistent with x-ray diffraction. (d) Bifurcation diagram of structures as a function of aspect ratio $L/\tau$. (e) Selected stationary states obtained at different aspect ratios $L/\tau$. The top row represents the lowest-energy solution found. For each solution, the value of the energy functional per unit area is displayed below it, with asterisks indicating stable profiles.