Thick smectic shells

• The ground state of two-dimensional smectic shells is reconsidered.
• The criterion for thick smectic shells is identified.
• Geometric frustration is relieved by the director tilt.
• The period of domains increases with thickness times curvature of a spherical shell.

The known ground state of ultrathin smectic films confined to the surface of a sphere is described by four +1/2 defects assembled on a great circle and a director which follows geodesic lines. Using a simple perturbative approach we show that for thick smectic films on a sphere with planar anchoring this solution breaks down, distorting the smectic layers. The instability happens when the bend elastic constant exceeds the anchoring strength times the radius of the inner sphere. Above this threshold, the formation of a periodic chevron-like structure, observed experimentally as well, relieves geometric frustration. We quantify the effect of thickness and curvature of smectic shells and provide insight into the wavelength of the observed texture.