Through the combination of three different, complementary techniques (optical microscopy, x-ray diffraction and atomic force microscopy), we reveal the deformations inside thin smectic films frustrated between two interfaces imposing antagonistic anchorings. We study the model system, 4-$n$-octyl-$4^{\prime }$-cyanobiphenyl (8CB) between ${\text{MoS}}_2$ and air, which is characterized by the competition between homeotropic anchoring at air and planar unidirectional anchoring on the substrate, with thicknesses varying around $0.3\mu \mathrm{m}$. Optical microscopy and x-ray diffraction demonstrate the continuous topology of smectic layers between the interfaces, which are stacked into periodic flattened hemicylinders. These latter are one-dimensional (1D) focal conic domains which form an optical grating in the smectic film, of a period ranging from 1 to $2.5\mu \mathrm{m}$. The interpretation of our results through an energetic model, associated with the atomic force microscopy (AFM) measurements, shows the presence below a critical thickness of a new type of curvature wall between neighboring hemicylinders.

• Received 4 December 2003

DOI:https://doi.org/10.1103/PhysRevE.70.011709