We report two distinct types of two-dimensionally periodic phases in different concentration regions of a binary system composed of the bent-core (BC) compound $1,3\text{-phenylene bis}\left[4\text{−}\right(3\text{−}\text{methylbenzoyloxy}\left)\right]4^{\prime }\text{−}n\text{-dodecylbiphenyl}$ $4^{\prime }\text{-carboxylate}$ (BC12) and the rodlike (R) compound $4\text{−}n\text{-octyloxy}{4}^{\prime }\text{-cyanobiphenyl}$ (8OCB). BC12 exhibits only the lamellar $B_2$ phase. 8OCB which has a highly polar cyano end group exhibits the ${\mathrm{smectic}\text{−}A}_d$ phase with a lamellar structure of partial bilayers made of antiparallel pairs of the polar molecules. The molecular arrangements in the two-dimensionally periodic phases have been deduced based on optical microscopy, polarized infrared and x-ray diffraction studies. The arrangement in the two-dimensionally periodic phase in lower concentration ranges of BC12 (24 to $35\mathrm{mol}\%$) is dictated by the partial bilayer structure formed by the rods. The BC molecules arrange themselves with their arrow axes parallel to the long axes of the R molecules and the structure conforms to the $c2\mathit{mm}$ space group symmetry. In higher concentration ranges of BC12 (35 to $60\mathrm{mol}\%$) the structure is dominated by the BC molecules, to form the familiar $B_1$ phase with the $p2\mathit{mg}$ space group symmetry. The R molecules lie at the interfaces of these domains stabilizing the structure.

• Received 17 April 2004

DOI:https://doi.org/10.1103/PhysRevE.71.011701