Periodic distorted nematic director structures in the intermediate Freedericksz transition geometries

The occurrence of periodically distorted director structures in planar and pre-tilted nematic slabs above the magnetically driven Fre´edericksz transition is investigated in the intermediate geometries between the pure splay, twist and bend Fre´edericksz transition geometries. Considering rigid boundary conditions the domain of existence of the periodic structures is determined as a function of the Frank elastic constants ratios K2=K1, K1=K3 and the magnetic field orientation. It is found that the periodic distorted state can be reached either directly from the undistorted state on increasing the magnetic field or indirectly through the homogeneously distorted state when pre-tilt is present. It is also found in pre-tilted slabs that the transition from the undistorted state to the homogeneously distorted state can be either continuous or discontinuous, and the corresponding lines of tricritical points are determined.