Effects of flexoelectricity and weak anchoring on a Freedericksz transition cell

Abstract

We consider a mathematical model that consists of a nematic liquid crystal layer sandwiched between two parallel bounding plates, across which an external field is applied. We investigate how the number and type of solutions for the director orientation within the layer change as the field strength, anchoring conditions, and material properties of the nematic liquid crystal layer vary. In particular, we focus on how the inclusion of flexoelectric effects alters the Freedericksz and saturation thresholds.

Dielectrowetting of a thin nematic liquid crystal layer

“…(where ν is the unit outward normal to the free surface), to the total energy [20]. In experiments, typical values for weak anchoring vary between 10 −5 − 10 −6 Jm −2 [19]. For the velocity v * , we assume no-slip and nopenetration conditions at the lower boundary, and a kinematic boundary condition together with a balance of normal and tangential stresses at the free surface.…”

“…Ref. [19]). The strong planar substrate anchoring dominates over both the weak homeotropic anchoring and the weak electric field in regions between the electrodes, forcing the director to align parallel to the substrate throughout the layer:…”