This work consisted of three chapters. First chapter contained an introduction to explain the historical view, physical properties, application and thermodynamic characterization of binary and tertiary system mixtures of liquid crystalline materials. Also it contained an introduction to Nanotechnology and nanosheets like graphene oxide and its functionalization and a summary about the dielectric permittivity and conductivity. The second chapter explained the experimental part including the synthesis of graphene oxide (GO) and its functionalization and general synthesis procedure of eight liquid crystalline compounds. The third chapter described the characterization of the prepared GO nanosheets with different functional groups. These nanosheets were characterized with multiple techniques (FT-IR, X-ray diffraction, SEM and AFM). The prepared liquid crystalline compounds were characterized by using FT-IR infrared and the liquid crystalline properties of compounds, the binary, tertiary systems and the mixtures with graphene oxide (GO) and GO functionalized nanosheets were examined with hot-stage polarizing microscopy, at the concentrations of the eutectic points.