Novel approach to study liquid crystal phase transitions using Legendre moments

A novel approach is proposed to investigate the phase transitions of cholesteric liquid crystals using the Legendre moments. The textures of cholesteric liquid crystals (cholesteryl butyrate, cholesteryl n-valerate, cholesteryl decanoate, and cholesteryl myristate) are captured as a function of temperature using high-resolution camera attached to the arthroscopic mode of polarizing optical microscope with hot stage. A recurrence formula is used to compute the Legendre moments of the liquid crystal textures based on the Legendre polynomial using MATLAB software. The abrupt change in the values of Legendre moments as a function of temperature gives the phase transitions of liquid crystals. The investigated transition temperatures of cholesteric liquid crystals are compared with other techniques.