Investigation of Phase Transitions in Nematic Liquid Crystals by Fractional Calculation

Abstract

In this study, we investigate nematic-isotropic phase transitions in liquid crystals using fractionallygeneralized form of the Maier-Saupe Theory (MST). MST is one of the mean-field theories commonly usedin the nematic liquid crystals which proved to be extremely useful in explaining nematic-isotropic phasetransitions. Fractionally obtained results compared with those of the experimental data for p-azoxyanisole(PAA) in the literature. In this context, the dependence of fourth rank order parameters on second rank orderparameters is handled by being a measure of fractality of space. It is observed that the variation of second-rank and fourth rank order parameters versus temperature are in accordance with some values of fractaldimensions. As a result, we can conclude that there is a close relationship between temperature and fractionalderivative order parameters.