Examination of phase transitions of liquid crystals by fractional calculation

In this study, nematic-isotropic phase transitions in liquid crystals have been examined using the Maier-Saupe Theory (MST) generalized with fractional derivatives and integrals (fractional). MST is a theory that is proven to be extremely useful in describing phase transitions in nematic liquid crystals, and is also one of the widely-used mean field theories. Fractional results and experimental data in the literature for p-azoxyansile (PAA is a nematic liquid crystal) were interpreted and compared. In this context, the dependence of the second degree order parameter on the fourth degree order parameter is considered according to the different dimensions of space. Furthermore in this study, the change of fourth rank order parameters (P4) of U_ij=-f(r_(ij)) P_L 〖(cos⁡〖θ)〗〗_ij potential with second rank order parameters (P2) was examined using fractionally generalized MST, for situations for L = 2 and L = 4 degrees, to explain the nematic-isotropic phase transitions in more detail, and the answers to some fractal dimensions of the dependence of the order parameter on temperature was interpreted. In conclusion, in this thesis study, the dependence of order parameters on the fractional derivative order as a measure of the space fractal has been examined. In addition, as an application of fractional formalism, the temperature-dependent behavior of PAA (p-azoxyanisole), which conventional MST is insufficient to explain, has been taken into account. Considering the result that there is a close relationship between the fractal and the fractional order parameters (depending on the temperature), this study can be developed for different fractal dimensions of space. Since the properties of liquid crystals have recently begun to be examined with fractional methods, it is thought that this thesis study will have a unique characteristic and fill an important gap in the literature since it applies fractional calculation methods.