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Calculation of the T-X Phase Diagrams for Binary Mixtures of Cholestanyl Myristate-Cholesteryl Myristate and Cholestanyl Myristate-Cholesteryl Oleate

T-X phase diagrams of binary mixtures of cholestanyl myristate (CnM)-cholesteryl myristate (CrM) and cholestanyl myristate (CnM)-cholesteryl oleate (CO) are calculated using the mean field theory. We expand the free energies for the phases of cholesteric, smectic, and solid solutions in terms of the order parameters for these binary mixtures (X is the concentration of CrM for CnM-CrM and the concentration of CnM for CnM-CO). From this expansion, we obtain the phase line equations for the transitions among the isotropic liquid, cholesteric, smectic, and solid solutions for both binary mixtures. Taking into account the temperature and concentration dependences of the coefficients in the free energy expansion, we fit our phase line equations to the experimentally measured T-X phase diagrams for these two binary mixtures. Our calculated phase lines coincide with the measured T-X phase diagrams, and the critical behavior of the thermodynamic quantities, including the order parameter, the specific heat, and the susceptibility, can be predicted from the mean field expansions.