Thermal and structural analysis of binary mixtures of pyrimidine liquid crystals using modulated differential calorimetry and synchrotron x-ray diffraction measurements.

We present a systematic experimental dataset on the temperature dependence of specific heat capacity in a binary mixture of the second and seventh homologous series of 5-alkyloxy-2-(4-nonyloxy-phenyl) pyrimidine (PhP) liquid crystal compound. These binary mixtures exhibit nematic, smectic-A, and smectic-C phases within a concentration range ofx_PhP1= 0-0.45. The liquid crystalline phases are structurally characterized using synchrotron x-ray diffraction. We determine the apparent molecular length in the nematic phase, smectic layer spacing, average distance between the long axes of molecules, correlation length, and orientational order parameters (<P₂> and <P₄>) as functions of temperature. The tilt angle in the SmC phase is inferred from the layer spacing data. To examine the critical behavior near the nematic to smectic A (NA) and smectic A to the smectic C (AC) phase transitions, we evaluate the critical exponents:αfrom specific heat capacity,βfrom the fitting of the temperature-dependent tilt angle, andν_ǁ,ν_⊥from the temperature-dependent longitudinal (ξ_ǁ) and transverse (ξ_⊥) correlation lengths. Modulated Differential Scanning Calorimetry (MDSC) measurements indicate the absence of phase shift, latent heat and imaginary specific heat capacity, suggesting that the AC transitions are second-order for all binary mixtures. The results obtained from heat capacity reveal that both the AC and NA transitions exhibit non-universal behaviors with effective exponents lying between the tricritical and 3D-XY values and follow nearly identical curve with decreasing width of the Sm-A and N phases. The Josephson hyper scaling relation is verified for both the NA and AC transitions in different mixtures. Moreover, knowing the heat capacity critical exponentαand the order parameter critical exponentβ, the susceptibility critical exponentγfor the AC transition can be estimated from Rushbrooke equalityα+ 2β+γ= 2, withγvalues ranging from 1.015 to 1.313, indicating the system's crossover character and apparently validating the Rushbrooke equality.