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 of xPhP1 = 0 to 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 ( and ) 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: α from specific heat capacity, β from the fitting of the temperature-dependent tilt angle, and ν_‖, ν_⊥from the temperature-dependent longitudinal (ξ_‖) 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 behaviours 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 hyperscaling relation is verified for both the NA and AC transitions in different mixtures. Moreover, knowing the heat capacity critical exponent α and the order parameter critical exponent β, the susceptibility critical exponent γ for the AC transition can be estimated from Rushbrooke equality α+2β+γ=2, with γ values ranging from 1.015 to 1.313, indicating the system's crossover character and apparently validating the Rushbrooke equality.