Critical Exponents for Thermal Expansion and Isothermal Compressibility near the Nematic to Smectic-A Phase Transition

High-resolution measurements of the molar volume, V, measured as a function of temperature at two different pressures allowed the calculation of the isobaric thermal expansion coefficient, α p ( T ), and isothermal compressibility coefficient, β T ( T ). Critical exponents for observed singularities in both thermodynamic quantities were found. It was confirmed that the same critical exponent α, usually assigned to heat capacity, describes singularities of the thermal expansion and the isothermal compressibility coefficients. Two compounds from the two different homologous series, n CB and m̄ S5, were studied. V ( T ) and β T ( T ) variations in 8CB showed a continuous phase transition with the effective critical exponent α = α‘ = 0.32 ± 0.02. For S5 a weakly first-order transition with a volume jump Δ V = 0.127 ± 0.001 cm 3 /mol (Δ V / V = 2.6 × 10 -4 ) was observed and an exponent α = α‘ = 0.50 ± 0.02 was found.