Critical behavior of the layer compressional elastic constantBat the smectic-A–nematic phase transition

The temperature dependence of the layer compressional elastic constant B has been studied in four different compounds. Two of them, 4-cyano-4’-(n-octyl)biphenyl and 4-cyano-4’-(n-octyloxy)biphenyl, are polar and give partially bilayered smectic-${\mathit{A}}_{\mathit{d}}$ phases while the remaining two are nonpolar and present monolayered smectic-${\mathit{A}}_{\mathit{m}}$ phases. In all cases, the smectic-A–to nematic phase transition was found to be second order. A second-sound resonance technique has been used to measure Φ, the critical exponent of B on approaching the nematic phase. The values found lie in between 0.39 and 0.42, while the uncertainty is about 0.03. Although the nematic–smectic-A transition does not belong to a single universality class the Φ exponents are much less scattered than previously reported, with a mean exponent of 0.41 being consistent with the four reported values. When available, in the case of polar compounds, the set of critical exponents measured by calorimetry or x-ray scattering together with Φ, seems to be accounted for by the anisotropic model of the smectic-A–nematic phase transition.