Critical behavior near the nematic—smectic-Atransition in butyloxybenzylidene octylaniline (40.8)

We report a high-resolution heat-capacity and x-ray study of the nematic—smectic-$A$ transition in the single-layer smectic material butyloxybenzylidene octylaniline (40.8). We find that the transition is second order to within 3 mK, with critical behavior closely similar to that observed previously in bilayer smectic materials such as octyloxycyanobiphenyl (8OCB). For the critical exponents we measure $\gamma =1.31\mathrm{}\pm 0.02$, ${\nu }_{\parallel }=0.70\mathrm{}\pm 0.01$, ${\nu }_{\perp }=0.57\mathrm{}\pm 0.01$, and $\alpha ={\alpha }^{\prime }=0.15\mathrm{}\pm 0.05$. These exponents are consistent with the anisotropic hyperscaling relation ${\nu }_{\parallel }+2\mathrm{}{\nu }_{\perp }=2-\alpha$. In addition, we find that the ratio of the amplitudes of the critical heat capacities in 40.8 and 8OCB is inversely proportional to the ratio of the correlated volumes as measured with x rays. The smectic longitudinal correlation length measured directly with x rays agrees quantitatively with that deduced by von Känel and Litster from the director fluctuations. Substantial disagreements with the superconducting analog model remain unexplained.