We report optical birefringence data by two different methods with high temperature resolution for octylcyanobiphenyl (8CB) near the smectic-$A$ to nematic (Sm-$A$-$N$) phase transition temperature $T_{AN}$. Within the resolution of our experiments, we find that the Sm-$A$-$N$ phase transition is continuous. For a possible discontinuity in the orientational order parameter $S\left(T\right)$ at $T_{AN}$, we arrive at an upper limit of 0.0002, which is substantially smaller than other estimates in literature, but consistent with the value of 0.00008 derived from the upper limit of the latent heat from high-resolution adiabatic scanning calorimetry (ASC), which is itself consistent with the Halperin-Lubensky-Ma theory. The temperature derivative of the order parameter exhibits a power law divergence with a critical exponent that is consistent with the value $\alpha =0.31\pm 0.03$ for the specific heat capacity obtained by ASC.

• Received 16 May 2013

DOI:https://doi.org/10.1103/PhysRevE.88.042502