Influence of nematic range on birefringence, heat capacity and elastic modulus near a nematic–smectic-Aphase transition

Abstract

The birefringence $\ensuremath{\Delta}n,$ the specific heat ${C}_{p},$ and the layer compressional elastic modulus B are reported for two liquid crystals near the nematic $(N)$ to smectic-$A$ $(\mathrm{Sm}A)$ phase transition. As predicted long ago by MacMillan and de Gennes [P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, Oxford, 1993)] the coupling of the nematic orientational order parameter to the smectic-$A$ layering order parameter can substantially alter the critical behavior near the $N\ensuremath{-}\mathrm{Sm}A$ transition if the nematic range is small and the nematic order parameter susceptibility is large. In this paper, we present a direct experimental comparison of two compounds: 4-octyloxy-${4}^{\ensuremath{'}}$-cyanobiphenyl (8OCB) with a short nematic range and 4-octyloxybenzoyloxy-${4}^{\ensuremath{'}}$-cyanotolane $({\mathrm{C}}_{8}\mathrm{tolane})$ with a very large $N$ range. The temperature variations of the apparent birefringence $\ensuremath{\Delta}n$ and the specific heat ${C}_{p}$ across the N-Sm$A$ phase transition show the definite influence of the proximity of the isotropic phase in the case of 8OCB while the ${\mathrm{C}}_{8}\mathrm{tolane}$ behaves as expected for the three-dimensional $\mathrm{XY}$ universality class. The elastic modulus B in the Sm$A$ phase, measured at several wave vectors by the second-sound resonance technique, was studied with high resolution as a function of temperature on approaching ${T}_{c}(N\ensuremath{-}\mathrm{Sm}A).$ These elastic data confirm the B leveling off in both cases with an apparent breakdown of hydrodynamics in the case of the ${\mathrm{C}}_{8}\mathrm{tolane}$ compound.