Dynamics of the lowest-order bend-twist director mode near nematic–smectic-Acriticality

A heterodyne light-scattering (LS) experiment that directly probes thermal fluctuations of the fundamental (lowest-order) bend director mode in homeotropic geometry, and a high-resolution Fréedericksz-transition (FT) experiment which excites the corresponding static mode magnetically were performed just above nematic–smetic-A criticality on the nonpolar wide-nematic-range material dihex- ylazoxybenzene over the reduced temperature ranges 3×${10}^{\mathrm{-}7}$≤t≤2.0×${10}^{\mathrm{-}3}$ and 2.7×${10}^{\mathrm{-}5}$≤t≤2.0×${10}^{\mathrm{-}2}$, respectively. It is found that over the nearly five decades of reduced temperature covered by these experiments, the enhancement of the bend elastic constant, ${\mathit{K}}_{33}$, obeys a simple power law with a critical exponent ${\mathrm{\rho }}_3$=0.825±0.008 (FT), ${\mathrm{\rho }}_3$=0.815±0.03 (LS); the error estimates include variations of ${\mathrm{\rho }}_3$ upon extensive range shrinking and gap expansion of the data sets. These studies cover a wider range of reduced temperature and extend two decades or more closer to the critical point than previous studies. Over the nearly five decades of reduced temperature covered by these experiments the bend constant ${\mathit{K}}_{33}$ increases by nearly four orders of magnitude to 5×${10}^{\mathrm{-}3}$ dyn corresponding to a longitudinal correlation length of ${\xi }_{\mathrm{\parallel }}$=7.9${\mathit{t}}^{\mathrm{-}0.82}$ Å (≃200 μm at t=3×${10}^{\mathrm{-}7}$). The measurement of correlation lengths of this magnitude may be unprecedented in the study of critical phenomena. In spite of accessing the regime where ${\xi }_{\mathrm{\parallel }}$ is comparable with the thickness of our films, ∼200 μm, finite-size and surface effects are not observed.