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 Fr\'eedericksz-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^-7{≤}t{≤}2.0×{}10^-3 and 2.7×{}10^-5{≤}t{≤}2.0×{}10^-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, K₃₃, obeys a simple power law with a critical exponent ρ₃=0.825±{}0.008 (FT), ρ₃=0.815±{}0.03 (LS); the error estimates include variations of ρ₃ 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 K₃₃ increases by nearly four orders of magnitude to 5×{}10^-3 dyn corresponding to a longitudinal correlation length of ξ_∥=7.9t^-0.82 {} ({}200 {μ}m at t=3×{}10^-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 ξ_∥ is comparable with the thickness of our films, {~}200 {μ}m, finite-size and surface effects are not observed.We also report the results of the above heterodyne experiment performed on another nonpolar material, hexyloxynonylbenzoate (6{}09), over a similar reduced-temperature range. This experiment yielded the same critical exponent within experimental uncertainty, ρ₃=0.84±{}0.03, contrary to previously reported Fr\'eedericksz-transition measurements which exhibited a crossover from {~}0.84 to 0.67 on range shrinking and were well represented over the entire experimental range of reduced temperature by a power-law term with ρ₃=0.67±{}0.02 augmented by an anomalously large negative correction to scaling term. This discrepancy is discussed briefly in the context of surface phenomena and is currently under study. We compare our results with theoretical predictions about nematic--smectic-A criticality and with the director normal-mode spectrum which we derive from linearized Erickson-Leslie-Parodi theory including the effects of finite-director anchoring and surface dissipation.