Light-scattering study of twist fluctuations near the nematic–smectic-Atransition of dihexylazoxybenzene

It is well known that the bend and twist elastic constants contain a term that diverges at the nematic–smectic-A phase transition according to a simple power law in reduced temperature; i.e., as & where t=(T-$T_{N\mathrm{-}\mathrm{Sm}\mathrm{-}\mathit{A})}$/$T_{N–\mathrm{Sm}\mathrm{-}\mathit{A}}$. We report here a high-resolution light-scattering measurement of the twist constant exponent ${\rho }_2$ (=0.66±0.03) in the four-decade range -6.5t<-2.5. Within experimental uncertainty, this is the correlation length exponent predicted by the well-known three-dimensional XY model, a result originally predicted by de Gennes [Solid State Commun. 10, 753 (1972); Mol. Cryst. Liq. Cryst. 21, 49 (1973)] and later by dislocation-mediated melting models due to Helfrich [J. Phys. (Paris) 39, 1199 (1978)] and Dasgupta and Halperin [Phys. Rev. Lett. 47, 1566 (1981)]. This is the largest value of ${\rho }_2$ reported to date and by comparison with previous results reveals a clear trend of increasing ${\rho }_2$ with increasing nematic range. This trend suggests that smaller values of ${\rho }_2$ observed for previously studied materials, may in fact be effective exponents associated with critical-tricritical crossover behavior but leaves open the question of whether there exists a universal value of ${\rho }_2$.