Static and dynamic behavior near a second-order smectic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi></mml:math>— nematic phase transition by light scattering

Abstract

Measurements are presented of the intensity and lifetime of Rayleigh light scattered from thermally excited twist and splay modes of $p$-cyanobenzylidine-$p\ensuremath{-}n$-octyloxyaniline (CBOOA) in the nematic phase near the smectic $A$---nematic phase transition. The temperature dependence of the twist and splay elastic constants and viscosities are deduced. The phase transition is continuous (${T}_{c}\ensuremath{-}{T}^{*}&lt;3\ifmmode^\circ\else\textdegree\fi{}$ mK); this contradicts the prediction of Halperin, Lubensky, and Ma that this phase transition would be weakly first order. The critical behavior of the twist elastic constant ${K}_{22}$ and the twist viscosity ${\ensuremath{\gamma}}_{1}$ is consistent with mean-field predictions from 3\ifmmode^\circ\else\textdegree\fi{}mK to 7\ifmmode^\circ\else\textdegree\fi{}K above the transition; these data are inconsistent with the critical behavior predicted by the helium analogy. The splay mode is not renormalized, as expected.