Measurement of Smectic-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi></mml:math>-Phase Order-Parameter Fluctuations 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

Abstract

The anisotropic liquid-structure factor of $p$ -cyanobenzylidene-amino-$p$-$n$-octyloxybenzene has been measured in the nematic phase using $\mathrm{Cu} K\ensuremath{\alpha}$ x rays. This material exhibits a second-order phase transition to the smectic $A$ phase at ${T}_{c}=82.8$ \ifmmode^\circ\else\textdegree\fi{}C. The liquid-structure factor shows a non-Lorentzian peak at a wave number of ${q}_{0}=0.179$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ (equivalent $d$ spacing 35.0 \AA{}) of the following form: ${S}_{q}=1+{{3.5{\ensuremath{\epsilon}}^{\ensuremath{\gamma}}+10{[\frac{({q}_{\ensuremath{\parallel}}\ensuremath{-}{q}_{0})}{{q}_{0}}]}^{2}+0.6{(\frac{{q}_{\ensuremath{\perp}}}{{q}_{0}})}^{\ensuremath{\eta}}}}^{\ensuremath{-}1}$, where $\ensuremath{\epsilon}=\frac{(T\ensuremath{-}{T}_{c})}{{T}_{c}}$, $\ensuremath{\gamma}=1.49\ifmmode\pm\else\textpm\fi{}0.1$, $\ensuremath{\eta}=2.5\ifmmode\pm\else\textpm\fi{}0.2$, and $\ensuremath{\hbar}{q}_{\ensuremath{\parallel}}(\ensuremath{\hbar}{q}_{\ensuremath{\perp}})$ are the momentum transfers parallel (perpendicular) to the orienting field.