Critical behavior at the nematic-smectic-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi></mml:math>transition in butyloxybenzylidene heptylaniline (4O.7)

Abstract

High-resolution ac calorimetric, x-ray, and light-scattering measurements have been made on $\mathrm{N}\ensuremath{-}[4\ensuremath{-}(n\ensuremath{-}\mathrm{butyloxy})\mathrm{benzylidene}]\ensuremath{-}{4}^{\ensuremath{'}}\ensuremath{-}(n\ensuremath{-}\mathrm{heptyl})\mathrm{aniline}$ (4O.7) near the nematic-smectic-$A$ phase transition. This transition is second order, with a variation in ${C}_{p}$ which is well described by a critical exponent $\ensuremath{\alpha}={\ensuremath{\alpha}}^{\ensuremath{'}}=\ensuremath{-}0.026$ corresponding to the three-dimensional $\mathrm{XY}$ model. The longitudinal and transverse correlation lengths exhibit single-power-law divergences over the reduced-temperature range ${10}^{\ensuremath{-}2}$ to 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ with exponents ${\ensuremath{\nu}}_{\ensuremath{\parallel}}=0.78\ifmmode\pm\else\textpm\fi{}0.02$ and ${\ensuremath{\nu}}_{\ensuremath{\perp}}=0.65\ifmmode\pm\else\textpm\fi{}0.02$, respectively. The anisotropic hyperscaling relation ${\ensuremath{\nu}}_{\ensuremath{\parallel}}+2{\ensuremath{\nu}}_{\ensuremath{\perp}}+\ensuremath{\alpha}=2$ is satisfied to within the errors. A dynamical-scaling analysis of light-scattering measurements of the bend-mode director fluctuations with elastic constant ${K}_{3}$ yields values for ${\ensuremath{\xi}}_{\ensuremath{\parallel}}$ which agree absolutely with the x-ray measurements. Thus the data are all internally consistent, and they appear to exclude all current theories of the nematic-smectic-$A$ transition. It is observed that the overall critical behavior in smectic liquid crystals is sensitive to the width of the nematic range; this may offer an explanation for the apparent nonuniversality of the exponents.