Equality of X-Ray and Light Scattering Measurements of Coherence Lengths at the Nematic-Smectic-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi></mml:math>Phase Transition

Abstract

We have measured by light scattering the divergence of the elastic constants ${K}_{2}$ and ${K}_{3}$ at the nematic-smectic-$A$ transition in the liquid crystals 8OCB, $\stackrel{-}{8}\mathrm{S}5$, and 8CB over a reduced temperature range ${10}^{\ensuremath{-}5}&lt;t&lt;{10}^{\ensuremath{-}2}$. We find critical exponents ${\ensuremath{\nu}}_{\ensuremath{\parallel}}$ and ${\ensuremath{\nu}}_{\ensuremath{\perp}}$ and power-law coefficients ${\ensuremath{\xi}}_{\ensuremath{\parallel}}^{0}$ and ${\ensuremath{\xi}}_{\ensuremath{\perp}}^{0}$ which agree with values obtained from x-ray scattering within experimental error.