Critical behavior at the nematic-smectic-Atransition in butyloxybenzylidene heptylaniline (4O.7)

High-resolution ac calorimetric, x-ray, and light-scattering measurements have been made on $\mathrm{N}-[4-(n-\mathrm{butyloxy}\left)\mathrm{benzylidene}\right]-4^{\prime }-(n-\mathrm{heptyl})\mathrm{aniline}$ (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 $\alpha ={\alpha }^{\prime }=-0.026\mathrm{}$ corresponding to the three-dimensional $\mathrm{XY}$ model. The longitudinal and transverse correlation lengths exhibit single-power-law divergences over the reduced-temperature range ${10}^{-2\mathrm{}}$ to 3×${10}^{-5\mathrm{}}$ with exponents ${\nu }_{\parallel }=0.78\mathrm{}\pm 0.02$ and ${\nu }_{\perp }=0.65\mathrm{}\pm 0.02$, respectively. The anisotropic hyperscaling relation ${\nu }_{\parallel }+2\mathrm{}{\nu }_{\perp }+\alpha =2\mathrm{}$ 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 ${\xi }_{\parallel }$ 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.