X-ray studies of transitions between nematic, smectic-$A_1$, -$A_2$, and -$A_d$ phases

We report high-resolution x-ray scattering measurements of the critical fluctuations in mixtures of hexylphenyl cyanobenzoyloxy benzoate (${\mathrm{DB}}_6$) and terephtal-bis-butylaniline (TBBA). The phase sequence exhibited on cooling pure ${\mathrm{DB}}_6$ (or mixtures with a low concentration of TBBA), is nematic (N) to smectic-$A_d$ ($A_d$) to smectic-$A_2$ ($A_2$). Mixtures with ≳12 molar percent (mol %) of TBBA have a smectic-$A_1$ ($A_1$) phase between the nematic and smectic-$A_2$ phases. For each of the second-order transitions the critical-temperature dependence of the susceptibility and correlation lengths are fit to power laws of the form $t^x$ where t=(T-$T_c$)/$T_c$.