X-Ray Studies of Transitions between Nematic, \(Smectic-A_1, -A_2, and -A_d\) Phases

Abstract

We report high-resolution x-ray scattering measurements of the critical fluctuations in mixtures of hexylphenyl cyanobenzoyloxy benzoate ((DB_6)) and terephtal-bis-butylaniline (TBBA). The phase sequence exhibited on cooling pure (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 (\gtrsim 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). For the (N-A_d) transition in pure (DB_6) the susceptibility exponent (\beta=1.29 \pm 0.05) and the parallel and perpendicular correlation-length exponents are (\nu_{\parallel} 0.67 \pm 0.03) and (\nu_{\perp} =0.52 \pm 0.03), respectively. Close to the multicritical point (12 mol% TBBA) where the second-order (N-A_1) line meets the first-order portion of the (A_1-A_2) line, the (N-A_1) exponents are (\beta =1.09 \pm 0.05, \mu_{\parallel} 0.57 \pm 0.03, and \nu_{\perp} =0.43 \pm 0.03). The correlation length anisotropy ((\nu_{\parallel} \neq \nu_{\perp})) persists along the entire (N-A_1) line, with the observed exponents decreasing as the concentration approaches the multicritical point. The (A_1-A_2) line has both first-order and second-order regions. All the measured exponents ((\beta, \nu_{\parallel}, \nu_{\perp})) were invariant along the second-order portion of the (A_1-A_2) line and the correlation-length exponents were isotropic ((\nu_{\parallel} = \nu_{\perp})). The measured exponents were (\beta = 1.46 \pm 0.05), and (\nu_{\parallel} = \nu_1 = 0.74 \pm 0.03). These numbers also held close to the tricritical point where the (A_1-A_2) transition became first order.