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 \((DB_6)\) 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.Engineering and Applied Science