# X-Ray Studies of Transitions between Nematic, $$Smectic-A_1, -A_2, and -A_d$$ Phases

 Title: X-Ray Studies of Transitions between Nematic, $$Smectic-A_1, -A_2, and -A_d$$ Phases Author: Chan, K. K.; Pershan, Peter S.; Sorensen, L. B.; Hardouin, F. Note: Order does not necessarily reflect citation order of authors. Citation: Chan, K. K., Peter S. Pershan, L. B. Sorensen, and F. Hardouin. 1986. X-ray studies of transitions between nematic, $$smectic-A_1, -A_2, and -A_d$$ phases. Physical Review A 34(2): 1420-1433. Full Text & Related Files: Chan_X-ray_1986.pdf (3.558Mb; PDF) 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. Published Version: doi:10.1103/PhysRevA.34.1420 Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10357581 Downloads of this work:

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