Critical behavior at nematic–smectic-A1phase transitions. I. High-resolution x-ray-scattering and calorimetric study of the liquid-crystal octyloxyphenylnitrobenzoyloxy benzoate
| Autor: | K. I. Blum, George Nounesis, M. J. Young, Carl W. Garland, Robert J. Birgeneau |
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| Rok vydání: | 1993 |
| Předmět: | |
| Zdroj: | Physical Review E. 47:1910-1917 |
| ISSN: | 1095-3787 1063-651X |
| Popis: | High-resolution x-ray scattering and ac-calorimetric measurements have been carried out near the nematic\char21{}smectic-${\mathit{A}}_{1}$ phase transition of the pure liquid-crystal compound octyloxyphenylnitrobenzoyl- oxy benzoate (${\mathrm{DB}}_{8}$${\mathrm{ONO}}_{2}$). Several forms of the structure factor S(q) for fitting the x-ray line shape have been tested. The critical temperature dependences of the resulting longitudinal and transverse correlation lengths ${\ensuremath{\xi}}_{\mathrm{\ensuremath{\parallel}}}$ and ${\ensuremath{\xi}}_{\mathrm{\ensuremath{\perp}}}$ and the smectic susceptibility \ensuremath{\sigma} are insensitive to the detailed form of reasonable choices for S(q). The behaviors of ${\ensuremath{\xi}}_{\mathrm{\ensuremath{\parallel}}}$, ${\ensuremath{\xi}}_{\mathrm{\ensuremath{\perp}}}$, and \ensuremath{\sigma} are analyzed here in terms of pure power laws; the effective critical exponents for the reduced temperature range 2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$\char21{}1.2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$ are ${\ensuremath{\nu}}_{\mathrm{\ensuremath{\parallel}}}$=0.69\ifmmode\pm\else\textpm\fi{}0.03, ${\ensuremath{\nu}}_{\mathrm{\ensuremath{\perp}}}$=0.59\ifmmode\pm\else\textpm\fi{}0.03, and \ensuremath{\gamma}=1.28\ifmmode\pm\else\textpm\fi{}0.05. Although ${\ensuremath{\nu}}_{\mathrm{\ensuremath{\parallel}}}$ and \ensuremath{\gamma} are quite close to three-dimensional (3D) XY values, the system is anisotropic with ${\ensuremath{\nu}}_{\mathrm{\ensuremath{\parallel}}}$-${\ensuremath{\nu}}_{\mathrm{\ensuremath{\perp}}}$=0.10\ifmmode\pm\else\textpm\fi{}0.03. The heat-capacity data are analyzed using a nonasymptotic power-law expression with first- and second-order corrections-to-scaling terms. This analysis yields a critical exponent \ensuremath{\alpha} which agrees with 3D XY theory: \ensuremath{\alpha}=-0.007\ifmmode\pm\else\textpm\fi{}0.003. Thus, anisotropic hyperscaling (\ensuremath{\alpha}+${\ensuremath{\nu}}_{\mathrm{\ensuremath{\parallel}}}$+2${\ensuremath{\nu}}_{\mathrm{\ensuremath{\perp}}}$=2) appears to be violated if effective exponents based on pure power-law fits to x-ray data are used. However, hyperscaling can be recovered by a preasymptotic XY analysis of the x-ray data, as shown in paper II [Phys. Rev. E 47, 1918 (1993)]. |
| Databáze: | OpenAIRE |
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