High-resolution x-ray scattering and ac-calorimetric measurements have been carried out near the nematic–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 ${\xi }_{\mathrm{\parallel }}$ and ${\xi }_{\mathrm{\perp }}$ and the smectic susceptibility σ are insensitive to the detailed form of reasonable choices for S(q). The behaviors of ${\xi }_{\mathrm{\parallel }}$, ${\xi }_{\mathrm{\perp }}$, and σ are analyzed here in terms of pure power laws; the effective critical exponents for the reduced temperature range 2×${10}^{\mathrm{-}5}$–1.2×${10}^{\mathrm{-}2}$ are ${\nu }_{\mathrm{\parallel }}$=0.69±0.03, ${\nu }_{\mathrm{\perp }}$=0.59±0.03, and γ=1.28±0.05. Although ${\nu }_{\mathrm{\parallel }}$ and γ are quite close to three-dimensional (3D) XY values, the system is anisotropic with ${\nu }_{\mathrm{\parallel }}$-${\nu }_{\mathrm{\perp }}$=0.10±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 α which agrees with 3D XY theory: α=-0.007±0.003. Thus, anisotropic hyperscaling (α+${\nu }_{\mathrm{\parallel }}$+2${\nu }_{\mathrm{\perp }}$=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)].

• Received 18 June 1992

DOI:https://doi.org/10.1103/PhysRevE.47.1910