Abstract
High-resolution x-ray scattering and ac-calorimetric measurements have been carried out near the nematic–smectic- phase transition of the pure liquid-crystal compound octyloxyphenylnitrobenzoyl- oxy benzoate (). 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 and and the smectic susceptibility σ are insensitive to the detailed form of reasonable choices for S(q). The behaviors of , , and σ are analyzed here in terms of pure power laws; the effective critical exponents for the reduced temperature range 2×–1.2× are =0.69±0.03, =0.59±0.03, and γ=1.28±0.05. Although and γ are quite close to three-dimensional (3D) XY values, the system is anisotropic with -=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++2=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
©1993 American Physical Society