CRITICAL-BEHAVIOR AT NEMATIC SMECTIC-A(1) PHASE-TRANSITIONS .1. HIGH-RESOLUTION X-RAY-SCATTERING AND CALORIMETRIC STUDY OF THE LIQUID-CRYSTAL OCTYLOXYPHENYLNITROBENZOYLOXY BENZOATE

High-resolution x-ray scattering and ac-calorimetric measurements have been carried out near the nematic-smectic-A1 phase transition of the pure liquid-crystal compound octyloxyphenylnitrobenzoyloxy benzoate (DB8ONO2). 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(parallel-to) and xi(perpendicular-to) and the smectic susceptibility a are insensitive to the detailed form of reasonable choices for S(q). The behaviors of xi(parallel-to), xi(perpendicular-to), and sigma are analyzed here in terms of pure power laws; the effective critical exponents for the reduced temperature range 2 X 10(-5)-1.2 X 10(-2) are nu(parallel-to)=-0.69+/-0.03, nu(perpendicular-to)=0.59+/-0.03, and gamma=1.28+/-0.05. Although nu(parallel-to) and gamma are quite close to three-dimensional (3D) XY values, the system is anisotropic with nu(parallel-to)-nu(perpendicular-to)=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 a which agrees with 3D XY theory; alpha=-0.007+/-0.003. Thus, anisotropic hyperscaling (alpha + nu(parallel-to) + 2nu(perpendicular-to)=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)].