Crossover from three-dimensionalXYto tricritical behavior for the nematic–smectic-A1phase transition

A high-resolution ac calorimetric technique has been employed to study the nematic–smectic-${\mathit{A}}_1$ (N–Sm-${\mathit{A}}_1$) phase transition in liquid-crystal binary mixtures of octyloxyphenyl-nitrobenzoyloxy benzoate (${\mathrm{DB}}_8$ ${\mathrm{ONO}}_2$) and decyloxyphenyl-nitrobenzoyloxy benzoate (${\mathrm{DB}}_{10}$ ${\mathrm{ONO}}_2$). The existence of a tricritical point on the N–Sm-${\mathit{A}}_1$ transition line has been reconfirmed in this study. This tricritical point occurs at mole percent X≃51 of the decyl homolog in the mixture. Heat-capacity measurements characterizing the N–Sm-${\mathit{A}}_1$ transition have been carried out for three samples in the vicinity of the tricritical point (X=47.0, 48.7, and 50.0) and for one sample with X=31.5. The results reveal a complete crossover behavior for the critical exponent α, which changes from the three-dimensional XY value (${\mathrm{\alpha }}_{\mathit{X}\mathit{Y}}$=-0.007) for X=31.5 to a value α=0.422 close to tricritical (${\mathrm{\alpha }}_{\mathit{t}}$=0.50) for x=50.0. The amplitude ratio ${\mathit{A}}^{\mathrm{-}}$/${\mathit{A}}^{+}$ for the X=31.5 sample conforms to that expected from the noninverted XY model. In addition, heat-capacity measurements on one sample with X=53.7 indicate that near the termination point of the Sm-${\mathit{A}}_{\mathit{d}}$–Sm-${\mathit{A}}_1$ transition line the phase sequence Sm-${\mathit{A}}_{\mathit{d}}$–${\mathit{N}}_{\mathit{d}}$–${\mathit{N}}_1$–Sm-${\mathit{A}}_1$ occurs, in accordance with theoretical predictions.