We report results of calorimetric studies for the binary mixture of rodlike host $n$-alkyloxy-cyanobiphenyl ($n$OCB, $n=8,9$) and bent-shaped guest 1,3-phenylene-bis[4-(3-methylbenzoyloxy)]-4${}^{\text{'}}$-$n$-dodecylbiphenyl-4${}^{\text{'}}$-carboxylate (BC12). The effect of bent-shaped dopant molecules on the critical behavior associated with the nematic-smectic-$A_d$ phase transition has been studied in detail. The transition temperature for the nematic-smectic-$A_d$ phase sharply decreases as the increase of the mole fraction of the dopant concentration (denoted $X$ for the BC12/9OCB mixture and $Y$ for the BC12/8OCB mixture). The dependence of the critical exponent $\alpha$ on $X$ and $Y$ is well explained in terms of the McMillan ratio. A nearly tricritical exponent has been obtained for the $X=0.01$ mixture. $X=0.02-0.03$ mixtures, pure 8OCB, and $Y=0.01-0.03$ mixtures exhibit nonuniversal behaviors with effective exponents lying between the 3D-$\mathit{XY}$ and tricritical exponents. The heat capacity anomaly for $Y=0.05$ has been well described with the 3D-$\mathit{XY}$ exponent. The critical amplitude ratio $A^{-}/A^{+}$ is close to $1$ and insensitive to the dopant concentration. No Fisher renormalization of the critical exponent has been observed even for nearly tricritical compositions, which indicates the smallness of the concentration plays a decisive role rather than the steepness of the $N$-Sm$A_d$ phase boundary.

• Received 23 December 2010

DOI:https://doi.org/10.1103/PhysRevE.83.061701