Heat capacity near the smectic-$A$—hexatic-$B$ and hexatic-$B$—$E$ transitions of $n$-hexyl-4′-$n$-pentyloxybiphenyl-4-carboxylate (65OBC)

High-resolution ac calorimetry was used to measure the heat capacity of $n$-hexyl-4′-$n$-pentyloxybiphenyl-4-carboxylate in the vicinity of the smectic-$A$ ($\mathrm{Sm}A$)—hexatic-$B$ and hexatic-$B-E$ transitions. The $\mathrm{Sm}A$—hexatic-$B$ transition was found to be continuous with critical exponents ${\alpha }^{-}={\alpha }^{+}=0.61\mathrm{}\pm 0.02$ and amplitude ratio $\frac{A^{+}}{A^{-}}=0.84\mathrm{}\pm 0.03$. The addition of a crystalline-$B$ material [N-(4-$n$-butyloxybenzylidene)-4′-octylaniline (4O.8), 10 wt.%] produced a weakly-first-order $\mathrm{Sm}A$—hexatic-$B$ phase transition. The data with $|T-T_c|\ge 100$ mK can be fitted by a power law with $\alpha =0.49\mathrm{}\pm 0.02$ and $\frac{A^{+}}{A^{-}}=0.82\mathrm{}\pm 0.03$. The large values for the critical exponents and the theoretical suggestion that the $\mathrm{Sm}A$—hexatic-$B$ transition may be near tricritical point (${\alpha }_t=0.5\mathrm{}$) are discussed. The hexatic-$B-E$ transition was found to be first order in nature.