Birefringence and tilt angle in the antiferroelectric, ferroelectric, and intermediate phases of chiral smectic liquid crystals

Using a high resolution optical polarimeter, we have measured the temperature dependence of the birefringence and optical rotation in chiral smectic liquid crystals that exhibit antiferroelectric, ferroelectric, and intermediate phases. The temperature dependence of the magnitude of the tilt angle was determined from the birefringence of 4-(1-methyl-heptyloxycarbonyl-phenyl) $4^{\prime }$-octylbiphenyl-4-carboxylate (MHPOBC) and of 4-(1-methylheptyloxycarbonyl-phenyl) $4^{\prime }$-octylcarbonyloxybiphenyl-4-carboxylate (MHPOCBC). Both substances exhibit a crossover of the order parameter exponent from the classical value of $\beta =0.5\mathrm{}$ close to the transition to the tricritical value $\beta =0.25\mathrm{}$ far away. This stresses the importance of the sixth order terms in the Landau free-energy expansion for ferroelectric and antiferroelectric liquid crystals. In addition, a discontinuous behavior in the magnitude of the tilt is observed when crossing the $\mathrm{smectic}{-C}_{\alpha }^{*}–\mathrm{smectic}{-C}^{*}$ or $\mathrm{smectic}{-C}^{*}–\mathrm{smectic}{-C}_A^{*}$ transitions, whereas the $\mathrm{smectic}-A–\mathrm{smectic}{-C}_{\alpha }^{*}$ transition is continuous. The simultaneously determined optical rotation is used to elucidate the structures and the nature of phase transitions. The results are well explained within the framework of a discrete phenomenological model with nearest and next nearest neighbor interactions between the smectic layers.