Among the chiral tilted smectics, the stable existence has been confirmed in numerous investigations of $\mathrm{Sm}{C}_A^{*},$ (antiferroelectric smectic-$C_A)$ $\mathrm{Sm}{C}_{\mathrm{F}11}^{*}$ $\left(\mathrm{Sm}{C}_{\gamma }^{*}\right),$ $\mathrm{Sm}{C}_{\mathrm{F}12}^{*}$ (antiferroelectric, AF) and $\mathrm{Sm}{C}^{*}$ phases. The structures of the ferrielectric $\mathrm{Sm}{C}_{\mathrm{F}11}^{*}$ and $\mathrm{Sm}{C}_{\mathrm{F}12}^{*}$ phases suggested by different models are essentially different although all the models use the three-layer and four-layer periodicity for them. The structures of the phases were investigated using the optical rotatory power (ORP) measurements technique. The ORP was simulated using Berreman’s $4\times 4$-matrix method. The compound under investigation $\mathrm{}\left(S\right)\mathrm{}$-1-methylheptyl 4-${(4\mathrm{}}^{\prime }-n$-undecyloxy-biphenyl-4-yl-carbonyloxy) [acronym (S)-11OF1M7] clearly provides $\mathrm{Sm}{C}_{\mathrm{F}11}^{*}$ and $\mathrm{Sm}{C}_{\mathrm{F}12}^{*}$ phases, the temperature range for the existence of these phases is about 5 °C each. This had not been achieved for the earlier investigated antiferroelectric liquid crystal (AFLC) samples. The results obtained confirm that the unit cell of the molecular structure of these subphases is highly biaxial. Due to the biaxiality the texture of the homeotropic cell under a polarizing microscope appears nonuniform. This requires a special approach to the measurements and a simulation of the ORP, which is discussed in detail. A technique has been designed where the transmitted intensity through a polarizing microscope is measured as a function of the angle of polarization of the incident light. From the observed output, which is a biased sine wave, the ORP is being determined. In the same scan, the wavelength of light is also being automatically altered. Comparing the simulated and measured data, we can conclude that in the $\mathrm{Sm}{C}_{\mathrm{F}12}^{*}$ phase the distortion angle of the directors in the Ising model is lower than 10°. Using the Ising model, the pitch in $\mathrm{Sm}{C}_{\mathrm{F}11}^{*}$ has been determined and this is found to have a strong temperature dependence.

• Received 14 February 2003

DOI:https://doi.org/10.1103/PhysRevE.68.021702