Nuclear Magnetic Resonance in the SmecticCPhase

We have determined the molecular arrangement that results when the smectic $C$ liquid-crystalline phase is subjected to large magnetic fields. Furthermore, a simple technique which makes use of the free-induction decay is used to obtain a precise determination of the smectic $C$ tilt angle. Uniformly aligned smectic $C$ samples are obtained by cooling through the nematic phase into the smectic phase in the presence of a 14 000-G magnetic field. Once aligned, the samples are then oriented at various angles relative to the magnetic field direction and the absorption line shape is recorded. A model is developed to describe the molecular arrangement in the smectic $C$ which results from reorientation of the sample in the magnetic field. This model allows for the reorientation of the long molecular axes within the smectic layers subject to the constraint that a constant tilt angle be maintained. The experimental test of the model comes from its ability to predict NMR line shapes and second moments. In terephthal-bis-4(4-$n$-butylaniline), we measure the temperature dependence of the tilt angle to be a ${(T_c-T)}^{\beta }$ dependence, where $\beta =0.40\mathrm{}\pm 0.04$ and $T_c$ is the smectic $A$-smectic $C$ transition temperature. This is compared with de Gennes's prediction of $\beta =0.35\mathrm{}$. In addition, a tilt angle of 45° was obtained for 4, 4′-bis-(heptyloxy)azoxybenzene.