Detection of Phase Biaxiality in Liquid Crystals by Use of the Quadrupole Shift in ${}^{131}\mathrm{Xe}$ NMR Spectra

An experimental method to unambiguously distinguish between uniaxial and biaxial liquid crystal phases is introduced. The method is based on the second order quadrupole shift (SOQS) observable in ${}^{131}\mathrm{Xe}$ NMR spectra of xenon dissolved in liquid crystals. It is shown that besides revealing the biaxiality, the ${}^{131}\mathrm{Xe}$ SOQS offers a novel method to determine the tilt angle in smectic $C$ phases. As an example, the ${}^{131}\mathrm{Xe}$ SOQS in a ferroelectric liquid crystal is reported. It yields up a biaxial phase in between isotropic and smectic $C$ phases.

Figure 1

${}^{129}\mathrm{Xe}$ and ${}^{131}\mathrm{Xe}$ central line position measured on a 300 MHz ($B_0=7.0\mathrm{T}$) and on a 400 MHz ($B_0=9.4\mathrm{T}$) spectrometer for xenon in the FELIX-R&D LC. The solid line is a result of a polynomial fit to the experimental points measured at 300 MHz. The dashed line in turn was obtained from the previous line by scaling the ${}^{131}\mathrm{Xe}$ SOQS by the square of the ratio of the Larmor frequencies, $(3/4{)}^2$, as explained in the text.

Figure 2

${}^{131}\mathrm{Xe}$ SOQS in the FELIX-R&D LC at variable temperatures and at two magnetic fields. The small black squares were obtained by scaling the 300 MHz data with the square of the ratios of the magnetic field strengths, $(3/4{)}^2$.

Figure 3

Temperature dependence of the tilt angle obtained from Xe NMR, as described in the text. The filled diamonds are from optical observations [18].

Figure 4

Relative ${}^{129}\mathrm{Xe}$ and ${}^{131}\mathrm{Xe}$ shielding for xenon in $S1114$ liquid crystal at variable temperatures.