A Twist in the Nematic Phase of Mixtures of Achiral Cyanobiphenyl Dimer Mesogens

The twist-bend nematic (N$_{\mathrm{tb}})$ phase characterized by a heliconical structure forms below the regular uniaxial nematic (N) phase in achiral mesogens, CB~(CH$_{2})_{\mathrm{n~}}$CB, constituted of two cyanobiphenyl (CB) moieties connected by a alkyl linkage with odd number $n$ of --CH$_{2}$-- segments. This phase is absent in the homologs with even $n$. The precise structure of the N$_{\mathrm{tb}}$ phase in these and other systems is intriguing and remains under investigation. To gain an insight into the N$_{\mathrm{tb}}$ phase, we studied the pure and mixtures of odd ($n~=$~7) and even ($n~=$~6) homologues using polarizing optical microscopy and high-resolution x-ray diffraction. The latter technique was used to calculate the orientational order parameters $\langle $P$_{2}$(cos$\theta )\rangle $, $\langle $P$_{4}$(cos$\theta )\rangle $, and $\langle $P$_{6}$(cos$\theta )\rangle $ as functions of temperature in the two nematic phases. The results show that order parameter $\langle $P$_{2}\rangle $ and its higher moment $\langle $P$_{4}\rangle $ increase with decreasing temperature in N phase as expected. The value of $\langle $P$_{6}\rangle $ remains relatively small at all temperatures in the two phases. In the N$_{\mathrm{tb}}$ phase, $\langle $P$_{4}\rangle $ decreases and eventually becomes negative. This behavior is consistent with heliconical arrangement of dimer molecules. The phase diagram, temperature-dependent heliconical tilt, and the pitch were measured optically. The behavior of the order parameters qualitatively remains the same in mixtures of CB (CH$_{2})_{7}$ CB and CB (CH$_{2})_{6}$ CB while their values vary with concentration.