The Twist Bend Nematic: A Case of Mistaken Identity

We review the physics underlying Meyer's conjecture of how macroscopic-scale twist and bend conspire within the Frank-Oseen elasticity theory of nematics to create a heliconical arrangement of the uniaxial, apolar nematic director, the so-called "twist bend nematic" $\rm N_{TB}$. We show that since 2011 a second, lower-temperature nematic phase observed in odd methylene-linked cyanobiphenyl dimers discovered by Toriumi and called $\rm N_X$, has been incorrectly identified as $\rm N_{TB}$. Moreover, as more quantitative data on the $\rm N_X$ emerged, Meyer's simple prediction has been distorted to accommodate those findings. In fact, the molecular organization in the $\rm N_X$ conforms to the $\rm N_{PT}$ phase, a polar, twisted arrangement of nonlinear mesogens advanced in 2016. The attributes of the $\rm N_{PT}$ are summarized and differentiated from those of the $\rm N_{TB}$ in an effort to contribute to a better understanding of the $\rm N_X$ phase and, equally important, to encourage researchers to continue to search for a liquid crystal that exhibits Meyer's pioneering theoretical suggestion, namely that form-chirality can exist in simple nematics composed of achiral molecules.