Nematic-like elastic coefficients of the SmA(b) phase

The synthesis of bent-shaped mesogens and mesogenic dimers has renewed the field of liquid crystals in many ways during the previous decades, for example, through the discovery of 'exotic' mesophases such as the twist-bend nematic phase and the biaxial SmA phase (SmA(b)). Recently, we reported on the observation of a SmA(b) with a bent-shaped dimer, and on its fast electro-optic effect that we interpreted as a biaxial Freedericksz transition (BFrTr) of the secondary m-director under applied electric field (C. Meyer et al., Phys. Rev. X, 11, 031012 (2021)). In this study, we used dielectric and birefringence techniques to directly measure the splay, K-11(m), and bend,K-33(m), elastic constants that characterise the elastic distortion modes of the m-director. We observed that during the BFrTr, domains of opposite tilt appear and are often enclosed in elliptical defect loops, just like those observed during the usual Freedericksz transition of common nematics, which allowed us to obtain the third (twist) elastic constant K-22(m), from the defect loop ellipticity. Although K-11(m) and K-33(m) are of the same order of magnitude as K-11 and K-33 in the nematic phase of bent-shaped dimers, K-22(m) is an order of magnitude smaller than K-11(m) and K-33(m) and also than K-22 of 5CB. We argue that these features could be generic for the intercalated SmA(b) phase of bent-shaped dimers.