Freeze-fracture transmission electron microscopy study of the nanoscale structure of the so-called "twist-bend" nematic phase of the cyanobiphenyl (CB) dimer molecule CB(CH 2 ) 7 CB reveals stripe-textured fracture planes that indicate fluid layers periodically arrayed in the bulk with a spacing of d ∼ 8.3 nm. Fluidity and a rigorously maintained spacing result in long-range-ordered 3D focal conic domains. Absence of a lamellar X-ray reflection at wavevector q ∼ 2π/d or its harmonics in synchrotron-based scattering experiments indicates that this periodic structure is achieved with no detectable associated modulation of the electron density, and thus has nematic rather than smectic molecular ordering. A search for periodic ordering with d ∼ in CB(CH 2 ) 7 CB using atomistic molecular dynamic computer simulation yields an equilibrium heliconical ground state, exhibiting nematic twist and bend, of the sort first proposed by Meyer, and envisioned in systems of bent molecules by Dozov and Memmer. We measure the director cone angle to be θ TB ∼ 25°a nd the full pitch of the director helix to be p TB ∼ 8.3 nm, a very small value indicating the strong coupling of molecular bend to director bend. R ecently there has been growing interest in the liquid crystal (LC) phase behavior of achiral dimer molecules, such as cyanobiphenyl-(CH 2 ) n -cyanobiphenyl (CBnCB), shown for n = 7 in Fig. 1 A (1, 2). This arises from the observation of a transition in these mesogens from a typical nematic (N) to a lower-temperature (NX) phase, also apparently nematic, which exhibits a variety of unusual characteristics (3-10). These include: (i) textural features in depolarized transmission light microscopy (DTLM) similar to those found in fluid, lamellar smectic phases but with no X-ray scattering to indicate lamellar ordering of molecules (8); (ii) a variety of other completely unfamiliar DTLM textures (6), including the spontaneous appearance of director field deformation and evidence for small Frank elastic constants (3); (iii) evidence for the chiral molecular organization on the NMR timescale (4), and in macroscopic conglomerate domains in electrooptic experiments on monodomain textures (9); (iv) distinctive odd/even effects in the linker length n, including, in particular, that i-iii are found only in the n-odd homologs (6).These observations, combined with the fact that the all-trans conformations of the n-odd homologous dimers are distinctly bent (Fig. 1B), have led to the notion that the NX is a "twistbend" (TB) phase, sketched in Fig. 1C, a nematic having a conically helixed ground state of the sort originally proposed by Meyer as the result of the spontaneous appearance of bend flexoelectric polarization (11). More recently Dozov proposed such a ground state as a spontaneously chiral conglomerate domain stabilized by molecular bend (12), and Memmer obtained such structures in computer simulations of systems of bent GayBerne dimers (13). This ground-state helix can be written for CB7CB in terms of a half-molecular director n(z), ...
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