Do the short helices exist in the nematic TB phase?

Dimeric compounds forming twist-bend nematic, Ntb, phase show unusual optical texture related to the formation of arrays of focal conic defects. Some of the focal conics show submicron internal structure with 8 nm periodicity, which is very close to that found in the crystalline phase of the material, suggesting surface freezing.

The nematic phase was considered for a long time as an educative example of the 'simplest' liquid crystalline phase, the phase is built of molecules having long range orientational order but lacking long range positional order. Though examples for the nematic-nematic phase transition have been shown for polymers [1] this simple picture was recently challenged significantly. It was shown that for some dimeric or bent-core molecules, more than one nematic phase exists [2][3][4][5][6], upon lowering temperature the 'classical' nematic phase with uniform orientation of the director transforms by a first order transition to a nematic phase with a spontaneous spatial modulation of the director. Chiral domain formation, associated with a very fast electro-optic response was also found [7][8][9] in the new nematic phase. Based on transmission electron microscopy (TEM) studies performed for replicas of freeze fractured samples [3,4], nuclear magnetic resonance (NMR) studies [10][11] and electro-optical investigations [9] a picture for the low temperature nematic phase was proposed as having short oblique helicoidal twist-bent (TB) modulations, with an extremely short helical pitch of the size of a few molecular lengths (8-10 nm), in line with theoretical models [12][13][14].
However, the phase structure assignment is problematic, as such a short, regular structures visible in TEM images are not detectable by other direct methods. Moreover, recent results of NMR studies suggest that the Ntb phase might not be composed of short twist-bend helices [15]. Here we show that periodic, submicron features can be ascribed to crystallographic planes of a solid crystal, easily formed during 'freezing' of the samples, so the alternative models for the structure of the Ntb phase need to be explored.
Materials of the homologous series CB-n-CB (with two 4-cyanobiphenyl mesogenic cores linked by flexible alkyl spacer with n carbon atoms), showing the N-Ntb phase transition, studied previously by the Boulder [3] and Kent [4] groups, were reinvestigated, mainly by atomic force microscopy (AFM) techniques. Samples were prepared in a similar manner as reported for transmission electron microscopy (TEM) studies [3,4], i.e. the material was placed between solid substrates (glass or metal), slowly cooled from the isotropic phase to the Ntb phase, and then quickly immersed in liquid nitrogen. Subsequently, one substrate was removed and the free surface of material was studied by AFM at room temperature.
For the cyanobiphenyl dimers with an odd number of carbon atoms in the linking group (homologues with n = 7, 9 and 11), the N-Ntb phase transition was easily detected by differential scanning calorimetry (DSC) and polarizing optical microscopy (POM). It was confirmed by XRD that both nematic phases have only short range positional order, with correlation length up to 1-2 molecular distances, in line with previous results [2].
The optical texture of the higher temperature phase is typical for the nematic phase; when placed between glass plates with uni-directionally rubbed aligning polymer layers, molecules are homogeneously oriented along the rubbing direction, the birefringence (close to the N-Ntb transition) is Δn=0. 15. The texture of the lower temperature phase (Ntb) shows a number of densely packed stripe-like defects aligned along the rubbing direction ( Fig. 1).   constant for the space modulated nematic [16]. Some of the focal conics are covered by a system of equidistant lines, having ~8 nm periodicity, corresponding to height differences of less than 0.5 nm (Fig. 3b). Under application of an a.c. electric field (~50Vpp/m) perpendicular to the sample surface, the optical stripe texture was irreversibly converted to an optically non-birefringent texture (homeotropic alignment).
Such samples after freezing were also examined with AFM, revealing that nonbirefringent areas are made of densely packed toric domains (Fig. 4). Apparently, under a strong electric field, reorientation of 'layers' takes place, FCDs are embedded into the system with layers mostly parallel to the surface (eccentricity of elliptical defect is close to 0). The areas covered by the solid crystal have very different morphology, in these regions nano-sized periodic structures were clearly visible (Fig.   5). Depending on the orientation of crystal planes toward the sample surface, different AFM images were registered, in some areas strongly curved layers are clearly detected, in others uniformly oriented crystallographic planes with a ~8nm periodicity were found. Knowing that the bi-phenyl CB-9-CB dimer crystalizes in a trigonal lattice with P3121 point symmetry [17], the layers could be identified as (001) crystallographic planes. It is quite striking that the crystal periodicity is very close to periodicities observed previously by TEM techniques in replica of freeze fractured samples [3,4] and to periodicity of tiny strips covering focal conic defects visible in AFM images (Fig.   3b). periodicity.
Crystalline and liquid crystalline areas of the samples were also distinguished by registration of force-versus-distance curves (Fig. 6), providing information on local material properties, such as elasticity, hardness, and adhesion, that are expected to be very different for a solid crystal and a liquid crystal [18]. The force-versus-distance curve for crystalline areas shows the typical shapes for solid state, with well-defined contact point (at the distance ~20 nm) and linear slope below the contact distance. When the tip was retracted from the surface, the force decreased very rapidly due to inelastic deformation of the surface, and its weak adhesion. On the other hand liquid crystalline regions have very different characteristic, the contact point is less defined (~400 nm), and the large hysteresis between approaching and retracting scans is found, due to the strong surface adhesion in the fluid state.
In summary, our results show that ~8 nm regular periodic structures, observed previously by TEM imaging, and being ascribed to the helical twist-bend structure, in many cases might evidence the formation of a solid crystal. The investigated materials, CB-n-CB, have a strong tendency to re-crystallize (Ntb is a monotropic phase), hence  [3,4], the structure must be similar to that found for the crystalline phase of CB-9-CB [17], but lacking positional order i.e. with three fold symmetry and a small cone angle of ~ 20 deg. Such a structure would be reminiscent of the SmC phase [19], but with short range positional order. Formation of short-wavelength helices averages molecular positions on nano-scale length and leads to optically uniaxial structure. In thin cells the spatial modulation of optical axis leads to appearance of stripe pattern, with periodicity driven by cell thickness. However, also the alternative explanation, that nematic phase has submicron, but larger than 8 nm periodicity has to be considered, while 8-nm structure visible in AFM studies reflects the surface freezing; the focal conics might be covered by a thin layer of either crystalline [20] or smectic phase [21].
Experimental: Optical examination of the characteristic textures of studied phases has been performed with a Zeiss Axio Imager A2m polarizing microscope equipped with a Linkam LTS-350 heating stage. For quantitative determination of sample birefringence and optical axis direction the CRI Abrio Imaging System integrated with microscope was used. Samples were prepared in glass cells with various thickness, 1.6 -10 micron, having surfactant layers for either planar or homeotropic alignment. The same cells were also used for preparation of the samples for AFM studiesafter the formation of a desired texture, the cell was immersed in liquid nitrogen, then brought to room temperature and broken. AFM images have been taken with Bruker Dimension Icon microscope, working in tapping mode at liquid crystalline-air surface. Cantilevers with a low spring constant, k = 0.4 Nm -1 were used, the resonant frequency was in a range of 70-80 kHz, typical scan frequency was 0.1 Hz. The AF microscope was equipped with a camera, this allowed to monitor the investigated areas optically, so the crystalline and nematic regions in the samples can be distinguished unambiguously. XRD experiments were performed with Bruker GADDS system.
The CB-n-CB compounds were prepared by Hull group and re-synthesized by Warsaw group.