Liquid crystal phases with unusual structures and physical properties formed by acute-angle bent core molecules

Liquid crystals formed by acute-angle bent core (ABC) molecules with a 1,7 naphthalene central core show an intriguing phase behavior with the nematic phase accompanied by poorly understood additional phases. In this work, we characterize the physical properties of an ABC material, such as birefringence, dielectric permittivities, elastic constants, and surface alignment and present x-ray diffraction and transmission electron microscopy studies of their ordering. The ABC molecular shape resembling the letter λ yields a very small splay elastic constant in the uniaxial nematic phase and results in the formation of a tetragonal positionally ordered columnar phase consisting of alternating polar and apolar molecular columns with a uniform uniaxial director that can be bent but not splayed.


I. INTRODUCTION
The molecular shape is a key factor responsible for physical properties of liquid crystals.The simplest rod-like molecules produce a uniaxial nematic (N), widely used in applications.Lately, there has been much interest in the so-called bent-core molecules, formed by two rod-like segments attached to each other at some angle  .This kinked shape leads to fundamentally new properties and phases, as reviewed recently [1,2].Nematics formed by molecules with o o 110 170   often exhibit a bend elastic constant that is smaller than the splay constant, 33 11 KK  , [1][2][3][4][5][6][7][8], which is opposite to the trend 33 11 KK  found in conventional rod-like nematics.The tendency to bend might be so strong that the bent-core materials exhibit new states, such as the twist-bend nematic [9][10][11][12][13] or a heliconical cholesteric [14].Most of the studies so far focused on the obtuse angle bent-core (OBC) molecules, 90   .Mesomorphism of the acute-angle bent-core (ABC) molecules with 90   is poorly understood.Kang, Watanabe and their colleagues [15-18]   brought about interesting results for ABC molecules such as the one in Fig. 1.The molecule is formed by two arms attached in an asymmetric fashion to the central 1,7-naphthalene core.It produces a high temperature uniaxial N and a low-temperature phase, identified as a tetragonal packing of long cylinders.It is claimed [15][16][17][18] that each cylinder contains a double-twisted director field which is necessarily associated with a bend.The cylinders are of alternating chirality: a left-twisted cylinder has four close neighbors of right twisted cylinders and vice versa.
Recent studies demonstrate that surprising new types of the nematic ordering can be formed even by seemingly simple rod-like molecules, such as 4-[(4-nitrophenoxy)carbonyl]phenyl2,4dimethoxybenzoate, abbreviated RM734.Mandle, Cowling and Goodby found that these materials could exhibit a transition from a uniaxial nematic to some other nematic upon cooling [19,20].In studies that followed, Mertelj et al [21,22] suggested that the transition is to a splay nematic, in which the director n experiences a periodic splay with a period 5 10 μm − [23].The spontaneous splay was attributed to the wedge shape of the molecules and by an ensuing smallness of 11 K [21].The situation is similar to the formation of a twist-bend nematic, which is heralded by a decrease of 33 K [13,24,25].The overall structure of the splay nematic was suggested to be of an antiferroelectric type [21].Clark et al [26] re-examined the electro-optical and textural properties of RM734 and concluded that the material is in fact a three dimensional ferroelectric uniaxial nematic in which the large longitudinal dipole moments (about 11 D ) are parallel to each other.A unidirectional ferroelectric order has been also announced by Kikuchi et al in 2017 [27] for a different compound with dipole moments 9.4 D .
Motivated by these recent advancements and by the need to establish a structure-property relationship for ABC compounds, in this work, we characterize mesomorphic properties of the liquid crystal 1,7-naphthylene bis(4-(3-chloro-4-(4-(hexyloxy)benzoyloxy)phenyliminomethyl) benzoate), abbreviated as 1Cl-N(1,7)-O6, Fig. 1; see Supplemental Material for the chemical synthesis details.The material shows a uniaxial N phase at high temperatures and transforms into a columnar Colt phase of tetragonal symmetry at lower temperatures.11 K in the N phase is smaller than the twist elastic constant 22 K by a factor of 2 and smaller than 33 K by a factor of 6.We explain this anomalous elasticity by the alignment of the longitudinal axes of  -shaped molecules parallel to the director.The splay is facilitated by flip-flops of the molecules.Using the X-ray diffraction data, we propose that the Colt phase is formed by columnar aggregates of a diameter roughly equals to the distance between the legs of a single  -molecule.The columns are of two types, one polar and one apolar.In the polar columns, all  -molecules point along the same direction in a ferroelectric fashion, either upward or downward along the column.In the apolar aggregates, one half of the molecules points upward and the other half points downward.Each polar column is neighbored by four columns of opposite polarity, which yields a tetragonal lattice.
The apolar columns fill gaps between the polar columns.

II. MATERIALS AND METHODS
The 1Cl-N(1,7)-O6 molecule in Fig. 1 is of a  -shape, with two legs being of slightly different length.Numerical simulations, Fig. 1b, suggest that the legs tilt away from the naphthalene core plane, to minimize the conformation energy.K is determined by fitting () CU well above the threshold, where splay is accompanied by bend [28].To measure 22 K , we add 2.8 wt% of a chiral dopant S-811 to 1Cl-N(1,7)-O6, and then use the electric field to unwind the resulting cholesteric helix in a homeotropic cell with SE-5661 alignment layers; the voltage at which the helix is unwould defines 22 K [29].The Freeze-fracture (FF) Transmission Electron Microscopy (TEM) and cryo-TEM of the samples follow the procedures described previously [30].In FFTEM, the samples are heated into the N phase and equilibrated at 190 C  .After that, they are slowly cooled down at a rate of Source II, Brookhaven National Laboratory.The beamline is configured for a collimated X-ray beam with a beam size of cross-section 0.2 mm 0.2 mm  and divergence of 0. ), we apply a sinusoidal voltage of the amplitude 100 V at the frequency 2 kHz , so that the director aligns along the field and perpendicular to the glass plates.The cell is mounted for transmission X-ray scattering with the incident beam normal to the plates, such that the director points along the beam.

A. Phase diagram
The phase diagram obtained by POM textural observations is shown in Fig. 2, which is consistent with the DSC data in Ref. [18].The POM textures of different phases are shown in Figs.does not allow one to establish unequivocally whether the Maltese cross is caused by a radial configuration of the director or by a concentric configuration, since both these configurations would yield four dark brushes in the regions where the director is parallel to the polarizer (P) and analyzer (A).To establish the director orientation around the defect core we use a full wavelength plate (FWP), also called a red-plate optical compensator.The FWP is a slab of a uniaxial crystal of positive birefringence that produces a 530 nm optical phase retardance.In POM observations, the FWP is placed between the crossed P and A with its optic axis along the angle bisector of quadrants I and III formed by P and A. In absence of any birefringent sample, it produces the redviolet interference color, which separates the first-and second-order interference colors on the Michel-Lé vy color interference chart.When a birefringent sample is present, the red-violet color remains in the region in which the sample's optic axis (the director in our case) is along the P and A directions.Other orientations of the director produce either a blue-green or yellow-orange color, depending on whether the additional phase retardance adds to the phase retardance of FWP or subtracts from it.This property is used either for the determination of the sign of optical birefringence of an optically anisotropic plate if the direction of the optic axis is known or for the determination of the direction of the optic axis if the optical sign is known [31].As will be demonstrated in section D below, the optical birefringence of the liquid crystalline phases of the explored material is positive.Observation of the Maltese textures of the N droplets with the FWP shows that the I and III quadrants acquire a blue interference color, while the II and IV quadrants become yellow, Fig. 3 e-g.Therefore, the director in the N droplets is perpendicular to the N-I interface and forms a radial point defect-hedgehog [32], Fig. 3e, with predominantly splay deformation of the director.Radial director field in the N nuclei and homeotropic alignment at the N-I interface are unusual for thermotropic nematics, since the director orientation at the N-I interface in many of them is tilted, as is the case of cyanobiphenyls [33].The nuclei grow and coalesce, Fig. 3b,c.When they touch the top and bottom glass plates, the director realigns perpendicularly to the plates, Fig. 3b-d., each with four extinction brushes, Fig. 5. Isolated semi-integer defects are prohibited at the tilted director alignment since the director projection onto the plates is a vector rather than a director; therefore, only integer strength defects could be observed [31].If the material is filled into the cell in the N phase, the resulting alignment by SE-1211 is tangential, showing Schlieren textures with isolated 1 / 2 + and 1 / 2 − disclinations.The reason is as follows.For strictly tangential boundary conditions, the surface orientations n and −n are not distinguishable from each other.Therefore, not only integer but also semi-integer defects are topologically permissible [31].If the director is even slightly tilted away from the surface, the tilts "up" and "down" are no longer indistinguishable: the "up" and "down" directors placed in the same point form a letter "x".
Therefore, if any semi-integer defect existed before the tilt, it would give rise to a wall defect that starts at the defect core and provides a reorientation from the "up" to "down" state through a strictly tangential director.Such a wall is energetically unfavorable.This is why under strictly tangential anchoring one could observe semi-integer defects-disclinations, while under titled conical boundary conditions the defects are of an integer strength, Fig. 5; these are typically surface point defects-boojums [32].For more details and for illustration of this effect, see Ref. [31], pages 395-396.

Alignment agent ABC nematic 5CB
PI   The temperature dependence of birefringence at the wavelength 546 nm was measured using PolScope and a planar cell of thickness 1.9 μm aligned by a unidirectionally rubbed SE-1211, Fig.

E. Frederiks transitions and elastic constants in the N phase
The temperature dependencies of the elastic constants are shown in Fig. 10 a.The most unusual result is that the splay elastic constant 11 K is much smaller than the twist modulus 22 K (by a factor ~1/ 2 ) and the bend modulus 33 K (by a factor of ~1/ 6 ), Fig. 10 a.The result is also supported by a qualitative feature in Fig. 10 b: the Schlieren N textures show a clear predominance of splay deformations over bend in the structure of +1 defects, which illustrates clearly that 11 K is much smaller than 33 K .To the best of our knowledge, this is the first report on an anomalously small splay elastic constant in ABC material.Previously, Lee et al [38] reported that ABC molecules, added in a weight proportion up to 10 wt% , decrease the splay constant of a rod-like nematic from 13 pN to 3 pN .A very small 11 1 pN K  is also reported for the uniaxial N phase of RM734 by Mertelj et al [21].
The Frederiks effect in 1Cl-N(1,7)-O6 can be triggered by a magnetic field.For a homeotropic cells of thickness 30 μm , the threshold field is 0.26 T at 203 C  , which yields  , at which 0   .The reorientation involves nucleation of domains resembling developable domains of columnar phases [31], Fig. 11.The transition is of the first order (as evidenced by nucleation and by the sharp interface between the two states), i.e., dramatically different from the second-order Frederiks The Frederiks transition in N can be of the first order only under very special circumstances, such as a strong difference in the values of splay and bend Frank constants and peculiar types of surface anchoring [39][40][41].On the other hand, layered and columnar phases in which either bend or splay deformations are prohibited by the requirement of equidistant positional order of layers or columns, routinely show the first-order Frederiks transitions with nucleation of domains such as focal conics [13,42,43].

G. Freeze-fracture and cryo-TEM of the material in the Colt phase
The freeze-fracture TEM textures, Fig. 12, and cryo-TEM textures, Fig. 13, prove periodic ordering of Colt but do not establish the predominant period since it varies broadly from sample to sample and even within the same sample.The FFTEM texture of the Colt phase quenched from 179 C  in Fig. 12a exhibits linear periodic structures with a period P in the range ( ) Unlike FFTEM, cryo-TEM produces direct images of ultrathin (up to 20 nm ) films of the material on a holey carbon substrate.In the area of carbon support, the structure shows periodic ordering with the period that wary broadly from 3.8 nm to 7 8 nm − and even 12  .The correlation length associated with this spacing is very small, roughly 0.3 nm, as can be estimated from the inverse of the half-width-at-half-maximum, which implies that there is no translational periodicity.
Because of this, the lateral spacing of 0.45 nm should be associated with the typical separations of molecular legs and their thicknesses.These legs are seen by the probing beam at different orientations; note that the basic element of the structure, a benzene ring, has a diameter of 0.45 nm.SAXS spectra depend strongly on the temperature.In the N phase, 204 C T = , there are broad meridional reflexes located along the line parallel to B , at q in the N and Colt phases.
The detail analysis of SAXS pattern of the Colt phase is presented in Fig. 15.The original SAXS pattern, Fig. 14(c), contains the grid lines, which are the dead zones between the segments of the detector.To eliminate the effect of the grid, we assume that the pattern possesses the inversion symmetry with respect to the beam center and substitute the dead zones with the pixels from the opposite side, Fig. 15(a).Both 2 M ( 5.8 nm ) and 3 M ( 4.1 nm ) reflexes exists at the direction perpendicular to the director, Fig. 15, which indicates an absence of positional order along the columns.However, the translational order of the columns themselves is strong, as indicated by the small widths of 2 M , Fig. 15d, and 3 M , Fig. 15f, reflexes in both radial and azimuthal directions.
We estimate the correlations lengths to be 400 nm for 2 M and 300 nm for 3 M reflexes.
Field aligned homeotropic Colt sample.In this case, the director is oriented along the incident X-ray beam.The WAXS peak at  Based on these results, we propose that the Colt phase is a tetragonal packing of columns of two types, one polar and one apolar, Fig. 18.In the cross-section of each column, one finds two ABC molecules, the  -planes of which are orthogonal to each other.These two molecules can point in the same direction, Fig. 18 a,b, or in the opposite directions, Fig. 18c.A column formed by the pairs of the same orientation is polar, with polarization vector either "up" (yellow columns in Fig. 18d) or down (blue columns in Fig. 18d).Columns formed by stacks of the apolar pairs are apolar themselves, and marked as green in Fig. 18d.The polar columns form an antiferroelectric lattice, in which any "up" column is neighbored by four "down" columns and vice versa.The polar character of the columns is essential as it allows the system to avoid hexagonal packing and to form a square lattice instead.The cross-section of each column is of a four-fold symmetry.The four arms of all polar columns are parallel to each other, while the four arms of the apolar columns are oriented by 45 with respect to the polar ones.The X-ray measured periodicity of 5.8 nm is associated with the distances between columns of the same polarity along the sides of a square lattice, while the 4.1 nm period with the distances along the diagonal direction.The correlation lengths corresponding to 2 M and 3 M reflexes are both about 600 nm .Note that the columnar phase formed by ABC molecules is very different from the columnar phase observed in disk like molecules because in the Colt phase molecular arms are almost parallel rather than perpendicular to the axes of columns.
The chemical composition of the studied material is C64H56Cl2N2O10, and the molecular weight  18 places all the molecular pairs in the same plane of view.This is done for clarity only, as in the real structure this restriction is absent: the molecules that align in the opposite direction have the centers of mass shifted along the columnar axis.The polar and apolar columns can be arranged in a variety of ways with each other.In Fig. 18, we show four possible local structures that show some of the possible geometries.A unifying theme of these arrangements is an antiferroelectric order of the polar columns with the gaps filled by apolar columns.The distinction comes from how the molecules in apolar columns contact the molecules in the polar ones.These contacts can be locally "parallel" (molecules from the neighbouring columns are of the same color) or "anti-parallel" (the neighbouring molecules are of the different colors).Note that the transition from one type of arrangement to another in Fig. 18d,e,f,g, requires only a simple 90-degree rotation of apolar columns.One might expect that all variations of polar-apolar columns arrangements are possible when the system is cooled down from the nematic phase into the Colt phase, since it would increase the entropy of packing.The possibility of different geometrical arrangements between the polar and apolar columns is probably the for multiple periodicities revealed by TEM observations in Figs.12,13.
An important feature of the proposed model of the columnar phase in Fig. 18 is that the plane of the ABC molecules is parallel to the columnar axes.This arrangement, supported by the X-ray, optical, dielectric and electro-optical data, is very different from the conventional columnar phases formed by disk like molecules that stack on top of each other, with their planes being perpendicular to the columns.

IV. DISCUSSION and CONCLUSION
The mesomorphism of ABC-compounds with 1,7-naphthalene central core was reported by Lee et al [45].This family of materials exhibits a broad variety of phases [17,45].Especially interesting phase sequence was suggested for the studied 1Cl-N(1,7)-O6 [18], with the N phase being accompanied at lower temperatures by a tetragonal packing of cylinders with double-twisted director.In the discussion below, we first address the properties of the N phase and then the properties of the Colt phase.
Homeotropic textures of the N phase and the fact that its birefringence is positive suggest that the director is defined by the bisectors of each

K K K
 in rod-like and OBC nematics, respectively.It would be of interest to explore whether the anomalous elastic properties of ABC materials extend also to the saddle-splay deformations and to the "biaxial splay" recently discussed by J. Selinger [46].
The appearance of a low-temperature Colt phase is associated with the gradual freezing of the flip-flops and appearance of the positional order of tetragonal symmetry.The trend is evidenced already in the N phase, as 11 K increases as the temperature decreases, which can be associated with the formation of molecular dimers such as shown in Fig. 18c.This temperature behavior differs from that of the bend modulus 33 K upon approaching the nematic to twist-bend nematic transition [7,9,14,25,26].In the latter case, the molecules acquire a more bent shape at lower temperatures and 33 K decreases, except in the very vicinity of the transition.
The Colt phase is of a tetragonal symmetry.The X-ray diffraction data suggests that this phase is formed by columnar aggregates of diameter roughly equal the distance between the legs of a single  -shaped molecule.The polar columns are of alternating up and down polarities.The director, being parallel to the columns, is unidirectional in the ground state, but can be bent easily.
Equidistance of columns makes splay and twist deformations difficult.The typical distances between columns of the same polarity are 5.8 nm and 4.1 nm.Apparently, the cohesive forces between the columns are weak, as the TEM study show a broad spectrum of periods, including the values close to distances 5.8 nm and 4.1 nm measured by X-ray scattering.Apolar (on average) antiferroelectric character of packing explains relatively weak dielectric permittivity of the material.were added to ethanol and reflux for 24 hours, after workup, the product was purified by silica gel column chromatography to give a white solid (2.38 g, 80 %). 1

Synthesis of Highly Bent
The optical and surface anchoring properties of the material 1Cl-N(1,7)-O6 are explored by polarizing optical microscopy (POM), PolScope observations, and by measurements of the birefringence.Dielectric properties are examined in the frequency range from 100 Hz to 1 MHz using LCR-meter (4284A, Hewlett-Packard) operated by a Labview program.The temperature of the cells is controlled by a LTS350 hot stage and a TMS-94 controller (both from Linkam Scientific Instruments).The dielectric permittivity  parallel to the director is measured in a cell of thickness15.5 μm with substrates covered with a surfactant hexadecyltrimethylammonium bromide (HTAB).The overlapped area of two square-patterned indium tin oxide (ITO) electrodes is 1 cm 1 cm  .The perpendicular component  ⊥ is measured using planar cells with SE-1211 coatings.The cells' gap is fixed by glass microspheres of calibrated diameter and measured by recording the light interference spectrum of an empty cell.The cells are filled by capillary action at 190 C T = .11 K and 33 K are measured in planar cell of thickness 5.8 μm d = with the aligning polyimide SE-1211 layers.11 K is determined from the threshold voltage of the splay Frederiks transition and 33

FIG. 1 .
FIG. 1.(a) Molecular formula and (b) one of the conformations of the studied ABC material 1Cl-N(1,7)-O6.Part (b) obtained by numerical simulation using software Gaussian 09W to find a minimum energy of a conformation based on density functional theory (DFT) at B3LYP 6-31G(d) level.
1 C/min to the desired temperatures and equilibrated for 5 min .The sample is then plunge frozen and fractured at 165 C − .Replicas are prepared by depositing thin ( 4 nm ) layers of Pt/C at a 45 angle, followed by 20 nm C film deposition at normal incidence.Unlike FFTEM, cryo-TEM produces direct images of ultrathin specimens.We use thin (up to 20 nm ) films of the material supported by a holey carbon film.For cryo-TEM observation, the material supported by the carbon film is heated to the N phase and slowly cooled down to the desired temperature.The equilibrated samples are then rapidly frozen in liquid ethane and observed under the TEM.X-ray experiments are performed the 11-BM CMS beamline at National Synchrotron Light

6 3- 6 .
On heating, the material forms a uniaxial N phase between 183 C -to-isotropic (I) transition point.On cooling, the I-N transition occurs through nucleation of spherical droplets, Fig.3.Each droplet shows a texture of a Maltese cross with four dark brushes and a point defect in the center, Fig.3a,b,c.Conventional POM with two crossed linear polarizers

FIG. 7 .
FIG. 7. (a) Frequency dispersion of parallel and perpendicular components of dielectric permittivity of 1Cl-N(1,7)-O6 at different temperatures.(b) Frequency dispersion of the dielectric anisotropy in the nematic phase at

20 
FIG. 8. Conoscopic patterns of the homeotropic cells with N (a,b) and Colt (c,d) phases of 1Cl-N(1,7)-O6; observations with two crossed polarizers in (a,c) and with an additional FWP in (b,d).
, which is comparable to the diamagnetic anisotropy of rod-like mesogens such as 5CB.
FIG. 11.(a) PolScope texture of the Frederiks transition in a homeotropic Colt cell of 1Cl-N(1,7)-O6; 24 U = V ; 200 kHz f = ; (b) optical retardance across the interface between the realigned material and the homeotropic region along the white line in part (a).Temperature
FIG. 14 X-ray diffraction data.(a) WAXS pattern of the N and Colt phases; (b) WAXS intensity vs. q in the N and Colt phase; (c) SAXS pattern of the N and Colt phases; (d) SAXS intensity vs.

20 FIG. 15 . 2 M
FIG. 15.Angular dependence of the SAXS signal in Capillary: (a) diffraction pattern; (b) signal intensity vs. the azimuthal angle  for 2 M peak, where FIG. 16 X-ray diffraction at the sample aligned by the electric field at 176 C T = in the Colt phase.(a)WAXS pattern; (b) WAXS intensity vs. q; (c) SAXS pattern; (d) SAXS intensity vs. q.

22 FIG. 17 2 M
FIG. 17 Angular dependence of the SAXS signal: (a) diffraction pattern; (b) signal intensity vs. the azimuthal angle  for 2 M  peak, where

 33 ~10
which is typical for liquid crystals[44], one can estimate that a a very reasonable result.The number of molecules in an elementary square cannot be reduced below 8 because for density prohibitively small.The model in Fig.

FIG. 18 .
FIG. 18. Columnar packings in Colt phase: (a) two ABC molecules point up (b) two ABC molecules point down (c) two molecules point in opposite directions; (d, e, f, g) Intercalated assembly of polar (a,b) and apolar (c) columns into tetragonal structures of Colt.
-shaped ABC molecule.The symmetry of a single

Liquid Crystal 1. Materials and methods
All reagents and solvents were available commercially and used as received unless otherwise stated.1Hand13CNMR spectra were recorded on a Bruker 400 MHz NMR spectrometer using CDCl3 as solvent.Chemical shifts are in δ unit (ppm) with the residual solvent peak as the internal standard.The coupling constant (J) is reported in hertz (Hz).NMR splitting patterns are designed as follows: s, singlet; d, doublet; t, triplet; and m, multiplet.Column chromatography was carried out on silica gel (230-400 mesh).Analytical thin layer chromatography (TLC) was performed on commercially coated 60 mesh F254 glass plates.Spots on the TLC plates were rendered visible by exposing to UV light.