Distinct twist-bend nematic phase behaviors associated with the ester-linkage direction of thioether-linked liquid crystal dimers †

demonstrated the distinct


Introduction
][3][4][5][6][7][8][9][10] At present, the twist-bend nematic (N TB ) phase, a new helical LC phase, is a hot research topic in the field of LCs.Although the N TB phase was theoretically proposed 11,12 and simulated in earlier works, 13 it has only recently been experimentally demonstrated with a bent achiral dimer. 14The N TB phase is believed to originate from the twist and bend deformations of bent molecules, resulting in a heliconically arranged director periodicity, wherein the local director tilts against the helical axis.Due to this phenomenon, right-and left-handed helical nanostructures and their associated degenerate domains are observed to spontaneously form, even from achiral molecules.6][17] Macroscopic chirality of the N TB phase was verified using circular dichroism spectroscopy. 18Several techniques, including electro-optical measurements, 19 freeze-fracture transmission electron microscopy, 20,21 and resonant soft, hard, and tender X-ray scattering measurements, [22][23][24][25][26][27] suggest that the helical pitch of an N TB phase formed by several molecules is B10 nm, which is significantly shorter than the pitch of a typical chiral N phase or cholesteric phase exhibiting a helicoidal helix (generally hundreds of nanometers).Materials that exhibit the N TB phase have been employed for various LC applications, such as wavelength-tunable selective light reflection [28][29][30][31] and optical memory 32 devices, LC physical gels, 33 photo-switchable viscoelastic bodies, 34 and photoalignment technology. 35o date, a number of bent LC dimers composed of two mesogenic structures connected with an odd-numbered oligomethylene spacer have been shown to exhibit the N TB phase.  In ation, several LC oligomers (e.g., trimers, 53,[58][59][60][61][62][63] tetramers, 58,59,64 a hexamer, 65 and other types of oligomers [66][67][68][69] ), polymers, 70 and bent-core molecules 71,72 have also been identified as twist-bend nematogens.It should be noted here that the bent molecular geometry is key to designing twist-bend nematogens.The angle of the molecular bend and the stability of the N TB phase are highly dependent on the bonds linking the two rigid mesogenic arms and the flexible oligomethylene spacer; e.g., methylene-linked cyanobiphenyl (CB)-based CBnCB dimers (representative twist-bend nematogens) 14,36,37 and ether-linked CBOnOCB dimers (conventional nematogens). 73Mandle et al. comprehensively studied the relationship between the bend angle of several CB dimers with different linkages and their N TB formation using both experimental and quantum calculation approaches. 45,54In addition, the influence of various combinations of chalcogens and other linkages on the N TB phase incidence and stability has been studied. 52,53We previously reported 53 a number of systematically designed thioetherlinked LC dimers to ascertain the molecular design necessary to form the N TB phase; unsymmetrical ester-and thioetherlinked CB-based dimers with a butylene spacer, viz.CBCOO4SCB and CBOCO4SCB (Fig. 1), formed N TB phases when supercooled to room temperature to be a N TB glass (N TB G).The latter displayed behaviors typically observed in twist-bend nematogens, including a second-order-like N-N TB transition and clear blocky, focal conic, and striped textures.Whereas the former CBCOO4SCB exhibited unusual behaviors such as a first-order-like N-N TB transition and ambiguous striped optical textures that were extremely thin.The origin of such differences between the dimers is yet to be determined.One possibility is that these phenomena may be a consequence of the distinct helical structures present at the nanoscale due to oppositely directed ester-linkages.][26][27] This is the first report of the synthesis, detailed phasetransition behaviors, and distinct nano-to-macroscopic N TB phase behaviors associated with different heliconical nanostructure modes of two homologous series of sulfur-containing LC dimers with oppositely directed ester-linkages.Unsymmetrical ester-and thioether-linked CB-based dimer homologues were synthesized, viz.CBCOOnSCB and CBOCOnSCB (n = 2-10, even numbers only), which contain oppositely directed esters (i.e., -CQOO-and -OCQO-, respectively).The number of carbon atoms in the oligomethylene spacers (n) were selected such that the total number of atoms in the linkage and the spacer along the chain is an odd number, thereby giving an overall bent molecular geometry.We evaluated the phase transitions and mesomorphism of the dimers using polarized optical microscopy (POM), differential scanning calorimetry (DSC), and conventional X-ray diffractometry (XRD), and analyzed the heliconical structures using TReXS at the sulfur K-edge.

Results and discussion
The synthetic procedures and characterization of the homologous series of CBCOOnSCB and CBOCOnSCB are described in the ESI.† Their phase sequences, phase-transition temperatures at crystallization (T Cr ), glass transition (T g ), N-N TB phase transition (T NNTB ), isotropic (I)-N phase transition (T IN ), entropy changes (DS) scaled by the gas constant (R) at the I-N and N-N TB phase transitions (DS IN /R and DS NNTB /R, respectively), and T NNTB /T IN at a cooling rate of 10 1C min À1 are summarized in Table 1.The phase-transition data obtained during the first heating are listed in Tables S1 and S2 (see ESI †).
In terms of the phase-transition behavior of the CBCOOnSCB series, the dimers with n = 4, 6, 8, and 10 exhibited a monotropic N TB phase below the N phase, whereas the shortest CBCOO2SCB dimer exhibited only a monotropic N phase.The monotropic N phase of CBCOO2SCB appeared at 83 1C and was partially supercooled to room temperature upon cooling.This N phase could only be observed using POM due to crystallization of the dimer (Fig. S1 and S9, ESI †).CBCOO6SCB and CBCOO8SCB displayed transitions to the N TB phase from the corresponding N phase at 75 and 85 1C, respectively.Notably, CBCOO6SCB exhibited the N TB phase across a broad temperature range, which was supercooled to room temperature and ultimately underwent vitrification to form a N TB G, similar to CBCOO4SCB. 53he DSC curves of CBCOO6SCB are shown in Fig. 2(a).The N-N TB phase-transition peak was identified as a first-order-like transition with a DS NNTB /R value of 0.54, which differs from the second-order-like transition behavior typically observed for twist-bend nematogens.The N TB phase of CBCOO8SCB crystallized at 76 1C and the dimer bearing the longest spacer (i.e., CBCOO10SCB) also exhibited the N TB phase, but underwent crystallization at approximately 90 1C, as can be seen from the DSC curves (Fig. S11 and S12, ESI †); the N TB phases could be observed only in small supercooled N domains using POM (Fig. S3, S5, S7 and S8, ESI †).
Regarding the phase-transition behavior of the CBOCOnSCB series, dimers with n = 4, 6, 8, and 10 formed a monotropic N TB phase below the N phase temperature.Like CBCOO2SCB, the dimer with the shortest spacer (CBOCO2SCB) only formed the monotropic N phase.The N phase of CBOCO2SCB was very narrow, which could be observed by POM but was not detected by DSC due to crystallization during cooling (Fig. S6 and S13, ESI †).As shown in Fig. 2(b), CBOCO6SCB exhibited a remarkably stable N TB phase when supercooled to room temperature, with vitrification taking place at 14 1C to form the N TB G phase; this behavior is similar to that of CBOCO4SCB. 53Furthermore, the N-N TB phase transition at 94.9 1C is similar to the secondorder-like phase-transition typically observed for the majority of twist-bend nematogens.CBOCO8SCB exhibited the N TB phase at temperatures ranging from 93 to 79 1C, below which it underwent crystallization.The N-N TB phase transition at 85 1C could not be detected by DSC due to crystallization (Fig. S16, ESI †).Moreover, the N TB phase was observed only in the supercooled N domains of CBOCO10SCB; hence, no N-N TB transition peak could be detected via DSC (Fig. S8 and S17, ESI †).Unlike CBCOOnSCB, which exhibited monotropic mesophases, CBOCOnSCB with n = 4, 6, 8, and 10 gave rise to enantiotropic N phases.In addition, the abovementioned observations indicate that mid-length spacers (n = 4 and 6) of both homologous series enhanced the N TB phase ranges, which ultimately resulted in the formation of a room-temperature N TB phase or N TB G phase.
The T IN , T NNTB , and DS IN /R values as a function of n for CBCOOnSCB and CBOCOnSCB (n = 4, 6, 8, and 10) are displayed in Fig. 3.The phase-transition temperatures are higher for CBOCOnSCB than for CBCOOnSCB, except T g .This difference can be attributed primarily to their different geometries according to the all-trans model of spacer chains; in other words, their molecular biaxiality and shape anisotropy.The inter-arm bend angle (a) between the para-axes of the two mesogenic arms of CBCOO4SCB (a = 1051) is significantly smaller than that of CBOCO4SCB (a = 1271). 53This difference is caused by the opposed ester-bond directions or the different positions of carbonyl (CQO) and -O-C-bonds in the esters.Notably, the T IN values of CBCOOnSCB were found to strongly depend on n, whereas those of CBOCOnSCB were only slightly affected by n.The T NNTB values of CBCOOnSCB sharply decreased with a decrease in n, while the corresponding values of CBOCOnSCB did not.It is worth noting that the DS IN /R values are significantly smaller for CBCOOnSCB than for CBOCOnSCB.The abovementioned trends may be associated with the more bent geometry of CBCOOnSCB with the smaller bend angle or the more anisotropic geometry of CBOCOnSCB. 48he DS IN /R values of both homologous series were found to gradually decrease with decreasing n, which can be ascribed to the molecular structural biaxiality that is enhanced by  decreasing the spacer length, thereby reducing molecular anisotropy.In addition, the reduced temperature, T NNTB /T IN , values for CBOCOnSCB (B0.86) were smaller than those for CBCOOnSCB (B0.96), and these values remained nearly constant within each homologous series.This reflects that the N-N TB phase of CBOCOnSCB originates from the supercooled N phases, which undergo a greater degree of supercooling than those of CBCOOnSCB.These trends can also be reasonably associated with their molecular geometry or anisotropy.More bent molecules can effectively form the N TB phase, whereas more linear molecules typically favor formation of the conventional N phase.Hence, appearance of the N TB phase for CBOCOnSCB is naturally induced from the more supercooled N phase, resulting in lower T NNTB /T IN values. 56ing POM, we observed different optical textural behaviors in the N TB phases for each homologous series when n = 4 and 6.In non-treated glass cells, CBCOOnSCB (n = 4 and 6) exhibited focal conic textures (Fig. S2, ESI †), 53 which are typical of the N TB phase.In addition, they displayed textures characterized by an elastic behavior (Fig. S2, ESI †); these textures could be recovered even when expansion took place through pressing and shearing.In our previous report, 53 we noted that CBCOO4SCB exhibited unusual striped texture with an obscure thinnerstriped texture as shown in Fig. 4(a) using POM with a uniaxially rubbed planar cell.In this study, we conducted further POM analyses of CBOCO4SCB, CBOCO6SCB, CBCOO6SCB, and CBCOO8SCB using 5 mm-thick uniaxially rubbed polyimidesurface-treated planar alignment cells.We found that CBOCO4SCB exhibited the usual optical texture of the N TB phase with clear stripes [Fig.4(c)], which is distinct from the obscure thin stripes found in CBCOO4SCB [Fig.4(a)].The two dimers with n = 6 also displayed clearly different optical texture behaviors: CBCOO6SCB exhibited a distinct thinner-striped texture [Fig.4(b)]; however, CBOCO6SCB displayed a more typical striped texture [Fig.4(d)].These were similar to the different texture behaviors of CBCOO4SCB and CBOCO4SCB.Meanwhile, CBCOO8SCB exhibited a conventional striped texture that was similar to those of the typical twist-bend nematogens and the oppositely directed esters, CBOCO4SCB and CBOCO6SCB (Fig. S4, ESI †).It seems that the unusual textures with thinner stripes observed for CBCOOnSCB were changed to the typical ones with increasing length of the central spacer.In addition to the properties associated with the first and second order phase-transitions of the N TB phases of CBCOOnSCB and CBOCOnSCB (n = 4 and 6), respectively, the observed textural patterns inspired us to study the helical structures of the N TB phases by means of comprehensive X-ray techniques, since previous studies suggested the presence of heliconical structures [19][20][21][22][23][24][25][26][27] and pseudo-layer nature in the N TB phase. 74,75o analyze the structures of the observed mesophases, we firstly conducted conventional XRD measurements for both homologous series with n = 4 and 6 (Fig. S18-S21, ESI †).In both the N and N TB phases, broadened diffraction peaks were observed in the small-and wide-angle regions.These results suggest that there is no apparent positional order along the long molecular axis, and liquid-like correlations exist among lateral molecules, thereby indicating the nature of the N phase.In addition, the small-angle diffraction pattern corresponds to pseudo-layered structures that originate from the smectic (Sm)-like or cybotactic molecular clusters in the N and N TB phases.The pseudo-layer lengths in the N TB phase were estimated to be similar: 1.15 nm (2y = 7.61) for CBCOO4SCB, 1.27 nm (2y = 6.91) for CBCOO6SCB, and 1.32 nm (2y = 6.71) for CBOCO6SCB in each N phase.The intensity of the small-angle diffraction was weaker in the N TB phase than in the N phase, and the 2y values (or the pseudo-layer lengths) were temperature-independent over the entire N TB phase range, which is typical of N TB phases.In the case of CBOCO4SCB, the small-angle diffraction could We performed TReXS measurements at the sulfur K-edge to determine the helical pitch in the N TB phases of CBCOOnSCB and CBOCOnSCB (n = 4 and 6).][26][27] The two-dimensional (2D) and one-dimensional (1D) resonant X-ray scattering patterns obtained from the helical pitch periodicity in the N TB phase of CBCOO4SCB are shown as representative images in Fig. 5.These scattering patterns appeared at temperatures below the N phase upon cooling and disappeared upon re-entering the N phase upon reheating.The 2D scattering images of the other dimers and the corresponding 1D patterns are shown in Fig. S22-S27 (ESI †).Fig. 6(a) shows the temperature dependence of the helical pitch in the N TB phase for both the homologous series (n = 4 and 6) as a function of the shifted temperature (DT = T NNTB À T).The helical pitch lengths ( p h ) were calculated from the wavenumber q = 2p/p h .Upon decreasing the temperature, the p h values decreased from 8.1 to 6.8 nm for CBCOO4SCB and from 9.3 to 7.4 nm for CBCOO6SCB, while those of CBOCO4SCB and CBOCO6SCB decreased from 20.3 to 11.9 nm and from 24.4 to 13.8 nm, respectively.Compared with those of CBOCO4SCB and CBOCO6SCB, the helical pitches of CBCOO4SCB and CBCOO6SCB were not only significantly shorter but also less temperature-dependent.The helical pitch lengths of  CBOCO4SCB and CBOCO6SCB decreased upon lowering the temperature, as is typical for N TB phases; this temperature dependence may be attributed to the lower number of twisted molecular conformations (or an increase in straightened conformers) 76 and fluctuations in the unwinding process related to helical ordering at high temperatures, which relate to decreased precession of the molecules in the helices at high temperatures.However, the helical pitch lengths of CBCOO4SCB and CBCOO6SCB do not vary significantly at different temperatures.Furthermore, it is noteworthy that the p h ratios of p h (CBOCO4SCB)/p h (CBCOO4SCB) and p h (CBO-CO6SCB)/p h (CBCOO6SCB) are close to 2, i.e., the helical pitch lengths of CBOCOnSCB (n = 4 and 6) were twice those of CBCOOnSCB (n = 4 and 6), as shown in Fig. 6(b).Density functional theory (DFT) calculations using Gaussian 16 at the B3LYP 26/6-31G(d) level of theory show that the difference in the overall molecular lengths of CBCOO4SCB (2.56 nm) and CBOCO4SCB (2.78 nm) is small; therefore, the considerable difference in their helical pitches cannot be qualitatively accounted for by the molecular lengths, which will be discussed later.
The helical pitch length is associated with the tilt angle from the helical axis (y), molecular length (L), and molecular number per turn (n m ) (see Fig. 7); p h = n m L cos y, and hence n m can be estimated by calculating the value of 2p/qL cos y.8][79][80][81] Nevertheless, it is realistically assumed that y does not significantly influence the n m values within the heliconical region.In the low temperature region of the N TB phase, the n m values were estimated as n m = 3-4 for CBCOO4SCB and CBCOO6SCB and n m = 5-6 for CBOCO4SCB and CBOCO6SCB within a similar DT region.
Next, the helical models of the dimers were considered based on XRD and TReXS.The azimuthal precession (j) per  View Article Online pseudo-layer was estimated from the following equation: Dj = 3601 Â (pseudo-layer length on XRD)/(p h on TReXS); this can be used to elucidate the heliconical models by utilizing the polygon models. 61The j values were estimated to be B601 in the N TB phase of CBCOOnSCB (n = 4 and 6).These j values indicate a hexagonal model separated by pseudo-layers for the N TB phase of CBCOOnSCB (n = 4 and 6).On the other hand, the j values of CBOCOnSCB (n = 4 and 6) essentially became smaller (approximately 30-401) within the tested temperatures or led to the formation of larger polygonal structures such as a decagon due to their abnormally long helical pitches.The j values of CBOCO4SCB were estimated using the pseudo-layer length in the N phase since the pseudo-layer peak almost disappeared below the N TB phase.
Using the values of n m and Dj, we constructed two heliconical models in the N TB phases of CBCOOnSCB and CBOCOnSCB (n = 4 and 6).Fig. 7(a) and (b) illustrate plausible heliconical models with n m = 3-4 and Dj = 601 for a hexagon model of CBCOOnSCB (n = 4 and 6) and with n m = 6-7 for CBOCOnSCB (n = 4 and 6), respectively.Considering the strong temperature dependence of the helical pitches in the latter, it is assumed that the bent conformation and the stacking extent of the rigid CB arms among the dimers may also be influenced by temperature, changing the precession angles.
As described in the Introduction, the p h values of the N TB phase are B10 nm, [19][20][21][22][23][24][25][26][27] corresponding to several dimers.For example, the p h of CB7CB, which is a representative twistbend nematogen structurally analogous to CBCOOnSCB and CBOCOnSCB dimers, has been found to vary between 8 and 10 nm depending on the temperature. 22However, the p h values of both CBCOOnSCB (n = 4 and 6) were found to be somewhat smaller than those of CB7CB, while those of CBOCOnSCB (n = 4 and 6) were larger.That is, the oppositely directed esters caused unique and distinct helical structural modes in the N TB phases of these dimers which differ from those of the typical dimer.CBCOOnSCB (a = 1051) can be bent to a higher extent than CBOCOnSCB (a = 1271), which are ascribed to the opposed ester-bond directions or the different positions of carbonyl (CQO) and -O-C-bonds in the two type esters. 53In addition, the linkage point between CB and -COO-of CBCOOnSCB is more rigid than that between CB and OCO CBOCOnSCB.][84][85] Thus, the increased bending and more rigid structure of CBCOOnSCB should result in shorter helical pitches and a weaker temperature dependence, as compared with those of CBOCOnSCB and the other reported twist-bend nematogenic dimers.This can be associated with the first-order-like N-N TB transition peak that corresponds to the changes in the phase structure.
The main factor responsible for the longer helical pitch of CBOCOnSCB (i.e., approximately 10-25 nm) as compared to that of CB7CB (8-10 nm) is likely to be the molecular bend (or the molecular biaxiality) and the resulting precession angles of the helices.The molecular bend angle of CBnCB is estimated as 1111 based on its all-trans model, 45 leading to a more bent geometry for CBnCB than for CBOCOnSCB (1271). 53n the other hand, the p h values of both ester homologous series were marginally shorter in homologues with n = 4 than those with n = 6, due to the different lengths of flexible spacer chains.As illustrated in Fig. 6, the temperature dependence of the p h values remained essentially unchanged for both the systems.
Finally, we estimated the correlation lengths of the helices and the number of the helical stacks in the N TB phases of CBCOOnSCB and CBOCOnSCB (n = 4 and 6).Using the full width at half maximum (FWHM) of the Lorentzian fitting (FWHM = 2/x, where x is the Lorentzian length) applied to the TReXS data, the Scherrer equation (t = 2p/FWHM; wherein the shape factor is set to unity) can be used to estimate the longitudinal heliconical correlation or domain size. 23In addition, the number of helical stacks was estimated by calculating t/p h .The longitudinal correlation lengths and helical stacks are plotted as a function of DT, as shown in Fig. 8.The t values tend to slightly increase initially with decreasing temperature in the higher N TB temperature region, immediately below the N phase.This initial increase in t is attributable to heat fluctuations that occur close to the fluidic N phase, such that t becomes larger.It is interesting to note that the correlation lengths and the resulting number of the helical stacks of CBCOOnSCB are calculated to be more than twice the corresponding values of CBOCOnSCB (Fig. 8).These larger correlation lengths of the helices of CBCOOnSCB as compared to those of CBOCOnSCB are reasonable, considering their rigid molecular structures and approximately temperatureindependent helical behavior, which are reminiscent of rigid packing.The helical pitches and correlation lengths of CBCOOnSCB are also essentially temperature-independent; and the estimated helical stacks naturally display a similar behavior.On the other hand, since the helical pitches of CBOCOnSCB typically depend on temperature, the helical stacks increase with decreasing temperature.

Conclusions
We herein reported the development of two homologous series of unsymmetrical ester-and thioether-linked cyanobiphenylbased LC dimers, viz.CBCOOnSCB and CBOCOnSCB (n = 2, 4, 6, 8, and 10).We observed that all the dimers were mesogenic, and that CBCOOnSCB and CBOCOnSCB (n = 4, 6, 8, and 10) formed N TB phases.In particular, CBCOOnSCB and CBOCOnSCB (n = 4 and 6) exhibited the N TB phase across a wide temperature range.These phases were stable down to room temperature and eventually formed N TB glasses.The phase-transition temperatures (excluding glass transition temperatures), and associated enthalpy and entropy changes were mostly lower for CBCOOnSCB than those observed for CBOCOnSCB.In addition, CBCOOnSCB and CBOCOnSCB (n = 4 and 6) displayed different phase-transition properties and striped optical textures.Finally, their distinct helical structures were elucidated using TReXS measurements at the sulfur K-edge.Compared with those of the typical twist-bend nematogenic dimers, CBCOOnSCB (n = 4 and 6) exhibited smaller pitch lengths with weaker temperature dependence, whereas CBOCOnSCB (n = 4 and 6) exhibited greater helical pitch lengths.The difference is ascribed to the molecular bend (or the molecular biaxiality) and structural rigidity.This study therefore provides new insights into the influence of molecular design in the N TB phase, revealing that subtle structural modifications (i.e., oppositely directed esters) crucially impact helical nanostructures in the N TB phase.

Experimental section
The synthetic scheme and procedures and characterization data for CBCOOnSCB and CBOCOnSCB are described in the ESI.† The molecules were purified using column chromatography on silica gel and recrystallization. 1 H and 13 C nuclear magnetic resonance (NMR) spectroscopy were recorded on a JNM-ECS400 (400 MHz for 1 H and 100 MHz for 13 C) or a JNM-ECX500 (500 MHz for 1 H NMR and 126 MHz for 13 C NMR) (JEOL Ltd, Tokyo Japan).Fourier transform infrared spectroscopy (FTIR) were performed by the KBr (purchased from FUJIFILM Wako Pure Chemical Co.) method using a JASCO FT/IR-4200.High-resolution mass spectrometry (HRMS) using high-performance liquid chromatography (HPLC) (Agilent 1200 HPLC-Chip and 6520 Accurate-Mass Q-TOF) was conducted.Phase-transition behavior was studied based on POM with an Olympus (Tokyo, Japan) polarized optical microscope (BX50) with a Linkam (Surrey, UK) temperature controller LK-600PM and differential scanning calorimetry (DSC) with a Shimadzu (Kyoto, Japan) DSC 60 at a rate of 10 1C min À1 under a flow of nitrogen gas (50 mL min À1 ).The POM images and DSC results for all the compounds are shown in the main text or ESI.† X-ray diffraction (XRD) measurements were conducted using a Bruker D8 DISCOVER equipped with a Vantec-500 detector using Cu-K a radiation.The specimens, kept in capillary glass tubes of 1.5 mm diameter (purchased from WJM-Glass Mu ¨ller GmbH), were aligned under a magnetic field (B = 300 mT).According to the literature, 25 TReXS measurement was performed at the beamline 5.3.1 at the Advanced Light Source, Lawrence Berkeley National Laboratory.The X-ray beam energy was tuned around the S K-edge, 2472 eV, with a channel cut double-bounce silicon (111) monochromator.A two-dimensional (2D) Pilatus detector (300 K, Dectris, Inc.) was used to collect the scattering patterns, which were subsequently converted to onedimensional line profiles using the Nika software package. 86The scattering patterns were viewed with the Xi-Cam interface 87 at the beamline.The sample-detector distance was tuned between 488 mm and 250 mm to access relevant q range.The beam centers and the sample-to-detector distances were calibrated using both silver behenate and 8CB.

Conflicts of interest
There are no conflicts to declare.

Fig. 4
Fig. 4 POM images of the N TB phases of (a) CBCOO4SCB, (b) CBCOO6SCB, (c) CBOCO4SCB, and (d) CBOCO6SCB in a uniaxially rubbed cell with planar alignment.The POM image in panel (a) is reproduced from ref. 53 with permission from Elsevier.

Fig. 5
Fig. 5 (a) Typical 2D-scattered patterns and (b) the corresponding 1D patterns in the N TB phase of CBCOO4SCB.Note the horizontal blue streaks in (a) are areas with no data, either due to gaps between detector modules or the beam stop used to block the direct X-ray beam.

Fig. 7
Fig. 7 Plausible heliconical helix models in the N TB phases of (a) CBCOO4SCB and CBCOO6SCB, and of (b) CBOCO4SCB and CBOCO6SCB.

Table 1
Phase sequences, transition temperatures (1C), and entropy changes scaled by the gas constant (DS/R) of CBCOOnSCB and CBOCOnSCB upon cooling a Determined by POM.