Effect of Pressure on Dielectric and Frank Elastic Constants of a

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Effect of Pressure on Dielectric and Frank Elastic Constants of a Material Exhibiting the Twist Bend Nematic Phase Srividhya Parthasarathi, D. S. Shankar Rao, Nani Babu Palakurthy, Channabasaveshwar V. Yelamaggad, and Subbarao Krishna Prasad J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b10563 • Publication Date (Web): 09 Jan 2017 Downloaded from http://pubs.acs.org on January 10, 2017

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The Journal of Physical Chemistry

Effect of Pressure on Dielectric and Frank Elastic Constants of a Material Exhibiting the Twist Bend Nematic Phase Srividhya Parthasarathi, D.S. Shankar Rao*, Nani Babu Palakurthy, C.V. Yelamaggad and S. Krishna Prasad Centre for Nano and Soft Matter Sciences, Jalahalli, Bangalore 560013, INDIA *[email protected]; Tel: 91-80-23084218

Abstract We report the first investigation on the effect of applied pressure on the now well known dimer α,ω bis(4,4’-cyanobiphenyl)heptane (CB7CB) that exhibits two types of nematic: the regular uniaxial nematic (N) and the recently discovered twist-bend nematic (NTB) phase. At atmospheric pressure, the thermal behaviour of ε⊥, the permittivity normal to the director in the N phase decreases on entering the NTB wherein the value represents permittivity orthogonal to the helical axis. Application of pressure initially decreases the magnitude of the change in ε⊥, and with further increase in pressure exhibits an increase in the value. Such a change in the feature of ε⊥ is similar to that obtained at room pressure when the monomeric heptyloxy cyanobiphenyl (7OCB) is doped to CB7CB at a high concentration of 50%. The dielectric anisotropy exhibits a trend reversal with temperature, the extent of which is affected at high pressures. Another salient feature of the study is the effect that pressure has on the Frank bend elastic constant K33. Over the pressure range studied K33 enhances by a large factor of 5. In contrast, the splay elastic constant exhibits a much smaller change of only 70%. The pressure-temperature phase boundary has a much smaller slope for the N-NTB transformation than for the isotropic-N transition. We propose that all these features can be understood in terms of the relative population of the more energetic horseshoe, and lower energy extended conformer adopted by the CB7CB molecule. The extended conformer is favoured at lower temperatures, or at higher pressures. This argument is validated by Xray

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diffraction experiments at atmospheric pressure on the binary mixture of CB7CB and 7OCB, mentioned above.

1. Introduction The uniaxial nematic phase (N) is an orientationally ordered fluid phase commonly seen, especially in organic materials composed of rod-like molecules. It is characterized by long range orientational order, optical anisotropy and response to low-magnitude electric fields.1 These features have made it ubiquitous in the form of the active material for the technologically important display devices.2-3 If the nematic phase is composed of achiral molecules, the director can remain uniform throughout the sample even in the absence of an external field. If the constituent molecules are chiral, the phase termed as chiral nematic or cholestric (N*), has a spontaneous twist superimposed normal to the director. If the helical rotation of the director about the twist axis occurs with having a finite tilt, then a new phase emerges, labelled as twist-bend nematic or NTB.4-18 The structure of this phase is quite similar to that of chiral smectic C* except that there is no layering and no chirality. Features similar to those predicted theoretically for the NTB phase have been observed in strongly bent achiral molecules. Interestingly, from the view point of the present article, the NTB phase has been evidenced to exist in certain dimeric molecules with odd number of carbon atoms in the spacer unit linking the two mesogenic arms,19 and attributed to their bent shape.

Notably in a particular homologous series, termed CBnCB, where n

indicates an odd number of methylene units, the existence of this phase, and a transition at a higher temperature to its ordinary form (N) has been well established. In fact, the seventh member, CB7CB, is the most well studied compound.9,20-21 The induction of the NTB phase has been argued to occur owing to either of the two possible mechanisms. A model wherein the occurrence is due to spontaneous electric


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polarisation was originally proposed by Meyer22 and developed subsequently by Lorman & Mettout.23 An entirely different mechanism was put forth by Dozov.4 This model argues that the NTB phase occurs as a pure elastic instability in a nematic comprising bent-shaped molecules. A more important aspect of the model is that the chiral symmetry breaking appears in the nematic phase, even without smectic ordering due to pathological elasticity of banana shaped molecules. It is well known that in the N phase, the elastic constants measurements are very important not only for the basic understanding but also from a technological point of view.2-3 Such an understanding becomes all the more important in the case of the NTB phase owing to the specific theoretical expectation that the bend elastic constant should become negative. Systematic measurements of permittivity and elastic constant have been reported on a few materials, including 7, 9 &11th homologues of CBnCB series, known to exhibit the NTB phase.9, 24-26 Due to the difficulty in getting proper uniform reorientation in the NTB phase the elastic constant measurements are limited to the N phase only. These studies show that the splay elastic constant, K11, has a monotonic increase on lowering the temperature although presenting a pre-transitional divergence on approaching the N-NTB transition. On the other hand, the bend elastic constant, K33, shows a slight increase with decreasing temperature, immediately below the isotropic point but exhibits a much weaker temperature-dependence with further decrease in temperature. In materials possessing a wider thermal range of N phase, there is even a trend reversal: K33 diminishes on lowering the temperature after exhibiting a maximum in the value. High resolution experiments have been performed to find out whether such a trend reversal can be indications of negative K33 in the NTB phase. To the contrary, the data exhibit a limiting behaviour in the immediate vicinity of the N-NTB transition. In fact, there has been no experimental report of the observation of negative K33 values. The permittivity also shows an interesting thermal variation. In the N phase, behaviour typical of positive dielectric anisotropy material, viz.,



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monotonic increase with decreasing temperature, is seen. However, on transforming to the NTB phase both parallel (ε||) and perpendicular (ε⊥) dielectric constants diminish, a feature attributed to a lowering of the order parameter.13-14 We have recently shown that the magnitude of the ε⊥ decrease across the N-NTB transition reduces on adding a rod like component to CB7CB, with the trend reversing for higher concentration of the former substance.21 Despite the increasing interest in studies on materials having the NTB phase, all the measurements till date are restricted to atmospheric pressure. Here we report the first high pressure study on the behaviour of dielectric and elastic constants measurement in the nematic phase of a system exhibiting the N-NTB phase sequence. The magnitude and thermal variation of the perpendicular permittivity and the bend elastic constant are strongly influenced by pressure. The behaviour bears strong resemblance to the results obtained at atmospheric pressure in a binary system comprising CB7CB and a monomeric material with a similar chemical structure.21 The data are analysed in terms of the conformers of the CB7CB molecule. 2. Experiment The molecular structure of the dimer α,ω bis(4,4’-cyanobiphenyl)heptane (CB7CB) used along with its transition temperatures is shown in Figure 1. The dimer was synthesized in our laboratory using the procedure described in an earlier paper.21 Certain experiments were also conducted on by adding a structurally similar monomer, n-heptyloxy cyanobiphenyl compound (7OCB), whose structure and transition temperatures are also given in Figure 1. Mixtures indicated as Xn, where n indicates the mole percent of 7OCB in CB7CB. While CB7CB exhibits two nematic phases, 7OCB has only the uniaxial nematic. Dielectric and Freedericksz transformation measurements were obtained with the help of a high precision LCR meter (Agilent 4284A) at a constant frequency of 10 KHz. The latter measurements yielding capacitance vs. voltage profiles were used to extract the elastic constants with the 4 ACS Paragon Plus Environment

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help of the procedure described in Section 3. The high pressure equipment employed has already been described elsewhere 27: only the salient features are recalled here. The sample contained in a PTFE ring (≈60 µm) is sandwiched between two steel cylinders with provision to establish electrical contact with the measuring apparatus. This whole assembly is enclosed in an elastomer tube. The elastomer tube has the property of not only transferring the applied pressure effectively to the sample, but also prevents any contamination of the sample by the pressure transmitting oil. The sample pressure is measured with a precision of 1 bar using a calibrated Heise gauge. These experiments were isobaric in nature, i.e., the pressure was held constant while the temperature was swept. For promoting the planar alignment of the liquid crystal molecules the inner surfaces of the steel cylinders had a thin layer of a polyimide. In the high pressure set up, the measured capacitance contains the unavoidable contribution from the spacer that holds the sample. The spacer contribution was eliminated in the calculations of the permittivity by considering the measured capacitance (Cmeas) to be a simple addition of the sample capacitance (CLC) and that due to the spacer (Cspacer), i.e., Cmeas =CLC+Cspacer and solving the two simultaneous equations Ciso = C o ε iso + Cspacer

(1)

C N = C o ε N + Cspacer

(2)

Here Co is the empty cell capacitance, Cspacer the spacer contribution, Ciso and CN, the measured capacitances at the nematic to isotropic (NI) transition and in the N phase at T-TNI = 5K, with the corresponding permittivity values, εiso and εN, measured at room pressure using samples in glass cells.



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3. Results 3.1. Thermal variation of capacitance The temperature dependences of C⊥, the sample capacitance obtained with low probing voltage (0.5V) for several pressures are shown in Figure 2(a). Over the entire range of pressure studied, the low voltage retains the molecular orientation in the surface determined planar geometry, as indicated by a large decrease in the C⊥ value when the material transforms from the isotropic to the N phase. Interestingly, a clear change is also seen across the N-NTB transition. At low pressures, the transition is marked by a lowering of the C⊥ value. However, with increasing pressure the magnitude of change reduces initially, and with further increase in pressure changes sign exhibiting an enhancement on entering the NTB phase (see Figure 2b). Such a change in the sign of C⊥ (or ε⊥) variation has been reported recently by us,21 [see Figure S1, see ESI†]. and Luckhurst28 in binary mixtures involving CB7CB. The highlight of the present study is that this effect brought about by the addition of another chemical component can be realized for CB7CB itself subjected to elevated pressures. In fact, data obtained for the X5 mixture, not only corroborate this feature, but exhibit much larger variations with pressure (see Figure 3a-b). We shall return to this point later. Employing a much higher (20V) probing voltage we could observe an increase in the measured capacitance at the isotropic-N transition, followed by weak decrease deeper in the N phase, but again a substantial reduction at the NTB phase. The thermal variation of the capacitance obtained with 20V probing voltage is shown for a representative pressure (0.21 kbar) is given in the Figure 2(c); the profile is similar to that observed at atmospheric pressure. Polarizing microscopy observations at atmospheric pressure (using the glass cell) however show that with this voltage the reorientation of molecules is complete to the homeotropic geometry only in N phase. In contrast, for the same voltage no change in the birefringence was observed in the NTB phase (For a fully homeotropically aligned sample, the small tilt in the NTB phase


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should result in a field of view of low birefringence. Under conditions that the optic axis would be normal to the substrate – as is the case with homeotropic – the field of view should be completely dark). Thus, unlike in the N phase the capacitance values obtained with 20 V do not yield C||. 3.2. Phase diagram From the data presented in Figures 2 and 3, we have constructed pressure-temperature phase diagram for pure CB7CB (see Figure 4). Several interesting features are seen in the phase diagrams: (i) The NTB phase exists over the entire pressure range studied. (ii) The transition temperatures of both transformations, TN-I and TN-NTB increase with increasing pressure. (iii) The thermal range of the N phase increases at the expense of the NTB phase indicating that the latter phase is less favoured by packing density considerations. (iv) Noting that the pressuredependence is essentially linear, we fitted a straight line to the two boundaries. The slope values obtained for both phase lines in the three materials are shown in Table 1. While the values are comparable for the pure and X5 materials, they differ for the higher concentration (X15) mixture (see Fig.S2 and S3 [see ESI†]). In fact, the data suggesting that the extent of pressure-stabilization of the N phase gets reduced for the X15 mixture is counterintuitive. It is possible that the dielectric features discussed wherein the presence of a rod-like component enhances the permittivity variation across the N-NTB transition is also responsible for the pressure behaviour. 3.3. Elastic constants The raw profiles of the dependence of reduced sample capacitance C on applied voltage V obtained at several temperatures and a fixed pressure of 0.83 kbar for pure CB7CB are presented in Figure 5. Sharp electric-field induced Freedericksz transformation feature with a clear threshold is seen at all temperatures in the N phase. For comparison a dataset collected in the NTB phase is also shown. Although threshold-type behaviour is seen the saturation



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capacitance is very small as compared to that in the N phase, indicating that the reorientation is far from being complete. Hence we restrict the discussion to the results in the N phase. The profiles were analyzed using procedure described earlier,29 which is based on the continuum description of the Freedericksz behaviour by Deuling,30-31 the procedure is briefly recalled here. Under equilibrium conditions the LC molecules, contained in a sandwich type cell, are oriented parallel to the substrate surface in a uniform planar manner. An electric field applied normal to the substrates exceeding a critical threshold voltage, Vth, brings on a molecular reorientation process which at high enough voltages (V >> Vth) makes the molecules to be normal to the surface. In the method employed the threshold parameters provide the splay (K11) elastic constant, whereas the full profile fit of eq. (2) using a MATLAB script yields the bend (K33) elastic constant. The expressions employed for the purpose are

K 11 = ε 0 ε aV th2 / π

2

(1)

() −

(1 + sin )(1 − sin ) 2 1 + sin = − cos # (2) (1 + sin )(sin − sin )

Here εο is the permittivity of free space, and εa (= ε|| − ε⊥), the dielectric anisotropy of the sample, where ε|| and ε⊥ corresponding to the dielectric constant measured in terms of the capacitances

parallel (C||) and

perpendicular

(C⊥) to

the

nematic

director.

κ =( Κ3/Κ1)−1, γ = (ε||/ε⊥)−1, φ is the angle between the director and the walls of the substrate with φm being the value in the mid plane of the sample. Before deliberating on the results of the elastic constants, let us discuss the behaviour of the threshold voltage Vth and the permittivity anisotropy εa. The temperature dependence of Vth at a representative pressure (0.83 kbar) is shown in the inset Figure 5 displaying the expected monotonic increase on lowering the temperature. A similar variation is seen for the 8 ACS Paragon Plus Environment

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case of a fixed temperature and the pressure increased. However, if the reduced temperature Tred (=T-TNI, TNI is the nematic to isotropic transition temperature) is considered, pressure hardly alters the value of Vth. In contrast, εa exhibits a rich behaviour on application of pressure, as seen in Figure 6. At all pressures, the data exhibit a non-monotonic thermal variation assuming a convex-shaped profile, i.e., as the temperature is lowered, the value increases, reaches a maximum and then decreases with further lowering of temperature. The profile obtained at the lowest pressure is quite similar to that for the glass-cell measurements at atmospheric pressure.21 The extent in the trend reversal in the profile is seen to diminish as a function of pressure, with the behaviour moving towards that usually seen for nematics. This feature is clearly seen in the slope of dεa/dT obtained by considering the data at temperature below the maximum in the profile (see inset of Figure 6). Owing to the convexity, the εa value well in the phase, say TNI–20 K, has a substantial variation, increasing by ~ 70% between the lowest and highest pressure studied. It may be mentioned that at atmospheric pressure the trend reversal of εa has been observed for all the three homologues of CBnCB21,24,26 for which dielectric measurements are reported. It is thus tempting to associate the presence of the convex profile with the presence of the NTB phase below the N phase. However, in the light of a similar observation for a dimer not reported to have the NTB phase,32 suggests that perhaps the dimeric aspect and the soft nature of the central linking group, leading to drastic conformational changes with temperature (a topic to be discussed later), and not necessarily the presence of the NTB phase, are responsible for the trend reversal. We now return to our primary objective of looking at the elastic behaviour. Figures 7 and 8 present the temperature dependence of K11 and K33 at several pressures. The behaviour of K11 does not have any surprises, with the value increasing monotonically with decreasing temperature at a fixed pressure, or as a function of pressure at a fixed reduced temperature 9 ACS Paragon Plus Environment


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(T-TNI). The magnitude of increase at a certain T-TNI is, in fact, comparable to that seen for a calamitic monomer,33 and can be explained by the variation in εa. On the other hand, K33 exhibits contrasting features. There is again a trend reversal in the temperature dependence. More importantly, the magnitude of increase in the value at a fixed T–TNI is much larger. For instance, at T–TNI = 15K, between the lowest and highest pressures studied there is a factor of 5 increase in the value. This is much larger than not only K11, but also higher than the K33 increase in a calamitic monomeric system.33 Consequently, the anisotropy of the elastic constants, defined as the ratio K33/K11 exhibits a crossover from < 1 to >1 (see Figure 9). It may be mentioned that the ratio being 1 is almost always seen for calamitic monomeric systems. Again, the conformational argument, presented below, is able to account for the observed behaviour. Discussion Let us first recall the salient features in this high pressure investigation: (i) For the pure compound, CB7CB, the N-NTB transition is marked by a decrease in ε⊥ at lower pressures, whereas at higher pressures it increases. This effect is augmented by the addition of a rod-like monomeric component. (ii) The permittivity anisotropy has a trend reversal behaviour with temperature, the extent of which reduces with increasing pressure. (iii) The bend elastic constant gets enhanced by a large factor at the highest pressure investigated. (iv) In the pressure-temperature plane both the I-N and N-NTB phase boundaries have a positive slope, but the former has a larger slope, owing to which the range of the N phase increases with pressure. In the following we look at the molecular conformational aspect to explain these features. For the dimeric CBnCB wherein the two rigid mesogenic cyano biphenyl arms are connected by a floppy hydrocarbon spacer chain, absolute minimum energy conditions lead to two different types of conformers depending on the spacer (n) parity. An even parity, i.e.,


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even number of carbon atoms, will result in an essentially linear molecule, whereas an odd parity linker favours a bent conformation. If we relax the condition of absolute minimum energy, then other conformations also have to be considered. This consideration is validated since at finite temperatures thermal fluctuations of the nematic can support some of the conformers realized as local energy minimum states. Even without taking into account the higher-energy gauche forms of the spacer chain, two principle conformers are considered9, 28 for an odd parity molecule, such as the studied CB7CB: A horseshoe (or hairpin-like) conformer (see Figure 10a), wherein the angle between the two arms is ~ 30o, and an extended conformer (see Figure 10b) having an angle of 120o. A probability distribution mapping shows that the latter conformer has a smaller energy than the former. From an orientational ordering point of view, the extended conformer should be favoured at high order parameters, and the horseshoe at lower order parameters. This provides built-in temperature dependence for the population of the two conformers. As illustrated in Figure 10c the dipole moment (of the CN dipole having a value of ~ 4 D) contribution along and perpendicular to the director depends on the type of conformer. Accordingly, ε|| receives contribution which is negligible from the extended conformers, but substantial from each horseshoe conformer. In contrast, both conformers provide appreciable contributions to ε⊥, although that from the extended is higher than that from the horseshoe conformer. With this background let us look at the results obtained in the current study. On cooling the sample from the isotropic phase, C⊥ (ε⊥) drops as should be expected for positive εa materials, and continues to decrease in the N phase owing to the growing order parameter and the nematic potential. In combination with the fact ε|| also exhibits an increase in the immediate vicinity of the Iso-N transition, it can be safely argued that the molecules are predominantly in the horseshoe conformation. At atmospheric pressure, this status continues right through the NTB transition although the population of the extended conformers increases weakly with decreasing temperature 11 ACS Paragon Plus Environment


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(resulting in ε|| as well as εa decreasing on reducing the temperature). On increasing the pressure the scenario changes as the increased packing density favours the extended conformers than the horseshoe ones. Consequently, the predominance of the horseshoe conformer gets reduced, especially before the material transforms to the NTB phase, resulting in ε⊥ exhibiting an increase at the N-NTB transition in contrast to the opposite behaviour at lower pressures. The extent of trend reversal in εa is also diminished for the same reason, moving towards the behaviour typical of strongly polar monomeric materials such as alkyl cyanobiphenyl compounds. In the light of this it may be argued that addition of such monomeric substances should enhance the pressure-effect, a feature indeed observed: the change from a decrease to increase at the N-NTB transition occurs at lower pressures, and the step-size at the highest pressure is much larger for the X5 mixture than for the pure CB7CB. At elevated pressures the preference for the extended conformer can very well explain the behaviour of the elastic constants. Assembling the horseshoe conformers to form a nematic phase certainly favour the bend over the splay deformation of the nematic director. The situation is similar to that for the rigid bent core systems, wherein K11 is commonly observed to be higher than K33. The opposite would be true for the population inversion case with the extended conformers dominating. The results (Figures 7 and 8) indeed show that while increase in K11 is comparable to that seen even for monomeric alkyl cyanobiphenyls, K33 has a large increase under pressure. Higher the pressure more would be the dominance of the extended conformers, and thus less favour for the bend deformation resulting in an enhancement of K33. Finally, we discuss results of Xray diffraction measurements which corroborate the above ideas of the population change in the type of conformers. With the existing apparatus experiments could be performed only at atmospheric pressure. Ascribing the step-like variation in ε⊥ to be a measure of the population change at the N-NTB transition, and from the 12 ACS Paragon Plus Environment

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data presented in Figure S1, the X49.6 mixture can be considered to be a good candidate for the Xray measurements. Figure 11(a) presents the small angle region of the Xray diffraction scans obtained in the N (T = 75 oC) and NTB (T = 35 oC) phases of the X49.6 mixture. Diffuse reflections (characteristic of the nematic nature) with two different length scales are observed. For comparison, scans obtained for pure 7OCB (T=40 oC, N) and for pure CB7CB (T=50 oC, NTB) are presented in Figures 11(b) and 11(c) respectively, and represent the pattern obtained over the entire mesophase temperature range in the two materials. In contrast, to the data in Figure 11a, only a single peak is seen for the two pure materials. In addition to the sharp transitions, uniform field of view under the microscope, the spacings associated with the reflections also rule out the possibility of demixing to be the cause of the two-peak pattern for the X49.6 mixture. Molecular modelling shows that the molecular lengths of 7OCB, horseshoe and extended conformers of CB7CB are 1.96, 1.13 and 2.56 nm respectively. The peak for 7OCB with a spacing of 2.97 nm can be associated with the length of a pair of 7OCB molecules having a partial overlap, a feature well known with such molecules.34 On the other hand, the reflection for pure CB7CB occurs at 1.21 nm, which can be correlated with the length of its molecule from molecular model in the horseshoe conformation. This is in line with the aforementioned dielectric data showing that in pure CB7CB the horseshoe conformers are predominant. Now let us look at the data for the X49.6 mixture. The spacings of the two reflections are 1.27 nm and 2.32 nm. If phase segregation were to be the cause the second reflection should have at 2.97 nm as observed for pure 7OCB. A possible explanation that agrees with the presence of the two reflections is the following: The higher angle reflection arises due to contributions from non-paired 7OCB molecules as well as the horseshoe conformers of CB7CB. The lower angle one is caused by the extended conformers of CB7CB. Keeping this scenario in mind let us compare the patterns obtained for the X49.6 mixture at the two temperatures. As the temperature is lowered,



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the intensity of the higher angle peak representing the combined contribution increases marginally, that of the low angle peak due to the extended conformer of CB7CB increases by more than 50%. This is a clear indication of the population of the extended conformer appreciating significantly at a lower temperature, supporting our arguments made above. A similar feature must be occurring as a function of pressure accounting for the results observed in the present study. Xray diffraction experiments at elevated pressures would confirm this proposal. Summary In this first investigation on the influence of pressure on the α,ω bis(4,4’cyanobiphenyl)heptane exhibiting a transition between the regular nematic to the recently observed twist-bend nematic phase, we have observed several interesting features. In the pressure-temperature plane the N-NTB phase boundary has a much smaller slope than for the isotropic-N transition. The thermal behaviour of the permittivity, especially perpendicular to the nematic director (or orthogonal to the helical axis in the NTB phase), ε⊥, shows a clear change across the transition between the two nematics, the magnitude and sign of which is significantly influenced by application of pressure. In fact, the sign change from negative (decrease in ε⊥ from N to NTB) to positive (increase in from N to NTB) obtained for pure CB7CB at 1.10 kbar pressure is seen at atmospheric pressure by the addition of 50% of the monomer heptyloxy cyanobiphenyl.20 The dielectric anisotropy exhibits a trend reversal with temperature, which is again affected at elevated pressures. Pressure also has a strong effect on the Frank bend elastic constant, the magnitude of which is much larger than that for an archetypal compound, such as the monomeric octyloxy cynaobiphenyl. This is in contrast to the behaviour of the splay elastic constant. All these features have been explained using the relative population of the two conformers that CB7CB can exhibit. On lowering temperature or increasing pressure the extended conformer is more favoured over the horseshoe 14 ACS Paragon Plus Environment

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conformer, a feature substantiated by Xray diffraction experiments at atmospheric pressure. A theoretical model or simulation that tunes the population and evaluated the physical properties should be able to bring out the experimentally observed results.

†Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: S1 shows the thermal variation of permittivity for selected mixtures of 7OCB in CB7CB. S2 and S3 show the pressure-temperature phase diagram for X5 and X15 respectively.

Acknowledgement C.V. Yelamaggad thanks SERB, DST, Govt. of India for financial support under the Project No. SR/S1/OC- 04/2012.

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Dozov, I. On the Spontaneous Symmetry Breaking in the Mesophases of Achiral Banana-Shaped Molecules. Europhys. Lett. 2001, 56, 247-253.

5)

Henderson, P. A.; Imrie, C. T.; Methylene-Linked Liquid Crystal Dimers and the Twist- Bend Nematic Phase. Liq. Cryst., 2011, 38, 1407-1414.



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6)

Jansze, S.M; Felipe, A. M.; Storey, J. M. D.; Marcelis, A. T. M.; Imrie, C. T. A Twist-Bend Nematic Phase Driven by Hydrogen Bonding. Angew. Chem. 2015, 127, 653 –656.

7)

Krishnamurthy, K.S.; Kumar, P.; Palakurthy, N.B.; Yelamaggad, C.V.; Virga, E.G. Interfacial and Morphological Features of a Twist-Bend Nematic Drop. Soft Matter. 2016, 12, 4967- 4978.

8)

Panov, V. P.; Nagaraj, M.; Vij, J. K.; Panarin, Y. P.; Kohlmeier, A.; Tamba, M. G.; Lewis, R. A.; Mehl, G. H. Spontaneous Periodic Deformations in Nonchiral PlanarAligned Bimesogens with a Nematic-Nematic Transition and a Negative Elastic Constant. Phys. Rev. Lett. 2010, 105, 167801-1-4.

9)

Cestari, M.; Diez-Berart, S.; Dunmur, D.A.; Ferrarini, A.; Rosario de la Fuente, M.; Jackson, D. J. B.; Lopez, D. O.; Luckhurst, G. R.; Perez-Jubindo, M. A.; Richardson, R. M. et al, Phase Behavior and Properties of the Liquid-Crystal Dimer 1′′,7′′-bis(4-cyanobiphenyl-4′-yl) heptane: A Twist-Bend Nematic Liquid Crystal, Phys. Rev. E 2011, 84, 031704-1-20.

10) Tripathi, C. S. P.; Losada-P´erez, P.; Glorieux, C.; Kohlmeier, A.; Tamba, M. G.; Mehl, G. H.; Leys, J. Nematic-Nematic Phase Transition in the Liquid Crystal Dimer CBC9CB and its Mixtures with 5CB: A High-Resolution Adiabatic Scanning Calorimetric Study, Phys. Rev. E 2011, 84, 041707-1-7. 11) Meyer, C.; Luckhurst, G. R.; Dozov, I. The Temperature Dependence of the Heliconical Tilt Angle in the Twist-bend Nematic Phase of the Odd Dimer CB7CB. J. Mater. Chem. C, 2015, 3, 318-328. 12) Chen, D.; Porada, J. H.; Hooper, J. B. ; Klittnick, A; Shen, Y.; Tuchband, M. R.; Korblova, E.; Bedrov, D.; Walba, D. M.; Glaser, M. A. et al, Chiral Heliconical Ground State of Nanoscale Pitch in a Nematic Liquid Crystal of Achiral Molecular Dimers. PNAS, 2013, 110, 15931-15936. 13) Borshch, V.; Kim, Y.-K.; Xiang, J. ; Gao, M.; Jakli, A.; Panov, V.P.; Vij, J.K.; Imrie, C.T.; Tamba, M.G.; Mehl, G.H.; Lavrentovich, O.D. et al., Nematic TwistBend Phase with Nanoscale Modulation of Molecular Orientation. Nature Communications, 2013, 4, 2635. 14) Gautam Singh.; Jinxin Fu.; Agra-Kooijman, D. M.; Jang-Kun Song.; Vengatesan, M. R.; Srinivasarao, M.; Fisch, M. R.; Kumar. S.; X-ray and Raman Scattering Study of Orientational Order in Nematic and Heliconical Nematic Liquid Crystals, Phys. Rev. E, 2016, 060701-1-6. 16 ACS Paragon Plus Environment

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15) Parsouzi, Z.; Shamid, S.M.; Borshch, V.; Challa, P. K.; Baldwin, A. R.; Tamba, M. G.; Welch, C.; Mehl, G. H.; Gleeson, J. T.; Jakli, A.et al. Fluctuation Modes of a Twist-Bend Nematic Liquid Crystal, Phys. Rev. X 2016, 6, 021041-1-16 (2016). 16) Paterson, D.A.; Xiang, J.; Singh, G.; Walker, R.; Agra-Kooijman, D. M.; MartinezFelipe, A.; Gao, M; Storey, J.M.D.; Kumar, S.; Lavrentovich, O.D. et al., Reversible Isothermal Twist−Bend Nematic−Nematic Phase Transition Driven by the Photoisomerization of an Azobenzene Based Nonsymmetric Liquid Crystal Dimer, J. Am. Chem. Soc. 2016, 138, 5283−5289. 17) Panov, V. P.; Vij, J. K.; Mehl, G. H. Twist-Bend Nematic Phase in Cyanobiphenyls and

Difluoroterphenyls

Bimesognes,

Liq.

Cryst.,

2016,

http://dx.doi.org/10.1080/02678292.2016.1254289 18) Osipov, M. A.; Pająk, G. Polar Interactions between Bent–Core Molecules as a Stabilising Factor for Inhomogeneous Nematic Phases with Spontaneous Bend Deformations, Liq. Cryst., 2016, http://dx.doi.org/10.1080/02678292.2016.1247474. 19) However, an exception to this feature, has been just reported although the asymmetric arms indeed lead to a bent shape of the molecule, see Paterson, D.A.; Gao, M; Kim, Y-Ki; Jamali, A.; Finley, K. L.; Robles-Hernandez, B.; Diez-Berart, S.; Salud, J. ; Rosario de la Fuente, M.; Timimi, B. A. et al, Understanding the Twist-Bend Nematic Phase: the Characterisation of 1-(4-cyanobiphenyl-4’-yloxy)-6(4-cyanobiphenyl-4’-yl)hexane (CB6OCB) and Comparison with CB7CB. Soft Matter, 2016, 12, 6827-6840. 20) Yun, C.J.; Vengatesan, M. R.; Vij, J. K.; Song, J.K. Hierarchical Elasticity of Bimesogenic Liquid Crystals with Twist-Bend Nematic Phase. Appl. Phys. Lett. 2015, 106, 173102-1-5. 21) Srividhya Parthasarathi; Shankar Rao, D. S.; Palakurthy, N. B.; Yelamaggad, C. V.; Krishna Prasad, S. Binary System Exhibiting the Nematic to Twist-Bend Nematic Transition: Behavior of Permittivity and Elastic Constants. J. Phys. Chem. B 2016, 120, 5056-5062. 22) Meyer, R. B. in Molecular Fluids, ed. Balian, R. and Weill, G. Gordon and Breach, New York, 1976, vol. XXV-1973 of LesHouches Summer School in Theoretical Physics, pp. 273–373.



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23) Lorman, V. L.; Mettout, B. Unconventional Mesophases Formed by Condensed Vector Waves in a Medium of Achiral Molecules. Phys. Rev. Lett. 1999, 82, 940943. 24) Robles-Hernández, B.; Sebastián, N.; Rosario de la Fuente, M.; López, D. O.; DiezBerart, S.; Salud, J.; Blanca Ros, M.; Dunmur, D. A.; Luckhurst, G. R.; Timimi, B. A. et al., Twist, Tilt, and Orientational Order at the Nematic to Twist-Bend Nematic Phase Transition of 1”,9”-bis(4-cyanobiphenyl-4’-yl) nonane: A Dielectric, 2H NMR, and Calorimetric Study. Phys. Rev. E, 2015, 92, 062505-1-16. 25) Cachitas, H.M.M. Thesis, Instituto Superior Técnico, Lisboa, November 2013, Portugal. 26) Balachandran, R.; Panov, V.P.; Vij, J.K.; Kocot, A.; Tamba, M.G.; Kohlmeier, A. ; Mehl, G.H.; Elastic Properties of Bimesogenic Liquid Crystals. Liq. Cryst. 2013, 40, 681-688. 27) Sandhya, K. L.; Shankar Rao, D.S.; Krishna Prasad, S.; Hiremath, U.S.; Yelamaggad, C.V. Dielectric Studies Under High Pressure on Strongly Polar Liquid Crystals Exhibiting Monolayer Smectic A Phase. Thermochimica Acta 2007, 452, 65-70. 28) Hernandez, B. R.; Sebastian, N.; Salud, J.; Berart, S. D.; Dunmur, D. A.; Luckhurst, G. R.; Lopez, D. O.; Rosario de la Fuente, M. Molecular Dynamics of a Binary Mixture of Twist-Bend Nematic Liquid Crystal Dimers Studied by Dielectric Spectroscopy. Phys.Rev. E. 2016, 93, 062705-1-7. 29) Madhuri, P.L.; Krishna Prasad, S.; Hiremath, U. S.; Yelamaggad, C. V. PhotoDriven Giant Reduction of the Frank Elastic Constants in a Bent-Core Nematic Liquid Crystal. Appl. Phys. Lett. 2014, 104, 241111-1-5. 30) Deuling, H. J. Deformation of Nematic Liquid Crystals in an Electric Field. Mol. Cryst. Liq. Cryst. 1972, 19, 123−131. 31) Gruler, H.; Elastic Properties of the Nematic Phase Influenced by Molecular Properties. J. Chem. Phys. 1974, 61, 5408-5412. 32) Balachandran, R.; Panov, V. P.; Vij, J. K.; Shanker, G.; Tschierske, C.; Merkel, K.; Kocot, A. Dielectric and Electro-Optic Studies of a Bimesogenic Liquid Crystal Composed of Bent-Core and Calamitic Units, Phys. Rev. E 2014, 90, 032506-1-7. 33) Bapat, P. N.; Shankar Rao, D.S.; Krishna Prasad, S.; Hiremath, U.S. Effect of Hydrostatic Pressure on the Frank Splay and Bend Elastic Constants. Thermochimica Acta 2012, 537, 65-69. 18 ACS Paragon Plus Environment

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34) Leadbetter, A.J.; Frost, J.C.; Gauglan, J.P.; Gray, G.W.; Mosley, A. The Structure of Smectic A Phases of Compounds with Cyano End Groups. J. Phys. France 1979, 40, 375-380.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 1: The slope values obtained for different phase boundaries for the three materials. X0 X5 X15

Iso - N 57.4 ± 1.3 56.9 ± 0.9 42.3 ± 1.2

N - NTB 38.8 ± 1.2 36.8 ± 0.7 25.9 ± 0.6


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


CB7CB

Iso

114.1oC

N

102.3oC

NTB

7OCB

Iso

73.8 oC

N

Figure 1: Molecular structures and transition temperatures of the covalent dimer CB7CB that exhibits the twist bend nematic (NTB) phase in addition to the regular nematic (N), and the monomeric 7OCB compounds.



9

1.0

ε⊥

C⊥/CIso

6 100

o

T ( C)

115

(a)

0.8

100

130

o

160

190

T ( C)

C/CIso

2k b ar

c||

N

0. 2

1k

bar

(c)

Iso

1.02

(b)

1. 5

0.89

C⊥/CIso

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 32

0.84

c⊥

NTB

0.74 80

120

o

102

160

112

o

122

132

T ( C)

T ( C)

Figure 2: (a) Influence of the applied pressure on the thermal variation of capacitance normalized with respect to that in the isotropic phase for pure CB7CB; pressure values are P = 0.21, 0.48, 0.83, 1.10, 1.31 and 1.52 kbar respectively for the scans from left to right. Especially to be noted is that across the N-NTB transition the value decreases at low pressure, but shows an increase at higher pressure as shown in (b). (c) Exemplary thermal variation of C|| and C⊥ at a fixed pressure of 0.21 kbar. Inset of Figure 2(a) shows thermal variation for ε⊥ for the pure material at atmospheric pressure. In the main diagram as well as the inset, the isotropic-nematic and N-NTB transition points are indicated by downward and upward arrows, respectively for representative pressures.


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1.0

(a) C⊥/CIso 0.8

100

130

(b) 0.80

o

T ( C)

160

190

P = 1.31 kbar X5

C⊥/CIso

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


re u P

0.77 130

145

o

160

T ( C)

Figure 3: (a) Influence of the applied pressure on the thermal variation of capacitance normalized with respect to that in the isotropic phase for X5; pressure values are P = 0.21, 0.41, 0.62, 0.83, 1.03, 1.31, 1.52 and 1.72 kbar respectively for the scans from left to right. The interesting point here is that at any given pressure the change across the N-NTB transition is enhanced from the variation seen for the pure compound. To illustrate this point, the profiles at a fixed pressure for pure CB7CB and the mixture X5 are given in the Figure (b). The isotropic-nematic and N-NTB transition points are indicated by arrows for representative pressures in Figure (a).



210

T ( C)

Iso

o

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

150

N

NTB 90 0.0

0.5

1.0

1.5

P ( kbar )

Figure 4: Pressure-Temperature (P-T) phase diagram for pure CB7CB displaying the isotropic-nematic and nematic-NTB phase boundaries. It is evident that the thermal range of the nematic phase increases with increasing pressure.


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48

C (pf) 44

3

Vth (V)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0 -25 T (oC) 0 red

NTB

40 2

V (volts)

10

18

Figure 5: Freedericksz transformation profiles at different temperatures spanning the thermal range of the nematic phase at a constant pressure of 0.83 kbar; temperature values are T = 160.5, 157.3, 154.6, 152, 149.5, 146.6, 143.8, 139.5 oC respectively for the scans from top to bottom. A representative scan in the NTB phase (T=133.7oC) is also shown. The inset presents the extracted threshold voltage Vth as a function of reduced temperature {Tred = (TTIN), where TIN is the isotropic-nematic transition temperature} at P=0.83 kbar.



1.52

2.5 0 1.1

εa

1.3

1

3 0.8

62

1k 0.2

-3

-1

dεa/dTred ( x 10 K )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1.0

-40

ba

r

22 0.0 P (kbar)

-30

1.6

-20

-10

0

o

Tred ( C)

Figure 6: Dependence of dielectric anisotropy (εa) on Tred (=T-TNI, TNI is the nematic to isotropic transition temperature) for different pressures (indicated against each data set in the nematic phase). At any Tred value, εa increases as P is increased. The inset shows the pressure dependence of the slope dεa/dT calculated from the data at temperatures below the maximum point for each data set.


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1.52

18

K11 (pN)

1.31 1.10 0.83

10 10

K11 ( pN)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.21 kbar

7

2

0.0 P (kbar) 1.6

-40

-30

o

-20

-10

0

Tred ( C)

Figure 7: Thermal variation of the splay elastic constant (K11) for pure CB7CB at various pressures (indicated against each data set). K11 increases with increase in pressure, the extent of increase being higher for larger Tred. The inset shows such a variation at Tred = -15K.



1.52

18

1 1.3

K33 (pN)

1.10

0.83

10 16

K33 ( pN)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.21 kbar

2

2

0.0 P (kbar) 1.6

-40

-30

o

-20

-10

0

Tred ( C)

Figure 8: Thermal variation of the bend elastic constant (K33) for pure CB7CB at different pressures (indicated against each data set). Interestingly the trend reversal behaviour in the value is augmented with pressure. The value at a fixed Tred = -15K indicates that K33 increases by more than a factor of four, as depicted in the inset.


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1.6

K33/K11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


r kba 2 1.5

1.0

0.21 kbar 0.4

-30

-20

-10

0

o

Tred ( C )

Figure 9: The ratio of the elastic anisotropy K33/K11 against Tred for two representative pressures 0.21 kbar and 1.52 kbar. The dashed horizontal line represents the isotropy point, K33=K11.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 10: Two possible molecular conformations representing the extreme situations of (a) horse-shoe and (b) extended conformers. (c) Illustration to show that in the latter case the dipoles moments of the terminal CN dipoles contribute a finite value to the horizontal direction (X), which will be normal to the director in a nematic.


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10

o

T=75 C

Int. (arb. units)

(a)

0 o

T=35 C

10

0 3

5

7

9

2θ (deg) (b)

o

T=40 C

12

Int. (arb. units)

60

Int. (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(C) o

T=50 C

0

0 2.5

3.0

3.5

5

2θ ( deg )

7

9

2θ (deg)

Figure 11: Low-angle Xray diffraction profiles for (a) the X49.6 mixture, and the pure compounds (b) 7OCB and (c) CB7CB.



TOC Graphic 0.2

1.4

P (kbar)

2.2

K33/K11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fixed P

, Varyin

gT

1.0 , Varyin Fixed T

-10

o

gP

Tred ( C )

-30


Page 32 of 32

Effect of Pressure on Dielectric and Frank Elastic Constants of a

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