Conformational flexoelectricity in nematic liquid crystals

2014 Using the direct flexoelectric effect in an hybrid (homeotropic-planar) nematic cell, we have measured the bulk flexoelectric coefficient e* for two cyanobiphenyl compounds, 8CB and 8OCB. For 8CB, the flexo coefficient is comparable in sign and magnitude with that of MBBA, i.e. e* ~ + 10-4 cgs. 8OCB presents an anomalously large and negative e* ~ 5 x 10-4 cgs. The small influence of the cyano group can be explained by molecular pairing. The large effect from the oxygen is interpretated by a coupling between the macroscopic bend distortion and conformations of the alkoxy chains, i.e. as conformational (dipolar) flexoelectricity. The temperature dependence of e* shows an unexpected proportionality to the nematic order parameter S. This may be related to the steric constraint, from the rigid rod cores, on the entropy of the alkoxychains. J. Physique LETTRES 44 (1983) L-817 L-822 ler OCTOBRE 1983, Classification Physics Abstracts 61.30 78.20H Nematic liquid crystals are flexoelectric, i.e. present a volume electric polarization P when distorted. In his first paper [1], R. Meyer had imagined that P was related to molecular dipoles along (or across) pearlike (or banana shaped) nematic molecules. Later, it was argued [2] that, in the case of weak distortions, the only flexoelectric bulk effect was due to the molecular quadrupolar momentum. According to the Bordeaux group [3], the temperature dependence of the flexoelectric effect should give information on its molecular nature. The quadrupolar contribution was expected to give flexo coefficients varying as the nematic order parameter S, contrary to the dipolar contribution which gives a S 2 dependence. The experimental results on molecules like MBBA, or more symetrical ones like tolanes have reinforced the general idea that the flexoelectric effect in nematics has a quadrupolar origin. In a recent work [4], we have described the first observation of the direct bulk flexoelectric effect in the nematic MBBA (methyloxybenzyli(*) Present address : Institute of Solid State Physics, Sofia, Bvd. Lenin 72, Bulgaria. L-818 JOURNAL DE PHYSIQUE LETTRES denebutylaniline). Using the same technique, we have measured the flexoelectric constant for two nematic compounds 8CB and 80CB (octyl and octyloxycyanobiphenyls) which differ only by the presence of a molecular dipole related to the oxygen. Our results give the first experimental evidence of conformational dipolar flexoelectricity with an unexpected S-like temperature dependence. Our experimental set up has already been described [4]. A nematic cell with antagonistic (planar and homeotropic) anchoring is submitted to an electric field E parallel to the plates and perpendicular to the nematic director. The DC electric field induces a torque on the bend splayed nematic texture, and creates a twist which is measured by the observed rotation of polarized light propagating through the sample. The experiment gives the ratio ~e~/K of the flexoelectric coefficient to an effective Frank curvature elastic constant K for the splay bend cell. We have plotted on figure 1 the observed optical texture twist 0, versus the applied electric field, for the two compounds 8CB (curve a) and 80CB (curve b). The two samples have comparable thicknesses, d = 12 ~m for 8CB and d = 15 ~m for 80CB. The data are taken at T = 36.3 ~C for 8CB, i.e. at 2.7 oC below Tc = 39 ~C, and at T = 77.0 ~C for 80CB i.e. 4.3~ below T~ = 81.3 ~C. All the data represent static distortion of the nematic texture. No flow is observed for such thin samples in the range of the used electric fields. Fig. 1. Angle of rotation of the polarized light propagating through the sample, versus the applied electric field for two compounds at comparable temperatures : a) 8CB at 2.7 ~C below T~ ; b) 80CB at 3.3 ~C below T~. Let us first describe the results from 8CB. For low values of the field (E 20-30 V/mm), 4> shows a linear dependence on E. Using the formula [4] e*/K = ~~/Ea~ we derive e*/K = + 0.227 x 103 cgs, i.e. the same sign as for MBBA with a comparable value (e*jK = + 0.25 x 103 cgs). For higher values of the field, (E > 30-50 V/mm) 0 increases sharply up to ± 90~. The sharp increase of ~ must be attributed to the destabilizing dielectric torque density E. E2 sin 4> cos 4> which tends to align the molecules along E (4) = 9Qo) because 8CB has a large positive dielectric anisotropy 8a ~ 10. The resulting Freedericksz instability threshold field Eth is given by Ea E; ~ Kn2 jd2. Eth is of the order of 1 cgs, comparable to the observed value, Note that the dielectric torque, quadratic in E, always adds its effect to the flexoelectric L-819 CONFORMATIONAL FLEXOELECTRICITY IN NEMATICS torque P x E. The observed lack of symmetry in figure 1 a is related to a small initial tilt of the molecular orientation compared to the normal to E. This large field effect was not observed in our previous experiment with MBBA, since, for this compound was negative, resulting in a stabilizing dielectric torque. We now describe our results for 80CB. The first observation is that the linear range of 0 close to zero field has a larger slope, of opposite sign compared to 8Ca. We find e*/K = -1.4 x 103 cgs. e*/K is a factor 5 larger than for 8CB and MBBA. Increasing the field, we find again a sharp increase of cp around E ~ 20-30 V/mm. Finally, the molecular twist saturates of about 0 = ± 90~, as for 8CB. As previously, we understand the sharp increase of 0 by the destabilizing effect of the dielectric torque. However, as the slope OIE in the linear region is larger than for 8CB, the dielectric Freedericksz instability happens with an apparent threshold lower than for 8CB. 8CB and 80CB have in common a large longitudinal dipole ( ~ 4.3 Debye) [5] from the C = N group, and a tendency to form antiferroelectric pairs, in the smectic A phase, where they build layers with a thickness 1.4 times the molecular length [6]. The only electric difference between these molecules comes from the oxygen dipole P, of the order of 1.25 Debye [5], which gives both longitudinal and transverse contributions. We must attribute the large increase (and sign change) of e*/K in going from 8CB to 80CB to a large dipolar contribution from the oxygens. To explain the relatively small influence of the large CN dipoles on the flexo coefficient, we assume that 8CB and 80CB form also antiferroelectric pairs in the nematic phase. For these pairs, the longitudinal components of the oxygen dipoles cancel each other. The transverse components cancel also on the average in a non distorted texture. In the presence of a macroscopic bend, the alkoxychain conformations which fit the director curvature are favoured, and the transverse oxygen dipoles become correlated. We visualize the 80CB molecule, of length m 30 A, as a rigid rod, the cyanobiphenyl group, and a flexible tail, the octyl chain, rotating around the oxygen, on a cone of half angle cx ’" 600, centred along the rigid core. The maximum transverse molecular polarization is of the order of P for a molecular bend", a Jm. Calling V 300 A3 the mean molecular volume, this results in a bend flexo coefficient Neglecting the contribution to the splay constant e1 coming from the molecules oriented transverse to the director, and using the relationship [4] e* = e1 e3, we get an estimate of e* of the right sign (negative) and of the right order of magnitude. We can on the other hand calculate el and e3 for 80CB from our measurement of e* and the data of reference 3, giving for the same temperature ei + e3 I = 5 x 10-4 cgs. Taking K ~ K2 N 3 x 10-’ cgs, we obtain e* = 5 x 10-4 cgs, i.e. e3 = 5 x 10-4 cgs and ei ~ 0, or e1 = 5 x 10-4 cgs and e3 = 0. With our interpretation which implies a large positive e3, e1 + e3 should be positive. A direct measurement of the sign of the quadrupolar coefficient e1 + e3 would be important to confirm our model. To further verify our interpretation, we have studied the temperature dependence of the bulk flexoelectric coefficient e*, by measuring the slope of the ljJ(E) curve versus temperature. Our data are plotted on figure 2, for two samples of thicknesses d = 15 ~m and 33 Jln1. We observe a large temperature effect, e*/K decreasing by a factor 5 from the T ~ down to T ~ T N 15 ~C. For comparison, we have also measured by the same technique e*/K for MBBA. In this latter compound, the temperature effect is very weak and compares with the experimental uncertainty. As K varies as S 2, the data for 80CB show clearly that e* is not proportional to S 2, as one would predict from the Bordeaux Group analysis [3]. To check the possible dependence of e* on S, we have measured, on the same cell, the magnetic Freedericksz critical field ~1~, by placing the L-820 JOURNAL DE PHYSIQUE LETTRES sample inside a magnet H is aligned in the same direction as E, in the previous experiment, i.e. H is perpendicular to the rubbed direction. One can show [7] that the elastic energy density for a twist 0 is the same for the flexoelectric and the magnetic induced distortion. He is then given by the relationship Xa H~ K(7r/J)~. H; is proportional to K/~, i.e. to S. Using the K/xa values from He and the estimated value xa/S = 2 x 10-’ cgs (the right figure for MBBA), we can plot (Fig. 3) the temperature dependence of e*/S for 80CB and MBBA. We see immeFig. 2. Flexoelectric coefficient e* divided by K (a Frank curvature constant) versus the temperature for 80CB and MBBA. T c is the transition temperature between isotropic and nematic phases. Fig. 3. Flexoelectric coefficient e* divided by S (the order parameter of the nematic phase) versus temperature. S is obtained by magnetic Freedericksz instability in the same cell. L-821 CONFORMATIONAL FLEXOELECTRICITY IN NEMATICS diately that in a 10 ~C range below 7~, 80CB has a flexo coefficient e* proportional to S. At lower temperatures, the observed decrease should be related to the divergence of the bend and twist Frank constants due to the smectic A pretransitional order fluctuations. For MBBA, the temperature dependence is less clear; our data are not accurate enough, but it was previously established [3] that the flexo coefficient was more S-like than S 2-like. For 8CB, the observed effect is so weak compared to the quadratic dielectric distortion that we have not been able to measure a well defined temperature dependence. We must try to understand why an almost purely dipolar flexoelectric effect depends linearly (and not quadratically) on the nematic order parameter S. The predicted 82 law for e* comes from the anisotropic Van der Waals interaction between rigid rod molecules. Assume a rigid conical molecule; it would induce in a ferroelectric ordered system a spontaneous splay a. In the presence of a macroscopic splay the Frank curvature energy is 2 K(div n ± a)2. The difference in free energy between two antiparallel molecular orientations is ’" Ka div n. The relative number of aligned molecules contributing to the flexo effect is ~ exp( Ka div n/kB T) 1 ~ Ka div n/kB T, where kB is the Boltzmann constant. The flexo coefficient is then proportional to K, i.e. to 82. In the case of the cyanobiphenyl, the CSH17 chain is a non rigid, weakly polarizable part of the molecule. The chain does not participate to the nematic ordering. On the contrary, it is acted upon by the rigid rod neighbouring molecules. The difference in free energy between a well or badly aligned chain in presence of a curvature distortion should imply only an entropic term. Our data suggest that the steric constraint on the chain entropy could be a function of S (and S 2). In conclusion, we have measured the bulk flexoelectric coefficient e*/K on two closely related biphenyl compounds, 8CB and 80CB in their nematic phases. For 8CB, we find e*/K = 0.27 x 103 cgs at 36.3 ~C, i.e. a value and sign comparable to MBBA. For 80CB, we measure e*/K = 1.4 x 103 cgs at 77 ~C. The absence of significant contribution from the large longitudinal cyano group dipole can be attributed to a molecular pairing. The large increase and change of sign of e* for 80CB is attributed to a dipolar contribution from the additional oxygen. We interpretate the correlated orientation of the oxygen dipoles across a bend by a coupling between configurations of the alkoxy chains and the bend curvature distortion of the director. In a sense, the non rigid molecules present a « banana » shape (in the sense of Meyer [ 1 ] ) induced by the mechanical distortion. This conformational flexoelectric polarization in nematics was previously discussed by Derjanski [8], but considered as inefficient for paraazoxyanisole, which has very short (methyloxy) end chains. In most of the nematic range, the bulk flexo coefficient e* in 80CB shows a linear dependence on the nematic parameter. We interpretate this anomalous behaviour by relating the orientation of the oxygen dipole responsible for the flexoelectricity, to a simple change in entropy of the octyl chain constraint by the nematically ordered molecular rigid cores. This steric interaction is reminiscent of an old proposal by Straley [9], but applied here to non rigid molecules. Finally, we can remark that the large flexo coefficient recently observed in discotic materials [10] could have a dipolar origin since the end chains of the used triphenylene discotic molecules are alkoxy chains.