Alignment of cholesteric liquid crystals using the ...

Alignment of cholesteric liquid crystals using the macroscopic flexoelectric polarization contribution to dielectric properties B. I. Outram and S. J. Elston Citation: Appl. Phys. Lett. 103, 141111 (2013); doi: 10.1063/1.4824034 View online: http://dx.doi.org/10.1063/1.4824034 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v103/i14 Published by the AIP Publishing LLC.

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APPLIED PHYSICS LETTERS 103, 141111 (2013)

Alignment of cholesteric liquid crystals using the macroscopic flexoelectric polarization contribution to dielectric properties B. I. Outrama) and S. J. Elston Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdom

(Received 29 July 2013; accepted 17 September 2013; published online 2 October 2013) By considering the contribution of flexoelectricity to a cholesteric liquid crystal’s dielectric permittivity, we show that both flexoelectric and dielectric effects allow the alignment of the Uniform Lying Helix (ULH) in devices with in-plane-switching (IPS) electrodes. The nonuniformity of fields produced by IPS electrodes is found to be crucial to allow ULH formation. The ULH is stabilised using homeotropic alignment conditions without polymer networks. Thus, a framework has been developed and tested for aligning and making stable cholesteric liquid crystals that incorporates both flexoelectric and dielectric field effects. Applications include bistable and C 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4824034] ultra-fast display technology. V

Cholesteric liquid crystals (CLCs) have been exploited and commercialised within bistable reflective display technology1,2 and have the potential to provide sub-millisecond switching times in transmissive displays when aligned in the Uniform Lying Helix (ULH) geometry.3,4 A key component in any CLC technology is the alignment of the helicoidal axis in a desired orientation, which depends on the application. ULH alignment has proven particularly problematic and has been the focus of a large amount of research.5–10 In most liquid crystal technology, field induced reorientation of the director is achieved via a coupling to the material’s dielectric anisotropy, De, which here we refer to as the dielectric effect. However, in liquid crystals with very low De, the dielectric effect cannot be exploited. In this paper, we discuss the contribution to the dielectric permittivity of CLCs due to flexoelectricity, in which a field couples to curvature distortions in liquid crystals, and explain how it can also be used to align CLCs. In particular, we examine the case of interdigitated electrodes, which provide a field in the plane of a liquid crystal device, and allow the alignment of the ULH geometry. ULH alignment of materials whose field interactions are either flexoelectric or dielectric dominated are demonstrated experimentally. The inhomogeneity of fields produced by interdigitated electrodes is found to be crucial to the alignment technique. It is known that cholesteric liquid crystals naturally adopt a Grandjean geometry in the absence of any fields in cells with planar alignment, but we demonstrated that this problem can be mitigated by employing a weak homeotropic alignment condition, which has been shown to destabilise the Grandjean in favour of the lying helix geometry and allow the ULH to remain stable over long periods.7,8,11 IPS cells used in this study contain a series of interdigitated electrodes that are etched onto one glass substrate surface. Electrodes are 5 lm wide and separated by a gap of 9 lm. A voltage difference between alternating electrodes results in a non-uniform field with a large component in the plane of the device. A simulation of the electric field, executed using a commercial electrostatics finite-element a)

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0003-6951/2013/103(14)/141111/5/$30.00

software package (COMSOL multi-physics), is shown in Figure 1, and shows several significant features. There is a large component of the field in the plane of the device between the electrodes; however, the field is non-uniform and much stronger near the electrode edges. The field also has a vertical component, and is purely vertical directly above the electrodes. For a material with De > 0, the dielectric energy is mini^ is parallel to an applied field E, mised when the director n ^ such that n E ¼ jEj. In the case of an undistorted CLC, the director can never be uniformly parallel to the field. However, the dielectric energy is minimum where as much of the director is parallel to the field as possible, which occurs when the helicoidal axis is perpendicular to the field. We can determine the difference in energy between cases where the helicoidal axis is parallel and perpendicular to the field by considering the dielectric energy given by 1 ^ EÞ2 : fdielectric ¼ Dee0 ðn 2

(1)

Let us allow E ¼ Ex x^. For the case that the helicoidal axis is parallel to the field, nx ¼ 0 and therefore fdielectric ¼ 0. On the other hand, if the field is perpendicular to the helicoidal axis,

FIG. 1. A numerical simulation of the electric field in a 5 lm thick device with interdigitated electrodes. The simulation shows a cross-section of a single repeating unit of 28 lm, in which the electrodes are separated by 9 lm and are 5 lm wide.

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Appl. Phys. Lett. 103, 141111 (2013)

such that, for example, nx ¼ cosðqzÞ, then the dielectric energy becomes 1 fdielectric ¼ Dee0 cos2 ðqzÞE2x : 2

(2)

Averaging over a half-pitch repeating unit of the helicoid, we can take hcos2 ðqzÞi ¼ 1=2. The difference between fdielectric for cases with the helicoidal axis parallel and perpendicular to the field is therefore given by 1 df ¼ Dee0 E2x : 4

(3)

If the liquid crystal is not otherwise confined, then a reorienting torque will align the helicoidal axis perpendicular to the field in the case of a positive dielectric anisotropy. In the case of a negative dielectric anisotropy, De < 0, then the difference in energy between the two alignment cases is reversed, and the helicoidal axis will align parallel to the field. For typical material parameters of a mono-mesogenic liquid crystal (De ¼ 10), and a field of 10 V lm1, we find that dfeffective ¼ 250 lJ m3. The field that is produced by interdigitated electrodes, shown in Figure 1, has components in the plane and out of the plane of the liquid crystal device, but always within a plane perpendicular to the electrodes. Therefore, in order for the helicoidal axis orientation to be uniformly perpendicular to the field, the helicoidal axis must orient parallel to the electrodes. If the field were uniform, either purely in the plane of the device or purely vertical, then there would be degeneracy in the energy of the helicoidal axis orientation about the applied field. Therefore, field inhomogeneity breaks degeneracy in the helicoidal axis orientation, and is crucial in allowing uni-

directional ULH alignment. Indeed, in cells that have standard planar indium-tin-oxide (ITO) electrodes on top and bottom in order to produce a uniform vertical field, a focal-conic with the ULH oriented randomly in the plane of the device is commonly observed for materials with positive dielectric anisotropy when a field is applied.12–14 For a CLC in which there is no flexoelectric polarization, the effective dielectric permittivity along the helicoidal axis is e? , and perpendicular to the helicoidal axis is ðek þ e? Þ=2. However, the flexoelectric polarization enhances the effective dielectric permittivity perpendicular to the helicoidal axis of a cholesteric (see Ref. 15 for a derivation) by an amount ! 1 ðe1 e3 Þ2 : (4) eflexo ¼ e0 2ðK1 þ K3 Þ Therefore, the difference between the effective permittivity parallel and perpendicular to the helicoidal axis is given by ek þ e? 1 þ eflexo ¼ ðDe þ 2eflexo Þ; (5) De0 ¼ e? 2 2 where De0 is the cholesteric effective dielectric anisotropy. In relation to De0 , the flexoelectric contribution to the permittivity is equivalent to a positive De, independent of the sign of e1 e3 . Bimesogenic materials have a very small De; however, their large e1 e3 allows them to be reoriented using a field whose frequency is sufficiently small to couple to flexoelectric polarization. The free energy difference between parallel and perpendicular alignment of the helicoidal axis with the field, after considering now both flexoelectric and dielectric contributions to the effective permittivity, is given by

FIG. 2. Polarizing optical micrographs of 5 lm planar IPS cells filled with cholesteric material ZLI-4792 þ 2.7 wt. %R5011. (a) On cooling from the isotropic phase, the Grandjean texture forms. The application of 10 Vrms lm1 at 1 kHz results in a ULH texture, which is shown here with the helicoidal axis (b) parallel and (c) at 458 to the polarizer. (d) One second after the field is removed, the ULH reverts to a Grandjean texture, due to the planar surface alignment.

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FIG. 3. Polarizing optical micrographs showing a high-viscosity bimesogenic cholesteric mixture (a) forming just below the nematic-isotropic transition temperature, (b) having formed the Grandjean, (c) on application of 20 Vrms lm1 at 100 Hz parallel to the polarizer, (d) rotated by 45 ; (e) and (f) are taken immediately after the field is removed. The field promotes the ULH alignment, but the cholesteric reverts to the Grandjean texture after several minutes. A relatively low frequency of 100 Hz is used to drive the liquid crystal in order to ensure that the flexoelectric polarization is not suppressed, which happens at frequencies greater than many hundreds of Hz for the bimesogenic mixture used here.

! 1 0 2 1 ðe1 e3 Þ2 2 Dee0 þ df ¼ De e0 E ¼ E : K1 þ K3 2 4

(6)

Since bimesogenic materials have De 0, only the second term is important. Estimating typical parameters for bimesogenic materials (e1 e3 ¼ 10 pCm1, K1 þ K3 ¼ 10 pN) then for a field strength of E ¼ 10 V lm1, we find, df ¼ 25 lJ m3. This is smaller than the df ¼ 250 lJ m3 in the previous case of a typical positive dielectric anisotropy, monomesogenic liquid crystal, andp therefore we may expect that a ffiffiffiffiffi larger field (by a factor of 10) will be required to orient bimesogenic liquid crystals. In cells with standard ITO electrodes on top and bottom substrate surfaces that produce a uniform transverse field, filled with a bimesogenic material, the application of a field that couples to the flexoelectric polarization results in a focal conic texture, in which the helicoidal axis is perpendicular to the field but randomly oriented in the plane of the cell.15,16 This behaviour is analogous to the same experiment using

mono-mesogenic materials described earlier. Again, this suggests that the inhomogeneity in the field produced by interdigitated electrodes is crucially important for field-induced ULH alignment. Here, it has been shown that the effect of flexoelectricity on the effective dielectric anisotropy of cholesteric liquid crystals is equivalent to that of a positive De; both give the cholesteric a negative effective dielectric anisotropy, in which the permittivity along the helicoidal axis is smaller than that perpendicular. We have explained how the effective dielectric anisotropy resulting from the two effects can be used to uniformly orient the helicoidal axis in cells with interdigitated electrodes, including the crucial role of the field inhomogeneity produced by interdigitated electrodes. Now we will discuss the experimental results. Figure 2 shows optical polarizing microscope photographs of a 5 lm thickness, planar-aligned IPS cell (electrode width 5 lm, gap between electrodes 9 lm), containing a positive dielectric anisotropy, mono-mesogenic cholesteric mixture ZLI-4792 doped with 2.7 wt. % R5011. On cooling from

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isotropic, a Grandjean texture forms owing to planar surface alignment. With the application of 10 Vrms lm1 at a ULH texture forms, as expected from the discussion in the theory section. A driving frequency of 1 kHz is used in order to remove any influence of ionic impurities at lower frequencies. On removal of the field, the liquid crystal reverts to the Grandjean texture within approximately one second, shown in Figure 2(d). The Grandjean is the lowest energy state for CLCs within cells with planar surface alignment, due to the compatibility of the Grandjean structure with the planar condition. Figure 3 shows polarising micrographs of the same type of interdigitated electrode cell filled with low-dielectricanisotropy bimesogen mixture MDA-4407 mixed with 1.8 wt. % of chiral dopant R5011. On application of 20 V lm1, defects form and a ULH texture forms, as expected. As suggested from the discussion in the theory, a larger field was indeed required to align the bimesogenic liquid crystal, which corresponds to the different df calculated for the cases of flexoelectric and dielectric dominated materials. Flexoelectric switching is suppressed at frequencies of several hundred Hz in the bimesogenic liquid crystal, and so a driving frequency of 100 Hz was chosen. The bimesogenic material used is known to have a very low conductivity, and so there is no significant influence of ionic impurities on the switching. On removal of the field, the ULH texture remains for some time. The bimesogenic liquid crystal takes a relatively long time (several minutes) to return to the Grandjean texture, which may be due its relatively high viscosity. Alignment of the ULH using bimesogenic CLCs in cells with interdigitated electrodes has also been observed by Gardiner et al.10 While the two examples and discussion above demonstrate that both flexoelectric and dielectric effects can be

Appl. Phys. Lett. 103, 141111 (2013)

used to orient the ULH in cells with interdigitated electrodes, the resultant ULH is unstable, and reverts to the Grandjean on field removal. This observation has also been made by Gardiner et al., who suggested that after alignment using interdigitated electrodes, a polymer network could be used to stabilise the ULH.10 However, a homeotropic alignment can stabilise the ULH from reverting to the Grandjean.8 Figure 4 shows analogous polarizing microscope images to those in Figure 2, of cells containing the mono-mesogenic ZLI-4792 mixture, but this time with a homeotropic alignment created using lecithin. In contrast to the case with planar alignment, which returns to the Grandjean geometry within approximately one second after removing the field, the homeotropic anchoring makes the ULH stable indefinitely. This is advantageous, as it removes the requirement for a polymer network, making the method far less complicated. By considering the effective dielectric permittivity of cholesteric liquid crystals, we have explained how interdigitated electrodes can be used to promote ULH alignment via a coupling of the field to both the dielectric anisotropy and via the flexoelectric contribution to the dielectric permittivity. We have shown that the field inhomogeneity produced by interdigitated electrodes is critical to allow the formation of the ULH using this method. We have demonstrated that devices exhibit the predicted behaviour by using positive dielectric anisotropy, mono-mesogenic liquid crystal, and small dielectric anisotropy, highly flexoelectric bimesogenic liquid crystal mixtures, which have also been found to form ULH in devices with interdigitated electrodes elsewhere.10 In addition, a homeotropic alignment condition has been demonstrated to prevent the cholesteric from reverting to Grandjean alignment after the field is removed, without the requirement of polymer stabilisation. Thus, a theoretical

FIG. 4. Polarizing optical microscope photographs of 5 lm homeotropic IPS cells filled with cholesteric material ZLI-4792 þ 2.7 wt. % R5011. (a) On cooling from isotropic, randomly oriented domains of ULH form spontaneously. On application and removal of 10 Vrms lm1 at 1 kHz, a ULH texture forms. Photographs show the same state where the ULH axis is (b) parallel and (c) at 45 to the polarizer. The texture is stable against forming a Grandjean texture.

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framework has been developed and tested for aligning and making stable CLCs that incorporates both flexoelectric and dielectric field effects. This framework will be applicable to both reflective bistable and transmissive ultra-fast display technology, as well as potential dual-mode and transflective CLC devices. B.I.O. wishes to thank Merck Chemicals Ltd., United Kingdom, a subsidiary of Merck KGaA, Darmstadt, Germany, for the supply of materials, and the EPSRC and Merck for financial support through a CASE award. 1

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