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Abstract
We demonstrate a bistable switching liquid crystal (LC) mode utilizing a topologically self-structured dual-groove surface for degenerated easy axes of LC anchoring. In our study, the effect of the bulk elastic distortion of the LC directors on the bistable anchoring surface is theoretically analyzed for balanced bistable states based on a free energy diagram. By adjusting bulk LC chirality, we developed ideally symmetric and stable bistable anchoring and switching properties, which can be driven by a low in-plane pulsed field of about 0.7 V/µm. The fabricated device has a contrast ratio of 196:1.
© 2017 Optical Society of America
1. Introduction
The bistable switching ability of nematic liquid crystals (LC) has received considerable attention in an effort to overcome power consumption issues in mobile or wearable displays. Power consumption of driving circuits can be reduced effectively utilizing bistable LC modes, as in such devices, one of two different stable LC states can be maintained, even without a bias voltage to the LC layer. Pulsed driving schemes can be used for image refreshing, allowing power consumption by the driving circuits to be totally removed, when displaying a static image. In contrast, even when static images are displayed, conventional monostable LC modes require continuous power consumption to maintain LC configurations.
The switching features of bistable LCs can be achieved using several approaches, which utilize the bulk elastic or surface anchoring properties of LCs. Bistable twisted nematic (BTN) modes [1–4], bistable bend-splay (BBS) modes [5], and bistable chiral splay nematic (BCSN) modes [6–11], which function by controlling the bulk elastic free energy of LCs on monostable planar anchoring surfaces, have been demonstrated. In addition to the bulk elastic properties of LCs, polar anchoring transition behaviors can be utilized for bistable LC switching like bistable nematic (BiNem) modes [12–16] and zenithal bistable displays (ZBD) [17–19].
In another interesting bistable LC operation, planar LC anchoring, easy axes were degenerated on topologically patterned surfaces, where two degenerated easy axes were switched by in-plane fields [20–38]. Yokoyama et al. developed bistable or tristable switching LC modes using mutually orthogonal patterned surfaces in sub-micron-sized domains. The sub-micron-sized domains were created by inducing frustrated LC alignment, where each domain was locally rubbed with a scribing atomic force microscopy tip, or optically patterned using a hard contact photo-alignment method [22–26].
Recently, surface-induced bistable LC modes have been demonstrated on two-dimensional (2D) complex surface morphologies using azimuthal anchoring competition effects [31–37]. A robust theoretical model for understanding the LC alignments on a complex 2D surface has been introduced by Fukuda [39,40]. LC alignment effects on a surface topology of one-dimensional (1D) groove structure, were first introduced by Berreman [41,42]. On a sinusoidally grooved surface, the surface LC directors are aligned to the direction of the groove structure, to minimize the Frank elastic energy. However, there was invalid assumption for explaining LC alignments on a complex 2D structure. Fukuda et al. reexamined Berreman’s LC anchoring potential model, further considering small azimuthal angle director deviations and saddle-splay surface elasticity, which provided a theoretical model to interpret the of LC alignments on more complex surfaces, like 2D periodic groove structures [39,40]. Gwag et al. demonstrated a bistable switching mode utilizing a 2D periodic groove structure, fabricated using a two-step nanoimpring process with the same unidirectional 1D groove template. Similar 2D degenerated LC anchoring effects were also induced by the second easy axis, which was created using a conventional rubbing or photo-alignment technique, along the orthogonal direction with respect to the first easy axis created by the nanoimprinted 1D groove surface, which proved Fukuda’s model experimentally [35,36].
The 2D degenerated LC anchoring properties could be delicately controlled by using a self-structured dual-groove structure as shown in our recent report [37], where our dual-groove surface patterns comprised a micro-groove with a periodicity on the order of sub-micrometers on a macro-groove with a relatively larger periodicity than the micro-groove. The micro-groove could be self-structured along the perpendicular direction to the macro-groove, forming the mutually orthogonal dual-groove structure [37]. Contrary to conventional 2D topological patterns [31–36], the micro-groove patterns were formed on the macro-grooved patterns at every point of the LC anchoring surface, and LC directors on the dual-groove structure exhibited monostable or bistable properties, depending on the relative ratio of the azimuthal LC anchoring effects produced by the macro-groove and the micro-groove. The aspect ratio of the micro-groove patterns could be finely controlled utilizing the anisotropic surface stress distribution during preparing the elastomeric template. By using the 2D self-structuring effect, the topologically patterned dual-groove LC anchoring surface could be made easily and precisely. The experimental results obtained using this structure were well matched with the Fukuda’s equation. In addition, the presented fabrication method of the dual-groove structure using a nanoimprinting and self-patterning process, enables the topological complex surface patterns to be scaled up for use as an LC alignment surface.
In previous analysis of the degenerated LC anchoring effects on a 2D topological complex surface, however, the elastic distortion energy produced by the opposite LC anchoring surface was not been considered, under an assumption of an infinite LC gap condition. In practical applications, a finite LC gap and the LC anchoring effect from the opposite surface, as shown in Fig. 1, need to be considered for suitable bistable switching operation between bright and dark states. If the azimuthal anchoring energy of the bistable anchoring surface is much strong (> 10−4 N/m), the effect of bulk elastic distortion energy additionally produced by the opposite surface can be disregarded also for a finite LC gap condition. But, in this case, due to the increased LC anchoring energy, the switching field required for bistable operation between two stable states is extremely increased (> 5 V/μm) [22–24,33], which are impractical for real applications. Instead, in case of using relatively weak surface anchoring energy conditions for the topologically patterned bistable surfaces, the bulk elastic stress of the LCs induced by the opposite LC alignment surface should be further considered, to obtain a precise interpretation of LC bistability on the topologically-induced degenerate anchoring surface. The bistable switching properties need to be analyzed to enhance the contrast ratio even when the bistable switching is operated with a lower switching field.
Fig. 1 Schematic of the bistable liquid crystal modealigned to a topologically self-patterned dual-groove surface, with coexisting macro-groove and micro-groove structures. LC states can be switched between homogeneously planar (HP) and twisted nematic (TN) configurations using a pulsed driving field.
In this work, we present a bistable LC switching mode by utilizing a self-structured dual-groove structure in which the relative anchoring energy ratio between the macro-groove and the micro-groove is delicately controlled to be close to the condition of 1 [37]. The effects of degenerate LC anchoring produced by the topologically patterned dual-groove structure, as well as by the opposite LC alignment surface, are theoretically and experimentally analyzed with respect to conditions of azimuthal anchoring energy. On the dual-groove structure, the surface LC directors are aligned to the degenerated easy-axes, which are at ± 45° angle with respect to the directions of the macro-groove and the micro-groove surface patterns. However, in the case of the bistable LC switching device shown in Fig. 1, asymmetric free energy diagram between the two stable degenerate states i.e., the homogeneous planar (HP) and the twisted nematic (TN) state, is caused by the bulk elastic stress of the LCs. Importantly, this might lead to asymmetric switching fields between the HP and TN states, owing to asymmetric energy barriers between two bistable points, which also reduces the stability of the bistable states. To analyze the problem analytically, we suggest a total-free energy density equation that considers the bulk elastic energy, and we controlled the LC chirality to balance the energetic barriers between the HP and TN states. After optimizing LC chirality, we demonstrate a bistable LC switching device exhibiting a contrast ratio of 196:1. Relatively reduced and symmetric switching fields (0.70 V/µm and 0.71 V/µm) can be achieved with this device.
2. Total free energy analysis on 2D topologically patterned LC anchoring surface
2.1 Surface free energy density on dual-groove surface
To analyze LC alignment behavior on a topologically patterned surface, the geometry of a dual-groove structure is described using two orthogonally oriented sinusoidal functions as follows [36–40]:
where AM and Am are the amplitude of the macro-groove and the micro-groove, and λM and λm are the pitch of the macro-groove and the micro-groove, respectively. ϕ is defined as the azimuthal angle with respect to the vector direction of the macro-groove (), which is aligned with the x-axis, as shown Fig. 1. The vector direction of the micro-groove is denoted as in Fig. 1. The Frank elastic energy is expressed as [36–40]:where K1, K2, K3, and K24 are the splay, twist, bend, and saddle-splay elastic constants of an LC, respectively, and is the average orientation of the LC director. To investigate the stable state of the LC director, the Euler-Lagrange equation is applied to Eq. (2), using Eq. (1) as the boundary condition. The surface free energy density induced on the dual-groove structure is expressed as follows [36–40]:where ϕ0 is the angle between the surface LC director and , k3 = (K2 + K24)/ K3, pi(ϕ0) = {cos2ϕ0 + (K3/Ki)sin2ϕ0}1/2, qi(ϕ0) = {cos2ϕ0 + (K3/Ki)sin2ϕ0}1/2, (i = 1, 2), and g = (Am/AM)2(λM/λm)3. The g parameter is the relative azimuthal anchoring energy ratio between the macro-groove and the micro-groove [37]. Although the dimensions of the macro-groove and micro-groove are different, we can obtain bistable anchoring on the dual-groove structure when the relative azimuthal anchoring energy ratio (g) approaches 1, which means that the azimuthal anchoring energies induced by the macro-groove and the micro-groove are the same [36–40].When bistable anchoring is realized on the ideal dual-groove structure (g = 1), the azimuthal anchoring energy can be defined using the geometries of the dual-groove structure as follows [33,38]:
where WG and Wp are the respective azimuthal and polar anchoring energies of the dual-groove structure. If Wp ≫ K3/λM, the azimuthal anchoring energy can be simplified to WG = 1/2{K3AM2(2π/λM)3} = 1/2{K3Am2(2π/λm)3}, which corresponds to Berreman’s theory.2.2 Relationship between azimuthal anchoring energy and switching field on dual-groove surface
To analyze its relationship between the azimuthal anchoring energy of the topologically patterned dual-groove surface and the switching field required for bistable operation, the azimuthal anchoring energy of the dual-groove structure is expressed in terms of the in-plane switching field (Ec) as follows [22,23]:
where Δε is the dielectric anisotropy constant of the LC. From Eq. (5), the in-plane electric field for switching between the two stable states is proportional to the azimuthal anchoring energy of the dual-groove structure. Figure 2(a) shows the analytically calculated surface free energy density of the dual-groove structure, obtained when g = 1, as a function of the azimuthal angle of the surface LC director. Using Eq. (3), two different anchoring energy conditions of WG = 10 µN/m and WG = 5 µN/m, were considered. The material parameters of 5CB were used, with K3/K1 = 1.3, K3/K2 = 2.7, K2 = 3 pN, and k3 = 0.04. Both plots show the two stable states are obtained at ϕ0 = ± 45° exactly, and the energy barriers between the bistable states are symmetric even for the sufficiently low anchoring energy condition because the same azimuthal anchoring energies between the macro-groove and the micro-groove are considered and the elastic LC bulk distortion effects produced by the opposite LC anchoring surface was not considered in this analysis of the surface free energy density shown in Fig. 2(a).Fig. 2 (a) The surface free energy density (fs) of dual-groove structures with g = 1 condition, as a function of the azimuthal angle (ϕ0) of the surface LC director, presented for azimuthal anchoring energies of WG = 10 µN/m and WG = 5 µN/m. (b) The potential energy barrier (ΔH) and the switching field (EC) of the bistable switching LC mode with respect to WG. ΔH and EC are co-plotted in the inset graph with respect to the log scaled WG.
When the azimuthal anchoring energy of the dual-groove structure is increased, the potential energy barrier (ΔH) between the two stable states increases proportionally as shown in Fig. 2(b). The increase in the potential energy barrier means that the thermal stability of the bistable states is increased; the operating field required for switching between the two stable states is also increased proportionally. In the case of a stiffer LC anchoring surface (> 10−4 N/m), the elastic LC bulk distortion effect, induced by the opposite LC anchoring surface on the degenerate easy axes, can be neglected and the energy barrier is highly symmetric, even after considering the effects of the opposite surface. However, as seen in the inset in Fig. 2(b), simulations show that for LC surface anchoring energies of 10−4 N/m, the switching field is increased to 6.9 V/µm. In previous studies [22–24,33], the switching fields required for bistable operation were also relatively high, at over 5 V/µm. The azimuthal anchoring energy of the topologically patterned bistable LC anchoring surface should therefore be designed properly, taking the stability of the bistable states and the switching field of the bistable device into consideration.
2.3 Total free energy density considering bulk elastic distortion
In a switchable bistable LC device with bright and dark states, the bottom substrate, which has a unidirectionally rubbed planar LC alignment layer, needs to be introduced with an adequate cell-gap, to form the HP and TN LC configurations shown in Fig. 1. A hard anchoring condition (> 10−4 N/m) is desirable in the planar LC alignment layer. In this case, additional LC distortion needs to be considered; previous studies disregarded the bulk elastic distortion induced by the opposite surface of the LC alignment.
To understand LC alignment on a dual-groove structure, as in the practical bistable switching device which can be operated by a relatively lower switching field as shown in Fig. 1, we considered not only the geometrical alignment effect of the dual-groove structure but also the bulk elastic energy of LCs induced by the bottom surface LC director on the strong anchoring planar LC alignment layer. To retrieve the LC alignment easy axes on the dual-groove structure when both effects are considered, the total free energy density was calculated with ϕ(0) = ϕ0 and ϕ(d) = -π/4 as the boundary conditions. These boundary conditions mean that the rubbing direction of the strong anchoring bottom surface is −45°, such that,
where, FT is the total free energy density, d is the cell-gap of the LC layer and fs is the surface free energy density on the dual-groove structure, defined in Eq. (3).To demonstrate the effect of the LC elastic energy induced by the bottom alignment surface, we compared two bistable LC devices with two different alignment conditions (vertical and planar) at the reference surface, and the same dual-groove conditions (g = 1) at the bistable LC alignment surface. Figure 3(a) plots the total free energy density as a function of ϕ0 in the bistable LC cells, where the azimuthal anchoring energy of the dual-groove structure is 2.72 µN/m, the relative anchoring energy ratio is identically g = 1, and the LC cell-gap is d = 10 µm. In Fig. 3(a), ϕHP and ϕTN are the degenerated easy axes on the dual-groove structure for the HP and TN LC configurations respectively, and ΔHHP and ΔHTN indicate the potential energy barrier required for switching from one bistable state to the other (from ϕHP to ϕTN, or from ϕTN to ϕHP, respectively).
Fig. 3 (a) Total free energy density (FT) of the LC layer for different values of ϕ0 conditions, obtained after assuming that the vertical or planar LC alignment layer is the opposite bottom surface with respect to the dual-groove substrate (g = 1). (b) The ratio of ΔHTN to ΔHHP, and the absolute values of ΔHHP and ΔHTN as a function of ϕ0 of the bistable LC anchoring surface (g = 1). (c) Bistable degenerated easy axes of ϕTN and ϕHP for different values of WG when g = 1.
When the vertical alignment layer is assumed as the bottom alignment layer, the surface LCs on the dual-groove structure are aligned to the degenerated easy axes, with two stable states at exactly ± 45°. ΔHHP and ΔHTN are identical because there is no bulk elastic distortion of LCs disturbing the azimuthal easy axes determined by the dual groove structure. However, when the bottom substrate is the planar alignment layer, the free energy between the two stable states is imbalanced and the total free energy density diagram is biased to one of the bistable states due to the bottom surface LC director being aligned to −45° in a strong anchoring condition. Figure 3(a) shows that ΔHHP becomes higher than ΔHTN after adopting the opposing LC anchoring surface as the planar LC alignment layer. ϕTN is also shifted from the ideal 45° angle, to 38.7°, due to the competition between the symmetric bistable anchoring of the dual-groove structure and the biased bulk elastic energy of the LCs. As shown in Eq. (6), the additional contribution of the biased bulk elastic energy to the total free energy density can be analyzed as a quadratic function of ϕ0, biased with respect to the easy axis angle (−45° in our case) of the opposite LC alignment surface. To analyze the asymmetric free energy in the practical bistable device quantitatively, we plotted the ratio of ΔHTN to ΔHHP, and the absolute values of ΔHHP and ΔHTN, as functions of the azimuthal anchoring energy of the bistable anchoring surface when g = 1. These plots are shown in Fig. 3(b). When the azimuthal anchoring energy of the bistable anchoring surface is decreased, ΔHHP and ΔHTN are decreased. The ratio of ΔHTN to ΔHHP is also decreased, apart from the ideal conditions of 1, which means that the asymmetry of the free energy between the two stable states increases as the azimuthal anchoring energy of the bistable anchoring surface is decreased.
Figure 3(c) shows the degenerated easy axes, ϕHP and ϕTN, for the HP and TN state in our bistable device as a function of the azimuthal anchoring energy of the bistable anchoring surface. ϕHP is constant, irrespective of the azimuthal anchoring energy of the bistable anchoring surface, because the symmetry axis of the quadratic terms added by the bulk elastic energy, shown in Eq. (6), corresponds to ϕHP (−45°). ϕTN shifts from 45° when the azimuthal anchoring energy of the bistable anchoring surface is increased, due to the bulk elastic energy. This shift is shown in Fig. 3(a), where the position of the local minimum for total free energy density is modified.
2.4 Symmetric bistable switching utilizing LC bulk chirality
As shown in Fig. 3, when LCs are anchored by the opposing alignment surface, the asymmetric total free energy between the two stable states is obtained using the additional bulk elastic energy term from Eq. (6). To balance the total free energies between the HP and TN states, we controlled the bulk elastic energy by changing the chiral pitch of the LCs. The total free energy equation after considering the chirality of the LC is written as follows:
where p is the chiral pitch of the LC. We plotted the total free energy diagram as a function of ϕ0, with different cell-gap to chiral pitch ratios (d/p), as shown in Fig. 4(a). When d/p = 0, there is no chirality within the LC cell. The value of d/p in Eq. (7) and Fig. 4(a) is increased when LC chirality increases.Fig. 4 (a) Total free energy density (FT) of the LC layer for different d/p conditions, with respect to ϕ0. These values are obtained after considering the bulk elastic distortion energies induced by the opposite side of the LC alignment surface on the dual-grooved bistable LC anchoring surface. (b) Potential energy barriers of HP (ΔHHP) and TN (ΔHTN) states, as well as the difference between the potential energy barriers (ΔHHP-ΔHTN), for varying d/p.
Of the values of d/p depicted in Fig. 4(a), a symmetrical bistable free energy diagram is obtained only when d/p = 1/8. ΔHHP decreases when d/p is increased. Conversely, ΔHTN increases with d/p. Compared to Eq. (6), which is obtained without LC bulk chirality, the symmetry angle condition of the quadratic term in Eq. (7) added for the bulk elastic energy, shifts from the ϕHP condition to the ϕTN condition when LC chirality increases. Figure 4(b) shows the free energy barriers, ΔHHP and ΔHTN, of the bistable states, as well as the difference between ΔHHP and ΔHTN. ΔHHP and ΔHTN are the same when d/p is 1/8. This is because when d/p = 1/8, the natural twist angle induced by the bulk chirality of the LC is 45°. When d/p = 1/8, the additional elastic distortion propagating from the strong anchoring surface affects both degenerated easy axes, ϕHP and ϕTN, on the dual-groove surface equally. When d/p is increased from its optimal value, 1/8, to 1/4, ΔHTN becomes larger than ΔHHP, because the twist LC angle induced by the bulk chirality of the LC from the LC director at the bottom surface is 90°. When d/p is larger than 1/8, the symmetry angle axis of the quadratic term in Eq. (7) becomes more biased towards the ϕTN condition, which results in free energy diagrams of ΔHTN > ΔHHP. In contrast, when d/p is lower than 1/8, the symmetry angle axis of the quadratic term is more biased towards the ϕHP condition, because of the strong LC anchoring of the opposite surface and the bulk elastic effect. This bias condition results in free energy diagrams of ΔHTN < ΔHHP.
3. Experiment
3.1 Fabrication of the self-structured dual-groove structure
Figure 5(a) shows a schematic illustration of the fabrication process for the dual-groove structure, used as the topologically patterned degenerated LC anchoring surface in the bistable LC switching device. In our method, a dual-groove effect is provided by the macro-groove and the micro-groove at every point of the anchoring surface. Although the dimensions of the macro- and micro-groove are different, the g parameter in Eq. (3) was carefully controlled to be the value corresponding to the ideal bistable anchoring surface. The macro-groove was patterned photo-lithographically. Following this, the micro-groove was spontaneously self-structured as a result of an anisotropic surface stress effect guided by the macro-groove structure. The aspect ratio of the macro-groove was defined by the photoresist used in the photolithography process (AZ1512, AZ Electronics Materials). The height of the macro-groove was controlled by the spin-coating condition of the PR layer. The pitch of the macro-groove was photo-lithographically defined using a photomask.
Fig. 5 (a) Schematic illustration of the fabrication procedures for the bistable LC anchoring surface: preparation of an elastomeric template using the self-patterned dual-groove structure followed by preparation of the topologically patterned LC alignment surface using a UV-assisted replica-molding process. (b) An atomic force microscope (AFM) image of the dual-groove structure, where the micro-grooves are self-structured on the macro-grooves. The direction of the micro-grooves is perpendicular to the macro-groove direction, as shown in the enlarged figure. (c) Cross-sectional surface profiles of the dual-groove structure measured along the A-A’, B-B’, and C-C’ lines of Fig. 5(b).
The macro-groove pattern was replicated on an elastic PDMS surface using a replica-molding process. Following detachment from the master, the PDMS mold was heated for anisotropic thermal expansion. Thermal treatment was performed at 180 °C for 30 minutes on a hot plate. Thermal expansion in the direction of the macro-groove pattern is much larger than in the perpendicular direction (the groove vector direction) because of the anisotropic surface geometry of the patterned PDMS surface [43,44]. The thermally swollen PDMS surface was treated with oxygen plasma (250 mTorr, 50 W, 30 mL/min), which formed a thin silica-like surface layer on the PDMS macro-groove pattern. After this, the PDMS mold was gradually cooled to room temperature. During the cooling process, the micro-groove was spontaneously formed on the PDMS surface, in a direction perpendicular to the macro-groove. The amplitude and pitch of the self-structured micro-groove pattern can be controlled by modifying the oxygen plasma treatment conditions and the thermal treatment conditions [37].
The dual-groove structure was duplicated using a UV curing process (> 1400 mJ/cm2) with a UV curable photo-polymer (NOA89, Norland Products Inc.), on a finger-patterned electrode substrate. The topology of the dual-groove structure was inspected using the atomic force microscopy (AFM) image shown in Fig. 5(b), where AM, Am, λM, and λm are 770 nm, 40 nm, 6 µm, and 0.835 µm, respectively. The value of g was calculated to be 1.0037. The polar anchoring energy of NOA89, used for the final LC anchoring surface, was about 1.59 × 10−4 N/m. This value was measured using a conventional high field method [45]. Since the polar anchoring energy of NOA89 is sufficiently larger than K3/λM, the azimuthal anchoring energy can be expressed using Berreman’s theory as WG = 1/2{K3AM2(2π/λM)3} = 1/2{K3Am2(2π/λm)3} with the simplified form from Eq. (4), where the azimuthal anchoring energies, obtained from the AFM-measured topological values of the dual-groove structure, of the macro-groove and the micro-groove were about 2.72 µN/m, and 2.73 µN/m, respectively.
We experimentally measured the azimuthal anchoring energy of the macro-groove structure by preparing the TN LC cell as shown in Fig. 6(a). For this characterization, the topological surface having the macro-groove only was used before forming the micro-groove structure. For the opposite substrate, a unidirectionally rubbed planar-anchoring PI layer was used for a strong anchoring reference surface. The total twisting angle (Φ) of the LC layer was measured by the optical setup shown in Fig. 6(b). The normalized light transmittance measured by rotating the transmission axis of the analyzer revealed the Φ = 81°, as shown in Fig. 6(c). From the result, the azimuthal LC anchoring energy of the macro-groove can be obtained by
, where d was the cell-gap of 10 μm [46]. The experimentally measured azimuthal LC anchoring energy of the macro-groove using the TN LC cell was about 2.74 μN/m, which was well-matched with the analytic value of 2.72 μN/m obtained by the Berreman’s theory using the AFM-measured topological values although the surface profile of the macro-groove shown in Fig. 5(c) was slightly deviated from the sinusoidal shape. This measured value of the azimuthal anchoring energy also supports the relationship of Wp ≫ K3/λM applied to our analysis for analytic characterization of the azimuthal anchoring with Eq. (4).Fig. 6 (a) Schematic diagram of the twisted LC cell for measuring the azimuthal LC anchoring energy of the macro-groove surface. (b) Optical setup for the azimuthal anchoring measurement. (c) Normalized light transmittance of the twisted LC cell measured by rotating the transmission axis of the analyzer with respect to the transmission axis of the input polarizer. (d) Schematic diagram of the bistable LC cell aligned with the homeotropic-planar LC geometry using the dual-groove surface and the non-rubbed homeotropic anchoring surface. (e,f) Polarized optical microscope (POM) images of the LC cell prepared with the bistable LC geometry shown in Fig. 6(d), measured under the crossed polarizers, when the LC cell is rotated (e) clockwise and (f) counterclockwise with respect to the polarizers, where the rotation angle is ± 45°.
To evaluate the azimuthal anchoring energy of the micro-groove which was self-structured on the macro-groove pattern, we prepared the LC cell aligned between the dual-groove surface and the non-rubbed homeotropic anchoring PI layer, as shown in Fig. 6(d). In this homeotropic-planar geometry, the degenerated easy axes of the dual-groove surface are determined by the relative azimuthal anchoring energy ratio of the macro-groove and the micro-groove, defined by the g value, with excluding the bulk elastic effect from the opposite surface. In this LC geometry, our previous research shows that the degenerated easy axes are formed toward the macro-groove direction, deviated from the ± 45° condition, when the azimuthal anchoring energy of the macro-groove is higher (g < 1) than that of the micro-groove [37]. In the case of g > 1, the degenerated easy axes are formed toward the micro-groove direction. Only under the g = 1 condition, the degenerated easy axes of the dual-groove surface aligned with the homeotropic-planar LC geometry are formed along the ± 45° directions. The polarized optical microscope (POM) LC textures, shown in Figs. 6(e) and 6(f), revealed that the degenerated easy axes of two LC domains, separated by the disclination line of the LC textures, were ± 45° with respect to the macro-groove and the micro-groove directions and this meant that the azimuthal anchoring energy of the micro-groove was almost the same with that of the macro-groove in our dual-groove pattern. Compared with the topological shape of the macro-groove, Fig. 5(c) showed that the surface profiles of the micro-grooves were closer to the ideal sinusoidal shapes for applying the Berreman’s theory. The results of Fig. 6(e) and 6(f) showed that the effect of the geometrical deviation from the sinusoidal shape on the azimuthal anchoring energy was not high in our dual-groove surface. Figure 5(c) showed that the surface profiles of the micro-grooves, self-structured on the crest and valley regions of the macro-groove, were almost identical each other.
3.2 Fabrication of bistable switching LC cells
We fabricated two kinds of bistable switching LC cells, to compare their chirality-dependent field switching properties: one kind for switching from the initial TN state to the final HP state, and the other kind for switching from the initial HP state to the final TN state. The dual-groove structure was replicated on the top glass substrate, which had finger-shaped Al electrodes, where the line width, space, and thickness were 10 µm, 30 µm, and 100 nm, respectively. The relative angle between the direction of the macro-groove and the in-plane electrodes was 45°. A unidirectionally rubbed planar anchoring polyimide (PI) layer was formed on the opposite bottom glass substrate for use as the reference surface. The azimuthal anchoring energy of the rubbed PI layer was 1.701 × 10−4 N/m, which was measured by the effective cell gap method from the falling response time after preparing an in-plane switching LC cell [47]. The top and bottom substrates were assembled with a 10 µm cell-gap, where the rubbing direction of the PI layer at the bottom substrate was orthogonally aligned to the direction of the in-plane electrodes used for switching the LCs from the TN to the HP state. For switching the LCs from the HP to the TN state, the rubbing direction of the PI layer was parallel to the direction of the in-plane electrode. To modify the bulk chirality of the LC, a nematic LC (5CB, Sigma-Aldrich) was mixed with a chiral dopant (S-811, Merck) at d/p ratios of 1/6, 1/8, and 1/12. The chiral LCs were injected into empty cells using the capillary action over the clearing temperature (> 45°C). The filled LC cells were cooled to room temperature for the surface-induced LC domain textures. The randomly distributed bistable LC domain textures were obtained as the initial LC alignment conditions.
To demonstrate the reversible bistable switching device, in-line patterned Al electrodes were formed for top and bottom substrates using the previously described electrode parameters. The dual-groove structure was replicated on the top substrate, where the relative angle between the direction of the macro-groove and the finger-patterned electrodes was 45°. A planar PI layer was formed on the bottom substrate, where the rubbing direction was parallel to the direction of the in-line patterned electrode. The top and bottom substrates were assembled with a 10 µm cell-gap, where the directions of the in-plane electrodes of the bottom and top substrates were orthogonal. For this reversible bistable switching device, the chiral LC prepared using the optimized d/p condition (1/8) was injected into the empty cell at a temperature over the clearing temperature, and the LC cell was subsequently cooled.
4. Results and discussion
Figure 7 shows the initial and in-plane-field switched LC textures, observed the polarized POM under the crossed-polarizers, of the bistable switching LC cells, prepared with d/p = 1/6, 1/8, and 1/12. In Fig. 7, the transmission axis of the polarizer is parallel to the rubbing direction of the PI layer. The transmission axis of the analyzer is orthogonal to the ϕHP direction between the two degenerated easy axes of the bistable LC anchoring surface. In Fig. 7, the images on the left depict the initial states of the LC cells, observed before in-plane field switching. From these images, we can see the LC domain textures with mixed HP and TN configurations. After cooling down the initial LC cells from the clearing temperature to the room temperature, the randomly distributed HP and TN LC domains are obtained owing to the bistable surface anchoring of the dual-groove structure for all the LC cells (d/p = 1/6, 1/8, and 1/12) regardless of the cooling rates at the initial states. The field-switched LC cells recovered to the randomly distributed states after reheating the LC cell to the clearing temperature, and cooling down to room temperature. However, the precise distributions of the mixed HP and TN states were changed following this heating and cooling cycle. The LC cell with no chirality, i.e. d/p = 0, could only display a HP state over the whole area when the cooling rate was very slow, as a result of the thermal annealing effect and the LC redistribution induced by the strong anchoring PI surface.
Fig. 7 Polarized microscope (POM) images of the bistable LC devices, prepared with the d/p LC bulk conditions of 1/6, 1/8, and 1/12 for the figure sets (a) and (a’), (b) and (b’), and (c) and (c’), respectively. The pulse shape of the in-plane field used for the bistable switching is presented for Fig. 7(a). Images of the initial states are obtained after thermal annealing at the isotropic LC temperature and cooling to room temperature, and before pulsed field switching. All LC textures are obtained without applying any electric field. The dark and bright areas represent the HP and TN states, respectively. The width and spacing of Al electrodes used for in-plane switching are 10 µm and 30 µm, respectively. (a), (b), and (c) are POM images of the initial LC textures with coexisting HP and TN states, and the HP state after uniformly switched by the x-axis electric field. (a’), (b’), and (c’) are the POM images of the initial LC textures and the TN state after uniformly switched by the y-axis electric field.
POM images on the right of Figs. 7(a)–7(c), depict LC textures switched from mixed domain states to uniform, single domain HP states. Switching was performed using a pulsed electric field propagating along the x-axis (Ex) with magnitudes of 0.84 V/µm, 0.68 V/µm, and 0.50 V/µm, for the LC cells with chirality conditions of d/p = 1/6, 1/8, and 1/12, respectively. As shown in Fig. 7, the duration of the pulsed in-plane electric field applied for the bistable switching was 200 ms and its frequency was 100 Hz. For different sets of the experiments shown in Fig. 7, the applied voltage (Va) required for the bistable switching were different but the experiments were performed under the same pulsed field duration and frequency conditions. HP states, which are observed as dark regions through the crossed polarizers, were stable after the pulsed switching field (Ex) was applied and removed. POM images on the right of Fig. 7(a’)–7(c’) depict the switch from the initial state to single domain TN states, driven by a pulsed electric field propagating along the y-axis (Ey). The magnitude of the pulsed fields for each LC cell were 0.56 V/µm, 0.66 V/µm, and 0.81 V/µm, for LC cells prepared with d/p conditions of 1/6, 1/8, and 1/12, respectively. In these cases, the TN states observed as uniform bright regions in Figs. 7(a’)–7(c’), were also preserved well after being driven by the pulsed field, Ey.
We observe that when d/p is decreased, the magnitude of Ex and Ey required for switching from the initial states to the HP and TN states, are decreased and increased respectively. The magnitude of the switching field is related to the potential energy barrier between the bistable HP and TN states, which varies according to d/p, as shown in Fig. 4(b). The calculated values of ΔHHP were 0.4857 µN/m, 0.4267 µN/m, and 0.3707 µN/m, for bulk chirality conditions of d/p = 1/6, 1/8, and 1/12, respectively. ΔHTN was 0.3707 µN/m, 0.4267 µN/m, and 0.4857 µN/m, for d/p LC conditions of 1/6, 1/8, and 1/12, respectively. In Fig. 4(b), the analytical values of ΔHHP - ΔHTN were 0.1151 µN/m, 0 µN/m, and −0.1151 µN/m at d/p = 1/6, 1/8, and 1/12, respectively. When d/p deviates from 1/8, the optimum condition, one of the potential energy barriers increases with respect to the other bistable point, increasing the pulsed field required for switching to the other bistable state in turn. This results in the need for a highly asymmetric field to switch between two stable states. However, when d/p = 1/8, the bulk chiral elastic energy from the PI surface is not biased towards a particular bistable state on the easy axis determined by the dual-groove surface. Both bistable states are equally energetically stable, resulting in similar in-plane pulsed field magnitudes being required to switch from HP to TN states and vice versa. The pitch-dependent bistable anchoring and switching behaviors of the dual-groove surface showed the same experimental tendencies when the R811 chiral dopant (Merck), having the opposite chiral handedness to that of the S811, was used for the chiral pitch control of the 5CB LC layer.
Using the ideal bulk chirality condition (d/p = 1/8) for two balanced stable states, and the ideal dual groove structure (g = 1) for degenerated LC anchoring, we demonstrated a reversible bistable switching LC device, shown in Fig. 8(a). Figures 8(b)-8(d) show POM images of the LC textures observed at the initial state after cooling from the clearing temperature, the HP state initialized by the pulsed switching field, Ex, and the TN state initialized by the pulsed switching field, Ey, respectively. The pulsed switching field condition was the same with those used for the experiment shown in Fig. 7. In Fig. 8(b)–8(d), the transmission axes of the polarizer and the analyzer were parallel and perpendicular, respectively, to the rubbing direction of the bottom PI substrate. The ϕHP angle deviates from the analyzer angle by 3.5°, as shown in Fig. 4(a), using theoretical analysis. The contrast ratio of the presented device was 196:1. When the in-plane switching fields acting on the surface LC director of the dual-groove were calculated using a commercial LC simulator, TechWiz LCD 2D (Sanayi System Co., Ltd., Korea), with voltages applied to the top and bottom in-plane electrodes (45 V was applied to the top electrode and 50 V was applied to the bottom electrode), the effective fields were 0.70 V/µm, for switching from the TN to HP state and, 0.71 V/µm, for switching from the HP to TN state. The magnitudes of these fields are almost identical. The device thus exhibits the ideally symmetric bistable switching property. The magnitude of the switching field was nearly ten times lower than those reported in previous studies [21–26,33–36]. Without applying fields, the bistable states sustained for over one month during our investigation.
Fig. 8 (a) The schematic structure of the bistable switching LC mode. POM images depicting, (b) the initial state with coexisting HP and TN states, (c) the HP state after switching by the pulsed field, Ex, applied by the in-plane electrodes on the top substrate, and (d) the TN state after switching by the pulsed field, Ey, applied by the in-plane electrodes on the bottom substrate.
5. Conclusion
We have presented a bistable LC switching mode using a self-structured dual-groove surface topology for ideal bistable LC anchoring. The bulk LC elastic effect was carefully controlled to introduce the optimum bulk chirality condition, necessary for obtaining symmetric switching between two stable LC configurations. Compared with previous reports utilizing surface-topological effects for bistable switching LC modes, the magnitude of the switching field could be lowered by about 0.7 V/µm in the proposed switching scheme. Due to the symmetric free energy diagram in our bistable design utilizing the optimum bulk chiral effect which was obtainable even without much increasing the azimuthal surface anchoring, both of the bistable states were well preserved. These properties, together with the high contrast ratio (~196:1) are desirable for power-saving memory-mode switching LC devices driven by pulsed electric fields.
Funding
This work was supported by “The Cross-Ministry Giga KOREA Project” grant from the Ministry of Science, ICT and Future Planning, Korea.
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