Fast-Switching Liquid-Crystal Effects for Displays

A fast liquid-crystal response time is needed in order to reduce motion blur, to allow field-sequential color, to improve low-temperature operation, and for use in some stereoscopic displays. A review of the factors that control the response time in nematic LCDs follows.

by Philip Bos

FAST-SWITCHING liquid-crystal mechanisms are required to reduce the effects of motion blur in display devices and also are of interest if field-sequential color or digital gray scale is considered. In this article, the main factors that control the speed in nematic liquid-crystal devices are reviewed, particularly the twisted-nematic (TN), electrically controlled birefringence (ECB), vertically alignment (VA), and, to some extent, the in-plane-switching (IPS) mode. Emphasis is placed on understanding the basic issues controlling the speed of these devices and the motivation for faster modes such as the π-cell and those that do not use the nematic phase.

The optical switching time of a liquid-crystal device is related to the dynamics of the liquid-crystal material and the optics of the considered liquid-crystal mode used.

When considering the material dynamics, the change of the "director field" is of particular interest. The local director is defined as that being along the direction of the average long molecular axis (which is undergoing considerable thermal motion) within a nanoscale area. The director field describes the orientation of the local director through a macroscopic region of the display cell. Figure 1 shows the director field of the voltage-applied and voltage-removed states of a uniformly aligned pixel in a display device.The director field dynamics are primarily influenced by three material factors: the elastic energy associated with a deformation of its equilibrium director field, the vis-cosity of the material, and its dielectric properties. These material factors are strongly affected by the liquid-crystalline phase being used.

Fig. 1: The director field in a uniformly aligned device with voltage applied (left) and relaxed (right). The director field dynamics are primarily influenced by three factors related to the liquid-crystal material used and two that are influenced by the cell that contains that material.

Most commercial devices use liquid crystals in the nematic phase (that has orientational but not translational molecular order). The torques associated with these factors are shown in Eq. (1) for the rate change of the polar angles describing the local director. Here, the following simplifying assumptions are made: the variation in the director field only occurs along the direction normal to the cell substrates (typically a pixel is about 100 μm in size, whereas the cell is about 4-μm thick); the elastic torque and viscosity are each described by a single material constant; and the value of Δθ is small compared to the magnitude of the average value of θ.

θ_new= θ_previous + Δθ

(1)

Here, z is the distance in the cell perpendicular to the plane of the cell, θ is the angle that the director makes with the z axis, Δθ is the change in θ in the time interval Δt, γ is the rotational viscosity, K is the averaged elastic constant, and Δε is the dielectric anisotropy of the LC material.

To determine how quickly the director field relaxes after an applied voltage, the main factors are how distorted the director field is (how large is d²θ/dz²) and the elastic constant and viscosity of the material. As shown in Fig. 1, there is considerable distortion of the director field near the surface in the presence of the electric field. Upon removal of the field, this will drive the relaxation toward the voltage-removed state.

The direction and magnitude of the applied electric field [that enters into Eq. (1)] and the boundary conditions of the director field at the cell surfaces are determined by the cell that contains the liquid-crystalline material. Considering Fig. 1, the alignment layers on the cell's substrates set the boundary conditions of the director, and the electrodes on the top and bottom of the cell fix the electric-field direction to be along the cell's normal direction.

By examining Eq. (1), taking into consideration the influence of the cell thickness, for the voltage-removed relaxation, the d²dependence of the elastic torque will yield a strong thickness dependence. Based on this, it is often noted that the relaxation time of a liquid-crystal device is given by Eq. (2), which shows the approximate expression for the field-free relaxation of the director field:

t ∝ γd²/K. (2)

Optical Response

However, the optical response time is more complicated. The optical response is related to both the change in the director field and also to the particular optical effect that is being used. For the tunable birefringence effect that can be used with the cell shown in Fig. 1, the transmission between crossed polarizers (aligned at 45° to the rub axes of the cell) is given by sin²(πΔn′d/λ), where Δn′d is determined by averaging Δnd over the thickness of the cell using n_e²(z) = {n_on_e/[n_o²sin²(θ) + n_e²cos²(θ)]} and Δn(z) = n_e(z) – n_o. In a cell when no voltage is applied, the value of Δn′d/λ is determined by the product of the cell thickness and the material value of birefringence and is equal to Δnd/λ.

When a voltage is applied, the reorientation of the director will cause a lowering of the value of Δn′ as shown above. In the limit of a very high voltage applied to the device, the value of Δn′d/λ and the transmission would both be zero. For this type of device, it is logical to relate the optical response time to the time required to go between a state of near-zero transmission and one near a near-maximum transmission. The thinnest cell that can be considered is one where Δn′d/λ = 0.5. Note that if the cell is thicker and the director response changes as described in Eq. (2), a full optical response does not require a full director response. For example, if we compare two cells that use the same LC material, but where the thickness of one is chosen so that Δnd/λ = 0.63, and another cell that is 3.16 times thicker so that Δnd/λ = 2, it may be expected that a the relaxation rate of the director field will be 10 times slower for the thicker cell. But note the director only needs to relax to where Δn′d/λ is 25% of its equilibrium value to achieve maximum transmission for the thicker cell, were it requires 80% to relax for the thinner cell. So, in the thinner cell, the director needs to complete nearly full relaxation to the zero-field equilibrium state, but the thicker cell's director field only needs to change a smaller degree to achieve optical switching.

Figure 2 shows the director response and optical response of tunable birefringence cells for two thicknesses. The thicker cell is only slightly slower in terms of optical response, despite the expected factor of 10 for the director-field response.

In real cells, where fluid flow is taken into account (as will be discussed later), a fairly thick cell can actually be slightly faster than a very thin one. This effect was first pointed out by Kobayashi in consideration of a fast-switching device.¹ This effect was later called the "surface mode." As pointed out by Kobayashi, the drawback of this approach is its poor viewing-angle characteristics.

Although the example of the tunable-birefringence optical effect demonstrates the non-linear connection of the director response and optical response, other effects have different dependences. Guest-host cells, for example, may be expected to require almost full director reorientation to achieve a full optical response (and therefore are relatively slower).

While the above makes it clear that making a cell thinner while using the same liquid crystal may not lead to a decrease in the response time shown in Eq. (2) because of the decrease in the optical thickness of the device; making a cell thinner while holding the optical thickness constant can be expected to have a significant effect. For example, when considering devices that have the same optical thickness, we can combine Eq. (2) with the expression Δnd = C (a constant) to yield the ratio γ/(KΔn²) of material parameters, which is proportional to the relaxation time. A recent paper on the use of high-birefringence materials leading to thin, fast devices has been published by Wu.² A method to make very thin cells has been proposed by Kumar.³

As an alternative to a single thin cell, multiple cells have been considered. Because the relaxation speed of a device is directly propor-tional to the thickness squared, dividing a thick cell into two thinner ones can be expected to make a device that is four times faster. Also, it is possible to design devices where the response times are only controlled by the field-applied transition time to yield devices with response times of less than 100 μsec.⁴

An approach to speed up the switching time of a liquid-crystal device is to use "overdrive" or "underdrive" during the switching. Consider that the desired director configuration is one where it is in equilibrium (dθ/dt = 0) when a voltage V_t is applied. If the initial state has a lower applied voltage and it is desired that θ decrease in value, then [from Eq. (1)] applying a voltage as high as possible will cause the largest change in θ with time. On the other hand, if the initial state has an applied voltage higher than V_t, then applying 0 V will maximize the rate of increase in θ. In either case, when the desired value of θ is reached, the voltage can be set to V_t. Wu⁵has combined the idea of using a thick cell with overdrive and demonstrated 100-μsec response times.

A significant impact on the switching speed that can also be implied from Eq. (1) is the impact of the temperature dependence of the viscosity. The viscosity of liquid-crystal material is exponentially dependent on temperature, which means that a significant decrease in the switching speed can be obtained by heating. However, the other material parameters are also somewhat dependent on temperature, so that if the temperature is taken too high, the response time no longer decreases. Wu and Yang⁶ have shown that this leads to an optimum temperature for high-speed operation that is about 20° below the isotropic–nematic transition for a given material. Furthermore, they derive a material figure of merit that shows that high clearing-point materials will have a faster response when operated at their optimum temperature.

Additional Response-Time Considerations for Nematic Devices

The basic considerations discussed in the previous section point to basic material and cell-design factors that can lead to decreased switching speed. But other factors can be considered to improve performance. Factors considered here are material flow in the cell, "two-frequency" materials, the electrode structure, and the flexoelectric effect.

Devices with the structure shown in Fig. 1 are known to suffer from an "optical bounce" effect that lengthens the response time as shown in Fig. 4(a). Van Doorn⁷ first made clear that this effect is due to material flow in the device after an electric field is removed. As shown in Fig. 3 in the drawing on the left, the material flow shown by the arrows in a relaxing device imparts a torque on the director near the center of the cell in a "backwards" direction relative to the direction of lower elastic energy. TN devices also show this phenomenon as was explained by Berreman.⁸ Faster relaxation can be achieved by removing this effect through a cell re-design where the material flow is considered. For a TN device, a –3π/2 cell was proposed⁹ (where the 3π/2 refers to the twist of the device and the negative sign indicates that the chiral additive used to achieve the twist has the opposite sign of the twist sense caused by the surface pretilt in the absence of the any dopants).

For a tunable birefringence device, a device called the π-cell has been proposed,¹⁰ where the rotational sense of the pretilt on the two cell surfaces has the opposite sense as shown in Fig. 3 on the right side. In this case, the "backwards" torque due to flow has been eliminated. An additional advantage of the π-cell device is its excellent off-axis optical properties that can be further improved through the use of external compensation layers. Uniaxial retrarders have been considered by Bos¹¹ and Mori,¹² whereas biaxial compensators have been considered by Uchida¹³ who proposed the name "OCB" for this device. Uchida's group and others have subsequently provided in-depth studies and improvements related to this type of device.

One issue with low-surface-pretilt π-cell devices is that the zero-field director field is splayed and topologically not equivalent to the desired bent director field, so that the director field must be transitioned from the splay to the bend state before it is operational.

Several papers have considered this transition and ways to speed it up.¹⁴ A method using a new technique for obtaining high pretilt angles that can yield a stabilized bend state has been recently suggested by Kwok.¹⁵

Fig. 2: Transmission vs. time for the field-free relaxation of a uniformly aligned cells of 3.46 (green) and 11 (blue) μm. Shown is the optical transmission of the cell between crossed polarizer aligned at 45° to the cell rubbing direction. 5 V was applied for 500 msec before the plotted data for the thin cell and 50 V for the thick cell. The effects of flow are not included in this calculation. The assumed birefringence of the material was 0.1 and the wavelength of light was 550 nm.

For most nematic devices, the response time for the "voltage-removed" relaxation is the limiting factor related to the image-update time. However, there are nematic liquid-crystalline materials called "two-frequency" materials, where the sign of the dielectric anisotropy changes as a function of frequency. For these types of materials, the director tends to align along the electric-field direction when a low-frequency field is applied, but perpendicular to it when a high-frequency field is applied. This technique was first shown by Bucher and Raynes,¹⁶ with some of the most recent work reported by Lavrentovich¹⁷ who shows a response time of 150 μsec.

Another way to use the electric field to drive the director field to two different preferred director orientations is to use a normal (single-frequency) material with more complicated electrode structures. RCA showed a device called the "triode optical gate" where interdigitated electrodes were used to provide an "in plane" electric field, whereas a conventional counter-electrode could provide a field along the cell normal. A similar approach has recently been applied to fast VA devices having 1-msec switching times.¹⁸

The "flexoelectric" effect is a linear coupling of the electric field with the molecular orientation that causes a director deformation.¹⁹Recently, Coles used this effect to design fast-switching devices and improved materials.²⁰ In these devices, chiral molecules are used to provide a spontaneous twist of the director field that is short compared to the wavelength of light. In this case, with no electric field applied, the optic axis is along the helical axis that is designed to be in the plane of the LC cell. The application of an electric field along the cell normal causes a flexoelectric distortion of the director field that results in the optical axis being rotated in the plane of the device.

Because of the large amount of elastic energy associated with this distortion, the relaxation time can be very fast. Also, because of the linear dependence of this tilting with the applied electric field, the rotational sense of the in-plane optic-axis motion is related to the polarity of the applied field. This interesting effect has been used to show in-plane director rotation angles of more than 90° and response times of less than 20 μsec.

Polymers in Nematic Liquid-Crystal Devices

Polymers can be combined with nematic liquid crystals to improve the response time. There are two basic approaches: One is to confine the liquid crystal into small droplets²¹ and the other is to form a spider-web-type structure of a polymer in the liquid-crystal material that is aligned along a particular direction.²² The first approach has been exploited by Bunning,²³ where the droplet size is smaller than a wavelength of light. In these cases, response times of 40 μsec have been reported. The second approach was first shown by Kelly,²² where an elongated monomer that is aligned by the host LC is polymerized with the director in the desired orientation. The resulting polymer network causes the director to have a larger energy if distorted away from the state that was polymerized. Two examples of the use of this method have been to speed the response of IPS devices²⁴ and also to stabilize a "splay cell".²⁵ A different approach using monomers that are not necessarily elongated has been demonstrated by West²⁶ and Wu. In this case, a non-aligned polymer network is formed, which is then sheared by mechanical displacement of the cell substrates. This approach has been shown to allow for thick cells that would ordinarily have slow director relaxation to be very fast. Response times of less than 2 msec have been demonstrated. Another example of the use of polymer additives has been to stabilize the "blue phase" of chiral nematic liquid crystals, where fast modulation of color switchable pixels has been shown.²⁷

Devices Using Other Liquid-Crystalline Phases

Although nematic LCs are used in most display devices, higher-order smectic phases can provide faster switching times.

The most researched of these is the ferroelectric smectic-C phase. Clark introduced the Surface-Stabilized Ferroelectric-Liquid-Crystal Device that is bistable and has demonstrated sub-microsecond response.²⁸ Handschy, along with others at Displaytech, have used these devices to achieve very fast digital gray-scale field-sequential displays²⁹ that operate over a wide temperature range. Analog versions of this technology have been considered by Kobayashi³⁰ (based on polymer stabilization) and O'Callahan³¹ (based on polarization-stabilized devices). The chiral smectic-A phase has also been used for very-fast-switching devices that are based on the electroclinic effect.³² In these materials, a DC electric field causes a high-energy distortion of the ordered smectic-layer structure and, as a result, the response time when the field is removed is very fast. Walba and the NRL have advanced LC materials for this effect.³³

Fig. 3: The effect of cell design on flow shown by arrows for a uniformly aligned cell (left) and a π-cell (right).

Looking toward the future, new effects in liquid crystals include the use of the bent-core molecules, or "bananas." Recent work in the area of induced biaxiality in these materials has shown response times in the hundreds of microseconds.³⁴

Conclusion

The field of fast-switching liquid-crystal devices is large and contains many approaches. The best for a particular display application also needs to include considerations of the viewing angle, voltage requirements, and cell-fabrication costs. Devices such as the π-cell and the digital ferroelectric gray-scale device have been optimized for these characteristics and applied to commercial devices. However, others of the above methods that may provide faster response times can be considered for applications where either the voltage or viewing angle are not so important. Also, effects currently being researched, such as the flexoelectric, electroclinic, polymer-stabilized, and those using new LC phases based on bent-core molecules all have potential for providing improved fast-switching devices.

References

¹K. Uehara, H. Mada, and S. Kobayashi, "Reduction of electro-optical response times of a field-effect liquid-crystal device," IEEE Trans. Electron. Dev. 22, 804 (1975); S. T. Wu and C. Wu, "High-speed liquid-crystal modulators using transient nematic effect," J. Appl. Phys. 86, 527-532 (1989).
²S. Gauza, X. Zhu, W. Piecek, R. Dabrowski, and S-T Wu, J. Display Tech. (September 2007); S. Gauza, X. Zhu, and S.-T. Wu, "High-Birefringence LCs for Color-Sequential LCDs," SID Symposium Digest Tech Papers 38, 142-145 (2007).
³Q. Wang and S. Kumar, "Submillisecond switching of nematic liquid crystal in cells fabricated by anisotropic phase separation of liquid crystal and polymer mixture," Appl. Phys. Lett. 86, 071119 (2005).
⁴T. J. Haven, "A liquid-crystal video stereoscope with high extinction ratios, a 28% transmission state, and 100-msec switching," Proc SPIE: True 3-D imaging Techniques and Display Technologies 761, 23-26 (1987).
⁵S. T. Wu, "Nematic modulators with response time less than 100 μsec at room temperature," Appl. Phys. Lett. 57, 986-988 (1990).
⁶S.-T. Wu and D-K Yang, Reflective Liquid Crystal Displays, A. C. Lowe, ed. (John Wiley & Sons, Ltd., 2001).
⁷C. Z. V. Doorn, "Transient behavior of a twisted-nematic liquid-crystal layer in an electric field," J. Phys. 36, C1-261 (1975).
⁸D. W. Berreman, "Liquid-crystal twist-cell dynamics with backflow," J. Appl. Phys. 46, 3746 (1975).
⁹R. Hubbard and P. Bos, "Optical bounce removal and turn-off time reduction in twisted nematic displays," Proc IEEE 28, No.6, 723 (1981).
¹⁰P. Bos and K. Koehler-Beran, "The π-cell: A fast liquid-crystal optical switching device," Mol. Cyst. Liq. Cryst. 113, 329 (1984).
¹¹P. Bos and J. Rahman, "An optically self-compensating electro-optical effect with wide angle of view," SID Symposium Digest Tech Papers 24, 273 (1993).
¹²H. Mori and P. Bos, "Optical performance of the π-cell compensated with a negative birefringence films and an a-plate," Jpn. J. Appl. Phys. 38, 2837-2844 (1999).
¹³Y. Yamaguchi, T. Miyashita, and T. Uchida, "Wide-viewing-angle display mode for the active-matrix LCD using bend-alignment liquid-crystal cell," SID Symposium Digest Tech Papers 24, 277-280 (1993).

Fig. 4: The optical transmission after 10 V has been applied to a 7-μm-thick cell for 500 msec. The green curve is for a uniform device, while the blue curve is for a π-cell. The birefringence of the liquid crystal is 0.1. The cell is assumed to be between crossed polarizers aligned at 45° to the rub axis of the cells, and the wavelength of light is 550 nm. Flow is taken into account in this calculation.

¹⁴H. Nakamura and M. Noguchi, Jpn. J. Appl. Phys. 39, 6368 (2000); T. Konno, T. Miyashita, and T. Uchida, Proc. Asia Display '95, 581 (1995); M. Xu, D. K.Yang, and P. J. Bos, SID Symposium Digest Tech Papers, 139 (1998); N. Nagae, T. Miyahita, T. Uchida, Y. Yamada, and Y. Ishii, Proc. IDRC, 26 (2000); K. Kuboki, T. Miyashita, T. Ishinabe, and T.Uchida, Mol. Cryst. Liq. Cryst. 410, 391 (2004); N. Koma, T. Miyashita, T. Uchida, and K. Yoneda, SID Symposium Digest Tech Papers 30, 28 (1999); C. H. Lee, H. S. Chang, J. J. Lyu, K. H. Kim, and J. H. Souk, SID Symposium Digest Tech Papers, 570 (2002); R. Hasegawa, Y. Kidzu, I. Amemiya, and S. Uchikoga, "Electro-optical properties of polymer-stabilized OCB and its application to TFT-LCDs," SID Symposium Digest Tech Papers38, 995-998 (2007); P. Xu, V. Chigrinov, and A. D. Kiselev, "Optical response of a nematic liquid crystal cell at the splay–bend transition: a model and dynamic simulation," Liquid Crystals 32, No. 6, 699-706 (2005); Y. Zhang and P. Bos (to be published in Liquid Crystals).
¹⁵F. S. Yeung, Y. W. Li, and H-S. Kwok, "Pi-cell liquid crystal displays at arbitrary pretilt angles," Appl. Phys. Lett. 88, 041108 (2006).
¹⁶H. K. Bucher, R. T. Klingbiel, and J. P.VanMeter, "Frequency addressed liquid crystal field effect," Appl. Phys. Lett. 25, 186 (1974); E. P. Raynes and I. A. Shanks, "Fast switching twisted nematic electro-optical shutter and color filter," Electron Lett. 4, 114 (1974).
¹⁷A. B. Golovin, S.V. Shiyanovskii, and O. D. Lavrentovich, "Fast switching dual-frequency liquid crystal optical retarder driven by an amplitude and frequency modulated voltage," Appl. Phys. Lett. 83, 19 (2003).
¹⁸X. W. Sun and C. Y. Xiang, "Fast Response LCD with Alternate Vertical and Fringe Field Switching," SID Symposium Digest Tech Papers 35, 1424 (2004).
¹⁹J. S. Patel and R. B. Meyer, "Flexoelectric electro-optics of a cholesteric liquid crystal," Phys. Rev. Lett. 58, 1538-1540 (1987); P. Rudquist, L. Komitov, and S.T. Lagerwall, "Linear electro-optic effect in a cholesteric liquid crystal," Phys. Rev. E, 50 (1994).
²⁰H. J. Coles, M. J. Clarke, S. M. Morris, B. J. Broughton, and A. E. Blatch, "Strong flexoelectric behavior in bimesogenic liquid crystals," J. Appl. Phys. 99(3), 34104 (2006); B. J. Broughton, M. J. Clarke, S. M. Morris, A. E. Blatch, and H. J. Coles," Effect of polymer concentration on stabilized large-tilt-angle flexoelectro-optic switching," J. Appl. Phys. 99, 023511 (2006); B. J. Broughton, M. J. Clarke, A.E. Blatch, and H. J. Coles, "Optimized flexoelectric response in a chiral liquid-crystal phase device," J. Appl. Phys. 98, 034109 (2005).
²¹J. W. Doane, A. Golemme, J. L. West, J. B. Whitehead, Jr., and B. G. Wu, "Polymer Dispersed Liquid Crystals for Display Applications," Mol. Cryst. Liq. Cryst. 165, 511-532 (1988).
²²S. M. Kelly, "Anisotropic networks, elastomers, and gels," Liq. Cryst. 24, No. 1, 71-82 (1998).
²³V. P. Tondiglia, L. V. Natarajan, R. L. Sutherland, T. J. Bunning, and W. W. Adams, "Volume holographic image storage and electro-optical readout in a polymer-dispersed liquid crystal film," Opt. Lett. 20, No. 11, 1325-1327 (June 1, 1995).
²⁴M. S. Escuti, C. C. Bowley, G. P. Crawford, and S. Zumer, "Enhanced dynamic response of the inplane switching liquid crystal display mode through polymer stabilization, Appl. Phys. Lett. 75, 3264 (1999).
²⁵V. Sergan, X. Wang, P. Bos, and G. Sharp, "Fast switching polymer stabilized splay cell (PSSC)," Mol. Cryst. Liq. Cryst. 410, 1015-1021 (2004).
²⁶J. West, G. Zhang, A. Glushchenko, and B.-S. Ban, "Stressed Liquid Crystal Materials for Fast Display Application," SID Symposium Digest Tech Papers 37, 761 (2006).
²⁷H. Kikuchi and H. Higuchi, "Fast electro-optical switching in polymer-stabilized liquid crystalline blue phases for display application,"SID Symposium Digest Tech Papers 38, 1737-1740 (2007); H. Coles and M. Pivnenko, "Liquid crystal 'blue phases' with a wide temperature range," Nature 436, 997-1000 (August 18, 2005).
²⁸N. A. Clark and S. T. Lagerwall, "Sub-miscrosecond bistable electro-optic switching in liquid crystals, Appl. Phys. Lett. 36, 899 (1980).
²⁹D. Banas, H. Chase, J. Cunningham, M.A. Handschy, R. Malzbender, M.R. Meadows, and D. Ward, "Miniature FLC/CMOS color-sequential display systems, J. Soc Info. Display 5, 27 (1997); N. Clark, C. Crandall, M. Handschy, M. Meadows, R. Malzbender, C. Park, and J. Xue, "FLC Microdisplays," Ferroelectrics 246, 97-110 (2000).
³⁰T. Fujisawa, M. Hayashi, H. Hasebe, K. Takeuchi, H. Takatsu, and S. Kobayashi, "Novel PSV-FLCDs with high response speed, high optical throughput, and high contrast ratio with small voltage shift by temperature: Application to field-sequential full-color LCDs, SID Symposium Digest Papers 38, 633-636 (2007).
³¹M. J. O'Callaghan, M. Wand, C. Walker, W. Thurmes, and K. More, "High-Tilt, High-PS, de Vries FLCs for Analog Electro-Optic Phase Modulation," Ferroelectrics 343, 201–207 (2006).
³²S. Garoff and R. B. Meyer, "Electroclinic Effect at the A-C Phase Change in a Chiral Smectic Liquid Crystal," Phys. Rev. Lett. 38, 848-851 (1977); S. Garoff and R. B. Meyer, "Electroclinic effect at the AC phase change in a chiral smectic liquid crystal," Phys. Rev. A 19, 338-347 (1979).
³³R-F Shao, J. E. Maclennan, N. A. Clark, D. J. Dyer, and D. M. Walba, "Giant surface electroclinic effect in a chiral smectic-A liquid crystal," Liq.Cryst. 28, No. 1, 117-123 (2001); M. S. Spector, P. A.Heiney, J. Naciri, B. T. Weslowski, D. B. Holt, and R. Shashidhar, "Electroclinic liquid crystals with large induced tilt angle and small layer contraction," Phys. Rev. E 61, No. 2, 1579-1584 (2000).
³⁴K. Fodor-Csorba, A. Jakli, A. Vajda, S. K. Prasad, D. S. S. Rao, R. Y. Dong, J. Xu, and G. Galli, "Intercalated Smectic A Phases in Banana-Shaped Liquid Crystals with Carbonate End Groups," Chem. Phys. Chem 7, 2184–2188 (2006). •