"Thresholdless" hysteresis-free switching as an apparent phenomenon of surface stabilized ferroelectric liquid crystal cells

Biaxial potential of surface-stabilized ferroelectric liquid crystals

A biaxial surface potential Φ_{s} of smectic-C^{*} surface-stabilized ferroelectric liquid crystals (SSFLCs) is introduced in this paper to explain the experimentally observed electric-field dependence of polarization P[over ̃]_{cell}(E), in particular the shape of the static hysteresis loops. Our potential consists of three independent parts. The first nonpolar part Φ_{n} describes the deviation of the prime director n (which is the most probable orientation of the long molecular axes) from the easy alignment axis R, which is located in the boundary surface plane. It is introduced in the same manner as the uniaxial Rapini potential. The second part Φ_{p} of the potential is a polar term associated with the presence of the polar axis in a FLC. The third part Φ_{m} relates to the inherent FLC biaxiality, which has not been taken into consideration previously. The Φ_{m} part takes into account the deviations of the secondary director m (which is the most probable orientation of the short molecular axes) from the normal to the boundary surface. The overall surface potential Φ_{s}, which is a sum of Φ_{n},Φ_{p}, and Φ_{m}, allows one to model the conditions when either one, two, or three minima of the SSFLC cell free energy are realized depending on the biaxiality extent. A monodomain or polydomain structure, as well as the bistability or monostability of SSFLC cells, depends on the number of free-energy minima, as confirmed experimentally. In this paper, we analyze the biaxiality impact on the FLC alignment. We also answer the question of whether the bistable or monostable structure can be formed in an SSFLC cell. Our approach is essentially based on a consideration of the biaxial surface potential, while the uniaxial surface potential cannot adequately describe the experimental observations in the FLC.

Influence of virtual surfaces on Frank elastic constants in a polymer-stabilized bent-core nematic liquid crystal

Effect of a polymer network on the threshold voltage of the Fréedericksz transition, Frank elastic constants, switching speed, and the rotational viscosity are investigated in a polymer-stabilized bent-core nematic liquid crystal with different polymer concentrations. These polymer networks form virtual surfaces with a finite anchoring energy. The studies bring out several differences in comparison to similar studies with a calamitic liquid crystal as the nematic host. For example, on varying the polymer content the threshold voltage decreases initially, but exhibits a drastic increase above a critical concentration. A similar feature-reaching a minimum before rising-is seen for the bend elastic constant, which gets enhanced by an order of magnitude for a polymer content of 2.5 wt %. In contrast, the splay elastic constant has a monotonic variation although the overall enhancement is comparable to that of the bend elastic constant. The behavior changing at a critical concentration is also seen for the switching time and the associated rotational viscosity. The presence of the polymer also induces a shape change in the thermal dependence of the bend elastic constant. We explain the features observed here on the basis of images obtained from the optical and atomic force microscopy.

A Review of Polymer-Stabilized Ferroelectric Liquid Crystals

The polymer stabilized state of ferroelectric liquid crystals (FLC) is reviewed; and the effect of a dispersed polymer network in an FLC outlined and discussed. All fundamental material aspects are demonstrated; such as director tilt angle; spontaneous polarization; response time and viscosity; as well as the dielectric modes. It was found that the data can largely be explained by assuming an elastic interaction between the polymer network strands and the liquid crystal molecules. The elastic interaction parameter was determined; and increases linearly with increasing polymer concentration.

Reorientation effect and electrical current in a weakly anchored nematic cell

A nematic cell subjected to a large electric field undergoes a molecular reorientation that affects the electrical current flowing through it. To analytically establish the dependence of the current on the applied voltage, the cell is considered as parallel of resistance, R(t) , and capacitance, C(t) , that are connected with the nematic director profile. This profile is determined in the quasistatic regime in which the nematic orientation follows the time variation in the external field normal to the cell plates without delay. The analysis performed for a weakly anchored cell shows that the current presents a peak when the applied voltage overcomes the threshold voltage for the transition of Fréedericksz at a critical time t* as in the case of strong anchoring. For large voltages, R(t)-->R|| and C(t)-->C||, where parallel refers to the nematic director. We show that, for large enough time t>>t*, it is possible to connect the measured current with the extrapolation length characterizing the sample by means of simple analytical expressions. This connection can be used to experimentally estimate the anchoring energy by means of current measurements.

V -shaped switching ferroelectric liquid crystal structure stabilized by dielectric surface layers

The " V -shaped switching" mode in high polarization ferroelectric liquid crystals was studied with the aim of stabilizing the monostable bookshelf structure with the spontaneous polarization parallel to the glass plates. The director field in such cells was confirmed to be sensitive to both the liquid crystal properties and the cell parameters. In cells with only polyimide alignment layers, hysteresis free switching was never obtained, with bistable and asymmetric monostable structures compromising the zero-field dark state and preventing an ideal, hysteresis-free analog response. By incorporating a SiO(2) layer between the ITO electrode and the polyimide, the undesired states were suppressed and essentially hysteresis-free switching was obtained for driving frequencies in the range 0.2-200 Hz . Cells rubbed only on one side give more uniform alignment than cells rubbed on both sides but their inherent asymmetry shifts the long-term dark state away from 0 V and causes the response to gray level voltage modulation to be slightly asymmetric. The formation of different types of states as a function of the values of the surface parameters, and the observed stabilization of the V -shaped switching structure by the dielectric surface layers, are in good agreement with an earlier analysis by Copic [Phys. Rev. E 65, 021701 (2002)].

Switching dynamics of surface stabilized ferroelectric liquid crystal cells: effects of anchoring energy asymmetry

We study both theoretically and experimentally switching dynamics in asymmetric surface stabilized ferroelectric liquid crystal cells where the bounding surfaces are treated differently to produce asymmetry in their anchoring properties. Our electro-optic measurements of the switching voltage thresholds, V+ and -V{-}, that are determined by the peaks of the reversal polarization current reveal the frequency dependent shift of the hysteresis loop, V{+}-V{-}. We examine the predictions of the uniform dynamic model with the anchoring energy taken into account. It is found that the asymmetry effects are dominated by the polar contribution to the anchoring energy. Frequency dependence of the voltage thresholds is studied by analyzing the properties of time-periodic solutions to the dynamic equation (cycles). For this purpose, we apply the method linking the cycles and the fixed points of the composition of two parametrized half-period mappings for the approximate model. It is found that the cycles are unstable and can only be formed if the driving frequency is lower than its critical value. The polar anchoring parameter is estimated by making a comparison between the results of modeling and the experimental data for the shift vs frequency curve.

High frequency hysteresis-free switching in thin layers of smectic-C* ferroelectric liquid crystals

The insulating layers used for the alignment of ferroelectric liquid crystals (FLC) in electro-optical cells usually have non-negligible thickness and their capacitance determines the type of the director switching caused by a triangular-form external voltage U(tr) . With decreasing frequency of U(tr) , the hysteresis in a switching direction changes from the normal to the abnormal one at a characteristic hysteresis inversion frequency f(i) . In the vicinity of f(i) , the electro-optical response is thresholdless and the optical transmission manifests the V -shape field dependence. The V -shape regime is very interesting for certain applications, in particular to microdisplays due to a possibility of the gray scale realization. However, f(i) has to be enhanced from the usually observed frequency of a few Hz up to the range of hundreds of Hz. To this effect, a special FLC material has been designed and its basic properties (tilt angle, spontaneous polarization, rotational viscosity, and electric conductivity) have been measured over the entire range of the smectic-C* phase. Upon variation of cell parameters (thickness of both the FLC and alignment layers), temperature, and external voltage, the frequency of the V -shape effect as high as 150-1000 Hz (in the temperature range 30-75 degrees C) has been found experimentally. The operating voltage remains lower than 8 V. A quantitative interpretation of these results has been done using the modeling procedure developed earlier [S.P. Palto, Cryst. Rep. 48, 124 (2003)]. The modeling has been performed with the experimental values of the FLC material and the cell parameters and has shown very good agreement with experiment. The key point of this approach is consideration of the internal voltage on the FLC layer, the sign, amplitude, and form of which differ from U(tr) . The results of the modeling allow further improvement of the performance of electro-optical FLC cells for high frequency V-shape effect.

Thresholdless, hysteresis-free, V-shaped, electro-optical switching for a ferroelectric liquid crystal cell

A ferroelectric liquid crystal (FLC) cell can be modeled as a combination of capacitors and resistors. In accordance with the properties of the FLC cell, external electric elements, such as capacitors and resistors, are usually connected to achieve a V-shaped performance at a driving inversion frequency fi. However, the inversion frequency is strongly dependent on the external electric elements and the applied voltage. In this paper, the relation between the inversion frequency and the applied voltage is discussed. Additionally, the inversion frequency is found to be approximately proportional to (ReqCeq)(-0.52), where Req and Ceq are equivalent resistance and capacitance, respectively. Based on the above properties, a useful driving scheme is proposed to achieve thresholdless, hysteresis-free, V-shaped characteristics for FLC cells at a driving frequency of 100 Hz. The driving scheme can be applied to fast-response FLC display.

Effect of spontaneous polarization and polar surface anchoring on the director and layer structure in surface-stabilized ferroelectric liquid crystal cells

We use the Landau-de Gennes model to study theoretically the effect of the magnitude of the spontaneous polarization (P(S)), the ratio (r) between the equilibrium layer tilt and the smectic cone angle, the thickness of the insulating alignment layers and the strength of the polar and nonpolar surface anchoring on the director and layer structure in surface-stabilized ferroelectric liquid crystal cells with the chevron structure of smectic layers. The system shows a surprising number of stable structures, accompanied by one or two metastable ones. At P(S) greater than the critical value only quasimonostable structures, which can exhibit the thresholdless (V-shaped) switching, exist at all r and both at weak and strong polar surface anchoring. At lower P(S) bistable and monostable structures can coexist. Bistable structures can be expected at high r, low P(S) and if polar surface anchoring is weaker than the nonpolar one. Lowering the ratio r and/or increasing the strength of polar anchoring promotes the stability of monostable structures. Thicker insulating alignment layers also drive the system into the monostable state. Polar surface anchoring induces a large surface electroclinic effect. As a result the nematic deformations close to the surfaces are very strong and the stress is relieved by bending of the smectic layers. This leads to the formation of a double chevron structure which is stable at very large polar anchoring and due to the surface electroclinic effect it is metastable also at lower values of polar anchoring.

Intrinsic aspect of V-shaped switching in ferroelectric liquid crystals: biaxial anchoring arising from peculiar short axis biasing in the molecular rotation around the long axis

To clarify the intrinsic aspect of practically usable thresholdless V-shaped switching in ferroelectric liquid crystals, we have observed textures and measured polarized Raman scattering as well as optical transmittance in a thin homogeneous cell of a single compound by applying an electric field. The results indicate that the so-called surface stabilized ferroelectric states are destabilized, and that there exist rather stable two domains with broad and narrow molecular orientational distributions, both of which show the almost ideal V-shaped switching with considerably low transmittance at the tip of the V. We have concluded that the main cause of the V-shaped switching is the biaxial anchoring on the substrates coated with polyimide, which makes the most polarizable short axis normal to the substrates. It is in competition with the ordinary anchoring that favors the director parallel to the substrates, when the material has such a bulk intrinsic property that this short axis is parallel to the tilt plane. The competition makes the total anchoring energy almost independent of the azimuthal angle and gives rise to the V-shaped switching.

Switching dynamics and surface forces in thresholdless "V-shaped" switching ferroelectric liquid crystals

The electrostatic model of thresholdless V-shaped switching is able to explain the general low frequency (quasistatic) electro-optic behavior of smectic-C* ferroelectric liquid crystals (vFLCs). Here, dynamical equations based on the electrostatic model are developed which predict a vFLC cell's small-amplitude switching speed and which also show that a strongly amplitude-dependent switching speed is expected. A relationship between the switching time constants of analog vFLCs and of the faster, yet structurally similar, binary FLCs is found. The electrostatic model applies in the limit where the FLC's spontaneous polarization is large enough to completely overwhelm surface and elastic forces. This analysis suggests that, in many cases of practical interest, electrostatic energies may be low enough for surface forces to play an important role even when the director structure is strongly stiffened by a large polarization charge. It is shown that the addition of surface forces to the electrostatic model can improve agreement between the model and the observed dynamical response of vFLC cells.