Chapter 2 Overview of Cholesteric Liquid Crystals
2.3 Optical Properties of Cholesteric Liquid Crystals
For CLCs, several types of electro-optic effects have been observed which depending on the surface treatment (boundary conditions), the helical pitch P, the thickness to pitch ratio d/P, the dielectric anisotropy , the external field, and the frequency of the applied field.
The CLCs textures influence the electro-optical behaviors when the textures are changed. The typical cholesteric textures for the orientation of the liquid crystal are shown in Fig. 2.2.
The CLCs with a given pitch, its texture is characterised by the direction of the helical axis. When the helical axis is perpendicular to the cell surface, the texture is called planar texture, as shown in Fig. 2.2(a). When, on the other hand, the helical axis is more or less parallel to the cell surface, the texture is called focal conic texture, as shown in Fig. 2.2(b).
However, when the pitch of the CLCs are long and the helical axis is parallel to the cell surface, the texture is called fingerprint texture, as shown in Fig. 2.2(c).
With the appropriate substrate surface treatment or dispersed polymer, the planar
texture and focal conic texture can be stable at zero field. For the CLCs with appositive the relaxation occurs that results in the formation of the transient planar texture.
(a) (b)
(c) (d)
Fig. 2.2 Schematic of the textures in CLCs: (a) planar, (b) focal conic, (c) fingerprint, and (d) isotropic or homeotropic cholesteric texture [4]
In order to study the electro-optic effects, the CLCs are usually sandwiched between two parallel plates with transparent ITO electrodes. Many optical properties of CLCs are
Bragg Reflection
When the CLCs are in the planar texture, the circularly polarized light is reflected by Bragg theory because of their chiral and periodic structure. Selective reflection occurs when the white light is incident on a cholesteric cell. In various cholesteric systems, the period of the helical pitch varies by a wide range (about 0.1μm to several hundred μm). For the long pitch (low concentration chirality) P >>λ (where λ is the wavelength of light), the light propagation parallel to the helical axis may be described by a superposition of two eigenwaves having electric field vectors parallel and perpendicular to the director. The long pitch case was studied for the first time by C. Mauguin [5] [6].
For the short pitch (high concentration chirality), when λ and P are comparable, the eigenwaves become elliptical and circular in the limiting case. It is well known that the selection reflection occurs in the limiting case due to the Bragg diffraction at a wavelength λ :
2( / 2) cosP m/navemn Pave cos. (2.3)
Where m is the diffraction order, α is the angle of light incidence and reflection, and nave is the average refractive index of the CLC medium. There are some characteristics and restrictions for the light propagating along the helical axis as following:
Only the first order Bragg reflection is possible in this case. This is confirmed by experimental results and theoretical considerations [7]. According to Eq. (2.3), the maximum selective reflection occurs at the wavelength n Pave when the angle of incident light is
reflection spectrum for CLCs. The reflected and transmitted light is circularly polarized. The circularly polarised light with the same handedness as the helical structure is reflected strongly because of the constructive interference of the light reflected from different positions, while circularly polarised light with the opposite handedness to the helical structure is not reflected because of the destructive interference of the light reflected from different positions.
If the (normally) incident light is unpolarised, then the maximum reflection from the CLCs are 50%. 100% reflection can be achieved by stacking a left-handed cholesteric liquid crystal and a right-handed cholesteric liquid crystal, as shown in Fig. 2.5.
Fig.2.3. Bragg reflection from a cholesteric planar texture film
Fig. 2.4 Reflection spectrum is in the planar texture for CLCs
Fig.2.5. Reflection spectrum is in the planar texture for
stackingCLCs
II. Optical properties in different textures
CLCs exhibit three major texture. The state of a cholesteric liquid crystal is mainly determined by the surface anchoring and cell thickness, and the CLCs are easy to change its texture by adding electric or magnetic field. When an electric field applied to the CLCs cell, a texture transition occurs to minimize the free energy system. The texture transition is strongly associated with alignment layer, dielectric anisotropic, field amplitude, and the frequency
Δλ
of the external field. The generally operating modes are described as following:
(i) When the dielectric anisotropy>0:
Fig. 2.6 schematic diagram showing the possible transitions among the cholesteric textures
Fig. 2.7 Schematic diagram of the states of the CLCs which dielectric anisotropy is positive (a) Planar texture (b) Focal conic texture (c) Homeotropic texture
When the CLCs are in the planar texture at zero field, the helical axis is
sufficiently high external electric field is applied cross the cell. In the focal conic texture, the helical axis is more or less parallel to the surface as shown in Fig. 2.7(b). Incident light is diffracted or scattered in the forward direction and the material in this state has less reflective color appearance. There are two possible mechanisms for the transition from the planar texture to the focal conic texture: oily streak and Helfrich deformation.
A microphotograph of the oily streak in a cholesteric liquid crystal is shown in Fig.
2.8. By bending the cholesteric layers, the electric energy is reduced as a sacrifice of the elastic energy, surface energy at the cell surface and wall energy in the vertical middle plane [8]. The transition is nucleation process. Sufficiently large oily streaks have to be created by irregularities, such as spacers, impurities and surface defect, in order to overcome the energy barrier. The applied field has to be higher than a threshold given by
0 0
Where h is the cell thickness, w is the surface energy and K is the elastic constant. In deriving the equation. Because it is nucleation transition, the transition time is long. Once the applied voltage is above Voily, the oily streaks grow until the liquid crystal is switched to the focal conic texture.
The Helfrich deformation is a two-dimensional undulation in the plane parallel to the cell surface [9, 10, 11], as shown in Fig. 2.9. The helical pitch is dilated in some regions and compressed in other regions. The energies involved are elastic energy, which increases with the amplitude of the undulation, and electrical energy, which decreases with the amplitude of the undulation. The electrical energy decrease of the electrical energy is able to compensate for an increase of the elastic energy, and therefore Helfrich deformation takes place. VHelfrich is given by
2 1 / 2
The wavelength of the undulation is λ=(2K33/K22)1/4(hP2)1/2. The threshold is pitch-dependent.
It is usually experimentally observed that VHelfrich is higher than Voily. If the applied voltage is increased gradually, the oily streaks appear. If the voltage is increased abruptly above VHelfrich, the Helfrich deformation dominates. Once the applied voltage is above VHelfrich, the amplitude of the undulation increases with increasing voltage and the liquid crystal transforms into the focal conic texture.
It is noticed that CLCs exhibit two stable states. One of them is the planar state, and the other one is the focal conic state when the applied voltage is turned off. So the CLCs material has the bistable property that is an advantage for display technology. There are two ways to switch it back to planar texture. If the CLCs have appositive dielectric anisotropy, a high voltage has to be applied to switch it to the homeotropic texture, then it relaxes back to the planar texture. If the liquid crystal is a dual frequency material, exhibiting positive dielectric anisotropy at low-frequency voltages and negative dielectric anisotropy at high-frequency voltages, it can be switched back directly to the planar texture by applying a high-frequency voltage.
When the liquid crystal is in the focal conic texture and the externally applied electric field is increased, more and more of the liquid crystal molecules are aligned parallel to the field, and the pitch of the liquid crystal becomes longer. When the applied field is above a threshold E , the helical structure is unwound; the pitch become s infinitely long and the
Fig. 2.8 Microphotograph of the planar texture is transferred to the focal conic texture when applied electric field
Fig. 2.9 Schematic diagram showing the structure of Helfrich deformation in a plane perpendicular to the cell surface
Planar texture Oily streak and
focal conic texture
(ii) When the dielectric anisotropy<0:
Fig. 2.10 Schematic diagram of the states of the CLCs which the dielectric anisotropy is negative (a) Initial texture in the planar state (b) Initial texture in the focal conic state (c) Planar texture (d) Homeotropic texture
No matter the CLCs cells are the in planar or focal conic state firstly as shown in Fig.
2.10(a) and (b), they have the same operating features when applied electric field. When an electric field E applied parallel to the axis h of the helix, it is a stable configuration and is shown in Fig. 2.10(c). In this instance the field only induces stabilization of the fluctuations.
As a consequence, the order parameter is increased and displacement of the selective reflection maximum in the longwave spectral region (red shift) is observed.
Another situation is the electric field applied perpendicular to the axis of the helix as shown in Fig. 2.10(d). This situation was investigated experimentally and theoretically when the applied voltage V>>Vth [12]. The helix deformations and the threshold field are described the by the same expression as in the case of CLCs with dielectric anisotropy>0, E || h. It is a threshold voltage that the CLCs switch from the planar texture to focal conic texture.
III. Gray Scale property of Cholesteric Liquid crystals
CLCs exhibit gray scale property because of their multi-domain structure if the planar texture and the focal conic texture are appeared at the same time. Starting from the imperfect planar texture, there are some domains can be switched to the focal conic texture when the threshold field is exceeded. The planar texture will be broken up into small domains and the incident is scattered [13, 14], as shown in Fig. 2.8. The reflective color will be decreased. Once a domain has been switched to the focal conic texture, it remains there even after the applied voltage is turned off because of the bistable property. The diagram of the gray scale states of a CLCs display is shown in Fig. 2.11. From right to left, the states are achieved by applying voltage pulses with increasing amplitude, and the reflectance decreases.
The domain is around 10 μm and the domain structure cannot be observed by the naked eye.
A cholesteric domain has only two stable states at zero field: it is either in the planar texture or in the focal conic texture. In a cholesteric display, it is observed that the domains in the planar texture have the same optical properties, independent of the states of other domains.