Chapter 1 Introduction
1.4 Motivation
When the CLCs cells are wanted to control the intensity of reflective light, it must be applied the field across the cells. It causes to the pitch contraction and the perturbations in the helix if the field parallel to the helical axis. Thus, the color of the reflective light would be changed and shifted to the shorter wavelengths. In order to solve this phenomenon, a study of molecular behaviors of CLCs is important for us to discover more information.
For the reason, the main objective of this thesis is to understand how the external field affects the helical axis, and propose a method based on these effects to enhance the stability of the helical axis. We infer the host dielectric anisotropic (ε) and birefringence (n) to influence the CLC’s behavior. Besides, a discussion of the results will be given in this thesis.
1.5 Organization of Thesis
In this thesis, the contents would be presented as following. Chapter 2 introduces the basic optical properties and the theories of field-induced wavelength shift for CLCs display.
Chapter 3 describes the measurement instruments which are used in experiments. The experiment processes, results, characteristics measurements and performance evaluation including color shift, dielectric anisotropic, birefringence and spectrums that measured by spectrometer are in Chapter 4. Conclusions are finally drawn in Chapter 5 along with future research directions pointed out.
Chapter 2
plane are twisted slightly with respect to one another. The distance along the helical axis for the director to rotate 2π is called the pitch P0 as shown in Fig. 1.2. The unique optical properties of the cholesteric phase are recognized by both Reinitzer and Lehmann at the time of their early investigations which culminated in the discovery of the liquid crystalline state.CLCs have a supermolecular periodic helical structure. The helical pitch of cholesteric can be the same order of magnitude as the wavelength of visible light, thus the Bragg reflection occurs. In this chapter, we consider the general optical properties of CLCs, such as the influences of chiral material, Bragg diffraction due to the periodical helical structure, and induced circular dichroism. The influences of external field are also discussed briefly in order to understand the phenomenon of color change effect.
2.2 Effect of Chiral Material
Chirality may cause an intrinsic helical structure of the director field as shown in Fig.
2.1. Instead of the uniform alignment of the director field occurring in the nematic phase, the respective chiral nematic phase exhibits a helical structure such like CLCs. For practical application, CLCs are usually formed by adding some chiral dopants into a nematic host. In the preparation of a CLCs mixture, the helical pitch is controlled by the concentration of the chiral material and the helical twisting power (HTP) of the chiral dopant. The HTP is defined
as:
c P HTP
1
. (2.1)
Where c is the concentration of the chiral dopant in [weight %], and P is the helical pitch of the CLCs mixture in [μm]. Both the magnitude and sign of HTP are meaningful. It is customary to assign a positive HTP and a negative HTP to materials that exhibit the right-handed helix, and the left-handed helix, respectively. In practice, more than one chiral dopants are often added in a mixture to obtain desired properties. The pitch of the mixture with multiple dopants can be conveniently approximated by:
1 1 2 2
1
... n n Pc HTP c HTP c HTP
. (2.2)
Where ci and HTPi are the concentration and helical twisting power of the ith chiral dopant, respectively. For most cholesteric materials P is decreased with temperature:
dP 0
dT , (2.3)
Fig. 2.1 Helical structures formed in chiral liquid crystal. (a) N* is the cholesteric phase, (b) BP is the blue phase, (c) SmC* is the chiral smectic-C, and (d) TGBA is the twist grain boundary phase [4].
2.3 Optical Properties of Cholesteric Liquid Crystals I. Textures in 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.
Fig. 2.11 The diagram of the gray scale states of the CLCs display [3]
2.4 Reflective Color for CLCs I. Controlling Cholesteric Color
In the preceding section, the theories of reflective color for CLCs are discussed generally. The cholesteric color is controlled by temperature, electric field, chiral doping ratio, etc. However, if the cholesteric color is easily changed by the temperature of the environment, it is not suitable for CLCs to be a communication of information [15].
The pitch length increases or decreases depending on the environment temperature because of the helical twisting power will be changed. It may cause the pitch length to become longer or shorter and lead the cholesteric reflected color to be different [16] [17].
Therefore, it is important that the CLCs material is not sensitive to the temperature and the color can be well controlled and fixed if it wants to use on the display applications.
The color change of the CLCs by electric fields was proposed by Harper, Hansen, and Schneeberger [18] [19]. It is also called the ETC (Electrically Tunable Color) [20]. In 1968, de Gennes [21] and Meyer [22] proposed that an electric or magnetic field perpendicular to helical axis of the CLCs would elongate the cholesteric pitch and thereby modifying the reflected color according to the Bragg’s Law [23]. It is observed that the color change from blue to red (redshift) with increasing electric field which applied perpendicular to the helical axis. In contrast, the effects observed from Harper change from red to blue (blueshift) with increasing electric field which applied parallel to the helical axis. The helical axis will be disturbed or unwind and resulting in an aligned homeotropic configuration finally.
II. Blueshift
The reflected color of the CLCs can be turned by varying the voltage across the cell.
It is defined for the short pitch, a shift of the selective reflection peak to shorter wavelengths
shorter area. However, it is shown that the blueshift of the selection reflection results from a helix distortion of the texture, and it causes a larger angle with the incident light and the blueshift can be observed given by Eq. (2.3). The undesirable blue shift, however, emerges within this region. This phenomenon is associated with the LCs’ Δε and Δn based on the Helfrich deformation. In this thesis, the main purpose is to resolve the blueshift when the CLCs cells are driving. The blue shift has been modeled by Meyer .
2.5 Proposed Method to Resolve Blueshift I. Effects of Electric Field on CLCs
Electric field acts on the anisotropic of the electric susceptibility exert torques within a LC which may compete with the elastic torques determining its internal structure. R. B.
Meyer was proposed [22] [24] [25] and use the Frank’s theory of curvature elasticity in molecularly uniaxial LC is used and calculates the effects of external field on the helical structure of cholesteric materials.
Frank’s theory assumes that in cholesteric materials, only one molecular axis is aligned. They are equivalent to nematic materials on a small scale. A unit vector L is defined which is parallel to the axis of molecular alignment at any point. Frank derives an expression for the elastic free energy density in a cholesteric substance:
2 2 2
right-handed (x, y, z) coordinate system is
L ( c o s q
0z , s i n q
0z , 0 )
. (2.7)Since there is local cylindrical symmetry about L, the electric susceptibility has only two components, χ║and χ⊥, parallel and perpendicular to L, respectively. Assuming that the system is neither ferroelectric nor ferromagnetic, the field (F) energy density is given by
1 1( ( ) ( ) )2
2 2
F ll
g FF F L FL , (2.8)
The general procedure for calculating the effect of the field is to find the structure, characterized by L as a function of position in the sample, which minimizes the total free energy.
G sample( g
E g
F) dV
(2.9)
The field dependence of the structure is in general a perturbation of the helix at low fields, followed by complete breakdown of the helix at some critical field.
Without following this general procedure, in simple situations, it can guess at the form of the perturbation in material far from surfaces. For example, consider the uniform helix of Eq. (2.7), and apply a F=Fx . Assuming that Lˆ z remains 0, the general form of the perturbed helix is
In which f(0)0, and f has period /q. By varying the integral G, one can find the different equation for f. Solve this, one can then find the q which minimizes G for a given value of the field. The pitch of the helix can often be observed as the color of light reflected by the helical structure. The result in this case, to lowest order approximation, is
As another example, apply to the uniform helix the field
F=Fz ˆ
, and assume that the boundary condition will maintain the axis of the helix parallel to the field. Then a likely form of perturbation, if ll , is to rotate L at every point through an angle ρ toward the field;
L ( c o s c o s qz , c o s s i n qz , s i n )
(2.12)In this case, the perturbation involves both bending and torsional strains, and depends on the relative magnitudes of the moduli of these strain, k33 and k22, respectively. If k33 ≧
For k33 ＞ k22, the breakdown will involve hysteresis around this field value, since high energy configurations exist between the unperturbed helix and the breakdown
configuration. For k33 ＜ k22, there is a range of field for which ρ and q change continuously:
Below this range, there is no perturbation, and above it there is complete breakdown.
II. Propose Method to Improvement Blueshift
In some cases, applying a electric field perpendicular to a thin film of the CLCs in the planar texture, rather than changing the wavelength of light reflected by the helical structure.
This case can be obtained by the present theory by assuming that
ll in CLC’s nematic host and the reflective color will be uniform when CLCs are driving, withF=Fz . The ˆ diagram of electric susceptibility for LC molecular is shown in Fig. 2.12. Here we use the relative permittivity to substitution the electric susceptibility is given by:
e
r
1 , (2.16)
pitch is difficult to decrease when CLCs are driving. This explains the blue shift is suppressed.
pitch is difficult to decrease when CLCs are driving. This explains the blue shift is suppressed.