Chapter 1 Introduction
1.5 Organization of This Thesis
The thesis is organized as following︰The principle of the polarization and the mechanism of one-dimensional linearly and two-dimensional radially stretched PDLC films are presented in Chapter 2. In Chapter 3, the fabrication process of the PDLC films and the measurement instruments are introduced in detail. The discussion of the experimental results and the conclusion of this thesis will be presented in Chapter 4 and 5.
Chapter 2
Principle
2.1 Polarization of Optical Waves
Light which can be treated as transverse electromagnetic waves in the electromagnetic theory of light is often represented by its electric field vector[10, 11].
The orientation of the electric field is constant, although its magnitude and sign vary in time and space as the light propagates. A transverse optical wave that propagates along the z axis can be decomposed into two orthogonal components of electric field, which are expressed as below :
) difference between the two waves and limited in the region -π <δ ≤π . The resultant optical wave is the vector sum of these two orthogonal waves :
t) wave whose electric field vector oscillates cosinusoidally along a constant direction in xy plane is said to be linearly polarized, as shown in Fig. 11.
(a) (b)
Fig. 11 Light linearly polarized (a) in the first and third quadrants (δ = 0) (b) in the first and third quadrants (δ = π) oscillating in time
Another case of importance is the circular polarization, which occurs when E0x = E0y and δ = ±
The light is right-hand circularly polarized with δ = ﹣ 2
1 π, which undergoes a
clockwise rotation of the electric field vector in the xy plane and left-hand circularly polarized with δ =
2
1π, which undergoes a counterclockwise rotation of the electric
field vector in the xy plane, as seen by an observer looking back at the source. The circularly polarized light is depicted in Fig. 12.
(a) (b)
Fig. 12 (a) Right-hand circularly polarized light with the electric field rotating clockwise (b) left-hand circularly polarized light with the electric field rotating counterclockwise
The elliptical polarization is the most general case of a polarized light. Both linear polarization and circular polarization are considered to be special cases of elliptical polarization. The equation of the ellipse making an angle θ with the xy coordinate can be obtained by several steps of elementary algebra of combining the two equations in Eq. (1).
δ
Eq. (5) can be diagonalized by a transformation of the coordinate system. The new axes of the new coordinate system, x’ and y’, are along the principal axes of the ellipse, as shown in Fig. 13. Thus the new equation of the ellipse in the x’y’
coordinate becomes
The length of the principal semi-axes of the ellipse are given by
θ
Fig. 13 Elliptically polarized light
The light is right-hand elliptically polarized with sinδ < 0 and left-hand elliptically polarized with sinδ > 0, as shown in Fig. 14. The comparison of the linear and circular polarizarion which is the special case of the elliptical polarization is listed in Table 1.
(a)
(b)
Fig. 14 Elliptical polarization configuration at various relative phase difference δ when (a) E0y = E0x and (b) E0y > E0x
Tab. 1 Comparison of state of polarization
2.2 Spatially Inhomogeneous Polarized Beam
The spatially homogeneous polarized beam is defined as the beam with the same polarization at all points in the pupil plane, i.e. Eρ(x,y)=Exiˆ+Eyˆj
. The homogeneous polarized beam with linear polarization (in x-direction), right-hand circular polarization and left-hand polarization are depicted in Fig. 15(a).
In addition, the spatially inhomogeneous polarized beam has specific state of polarization at every local point in the pupil plane, as shown in Fig. 15(b). The local electric field can be defined as Eρi(xi,yi )=Ex,i ˆi+Ey,i ˆj
where i is the positional index of a local point. The total field can be presented by the summation of each local state of polarization：
∑
== n
1
i i i i
total(x,y) E (x ,y )
Eρ ρ
(9)
(a) (b)
Fig. 15 (a) The spatially homogeneous polarized beam and (b) the spatially inhomogeneous polarized beam
2.2.1 Cylindrical Vector Beam
The cylindrical vector beam which has symmetric distribution on polarization is the special case of the spatially inhomogeneous polarized beams [12]. The cylindrical vector beam has been researched in recent years due to its unique properties resulted from the state of polarization. The general solutions of the wave equation for the cylindrical vector beam are two independent ones which are azimuthally polarized beam and radially polarized beam. The azimuthally and radially polarized beams have cylindrical symmetry in field-amplitude and polarization. The two normal cylindrical vector beams have donut-like field distribution and are symmetric in r-direction and ψ-direction, as shown in Fig. 16. The field of azimuthally and radially polarized beams can be presented by Eρap(r,φ )=E0(φ)φˆ
and Eρrp(r,φ )=E0(r)rˆ respectively.
(a) (b)
Fig. 16 The field distribution of the cylindrical vector beams (a) radially polarized beam and (b) azimuthally polarized beam where the arrows represent the polarization directions
2.3 Polymer dispersed Liquid Crystal ( PDLC )
2.3.1 PDLC Light Modulator [13]
A polymer dispersed liquid crystal film is a homogeneous mixture of polymer and micro-sized nematic liquid crystal droplets, as shown in Fig. 17. The liquid crystal material of the microdroplets is positive birefringent (ne > no), and the refraction index np of the polymer is chosen to be close to the ordinary refraction index no of the liquid crystal.
In the undriven state, the orientation of the nematic liquid crystal in the microdroplets is arbitrary with respect to the plane of the film, and the difference between the refraction index of the polymer and the effective refraction index of the liquid crystal results in scattering of the incident light. The film appears opaque for the severe scattering of light. When the external electric field is applied to the film, the liquid crystal in the droplets is aligned , and the director is parallel to the field because of the
positive birefringence. Since the ordinary refraction index of the liquid crystal is matched to the refraction index of the polymer, the incident light with a normal incident angle encounters no variation in refraction index and transmits through the film without being scattered. Thus it’s possible to control the intensity of transmitted light by changing the orientation of the liquid crystal molecules with an electric field.
Fig. 17 Polymer dispersed liquid crystal (PDLC) light modulator
For angles of the incident light other than normal, the liquid crystal droplets are optically birefringent. One polarization component will see the ordinary refraction index no, while the other polarization component will see the effective refraction index ne (θ) as below :
2 o
2 2
e 2 2
e n
con n
sin ) ( n
1 θ θ
θ = + (11)
where θ is the angle between the optical axis and the direction of propagation in the droplets. The difference between np and ne (θ) results in a small amount of scattering at the boundary of the droplets, increasing with angle θ, as shown in Fig. 18. The films appear hazy because of the decrease in the transmission when viewed at large viewing angles.
(a)
(b) (c)
Fig. 18 The scattering mechanism of the PDLC operation. (a) Off-state (b) On state – viewing at the normal (c) On state – viewing off-axis
2.3.2 Elongation of Liquid Crystal Droplets
In PDLC films, the liquid crystal droplets are non-spherical and can be
approximated by an ellipse with a small aspect ratio. The strain arising from the matrix polymerization process during solvent evaporation results in the distortion of droplet shape. The liquid crystal molecules in the droplets can be aligned in different director fields depending mainly on the interface-anchoring and elastic properties.
Thus the bipolar tangential alignment illustrated in Fig. 20(a) is usually observed where the director fields develop along the major axes of the ellipsoidal cavities.
With one-dimensional elongation of liquid crystal droplets, the liquid crystal molecule in the droplets will be also be aligned in the long axis of the prolate droplet.
Therefore, the scattering behavior of the PDLC films can be partly controlled. There are three ways to obtain elongated liquid crystal droplets, as shown in Fig. 19 [14]. In the first way, the PDLC film is stretched above the plastic deformation and therefore liquid crystal droplets are deformed and elongated along the stretching direction. The second way is to apply high electric field (about 10-15 V/µm) on the PDLC film during polymerization. The electric contribution to the liquid crystal elastic deformation free energy enforces droplets elongation. In the third method, curable polymer is utilized. Shearing force is adopted during curing the polymer. Among these three methods, the stretching of the PDLC film is considered to be the simplest and most effective process and adopted in this research.
(a) (b)
(c)
Fig. 19 Technique of elongating liquid crystal droplets (a) Stretching of PDLC film (b) deforming effect of electric field (c) shearing of system
2.3.3 One-dimensional Linearly Stretched PDLC Film
When the one-dimensional strain is applied on the PDLC film, the droplet is elongated along the stretching direction, and the bipolar axes in the cavities are also aligned along this direction due to the anchoring effect of the interface, as shown in Fig. 20(b). A refraction index difference between the axes parallel and perpendicular arises from the parallel alignment of the fields to the stretching direction, as shown in Fig. 21. Since the refraction index of the polymer matrix is almost isotropic, a large refraction index mismatch exists in the direction parallel to the stretching direction while the ordinary refraction index of the liquid crystal no is close to the refraction index of the polymer np in the direction perpendicular to the stretching direction.
(a)
(b)
Fig. 20 PDLC films (a) before and (b) after stretching
Fig. 21 The refraction index difference in the stretched PDLC films
The one-dimensionally stretched PDLC films can be employed as scattering polarizers due to the polarization selectivity resulting from the unidirectional
alignment of the LC droplets and the parallel alignment of the LC director fields [15].
The linear polarized light whose direction of polarization is perpendicular to the stretching direction can transmit for the refraction index match of np and no, while the light polarized in the direction of the droplet ordering is strongly scattered due to the mismatch between np and ne, as shown in Fig. 22. Thus the stretched PDLC films as scattering polarizers can enhance light efficiency through polarization recycling.
Fig. 22 Mechanism of a scattering polarizer based on PDLC technology
2.3.4 Two-dimensional Radially Stretched PDLC Film
Since the transmission axis of the stretched PDLC films is normal to the stretching direction, special polarizers can be obtained by applying strain in different directions on the PDLC films. The azimuthal polarizer which can be used as a polarization axis finder is fabricated by radially stretching of the film. Thus the transmission axis is along the azimuthal direction, and the unpolarized light can be converted into the state of azimuthal polarization, as shown in Fig. 23.
Fig. 23 Mechanism of an azimuthal polarizer by radially stretching of PDLC film
Chapter 3
Fabrication and Measurement Instruments
3.1 Preparation of Stretched PDLC Films
3.1.1 Fabrication of PDLC Films
PDLC films were prepared by encapsulation method in this research[16]. The system was heterogeneous during the whole fabrication process. Liquid crystal was dispersed in a polymer solution , the solvent of which did not dissolve liquid crystal.
Polyvinyl-alcohol (PVA) was chosen as the PDLC binder. The solvent evaporation stabilized the obtained composite structure due to polymer solidification.
The detailed steps of fabrication are listed below, and the preparation of the PDLC films is shown schematically in Fig. 24.
(a) PDLC solution preparation:
(1) PVA, a water-soluble polymer, was used as the solvent. The nematic liquid crystal E7 (Merck Display Technology, Ltd.) was mixed with a 20 wt% aqueous solution of PVA (PVA 81381, molecular weight 31000, Fluka Analytical) , and the liquid crystal concentration in the PDLC films ( PVA with E7) was set 20-45 wt %.
(2) The solution was then emulsified by agitators, and the bubbles in the solution were driven out by soaking the beaker containing the solution into a ultrasonic
tank.
(b) Film process:
(1) The emulsion was coated on a polyethylene terephthalate (PET) substrate using a Meyer Bar (coating rod) driven by hands.
(2) The thin film was dried in the sweatbox to have the water evaporated from the film surface.
(3) The dried PDLC films were peeled from the PET substrate. The film thickness was 8 to 24 µm depending on the wire size of the Meyer Bar.
(4) The samples were cut into the H-shape according to the ASTM Standard D 1708 (American Standards for Testing and Materials) and one-dimensionally stretched by a micro-tensile tester with the drawing rate of 0.5 mm/min.
The refraction indices of E7 and PVA is shown in Table 2.
Tab. 2 Refraction indices of E7 and PVA
(a)
(b)
(c)
(d)
Fig. 24 Flow of preparation of PDLC films (a) the emulsion applied on the PET substrate (b) Meyer Bar coating (c) the film dried in sweatbox (d) the film one-dimensionally stretched by micro-tensile tester
3.1.2 Real-time Measurement Set-up of Optical Properties
The measurement of optical transmittance under different strain as defined in Eq.
(12) can be achieved by a real-time measurement set-up as shown in Fig. 25 and 26. The unstretched PDLC film were cut in the shape defined by the American Society for Testing and Materials (ASTM) Standard D 1708, as shown in Fig. 27. The sample was connected to a stress sensor, with a Helium-Neon (He-Ne) laser operating at 633 nm as the light source directed at normal incidence on it. A rotating polarizer was set between the laser and the sample, and polarizations parallel and perpendicular to the stretching direction were investigated. The sample was then one-dimensionally stretched by the micro-tensile tester with the draw rate of 0.5 mm/min. The intensity of the transmitted light was detected by a photodetector while the sample is simultaneously stretched.
length film
Unstretced
n deformatio
Strain= Film (12)
Fig. 25 Schematic representation of real-time measurement set-up
Fig. 26 The pictures of real-time measurement set-up
Fig. 27 Samples cut in the shape defined by ASTM standard D 1708
3.1.3 Radially Stretching Process
In the former section, the PDLC films were one-dimensional linearly stretched to obtain linear polarizer. Polarizers with specific polarization function can be achieved by varying the stretching direction. Here the azimuthal polarizer was obtained by radially stretching of the PDLC film.
The steps of fabrication are listed below, and the set-up of radially stretching is shown in Fig. 28.
Power-meter Load Cell
Movable Clips Polarizer
He-Ne Laser
(1) The PDLC films whose concentration of E7 is 25 wt% was cut into ‘donut’
shape with radius of 16 mm and attached to the film holder. An o-ring was used at the center of the sample to prevent the sample from breaking.
(2) A screw across the central hole of the sample was attached to the micro-tensile tester.
(3) The samples were radially stretched by applying strain at the center of the samples, and the drawing rate of the micro-tensile tester was 0.5 mm/min.
Fig. 28 The set-up of radially stretching process
3.2 FT-IR Spectrometer
A Fourier transform infrared spectrometer (FT-IR) (Nicolet 380, Thermo Electron) with a rotating polarizer, as shown in Fig. 29, is used to investigate the macroscopic orientation of the liquid crystal directors.
Fig. 29 Inside layout of the FT-IR Spectrometer
The C≡N band is representative functional group in E7. When the light is polarized in the direction parallel to the optical axes of E7, a specific wave band at wavenumber 2230 cm-1 will be absorbed by the C≡N band .The orientation of E7 can be represented by the ordering parameter S defined by Eq. (13)
2
where θ is the angle between the optical axes of E7 and the stretching direction. S is converted into Eq. (14) by infrared dichroism technique [17].
2
where A∥ and A⊥ are the absorbances of the C≡N band of E7 at 2230 cm-1, with the infrared beam polarized parallel and perpendicular to the stretching direction of the film.
A sample of the IR dichroism in Fig. 30 is indicative of a macroscopic orientation of E7 aligned in the stretching direction where A∥ is greater than A⊥.
Fig. 30 Polarized infrared spectra of a stretched PDLC film (PVA/E7) with the polarizations of the incident beam parallel and perpendicular to the stretching direction
Chapter 4
Experimental Results and Discussion
4.1 Introduction
The scattering polarizers with polarization recycling can be employed in liquid crystal displays instead of the conventional absorbing polarizers to improve the optical efficiency as mentioned before. Because the scattering polarizers are relatively simple in fabrication process, which can be a potential candidate in portable LCDs where power saving is one of the key issues. Stretching of the PDLC films is one of the most effective way to fabricate scattering polarizers. Besides, the azimuthal polarizer which converts the unpolarized light into azimuthal polarization can be achieved by two-dimensional radially stretching of the PDLC films instead of one-dimensional linearly stretching. A study of the optical properties under different strain will be investigated in this chapter, and the experimental results will discussed.
4.2 Optical Properties of Stretched PDLC Films
4.2.1 Elongated LC Droplets in Stretched PDLC Films
The PDLC films were stretched under different strain where the liquid crystal droplets were elongated and attained different range of deformation as shown in Fig. 31 and Table 3. The liquid crystal droplet were on the order of several microns as indicated in the optical microscope image. As the films were stretched longer, the aspect ratios of the liquid crystal droplets increased, and the droplets were aligned along the stretching direction.
(a) (b)
(c) (d)
(e) (f)
Fig. 31 The PDLC films stretched under the strains of (a) 0% (unstretched) (b) 20% (c) 30% (d) 40% (e) 50% (f) 70%
Tab. 3 Strain and range of deformation of the stretched PDLC films
Strain (%) Range of deformation
0 1 : 1
20 1.6-2 : 1
30 1.6-2 : 1
40 2 : 1
50 2.5-2.8 : 1
70 3-4 : 1
4.2.2 Dependence of LC Concentration on Optical Properties
The dependence of LC concentration on transmittance under different strain was discussed. The film thickness was fixed at 10 µm in this experiment. The concentration of the liquid crystal (E7) in the PDLC films were adjusted, and the optical transmittances under different strain were measured while the PDLC films were stretched. The measurement results are shown in Fig. 32 where T∥ and T⊥ are the transmittances of the PDLC films, with the parallel and perpendicular polarization state to the stretching direction of the film. When the concentration of E7 was 20 wt%, most of the light transmitted at the normal direction without being scattered by the liquid crystal droplets, and the transmittance was highest among all the samples. The highest T∥ (50%) was achieved under the strain of 30%. The defects which occurred on the surfaces of the films occasionally due to air bubbles in the films as the stain was higher than 50% would result in intensive and predominantly forward scattering for both ∥ and ⊥ polarizations and strongly altered T∥ and T⊥ accordingly.
Fig. 32 The strain-transmittance curve of the PDLC films with different concentration of E7
In order to further evaluate the film quality, the extinction ratio was defined as
1 2
T ratio T
Extinction = (15)
where T1 (T⊥) was the transmittance with polarization parallel to the transmission axis, and T2 (T∥) was the transmittance with polarization perpendicular to the transmission axis. An ideal polarizer has extinction ration = 0. For real polarizers, extinction ratio is always larger than 0. The extinction ratio properties of the PDLC films with different
concentration of E7 are shown in Fig. 33. The extinction ratio dropped more rapidly as the concentration of E7 was over 25 wt% than it was 20 wt%. When the concentration of E7 was 25-45 wt%, the extinction ratio was lower than 0.1. Thus a sample with the concentration of E7 over 25 wt% had better extinguishing efficiency. Considering both transmittance and extinction, the sample had better performance with 25 wt% of E7.
Fig. 33 The extinction ratio properties of the PDLC films with different concentration of E7
4.2.3 Effect of Relative Humidity during Drying Process
The optical performance of the films was unstable when the films are dried in ambient condition. The behavior of the relative humidity which was a parameter of evaporation of water from the film surface was investigated. The concentration of E7 was fixed at 25 wt%. The definition of the relative humidity is the ratio of the partial
pressure of water vapor in air-water mixture to the saturated vapor pressure of water at a prescribed temperature. The relative humidity was controlled while the thin film was
pressure of water vapor in air-water mixture to the saturated vapor pressure of water at a prescribed temperature. The relative humidity was controlled while the thin film was