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CHAPTER – 3

ELECTRO OPTICAL METHODS

3.1 Introduction: Reorientation of the molecules in electric fields:

An electric field experiences a different dielectric constant when oscillating in a

direction parallel or perpendicular to the director. The difference is called the dielectric

anisotropy. Positive anisotropy means that the dielectric constant along the director is

larger than in the direction perpendicular to it. Due to the anisotropy, the dielectric

displacement and the induced dipole moment are not parallel to the electric field, except

when the director is parallel or perpendicular to the electric field. As a result, a torque is

exerted on the director. For materials with positive anisotropy, the director prefers to

align parallel to the electric field. Liquid crystals with a negative anisotropy tend to

orient themselves perpendicularly to the electric field.

The effect of an electric field on a liquid crystal medium with positive

anisotropy is illustrated in the pictures below. Originally the orientation is almost

horizontal parallel to the surface of glass. This is called homogeneous alignment and is

achieved by special treatment of the glass and rubbing in parallel direction to the glass

plate. When an electric field with direction along the blue arrow is applied, a torque

(represented in green) rising from the dielectric anisotropy, acts on the molecule. The

torque tends to align the molecule parallel to the field. This is called homeotropic

alignment. When the field strength is increased, the molecule will orient parallel to the

field.

The technological importance of the reorientation is obvious: it gives a

switchable medium by simply varying the applied electric field in the liquid crystal

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medium. In most applications a liquid crystal is used in a thin layer between two

conductive glass surfaces. To generate the electric field, thin electrodes layers are

deposited on the bottom and top of glass surface. For optical devices transparent

electrodes are used, made from Indium Tin Oxide (ITO). If the generated field is strong

enough, the molecules will reorient to follow its direction.

Original orientation Situation in electric field

Result electric field Result strong electric field

3.2. Optical birefringence

Applications of liquid crystals always involve optics associated with electric

fields. Hence they are called electro optic devices. The dielectric constants, which arise

from the electronic response of the molecules to the externally applied fields, are

different. To make the distinction, the refractive index is usually given for optical waves

instead of the dielectric constant. Due to their shape and structure, nematic liquid

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crystals behave as positive uniaxial birefringent crystals. The birefringence of a liquid

crystal is dependent on applied voltage, wavelength, and temperature.

Optical waves can also reorient the liquid crystal director in an analogue manner

as the electrically applied fields. In a display this can be neglected, since both the

optical dielectric anisotropy and the intensity of the optical fields are typically much

lower than those used in the static case. Therefore the optical transmission is mostly

independent of the director calculations.

To understand the influence of birefringence on the propagation of light

through a liquid crystal, the light must be represented by an electric field. This electric

field is described by a wave vector at each point. At a certain time and location, the

direction and the length of the vector correspond with the direction and magnitude of

the electric field. For a plane wave propagating in a specific direction, the electric field

vector in an isotropic medium describes an ellipse in the plane perpendicular to the

propagation direction. This ellipse represents the polarization of the light. Some special

cases are the linear polarization and the circular polarization where this ellipse is

distorted to a straight line or a perfect circle. Generally each ellipsoidal polarization can

be decomposed as a superposition of linear polarizations along two perpendicular axes.

In an isotropic medium, both linear polarizations move with the same speed. The speed

of the wave is determined by the refractive index of the medium.

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Figure 3.1 Light passing through a bi refringent block of material.

When light passes between media of different density, the direction of the beam

is changed as it passes through the surface, and this is called refraction. In the first

medium, the angle between the light ray and the perpendicular is called the angle of

incidence (i), and the corresponding angle in the second medium is called the angle of

refraction (r).

The ratio is called the index of refraction, and usually the

Assumption is that light is traveling from the less dense (air) media to denser media,

giving an index of refraction that is greater than 1. The theoretical reference is a

vacuum, or air (0.03% different) is usually used. The refractive index of a compound

decreases with increasing wavelength (dispersion), and increase of temperature, except

where absorption occurs.

The frequency is constant, but the vertically polarized light travels more slowly,

and waves are bunched together inside the material. The refractive index (n) is defined

as

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The crystal in Fig 3.1 has two refractive indices: one higher (corresponding to

slow propagation) for light polarized in the direction in which charge can move and

another, lower, value for light polarized perpendicular to this. These two indices are

usually denoted by ne and no. Birefringence is characteristic of a material, and is defined

simply as the difference between the maximum and minimum refractive index values.

Fig 3.2. The reflection and refraction of light at the boundary layer of two media

with Different refractive index.

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The optical density (refractive index) of the upper medium is lower than the

bottom one. The angle of incidence, θi, and the angle of reflection, θr are identical. The

angle of transmitted ray θt to the normal direction is smaller than θi . Using Fermat’s

principle, which states that light waves of a given frequency traverse the path between

two points which takes the least time, another relation can be derived for refractive

indices (Schnell’s law)

The sine of angle of incidence is inversely proportional to the refractive index of

the medium; see the notation in Fig. 3.2. We can clearly define the relative refractive

index, nr. Temperature increases, refractive index decreases (and subsequent

concentration readings decrease). Liquid refractive index and its dependence on

temperature or concentration are important for light-liquid interaction and liquid

thermo-optical property measurements.

A liquid-crystal cell consists of a thin nematic LC layer placed between two

parallel glass plates that are coated with thin layers of transparent conductive material.

A special transparent glass with conductive coatings was imported from USA. The

description of the cell is given in the chapter 4. The material then acts as a uniaxial

crystal with the optical axis parallel to the molecule orientation. We use a Cartesian

coordinate system with its z-axis perpendicular to the LC layer. The fast axis of the LC

molecule, so called ‘‘active molecular director’’ specified by the vector u, is oriented at

an angle of 450 with respect to the y-axis. When a polarized monochromatic light

propagates in the z direction through the LC cell with its polarization axis along the y-

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axis of the Cartesian coordinate system, a cell of thickness “t” provides phase

retardation.

3.3. Tunable opto electric studies

The reorientation of an LC can be achieved by the effect of an external electric bias

field.

Applying such a field, the molecules, long axis rotates such that the director

points mainly towards the same direction as the exciting electric field lines

(Homeotropic alignment with electric field).

When a liquid crystal placed in between a dielectric cell, this mechanism can be

used for continuous tuning of the effective permittivity of the cell.

DC biasing:

An electric bias field generates anisotropy of polarization in LC material.

This leads to an electric torque for the considered director given by the cross

product of the bias field with the polarization

Bias voltage is removed these torques leads the molecules back to the original

state caused by the minimum energy principle.

Ultimately the plane of optical polarization varies with the applied electric field.

The external bias voltage is <20v.

AC biasing (Electro-optic Modulator):

Liquid crystal has been given much attention due to its dielectric anisotropy

property that allows the change in the frequency. A sine wave of variable frequency is

used to energize the dielectric cell. The voltage was varied between 0 -20v till the

threshold voltage is exceeded. We see the same waveform from the photo detector.

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Then the frequency is varied and the output is monitored till we get the undistorted

waveform.

3.4 Phase Transition Studies

A thermo dynamic system transform from one phase to another phase is called

transition. The phase transitions are distinguished by an abrupt sudden change in one or

more physical properties like the heat capacity with a small change is thermodynamic

change such as temperature. A phase transition does not occur in a system having

extremely small number of particles. Non adiabatic change of the system takes a fast

phase transitions without undergoing phase transition. This state is called Metastable,

which is not theoretically stable but quasi stable. Super heating, super cooling, super

saturation occur under this condition

Based on non analyticity, Ehrenfest6 classification is the first classifying type of

phase transition, depending on the relation between the thermodynamic quantity

undergoing discontinuity and the Gibbs free energy function. These classes of phase

transitions are labeled by the lowest derivative of the free energy that is discontinuous at

the transition.

If there is discontinuity in the second derivative of the free energy, second order phase

transitions takes place.

Phase transitions are divided into two types depending upon this classification:

First order phase transitions:

During this phase transition, the system absorbs or releases a fixed amount of

energy. These phase transitions are involved with latent heat. First order phase

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transitions are associated with mixed phase regime, i.e., some parts of the system have

completed the transitions and others have not.

Second order phase transitions:

Second order phase transitions are also called as continuous phase transitions.

These are not associated with the latent heat.

Phase Transitions in Liquid Crystals

During a phase transition, the free energy of the system remains continuous,

while thermodynamic quantities like volume, entropy, heat capacity etc., undergo

discontinuity and the Gibb’s free energy function, Ehrenfest’s52 simple scheme of

classification of phase transition defines that the transition is of the same order as the

derivative of Gibb’s free energy which shows a discontinuous change at the transition.

G = H – Ts

Where H = U + pv

dG = dU + pdv + vdp – Tds – sdT

But dQ = dU + pdv (first law of thermodynamics) and change of entropy as

ds = dQ/T

dQ = dH – Tds

dG = vdp – sdT

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The first and second derivatives of free energy 59 may be written as , Cp and

where , Cp and are volume thermal expansively, specific heat, and

compressibility respectively. Thus the phase transformations, which involve a

discontinuous, change in volume (specific volume or density) and entropy (i.e., a latent

heat of transition accompanying the transition) belong to first order transition.

The different experimental techniques viz., density, 60 high resolution

calorimetric61 studies, specific heat, refractive index62 ultrasonic velocity, 63 X-ray

diffraction, 64 light scattering65 and magnetic resonance66 studies confirm that whether a

phase transformation is first order or second order and also infer the pretransitional

effects. Further, the concept of critical exponents67 and their interrelations in the form of

scaling laws are introduced to understand the molecular phenomena with universality

characteristics.

In the present work we determine phase transition temperatures using

Rotating Polarizing technique and compare the results obtained with Thermal

Microscopy (TM) and Differential Scanning Calorimeter (DSC).

3.5 Optical Switching

The electro-optic response is investigated for an LC having a moderate value

of spontaneous polarization and a small helical pitch with a cell thickness of

1.5mm. Initially no electric field is applied and the average optical axis of the

helical structure coincides with the helical axis. AC voltage applied across the

electrodes switches the optical axis by an angle depending on the magnitude and

direction of the field. An alternating voltage applied to the specimen in conjunction

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to this DC voltage produces oscillations of the optical axis about this mean position.

Hence the light transmission through the LC varies linearly with the applied voltage.

This electro-optic modulation is studied for signals of frequencies from 30 Hz to 1

MHz. With suitable modifications to compensate for the decrease in response at

high frequencies, the LC gives fairly uniform response over this frequency range.