Kurdistan Iraqi Region Ministry of Higher Education University of Sulaimani College of Science Physics Department

Optical Properties of Polyvinyl - chloride

Alumina Composite

Prepared by

Aso Abu-Baker Husain Samira Ali Faraj

Bakhtear Rasul Sulaiman

Supervised by

Dr. Omed Ghareb Abdullah

2009 – 2010

ii

Dedication

Dedicated to our family especially our

faithful fathers and mothers.

Dedicated to our teachers in physics

department.

Dedicated to all our best friends.

Dedicated to University of Sulaimani.

iii

Acknowledgement

Praise to God that afford us to complete this

work.

Thanks for physics Department that let us to

perform this study.

Thanks to our instructor Dr. Omed Ghareb

who supervised the current study and

guided us loyally.

Thanks to all our friends and teachers who

helped us.

Aso, Samira and Bakhtear

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Contents

Chapter One: Polymer Structure.

1.1 Introduction…………………………………………………………. 1 1.2 Polymerization Reaction………………………………………….… 2

1.2.1 Chain-Reaction (addition) Polymerization……………………. 2 1.2.2 Step-Reaction (Condensation) Polymerization……………...… 5

1.3 Polymer Chemical Structure………………………………………… 6 1.4 Polymer Physical Structure……………………………………..…… 7 1.5 Classification of Polymers……………………………………..……. 8

Chapter Two: Theoretical Background.

2.1 Introduction ……………..………………………………………… 10 2.2 Band Theory ……………………………………………..……...… 10 2.3 Density of State ……………………………………..…………….. 12 2.4 Band Structure of Crystalline and Amorphous Material ………..… 13 2.5 Optical Properties of Polymers …………………...………..……… 16 2.6 Refractive Index (n) …...………………………………..…………. 17 2.7 Dielectric Polarization………………………………..……………. 18

2.7.1 Atomic Polarization………………………..……………….. 19 2.7.2. Dipolar Polarization…………………..………………….... 20 2.7.3. Ionic Polarization…………………..……………………… 20

2.8 Dielectric Dispersion…………………...………………………….. 21

Chapter Three: Optical Properties.

3.1 Introduction ………………………..……………...………………. 22 3.2 Absorption Coefficient ….……..………………………………….. 23 3.3 The Optical Energy Gap…………………………………..……….. 25 3.4 Optical Absorption …………...………………………..………….. 26 3.5 Optical Properties of Thin Film …….……………..…………….... 28 3.6 Absorption Edge ……..………………………...………………….. 30 3.7 Optical Constants of Thin Films …………….…………………….. 32

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Chapter four: results and conclusion.

4.1 Introduction ……………………………..………………………… 34 4.2 Experimental detail …………………..…………………………… 34 4.3 The Absorbance…………………………………………………… 35 4.4 The Transmittance Spectra ………………………...……………… 35 4.5 The Reflectance Spectra ………………………...………………… 36 4.6 Refractive Index ……………………………..….………………… 37 4.7 Extinction Coefficient …………………………….…..….…...…… 38 4.8 Dielectric Constants …………………………………………..…… 39 4.9 The Optical Energy Gap ……………………………………..….… 40 4.10 Width of the tail of localized states ……………………………… 43 4.11 Conclusion…………………………………………….….….…… 45 References …………………………………………………………….. 46 Appendix ………………………………………………………………. 48

vi

Abstract

The study of optical absorption has been one of the most productive

methods in understanding the band structure and energy gap of both

crystalline and amorphous materials. It was well known when the light

incident on a material, the optical phenomena of absorption, reflection and

transmission are observed, the optical absorption constitutes the most

important information to determining the band structures, direct and indirect

transitions, and absorption edge of amorphous and crystalline materials which

illustrated the transition of electron between conduction and valence band.

The measurement of optical absorption coefficient, particularly near the

fundamental absorption edge, is a standard method for the investigation of

optically induced electronic transitions.

The optical properties of prepared Polyvinyl-chloride (PVC) films with

difference filling levels of Alumina were studied in the visible and ultraviolet

wavelength regions. It was found that the optical absorption is due to direct-

allowed transitions, and the energy gaps decrease with increasing Alumina

content for all transitions, while the width of the tail localized states increase

with increasing Alumina content.

All the other optical constants Transmittance, Reflectance, refractive

index 𝑛𝑛, extinction coefficient 𝑘𝑘, the complex dielectric constant have been

also calculated. The dielectric constant increased in the composite samples as

compared with the pure PVC sample prepared by the same method.

1

Chapter One

Polymer Structure

1.1 Introduction:

Over half a century ago, Wilhelm Ostwald (1914) coined the phrase “the

land of neglected dimensions” to describe the range of sizes between

molecular and microscopic within which occur most colloidal particle. The

term “neglected dimensions” might have been applied equally well to the

work of polymer molecules, the high-molecular-weight compounds so

important to man and his modern technology. It was not until the 1930’s that

the science of high polymers began to emerge, and the major growth of the

technology of these materials came even later. Yet today polymer dimensions

are neglected no more, for industries associated with polymeric materials

employ more than half of all American chemists and chemical engineers.

A polymer is a large molecule built up by the repetition of small, simple

chemical units. In some cases the repetition is linear, much as a chain is built

up from it is links. In other cases the chains are branched or interconnected to

form three-dimensional networks. The repeat unit of the polymer is usually

equivalent or nearly equivalent to the monomer, or starting material from

which the polymer is formed.

The length of the polymers chain is specified by the number of repeat

units in the chain. This is called the degree of polymerization (DP). The

molecular weight of the polymer is the product of the molecular weight of the

repeat unit and the degree of polymerization. Using poly(vinyl chloride) as an

example, a polymer of degree of polymerization 1000 has a molecular weight

of 63 * 1000 = 63000. Most high polymer useful for plastics, rubbers, or

fibers have molecular weights between 10 000 and 1000 000.

2

Gradually the study of polymer properties began. Almost all were first

called anomalous because they were so different from the properties of low-

molecular- weight compounds. It was soon realized, however, that polymer

molecules are many times larger than those of ordinary substance. The

presumably anomalous properties of polymers were shown to be normal for

such materials, as the consequences of their size were included in the

theoretical treatments of their properties.

Primary chemical bonds along polymer chains are entirely satisfied. The

only forces between molecules are secondary bond forces of attraction, which

are week relative to primary bond forces. The high molecular weight of

polymer allows these forces to build up enough to impart excellent strength,

dimensional stability, and other mechanical properties to the substances.

1.2 Polymerization Reactions:

The chemical reaction in which high molecular mass molecules are

formed from monomers is known as polymerization.

There are two basic types of polymerization: chain-reaction (or addition)

and step-reaction (or condensation) polymerization.

1.2.1 Chain-Reaction (addition) Polymerization:

One of the most common types of polymer reactions is chain-reaction

(addition) polymerization. This type of polymerization is a three step process

involving two chemical entities. The first, known simply as a monomer, can

be regarded as one link in a polymer chain. It initially exists as simple units.

In nearly all cases, the monomers have at least one carbon-carbon double

bond. Ethylene is one example of a monomer used to make a common

polymer.

3

The other chemical reactant is a catalyst. In chain-reaction polymerization, the

catalyst can be a free-radical peroxide added in relatively low concentrations.

A free-radical is a chemical component that contains a free electron that forms

a covalent bond with an electron on another molecule. The formation of a free

radical from an organic peroxide is shown below:

In this chemical reaction, two free radicals have been formed from the one

molecule of R2O2

Step 1:

. Now that all the chemical components have been

identified, we can begin to look at the polymerization process.

Initiation

The first step in the chain-reaction polymerization process, initiation,

occurs when the free-radical catalyst reacts with a double bonded carbon

monomer, beginning the polymer chain. The double carbon bond breaks

apart, the monomer bonds to the free radical, and the free electron is

transferred to the outside carbon atom in this reaction.

Step 2: Propagation

The next step in the process, propagation, is a repetitive operation in

which the physical chain of the polymer is formed. The double bond of

successive monomers is opened up when the monomer is reacted to the

4

reactive polymer chain. The free electron is successively passed down the line

of the chain to the outside carbon atom.

This reaction is able to occur continuously because the energy in the chemical

system is lowered as the chain grows. Thermodynamically speaking, the sum

of the energies of the polymer is less than the sum of the energies of the

individual monomers. Simply put, the single bounds in the polymeric chain

are more stable than the double bonds of the monomer.

Step 3: Termination

Termination occurs when another free radical (R-O.), left over from the

original splitting of the organic peroxide, meets the end of the growing chain.

This free-radical terminates the chain by linking with the last CH2.

component

of the polymer chain. This reaction produces a complete polymer chain.

Termination can also occur when two unfinished chains bond together. Both

termination types are diagrammed below. Other types of termination are also

possible.

5

This exothermic reaction occurs extremely fast, forming individual chains

of polyethylene often in less than 0.1 second. The polymers created have

relatively high molecular weights. It is not unusual for branches or cross-links

with other chains to occur along the main chain.

1.2.2 Step-Reaction (condensation) Polymerization:

Step-reaction (condensation) polymerization is another common type of

polymerization. This polymerization method typically produces polymers of

lower molecular weight than chain reactions and requires higher temperatures

to occur. Unlike addition polymerization, step-wise reactions involve two

different types of di-functional monomers or end groups that react with one

another, forming a chain. Condensation polymerization also produces a small

molecular by-product (water, HCl, etc.). Below is an example of the

formation of Nylon 66, a common polymeric clothing material, involving one

each of two monomers, hexamethylene diamine and adipic acid, reacting to

form a dimer of Nylon 66.

At this point, the polymer could grow in either direction by bonding to

another molecule of hexamethylene diamine or adipic acid, or to another

dimer. As the chain grows, the short chain molecules are called oligomers.

This reaction process can, theoretically, continue until no further monomers

and reactive end groups are available. The process, however, is relatively

slow and can take up to several hours or days. Typically this process breeds

6

linear chains that are strung out without any cross-linking or branching, unless

a tri-functional monomer is added.

1.3 Polymer Chemical Structure:

The monomers in a polymer can be arranged in a number of different

ways. As indicated above, both addition and condensation polymers can be

linear, branched, or cross-linked. Linear polymers are made up of one long

continuous chain, without any excess appendages or attachments. Branched

polymers have a chain structure that consists of one main chain of molecules

with smaller molecular chains branching from it. A branched chain-structure

tends to lower the degree of crystallinity and density of a polymer. Cross-

linking in polymers occurs when primary valence bonds are formed between

separate polymer chain molecules.

Chains with only one type of monomer are known as homopolymers. If

two or more different type monomers are involved, the resulting copolymer

can have several configurations or arrangements of the monomers along the

chain. The four main configurations are depicted in Figure (1.1):

Figure (1.1): Rrandom, alternating, block and graft Copolymers

configurations.

A: Random copolymers: The repeating units are arranged randomly on the

chain molecule.

7

B: Alternating copolymers: There is an ordered (alternating) arrangement of

the two repeating units along the polymer chain.

C: Block copolymers: The chain consists of relatively long sequences

(blocks) of each repeating unit chemically bound together.

D: Graft copolymers: Sequences of one monomer (repeating unit) are

“grafted” onto a backbone of another monomer.

1.4 Polymer Physical Structure:

Segments of polymer molecules can exist in two distinct physical

structures. They can be found in either crystalline or amorphous forms.

Crystalline polymers are only possible if there is a regular chemical structure

(e.g., homopolymers or alternating copolymers), and the chains possess a

highly ordered arrangement of their segments. Crystallinity in polymers is

favored in symmetrical polymer chains, however, it is never 100%. These

semi-crystalline polymers possess a rather typical liquefaction pathway,

retaining their solid state until they reach their melting point at Tm.

Amorphous polymers do not show order. The molecular segments in

amorphous polymers or the amorphous domains of semi-crystalline polymers

are randomly arranged and entangled. Amorphous polymers do not have a

definable Tm

(T

due to their randomness. At low temperatures, below their glass

transition temperature g , the segments are immobile and the sample is

often brittle. As temperatures increase close to T

)

g, the molecular segments can

begin to move. Above Tg

viscosity

, the mobility is sufficient (if no crystals are present)

that the polymer can flow as a highly viscous liquid. The decreases

with increasing temperature and decreasing molecular weight.

In cooling an amorphous material from the liquid state, there is no abrupt

change in volume such as occurs in the case of the cooling of a crystalline

material through its freezing point, 𝑇𝑇𝑓𝑓 . Instead, at the glass transition

temperature, there is a change in the slope of the curve of specific volume

versus temperature, moving from low value in the rubbery state over a range

8

of temperature. This comparison between a crystalline material (1) and an

amorphous material (2) is illustrated in Figure (1.8).

Figure (1.2): Specific Volume versus Temperature graph.

1.5 Classification of Polymers:

Polymers may be classified as follows, according to the mechanical

response at elevated temperatures:

1. Thermoplasts

2. Thermosets

1- Thermoplasts:

Thermoplast polymers soften when heated and harden when cooled.

Simultaneous application of heat and pressure is required to fabricate these

materials. On the molecular level, when the temperature is raised, secondary

bonding forces are diminished so that the relative movement of adjacent

chains is facilitated when a stress is applied.

Most Linear polymers and those having branched structures with flexible

chains are thermoplastics. The commercial available thermoplasts are:

Polyvinyl Chloride (PVC) and Polystyrene, Polymethyl methacrylate, and

Polystyrene.

9

2- Thermosets:

Thermosetting polymers become soft during their first heating and

become permanently hard when cooled. They do not soften during subsequent

heating. Hence, they cannot be remolded (reshaped) by subsequent heating. In

thermosets, during the initial heating, covalent cross-links are formed between

adjacent molecular chain. These bonds anchor the chains together to resist the

vibration and rotational chain motions at high temperatures. Cross linking is

usually extensive in that 10 to 15% of the chains per units are cross linked.

Only heating to excessive temperatures will cause severance of these

crosslink bonds and polymer degradation.

Thermoset polymers are harder, stronger, more brittle than thermoplastics

and have better dimensional stability, and they are more usable in processes

requiring high temperatures.

Most of the cross linked and network polymers which include, Vulcanized

rubbers, Epoxies, Phenolic, Polyester resins, are thermosetting.

Thermosets cannot be recycle, do not melt, are usable at higher

temperatures than thermoplastics, and are more chemically inert.

10

Chapter Two

Theoretical Background

2.1 Introduction:

When light is incident on a materials, the optical phenomena of

absorption, reflection, and transmission are observed. From these optical

effects, we obtain much of the information. From absorption spectrum as a

function of photon energy, a number of processes can be contributed to

absorption. At high energies photons are absorbed by the transitions of

electrons from filled valence band states to empty conduction band states.

For energies just below the lowest forbidden energy gap, radiation is

absorbed due to the formation of excitants, and electron transitions between

band and impurity states. The transitions of free carriers within energy bands

produce an absorption continuum which increases with decreasing photon

energy. Also, the crystalline lattice itself can absorb radiation, with the energy

being given off in optical phonons. Finally, at low energies, or long

wavelengths, electronic transitions can be observed between impurities and

their associated bands.

2.2 Band theory:

Band theory is a part of solid state physics that examines the behavior of

the electrons in solids. It postulates the existence of energy bands, continuous

ranges of energy values which electrons may or may not occupy.

Band theory is used to explain why different substances have varying

degrees of electrical resistance. The electrons of a single free-standing atom

occupy atomic orbitals, which form a discrete set of energy levels. According

to molecular orbital theory, if several atoms are brought together into a

molecule, their atomic orbitals split, producing a number of molecular orbitals

proportional to the number of atoms. When a large number of atoms (of

11

order 1020

1- The

or more) are brought together to form a solid, the number of

orbitals becomes exceedingly large, and the difference in energy between

them becomes very small. However, some intervals of energy contain no

orbitals, no matter how many atoms are aggregated.

Any solid has a large number of bands. In theory, it can be said to have

infinitely many bands (just as an atom has infinitely many energy levels).

Many models have been constructed to try to explain the origin and behavior

of bands. These include:

nearly-free electron model, a modification of the free electron model.

2- The Kronig-Penney mode.

Bands have different widths, based upon the properties of the atomic

orbitals from which they arise. Also, allowed bands may overlap, producing

(for practical purposes) a single large band. While the density of energy states

in a band is very great, it is not uniform. It approaches zero at the band

boundaries, and is generally greatest near the middle of a band. Not all of

these states are occupied by electrons ("filled") at any time. The likelihood of

any particular state being filled at any temperature is given by the Fermi-

Dirac statistics.

The probability is given by the following:

𝑓𝑓(𝐸𝐸) =1

1 + 𝑒𝑒𝐸𝐸−𝐸𝐸𝑓𝑓𝐾𝐾𝐾𝐾

(2.1)

where:

𝐾𝐾 is Boltzmann's constant,

𝐾𝐾 is the temperature,

𝐸𝐸𝑓𝑓 is the Fermi energy (or 'Fermi level').

Regardless of the temperature, 𝑓𝑓�𝐸𝐸𝑓𝑓� = 1/24T, at 𝐾𝐾 = 0, the distribution is

a simple step function:

𝑓𝑓(𝐸𝐸) = �1 𝑖𝑖𝑓𝑓 0 < 𝐸𝐸 ≤ 𝐸𝐸𝑓𝑓

0 𝑖𝑖𝑓𝑓 𝐸𝐸𝑓𝑓 < 𝐸𝐸 � (2.2)

12

At non zero temperatures, the step "smooth’s out", so that an appreciable

number of states below the Fermi level are empty, and some states above the

Fermi level are filled. As shown in figure (2.1).

Figure(2.1): Distribution function at three temperatures in Fermi-Dirac

statistics.

2.3 Density of State:

Density of state can be defined as the density of energy levels per unit

energy interval. Density of state (DOS) is a property in statistical

and condensed matter physics that quantifies how closely packed energy

levels are in some physical system. It is often expressed as a function 𝒈𝒈(𝑬𝑬) of

the internal energy 𝑬𝑬, or a function 𝒈𝒈(𝒌𝒌) of the wavevector 𝒌𝒌. It is usually

used with electronic energy levels in a solid. In 3-dimensions, for example,

the density of states in reciprocal space (𝒌𝒌0T-space

𝒈𝒈(𝒌𝒌) =𝑽𝑽𝟐𝟐𝝅𝝅𝟐𝟐

𝒌𝒌𝟐𝟐 𝒅𝒅𝒌𝒌 (𝟐𝟐.𝟑𝟑)

) is:

where 𝑽𝑽 is the volume of the solid. A more precise definition is as;

𝒈𝒈(𝑬𝑬)𝒅𝒅𝑬𝑬 is the number of allowed energy levels per unit volume of the

material, within the energy range 𝑬𝑬 𝒕𝒕𝒕𝒕 𝑬𝑬 + 𝒅𝒅𝑬𝑬 (and equivalently for 𝒌𝒌).

To find the density of energy states, the relation between energy and

momentum for a particular particle is used, to express 𝑘𝑘 and 𝑑𝑑𝑘𝑘 in 𝑔𝑔(𝑘𝑘)𝑑𝑑𝑘𝑘, in

terms of 𝐸𝐸 and 𝑑𝑑𝐸𝐸. For example for a free electron:

13

𝐸𝐸 =𝑝𝑝2

2𝑚𝑚=

(ℏ𝑘𝑘)2

2𝑚𝑚 ⇛ 𝑑𝑑𝐸𝐸 =

ℏ𝑘𝑘𝑚𝑚𝑑𝑑𝑘𝑘 (2.4)

This gives a density of states at energy 𝐸𝐸 per unit volume,

𝑔𝑔(𝐸𝐸) =𝑑𝑑𝑑𝑑𝑘𝑘

�∫ 𝑑𝑑3𝑘𝑘𝑘𝑘

0(𝜕𝜕𝑘𝑘)3 �

𝑑𝑑𝑘𝑘𝑑𝑑𝐸𝐸

(2.5)

2.4 Band structure of Crystalline and Amorphous material:

The crystalline state can be distinguished from the existence of the long-

range order in three dimensions or from the arrangement of atomic structure,

in crystalline material the atomic structure repeat itself in a periodical way.

The crystal has a band contain a huge number of energy levels equal to

the number of atoms; therefore the band energy appears as a continuous

spectrum. If the atom in crystal becomes close to neighboring atom, each

energy level will split into two level and if the atoms get closer up to distance

equal to the atomic equilibrium distance for lattice, the energy level will split

into two well separated bands, as in the figure (2.2):

Figure (2.2): The energy band formation.

The distance between the two bands is called the forbidden gap. There are

no energy levels in the forbidden gap or (energy gap). The two splitted bands

Electron Energy

Lattice Spacing

Valence Band

Conduction

Band

Eg

14

called the valence and conduction band. The electrons in valence band have a

possibility of moving to the conduction band if they have a chance to get

energy equal or more than the energy gap.

The band energy can be divided to two sub-band, the extended band

which is related to long range order and the charge carrier have a possibility

of moving in a certain path through the material. The charge carrier in this

band can move by hopping only. The space of energy between extended

conduction band and extended valence band called the mobility gap as

illustrated in figure (2.3).

Figure (2.3): Energy (𝐸𝐸) verse Density of state 𝑔𝑔(𝐸𝐸) diagram for crystalline

materials.

It should be noted that the local energy gap (the separation between the

top of the valence band and the bottom of the conduction band) is everywhere

maintained constant. But the density-of-states distribution, which integrates

the number of states at each energy inside the whole volume shows that there

are conduction band states at relatively low potentials and valence band states

in high-potential regions.

The density of states of amorphous is not nil at the band gap of the

material, due to existence of the band tails, i.e., a perturbation of the

conduction and valence bands by the formation of tails of states extending the

15

bands into the energy gap. Since impurities are distributed randomly in the

host crystal, the local interaction will be more or less strong depending on the

local crowding of impurities, as illustrated in figure (2.4).

Figure (2.4): The left diagram shows the perturbation of the band edges by

Coulomb interaction with inhomogeneously distributed impurities. This leads

to the formation of tails of states shown on the right side. The dashed lines

show the distribution of states in the unperturbed case.

In figure (2.4), the region of extended state originated from the

crystallization structure of material. The charge carriers in this region are free

to move. The tall state region is originated from the disordering, dangling

bonds, impurities and defects. Therefore the density of localized tail state

proportion with the increase in disordering, while the extended state of

conduction and valence inversely proportion with disordering.

It has been noted that the absorption edge curves of many amorphous

solids exhibit similar shapes. The absorption edge of such materials can be

recognized by three major regions, shown in figure (2.5).

g

16

Figure (2.5): An absorption spectrum of amorphous solids consisting of three

major regions of interest.

The behavior in region A arises directly from defect states transitions. The

absorption edge extending in regions A and B is rather complicated and

contains defect-induced tail at the lowest energies, an exponential region at

intermediate energies, and a power-law at the highest energies. The high

absorption coefficient in region A is caused by the transitions between the

extended states. This is then followed by an exponential region B, which

extends over 4 orders of magnitude of the absorption coefficient.

It has been suggested by Tauc that the exponential absorption edge in

interband absorption arises from the electronic transitions between the

localized states in the band edge tails. The density of these localized states is

assumed to fall off with energy, giving rise to the exponential absorption edge

characteristics.

2.5 Optical Properties of Polymers:

The optical properties of polymer depend basically on the reaction

happening between the polymers charge and the electromagnetic field rays.

Therefore, it must be understood that the nature of these charges (ionic,

17

electronic) and their distribution may be bonded as in semiconductors and

insulators may be free as in metals.

The study of optical properties of polymer requires the introduction of

bonds nature and the type of internal structure.

Good optical properties, especially in bulk materials, need a detailed

Knowledge of polymer structure, Generally speaking most of polymers are in

a non-crystalline state. This makes them suffer the softness and cracks. This is

in turn constitutes one of their disadvantages in much application.

However stopping the growth of mer unit can prevent the crystalline.

This will overcome the afro mentioned disadvantages, specifically, this

will produce a thin film of hard surface which provides the strength and

transmittance requirements at the same time.

2.6 Refractive Index (𝒏𝒏):

The speed of the light in the vacuum is constant. However, in other

medium it is inversely proportional to the density of the medium. The ratio of

the light speed in vacuum to the light speed in medium is known as the

refractive index of the medium, which is represented by the symbol (𝑛𝑛).

The electrical component of the incident electromagnetic wave in a

material is work to drift different charge from their original place and produce

dipole moment.

If the frequency of the alternating electric components of electromagnetic

wave is (𝜐𝜐), then the electrical polarization of atoms will oscillate in the same

frequency, and a part of electromagnetic energy will be converts to oscillating

energy for creating dipoles, causing a decrease in the amplitude of the

incident wave.

That loss in energy causes a little dipole oscillates, i.e. the interaction of

charges with electromagnetic wave doesn’t cause losses in energy but

produces recombination of radiation state. The material becomes transmitter

18

for this radiated wave. However, the lack in recombination decreases the light

speed. Then it can be said that the material has (𝑛𝑛) which is given by:

𝑛𝑛 =𝑐𝑐v

(2.6)

Where 𝑐𝑐 is the velocity of light in vacuum, and v is the velocity of light in

medium. Obviously, the polarization in material is caused by incident

electromagnetic wave and its measured of (𝑛𝑛). Therefore, as the polarization

increases the lacking increases, and also whenever the light velocity is

decreased (𝑛𝑛) is increased too. In other words, it can be said that any

increment in the dipoles density of the material will result in an increment in

refractive index (𝑛𝑛).

2.7 Dielectric Polarization:

One main goal of studies of dielectric polarization is to relate macroscopic

properties such as the dielectric constant to microscopic properties such as the

polarizability.

Dielectric polarization arises from the electrical response of individual

molecules of a medium and may be classified as electronic, atomic,

orientation, and space-charge or interfacial polarization, according to the

mechanism involved.

Electronic polarization represents the distortion of the electron

distribution or motion about the nuclei in an electric field.

Atomic polarization arises from the change in dipole moment

accompanying the stretching of chemical bonds between unlike atoms in

molecules.

Orientation polarization is caused by the partial alignment of polar

molecules, that is, molecules possessing permanent dipole moments, in an

electric field. This mechanism leads to a temperature-dependent component of

polarization at lower frequencies.

19

Space-charge or interfacial polarization occurs when charge carriers are

present which can migrate an appreciable distance through a dielectric but

which become trapped or cannot discharge at an electrode. This process

always results in a distortion of the macroscopic field and is important only at

low frequencies.

2.7.1 Atomic Polarization:

In the classical approach to the dielectric model, a material is made up of

atoms. Each atom consists of a cloud of negative charge bound to and

surrounding a positive point charge at its center. Because of the comparatively

huge distance between them, none of the atoms in the dielectric material

interact with one another. In the presence of an electric field the charge cloud

is distorted, as shown in the figure (2.6).

Figure (2.6): Schematic to illustrate the atomic polarization.

This can be reduced to a simple dipole using the superposition principle. A

dipole is characterized by its dipole moment, a vector quantity shown in the

figure as the blue arrow labeled M. It is the relationship between the electric

field and the dipole moment that gives rise to the behavior of the dielectric.

When the electric field is removed the atom returns to its original state. The

time required to do so is the so-called relaxation time; an exponential decay.

20

The relationship between the electric field 𝐸𝐸 and the dipole moment 𝑀𝑀

gives rise to the behavior of the dielectric, which, for a given material, can be

characterized by the function 𝐹𝐹 defined by the equation:

𝑀𝑀 = 𝐹𝐹(𝐸𝐸) (2.7)

When both the type of electric field and the type of material have been

defined, one then chooses the simplest function 𝐹𝐹 that correctly predicts the

phenomena of interest.

2.7.2. Dipolar Polarization:

Dipolar polarization is a polarization that is particular to polar molecules.

This polarization results from permanent dipoles, which retain polarization in

the absence of an external electric field. The assembly of these dipoles forms

a macroscopic polarization.

When an external electric field is applied, the distance between charges,

which is related to chemical bonding, remains constant in the polarization;

however, the polarization itself rotates. Because this rotation completes not

instantaneously but in the delay time 𝜏𝜏, which depends on the torque and the

surrounding local viscosity of the molecules, dipolar polarizations lose the

response to electric fields at the lowest frequency in polarizations. The delay

of the response to the change of the electric field causes friction and heat.

2.7.3 Ionic Polarization:

Ionic polarization is polarization which is caused by relative

displacements between positive and negative ions in ionic crystals.

If crystals or molecules do not consist of only atoms of the same kind, the

distribution of charges around an atom in the crystals or molecules leans to

positive or negative. As a result, when lattice vibrations or molecular

vibrations induce relative displacements of the atoms, the centers of positive

and negative charges might be in different locations. These center positions

are affected by the symmetry of the displacements. When the centers don't

21

correspond, polarizations arise in molecules or crystals. This polarization is

called ionic polarization.

2.8 Dielectric Dispersion:

In physics, dielectric dispersion is the dependence of the permittivity of a

dielectric material on the frequency of an applied electric field. Because there

is always a lag between changes in polarization and changes in an electric

field, the permittivity of the dielectric is a complicated, complex-valued

function of frequency of the electric field. It is very important for the

application of dielectric materials and the analysis of polarization systems.

This is one instance of a general phenomenon known as material

dispersion: a frequency-dependent response of a medium for wave

propagation.

When the frequency becomes higher:

1- it becomes impossible for dipolar polarization to follow the electric

field in the microwave region around 1010 Hz;

2. in the infrared or far-infrared region around 1013 Hz, ionic polarization

loses the response to the electric field;

3- electronic polarization loses its response in the ultraviolet region

around 1015 Hz.

In the wavelength region below ultraviolet, permittivity approaches the

constant ε0 in every substance, where ε0 is the permittivity of the free space.

Because permittivity indicates the strength of the relation between an electric

field and polarization, if a polarization process loses its response, permittivity

decreases.

22

Chapter Three

Optical Properties

3.1 Introduction:

Optical absorption analysis has widely proven to be an important and

efficient tool in exploring and interpreting the various phenomena of

electronic structures and processes in the materials subjected to radiation. The

considerable theoretical investigations on the optical behavior of thin films

deal primarily with optical reflection, transmission, and adsorption properties,

and their relation to the optical constants of films. The importance of studying

the optical properties of a material is offered by the ability of this technique to

provide information regarding the fundamental gap, electronic transition,

trapping levels, and localized states. In general, films are amorphous, and at

most they are polycrystalline in nature.

Over the last decades, advances have been made in understanding the

problem of how the disorder in amorphous materials influences the band

structure and hence the electrical and optical properties of the material.

Optical absorption in solids occurs by various mechanisms, in all of which

the photon energy is absorbed by either the lattice or by electrons, where the

transferred energy is conserved. The lattice (or phonon) absorption gives

information about the atomic vibrations involved. This absorption of radiation

normally occurs in the infrared region of the spectrum. Higher energy parts

could provide information associated with the interband electronic transition.

In these processes, the electrons are excited from the filled band to an empty

band by the photon absorption, and, as a consequence of this, a sharp increase

in the absorption coefficient will result.

23

3.2 Absorption Coefficient:

The absorption coefficient determines how far into a material light of a

particular wavelength can penetrate before it is absorbed. In a material with a

low absorption coefficient, light is only poorly absorbed, and if the material is

thin enough, it will appear transparent to that wavelength. The absorption

coefficient depends on the material and also on the wavelength of light which

is being absorbed. Semiconductor materials have a sharp edge in their

absorption coefficient, since light which has energy below the band gap does

not have sufficient energy to raise an electron across the band gap,

consequently this light is not absorbed.

The appearance of high band in certain range of the absorption spectrum

means the absorbance of a high amount of energy. That is, this amount of

energy, which has been absorbed, is high. This is caused by the transfer

(jump) of a number of molecules from lower energy to a higher one.

However, when a little number of molecules is transferred the total

absorbed energy will be less than the previous case and produce a lower band.

These notes are the basic fundamentals of Beer-Lambert law. The

absorbed parts of incident radiation are directly proportional to the number of

absorbed molecules in the radiation direction.

The Amount of absorbed and transmuted wave in any material is

exponentially proportional to the distance passed through the material (𝑑𝑑) and

the absorption coefficient (𝛼𝛼) It can be calculated from Lambert law as

follows:

𝐼𝐼 = 𝐼𝐼𝑜𝑜 exp(−𝛼𝛼𝑑𝑑) (3.1)

Where,

𝐼𝐼𝑜𝑜 : incident light intensity,

𝐼𝐼 : transmitted light intensity,

𝑑𝑑 : substrate thickness, and

𝛼𝛼 : absorption coefficient.

24

The ratio 𝐼𝐼/𝐼𝐼𝑜𝑜 known as the transmittance (𝐾𝐾) and 𝑙𝑙𝑜𝑜𝑔𝑔 (𝐼𝐼𝑜𝑜/𝐼𝐼) as the

absorbance (𝐴𝐴). Therefore,

𝐴𝐴 = 𝑙𝑙𝑜𝑜𝑔𝑔 (𝐼𝐼𝑜𝑜/𝐼𝐼) = −𝑙𝑙𝑜𝑜𝑔𝑔 (𝐾𝐾) (3.2)

The absorption coefficient per unit length 𝛼𝛼 is, related to the extinction

coefficient, 𝑘𝑘, by the following formula:

𝛼𝛼 =4𝜋𝜋𝑘𝑘𝜆𝜆

(3.3)

Optical absorption and luminescence occur by transition of electrons and

holes between electronic states (bands, tail states, gap states). If electron-

phonon coupling is strong enough self-trapping occurs.

It is well known that an electron is transferred from the valence band to the

conduction band if sufficient energy (basically the gap energy) is provided to

the semiconductor. If the energy is delivered by incident photons the process

is called optical absorption. A number of different phenomena may be

associated with the incidence of light on a material. Figure (3.1) shows a

schematic of the optical absorption spectrum vs. energy of the photons. For

our discussion here, phenomena related to (2) excitons, (3) fundamental

absorption processes and (4) impurities are of interest.

Figure (3.1): Different types of optical absorption phenomena; (1) transitions of

high-lying bands, (2) excitons, (3) fundamental absorption (valence-band-to-conduction-band transition and Urbach-tail), (4) impurity absorption, (5) free-carrier absorption and (6) Reststrahlen absorption.

25

3.2 The Optical Energy Gap:

The optical energy gap 𝐸𝐸𝑜𝑜𝑝𝑝𝑜𝑜 is another important quantity that

characterizes semiconductors and dielectric materials since it has a paramount

importance in the design and modeling of such materials. The general theory

and many of the experimental results on amorphous semiconductors have

been summarized by Mott and Davis. They show that one feature of such

materials is some sort of energy band structure, but show also that the

normally sharp cutoff in the density of states curves at the band edges is

replaced by a tailing into the normally forbidden energy gap .Thus we expect

a difference in the absorption spectra, particularly at the fundamental

absorption edge, between samples of the same basic material but for which

one is crystalline and the other amorphous.

From the stand point of electron motion a mobility or pseudo gap is

defined and is larger for amorphous materials than for crystals having the

same chemical compositions. The equivalent gaps from the optical stand point

will depend on the form of excitation process taking place in the material

when photons are absorbed. Thus a variety of possibilities will arise,

depending on whether the transitions involved are direct or indirect.

The theory of such transitions has been presented by Davis and Mott and

they take account of the localized electronic states in the mobility or pseudo-

gap. In amorphous materials the k-conservation rule breaks down and thus k is

not a good quantum number .If we assume that the matrix element for optical

transitions has the same value whether or not the initial and final states are

localized, and also that the densities of states at the band edges are linear

functions of the energy, then we may deduce 𝛼𝛼. The equation for optical

absorption coefficient 𝛼𝛼 at a given angular frequency 𝜔𝜔 then reduces to the

form:

𝛼𝛼(𝜔𝜔) =𝐴𝐴�ℎ𝑣𝑣 − 𝐸𝐸𝑜𝑜𝑝𝑝𝑜𝑜 �

2

ℎ𝑣𝑣 (3.4)

26

where:

𝐴𝐴 = (4𝜋𝜋/𝑐𝑐)𝜎𝜎𝑜𝑜/𝑛𝑛𝑜𝑜∆𝐸𝐸 (3.5)

And where 𝜎𝜎𝑜𝑜 is the electrical conductivity at absolute zero, ∆𝐸𝐸 the width

of the tail of localized states in the normally forbidden band gap, 𝑛𝑛𝑜𝑜 the

refractive index and 𝐸𝐸𝑜𝑜𝑝𝑝𝑜𝑜 the optical energy gap.

Thus the optical energy gap may be determined from the extrapolation to

(𝛼𝛼ℎ𝑣𝑣)1/2 = 0 of a plot of (𝛼𝛼ℎ𝑣𝑣)1/2 v. (ℎ𝑣𝑣). Such a theory describes optical

absorption associated with forbidden indirect transitions.

3.3 Optical Absorption:

The energy gap in a material is responsible for the fundamental optical

absorption edge. The fundamental absorption process is one in which a

photon is absorbed and an electron is excited from an occupied valence band

state to an unoccupied conduction band state. If the photon energy (ℎ𝑣𝑣) is less

than the gap energy, such processes are impossible and the photon will not be

absorbed. That is, the material is transparent to electromagnetic radiation for

which (ℎ𝑣𝑣 < 𝐸𝐸𝑔𝑔𝑔𝑔𝑝𝑝 ). For (ℎ𝑣𝑣 > 𝐸𝐸𝑔𝑔𝑔𝑔𝑝𝑝 ) on the other hand, such inter band

absorption processes are possible. In high quality crystalline material at low

temperatures, the density of states rises sharply at the band edge and

consequently the absorption rises very rapidly when the photon energy

reaches the gap energy.

Now considering an inter band electronic transition, we see that such

transitions must be essentially vertical on the band diagram. This is required if

the process is to conserve momentum.

This condition is readily satisfied if the maximum of the VB and the

minimum of the CB occur at the same k-value (often k = 0 as in the figure

(3.1) below). If the band structure has this feature, the gap is said to be direct.

Such semiconductors are very useful for electro-optical applications.

27

Figure (3.1): Direct optical transition.

While in the case the VB maximum and CB maximum do not occur at the

same k-value, the gap is said to be an indirect gap, as shown in figure (3.2).

Absorption over the band gap cannot conserve energy and momentum without

the participation of another particle, usually a phonon. The process then

corresponds to photon→conduction electron plus phonon.

Energy conservation requires ℎ𝑣𝑣 = 𝐸𝐸𝑔𝑔𝑔𝑔𝑝𝑝 + ℎ𝑉𝑉 where 𝑉𝑉 is the frequency

of the phonon created in the process. Indirect absorption processes are

possible (after all they satisfy the necessary conservation conditions), but

because of the participation of a third particle (the phonon), their transition

probabilities are much lower than those of direct processes. This kind of

absorption process is illustrated in the diagram below.

28

Figure (3.2): Indirect optical transitions.

3.5 Optical Properties of Thin Film:

Optical measurement constitutes the most important means of determining

the band structures of materials. Photo induced transitions can occur between

different bands, which lead to the determination of the energy band gap, or

within a single band such as the free carrier absorption. Optical measurements

can also be used to study lattice vibrations.

The transmission coefficient T and the reflection coefficient R are the two

important quantities generally measured. For normal incidence they are given

by:

𝐾𝐾 =(1 − 𝑅𝑅2) 𝑒𝑒𝑒𝑒𝑝𝑝(−4𝜋𝜋𝑒𝑒/𝜆𝜆)1 − 𝑅𝑅2 exp(−8𝜋𝜋𝑒𝑒/𝜆𝜆)

(3.6)

𝐾𝐾 =(1 − 𝑛𝑛)2 + 𝑘𝑘2

(1 + 𝑛𝑛)2 + 𝑘𝑘2 (3.7)

Where, 𝜆𝜆 is the wave length, 𝑛𝑛 the refractive index, 𝑘𝑘 the absorption

constant, and 𝑒𝑒 the thickness of the sample.

A more realistic view of the energy band structure is displayed in figure

(3.3), where the valence and conduction bands are nonsymmetric. In addition,

29

the conduction band may have more than one minimum, and the valence band

may also have more than one maximum.

Near the absorption edge the absorption coefficient can be expressed as:

𝛼𝛼 ∝ �ℎ𝑣𝑣 − 𝐸𝐸𝑔𝑔𝑔𝑔𝑝𝑝 �𝛾𝛾 (3.8)

Where (ℎ𝑣𝑣) is the photon energy, (𝐸𝐸𝑔𝑔𝑔𝑔𝑝𝑝 ) is the band gap, and 𝛾𝛾 is a

constant. In the one electron approximation 𝛾𝛾 equals 12 and 3

2 for allowed direct

transitions and forbidden direct transitions, respectively 𝑘𝑘𝑚𝑚𝑖𝑖𝑛𝑛 = 𝑘𝑘𝑚𝑚𝑔𝑔𝑒𝑒 as

transitions (a) and (b) shown in figure (3.3); the constant 𝛾𝛾 equals 2 for

indirect transitions [transition (c) shown in figure (3.3)], where photons are

involved. In addition, 𝛾𝛾 equals 3 for allowed indirect transitions to exciton

states, where an exciton is a bound electron-hole pair with energy levels in the

band gap and moves through the crystal lattice as a unit.

Figure (3.3): Types of electron transition resulting by optical absorption:

(a) Allowed direct transition, (b) Forbidden direct transition

(c) Allowed indirect transition, (d) Forbidden indirect transition

Near the absorption edge, where the values of (ℎ𝑣𝑣 − 𝐸𝐸𝑔𝑔𝑔𝑔𝑝𝑝 ) become

comparable with the binding of an exciton, the coulomb interaction between

the free hole and electron must be into account. For (ℎ𝑣𝑣 ≤ 𝐸𝐸𝑔𝑔𝑔𝑔𝑝𝑝 ) the

30

absorption merges continuously into the absorption caused by the higher

excited states of the exciton. When (ℎ𝑣𝑣 ≫ 𝐸𝐸𝑔𝑔𝑔𝑔𝑝𝑝 ), higher energy bands

participate in the transition processes, and complicated band structures are

reflected in the absorption coefficient.

3.6 Absorption edge:

The study of optical absorption and particularly the absorption edge is a

useful method for the investigation of optically induced transitions and for the

provision of information about the band structure and energy gap in both

crystalline semiconductors and non-crystalline materials. The principle of this

technique is that a photon with energies greater than the band gap energy will

be absorbed. The absorption edge in many disordered materials follows the

Urbach rule given by:

𝛼𝛼(𝑣𝑣) = 𝛼𝛼𝑜𝑜 exp �ℎ𝑣𝑣∆𝐸𝐸

� (3.9)

Where 𝛼𝛼(𝑣𝑣) is the absorption coefficient at a frequency of 𝑣𝑣, and ∆𝐸𝐸 is

the width of the tail of localized states in the band gap.

There are two kinds of optical transition at the fundamental edge of

crystalline and non-crystalline semiconductors, direct transitions and indirect

transition, both of which involve the interaction of an electro-magnetic wave

with an electron in the valance band, which is then raised across the

fundamental gap to the conduction band. For the direct optical transition from

the valence band to the conduction band it is essential that the wave vector for

the electron be unchanged. In the case of indirect transition the interactions

with lattice vibrations (phonons) take place; thus the wave vector of the

electron can change in the optical transition and the momentum change will

be taken or given up by phonons. In other words, if the minimum of the

conduction band lies in a different part of 𝑘𝑘-space from the maximum of the

valence band, a direct optical transition from the top of the valence band to

the bottom of the conduction band is forbidden.

31

Mott and Davis suggested the following expression for direct transitions:

𝛼𝛼(𝑣𝑣) = 𝐵𝐵�ℎ𝑣𝑣 − 𝐸𝐸𝑜𝑜𝑝𝑝𝑜𝑜 �𝑛𝑛/ℎ𝑣𝑣 (3.10)

Where ℎ𝑣𝑣 is incident photon energy, and exponent 𝑛𝑛 can take 0.5 or 1.5

for allowed and forbidden direct transitions respectively, 𝐸𝐸𝑜𝑜𝑝𝑝𝑜𝑜 the optical

energy gap, and 𝐵𝐵 is a constant nearly independent on photon energy:

𝐵𝐵 =4𝜋𝜋𝜎𝜎𝑜𝑜𝑐𝑐𝑛𝑛𝑜𝑜∆𝐸𝐸

(3.11)

Where 𝜎𝜎𝑜𝑜 is the electrical conductivity at absolute zero, ∆𝐸𝐸 the width of

the tail of localized states in the normally forbidden band gap, and 𝑛𝑛𝑜𝑜 is the

refractive index.

The following expression is suggested for indirect transitions:

𝛼𝛼(𝑣𝑣) = 𝐵𝐵�ℎ𝑣𝑣 − 𝐸𝐸𝑜𝑜𝑝𝑝𝑜𝑜 ± 𝐸𝐸𝑝𝑝ℎ�𝑛𝑛/ℎ𝑣𝑣 (3.12)

Where 𝐸𝐸𝑝𝑝ℎ is the photon energy and the value of exponent 𝑛𝑛 take the

values 2 and 3 for allowed and forbidden indirect transitions, see figure (3.4).

Thus, this model suggests that a plot of (𝛼𝛼ℎ𝑣𝑣)1/𝑛𝑛 as a function of (ℎ𝑣𝑣)

should be linear, when this procedure is used, from the zero absorption

extrapolatied value of (ℎ𝑣𝑣) the value of optical gap can be calculated.

Figure (3.4): Allowed and forbidden indirect transformation.

32

3.7 Optical Constants of Thin Films: The optical properties of a sprayed film depend strongly on the technique

of spray. Two of the most important optical properties are the refractive index

𝑛𝑛 and the extinction coefficient 𝑘𝑘, which are generally called optical

constants.

The theory of the optical absorption gives the relationship between the

absorption coefficient 𝛼𝛼 and the photon energy ℎ𝑣𝑣, for direct allowed

transition as mentioned before.

Using the fundamental relations of photon transmittance 𝐾𝐾 and

absorbance 𝐴𝐴, 𝐼𝐼𝑑𝑑 = 𝐼𝐼𝑜𝑜𝑒𝑒−𝛼𝛼𝑑𝑑 (3.13)

Where 𝐼𝐼𝑑𝑑 is the incident photon energy at thickness (𝑑𝑑) inside the

material, and 𝐼𝐼𝑜𝑜 is incident photon energy at surface of material and

𝐴𝐴 = 𝑙𝑙𝑜𝑜𝑔𝑔 �𝐼𝐼𝑜𝑜𝐼𝐼𝑑𝑑� (3.14)

We have:

𝛼𝛼 = 2.303 �𝐴𝐴𝑑𝑑� (3.15)

The reflectance (𝑅𝑅) has been found by using the relationship:

𝑅𝑅 + 𝐾𝐾 + 𝐴𝐴 = 1 (3.16)

For normal reflectance, we have:

𝑅𝑅 =(𝑛𝑛 − 1)2

(𝑛𝑛 + 1)2 (3.17)

By using the above relation, the refractive index can be determined from

the relation:

𝑛𝑛 =(1 + √𝑅𝑅)(1 − √𝑅𝑅)

(3.18)

The extinction coefficient is related to the absorption coefficient 𝛼𝛼 by the

relation:

𝑘𝑘 =𝛼𝛼𝜆𝜆4𝜋𝜋

(3.19)

33

Where 𝜆𝜆 is the incident photon wavelength.

The real and imaginary parts of dielectric constant (𝜀𝜀𝑟𝑟 and 𝜀𝜀𝑖𝑖 respectively)

can be calculated as follows:

Complex refractive index:

𝑁𝑁∗ = 𝑛𝑛 − 𝑖𝑖𝑘𝑘 (3.20)

Complex dielectric constant:

𝜀𝜀∗ = 𝜀𝜀𝑟𝑟 − 𝑖𝑖 𝜀𝜀𝑖𝑖 (3.21)

From the relation 𝑁𝑁∗ = √𝜀𝜀∗ , there fore:

(𝑛𝑛 − 𝑖𝑖𝑘𝑘)2 = 𝜀𝜀𝑟𝑟 − 𝑖𝑖 𝜀𝜀𝑖𝑖 (3.22)

So that:

𝜀𝜀𝑟𝑟 = 𝑛𝑛2 − 𝑘𝑘2 (3.23)

𝜀𝜀𝑖𝑖 = 2𝑛𝑛𝑘𝑘 (3.24)

34

Chapter four

Results and Conclusions

4.1 Introduction:

The study of the optical properties of materials is a huge field, this study was

attempted to touch on some of the most basic parts by considering the essential

properties such as absorption, reflection, transmission and refraction.

When white light strikes the surface of the materials, it may be scattered,

reflected, refracted, transmitted or absorbed. Light scattering and reflecting are

surface phenomena, while refracting, transmitting and absorbing are internal

affairs. With regard to surface phenomenon, if the surface is irregular, then the

light is reflected and scattered in all directions. Although the scattering and

reflecting of light is dependent upon the surface finish.

This chapter describe the discussion of results which were getting during

determination of optical properties of prepared films by casting technique with

different concentrations.

4.2 Experimental detail:

Films of PVC - Alumina composite were prepared by solution casting: 4 𝑔𝑔𝑔𝑔

of pure Polyvinyl-chloride (PVC ) supplied from Sigma-Aldrich company has

been dissolved in 20𝑔𝑔𝑚𝑚 of Tetrahydrofuran (THF) to obtain a pure PVC film,

then the same amount of PVC was dissolved with 0.5, 1,2, 𝑎𝑎𝑎𝑎𝑎𝑎 3 𝑔𝑔𝑔𝑔 of Alumina

to prepare the different filling levels of the PVC - Alumina composites, the

complete dissolution was obtained using a magnetic stirrer at room temperature

for 3hr, these homogeneous solutions were spread on a glass plate and allowed

to evaporate the solvent slowly in air at room temperature for 24ℎ. The thickness

of the films was in the range of (0.5 − 0.9)𝑔𝑔𝑔𝑔, it was determined using

35

micrometer at different places in each film and an average was taken. The

thickness of the PVC - Alumina composites are tabulated in table (4.1):

Table(4.1): Thickness of the PVC - Alumina composites:

PVC (gm) Tetra hydrofurain (ml) Al2O3 Thickness (cm) (gm)

4 20 0 0.0785

4 20 0.5 0.052

4 20 1 0.094

4 20 2 0.0545

4 20 3 0.078

4.3 The Absorbance:

The absorbance spectra for PVC - Alumina composite films, having different

concentration, are shown in figure (4.1) these spectra indicate that the films have

low absorbance in the visible and near infrared regions. However, the absorbance

in the near ultraviolet region is high.

Figure (4.1): The optical absorbance of PVC film polymer with difference

concentration of AlR2ROR3R.

00.050.1

0.150.2

0.250.3

0.350.4

0.45

320 330 340 350 360 370 380 390

A

Wavelength (nm)

PVC

PVC-0.5 Al2O3

PVC-1 Al2O3

PVC-2 Al2O3

PVC-3 Al2O3

36

4.4 The Transmittance Spectra:

The optical transmittance spectra for PVC - Alumina composite films, having

different concentration, are shown in figure (4.2). All the films demonstrate that

grate transmittance occurs at wavelengths longer than 360nm. Below this value

there is a sharp fall in transmittance of the films, this because of its high energy

gap value which renders strong absorbance of the films in this region. It is

observed that the overall transmittance decreases with the increase of Alumina

concentration. This is due to the overall increase in the absorbance with the

increase of Alumina contents.

Figure (4.2): Transmission spectrum of PVC film polymer with difference

concentration of Al2O3.

4.5 The Reflectance Spectra:

The reflectance of PVC - Alumina composite films, was calculated from

equation (3.16). The reflectance spectra represent the interference between the

rays that are reflected from the film faces. Figure (4.3) shows the optical

reflectance spectra for PVC - Alumina composite films. The overall reflectance

of the film increases with the increase Alumina concentrations.

0.35

0.45

0.55

0.65

0.75

0.85

320 330 340 350 360 370 380 390

Tran

smis

sion

Wavelength (nm)

PVC

PVC-0.5 Al2O3

PVC-1 Al2O3

PVC-2 Al2O3

PVC-3 Al2O3

37

Figure (4.3): The Reflectance spectra for PVC film polymer with difference

concentration of Al2O3.

4.6 Refractive Index:

The optical behavior of a material is generally utilized to determine its

optical constants [i.e. refractive index (𝑎𝑎), extinction coefficient (𝑘𝑘), real (𝜀𝜀𝑟𝑟 ),

and imaginary (𝜀𝜀𝑖𝑖) dielectric constants].

The Refractive index was determined from the reflectance data using

equation (3.18). Figure (4.4) shows the variation in the refractive index with the

incident photon wavelength. The increase of the Alumina concentration causes

an overall increase in the refractive index. The increase is due to the over all

increase in the reflectance with the increase of Alumina contents.

0

0.05

0.1

0.15

0.2

0.25

320 330 340 350 360 370 380 390

Ref

lect

ion

Wavelength (nm)

PVC

PVC-0.5 Al2O3

PVC-1 Al2O3

PVC-2 Al2O3

PVC-3 Al2O3

38

Figure (4.4): The Refractive Index (n) for PVC film polymer with difference

concentration of Al2O3

Figure (4.5): The Extinction coefficient (k) for PVC film polymer with difference

concentration of Al2O3.

.

4.7 Extinction Coefficient:

The extinction coefficient was determined by using the equation (3.19), after

calculating the absorption constant from equation (3.15). Figure (4.5) shows the

variation of extinction coefficient with the photon wavelength. The value of

extinction coefficient increases as the Alumina concentration increases.

1.5

1.7

1.9

2.1

2.3

2.5

2.7

320 330 340 350 360 370 380 390

n (R

efre

ctiv

e in

dex)

Wavelength (nm)

PVC

PVC-0.5 Al2O3

PVC-1 Al2O3

PVC-2 Al2O3

PVC-3 Al2O3

00.0000050.00001

0.0000150.00002

0.0000250.00003

0.0000350.00004

0.0000450.00005

320 330 340 350 360 370 380 390

K (a

bsor

ptio

n C

onst

ant)

Wavelength (nm)

PVC

PVC-0.5 Al2O3

PVC-1 Al2O3

PVC-2 Al2O3

PVC-3 Al2O3

39

4.8 Dielectric Constants:

The real and imaginary parts of the dielectric constant were determined using

equations (3.23) and (3.24) respectively. The illustrated in figures (4.6) and (4.7)

showing the variations of the real and imaginary parts of the dielectric constant

with the incident photon wavelength. The imaginary part represents the

absorption of radiation by free carriers. From figure we can see that the real and

imaginary dielectric constant have the same behavior of refractive and extinction

coefficient respectively.

Figure (4.6): Real dielectric constant (𝜀𝜀𝑟𝑟 ) for PVC film polymer with difference

concentration of Al2O3.

2

3

4

5

6

7

8

320 330 340 350 360 370 380 390

ε r

Wavelength (nm)

PVC

PVC-0.5 Al2O3

PVC-1 Al2O3

PVC-2 Al2O3

PVC-3 Al2O3

40

Figure (4.7): imaginary dielectric constant (𝜀𝜀𝑖𝑖) for PVC film polymer with

difference concentration of Al2O3.

4.9 The Optical Energy Gap:

Figure (4.8) shows the variation of (𝛼𝛼ℎ𝑣𝑣)2 as a function of (ℎ𝑣𝑣) for pure

PVC polymer, with different Alumina concentration. This plot indicates allowed

direct transition.

The optical energy gap 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜 was estimated from extrapolation of linear

portion of the graph to the photon energy axis. From the figure, it is observed

that the optical energy gap decreases with the increase of Alumina concentration.

This may be due to the possibility of structural defects in the films arisen due to

increase of Alumina concentration, which could give rise to the allowed states

near the conduction band in the bandgap. The values of 𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜 for allowed direct

transition for all composition are tabulated in Table (4.2).

0

0.00005

0.0001

0.00015

0.0002

0.00025

320 330 340 350 360 370 380 390

ε i

Wavelength (nm)

PVC

PVC-0.5 Al2O3

PVC-1 Al2O3

PVC-2 Al2O3

PVC-3 Al2O3

41

Figure (4.8): variation of (𝛼𝛼ℎ𝑣𝑣)2 as a function of (ℎ𝑣𝑣) for PVC polymer,

with different Alumina concentration.

Table(4.2): Optical energy gape for allowed direct transitions for all composite.

Samples Optical energy gap (eV)

PVC pure 3.52

PVC-0.5 Al2O3 3.38

PVC-1.0 Al2O3 3.26

PVC-2.0 Al2O3 3.10

PVC-3.0 Al2O3 3.04

In order to investigate the existing of forbidden direct, allowed indirect, and

forbidden indirect transitions, the graphs of (𝛼𝛼ℎ𝑣𝑣)2/3, (𝛼𝛼ℎ𝑣𝑣)1/2, and (𝛼𝛼ℎ𝑣𝑣)1/3,

as a function of (ℎ𝑣𝑣) for PVC polymer, with different Alumina concentration, as

shown in figures (4.9),(4.10), and (4.11) respectively. From these figures one can

simply conclude that this transformation was not available.

0

500

1000

1500

2000

2500

3000

3500

2.8 3 3.2 3.4 3.6 3.8

(αhv)^

2

hv(eV)

PVC

PVC-0.5 Al2O3

PVC-1 Al2O3

PVC-2 Al2O3

PVC-3 Al2O3

42

Figure (4.9): variation of (𝛼𝛼ℎ𝑣𝑣)2/3 as a function of (ℎ𝑣𝑣) for PVC polymer, with

different Alumina concentration.

Figure (4.10): variation of (𝛼𝛼ℎ𝑣𝑣)1/2 as a function of (ℎ𝑣𝑣) for PVC polymer,

with different Alumina concentration.

0

2

4

6

8

10

12

14

16

2.8 3 3.2 3.4 3.6 3.8

(αhv

)^2/

3

hv(eV)

PVC

PVC-0.5 Al2O3

PVC-1 Al2O3

PVC-2 Al2O3

PVC-3 Al2O3

0

1

2

3

4

5

6

7

8

3.2 3.3 3.4 3.5 3.6 3.7 3.8

(αhv

)^1/

2

hv(eV)

PVC

PVC-0.5 Al2O3

PVC-1 Al2O3

PVC-2 Al2O3

PVC-3 Al2O3

43

Figure (4.11): variation of (𝛼𝛼ℎ𝑣𝑣)1/3 as a function of (ℎ𝑣𝑣) for PVC polymer, with

different Alumina concentration.

4.10 Width of the tail of localized states:

Width of the tail of localized states (Urbach energy) inside the forbidden

bands, for all compounds can be found in the exponential region by using

the following relation:

( )

∆

=E

hvv expοαα (4.1)

( )

∆

+=E

hvv οαα lnln (4.2)

It is obvious when ( )αIn is plot against ( )hv , the inverse of slop will be

the value of tail localized state, as shown in figure (4.12). The values of

Urbach energy E∆ for all composition are tabulated in Table (4.3).

1

1.5

2

2.5

3

3.5

4

3.2 3.3 3.4 3.5 3.6 3.7 3.8

(αhv

)^1/

3

hv(eV)

PVC

PVC-0.5 Al2O3

PVC-1 Al2O3

PVC-2 Al2O3

PVC-3 Al2O3

44

Figure (4.12): Tail width of the localized states for PVC film polymer

with difference concentration of Al2O3

.

Table(4.3): width of the tail of localized states for all composites.

0

0.5

1

1.5

2

2.5

3

3.2 3.3 3.4 3.5 3.6 3.7 3.8

ln(α

)

hv(eV)

PVC

PVC-0.5 Al2O3

PVC-1 Al2O3

PVC-2 Al2O3

PVC-3 Al2O3

Samples Tail width E∆ (eV)

PVC pure 0.2605

PVC-0.5 Al2O3 0.4787

PVC-1.0 Al2O3 0.7358

PVC-2.0 Al2O3 0.8969

PVC-3.0 Al2O3 1.1198

45

4.11 Conclusions:

The following conclusions may be drawn from the results we obtained:

1- Optical studies reveal that these pure PVC film, and composite PVC

films with different concentration of Alumina, have an allowed direct

band gap and it’s observed that the bad gap decrease with increase the

concentration of Alumina.

2- Optical studies show that these films have high absorbance in the

ultraviolet and low visible wavelength regions, and a moderate

absorbance in the near infrared and height visible wavelength regions.

Hence they could be effective to use as a solar radiation absorbers for

solar cell. While, high transmittance properties of these films in the near

infrared and height visible wavelength regions, makes a good material for

thermal control window coating for cold climates and antireflective

coating.

3- The refractive index (𝑎𝑎) increase with increase the Alumina concentration

in the height frequency of visible region, this may be very interest in

manufacturing fiber optic.

4- Increase in Alumina concentration in PVC polymer, lead to more stability

in dielectric constant at height values, through a wide range of frequency.

This behavior may be more benefits in electronic devices.

46

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