Upd. Thesis

Electrical properties of Polyaniline–doped with copper (I) salt, (CuI) as a potential gas sensor.

By

Tareq M. Alqam

Supervisor

Prof. Sa’di M. Abdul Jawad

Co-Supervisor

Prof. Awni Hallak

Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in

Applied Physics

Deanship of Scientific Research and Graduate Studies The Hashemite University

May, 2008

This thesis”Electrical properties of Polyaniline–doped with copper (I) salt, (CuI) as a potential gas sensor” was successfully defended and approved on (15/05/2008). Examination Committee Signature Dr. Sa’di Abdul Jawad, Chairman --------------------- Professor of Materials Science. Dr. Awni Hallak, Member --------------------- Professor of Condensed Matter. Dr. Wa’l Naji Salah, Member --------------------- Associated Professor of Free Electron Laser. Dr. Mohamed Khaled AL-Sugueir, Member --------------------- Assistant Professor of Theoretical Condensed Matter

Dr. Mohammed Sarhan, Member --------------------- Assistant Professor of Condensed Matter Al al-Bayt University.

DEDICATION

To my Beloved

Prophet Muhammad "May God blessings be upon him".

And

To my Family

ACKNOWLEDGMENT

I am greatly indebted to my supervisors: Professor Sa’di Abdul Jawad and Prof.

Awni Hallak for their continuous encouragement and cooperation throughout the course

of this research.

My deepest gratitude and appreciation are extended to Dr. Hassan El-Ghanem

and Dr. Isam Arafa (Jordan University for Science and Technology) for providing their

help in preparation of samples.

Special thanks for Dr. Hamzeh Abdel-Halim, Mr. Abdussalam Qaroush and Ms.

Feda' Al-Qaisi chemistry department (The Hashemite University) for their help in

building set-up to produce Carbon Monoxide.

Finally, special thanks go to my family, my friends and Arab Institute for

Sustainable Development for their financial and moral support.

Tareq M. Alqam

LIST OF CONTENTS

Page

Committee Decision ii

Dedication iii

Acknowledgment iv

List of Contents v

List of Tables viii

List of Figures ix

Abstract in English. v

Chapter One: Introduction 1

1.1) Introduction 2

1.2) Conducting polymers 2

1.3) Polyaniline 9

1.4) Polymer gas sensors 12

1.5) Literature Survey 13

1.6) Current Study 16

Chapter Two: Theoretical Background 17

2.1) Polarizations 18

2.1-a) Electronic dipoles 18

2.1-b) Ionic Polarization 21

2.1-c) Orientation (dipolar) polarization 24

2.1-2) Total polarization 25

2.2) Dielectrics 26

2.2-1) Non-Polar Dielectric materials 26

2.2-2) Polar dielectric materials have ionic polarization 27

2.3) Dipolar Relaxations 27

2.3-1) The frequency dependence of polarization 30

2.4) Determination of the Relaxation Parameters ε∆ and τ of a Single

Debye Relaxation 36

2.5) RC Circuits 38

2.5.1) Parallel Connection 39

2.5.2) Series Connection 42

2.5.3) Impedance - Dielectric Properties Correlation 45

2.6) Temperature dependence of the relaxation time 47

Chapter Three: Experimental Part 49

3.1) Sample’s preparation 50

3.2) Sample’s set 51

3.3) Sample’s holder 52

3.4) Impedance measurements 52

3.5) The 1294 Impedance Interface 57

3.6) Impedance Measurement Software 58

Chapter Four: Results and Discussion 60

4.1) Introduction 61

4.2) XRD results 62

4.3) Impedance analysis 64

4.4) Conductivity 68

4.5) Dielectric Permittivity 71

4.6) Temperature Dependence 77

4.7) Conclusions 85

4.8) Recommendations 86

References 87

Abstract (in Arabic). 94

LIST OF TABLES

Table No. Title Page

1.1 Table (1.1) Sensitivity of PANI-CuPc (copper phthalocyanine)

polymer wit chemical vapors 14

3.1 PANI-Cul- 2I ratios 51

LIST OF FIGURES

Figure No. Title Page

1.1 Electrical conductivities of conjugated polymers compared with

other common materials. 3

1.2

a) The energy diagram of a neutral polymer chain. The

difference between high occupied molecular orbital (HOMO)

and low unoccupied molecular orbital (LUMO) defines the

bandgap Eg, b) The oxidation and reduction of the neutral

soliton, c) Positive soliton, d) Negative soliton and c) High

redox-doping forms soliton band.

6

1.3

The energy diagram of a polymer with a non-degenerate ground

state system. Upon doping new localized states are created. The

oxidation and reduction of the a) neutral polaron b) results in

positive and c) negative polaron. d) When two polarons bind

together a bipolaron will be formed. e) High redox doping

forms bipolaron bands.

7

1.4 Chemical structure of common conducting polymers. 9

1.5 The relative conductivities of some of conductive polymers

with respect to copper metal. 10

1.6

(a) Polyaniline in the emerladen oxidation state can exist in

either its undoped or doped form. (b) The doped intermediate

bipolaron form (c)converts rapidly to the electronic conducting

form.

12

2.1 Idealized atoms with spherical symmetry. 19

2.2 Ionic polarization. 21

2.3 (a) The NaCl crystal without an applied field. (b) The NaCl

crystal with an applied field. 22

2.4 Ionic dipole. 22

2.5 Dipole rotation in electric field. 24

2.6 Alternating electrical field E inter dielectric black box. 27

2.7 The dependence of polarization on time. 28

2.8 Frequency response of dielectric mechanism. 30

2.9 Schematic representation of frequency dependence ofε ′ , ε ′′

and δtan for a single relaxation time. 36

2.10 Cole-Cole representation.

37

2.11 (a) Pure resistance in an ac circuit. (b) Plot of V versus I across

resistor as a function of time. 38

2.12 (a) Capacitor in an ac circuit. (b) Plot of V versus I across

capacitor as a function of time. 39

2.13 Parallel combination of resistor and capacitor. 40

2.14 Complex-plane impedance plot for parallel RC circuit. 41

2.15 Series combination of resistor and capacitor. 43

2.16 Complex-plane impedance plot for series RC circuit. 44

3.1 Sample’s holder 52

3.2 1260 Impedance / Gain-Phase Analyzer. 53

3.3 The three FRA signals.

55

3.4 Circuit for charge amplifier-FRA setup.

56

3.5 1294 Impedance Interface.

58

3.6 Setup of experiment 59

4.1 XRD profile for C3 sample. 62



4.3 a) Z' versus frequency, b) Z'' versus frequency and c) Z'' versus

Z', before and after exposure to CO for C1 sample. 65





4.7

a) Z' versus frequency, b) Z'' versus frequency and c) Z'' versus

Z', before and after exposure to CO, after 1 day, 2 days and 3

days for C7 sample.

67

4.8 AC conductivity before and after exposure to CO for the C1. 69

4.9 AC conductivity before and after exposure to CO for the sample

C2 sample. 69

4.10 AC conductivity before and after exposure to CO for the C3

sample. 70

4.11 AC conductivity before and after exposed to CO and after one ,

two and three days after exposing process for C7 sample. 70

4.12 a) 'ε versus frequency, b) ''ε versus frequency and c) ''ε

versus 'ε before and after exposure to CO for C1 sample. 73


versus 'ε before and after exposure to CO for C2 sample.

73





4.16 M'' versus frequency before and after exposure to CO for C1

sample. 75


sample. 76


sample. 76


sample. 76

4.20 a) Z' versus frequency, b) Z'' versus frequency and c) Z' versus

Z'' at different temperatures for C1 sample. 78








versus 'ε at different temperatures for C1sample. 81


versus 'ε at different temperatures for C2 sample. 81





4.28 M'' versus frequency at different temperatures for C1 sample. 83




4.32 Plot of τln versus 1/T for C1, C2, C3 and C4 samples. 84

Abstract

Electrical properties of Polyaniline–doped with copper (I)

salt, (CuI) as a potential gas sensor.

By Tareq M. Alqam

Supervisor

Prof. Sa’di Abdul Jawad

Co-Supervisor

Prof. Awni Hallak

Impedance spectroscopy studies on polyaniline doped by various amount of I2

and I2 + CuI before and after exposure to CO are reported. The measurements were

performed at room temperature and at selected temperatures (25 – 65 0C) over a

frequency range 100 Hz to 10 kHz. The dielectric relative permittivity, dielectric loss,

electric modulus and conductivity were determined from the impedance measurements.

Models consist of Resistance (R) and Constant Phase Element (CPE) were proposed for

impedance for undoped and doped Polyaniline.

The bulk conductivity after exposure to CO was interpreted in terms of hopping

mechanism between localized state. The results showed that the bulk conductivity and

the dielectric strength increased when the samples were exposed to CO, implies that this

type of conductive polymer can be used as toxic gas sensor.

The frequency dependence of dielectric permittivity was interpreted in terms of

effective electric dipoles, where for doped PANI increased with increasing temperature.

The activation energy of the systems was estimated from the temperature dependence of

the relaxation time, where the activation energy changed slightly by changing doping

level.

1

CHAPTER ONE

INTRODUCTION

2

1.1) Introduction:

Conducting polymers have been widely studied in the last two decades, especially with an

aim to find suitable industrial applications. The development of conductive polymers became

one of the most promising fields since the discovery of conductive polymers by Alan Heeger

in 1976 for which they were awarded 2000 Nobel Prize in Chemistry. The potential uses of

conducting polymers as material in rechargeable batteries (Skotheim T. A. et al., 1998),

electromagnetic interference shielding (Angelopoulos M. 2001), sensors, and electro-chromic

display devices have been well-established (Baek Sungsik et al., 2002). Conducting polymers

have received increasing interest as an alternative to metal oxide semiconductors for smart

sensors. This is due to their room-temperature operation, low fabrication cost, ease of

deposition onto a wide variety of substrates, and their rich structural modification chemistry

(Sadek Abu Z. et al., 2007). Among the family of conducting polymers, Polyaniline is one of

the most highly studied materials because of its simple synthesis, environmental stability, and

straightforward nonredox acid doping/base dedoping process to control conductivity(Huang

W. S. et al., 1986). By changing the doping level and morphology, the conductivity of

Polyaniline can be tuned.

1.2) Conducting polymers:

Most commercially produced organic polymers are electrical insulators (MacDiarmid Alan

G. 2001). Conductive organic polymers often have extended delocalized bonds (often

3

composed of aromatic units). At least locally, these create a band structure similar to silicon,

but with localized states. When charge carriers (from the addition or removal of electrons)

are introduced into the conduction or valence bands, the electrical conductivity increases

dramatically. To increase the conductivity of the conjugated polymers, doping of these

materials is necessary. Doping can be obtained chemically via a redox molecule or

electrochemically by charge transfer with an electrode(Young R. J. et al., 1991). The first

high conducting polyacetylene was achieved via chemical doping when a film of polymer

was exposed to iodine vapor. Figure (1.1) illustrates the range of conductivities for

polyacetylene and other conjugated polymers compared with other common materials. In

electrochemical doping, the doping level is determined by the applied voltage between the

conducting polymer and the counter electrode. The doping charge is supplied by the

electrode to the polymer; while oppositely charged ions migrate from the electrolyte to

balance the electronic doping charge.

Figure (1.1): Electrical conductivities of conjugated polymers compared with other common

materials.

Technically almost all known conductive polymers are semiconductors due to the band

structure and low electronic mobility. However, so-called zero band gap conductive

4

polymers may behave like metals. The most notable difference between conductive polymers

and inorganic semiconductors is the mobility, which until very recently was dramatically

lower in conductive polymers than their inorganic counterparts, though recent advancements

in molecular self-assembly are closing that gap. Delocalization can be accomplished by

forming a conjugated backbone of continuous overlapping orbitals. For example, alternating

single and double carbon-carbon bonds can form a continuous path of overlapping p-

orbital’s. In polyacetylene, but not in most other conductive polymers, this creates

degeneracy in the frontier molecular orbitals (the highest occupied and lowest unoccupied

orbitals named HOMO and LUMO respectively), (Bueche F 1962). This leads to the filled

(electron containing) and unfilled bands (valence and conduction bands respectively)

resulting in a semiconductor. As mentioned previously, electrochemical doping and undoping

must involve counter-ion to stabilize the doped state. Doping can also occur without

involving any ions by charge injection at a metal – semiconducting polymer interface. At the

interface the polymer can be oxidized upon hole injection into HOMO or reduced when

electrons are injected into empty bands. The induced charge carriers will lead to increase the

electrical conductivity at the polymer interface. However, this induced conductivity (doping)

is maintained as long as the carriers are injected (e.g. by applying the bias voltage). Upon

removal of carrier injection, the doped polymer at the interface returns to its original state.

While in case of electrochemical doping, the doping level is permanent until carriers are

intentionally removed by undoping. Generally, charge carriers in conventional

semiconductors are created by addition or removal of electrons. These charge carriers

(electrons and holes) are delocalized in the crystal structure. While in conjugated polymers,

the nature of charge carriers is different. Electrons or holes will not be generated at HOMO

5

or LUMO upon addition or removal of electrons from the polymer, instead a defect, which is

associated to a molecular distortion in the polymer chain, is created (Said Elias, 2007).

Unlike conventional semiconductors, this defect is localized in the electronic structure of

conjugated polymers. These defects include the quasi-particles solitons, polarons and

bipolarons. Solitons as charge bearing species are characteristics for polymers with a

degenerate ground state system formed by two geometries of polymer units with the same

energy. The polymer with a degenerate system is trans-polyacetylene. Solitons originate

from odd number of carbon atoms in trans-polyacetylene chains. The soliton is an unpaired

electron located at the borderline between two phases with different bond length alternations.

This unpaired electron is lying in an energy level in the middle of the band gap of the

polymer (Figure (1.2 -b)). The unpaired electron in the state leads to a neutral soliton with

spin h21 . Unoccupied or doubly occupied of the state the soliton is charged and spineless.

The soliton is mobile along the polymer backbone. When doping levels become high enough,

the charged solitons start to interact with each other forming a soliton bands (Figure (1.2 -c)).

These bands will eventually merge with the edges of HOMO and LUMO to create metallic

conductivity.

6

Figure (1.2): a) The energy diagram of a neutral polymer chain. The difference between high

occupied molecular orbital (HOMO) and low unoccupied molecular orbital (LUMO) defines

the bandgap Eg, b) The oxidation and reduction of the neutral soliton, c) Positive soliton, d)

Negative soliton and e) High redox-doping forms soliton band.

Most of conjugated polymer systems are non-degenerate ground state systems. In these

polymers, the interchange of the single and double bonds produces higher energy geometric

configuration. Addition/removal of an electron on a neutral segment causes distortion and

formation of a localized defect that moves together with the charge. This combination of an

additional charge coupled to local lattice distortion is called a polaron. Depending on the sign

of the charge removal, one speaks about positive polarons or negative polarons. The polaron

has a localized electronic state in the bandgap. Upon further addition of charges to the

polymer chain, two charges might couple, despite electrostatic repulsion. At higher enough

doping level a bipolaron band is formed and eventually merges with the HOMO and LUMO

bands respectively to produce partially filled bands and metallic like conductivity. Unlike

polarons, bipolarons are always charged and have zero spin.

7

Figure (1.3): The energy diagram of a polymer with a non-degenerate ground state system.

Upon doping new localized states are created. The oxidation and reduction of the a) neutral

polaron b) results in positive and c) negative polaron. d) When two polarons bind together a

bipolaron will be formed. e) High redox doping forms bipolaron bands.

Conduction processes in conjugated polymers is often related to the mobility and the density

of charge carriers. For band-like transport, charge carriers are in delocalized states resulting

in a metallic like conductivity. This kind of transport is typical for metals. In conducting

polymers however, the transport is dominated by variable range hopping or tunneling

processes. The charge carriers are transported through hopping between localized states in

the band gap. Hopping to energetically states require energy, which is provided by the

phonons. Therefore, hopping conductivity increases with increasing temperature, opposite to

band-like conductivity decreases and is finite at zero temperature. Carriers with a little

energy are limited to hop to close levels. In case that transport mechanism is assisted by

tunneling, there are less conducting regions presented between highly conducting regions. It

should also be mentioned that charges are transported via interchain hops between π-orbitals

8

of adjacent chains. The transfer of the charge can be affected in this case of the intermediate

doping ions. Upon high doping, the charge transport of the conjugated polymers is based on

metallic grains surrounded by a media with localized states in the band gab. In the grains, the

transport is band-like because the polymer chains are densely packed that giving rise to

strong interaction between the chains, whereas the charge transport will be limited to hopping

or tunneling mechanism between the grains. However, conductive polymers generally exhibit

very low conductivities. In fact, as with inorganic amorphous semiconductors, conduction in

such relatively disordered materials is mostly a function of "mobility gaps" with phonon-

assisted hopping, polaron-assisted tunneling, etc. between localized states and not band gaps

as in crystalline semiconductors.

In more ordered materials, it is not until an electron is removed from the valence band (p-

doping) or added to the conduction band (n-doping, which is far less common) does a

conducting polymer become highly conductive. Doping (p or n) generates charge carriers,

which move in an electric field. Positive charges (holes) and negative charges (electrons)

move to opposite electrodes. This movement of charge is what is actually responsible for

electrical conductivity in crystalline materials. In contrast, typically "doping" in the

polyacetylene-derived conductive polymers involves actually oxidizing the compound.

Conductive organic polymers associated with a protic solvent may also be "self-doped".

Melanin is the classic example of both types of doping, being both an oxidized polyacetylene

and likewise commonly being hydrated.

9

Figure (1.4): Chemical structure of common conducting polymers.

1.3) Polyaniline:

Since electrical conduction was first reported in doped polyacetylene, increased

interests have existed in conducting polymers. Polyaniline PANI is the most promising

material for commercial applications in various conducting polymers because of its

environmental stability, easy processing, and economical efficiency (Kim H. M. et al., 2000).

The applications of PANI include potential gas sensor, electrodes for light-emitting diodes

(Burroughes J. H. et al., 1990), Li-ion battery (MacDiarmid A. G. et al., 1986),

electromagnetic interference (EMI) shielding (Joo J. et al., 1994), RF and microwave

absorbers (Epstein A. J. et al., 1996), corrosion protection (Racicot R. et al., 1997), and

10

antistatic materials. The emerladen base form of Polyaniline (PANI-EB) is an insulator with

a DC conductivity of 1010−≈ S/cm. PANI systems have a transition from the insulating state

to the metallic state through protonic acid doping (Wang Z. H. et al., 1991). It is well known

that the temperature dependence of the DC conductivity for disordered PANI samples

follows a quasi-one-dimensional variable-range-hopping model.

Figure 1.5: The relative conductivities of some of conductive polymers with respect to

copper metal.

The conducting polymer Polyaniline PANI is a very important conducting polymer.

Polyaniline is an organic conducting polymer, and can be synthesized by the oxidative

polymerization of the aniline monomer in an acidic medium. The conductivity of Polyaniline

11

can be tuned from 10-10 S/cm and 10 S/cm by a process called doping (Chiang J. C. et al.,

1986). This makes Polyaniline a very versatile conducting polymer. Polyethylene Oxide

(PEO) is a non-conducting polymer that is linear in its structure. Figure (1.6) shows the

chemical structure of doped PANI. As shown in Figure (1.6), two charges are delocalized

along the polymer chain. This overlap of charge along the chain is what is responsible for the

high conductivity in doped Polyaniline as compared to the non-doped form of Polyaniline.

The great instability of PANI has drawn us to study other ICPs (Intrinsically Conducting

Polymer), such as Polyaniline, polypyrrole, and polythiophene. Among the conducting

polymers, Polyaniline PANI was widely studied in the last decades because of its

environmental stability, low cost of raw materials, and easy synthesis. In addition, the large

range of conductivity versus doping level allowed the application of PANI to specific

applications in light-emitting diodes, batteries, electromagnetic shielding, antistatic coating,

gas sensors, and activators. (Kim Seong Hun et al., 2002)

12

Figure (1.6): (a) Polyaniline in the emerladen oxidation state can exist in either its undoped

or doped form. (b) The doped intermediate bipolaron form (c)converts rapidly to the

electronic conducting form.

1.4) Polymer gas sensor:

In recent years, many efforts have been focused on the development of sensor technologies to

detect the content of gases in various conditions, such as ion selective electrode, biochemical

sensor, optical sensor and solid electrolyte sensor (electrochemical sensors), (Plashnitsa

Vladimir. 2004). It is well known that a semiconducting oxide can change its electrical

resistance when its surface comes into contact with a gas (Ando M. et al., 1995), and as

mentioned before that the conducting polymers are a kind of semiconductor, such that a

material is thus a potential gas sensor. In an n-type semiconductor, the concentration of

13

conducting electrons can be decreased by an oxidation or increased by a reduction. In a p-

type semiconductor with holes as major charge carriers, the reverse changes in hole

concentration are observed. These phenomena are the result of the change in concentration of

the adsorbed gas and/or the gas vacancies on the surface of the semiconductor by the

adsorption of gases.

There are many types of gas sensors, but the most effective type is the Polymer gas sensor

because of low power consumption, Room operating temperature, ease of synthesis,

diversity, and low cost. The most promising conducting polymers for gas sensor is

Polyaniline because of their ease of preparation, relatively high electrical conductivity,

capable of n-type and p-type doping, good environmental stability, low cost, difficult to

dissolve and fabricate in thin film form, and need development for micro sensor

applications.( Huang. J et al., 2004)

1.5) Literature Survey:

Among so many publications in this area, most of them dealt with the detection of ammonia

(NH3) (Rodriguez-Gonzalez L. et al., 2005), (Franke M.E et al., 2003) and (Moos R. et al.,

2002) alongside with a few studies about Chloroform (Sharma et al., 2002), water vapor

(Syritski et al., 1998) and NO2 (Do J.S et al., 2004).

Radhakrsanan et.al 2002 reported that conductive polymers such as Polyaniline PANI,

polypyrroleand PPy and polythiophene PTh were functionalized with copper phthalocyanine

using chemical oxidation method. The obtained polymer (PANI-CuPc, PPy-CuPc and PT-

CuPc) were tested as chemical sensor by their response after exposure to various chemical

14

vapors such as methanol, ammonia and nitrogen dioxide. The results showed that these

polymers have moderate sensitivity towards methanol as well as ammonia vapors, but high

sensitive towards nitrogen dioxide (Do J.S et, al., 2004).

In addition, it is very high selectivity towards nitrogen dioxide may be explained on the basis

of charge transfer complex formed between the phthalocyanine donor and nitrogen dioxide

acceptor molecule. The results obtained from these investigations is given in table (1.1)

(Radhakrsanan et.al 2002)

Table (1.1): Sensitivity of PANI-CuPc (copper phthalocyanine) polymer wit chemical

vapors.

Sr. No. Cu-Pc content by

Wt %

Sensitivity factor (s)

Methanol Ammonia Nitrogen dioxide

1 0.0 11.0 6.0 100.0

2 2.0 20.0 18.0 970.0

3 5.0 40.0 30.0 1040.0

4 10.0 49.0 37.0 1000.0

5 20.0 57.0 44.0 930.0

It is quite interesting to note that PANI-CuPc polymers show tremendous sensitivity towards

nitrogen dioxide vapors. This very high response to nitrogen dioxide vapors cab be explained

as follows, nitrogen dioxide is a π -electron acceptor, and accepted electron would be

delocalized over the nitrogen dioxide planar structure, the columbic force between the

opposite charges is weakened and charge carrier movement is facilitated.

15

Watcharaphalakorn et.al (2005) studied the Polyaniline/polyimide blend as a gas sensor and

its electrical response to CO-N2 mixtures. Their results show the effect of doping type,

doping concentration, and the effect of temperature on the electrical conductivity response of

PANI upon exposure to CO, the conductivity values of this blend before exposed to gas

mixture is 10 1)( −Ωcm and after the exposure process reaches to 12 )(10 −Ωcm .

16

1.6) Current study:

In this research work. The electrical properties of Polyaniline emeralden base doped with

different concentrations of cuprous iodide CuI in order to improve the ability of Polyaniline

to coordinate CO gas will be reported. The change of conductivity in doped Polyaniline

allows the development of CO gas sensors. The research was accomplished through the

following steps:

1. Preparation of the emerladen base and the incorporation of CuI into Polyaniline

emeralden base.

2. Determination of AC conductivity before and after doping at different temperature.

3. Impedance spectroscopy measurements before and after exposure to CO to find the

optimal conditions for producing gas sensor.

4. Propose an appropriate models for structure of doped Polyaniline in order to

understand the mechanism of conduction.

The layout of the thesis will be as follows:

Chapter one covers the introduction and literature survey of Polyaniline and gas sensors. The

theoretical background of impedance spectroscopy and the theory of the dielectrics were

discussed in chapter two. Chapter three concerns with the samples perpetration and

experimental techniques. Discussion of the results was given in chapter four.

17

CHAPTER TWO

THEORETICAL

BACKGROUND

18

2.1) Polarizations:

The mechanisms with which atoms and molecules respond to an electrical field, leading to

the formation and/or orientation of dipoles are called polarization. The dielectric properties

of materials depend on the type of polarization. The polarization of dielectric arises from

three sources of dipole moments are:

a. Electronic dipoles.

b. Ionic dipoles.

c. Orientation of permanent dipoles.

2.1-a) Electronic dipoles:

Electronic polarization occurs in neutral atoms when an electric field displaces the nucleus

with respect to the electrons that surround it. Atomic polarization occurs when adjacent

positive and negative ions “stretch” under an applied electric field. For many dry solids, these

are the dominant polarization mechanisms at microwave frequencies, although the actual

resonance occurs at a much higher frequency. In the infrared and visible light regions, the

inertia of the orbiting electrons must be taken into account. The formation of molecules of

different types of atoms, result in the displacement of their electron clouds towards the

stronger binding atom. The atoms acquire charges of opposite polarity and an application of

applied field acting on these charges can change the equilibrium positions of the atoms.

Charge displacement occurs due to this displacement of positive and negative atoms.

19

For calculating the effect of electronic polarization, we consider an idealized atom with

perfect spherical symmetry. It has a point like charge + Ze in the nucleus, and the exact

opposite charge – Ze homogeneously distributed in the volume of the atom, which is:

3

34 RV π= (2.1)

Where R is the radius of atom, Figure (2.1).

Figure (2.1): Idealized atoms with spherical symmetry.

In an electrical field E, a force F1 acts on charges given by

F1 = Z. e. E (2.2)

Now consider the Coulomb force between electric point charges:

20

20

2 4 dqqF eN

πε= (2.3)

Where Nq =Ze and eq is the electron charge contained in the sphere with radius d,

3

3

3

3

3434

RZed

R

dZeqN ==

π

π (2.4)

At equilibrium F1 = F2

ZeERdZe

=30

2

4)(

πε (2.5)

EZe

Rd

)(4 3

0πε= (2.6)

The induced dipole moment ( Pe) can be written as:

ERdZePe

rrr3

04πε== (2.7)

The polarization Pr

finally is given by multiplying with N, the density of the dipoles; we

obtain:

ENRPrr

304πε= (2.8)

We assume that the dipole moment pr is proportional to the local electric field:

localEprr α= (2.9)

Where α is a constant called polarizability, which depends on the polarization mechanism of

the material concerned. The polarization can be given by:

localENPrr

α= (2.10)

21

Comparing Equation (2.15) with Equation (2.16), the electronic polarizability ( eα ) can be

given by:

304 Re πεα = (2.11)

Comparing Equation (2.7) with Equation (2.1), the dielectric susceptibility resulting from

atomic polarization can be given by:

34 NRe πχ = (2.12)

2.1-b) Ionic Polarization:

In materials where molecules of different atoms with different electronegativities (cations

and anions) form the structure, ionic polarization can occur. This mechanism arises from a

displacement of anions and cations in crystals relative to their normal positions when an

electric field is applied, resulting in net dipole moment as shown in Figure (2.2).For

calculating the effect of electronic polarization, consider a simple ionic crystal, e.g. NaCl.

The lattice can be considered to consist of Na+ - Cl– dipoles as shown in Figure (2.3 -a). Each

Na+ - Cl– pair is a natural dipole, no matter how you pair up two atoms.

Figure (2.2): Ionic polarization.

22

The polarization of a given volume, however, is exactly zero because for every dipole

moment there is a neighboring one with exactly the same magnitude, but opposite sign. In an

electric field, the ions feel forces in opposite directions. For a field acting as shown in Figure

(2.3 -b), the lattice distorts a little bit. The Na+ ions moved a bit to the right, the Cl– ions to

the left. The dipole moments between adjacent NaCl - pairs in field direction are now

different and there is a net dipole moment in a finite volume.

(a) (b)

Figure (2.3): (a) The NaCl crystal without an applied field. (b) The NaCl crystal with an

applied field.

From the above picture, it can be seen that it is sufficient to consider one dipole in field

direction. We have the situation where the distance between the ions increases by d, as

shown in Figure (2.4).

23

Figure (2.4): Ionic dipole.

The equilibrium distance d can be given by (Baird, 1968):

EYdqd

o

= (2.13)

Where Y is the Young Modulus, q is the net charge of the ion, and d0 is the equilibrium

distance between atoms. The induced dipole moment result from the applied electric field can

be given by:

EYdqpi

0

2

= (2.14)

Moreover, the polarization will be:

EYd

qNP ii

0

2

= (2.15)

Where Ni is the number of ion pairs per unit volume. Comparing Equation (2.20) with

Equation (2.4), the ionic polarizability can be given by:

0

2

YdqNi

i =α (2.16)

24

Ionic polarizations differ from electronic polarizations in that they occur due to the relative

motion of ions instead of a shift of the charge cloud surrounding atoms. Ionic and electronic

polarizations are referred to as instantaneous polarizations since they are completely formed

in a very short time with respect to the applied field.

2.1-c) Orientation (dipolar) polarization:

A molecule is formed when atoms combine to share one or more of theirs electrons. This

rearrangement of electrons may cause an imbalance in charge distribution creating a

permanent dipole moment. These moments are oriented in a random manner in the absence

of an electric field so that no polarization exists. The electric field E will exercise torque T on

the electric dipole, and the dipole will rotate to align with the electric field causing

Orientation polarization to occur (Figure 2.5). If the field changes the direction, the torque

will also change.

Figure (2.5): Dipole rotation in electric field.

Assuming Boltzmann statistics, the average dipole moment per molecule is:

25

kT

Epp o 3

20

rr

=>< (2.17)

Hence the average polarization due to orientation polarization:

kT

ENpENP ooo 3

2 rrr==>< α (2.18)

With the orientation polarizability given by:

kT

poo 3

2

=α (2.19)

2.1-2) Total polarization:

The total polarization is given by

ei PPPP ++= 0 (2.20)

Where 0P is the orientation polarization, iP is the ionic polarization, and eP electronic

polarization, so

EkT

pNP oe )

3(

2

0 ++= αα (2.21)

Since ( )EP r

rr10 −= εε (2.22)

Comparing Equation (2.21) with Equation (2.22), we obtain

( )1)3

( 0

2

0 −=++ ro

e kTpN εεαα (2.23)

From this equation, we can see that ( )1−rε is proportional to T/1 and to the electric dipole

moment in the material.

26

2.2) Dielectrics

2.2-1) Non-Polar Dielectric materials:

These materials have the same kind of atoms (hydrogen, diamond …) so that the only kind of

polarization presence in this material is the electronic polarization, which is given as

loce ENP α= (2.24)

Where locE is the local field given by

03ε

PEEloc += (2.25)

In addition, ( )EP r

rr10 −= εε we get

( )

32+

= rloc EE

ε (2.26)

( )

=+

= ENP re 3

2εα ( )Er

r10 −εε (2.27)

Then

( )( )2

13 0 +

−=

r

reNεε

εα (2.28)

( )33 0 +=

χχ

εα eN

(2.29)

This equation is called Clausius-Mossoti equation for electronic polarization.

27

2.2-2) Polar dielectric materials have ionic polarization:

These materials contain both the ionic and electronic polarization like NaCl. The polarization

in terms of polarizability can be written as

locie ENP )( αα += (2.30-a)

Using Equation (2.25), we get

( )

=+

+= ENP rie 3

2)(ε

αα ( )Er

r10 −εε (2.30-b)

Then ( )( ) ( )32

13

)(

0 +=

+−

=+

χχ

εε

εαα

r

rieN (2.30-c)

This equation is also called Clausius-Mossoti equation for ionic polarization.

2.3) Dipolar Relaxations:

we must expect that the (mechanical) response to a field will depend on the frequency of the

electrical field; on how often per second it changes its sign. If the frequency is very large, no

mechanical system will be able to follow. We thus expect that at very large frequencies all

polarization mechanisms will "die out", i.e. there is no response to an extremely high

frequency field. This means that the complex dielectric permittivity *ε will approach one

for ∞→ω . It is best to consider our dielectric now as a "black box". A signal in the form of

an alternating electrical field E goes in at the input, and something comes out at the output, as

shown below. Figure (2.6).

28

Figure (2.6): Alternating electrical field E inter dielectric black box.

With complex notation, the input will be can be written as :

Ein*= Ein · exp(iω t) (2.31)

And the output ,

Eout*= Eout · expi(ω t + Φ). (2.32)

Then

Eout*= f(ω ) · Ein (2.33)

With f(ω ) = complex number for a given ω or complex function of ω f(ω ) is what we are

looking after. This function is the relation between the output of a dielectric function of the

material to its input of the dielectric function of the material. We can however, calculate

dielectric functions for some model materials.

In polarization mechanisms, if a driving force is present (electric field), there is an

equilibrium state with an (average) net dipole moment. If the driving force were to disappear

suddenly, the ensemble of dipoles will assume a new equilibrium state (random distribution

of the dipoles) within some characteristic time called relaxation time. When the electrical

field is suddenly switched off, after it has been constant for a sufficiently long time, an

equilibrium distribution of dipoles could be obtained. We thus expect a smooth change over

29

from the polarization with field to zero within the relaxation time (τ ), or a behavior as


Figure (2.7): The dependence of polarization on time.

As shown at Figure (2.7) we can write the time dependence polarization as

( ) τtptP s −= exp (2.34)

Where sp is the static polarization and (τ ) is the relaxation time.

We thus have to consider the Fourier transform of P (t). Fourier transform is given by

dttitPP s ∫∞

=0

* expexp)( ωτω (2.35)

by evaluating this integral

( )

τπω

ωωω

2

*

=

+=

s

s

s

ipP

(2.36)

30

so we can write the Equation (2.7) in the complex form

)()()( *0

* ωωχεω EP = (2.37)

Where )(* ωχ is the complex susceptibility

)()()(* ωχωχωχ ′′+′= (2.38)

)())()(()( 0* ωωχωχεω EP ′′+′= (2.39)

Extracting a frequency dependent susceptibility )(* wχ , we can obtain that

)()(

)())()((0 ωωωωωχωχε

iEp

EP

ss

s

+==′′+′ (2.40)

Multiply by complex conjugate to get

22 )(1

)(

)(1))()((

s

ss

s

s iω

ωω

ωχ

ωωχ

ωχωχ+

−+

=′′+′ (2.41)

Where sχ is the static susceptibility, when ω = 0 given by

s

ss E

P

0εχ = (2.42)

2.3-1) The frequency dependence of polarization:

The various polarization mechanisms all depend differently upon frequency. Thus the

complex dielectric permittivity, *ε , will be controlled by different mechanisms as the

frequency changes. This is reflected by the strong variation of ε ′ and ε ′′ with frequency as


31

Figure (2.8): Frequency response of dielectric mechanism.

The frequency dependent response is due to many different factors. For electronic and atomic

polarization the inertia of orbiting electrons must be accounted for. Due to this inertia effect,

these polarization mechanisms will be small for any frequency other than the resonant

frequency. Far below this frequency, little contribution to ε ′ andε ′′ is given from these

mechanisms. At the resonant frequency, a peak inε ′′ will occur and a dispersion will occur in

ε ′ (Kingery et al., 1976). Materials, which undergo orientation polarization, will experience

dispersion at the relaxation frequency. In these materials, a large change in ε ′ and ε ′′ will

occur at this frequency. At the relaxation frequency, the oscillation of the applied field is “too

fast” for the molecules to have time to fully rotate. As a result, ε ′ will decrease when the

relaxation frequency is reached since less of the applied field is canceled by the dipoles as the

frequency is increased. A peak in ε ′′ also occurs at this frequency since the most energy is

dissipated at that point. This is due to the fact that at low frequencies rotation is slow, so

minimal energy is dissipated and above the relaxation frequency the molecules only rotate a

32

small distance, so again minimal energy is dissipated. The maximum lies in-between these

two extremes at the relaxation frequency.

Let us consider the time dependence of the dielectric displacement D for a time dependent

Electric field:

')'()'()( dttttEtD D

t

−= ∫∞−

φε (2.47)

Applying to the left and right parts the Laplace transforms, it can be obtained:

),(*)(*)(* ωωεω ED = (2.48)

Where

)]([)exp()()(0

* tLdtstts DsDs φεφεε =−= ∫∞

(2.43)

(s = γ+iω; γ 0 and we’ll write instead of s in all Laplace transforms iω).

it can be rewritten (2.43) in the following way:

)]([)()(* tLi orps φεεεωε ∞∞ −+= (2.44)

In the other hand, complex dielectric permittivity can be written in the following form:

)(")(')(* ωεωεωε i−= (2.45)

The Equation (2.44) justifies the use of the symbol ∞ε for the dielectric permittivity of

induced polarization, since for infinite frequency, the Laplace transform vanishes, and the

expression becomes equal to ∞ε .

The real part of complex dielectric permittivity )(ωε ′ is associated with real part of Laplace

transform of orientation pulse-response function:

33

∫∞

∞ +=0

cos)()(' dtttorp ωφεωε (2.46)

Moreover, the imaginary part of complex dielectric permittivity )(ωε ′′ is associated with the

negative imaginary part of the Laplace transform of orientation pulse-response function:

∫∞

=0

sin)()('' dtttw orp ωφε (2.47)

Where )(torpφ is the decay function of polarization after the electronic fields tends to zero.

On the other hand, the relationship between time dependent displacement and harmonic

electric field is given by

tiEtEtiEtE sss ωωω sincosexp)(* +== (2.48)

in this case the relation (2.43) can be written in the following form:

tEtEtD ss ωεωωε sin"cos)(')( += (2.49)

That can be presented as follows:

) cos( sinsincoscos)( δωωδωδ −=+= tDtDtDtD sss (2.50)

Where

22 "' εε += ss ED (2.51)

and )(')("=)(tan

ωεωεωδ (2.52)

From Equation (2.50) it clearly appears that the dielectric displacement can be considered as

a superposition of two harmonic fields with the same frequency, one in phase with electric

field and another with a phase difference 2π . The amplitudes of these fields are given by

34

sEε ′ and sEε ′′ , respectively. Calculation of the energy changes during one cycle of the

electric field shows that the field with a phase difference 2π with respect to the electric

field gives rise to absorption of energy.

The total amount of work exerted on the dielectric during one cycle can be calculated in the

following way:

2

/2

0

/2

0

2

/2

0

))((''41

sin cos)(''cos cos)(')(41

41

s

t ts

t

E

tdttdtE

EdDW

ωεπ

ωωωεωωωεπ

πωπ ωπ

ωπ

=

⎥⎦

⎤⎢⎣

⎡+=

=∆

∫ ∫

∫

= =

=

(2.53)

Since the fields E and D have the same value at the end of the cycle as at the beginning, the

potential energy of the dielectric is also the same. Therefore, the net amount of work exerted

by the field on the dielectric corresponds with absorption of energy. Since the dissipated

energy is proportional to "ε , this quantity is called the loss factor.

From Equation (2.53) we find the average energy dissipation per unit of time:

δπωωε

πω

sin8

)("8

)( 2

sss ED

EW ==& (2.54)

Where δ called a loss angle.

According to the second law of thermodynamics, the amount of energy dissipated per cycle

must be always positive or zero. It means that

( ) 0≥′′ ωε (2.55)

Let us back to Equations (2.47) and (2.48), )(torpφ is given by

35

τφφtor

porp eot )()( = (2.56)

Therefore, the complex dielectric permittivity is given by

∫∞

∞ +=0

* expexp)()( dttitoorp ωτφεωε (2.57)

The result of the integral is:

ω

τ

φεε

i

oorp

−+= ∞ 1

)(* (2.58)

when

b)-(2.59 )(

)(

a)-(2.59 )(,

*

τεε

φ

φτεε

εωε

ω

∞

∞

−=

+=

=

∞→

sorp

orps

s

o

o

By using Equations (2.59-b) and (2.58), we can obtain

∫∞

∞∞ −

−+=

0

* expexp)( dttits ωττεε

εωε (2.60)

By evaluating the integral, we get

ωτεε

εωεi

s

−−

+= ∞∞ 1

)(* (2.61)

Multiplying with complex conjugate

2*

)(1)()()(

ωτωτεεεε

εωε+

−−−+= ∞∞

∞ss i (2.62)

36

2)(1)(

ωτεε

εε+−

+=′ ∞∞

s (2.63 -a)

2)(1)(

ωτωτεε

ε+−

=′′ ∞s (2.63 -b)

These equations are called the “Debye equations”.

At which ε ′′ has maximum determine by

0=′′

ωε

dd (2.64)

If mωω = at constant T

τ

ω 1=m (2.65)

Then Debye equations read:

2)(

2)(

∞

∞

−=′′

+=′

εεε

εεε

s

s

(2.66)

And

)()(

tan∞

∞

+−

=′′′

=εεεε

εεδ

s

s (2.67)

The relationship between ε ′′ and ε ′ in the complex plan is called Cole-Cole plots which is a

semicircle, and the diameter of this semicircle is the dielectric strength of the dielectric

material.

37

Figure (2.9): Schematic representation of frequency dependence of ε ′ , ε ′′ and δtan for

a single relaxation time.

2.4 Determination of the Relaxation Parameters ε∆ and τ of a Single

Debye Relaxation:

The characteristic parameters ε∆ and τ of a single Debye relaxation can be determined

from both quantities, ε ′ and "ε . The physical background is that in the time domain there is

of course exactly one response function, consequently, both quantities contain the full

information. The relaxation time τ can be determined from the position of the loss

maximum or the turning point of the dielectric permittivity curve, respectively as shown in

Figure (2.9). The relaxation strength is the difference between the limits of )(ωε ′ for

0→ω and ∞→ω or twice of the maximum value of )(" ωε (Frübing, 2001). In

38

practice, however, it is often difficult to determine ε∆ and τ because real dielectric spectra

are generally broader than the Debye spectrum and their shape is not pre-defined.

Furthermore, the frequency range is often limited for technical reasons. Then, the

measurement of both parts of the dielectric permittivity gives more reliable information for a

proper determination of the relaxation parameters. Particularly, a useful way to obtain these

quantities is the so-called Cole-Cole representation (Cole and Cole, 1941). The locus of the

complex number ∗ε in the complex plane is a semicircle in the fourth quadrant as shown in

Figure (2.10), then:

2

22

2"

2⎟⎠⎞

⎜⎝⎛ −

=+⎟⎠⎞

⎜⎝⎛ +

−′ ∞∞ εεε

εεε ss (2.68)

From Equation (2.68) and Figure (2.10), it follows:

τωεε

εφ =−′

=∞

"tan (2.69)

Practically, ε ′ and "ε are measured in a middle frequency range and plotted in the complex

plane. Then the semicircle is extrapolated to sε and ∞ε . The relaxation time follows from

Equation (2.68).

39

Figure (2.10): Cole-Cole representation.

2.5 RC Circuits:

Let us consider the pure resistance shown in Figure (2.11 -a). At any particular instant,

Ohm’s law applied to the resistor tells us that RIV = . The ac voltage is given by:

tVV sin0 ω= (2.70)

We have: tsin0 ωR

VRVI == (2.71)

From Equations (2.70) and (2.71), we can see that the current and voltage in the pure

resistance circuit are in phase (see Figure (2.13 -b).

Figure (2.11): (a) Pure resistance in an ac circuit. (b) Plot of V versus I across resistor as a

function of time.

40

For a capacitor in ac circuit shown in Figure (2.12 -a), the relation between current and

voltage is given by:

)2

sin(0 πωχ

+== tV

dtdVCI

C

(2.72)

Where Cχ is the capacitor reactance ( 1)( −= CC ωχ ). Comparing Equation (2.71) with

Equation (2.72), we can see that there is a phase difference between the current and voltage

( 2/πφ = ) as shown in Figure (2.14 -b).

In the simplest case, a capacitor containing a lossy dielectric may be thought of as a pure

capacitance and resistance connected either in parallel or series (Hummel, 1992).

Figure (2.12): (a) Capacitor in an ac circuit. (b) Plot of V versus I across capacitor as a

function of time.

2.5.1 Parallel Connection:

In RC circuit shown in Figure (2.13), a capacitor PC is connected in parallel with

resistor PR , the total current is given by:

CR III += (2.73)

41

Substituting Equations (2.71) and (2.72) in Equation (2.73), we have:

)2

sin( sin 00 πωχ

ω ++= tV

tRV

ICP

(2.74)

The Ohm’s law equivalent for RC parallel circuit in Figure (2.14) is given by:

ZIV = (2.75)

Figure (2.13): Parallel combination of resistor and capacitor.

Where Z is called the impedance of the circuit. From Equation (2.74), we can see that:

PP

CiRZ

ω+=11

* (2.76)

P

P

CiR

Zω+

=1

* (2.77)

Since "iZZZ −′= ; we can separate the real and imaginary components via multiplication

by ( PPCRiω−1 ). Thus:

2

*

)(1)1(

PP

PPP

CRCRiR

Zωω

+

−= (2.78)

And: 2)(1 PP

P

CRR

Zω+

=′ (2.79)

42

2

2

)(1"

PP

PP

CRCR

Zω

ω+

= (2.80)

Figure (2.14) shows the graph of "Z versus Z ′ in the complex plane, it appears as a semi-

circle of radius 2/R and the maximum value of "Z defined by 1=PPCRω (Hodge et al.,

1976).

If we apply ac voltage across a capacitor filled with a dielectric material, the complex form

of the voltage is (Daniel, 1967):

tiVV ωexp0* = (2.81)

Figure (2.14): Complex-plane impedance plot for parallel RC circuit.

The complex charge in the capacitor at time (t) can be written as: VCQ ** = , where *C is the

complex capacitance that is given by:

0** CC ε= (2.82)

Where 0C is the geometrical capacitance (the space between the plates is vacuum) which has

the form:

d

AC 00

ε= (2.83)

"Z

Z ′

ω

2PR

PR

1=PP CRω

43

The current can be given by: dtdQI = , so

VCiI ** ω= (2.84)

Using Equation (2.82), we will get:

VCiI *0

* εω= (2.85)

Dividing by (V), the following impedance equation is obtained:

*0*

1 εω CiZV

I== (2.86)

Comparing Equation (2.86) with Equation (2.76), we will get the following formula for the

parallel RC circuit:

P

P

CiR

Ci ωεω +=1*

0 (2.87)

Using Equation (2.45) and equating the real and imaginary parts of Equation (2.87), we can

get a formula of real and imaginary components of the dielectric permittivity:

0C

C P=′ε (2.88)

PRC0

1"ω

ε = (2.89)

Consequently, the loss tangent can be given by:

PP RCωε

εδ 1"tan =′

= (2.90)

44

2.5.2 Series Connection:

In the series connection, a capacitor CS is connected in series with resistor RS in an ac circuit

as shown in Figure (2.15). The currents in the capacitor and resistor have to be equal each

other ( RC III == ) and the total voltage is the sum of the voltages across capacitor and

resistor.

The total voltage is given by:

)2

sin( sin πωχω ++= tItIRV CS (2.91)

Figure (2.15): Series combination of resistor and capacitor.

Following the same steps carried out in parallel, we can get the following formula for

complex impedance:

S

S CiRZ

ω+=* (2.92)

Separating the real and imaginary components of impedance, to get:

SRZ =′ (2.93)

45

CSC

Z χω

−=−=1" (2.94)

The complex plane impedance plot for series RC circuit in series is shown in Figure (2.16).

Where, CSR χ>> at high frequencies, and SC R>>χ at low frequencies (Bard and

Faulkner, 1980).

Figure (2.16): Complex-plane impedance plot for series RC circuit.

The impedance Equation (2.94) for the series RC circuit gives:

S

S CiR

Ci ωεω+=*

0

1 (2.95)

Using Equation (2.45) and equating the real and imaginary parts of the complex dielectric

permittivity in Equation (2.95), we can get the following formula of real and imaginary

components of the dielectric permittivity:

)1( 222

0 SS

S

RCCCω

ε+−

=′ (2.96)

46

)1(

" 2220

2

SS

SS

RCCRC

ωω

ε+

= (2.97)

Therefore,

SS RCωεεδ −=′

="tan (2.98)

2.5.3 Impedance - Dielectric Properties Correlation:

The four major properties reported in dielectric measurements are: complex impedance *Z ,

complex admittance *Y , complex electric modulus *M , and complex dielectric

permittivity *ε (Macdonald, 1987).

a) Complex impedance *Z :

is measured in ohms and can be expressed in terms of the real and imaginary

components, Z ′ and "Z respectively:

"* iZZZ −′= (2.99)

b) Complex admittance *Y :

The admittance is defined as the reciprocal of impedance. Thus:

** 1

ZY = (2.100)

and:

'''* iYYY −= (2.101)

Admittance is a complex number and measured in siemens. The real part Y', is called

conductance, and the imaginary part Y'', is called susceptance. Conductance and

47

susceptance are measured in siemens. Substituting Equation (2.100) in Equation

(2.101), we will get:

'''"

1* iYYiZZ

Y −=−′

= (2.102)

Multiplying by ( "iZZ +′ ), we have:

22 ""'''

ZZiZZiYY

+′+′

=− (2.103)

Separating the real and imaginary components, we will have the following formulas

for conductance and susceptance:

22 "'

ZZZY+′′

= (2.104)

22 ""''ZZ

ZY+′−

= (2.105)

c) The complex dielectric Permittivity *ε :

The complex dielectric permittivity is defined in Equation (2.51). In order to get a

relation between dielectric permittivity and impedance, we can rearrange Equation (2.91)

to have:

0

** 1

CiZ ωε = (2.106)

Where 0C is the vacuum capacitance of the sample, it can be given in terms of the

thickness (d) and the surface area (A) by:

d

AC 0

0ε

= (2.107)

48

Using Equations (2.45) and (2.99), we get:

)"(

1"0 ZZiC

i−′

=−′ω

εε (2.108)

Multiplying by ( "ZZi +′ ), we will get:

)"(

"" 220 ZZC

ZZii+′−′−

=−′ω

εε (2.109)

Separating the real and imaginary components of the dielectric permittivity, we will have:

)"(

"22

0 ZZCZ+′

−=′ω

ε (2.110)

)"(

" 220 ZZC

Z+′′

=ω

ε (2.111)

d) Complex electric modulus M* :

The dielectric modulus is related to dielectric permittivity through the relation:

*

* 1ε

=M (2.112)

Analyzing the real and imaginary components of electric modulus and dielectric

permittivity, we have:

"

1"εε i

iMM−′

=−′ (2.113)

Multiplying by the associate ( "εε i+′ ) we will get:

)"(

"" 22 εεεε

+′+′

=−′iiMM (2.114)

Separating the real and imaginary components of the electric modulus, we will have:

22 "εε

ε+′′

=′M (2.115)

49

22 "

""εε

ε+′−

=M (2.116)

2.6 Temperature dependence of the relaxation time:

Real loss peaks shift to higher maximum frequencies with increasing temperature because the

relaxation time decreases. This property is often used as a powerful tool to extend the

frequency range of dielectric spectroscopy indirectly by orders of magnitude. It can be easily

recognized particularly for the Debye relaxation. The temperature dependence of the

relaxation time follows that of the viscosity, which is determined by the empirical Arrhenius

relation (Frübing, 2004).

kTEa /exp0 ∆−=ττ (2.117)

From Equation (2.117), it is clear that for the Debye relaxation one obtains the same graph

whether one is plotting rεlog versus flog at fixed T or rεlog versus 1/T at fixed f. This

property is also called the time-temperature superposition principle. If the response is not of

the Debye type, then this is generally not true, and there is no unambiguous way to relate the

temperature dependence to the frequency dependence according to a theoretical model. Thus,

)(Tτ can only be determined from the frequency dependence. Nevertheless, for an overview

and for a more qualitative analysis it is frequently appropriate to plot the real loss maxima

versus temperature because they appear better resolved in this representation.

50

CHAPTER THREE

EXPERMENTAL

PART

51

3.1) Sample’s preparation:

Doped Polyaniline (PANI) were prepared by doping with 10% of copper salt CuI and with

different concentration of 2I (0 – 5%) by weight. All of cuprous iodide\iodine ratio where

determined gravimetrically i.e. by weight ratio.

The procedure of doping was performed as follows:

1. PANI was doped with CuI- 2I in the carbon tetrachloride ( 4CCl ) under continuous

sonication. The concentration of 2I varies from 0% to 5% and 10% of CuI of the

sample’s weight. 0.1 gm of Iodine was dissolved in 4CCl to get homogenous

solution of known concentration of 0% to 5% Iodine concentration was introduced

to polymer using the relation

iiVCVC =•• (3.1)

Where •C •V are the concentration and the volume of the prepared solution,

respectively and ii VC are the concentration and the volume of the requirement

solution, respectively.

2. The (PANI-CuI- 2I ) is dried under vacuum at room temperature for one day.

3. All samples were compressed to desk of 13 mm diameter under pressure of

15 ton\cm2 for 1 minute.

4. The desks were exposed to Carbon monoxide, which was prepare using the reaction

of sulfuric acid with formic acid, for one hour at room temperature, the reaction can

be expressed as:

(l)242(g)(l))(42 OHSOH CO HCOOH SOH ++→+l (3.2)

52

3.2) Sample’s set:

Seven samples were prepared and tabulated in table (3.1).

Table (3.1): PANI-CuI- 2I ratios

Sample Emeralden

PANI

Iodine

2I

cuprous

iodide

CuI

C1 100% 0% 0%

C2 99% 1% 0%

C3 90% 0% 10%

C4 89% 1% 10%

C5 88% 2% 10%

C6 87% 3% 10%

C7 85% 5% 10%

53

3.3) Sample’s holder:

The sample’s holder shown in figure (3.1) made of Teflon, two electrodes and isolated base

were used the measure the imaginary and real components of complex impedance for PANI

disks.

Figure (3.1): Sample holder

3.4) Impedance measurements:

A Solartron 1260 Impedance/Gain-Phase Analyzer, which shown in figure (3.2), was used to

obtain AC impedance measurements, in frequency rang 100Hz to 410 , at selected

temperatures from 25 oC to 65 oC , also the impedance measurement is done with DC bias =

0.3V with an amplitude of the AC signal of 0.5V, before and after exposed to Carbon

Monoxide. The following parameters were record from the Bridge (the impedance, real and

imaginary parts of admittance, electric modulus, capacitance, and tangent lossδ ).

54

Measurements can be obtained with considerable ease. The ability to interface these systems

with PCs enables the multitude of data to be recorded and analyzed. These measurements are

taken over a large frequency range and enable different circuit elements, which have different

time constants, to be resolved and have been particularly useful for the study of ionic

conduction, grain boundary impedance, and electrode/electrode interface characteristics and

also mixed conducting solid electrode materials.

Figure (3.2): A Solartron 1260 Impedance/Gain-Phase Analyzer

A comprehensive range of voltage and current transfer characteristics are given by the FRA,

each one available from the original base data, which includes:

- Polar and Cartesian coordinates of impedance and admittance,

- Inductance or capacitance values, with resistance, quality factor or dissipation factor,

for series or parallel circuits.

A PC can control the FRA through software, which is connected through the GPIB. In

addition, FRA can be controlled manually through a logically arranged keyboard and simple

menu on the front panel of the instrument.

FRA operational principles will be briefly outlined. At certain frequency (ω ), the generator

output is represented by:

55

)sin(0 tVV ω= (3.3)

Where the signal is applied to the system under test. The response signals from the system

are connected to the two channel inputs of the analyzer. Assuming that the voltage on

channel 1 is 1V and the voltage on channel 2 is 2V , and no harmonic distortion, these signals

can be represented as:

)](sin[)( 111 ωθωω += tVV (3.4)

)](sin[)( 222 ωθωω += tVV (3.5)

Where )(1 ωV , )(2 ωV , )(1 ωθ and )(2 ωθ are the signal amplitudes and their phases

respectively, with respect to the generator signal as shown in figure (3.3).

By using Fourier integrals, the in phase and out of phase of each signal are computed

separately as follows:

∫ +=n

iii dtttVn

a0

)sin()](sin[)(1 ωωθωω (3.6)

∫ +=n

iii dtttVn

b0

)cos()](sin[)(1 ωωθωω (3.7)

Where i = 1, 2. The complex voltage ratio is displaced as:

ibaVV

+=⎥⎦

⎤⎢⎣

⎡*

1

2 (3.8)

Where a is the real component and b is the imaginary component.

56

)(1 ωV

1θ

1V

t

)(2 ωV

2θ

2V

t

0V

V

t

Figure (3.3): The three FRA signals.

The user may choose the integration time he requires for sufficiently accurate calculation of

the Fourier integrals. In addition, a single measurement may be automatically repeated many

times, enabling the user to check for systematic variation in the results obtained and to make

sure that the material had reached thermal equilibrium.

A block diagram of the charge amplifier-FRA setup is shown in figure (3.5). The equivalent

circuit of a charge amplifier is an operational amplifier with a standard capacitor SC as its

57

feed back component. The goal of the measurement is to determine the unknown

capacitance XC . Since XC contains the lossy dielectric material, its capacitance is complex,

and is given by

0** CCX ε= (3.9)

Or 00* "CiCCX εε −′= (3.10)

Where 0C , ε ′ and ε ′′ are the capacitance of the air-filled capacitor, the real and imaginary

components of the complex dielectric constant ( *ε ) respectively.

Figure (3.4): Circuit for charge amplifier-FRA setup.

The charge amplifier in the Solartron system is used practically to convert the change in

charge on the plates of XC into a change in the output voltage of the amplifier. Analyzing

the circuit shown in figure (3.4), we have:

58

S

X

CC

VV **

1

2 −=⎥⎦

⎤⎢⎣

⎡ (3.11)

Using Equations. (3.7) and (3.9), we obtain:

SS CCi

CCiba 00 "εε

+′

−=+ (3.12)

Equating the real and imaginary components, we have:

0C

aCS−=′ε (3.13)

0

"C

bCS=ε (3.14)

The dielectric loss tangent is given by:

ab

−=′

=εεδ "tan (3.15)

The frequency response analyzer is used to measure the complex voltage ratio and display it

in the form of iba +− .

3.5) The 1294 Impedance Interface:

Figure (3.5) shows the 1294 Impedance Interface. It is used in conjunction with a FRA and

extends the measurement capabilities of the FRA to address such applications as high

impedance materials testing (Solartron, 2001).

59

Figure (3.5): 1294 Impedance Interface.

The 1294 Impedance Interface designed to be controlled by a PC, which communicates with

the 1294 via the parallel port. It can be configured locally through setup switches or remotely

through a PC compatible parallel port. The 1294 has two sets of connectors. One set is for

‘IEC601-1’ connections: these are current-limited and are designed specially for medical

applications. The other set of connectors is intended for non-medical applications such as

high impedance materials testing.

The FRA output drive signal can be amplified or attenuated by the 1294 before application to

the test sample. This will maximize the stimulus range and minimize noise and errors due to

input impedance.

3.6) Impedance Measurement Software:

The PC software for the 1294 is Microsoft Windows Z-60 and Z View based packages,

designed to run with Windows NT4, the measured quantities are the impedance Z, phase

angleθ , and the capacitance. The Z View program was used to analyze the data in the four

complex planes (impedance, dielectric permittivity, dielectric modulus, and admittance).

60

The Windows interface provided by the impedance measurement software (Z-60) offers a

simple and effective way of configuring the impedance measurement system for sample

measurement, graphical presentation and data archiving.

The samples were carried out at selected temperatures from 25 oC to 65 oC where it was

controlled by using oven. All data calculation was performed using Microsoft Excel 2003,

easy plot and Origin-5 programs.

The set up of our experiment as shown in figure (3.6).

Figure (3.6): Set up of our experiment.

61

CHAPTER FOUR

RESULTS

AND

DISCUSSION

62

4.1) Introduction:

Conducting polymers, such as Polyaniline (PANI), Polypyrrole (PPy), Polythiophene (PTh)

and their derivatives, have been used as the active layers of gas sensors since early 1980s

(Nylabder et al., 1983). In comparison with most of the commercially available sensors,

based usually on metal oxides and operated at higher temperatures, the sensors made of

conducting polymers have many improved characteristics. They have high sensitivities and

short response time; especially, these features are ensured at room temperature. Furthermore,

they are easy to be synthesized through chemical or electrochemical processes, and their

molecular chain structure can be modified conveniently by copolymerization or structural

derivations. Moreover, conducting polymers have good mechanical properties, which allow a

facile fabrication of sensors, and as a result, more and more attentions have been paid to

sensors fabricated from conducting polymers.

The sensing principle of electrical gas sensors is the interaction between gas and sensing

material. This interaction changes the physical properties of material such as conductivity,

capacitance and the electric field itself. Doped Polyaniline exhibits an electrical conductivity

response to CO, which is related to the content, pore size and ions of the dopant type and

concentration. Recently, AC impedance spectroscopy technique has been employed for

conducting polymer gas sensors. The most important advantage of this technique is the

possibility to distinguish different chemical species within a single sensor (Jin et al., 2001).

Organic vapors, such as carbon monoxide, methanol, acetone and ethyl acetate, could be

detected by measuring the change of AC conductance of a PANI gas sensor at different

frequencies (Hao Qingli, 2003).

63

4.2) XRD results:

Figures (4.1), (4.2), and (4.3) show the XRD profiles of C3, C5, and C7 respectively before

and after exposed to CO .

Figure (4.1): XRD profile for C3 sample.


64


Pure PANI and as well as most polymers exhibits three broad peaks. PANI in its solid phase

is found in its hexagonal closed pack structure. However, along hexagon, we expect to find

six PANI chains forming a bundle. With their separation d equals to the side of the hexagonal

which is expected to appear at large θ2 values, (Al-Omari M. R. 2006).

Figure (4.1) shows the XRD profile for C3 sample. Obviously, peaks became sharp and shift

in their position, this indicates that the spacing distance d decreases after exposure to CO .

Since CO tends to form clusters leading to appearance of sharper peaks after exposure.

Figure (4.2) shows the XRD profiles for C5 sample that was doped by 10% of CuI and 2% of

I2. The peaks became extremely sharp indicating that the sharpness of peaks is mainly due to

the increase of the concentration of Iodine. However, after exposure to CO, the peaks

became less sharp suggesting more amorphous materials exist in the bulk. For the C7 sample

which was doped with 10% of CuI and 5 % of I2 as shown in Figure (4.3) the XRD profile, a

65

large shift in the position of the peaks was occurred which is due to decrease in the

interplaner displacement as a result of doping. After exposing to CO, a more shift took place

and two new peaks observed at o2.302 =θ and o532 =θ indicating new cluster was formed in

the material as a result of CO absorption.

4.3) Impedance analysis:

Figure (4.4 -a) shows the frequency dependence of real part of complex impedance (Z')

before and after exposure to CO for undoped PANI (C1 sample). In the frequency range 100

up to 1000 Hz. There is a sharp decrease in Z' with increasing frequency, and no relaxation

peak was observed in the plot of imaginary part of impedance (Z``) as shown in Figure (4.4 -

b). The plot of Z' versus Z`` shows a part of semi-circle where fitting was employed as

shown in Figure (4.4 -c). The electrical impedance for such system can be modeled as shown

in Figure (4.4 -c) which consists of Resistance (R) and Constant Phase Element (CPE) in

parallel with additional Resistance (R) in series with the network. The diameter of the

semicircle represents the bulk resistance of pure PANI. It was found that the bulk resistance

decreases slightly when the sample was exposed to CO (varies from 1.0 810× to 5.3 710×

ohm). The decrease in resistance is due to reduction of the barrier height between grains. The

oxidation happened at grain surfaces in the presence of CO gas causing the surface coverage

of adsorbed oxygen to decrease. Thus, the surface potential, barrier height and the depletion

length are reduced, which leads to a decrease in resistance (Dixit et.al 2005 and

Densakulprasert 2005).

66

Figure (4.4): a) Z' vs. frequency, b) Z'' vs. frequency and c) Z'' vs. Z', before and after

exposure to CO for C1 sample.

When PANI was doped by 1% I2, the general features of the impedance components (Z` and

Z``) are similar to that observed for undoped PANI (C1 sample) as shown in Figure (4.5).

However, the same model can be employed with different values of Resistances and

Constant Phase Elements . A slight decrease in Z` was observed over the frequency range

100 up to 103 Hz when the measurements were carried out after exposing the sample to CO .

(b) (c)

(a)

67



The determined bulk resistance from the diameter of the semi-circle in the plot of Z' versus

Z'' Figure (4.5 -c),(varies from 2.8 x 108 to 1.7 x 108 ohm). While doping PANI by 10 %

of Couperus Iodide (CuI) when the sample was exposed to CO, the plot of Z' versus Z'', as

shown in Figure (4.6 -c), did not yield semi-circle, the electrical impedance for such system

can be modeled as shown in the Figure (4.4 -c) which consist from Resistance(R) and

Constant Phase Element (CPE) in series. In addition, all other general features are the same

as C1 and C2 samples. Furthermore, when the PANI was doped by 10% of CuI and 5% of

Iodine, the general features of the impedance spectroscopy are similar to Pure PANI (C1)

sample as shown in Figure (4.7), a semi-circle is more define due to the increase in Iodine

concentration where the bulk resistance decreased after exposure to CO (varies from 3.4 x

107 to 1.5 x 107 ohm). The electrical impedance for such system can be modeled as shown in

(a)

(b) (c)

68

the Figure (4.7 -c). However, when the measurements were repeated after three days of

exposu re , t he bu lk r e s i s t ance a t t a ins i t s i n i t i a l va lue be fo re exposu re .



(a)

(b) (c)

69


exposure to CO, after 1 day, 2 days and 3 days for C7 sample.

4.4) Conductivity:

Frequency dependent conductivity behavior due to two components expressed as,

acdc σσσ +=

The above equation represents the total conductivity, where dcσ is the DC conductivity,

which is frequency independent, and acσ is the AC conductivity, which can be determined

from AC measurements according to the relation

ωεεσ ''o=ac

Kim H. M. et al., (2000) found that the dependence of the conductivity on the frequency,

obeys the well known formula (),

sdc Aωσσ .+=

(a)

(b) (c)

70

The frequency dependent electrical conductivity have been presented in Figures (4.8), (4.9),

(4.10) and (4.11) for C1, C2, C3 and C7 samples respectively, before and after exposure to

CO. As shown in the Figures (4.8 – 4.11) as the frequency is increased, conductivity goes on

increasing.

Figure (4.8): AC conductivity before and after exposure to CO for the C1 sample.

71



72

Figure (4.11): AC conductivity before and after exposed to CO and after one, two and three

days after exposing process for the C7 sample.

The parameter ( sAω. ) related to AC conductivity, where (A) and (s) are temperature

dependent parameters. The parameter (s) is related to hopping in the disordered material

(Kim. H. M. et al., 2000). By fitting the conductivity curves as shown in Figures (4.8), (4.9)

and (4.11), it is found that the parameter (s) decreased after exposure to CO for C1 (s =

0.44 to 0.34), for C2 (s = 0.39 to 0.37) and for C7 (s = 0.76 to 0.61), so after exposure to CO

the frequency dependence of the conductivity decrease and hopping in the disordered chain

increases, this behavior is similar to that observed in most amorphous semiconductors

(Bhatangar V.K. et al.,1990). On the other hand, the parameter (s) increased after exposure to

CO for C3 sample as shown in Figure (4.10), so hopping in the disordered chain decreased.

73

4.5) Dielectric Permittivity:

The dependence of relative permittivity before and after exposure to CO for the C1, C2, C3

and C7 samples are shown in Figures (4.12 -a), (4.13 –a), (4.14 –a), and (4.15 –a)

respectively. 'ε is minimum in the frequency range higher than about 410 Hz. However, at

low frequencies a sharp decrease in 'ε was observed indicating that the mobility of charge

carriers has the same mechanism of ionic conduction, which is dominant in these samples.

The low frequency dispersion for 'ε and the absence of loss peak for ''ε are characteristics

of charge carriers systems, (Lian A. et al., 1995). The localized charge carriers, under the

applied alternating electric field, can hop to neighboring localized sites, like the reciprocating

motion of a jumping dipole, or jumping to neighboring sites, which form a continuous

connected network, allowing the charges to travel through the entire physical dimensions of

the samples.

However, the plot of 'ε versus ''ε (Cole-Cole) shows a part of semi-circle where fitting was

employed before and after exposure to CO as shown in Figure (4.12 -c), (4.13 -c), (4.14 -c)

and (4.15 -c) for the C1, C2, C3 and C7 sample respectively. The diameter of the semicircle

represents dielectric strength ( ∞−=∆ εεε s ). Where ∞ε is the relaxed dielectric

permittivity and sε is the unrelaxed dielectric permittivity, which represents the limiting

values at low and high frequency, they define relaxation strength ε∆ (number of effective

electric dipoles that relax after applying electric field) which depends on the volume

concentration of the dipole species. For pure PANI, it was found that the ε∆ increases by

three order of magnitude when the sample was exposed to CO, from 21.2 to 64.1. When

74

PANI was doped by 1% of Iodine, it was found that the ε∆ increases from 24.4 to 32.4

when the sample was exposed to CO. On the contrary, the doping of PANI by 10% of CuI,

ε∆ decreases when the sample was exposed to CO, from 17.2 to 14.6. Moreover, doping the

PANI with 10% CuI and 5% I2 , ε∆ increases when the sample was exposed to CO from

33.8 to 37.2. This can be interpreted as follows: in conducting polymers, there are no

permanent dipoles after exposure to CO in C2 and C7 samples. However, there is strong

charge (Polyron) trapping, and its localized (short-range) motion under the application of an

external field serves as an effective electric dipole, after exposure to CO, the sample has the

effect of mobilizing the polymer chains, reducing pinning and thereby leading to a greater

number of charges participating in the relaxation process.

Figure (4.12): a) 'ε vs. frequency, b) ''ε vs. frequency and c) ''ε vs. 'ε before and after


(a)

(b) (c)

75





(a)

(b) (c)

(a)

(b) (c)

76



On the other hand, the electric modulus can explain the dispersion of *ε with the frequency

without any “molecular” polarization phenomena. Therefore, to observe the relaxation

phenomenon in pure and doped PANI, the imaginary component of electric modulus M'' will

be presented for selected samples. Figures (4.16), (4.17) and (4.19) represent M'' as a

function of frequency before and after exposure to CO for C1, C2, and C7 samples, well

defined broad relaxation peaks were observed in the plot with a shift to higher frequencies

after exposure to CO. However, when the sample was exposed to CO the time scale of the

transition from long-range mobility will decrease and conductivity relaxation time will be

more defined. In addition, it is observed that by increasing Iodine concentration two

relaxation time will appeared in the frequency range as shown in Figure (4.19) for C7

sample, this indicates that Iodine has two preferable locations in the polymer. The first is

(a)

(b) (c)

77

loosely bound to the polymer while the second one is bounded relatively stronger than the

first one. This feature was observed in XRD data shown in Figure (4.3).

Figure (4.16): M'' vs. frequency before and after exposure to CO for C1 sample.


78



4.6) Temperature Dependence:

The measurements were carried out on pure and doped PANI at different temperatures as

shown in Figures (4.20), (4.21), (4.22), (4.23) and (4.24) for C1, C2, C3 and C4 samples

respectively. Figure (4.20-a) shows the frequency dependence (Z`) at different temperatures

for C1 sample. It is observed that Z' decreased in the range of frequency less than 1000 Hz

with increasing temperatures so the conductivity increased, while at higher frequencies Z'

increased with increasing temperatures indicating that the insulator to metal (I-M) transition

79

took place at higher frequencies. In addition, no relaxation peaks were observed in the plot of

Z`` versus frequency. The plot of Z` versus Z`` shows a part of semi-circle at lower

temperature while at higher temperatures no semi-circles were observed. When PANI was

doped by 10% CuI and by 1% I2 + 10% CuI, the general features of the impedance

spectroscopy were similar to that observed for undoped PANI (C1 sample) as shown in

Figure (4.21), (4.22) and (4.23) respectively, for C2, C3 and C4 samples.

Figure (4.20): a) Z' vs. frequency, b) Z'' vs. frequency and c) Z' vs. Z'' at different

temperatures for C1 sample.

(a)

(b) (c)

80





(a)

(b) (c)

(a)

(b) (c)

81



The frequency dependence of 'ε at different temperatures for C1, C2, C3 and C4 samples are

shown in Figures (4.24 -a), (4.25 -a), (4.26 -a) and (4.27 -a) respectively. It was found that as

the temperature increased the dielectric permittivity increased, for undoped PANI, this

feature is the same for all samples. Pasarras et al.,(2002), reported that as temperature

increased the dielectric permittivity increased, this is due to the increase in mobility of

effective electric dipoles. From Figures (4.24 -b), (4.25 -b),

(4.26 -b) and (4.27-b), which represent the frequency dependence of dielectric loss ''ε at

different temperatures for C1, C2, C3 and C4 samples respectively, no well-defined

relaxation peaks were observed with increasing in ''ε intensity as temperature increased.

The dispersion of ''ε indicates the presence of relaxation times distribution of conduction.

However, Cole-Cole plot of ( ''ε versus 'ε ) at different temperatures as shown in Figures

(a)

(b) (c)

82

(4.24 -c), (4.25 -c), (4.26 -c) and (4.27 -c). ε∆ increased with increasing temperature for C1,

C2 and C4 sample. If the results were represented by the plot of imaginary component of

electric modulus at different temperatures as shown in Figures (4.28), (4.29), (4.30) and

(4.31) for C1, C2, C3 and C4 respectively. It is clear that a well-defined relaxation peak was

observed in the plot of M`` versus frequency. For undoped PANI (C1 sample), there was an

increase in the intensity of the relaxation peaks with increasing temperature. This can be

interpreted as charge hopping among available localized sites. On the other hand, it is also

observed that the relaxation peak moves to higher frequency as the temperature increased.

However, when the temperature increases the time scale of the transition from long-range

mobility will decrease and conductivity relaxation time will be more defined. This result

implies that dipole motion or charge carriers diffusion becomes more active as the thermal

energy increased.

83

Figure (4.24): a) 'ε vs. frequency, b) ''ε vs. frequency and c) ''ε vs. 'ε at different




(a)

(b) (c)

(a)

(b) (c)

84





(a)

(b) (c)

(a)

(b) (c)

85

Figure (4.28): M'' vs. frequency at different temperatures for C1 sample.



86


Figure (4.32) shows the dependence of relaxation time based on Arrhenius relation which is

written as τ = τ0 exp -∆E/KB T where is the relaxation time and ∆E is the activation energy.

The relaxation time can be approximately given by the reciprocal of the frequency when the

loss peak is centered (τ = 1 / 2πf). The plot of ln τ versus 1/T yields straight lines for C1 ,C2,

C3 and C4 samples with an activation energy , 0.34, 0.37, 0.43 and 0.41 eV/particle for C1

,C2, C3 and C4 respectively implies that the characteristic activation energy slightly changed

by changing doping level.

Figure (4.32): Plot of τln vs. 1/T for C1, C2, C3 and C4 samples.

87

4.7) Conclusions:

The bulk conductivity and dielectric strength increased after exposure to CO for

undoped and doped PANI with I2 and I2 + CuI. It implies that it can be used as toxic gas

sensor. Moreover, the bulk conductivity after exposure to CO was interpreted in terms of

hopping mechanism, where the hopping between localized states increased after exposure to

CO for undoped and doped PANI with I2 and I2 + CuI, and by increasing Iodine

concentration. Furthermore, increasing Iodine concentration in the samples increases the bulk

conductivity after exposure to CO. Models consist of Resistance (R) and Constant Phase

Element (CPE) were proposed for impedance for undoped and doped Polyaniline.

Conductivity relaxation time decreased after exposure to CO.

The frequency dependence of dielectric permittivity was interpreted in terms of

effective electric dipoles, where for doped PANI increased with increasing temperature. The

activation energy of the system changed slightly by changing doping level.

88

4.8) Recommendations for future research:

• In order to study the phase changes associated with doped PANI with I2 DSC and

TGA are recommended techniques for such studies.

• AC Measurements can be performed on PANI samples doped with different I2

concentrations which is recommended to be more than 5% in order to evaluate the

best response of doped PANI to CO gas.

• Measurement of conductivity on the performance of doped PANI after storing it in air

for relatively long time in order to study the humidity of conductivity.

• More work is needed to study the dependence of doped PANI on ambient conditions.

89

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97

خالصة

و )يوديد النحاس)(I(الخصائص الكهربائية للبولي أنيلين المطعم بأمالح النحاس

استخدامه آمجس غازي

اعداد

طارق محمد علقم

مشرف ال

الدآتور سعدي عبد الجواد األستاذ

المشرف المشارك

الدآتور عوني حالق األستاذ

من اليود و يوديد مختلفة بتراآيز المطعمةوأنيلين لعينات البولي ةالطيفي ائيةالكهرب ةوقالمعا تم دراسة

عند درجة حرارة الغرفة و عند أنجزت التجارب .الكربون أآسيد أول إلى هابعد تعريضالنحاس قبل و

هرتز إلى 100منالترددات من على مدى نطاق سليسيوس 650إلى 250حرارة مختارة بين درجات

ائية و الخسارة في قيم دالة العزل الكهرب النسبية تم تحديد قيم دالة العزل الكهربائية و لقد.آيلو هرتز 10

. يةالكهربائ المعاوقة لية الكهربائية باستخدام تجاربيمعامل التوصيل الكهربائي و الموص و النسبية

الطور اقترحت لتمثل المعاوقة الكهربائية لعينات البولي أنيلين وعنصر ثابت من مقاومةمكونة نماذج

.لبولي أنيلين المطعماو غير المطعمة

98

ألول أآسيد الكربون تفسر على أنها تقنية القفز بين الحاالت ضيعربعد الت الموصيلية الكهربائية

ازدادت للعيناتشدة دالة العزل الكهربائية و الموصيلية الكهربائية أنوتبين النتائج . للتعاونالمتمرآزة

يمكن ةموصلالهذا النوع من البوليمرات أن وهذا يدل ضمنا الكربون ، أآسيد ألولعندما تعرضت

. السامةغازات لل آمجس هاستخدام

، حيث ائيةبالكهر األقطابثنائيات يفسر من خالل اعتماد دالة العزل الكهربائية النسبية على التردد

التي قدرت من اعتماد وقت االسترخاء للنظم الطاقة المفعلة . تزداد هذه الدالة بزيادة درجة الحرارة

.التطعيم في العينةتغيير مستوى بطفيف كل ت بشتغيير الطاقة المفعلة . الحرارةدرجة على

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