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UNIVERSITI TEKNIKAL MALAYSIA MELAKA OPTIMIZATION OF MIXING PARAMETERS TO PRODUCE PP/ENR BLEND VIA RESPONSE SURFACE METHODOLOGY This report submitted in accordance with requirement of the Universiti Teknikal Malaysia Melaka (UTeM) for the Bachelor Degree of Manufacturing Engineering (Engineering Material) by FAISAL FARIS BIN RAHIM B050910134 870116565273 FACULTY OF MANUFACTURING ENGINEERING 2012

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UNIVERSITI TEKNIKAL MALAYSIA MELAKA

OPTIMIZATION OF MIXING PARAMETERS TO PRODUCE

PP/ENR BLEND VIA RESPONSE SURFACE METHODOLOGY

This report submitted in accordance with requirement of the Universiti Teknikal

Malaysia Melaka (UTeM) for the Bachelor Degree of Manufacturing Engineering

(Engineering Material)

by

FAISAL FARIS BIN RAHIM

B050910134

870116565273

FACULTY OF MANUFACTURING ENGINEERING

2012

UNIVERSITI TEKNIKAL MALAYSIA MELAKA

BORANG PENGESAHAN STATUS LAPORAN PROJEK SARJANA MUDA

TAJUK: Optimization of mixing parameters to produce PP/ENR blend via response surface methodology.

SESI PENGAJIAN: 2011/12 Semester 2 Saya FAISAL FARIS BIN RAHIM mengaku membenarkan Laporan PSM ini disimpan di Perpustakaan Universiti Teknikal Malaysia Melaka (UTeM) dengan syarat-syarat kegunaan seperti berikut:

1. Laporan PSM adalah hak milik Universiti Teknikal Malaysia Melaka dan penulis. 2. Perpustakaan Universiti Teknikal Malaysia Melaka dibenarkan membuat salinan

untuk tujuan pengajian sahaja dengan izin penulis. 3. Perpustakaan dibenarkan membuat salinan laporan PSM ini sebagai bahan

pertukaran antara institusi pengajian tinggi.

4. **Sila tandakan (√)

SULIT

TERHAD

TIDAK TERHAD

(Mengandungi maklumat yang berdarjah keselamatan atau kepentingan Malaysia yang termaktub di dalam

AKTA RAHSIA RASMI 1972)

(Mengandungi maklumat TERHAD yang telah ditentukan

oleh organisasi/badan di mana penyelidikan dijalankan)

Alamat Tetap:

No.100 Jalan TC 1/5

Taman Cemerlang, Gombak

53100 Kuala Lumpur

Tarikh: 1/06/2012

Disahkan oleh:

PENYELIA PSM

Tarikh: _______________________

** Jika Laporan PSM ini SULIT atau TERHAD, sila lampirkan surat daripada pihak berkuasa/organisasi berkenaan dengan menyatakan sekali sebab dan tempoh laporan PSM ini perlu dikelaskan sebagai

SULIT atau TERHAD.

I hereby, declared this report entitled “Optimizing of mixing parameters to

produce PP/ENR blend via response surface methodology” is the results of my

own research except as cited in references.

Signature : ………………………………………….

Author’s Name : Faisal Faris Bin Rahim

Date : 1st June 2012

DECLARATION

This report is submitted to the Faculty of Manufacturing Engineering of

Universiti Teknikal Malaysia Melaka (UTeM) as a partial fulfillment of the

requirements for the degree of Bachelor of Manufacturing Engineering

(Engineering Material). The member of the supervisory committee is as

follow:

………………………………

(Official Stamp of Principal Supervisor)

APPROVAL

i

ABSTRAK

Termoplastik elastomer semakin mendapat perhatian kerana ciri-cirinya yang

menyerupai getah tervulkan dan mudah difabikat seperti termoplastik. Kajian ini

merupakan satu usaha untuk meneroka potensi polipropilena (PP) apabila

digabungkan dengan getah asli terepoksida ENR. Polipropilena (PP) dan getah asli

terepoksida(ENR) disediakan melalui kaedah penyebatian lebur menggunakan

pencampur dalaman dan pematangan sulfur. Parameter pencampur seperti nisbah,

suhu percampuran, masa percampuran dan kelajuan pemutar dioptimumkan dengan

kaedah metodologi permukaan sambutan dengan bantuan perisian Expert 6.0.10.

Suhu pencampuran dan terma interaksi telah dikenalpasti sebagai faktor tidak

signifikan dengan nilai P lebih daripada 0.0500. Beberapa ujian dan analisis

termasuk ujian ketumpatan, indeks kecairan aliran, ujian tegangan, ujian kekerasan,

kemikroskopan elektron imbasan (SEM) dan pemeteran kalori pengimbasan

kebezaan (DSC) dijalankan untuk mencirikan sifat-sifat PP/ENR. ENR berupaya

meningkatkan keliatan dan kebolehlenturan polipropilena. Nilai kiraan optimum

untuk pembolehubah yang dikaji (nisbah, suhu, kelajuan pemutar dan masa

pencampuran) untuk memaksimumkan pemanjangan sebelum putus telah

dikenalpasti sebagai ENR 16.33%, suhu 170oC, kelajuan pemutar 50rpm dan masa

pencampuran 6 minit dengan pemanjangan yang dijangkakan sebelum terputus pada

11.7171%, berbanding 9% PP tulen.

ii

ABSTRACT

Thermoplastic elastomers have become important because they have combination

properties of vulcanized rubbers and can be rapidly fabricated as thermoplastic. This

research is an effort to explore the potential of polypropylene (PP) when

incorporated with ENR. Polypropylene (PP) and epoxidized rubber (ENR) were

prepared by melt blending with internal mixer and sulfur curing. Mixer parameter

such as the ratio, mixing temperature, mixing time, and rotor speed were optimized

with response surface methodology with the assistance of Design Expert 6.0.10

software. The mixing temperature and its interaction terms were identified as

insignificant factors with a P value greater than 0.0500. Testing and analysis

including density test, melt flow index (MFI), tensile test, hardness test, impact test,

scanning electron microscopy (SEM) and differential scanning calorimetry (DSC)

were performed to characterize the properties of PP/ENR. The ENR is proven to

increase toughness and flexibility of polypropylene. The optimum calculated values

of the tested variables (ratio, temperature, rotor speed and mixing time) for the

maximum elongation to break was found to be at ENR of 16.33%, temperature of

170oC, rotor speed of 50 rpm and a mixing time of 6 min with a predicted elongation

to break of 11.7171%, compared to 9% of pure PP.

iii

ACKNOWLEDGEMENT

I would like to offer my unreserved gratitude and praises to Almighty Allah for His

generous blessing and the undying strength bestowed upon me during the course of

this research.

Special thanks to my supervisor, Dr. Noraiham Mohamad who guide, assist and

advice me all the way through this project.

Thanks to all my friends, who always give me the moral support and been there

whenever I am in need.

iv

TABLE OF CONTENT

Abstrak i

Abstract ii

Acknowledgement iii

Table of Content iv

List of Tables viii

List of Figures xi

List of Abbreviations xiv

List of Symbols xv

1. INTRODUCTION 1

1.1 Background 1

1.2 Problem Statement 2

1.3 Objective 3

1.4 Scope 3

1.5 Chapter Overview 3

2. LITERATURE REVIEW 5

2.1 Polymer Blends 5

2.1.1 Thermoset Elastomer (TSE) 7

2.1.2 Thermoplastic Elastomer (TPE) 8

2.1.2.1 Thermoplastic 9

2.1.2.2 Elastomer 10

2.1.2.3 Current Development of Thermoplastic Elastomer 12

2.2 Compounding Process 14

2.2.1 Melt Blending 15

2.2.1.1 Internal Mixer 15

2.2.1.2 Twin-Screw Extruder 16

2.2.1.3 Two Roll Mill 17

2.2.1.4 Injection Molding 18

v

2.2.2 Compressing Molding 19

2.3 Vulcanization/Curing Process 20

2.3.1 Sulfur Vulcanization 20

2.3.2 Peroxide Vulcanization 23

2.3.3 Mixed Vulcanization 24

2.4 Fabrication 24

2.4.1 Hot Press 24

2.4.2 Cold Press 25

2.4.3 Isostatic Press 25

2.5 Testing and Analysis 26

2.5.1 Physical Test 26

2.5.1.1 Density Test 26

2.5.1.2 Melt Flow Index (MFI) 26

2.5.2 Mechanical Test 27

2.5.2.1 Tensile Test 27

2.5.2.2 Izod Impact Test 28

2.5.2.3 Hardness Test 29

2.5.3 Morphological Study 31

2.5.3.1 Scanning Electron Microscopy (SEM) 31

2.5.4 Thermal Analysis 32

2.5.4.1 Differential Scanning Calorimetry 32

2.6 Optimization 32

2.6.1 Response Surface Methodology (SEM) 33

3. METHODOLOGY 38

3.1 Introduction 38

3.2 Raw Material 40

3.3 Characterization of Raw Material 40

3.3.1 Polypropylene 40

3.3.2 Epoxidized Natural Rubber 41

3.3.3 Sulfur 42

vi

3.4 Optimization of Internal Mixer Parameter using Response Surface

Methodology (RSM) 44

3.4.1 Design of Experiment 44

3.4.1.1 Screening Factor 44

3.5 Blending of PP/ENR Blends in Internal Mixer 46

3.6 Pelletizing 48

3.7 Hot Pressing 50

3.8 Testing and Analysis 52

3.8.1 Physical Test 52

3.8.1.1 Density Test 52

3.8.1.2 Melt Flow Index (MFI) 53

3.8.2 Mechanical Test 55

3.8.2.1 Tensile Test 55

3.8.2.2 Hardness Test 56

3.8.2.3 Izod Impact Test 58

3.8.3 Morphological Study 59

3.8.3.1 Scanning Electron Microscopy (SEM) 59

3.8.4 Thermal Analysis 60

3.8.4.1 Differential Scanning Calorimetry (DSC) 60

4. RESULT AND DISCUSSION 61

4.1 Introduction 61

4.2 Raw Material Characterization 62

4.2.1 Density 62

4.2.2 Melt Flow Index 62

4.3 Optimization of Physical and Mechanical Properties 63

4.3.1 Density Analysis 63

4.3.2 Hardness 70

4.3.3 Melt Flow Index 76

4.3.4 Impact Strength 82

4.3.5 Tensile Properties 89

4.3.5.1 Tensile Strength 90

4.3.5.2 Elongation to Break 95

vii

4.3.5.3 Young Modulus 101

4.4 Analysis 107

4.4.1 Scanning Electron Microscopy (SEM) 107

4.4.2 Differential Scanning Calorimetry (DSC) 110

4.5 Determination of the optimum formulation of PP/ENR using the

Response Surface Methodology (RSM) 111

5. CONCLUSION AND RECOMMENDATION 114

5.1 Conclusion 114

5.2 Recommendation 115

REFERENCES 116

APPENDIX

viii

LIST OF TABLES

Table 2.1: Basic recipe for the sulfur vulcanization system 21

Table 2.2: Sulfur vulcanization system 23

Table 2.3: Compounding formulation for ENR 23

Table 2.4: 23 Factorial Design Matrix Used for the Screening Factors 35

Table 2.5: Levels of Variables Chosen for Trial 36

Table 2.6: Full Factorial Central Composite Design for the Optimization

of Machine Parameters in the ENRAN Composite Preparation 36

Table 2.7: Levels of Variables Chosen for Trial in the

Optimization Experiments 36

Table 3.1 General properties of polypropylene 40

Table 3.2 Thermal properties of polypropylene 41

Table 3.3: Properties of sulfur 43

Table 3.4: Properties of zinc oxide 43

Table 3.5: Properties of stearic acid 44

Table 3.6: Combination of parameters internal mixer machine for 24 factorial

designs for screening factor 45

Table 3.7: Level of variables for the screening factor 45

Table 3.8: Composition of ENR vulcanization 46

Table 3.9: Design matrix of process parameter PP/ENR blends 47

Table 3.10: Level of variables 48

Table 3.11: The standard test conditions sample weight and

testing time for materials. 55

Table 4.1: Density Average of PP and ENR 62

Table 4.2: Melt Flow Rate of PP and ENR 63

Table 4.3: Density Average with Mixing Parameters and Ratios 64

Table 4.4: ANOVA for the Selected Factorial Models 66

Table 4.5: Observed Responses and Predicted Values 67

Table 4.6: Regression Coefficients and P Values as

ix

Calculated from the Models 68

Table 4.7: Hardness with Mixing Parameters and Ratios 70

Table 4.8: ANOVA for the Selected Factorial Models 72

Table 4.9: Observed Responses and Predicted Values 73

Table 4.10: Regression Coefficients and P Values as

Calculated from the Models 74

Table 4.11: Melt flow rate with Mixing Parameters and Ratios 77

Table 4.12: ANOVA for the Selected Factorial Models 79

Table 4.13: Observed Responses and Predicted Values 80

Table 4.14: Regression Coefficients and P Values as

Calculated from the Models 80

Table 4.15: Impact strength with Mixing Parameters and Ratios 83

Table 4.16: ANOVA for the Selected Factorial Models 85

Table 4.17: Observed Responses and Predicted Values 86

Table 4.18: Regression Coefficients and P Values as

Calculated from the Models 87

Table 4.19: Tensile strength with Mixing Parameters and Ratios 90

Table 4.20: ANOVA for the Selected Factorial Models 91

Table 4.21: Observed Responses and Predicted Values 92

Table 4.22: Regression Coefficients and P Values as

Calculated from the Models 92

Table 4.23: Elongation to break with Mixing Parameters and Ratios 96

Table 4.24: ANOVA for the Selected Factorial Models 98

Table 4.25: Observed Responses and Predicted Values 99

Table 4.26: Regression Coefficients and P Values as

Calculated from the Models 99

Table 4.27: Young Modulus with Mixing Parameters and Ratios 102

Table 4.28: ANOVA for the Selected Factorial Models 104

Table 4.29: Observed Responses and Predicted Values 105

Table 4.30: Regression Coefficients and P Values as

Calculated from the Models 105

Table 4.31: Glass Transition Temperature of samples 110

Table 4.32: Properties and characteristics processing of the need for

x

optimizing the formulation PP/ENR 111

Table 4.33: Optimum formulation with the processing characteristics and

properties generated for PP / ENR based on the degree of

desirability 112

xi

LIST OF FIGURES

Figure 2.1: Structure of Polypropylene 10

Figure 2.2: Structure of cis-Polyisoprene 11

Figure 2.3: Structure of Epoxidized Natural Rubber (ENR) 12

Figure 2.4: Schematic representation of the two-roll milling method 18

Figure 2.5: Schematic representation of the compressing molding 19

Figure 2.6: Schematic illustration of injection molding 20

Figure 2.7: The mechanism of peroxide vulcanization 24

Figure 2.8: Cold Compression Molding 25

Figure 2.9: Schematic illustration of how a tensile load produces an elongation

and positive linear strain 28

Figure 2.10: SEM micrographs of dynamically cured 60/40 ENR-30/PP

TPVs with sulphur system 31

Figure 3.1: Flow chart of the research project 39

Figure 3.2: Polypropylene 41

Figure 3.3: Epoxidized Natural Rubber 42

Figure 3.4: Stearic Acid (a), Zinc Oxide (b) and Sulfur (c) 43

Figure 3.5: ENR vulcanization; scale: 20cent Malaysia Diameter 23mm 46

Figure 3.6: HAAKE RHEOMIX OS internal mixer machine 48

Figure 3.7: PP/ENR using crusher machine 49

Figure 3.8: Crusher machine 49

Figure 3.9: Pellet compound is placed in the mold. 50

Figure 3.10: Gotech (GT 7014 – A) hot press machine 51

Figure 3.11: Gotech (GT 7016 –H) Specimen cutter machine 51

Figure 3.12: Electronic densimeter. 53

Figure 3.13: Melt Flow Indexer MH-525 equipment 54

Figure 3.14: Autograph AG-IC floor universal testing machine. 56

Figure 3.15: Dog bone type specimen size for ASTM D-638 Type 1 56

Figure 3.16: Shore D Durometer 57

Figure 3.17: Izod impact test equipment 58

xii

Figure 3.18: Zeiss EVO-50 ESEM machine 59

Figure 3.19: DSC Perkin Elmer DSC-7 60

Figure 4.1: Half Normal Plot for Density 65

Figure 4.2: Effects of the ENR and temperature on the density

of the PP/ENR blend 68

Figure 4.3: Density of all samples 69

Figure 4.4: Half Normal Plot for Hardness 71

Figure 4.5: Effects of the ENR and temperature on the hardness

of the PP/ENR blend 74

Figure 4.6: Hardness of all samples 75

Figure 4.7: Half Normal Plot for Melt Flow Rate 78

Figure 4.8: Effects of the ENR and temperature on the melt flow rate

of the PP/ENR blend 81

Figure 4.9: Melt flow rate of all samples 82

Figure 4.10: Half Normal Plot for Impact Strength 84

Figure 4.11: Effects of the ENR and temperature on the impact strength

of the PP/ENR blend 87

Figure 4.12: Impact strength of all samples 88

Figure 4.13: (a) Dogbone for PP, (b) Dogbone for PP/ENR 70/30 and

(c) PP/ENR 40/60 89

Figure 4.14: Half Normal Plot for Tensile Strength 91

Figure 4.15: Effects of the ENR and temperature on the tensile strength

of the PP/ENR blend 94

Figure 4.16: Tensile strength of all samples 94

Figure 4.17: Half Normal Plot for Elongation to Break 97

Figure 4.18: Effects of the ENR and temperature on the elongation to break

of the PP/ENR blend 100

Figure 4.19: Elongation to break of all samples 100

Figure 4.20: Half Normal Plot for Hardness 103

Figure 4.21: Effects of the ENR and temperature on the Young modulus

of the PP/ENR blend 106

xiii

Figure 4.22: Young modulus of all samples 106

Figure 4.23: (a) Scanning electron micrograph of unfilled PP at magnification

of 500x. (b) Scanning electron micrograph of PP/ENR 70/30

at magnification of 500x. (c) Scanning electron micrograph

of PP/ENR 40/60 at magnification of 500x. 108

Figure 4.24: (a) Scanning electron micrograph of unfilled PP at magnification

of 5000x. (b) Scanning electron micrograph of PP/ENR 70/30

at magnification of 5000x. (c) Scanning electron micrograph

of PP/ENR 40/60 at magnification of 5000x. 109

Figure 4.25: Fractional degrees of desire fulfilled the selection formula

for PP / ENR 113

xiv

LIST OF ABBREVIATIONS

ASTM - American Standard Test Method

ENR - epoxidized natural rubber

TPNR - thermoplastic natural rubber

NR - natural rubber

NBR - nitrile butadiene rubber

PP - polypropylene

RSM - response surface methodology

SEM - scanning electron microscopy

DSC - differential scanning calorimetry

FTIR - fourier transform infrared

EPR - ethylene propylene rubber

TPO - thermoplastic polyolefin

TPV - thermoplastic vulcanizate

TPE - thermoplastic elastomer

TSE - thermoset elastomer

IR - synthetic isoprene rubber

BR - polybutadiene rubber

SBR - styrene butadiene rubber

IIR - butyl rubber

CIIR - chloro butyl rubber

BIIR - bromo butyl rubber

DOE - design of experimental

rpm - rotation per minute

xv

LIST OF SYMBOLS

oC - Celsius

M/S - meter per second

% - percentage

kW - kilo watt

min - minute

kg - kilogram

mm - millimeter

μm - micrometer

s - second

nm - nanometer

g - gram

Hz - hertz

1

1.1 Background

Polyolefins are the largest group of thermoplastics, the two most important and

common types of polyolefins are polyethylene and polypropylene. They are very

popular due to their low cost and wide range of applications. Polyolefins are usually

processed by extrusion, injection molding, blow molding, and rotational molding

methods.

Polyolefin elastomers (POEs) are a relatively new class of polymers that emerged

with recent advances in metallocene polymerisation catalysts. Representing one of

the fastest growing synthetic polymers, POE’s can be substituted for a number of

generic polymers including ethylene propylene rubbers (EPR or EPDM), ethylene

vinyl acetate (EVA), styrene-block copolymers (SBCs), and poly vinyl chloride

(PVC). Polyolefin elastomers are compatible with most olefinic materials, are an

excellent impact modifier for plastics, and offer unique performance capabilities for

compounded products.

Thermoplastic elastomers based on natural rubber and thermoplastic blends are

classified as thermoplastic natural rubber (TPNR) blends. There are two types of

thermoplastic natural rubber. Blending of NR with thermoplastic (i.e., polyolefins)

to get co-continuous phase morphology is technologically classified as thermoplastic

polyolefin (TPO). The other class is known as thermoplastic vulcanizate (TPV),

which is prepared by blending NR with polyolefins and involve vulcanization

process. In type two, the rubber phase is vulcanized during the mixing process at

INTRODUCTION

CHAPTER 1

2

high temperature, and the process is known as dynamic vulcanization. Dynamic

vulcanization of epoxidized natural rubber (ENR) and polypropylene (PP) are also

performed by using either a sulfur based system or peroxide. The sulfur cured

system showed superior mechanical properties in term of tensile strength, elongation

at break and tension set compared to the peroxide system due to the polypropylene

degradation during dynamic vulcanization.

1.2 Problem Statement

Polypropylene (PP) is well-known of its outstanding dielectric properties under high

voltage and high frequency condition up to 30 kHz (Khachen et al., 1992). Due to

that, it is a suitable material for electrical insulator whether in interior or exterior

cables. However, PP is less flexible when the thickness of the cable is increases. The

epoxidized natural rubber (ENR) is a potential candidate to increase the flexibility of

polypropylene. Malaysia is known as the world’s major natural rubber producer.

ENR being a derivative of natural rubber is more readily available, and it has unique

properties offering high strength due to their ability to undergo strain crystallization,

along with increased glass transition temperatures and solubility parameter. These

properties are reflected in vulcanizates with increased oil resistance, enhanced

adhesive properties, high degree of damping and reduce gas permeation (Gelling,

1991). Response surface methodology (RSM) is reported to be an effective tool for

optimizing a process, as highlighted by various workers (Yadav et al., 2007). RSM

could save cost and time by reducing number of experiments required. The

application of RSM to design optimization is aimed at reducing the cost of

expensive analysis methods and their associated numerical noise. Originally, RSM

was developed to model experimental responses (Box and Draper, 1987), and then

migrated into the modeling of numerical experiments.

3

1.3 Objective

The main objectives on this research are:

i. To produce PP/ENR blend via melt blending using internal mixer.

ii. To determine the optimum formula and mixer parameter using response

surface methodology

iii. To characterize the properties of PP/ENR blend through testing and analysis.

1.4 Scope

This research is focusing on optimization of formulation and mixer parameter to

produce PP/ENR blend. Firstly, the experiment was designed using RSM. Then,

samples were prepared in different combination of process parameters in an internal

mixer followed by various physical and mechanical testing. Some analysis such as

thermal and morphology were performed to support the data.

1.5 Chapter Overview

There are five chapters in this report;

i. Chapter 1 is the introduction of the research. That consists of research

background, a problem statement, and objectives of the project, scope and

chapter overview.

ii. Chapter 2 is the literature review and covers the fundamental of polymer

blends, thermoplastic elastomer and also a general overview of the current

development of polymer blends.

4

iii. Chapter 3 is the methodology of this research, response surface methodology

and it discuss the raw material specification, equipment and experimental

procedures used in this study.

iv. Chapter 4 is the results and discussions of laboratory and field research work

described in this study.

v. Chapter 5 is formulate procurement review and list of potential research and

also proposed future work.

5

2.1 Polymer Blends

Basic principles of polymer blends are either homogeneous or heterogeneous (He et

al., 2004). In homogeneous blends, the final properties are often an arithmetic

average of the properties of the blend components. In heterogeneous blends, the

properties of all blend components are present. A deficiency in the properties of one

component can be camouflaged to a certain extent by strengths of the others (He et

al., 2004). Polymer blending is a convenient route for the development of new

polymeric materials, able to yield materials with property profiles superior to those

of the individual components (He et al., 2004). Blending of polymers is an effective

way to obtain materials with specific properties. Most polymers are immiscible,

therefore, blending usually leads to heterogeneous morphologies (Willemse et al.,

1997). Most polymer pairs are immiscible, and therefore, their blends are not formed

spontaneously. Moreover, the phase structure of polymer blends is not equilibrium

and depends on the process of their preparation. Five different methods are used for

the preparation of polymer blends are melt mixing, solution blending, latex mixing,

partial block or graft copolymerization, and preparation of interpenetrating polymer

networks (Anonymous, 2005).

Polymer blend constitute of 36 wt% of the total polymer consumption, and their

pertinence continues to increase (Utracki, 2002). About 65% of polymer alloy and

blend are produced by polymer manufacturer, 25% by compounding companies and

the remaining 10% by the transformer (Utracki, 2002).

LITERATURE REVIEW

CHAPTER 2