Yüksek Dönüşüm Oranında Gerçekleştirilen Kopolimerizasyonlarda Reaktiflik Oranlarının Belirlenmesi

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ISTANBUL TECHNICAL UNIVERSITY  GRADUATE SCHOOL OF SCIENCE ENGINEERING AND TECHNOLOGY

M.Sc. THESIS

JUNE 2012

DETERMINATION OF THE REACTIVITY RATIOS IN

COPOLYMERIZATIONS CARRIED OUT TO HIGH CONVERSIONS

Mustafa Gökhun YAYLA

Department of Physics Engineering Physics Engineering Programme

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JUNE 2012

ISTANBUL TECHNICAL UNIVERSITY  GRADUATE SCHOOL OF SCIENCE ENGINEERING AND TECHNOLOGY

COPOLYMERIZATIONS CARRIED OUT TO HIGH CONVERSIONS

M.Sc. THESIS Mustafa Gökhun YAYLA

(509091116)

Department of Physics Engineering Physics Engineering Programme

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HAZĠRAN 2012

ĠSTANBUL TEKNĠK ÜNĠVERSĠTESĠ  FEN BĠLĠMLERĠ ENSTĠTÜSÜ

YÜKSEK DÖNÜġÜM ORANINDA GERÇEKLEġTĠRĠLEN KOPOLĠMERĠZASYONLARDA REAKTĠFLĠK ORANLARININ

BELĠRLENMESĠ

YÜKSEK LĠSANS TEZĠ Mustafa Gökhun YAYLA

(509091116)

Fizik Mühendisliği Anabilim Dalı Fizik Mühendisliği Programı

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Thesis Advisor : Prof. Dr. Ahmet Togo GĠZ ... Ġstanbul Technical University

Jury Members : Prof. Dr. Nazmi POSTACIOĞLU ... Ġstanbul Technical University

Doç. Dr. Gülcemal YILDIZ ... Ġstanbul Technical University

Mustafa Gökhun YAYLA, a M.Sc. student of ITU Graduate School of Science Engineering and Technology student ID 509091116, successfully defended the thesis entitled “DETERMINATION OF THE REACTIVITY RATIOS IN COPOYLMERIZATIONS CARRIED OUT TO HIGH CONVERSIONS”, which he prepared after fulfilling the requirements specified in the associated legislations, before the jury whose signatures are below.

Date of Submission : 04 May 2012 Date of Defense : 05 June 2012

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ix FOREWORD

In this section; I would like to thank those who helped or supported me by either physical or psychological.

Because of their understanding, helpful behaviours and having confidence to people especially me; I really would like to thank my advisor, Prof. Dr. Ahmet Togo GĠZ, and his wife Prof. Dr. Hatice Hüceste ÇATALGĠL GĠZ.

Because their recommendations helped me in order to participate to Istanbul Technical University, I would like to thank to my teachers, Prof. Dr. Ahmet BULUT, Prof. Dr. Recep TAPRAMAZ and Doç. Dr. Hümeyra PAġAOĞLU who were at Ondokuzmayıs University when I was a bachelor student.

I would like to thank to my friends who are helped me while I am studying together with them.

There is a girl in my life who have changed many things positively since 2008. I would like to thank to my beautiful fiance NeĢe CERĠT due to her all supportings and because she is in my life.

I think any success that I had in any field of my life thanks to my great family. Here I would like to thank to my father Ahmet YAYLA, my mother Zahide YAYLA and my brother Alper YAYLA due to their all supportings.

June 2012 Mustafa Gökhun YAYLA

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xi TABLE OF CONTENTS Page FOREWORD ... ix TABLE OF CONTENTS ... xi ABBREVIATIONS ... xiii LIST OF TABLES ... xv

LIST OF FIGURES ... xvii

SUMMARY ... xix ÖZET ... xxi 1. INTRODUCTION ... 1 1.1 Introduction ... 1 1.2 Backgrounds of Polymerization ... 1 1.2.1 Monomer ... 1 1.2.2 Polymer ... 2

1.2.3 Polymerization and copolymerization ... 3

1.2.4 Conversion ... 4

1.2.5 Copolymer propagation types ... 4

1.2.6 Reactivity ratio ... 4

1.2.7 Random copolymerization ... 5

1.2.8 Alternating copolymerization ... 5

1.2.9 Block copolymerization ... 5

1.2.10 Mayo – Lewis equation ... 6

1.3 Backgrounds of Calculations ... 8

1.3.1 minimisation method ... 8

1.3.2 Runge – Kutta method ... 9

2. METHODS OF CALCULATION ... 11

2.1 Mayo Equation ... 11

2.2 Fineman – Ross Method ... 11

2.3 Kelen – Tudos Method ... 12

2.4 Extended Kelen – Tudos Method ... 12

2.5 Nonlinear Least Squares Method (NLLS)... 14

3. RESULTS ... 15

3.1 Experimental Data ... 15

3.2 Concentration and Conversions for MPMSK-co-St ... 15

3.3 Concentration and Conversions for APMA-co-EMA ... 15

3.4 Concentration and Conversions for CHMA-co-St ... 16

3.5 Calculated Reactivity Ratios for Certain Methods ... 17

3.5.1 Reactivity ratios and graphics for MPMSK-co-St ... 17

3.5.2 Reactivity ratios and graphics for APMA-co-EMA ... 19

3.5.3 Reactivity ratios and graphics for CHMA-co-St ... 21

3.6 Initial and Finish Concentrations of Different Experiments ... 23

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3.6.2 Results for APMA-co-EMA copolymerization... 28

3.6.3 Results for CHMA-co-St copolymerization ... 33

4. CONCLUSIONS AND RECOMMENDATIONS ... 39

4.1 Appraisal of Programming Methods ... 39

4.2 Appraisal of Calculation Methods ... 39

4.3 Appraisal of Experimented Copolymer Compositions ... 39

4.4 Appraisal of Results of Calculations ... 40

REFERENCES ... 41

APPENDICES ... 45

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xiii ABBREVIATIONS

ML : Mayo – Lewis Equation FR : Fineman – Ross Method KT : Kelen – Tudos Method

EKT : Extended Kelen – Tudos Method RC : Radical Copolymerization AC : Alternating Copolymerization BC : Block Copolymerization LS : Least Squares Method

NLLS : Non-linear Least Squares Method CS : Minimsation Method

RK4 : Runge – Kutta Forth Order Method RR : Reactivity Ratio

IC : Initial Concentration FC : Final Concentration

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xv LIST OF TABLES

Page

Table 3.1 : Concentration and Conversion for MPMSK-co-St ... 15

Table 3.2 : Concentration and Conversion for APMA-co-EMA ... 16

Table 3.3 : Concentration and Conversion for CHMA-co-St ... 16

Table 3.4 : Calculated Reactivity Ratios for MSMF-co-St ... 17

Table 3.5 : Calculated Reactivity Ratios for APMA-co-EMA ... 19

Table 3.6 : Calculated Reactivity Ratios for CHMA-co-St ... 22

Table 3.7 : 16% Conversion for Copolymer MPMSK-co-St ... 23

Table 3.12 : 32.9% Conversion for Copolymer APMA-co-EMA ... 28

Table 3.15 : 36% Conversion for Copolymer APMA-co-EMA ... 30

Table 3.18 : 14.4% Conversion for Copolymer CHMA-co-St ... 33

Table 3.19 : 12% Conversion for Copolymer CHMA-co-St ... 33

Table 3.20 : 12% Conversion for Copolymer CHMA-co-St ... 34

Table 4.1 : Calculated Reactivity Ratios for MSMF-co-St ... 39

Table 4.2 : Calculated Reactivity Ratios for APMA-co-EMA ... 40

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xvii LIST OF FIGURES

Page

Figure 1.1 : Random Copolymerization Chain Configuration ... 5

Figure 1.2 : Alternating Copolymerization Chain Configuration ... 5

Figure 1.3 : Block Copolymerization Chain Configuration ... 5

Figure 3.1 : Calculated Reactivities with FR for MPMSK-co-St...18

Figure 3.2 : Calculated Reactivities with KT for MPMSK-co-St ... 18

Figure 3.3 : Calculated Reactivities with EKT for MPMSK-co-St ... 19

Figure 3.4 : Calculated Reactivities with FR for APMA-co-EMA ... 20

Figure 3.5 : Calculated Reactivities with KT for APMA-co-EMA ... 20

Figure 3.6 : Calculated Reactivities with EKT for APMA-co-EMA ... 21

Figure 3.7 : Calculated Reactivities with FR for CHMA-co-St ... 21

Figure 3.8 : Calculated Reactivities with KT for CHMA-co-St ... 22

Figure 3.9 : Calculated Reactivities with EKT for CHMA-co-St ... 23

Figure 3.10 : The Comparison of the Methods on :10 – :90 for 16% Conversion MPMSK-co-St ... 24

Figure 3.15 : The Comparison of the Methods for 16% Conversion MPMSK-co-St ...27

Figure 3.16 : The Contours of Reactivity Ratios for MPMSK-co-St ... 27

Figure 3.17 : The Comparison of the Methods on :10 – :90 for 32.9% Conversion APMA-co-St ... 28

Figure 3.20 : The Comparison of the Methods on :50 – :50 for 36% Conversion APMA-co-St ... 30

Figure 3.23 : The Comparison of the Methods for APMA-co-St ... 32

Figure 3.24 : The Contours of Reactivity Ratio for APMA-co-St ... 32 Figure 3.25 : The Comparison of the Methods on :10 – :90 for 14.4%

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Conversion CHMA-co-St ... 33 Figure 3.26 : The Comparison of the Methods on :25 – :75 for 12%

Conversion CHMA-co-St ... 34 Figure 3.27 : The Comparison of the Methods on :50 – :50 for 10.8%

Conversion CHMA-co-St ... 36 Figure 3.30 : The Comparison of the Methods for CHMA-co-St ... 36 Figure 3.31 : The Contours of Reactivity Ratios for CHMA-co-St ... 37

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COPOLYMERIZATIONS CARRIED OUT TO HIGH CONVERSIONS SUMMARY

Copolymers are formed when more than one monomer is used in polymerization. In statistical copolymerization, the ratio of the rates of entry of the two monomers into a copolymer is given by the Mayo – Lewis equation.

{ }

Here [A] and [B] are the instantaneous concentrations of the two monomers in the feed at any moment. d[A] and d[B] are the incremental concentrations of the tow monomer taken up during a short time interval. Thus the ratio d[A]/d[B] gives the composition of the material polymerized during that interval. The parameters ra and rb, known as the reactivity ratios determine the copolymer composition. Knowledge of these ratios is important for predicting the composition and properties of the copolymer formed.

Various linear and nonlinear methods have been developed to determine these reactivity ratios. Reactions carried out to high conversions cause additional difficulty because the feed composition drifts during the reaction as the more active monomer is depleted faster and this drift must be taken into account.

Here the nonlinear least square technique developed by Sunbul and GIZ et al. for continuously monitored experiments has been adapted to batch experiments carried out to high conversion. The new method is applied to experimental data on Cyclohexene-3-yl Methyl Methacrylate (CHMA) / Styrene(St), 4- Acetylphenyl methacrylate (APMA) / Ethyl Methacrylate (EMA), 4-Methacryloyloxyphenyl-4'-Methoxystyryl Ketone (MPMSK) / Styrene (St) copolymerizations provided by Dr. G. BARIM. The results are compared to the results of two robust linear methods the Kelen-Tudos (KT) and Extended Kelen-Tudos (EKT). While the KT method does not take the composition drift into account the EKT method takes this effect into account. The nonlinear least squares technique based on numerical solution of the Mayo-Lewis equation not only takes the composition drift but also the nonliearity of the equation into account and has superior error handling properties.

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YÜKSEK DÖNÜġÜM ORANINDA GERÇEKLEġTĠRĠLEN KOPOLĠMERĠZASYONLARDA REAKTĠFLĠK ORANLARININ

BELĠRLENMESĠ ÖZET

Monomer, Yunanca‟daki tek anlamına gelen “mono” ve parça, bölüm anlamına gelen “meros” kelimelerinden türetilmiĢ bir kelimedir. Monomerler kimyasal yollarla birbirlerine bağlanabilirler. Bu sürec polimerizasyon olarak bilinir. Polimerizasyon sürecinde aynı tip monomerler bir araya geliyorsa bu süreç sonunda oluĢan ürüne homopolimer, farklı tip monomerler birleĢiyorsa bu süreç sonunda oluĢan ürüne de kopolimer denir.

Ġstatistiksel Kopolimerizasyonda farklı tip monomerlerin kopolimere katılımlarının oranı Mayo – Lewis denklemi ile verilir.

{ }

Bu denklemde ve ile verilen reaktiflik oranları, kopolimer kompozisyonunu belirleyen parametrelerdir. Bu oranların bilinmesi, oluĢan kopolimerin kompozisyonu ve özelliğini öngörmede önemlidir.

Reaktiflik oranlarının belirlenmesi için çeĢitli doğrusal ve doğrusal olmayan metodlar geliĢtirilmiĢtir. Bu metodların bazıları Mayo – Lewis denkleminin doğrusal olmayıĢını hesaba katarken bazıları denklemin bu özelliğini hesaba katmamakta ve belirli dönüĢümler altında denklemi doğrusal bir yapıya dönüĢtürerek analitik olarak çözmeye çalıĢmaktadır. Bazı yöntemler ise Mayo – Lewis denkleminin doğrusal olmamasını hesaba katmamasına rağmen yüksek dönüĢüm oranlarında ortaya çıkacak olan kompozisyon kaymasını da hesaba katmaktadır. Kompozisyon kayması, yüksek dönüĢümlerde gerçekleĢtirilen reaksiyonlarda reaksiyon sırasında daha aktif olan monomerin hızla tükenmesi sonucu oluĢan, kopolimer yapısında meydana gelen ve matematiksel olarak hesaplanmasında bir takım güçlükler bulunan bir etkidir denilebilir.

Kompozisyon kaymasının yol açtığı etkinin de hesaba katılarak reaktiflik oranlarının hesaplanabilmesi için Mayo – Lewis denkleminin doğrusal olmayan yapısını doğrusal yapıya çevirerek denklemi analitik olarak çözmek yerine, denklemi olduğu gibi kabul edip onu nümerik bazı yaklaĢtırma yöntemleri kullanarak çözmek daha iyi sonuç vermektedir. Burada reaktiflik oranları tespit edilirken, Sünbül ve Giz tarafından geliĢtirilmiĢ olan, kompozisyon kaymasından kaynaklanan hesaplama zorluğununu aĢmak için Mayo – Lewis denklemine uyarlanmıĢ doğrusal olmayan en küçük kareler yöntemi kullanılmıĢtır. Bu yöntem Mayo – Lewis denkleminin doğrusal olmayan yapısını hesaba katmanın yanı sıra yüksek konsantrasyonlarda meydana gelebilecek olan kompozisyon kaymasını da hesaba katmaktadır. Ayrıca bu yöntem deneysel hataları diğer yöntemlere oranla daha iyi değerlendirmektedir.

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GeliĢtirilen yöntem yüksek konsantrasyonlarda sürdürülen ve sürekli gözlemlenen deneyler topluluğu için doğrusal olmayan en küçük kareler yönteminin verilerin sadece deney sonunda toplandığı duruma uyarlanması ile gerçekleĢtirilmiĢtir. Sonuçlar Kelen – Tudos (KT) ve Extended Kelen – Tudos (EKT) olarak bilinen güvenilir iki doğrusal metod kullanılarak elde edilen sonuçlar ile karĢılaĢtırılmıĢtır. Bu yöntemlerden KT kompozisyon kaymasını dikkate almazken EKT metodu bu etkiyi dikkate alır.

KT metodu kullanılırken doğrusal olmayan Mayo – Lewis denklemi belirli değiĢken dönüĢümleri altında doğrusal hale getirilir. Bu doğrusal denkleme ait katsayılar hesaplamaya çalıĢtığımız reaktiflik oranlarıdır. Bilindiği üzere doğrusal bir denkleme ait katsayılar hesaplanırken aynı tipte farklı sonuçları olan birden fazla denklemin eleme veya eleme benzeri bir yöntemle ele alınması gerekmektedir. Bu hesaplama yapılırken farklı değerli denklemlere ait aynı anlamlı parametreler aynı sütunları oluĢturacak biçimde matrisler oluĢturulup MATLAB “backslash” iĢlemi ile reaktiflik oranlarını temsil eden katsayıların hesaplanması gerçekleĢtirilmiĢtir.

Yine benzer hesaplama tekniği kullanılarak EKT metodu için farklı değiĢken dönüĢümleri altında aynı hesaplamalar gerçekleĢtirilmiĢtir.

Doğrusal Olamayan En Küçük Kareler (NLLS) metodu, Mayo – Lewis denkleminin doğrusal olmayan yapısını göz önüne alarak herhangi bir değiĢken dönüĢümü yapmadan deneysel veri ile nümerik hesaplama sonucu elde edilen veri arasındaki farkı en küçük yapacak sonuçlara ait reaktiflik oranlarını tespit etmede kullanılmıĢtır. Bu hesaplama sırasında Runge – Kutta 4 diye bilinen ve baĢlangıç değer problemleri çözümlerinde kullanılabilen bir nümerik yönteme karĢılık gelen ode45 isimli MATLAB komutu kullanılmıĢtır.

Bu yöntemlere ek olarak Fineman – Ross (FR) adı verilen ve Tez‟in belli bölümlerinde bahsedilen bir yöntem daha vardır. Ancak bu yöntemin sonuçları KT, EKT veya NLLS metodları ile elde edilmiĢ sonuçlara göre çok daha az güvenilirdir. Bunun sebebi, bu yöntemle hesaplanan deney noktalarının çoğunun belirli bir değer etrafında hesaplanıyor olması ve reaktiflik oranlarını belirleyecek olan katsayıların kaderinin hesaplamaya ait az sayıda veri noktasına bağlı olmasıdır. Burada belirtilen ifade Tez‟in ilgili bölümlerinde yer alan reaktiflik oranlarının grafiksel sonuçlarından da kolayca gözlenebilir.

Fineman – Ross metodu günümüzde çağ dıĢı kalmıĢ bir yöntem olarak değerlendirilebilir. Bu sebeple olsa gerek artık reaktiflik oranları hesaplamalarında Fineman – Ross (FR) metodu neredeyse hiç kullanılmamaktadır. Bu Tez içeriğinde bahsedilmesinin sebebi ise sonuçlarının güvenilirliğini diğer yöntemlere ait sonuçların güvenilirliği ile kıyaslamaktır. Bu sebepten dolayı yalnızca reaktiflik oranı hesaplamalarında kullanılmıĢ olup, doğrusal olmayan en küçük kareler yöntemi (NLLS) ile KT ve EKT metodları kıyaslamalarının aralarında yer verilmemiĢtir. Son olarak hesaplanan reaktiflik oranları, farklı deney malzemeleri olan MPMSK-co-St, APMA-co-EMA ve CHMA-co-St kopolimeri için elde edilmiĢ deneysel verilerden faydalanılarak hesaplanmıĢ ve farklı tablolar halinde verilmiĢ olup, bu tablolardaki değerlerden, ilgili grafiklere bakıldığı takdirde NLLS metodu ile elde edilmiĢ olanlarının deneysel sonuçlara en yakın haline ait değerler olduğu kolayca anlaĢılabilir. Bu çalıĢmada Siklohekzan-3-il Metil Metakrilat (CHMA) / Stirene (St), 4- Asetilfenil Metakrilat (APMA) / Etil Metakrilat (EMA), 4-Metakriloiloksifenil-4'-Metoksistiril Keton (MPMSK) / Stirene (St) kopolimerizasyonlarının reaktiflik oranları Adıyaman Üniversitesi‟nden Dr. Gamze BARIM‟ın deneysel sonuçları

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analiz edilerek hesaplanmıĢtır. Tüm hesaplar MATLAB ile yapılmıĢtır. Doğrusal olan ve doğrusal olmayan yöntemlere ait tüm hesaplamalar MATLAB'ın özel komutları kullanılarak gerçekleeĢtirilmiĢtir.

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1 1. INTRODUCTION

1.1 Introduction

The take up rates of monomers into the copolymer is determined not only by the feed composition but also by two parameters known as the reactivity ratios. The composition and properties of the resulting copolymer depends on these ratios. For this reason many techniques have been developed to determine these ratios. Here the nonlinear least square technique by SUNBUL et al. for continuously monitored experiments has been adapted to batch experiments carried out to high conversion. [1].

1.2 Backgrounds of Polymerization 1.2.1 Monomer

A monomer (from Greek mono “one” and meros “part”) is a molecule that may bind chemically to other molecules to form a polymer. The term “monomeric protein” may also be used to describe one of the proteins making up a multiprotein complex. The most common natural monomer is glucose, whis is linked by gylcosidic bonds into polymer such as cellulose and strach, and is over 77% of the mass of all plant matter. Most often the term monomer refers to the organic molecules which form synthetic polymers, such as, for example, vinyl chloride, which is used to produce the polymer polyvinyl chloride (PVC).

The lower molecular weight componds built from monomers are also referred to as dimers, trimers, tetramers, pentamers, octamers, 20-mers, etc. If they have 2,3,4,5,8 or 20 monomer units, respectively. Any number of these monomer units may be indicated bu the appropriate Greek prefix; e.g. a decamer is formed from 10 monomers. Larger numbers are often stated in English or numbers instead of Greek. Molecules made of a small number of monomer units, up to a few dozen, are called oligomers, [2 – 4].

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2 1.2.2 Polymer

A polymer is a large molecule (macromolecule) composed of repeating structural units. These sub – units are typically connected by covalent chemical bonds. Although the term polymer is sometimes taken to refer to plastics, it actually encompasses a large class of compounds coprising both natural and synthetic materials with a wide variety of properties.

Because of the extraordinary range of properties of polymeric materials, they play en essential and uniquitous role in everyday life. This role ranges from familiar synthetic plastics and elastomers to natural biopolymers such as nucleic acids and proteins that are essential for life.

Natural polymeric materials such as shellac, amber, and natural rubber have been used for centuries. A variety of other natural polymers exist, such as cellulose, which is the main constituent of wood and paper. The list of synthetic polymers includes synthetic rubber, Bakalite, neoprene, nylon, PVC, polystrene, polyethylene, polypropylene, polyacrylonitrile, PVB, silicone, and many more.

Most commonly, the continuously linked backbone of a polymer used for the preparation of plastics consists mainly of carbon atoms. A simple example is polyethylene (“polythene” in Brithish English), whose repeating unit is based on ethylene monomer. However, other structures do exist; for example, elements such as silicon form familiar materials such as silicones, examples being Silly Putty and waterproof plumbing sealant. Oxygen is also commonly present in polymer backbones, such as those of polyethylene glycol, polysaccharides (in glycosidic bonds), and DNA (in phosphodiester bonds).

Polymer properties are broadly divided into several classes based on the scale at which the property is defined as well as upon its physical basis. The most basic property of a polymer is the identity of its constiuent monomers. A second set of properties, known as microstructure, essintially describe the arrangement of these monomers within the polymer at the scale of a single chain. These basic structural properties play a major role in determining bulk pysical properties of the polymer, which describe how the polymer behaves as a continuous macroscopic material. Chemical properties, at the nano – scale, describe how the chains interact through

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various physical forces. At the macro – scale, they describe how the bulk polymer interacts with other chemicals and solvents.

The identity of the monomer residues (repeat units) comprising a polymer is its first and most important attribute. Polymer nomenclature is generally based upon the type of monomer residues comprising the polymer.

Polymers that contain only a single type of repeat unit are known as homopolymers, while polymers containing a mixture of repeat units known as copolymers. Poly(strene), for example, is composed only of styrene monomer residued, and is therefore classified as a homopolymer.

Ethylene – vinyl acetate, on the other hand, contains more than one varety of repeat unit and is thus a copolymer. Some biological polymers are composed of variety of different but structurally related monomer residues; for example, polynucleotides such as DNA are composed of a variety of nucleotide subunits.

A polymer molecula containing ionizable subunits is known as a polyelectrolyte or ionomer [4 – 6].

1.2.3 Polymerization and copolymerization

Polymerisation is a process that the monomers create a polymer chain by connecting one of them to another. In this thesis, only the propagation stage of copolymerization is studied and the monomer consupmtion in other stages is assumed to be negligible. If the connected monomers have two different types then we call them as copolymer. Therefore copolymerization is a polymerization between different two monomers units. While one of the monomers are connecting to another the propagation step includes both homopropagation. This process can be shown as follows;

A + B A B A B B A A A B B B A B A B B B B A B A

A and B represent to the different type of monomers. The copolymer structure depends on the relative monomer concentrations in the feed and their rate of incorporation in the copolymer chains. In this research, free radical (chain growth) polymerization will be considered, [7,8].

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4 1.2.4 Conversion

Conversion is a ratio of how much monomer participating to the copolymer. Because conversion is a ratio of the same unit it is unitness.

Copolymers have two degrees of reedom (amount of A converted and amount of B converted) and the measurement of a single number does not suffice. Measurement of the copolymer composition in combination with gravimetry would be adequate, [5,6].

1.2.5 Copolymer propagation types

There are four propagation reactions are possible between different monomer types as follows;

● + A → ● (1.1)

● + B → ● (1.2)

● + A → ● (1.3)

● + B → ● (1.4)

● and ● are different type of radical polymer chains, A and B are different type of monomers. are the constants of combining velocities, [9 – 11].

1.2.6 Reactivity ratio

Reactivity ratio (RR) is a ratio which is used to determine how fast the monomer participates to a copolymer compound.

There are many methods created so as to determine RR by numerical and computational. Some of these methods Fineman – Ross, Kelen – Tüdös and Extended Kelen – Tüdös. In this thesis these methods are used to calculate to RR, [12 – 16]

Reactivity ratios are defined as the velocity of participating monomers to the copolymer compound by Mayo – Lewis equation.

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Mayo – Lewis equation is given by equation (1.21); { } and are known as reactivity ratios, [17].

1.2.7 Random copolymerization

In random copolymerization (RC) the two types of monomers are arranged randomly along the chain;

Figure 1.1 : Random Copolymerization Chain Configuration

If the probability of finding a given type monomer residue at a particular point in the chain is equal to the mole fraction of that monomer residue in the chain, then the polymer may be referred to as a truly random copolymer, [18].

1.2.8 Alternating copolymerization

In alternating copoymerization (AC) the two types monomers follow each other in an alternating order.

Figure 1.2 : Alternating Copolymerization Chain Configuration This is called as regular alternating A and B units, [19].

1.2.9 Block copolymerization

In block copolymers (BC) one finds groups (blocks) of a single type of monomer followed by blocks of the other type.

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Block Copolymers comprise two or more homopolymer subunits linked by covalent bonds. The union of the homopolymer subunits may require an intermediate non-repeating subunits, known as a junction block. Block copolymers with two or three distinct blocks are called diblock copolymers and triblock copolymers, respectively, [20].

1.2.10 Mayo – Lewis equation

One of the the most widely used copolymerization model is the Mayo – Lewis model (Mayo and Lewis, 1944). Mayo and Lewis assumed in quasi staead state;

●

(1.5)

With the type of propagations; ● ● (1.6) ● ● (1.7) ● ● ● (1.8) ● ● ● (1.9)

In quasi – static state the third equation can be written as;

● ● ● (1.10) So;

● ● _(1.11)

By using these equations we have; ● ● (1.12)

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7 From first equation;

● ● (1.13)

If this found [A●] in this equation is replaced to the place that in the other equation, the equation is written;

● ● (1.14) Then; ● ● (1.15)

To calculate how many A monomer participates to the copolymer while B monomer participates we make these two equations divided;

{ } ● { } ● (1.16) { } { } (1.17) If it is redefined; (1.18) (1.19)

Here it can be written as; {

} (1.20)

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8 Therefore; { } (1.21)

This nonlinear equation is called Mayo – Lewis Equation. There are many numerical and mathematical methods improved in order to calculate the reactivity ratios which are given by and for different type of A and B monomers, [17,21].

1.3 Backgrounds of Calculations 1.3.1 minimisation method

In probability theory and statistics, the distribution (CS) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. It is one of the most widely used probability distributions in inferential statistics, e.g., in hypothesis testing or in costruction of confidence intervals. When there is a need to contrast it with the non – central CS distibution, this distribution is sometimes called the central CS.

The CS is used in the common CS tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitive data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. Many other statistical tests also use this distribution, like Friedman‟s analysis of variance by ranks, [22 – 24].

The CS distribution is a special case of the gamma distribution is a special cases of the gamma distribution.

The definition:

∑

(1.22)

Is distibuted according to the CS distribution with k degrees of freedom. This is usually denoted as

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9

( ) _(1.23)

The CS distribution has one parameter: k – a positive integer that specifies the number of degrees of freedom. (i.e. the number of ‟s)

The CS distrubition is obtained as the sum of the squares of k independent zero – mean unit – variance Gaussian random variables. Generalizations of this distributions can be obtained by summing the squares of other types of Gaussian random variables. Several such distributions are described below, [25,26].

1.3.2 Runge – Kutta method

In numerical analysis, the Runge – Kutta (RK) methods are an important family of implicit and explicit iterative methods for the approximation of solutions of Ordinary Differantial Equations (ODE). These techniques were developed around 1900 by the German mathematicians C.Runge and M. W. Kutta.

One member of the family of RK methods is so commonly used that it is often referred to as RK4.

Let an initial value problem be specified as follows.

( ) ( ) _(1.24)

In words, what this means is that the rate at which y changes is a function of y itself and of t (time). At the start, time is and y is . In the equation, y may be a scalar or a vector.

The RK4 method for this problem is given by the following equations:

( ) (1.25)

And;

(1.26)

Where is the RK4 approximation of ( ), and

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10

( ) _(1.28)

( ) _(1.29)

( ) _(1.30)

Thus the next value ( ) is determined by the present value ( ) plus the weighted average of four increments, where each increment is the product of the size of the interval, h, and an estimated slope specified by function f on the right hand side of the differential equation.

 is the increment based on the slope at the beginning of the interval, using , (Eular‟s Method);

 is the increment based on the slope at the midpoint of the interval, using ;

 is again the increment based on the slope at the midpoint, but now using ;

 is the increment based on the slope at the end of the interval, using .

In averaging the four deltas, greater weight is given to the deltas at the midpint. The weights are chosen such that if f is independent of y, so that the differential equation is equivalent to a simple integral, then RK4 is Simpson‟s rule.

The RK4 method is a fourth – order method meaning that the error per step is on the order of h, while the total accumulated error has order h, [27 – 32].

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11 2. METHODS OF CALCULATION

2.1 Mayo Equation

This equation is given by Equation (1.21); { }

If the differential part of this equation is shown with a variable named Y;

(2.1)

And the rate of the monomers is shown with a variable named X;

(2.2)

Then the equation turns;

(2.3)

, [17].

2.2 Fineman – Ross Method

If some corrections are made with the equations 4.1 and 4.2, G and F would be written as;

( ) _(2.4)

And F can be written as;

(2.5)

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12

_(2.6)

This method is called Fineman – Ross Method. Now this equation can easly being solved. This method is an obsolete method because the results of the calculations mostly depend on the last calculated data points. As it is seen in my calculations, most of the points are placed together near a calculated data point whereas one or two data points are placed near a very different data point [33].

2.3 Kelen – Tudos Method

F and G are the variables which are given in Equation (3.4) and Equation (3.5) in Fineman – Ross method. In addition to this, there is a variable that is calculated with the help of the maximum and minimum values of F as shown below;

√ (2.7)

There are other variables different from Fineman – Ross method written as and as show below;

(2.8)

(2.9)

Using them, Kelen and Tudos developed an equation, which as shown below;

( ) _(2.10)

Therefore Equation (3.8) is a type of linear equation and it can be solved by elemination methods, [34].

2.4 Extended Kelen – Tudos Method

Kelen and Tudos was discovered a new method after they published KT. The name of this method is Extended Kelen – Tudos (EKT). This method can be used for experiments carried out to high conversion. The linear type of equation was not

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13

changed in this method; however, the techniques to get F and G are changed as shown below; (2.11) And (2.12)

Here and are the initial values of the monomer fractions in copolymer. By using and , Z variable can be written as;

( ) ( ) _(2.13)

Here if F is written as;

_(2.14)

And G is written as;

( ) _(2.15)

The ways to get and are not changed and they are still as shown below;

Kelen and Tudos wrote this equation for Extended Kelen – Tudos Method as it was in Kelen – Tudos Method.

( ) _(2.16)

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14 2.5 Nonlinear Least Squares Method (NLLS)

This method actually is not so different than the other methods. Mayo equation which is given with the equation (1.21) is written as shown below;

{

} (2.17)

Remained monomer number can be calculate as mathematical which is shown below;

_(2.18)

And from here;

∑

(2.19)

Therefore CS of the remained monomer number gives as the minimised point of theoretical calculated data point. Which is the most approximate result to the experiment than the other methods are; so if the minimum result of CS is chosed then the variables and would be the nearest reactivity ratios for monomers to the experiment, [38, 39].

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15 3. RESULTS

3.1 Experimental Data

There are three different experiments with three different copolymer composition. They are Cyclohexene-3-yl Methyl Methacrylate (CHMA) / Styrene(St), 4- Acetylphenyl methacrylate (APMA) / Ethyl Methacrylate (EMA), 4-Methacryloyloxyphenyl-4'-Methoxystyryl Ketone (MPMSK) / Styrene (St).

3.2 Concentration and Conversions for MPMSK-co-St

Data includes 5 MPMSK-co-St experiments. Therefore different experiments mean that [A] and [B] monomers participate to the copolymer on different rates and different conversions. Each column of the table is mentioned in Table 3.1.

Table 3.1 : Concentration and Conversion for MPMSK-co-St

Conversion % 10 90 22 78 16 20 80 36 64 20 50 50 50 50 26 70 30 55 45 31 90 10 80 20 42

= Start up mole fraction of MPMSK. = Start up mole fraction of St.

= Mole fraction of MPMSK on copolymer (calculated from 1H-NMR) = Mole fraction of St on copolymer (calculated from 1H-NMR) α=0,93

3.3 Concentration and Conversions for APMA-co-EMA

Data includes 6 APMA-co-EMA experiments. Therefore different experiments mean that [A] and [B] monomers participate to the copolymer on different rates and different conversions. Each column of the table is mentioned in Table 3.2.

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Table 3.2 : Concentration and Conversion for APMA-co-EMA

Conversion % 10 90 15 85 32,9 20 80 25 75 32,9 35 65 38 62 30,8 50 50 56 44 36 70 30 71 29 37 90 10 88 12 38

= Start up mole fraction of APMA = Start up mole fraction of EMA

= Mole fraction of APMA on copolymer (calculated from 1H-NMR) = Mole fraction of EMA on copolymer (calculated from 1H-NMR) α=0,87

3.4 Concentration and Conversions for CHMA-co-St

This experimental data table has 5 different results for the same copoylmer APMA-co-EMA. Each row of the table means different experiments for this copolymer. Therefore different experiments mean that [A] and [B] monomers participate to the copolymer on different rates and different conversions. Each column of the table is mentioned in Table 3.3.

Table 3.3 : Concentration and Conversion for CHMA-co-St

Conversion % 10 90 13 87 14,4 25 75 23 77 12 50 50 39 61 12 75 25 55 45 10,8 90 10 75 25 15,2

= Start up mole fraction of CHMA = Start up mole fraction of St

= Mole fraction of CHMA on copolymer (calculated from 1H-NMR) = Mole fraction of Ston copolymer (calculated from 1H-NMR) α=1,48

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3.5 Calculated Reactivity Ratios for Certain Methods

Each of experiments have results depend on which calculation method is used. In this thesis there are four method were used to determine the coefficients. These methods are Fineman – Ross, Kelen – Tüdös, Extended Kelen – Tüdös and minimisation method.

3.5.1 Reactivity ratios and graphics for MPMSK-co-St

Reactivity ratio is a word to say how different a type of monomer participates to the copolymer chain than the other type of monomer. Therefore it is important to know this ratio in order to say something about the process of copolymerization before it is started or it continues to the copolymerization. Reactivity ratios can be seen in Table 3.4.

Table 3.4 : Calculated Reactivity Ratios for MSMF-co-St

Reactivity Ratio FR KT EKT CS

0.29063 0.26846 0.21679 0.24

0.36853 0.26719 0.16832 0.19

is reactivity ratio of [A] monomer is reactivity ratio of [B] monomer

This table gives us information about copolymerization process for five different experiments being extinguished with the same copoymer named MSMF-co-St. There are 3 different graphics are drawn for this table as shown below. Each graphic represents results for different methods which were used to calculate reactivity ratio of monomers for MSMF-co-St copolymerization process. In Figure 3.1, Figure 3.2, Figure 3.3 one can easly see the results.

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Figure 3.1 : Calculated Reactivities with FR for MPMSK-co-St

As it is seen from Figure 3.1 there are many points on the bottom side of fitting line. Because those bunches Fineman – Ross Method (FR) is not good way so as to define reactivity ratios of monomers.

Figure 3.2 : Calculated Reactivities with KT for MPMSK-co-St

This result on Figure 3.2 is more likely to use than the results of FR. KT method is a way to calculate the ratios of monomers but in some cases EKT method is much likely to define the ratios of copolymerization process than KT.

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Figure 3.3 : Calculated Reactivities with EKT for MPMSK-co-St

As it is seen from Figure 3.3 this method is much profitible with the experiments. In this figure, experimental data lie down to the fit line in a good way.

3.5.2 Reactivity ratios and graphics for APMA-co-EMA

Reactivity ratio is a word to say how different a type of monomer participates to the copolymer chain than the other type of monomer. Therefore it is important to know this ratio in order to say something about the process of copolymerization before it is started or it continues to the copolymerization. Reactivity ratios can be seen in Table 3.5.

Table 3.5 : Calculated Reactivity Ratios for APMA-co-EMA

0.57743 0.61385 0.5376 0.49

0.71533 0.8142 0.76674 0.74

This table gives us information about copolymerization process for six different experiments being extinguished with the same copoymer named APMA-co-EMA. There are 3 different graphics are drawn for this table as shown below. Each graphic represents results for different methods which were used to calculate reactivity ratio of monomers for APMA-co-EMA copolymerization process. Figure 3.4, Figure 3.5 Figure 3.6 include the results for reactivity ratios.

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Figure 3.4 : Calculated Reactivities with FR for APMA-co-EMA

As it is seen from Figure 3.4 there are many points on the bottom side of fitting line like Figure 3.1. We mentioned before that because those bunches Fineman – Ross Method (FR) is not a good way so as to define reactivity ratios of monomers.

Figure 3.5 : Calculated Reactivities with KT for APMA-co-EMA

This result on Figure 3.5 is more likely to use than the results of FR. We also mentioned before that KT is a way to calculate the ratios of monomers but in some cases EKT is much likely to define the ratios of copolymerization process than KT.

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Figure 3.6 : Calculated Reactivities with EKT for APMA-co-EMA

3.5.3 Reactivity ratios and graphics for CHMA-co-St

Figure 3.7 : Calculated Reactivities with FR for CHMA-co-St

It can be easly seen from Figure 3.7 that why this method is obsolete. Calculated reactivity ratios with Fineman – Ross method are seen as points in this graphics. Most of the points seen at the bottom side of the grafic near the same data point; however, there is another point on the graphic that could be change the slope of the fit line. If this point changes its positions as a result of calculations then the slope

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changes and also reactivity ratios change. Reactivity Ratios are given as a table below for this copolmer with Fineman – Ross;

Table 3.6 : Calculated Reactivity Ratios for CHMA-co-St

0.64356 0.75566 0.74373 0.89

0.043741 0.20074 0.1717 0.21

As it is seen from Figure 3.7 there are many points on the bottom side of fitting line like Figure 3.1 and Figure 3.4. We mentioned before that because those bunches Fineman – Ross Method (FR) is not a good way so as to define reactivity ratios of monomers.

Figure 3.8 : Calculated Reactivities with KT for CHMA-co-St

This result on Figure 3.8 is more likely to use than the results of FR as well as the results on Figure 3.2 and Figure 3.5. We also mentioned before that KT is a way to calculate the ratios of monomers but in some cases EKT is much likely to define the ratios of copolymerization process than KT.

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Figure 3.9 : Calculated Reactivities with EKT for CHMA-co-St

3.6 Initial and Finish Concentrations of Different Experiments

Calculation gap for molecules those mentioned before are given in this section. The comperisons of the results calculated with the methods mentioned above could be found as a table with the fractions of experimental points in this section.

3.6.1 Results for MPMSK-co-St copolymerization

In Table 3.7 there are results to show the difference between the different methods. IC shows initial concentrations, FC shows final concentrations and the names of methods show the calculated concentrations.

Table 3.7 : 16% Conversion for Copolymer MPMSK-co-St

Monomers IC FC KT EKT CS

[A] 10 6.48 6.58 6.1426 6.3606

[B] 90 77.52 77.52 77.52 77.52

The graphich of Table 3.7 is below as Figure 3.10. In the graphic there is square point that represents the a data point of the experiment. As it is seen from the figure that plus shaped points represent to the results of method (CS). We are expecting that the results of CS are much profitible to the experimental points.Initial concentration are for [A]:10 and for [B]:90.

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24

Figure 3.10 : The Comparison of the Methods on :10 – :90 for 16% Conversion MPMSK-co-St………...

In Table 3.8 there are results to show the difference between the different methods. Table 3.8 : 20% Conversion for Copolymer MPMSK-co-St

[A] 20 12.8 13.7692 13.2542 13.5284

[B] 80 67.2 67.2 67.2 67.2

In this figure the conversion is 20% for monomers. Initial concentration of monomers are for [A]:20 and for [B]:80. Results can be seen on Figure 3.11.

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[A] 50 37 37.0122 37.4934 37.4971

[B] 50 37 37 37 37

In this experiment conversion of monomers is 26% and initial concentration of monomers are for [A]:50 and for [B]:50. These results are shown in Figure 3.12.

Some data points that are calculated with KT methods are in the same fit line with the calculated data points by NLLS method and there is another table to show 31% conversion for copolymer MPMSK-co-St as shown in Table 3.10;

[A] 70 52.95 48.5057 51.2693 50.7128

[B] 30 16.05 16.05 16.05 16.05

In this experiment the conversion of monomers is 31% and initial concentration of monomers are for [A]:70 and for [B]:30 The graphic for this table is Figure 3.13.

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26

Table 3.11 shows the results to compare for different methods.

[A] 90 56.4 49.5297 59.5554 57.2114

[B] 10 1.6 1.6 1.6 1.6

In this experiment the conversion of monomers is 42% and initial concentration for monomers are [A]:90 and for [B]:10 The graphic for this table is Figure 3.14.

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27

In Figure 3.15 they are showed the results of the experiments together. It is understand from this graphic CS results are much profitible with the experiment.

Figure 3.15 : The Comparison of the Methods for 16% Conversion MPMSK-co-St Reactivity ratios are shown as in Figure 3.16.

Figure 3.16 : The Contours of Reactivity Ratios for MPMSK-co-St

The contour lines show where the result points of the methods KT and EKT compared with the method of CS. One can understand this from this figure that the result point of CS calculated reactivity ratio for this copolymer composition is at the center and the result point of EKT calculated reactivity ratio for this copolymer composition is near to the center.

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3.6.2 Results for APMA-co-EMA copolymerization

There are tables below in order to show the last data points of the experiments for definite initial concentration on a certain percentage of conversation. In Table 3.12 there are results for differents methods.

Table 3.12 : 32.9% Conversion for Copolymer APMA-co-EMA

[A] 10 5.065 5.6933 5.3289 5.0644

[B] 90 62.035 62.035 62.035 62.035

In this table initial concentration of monomers are for [A]:10 and for [B]:90. The conversion of monomers is 32.9%. The graphic for this table is in Figure 3.17.

Figure 3.17 : The Comparison of the Methods on :10 – :90 for 32.9% Conversion APMA-co-St……….

The results of different methods are shown in Table 3.13.

[A] 20 11.775 11.9106 11.3523 10.9479

[B] 80 55.325 55.325 55.325 55.325

In this table initial concentration of monomers are for [A]:20 and for [B]:80. The conversion of monomers is again 32.9%. The result of this experiment can be seen of the figure below. The graphic for this table is Figure 3.18.

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29

[A] 35 23.296 22.0272 21.4548 21.0411

[B] 65 44.98 44.98 44.98 44.98

In this experiment initial concentration of monomers are for [A]:35 and for [B]:65. The conversion of monomers is 30.8% and the graphic for this table is Figure 3.19.

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30

Table 3.15 : 36% Conversion for Copolymer APMA-co-EMA

[A] 50 29.84 32.5241 32.1847 31.9279

[B] 50 34.16 34.16 34.16 34.16

In this experiment the conversion of monomers is 36% and initial concentration of monomers are for [A]:50 and [B]:50. The results of this calculation are drawn as a figure which is below. The graphic for this table is Figure 3.20.

Figure 3.20 : The Comparison of the Methods on :50 – :50 for 36% Conversion APMA-co-St……….…

[A] 70 43.73 45.2942 45.5562 45.6792

[B] 30 19.27 19.27 19.27 19.27

In this experiment the conversion of monomers is 37% and initial concentration of monomers are for [A]:70 and for [B]:30. The results on the table can be seen on the figure below. The graphic for this table is Figure 3.21.

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The results for different methods are shown in Table 3.17.

[A] 90 56.56 53.1775 54.4513 55.1815

[B] 10 5.44 5.44 5.44 5.44

In this experiment the conversion of monomers is 38% and initial concentration of monomers are for [A]:90 and for [B]:10. The graphic for this table is Figure 3.22.

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Figure 3.23 is a graphic which is drawn to show all experiments together experimented for APMA-co-St. As it is seen from this figure and the other figures for this copolymer composition the result point of CS is much likely to use than the results of the results of the other methods.

Figure 3.23 : The Comparison of the Methods for APMA-co-St

The contour lines for this experiments are drawn so as to show how far the results of the other methods than the result of CS. It can be easly understand that the most minimised reactivity ration point of the calculation is the result of CS. Reactivity ratios are shown in a contour graphic in Figure 3.24.

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In this contour it is seen that all methods are profitible with this experiment but the most profitible method is CS.

3.6.3 Results for CHMA-co-St copolymerization

In this result title there are five different results of five different experiments with same copolymer CHMA-co-St. The results on the tables show that the result of CS is mucj porfitible from the experiments than the results of the other methods. Table 3.18 includes the results for different methods.

Table 3.18 : 14.4% Conversion for Copolymer CHMA-co-St

[A] 10 8.128 8.3774 8.3612 8.5792

[B] 90 77.472 77.472 77.472 77.472

In this experiment the conversion of monomers is 14.4% and initial concentration of monomers are for [A]:10 and for [B]:90. The graphic for this table is in Figure 3.25.

Figure 3.25 : The Comparison of the Methods on :10 – :90 for 14.4% Conversion CHMA-co-St………

Table 3.19 : 12% Conversion for Copolymer CHMA-co-St

[A] 25 22.24 21.9794 21.974 22.2886

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In this experiment initial concentration of monomers are for [A]:25 and for [B]:75 and the conversion of the monomers is 12%. There is figure drown to show the result of this experiment below. Figure 3.26 show the results as a graphic for this table.

Figure 3.26 : The Comparison of the Methods on :25 – :75 for 12% Conversion CHMA-co-St……….…

Table 3.20 : 12% Conversion for Copolymer CHMA-co-St

[A] 50 45.32 44.9192 45.0085 45.2281

[B] 50 42.68 42.68 42.68 42.68

In this experiment the conversion of the monomers is 12% and initial concentration of monomers are for [A]:50 and for [B]:50. The result of the experiment can be seen from the figure below.

In Figure 3.27 the results in Table 3.20 are shown as a graphic.

As it is seen in tables and graphics the results calculated with Nonlinear Least Squares method is almost the nearest result with the experiments. The results that calculated with Fineman – Ross method aren‟t used in those graphics which are used to show the difference in different methods.

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Table 3.21 shows the result for different methods.

[A] 75 69.06 68.5563 68.8938 68.6534

[B] 25 20.14 20.14 20.14 20.14

In this table there are results for 10.8% monomer conversion. Initial concentraion of monomers are for [A]:75 and for [B]:25. The result of the experiment can be seen from the figure below. Figure 3.28 shows the results given in Table 3.21.

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[A] 90 78.6 78.9079 79.9442 78.7041

[B] 10 6.2 6.2 6.2 6.2

On this table, it can be seen that the conversion of the monomers is 15.2% and initial concentraiton of monomers are for [A]:90 and for [B]:10.

There is Figure 3.29 in order to show the result of the experiment below.

In Figure 3.30 there are the results of the experiments together. This experiment set shows us that the reactivity ratios given by CS meothod best fit the data.

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In this contour, it can be easly seen that the result of KT is near to the result point of CS. The result of EKT is out of the center contour. Figure 3.31 shows reactivity ratios as a contour graphic.

Figure 3.31 : The Contours of Reactivity Ratios for CHMA-co-St

The result of this experiment shows us that the most profitable method is CS for this copolymer composition.

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4. CONCLUSIONS AND RECOMMENDATIONS

In this section there are many calculation clues and techniques are mentioned and compared.

4.1 Appraisal of Programming Methods

Instead of using low level programming via programming languages, MATLAB hand in a simplified work station. There many commands that is to complate the programs with less codes than the others. Because of that MATLAB is a very easy program to use. If LS method is considered, there are many rows to complete the program compared with MATLAB. MATLAB has only one command to calculate the coefficients that is searched by LS sense. That command is back – divide. If it is compared with the other programming languages, MATLAB comes out with the easy usage. Therefore programs can take short times if they programmed with MATLAB.

4.2 Appraisal of Calculation Methods

If it is compared with the other methods of calculations minimisation method has the most approximate results. As it is shown in the figures, CS minimisation method closer to the experimental data point than the other calculation method‟s last points. Fineman – Ross method loses it‟s prestige nowadays because the calculation results have the points accumulated on a neighbor of point.

4.3 Appraisal of Experimented Copolymer Compositions Table 4.1 shows calculated reactivity ratios for MPMSK-co-St.

Table 4.1: Calculated Reactivity Ratios for MSMF-co-St

0.29063 0.26846 0.21679 0.24

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Table 4.2 shows reactivity ratios for APMA-co-EMA

Table 4.2: Calculated Reactivity Ratios for APMA-co-EMA

0.57743 0.61385 0.5376 0.49

0.71533 0.8142 0.76674 0.74

Table 4.3 shows reactivity ratios for CHMA-co-St

Table 4.3: Calculated Reactivity Ratios for CHMA-co-St

0.64356 0.75566 0.74373 0.89

0.043741 0.20074 0.1717 0.21

Those tables shows us that the most profitible method is CS for this type of copolymer compositions.

4.4 Appraisal of Results of Calculations

It is already mentioned before, the result of CS minimisation method has the most profitible results of the experimental.

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