Relaxation Phenomena studies on Some Polymers and polymer ... · EL-Mansoura University Faculty of Science Physics Department Relaxation Phenomena studies on Some Polymers and polymer

EL-Mansoura University

Faculty of Science Physics Department

Relaxation Phenomena studies on Some Polymers and

polymer blends

By:

Alaa El-din El-kotp Abd El-kader Mohammed Ass.Lect. at Physics Dept., Faculty of Science Mansoura University

Submitted for the Doctor Degree of Philosophy of Science /Physics

(Experimental Physics)

2002

بسم اهللا الرحمن الرحيم

وما اوتيتم من (

) العلم اال قليال

صدق اهللا العظيم

II

To my wife the one who Stay beside me always

And My children

And my parents

III

Supervisors Committee THESIS TITLE:

“Relaxation Phenomena Studies on Some Polymers and Polymer Blends”

RESEARCHER´S NAME:

Alaa El-din El-kotp abd El-kader Mohammed Supervisors: Name Position Signature Prof.Dr.M.D.Migahed Prof. of Experimental

Physics at Mansoura University, Mansoura, Egypt.

Prof.Dr.Christoph Schick

Prof. of Applied Physics at Rostock University, Rostock, Germany.

Ass.Prof.M.T.Ahmed Ass.Prof. Polymer Physics at Mansoura University, Mansoura, Egypt.

Head of Physics Department

Prof. Dr. A.Y. M. El-Tawansi

IV

Examiners Report

THESIS TITLE:

“Relaxation Phenomena Studies on Some Polymers and Polymer Blends”

RESEARCHER´S NAME:

Alaa El-din El-kotp Abd El-kader Mohammed No. Name Position Date of discussion: Degree of dissertation: Referee Signature: No. Name Signature

V

Contents Page Acknowledgements…………………………………………..…………….. XII

Abstract…………………………………………………………………...….XIV

Chapter1: Introduction and Aim of the work

1.1-Introduction…………………………………………………………… 2

1.2-Aim of the work………………………………………………………. 4

Chapter 2: Theoretical Background

2.1-Polymeric Materials…………………………………………………….6

2.1.1-Generel concepts……………………………………………..…….. 6

2.1.2-Polymer assemblies……………………………………………..….. 8

2.1.3-Melt states of polymers…………………………………………....…9

2.1.4-Semi-crystalline polymers………………………………………….10

2.1.5-Polymer blends…………………………….……………………..…14

2.2-Structural Transitions in Polymers ………………………….……….15

2.2.1-Polymer crystallization………………………………………………….15

2.2.2-Polymer melting……………….………………………………………....18

2.3-Relaxation Phenomena in Polymers…………………………………..20

2.3.1-Relaxation phenomena (Theoretical Approach)………………………20

2.3.2-Relaxation types in polymers………………………………………...…24

2.3.2.1-Structral relaxations……….……………………………….…25

2.3.2.2-Local relaxations……..…………………………………….….27

VI

2.3.3-Relaxation in semi-crystalline polymers………………………………..29

2.3.3.1-Relaxation in semi-crystalline polymers as

composite structure system …………………………………....29

2.3.3.2-Crystallization dynamics and relaxation

in semi-crystalline polymers………………………………..…30

2.3.3.3-Relaxation associated with crystalline phase……………… ….31

2.3.3.4-Mobility in ordered crystalline phase……………………..……34

2.3.4- The Glass –rubber relaxation phenomena………………….……..…39

2.3.4.1-Glass –rubber relaxation in polymers…………………..……..39

2.3.4.2-Classification of glass transitions temperatures……..………...41

2.3.4.3-Theories of glass-rubber relaxation.……………….....……..…43

2.3.5-Relaxation in the glassy state of polymers……………..………………47

2.3.6-Thermal transition and relaxation…..…………………………………48

2.4- Thermal Analysis…………………………………………..…………….50

2.4.1-Thermal analysis…………………………………………………………50

2.4.2-Theory of heat capacity……………………………………..…………...50 2.4.3-General theory of TMDSC………………….…………..…...……….…52

2.4.4-TMDSC as a tool to study relaxation in polymers…..………………...56

2.4.5-Three-phase model of semi-crystalline polymers……..…………….….61

5.4.5.1- Introduction of the rigid amorphous (RAF)…………………..61

2.4.6-The reversing melting relaxation at the lamellae surface…………..…67

2.5- Dielectric Spectroscopy…………………..………………………………72

2.5.1-Introduction………………………………………………………………72

2.5.2-The dipole moment…………………………….…………………………73

2.5.3-Permitivity spectroscopy (theory)….…………………………………....74

2.5.4-Arc diagrams…………………………………………………………...…76

2.5.5-Dielectric spectroscopy as a tool to study the relaxation in polymers…77

VII

Chapter3: Literature Survey

3.1-Previous selected work on Relaxation in Semi-crystalline Polymers

using TMDSC Technique………………………..……………..……81

3.2-Previous selected work on Relaxation in Semi-crystalline Polymers

using Dielectric Spectroscopy Technique……….....…..……..……..97

Chapter 4: Materials and Experimental Techniques

4.1-Materials…………………………...…………………………………...105 4.1.1-Pure polymers……………………………………………………………106

4.1.1.1-Poly (etheleneoxide) (PEO)……………………………………….106

4.1.1.2- Polypropylene (PP)……………………………………………….106

4.1.1.3- Poly (3-hydroxybutarate) (PHB)….…..…………………………107

4.1.1.4-Poly (ethylene terephthalate) (PET)……………………………..107

4.1.1.5-Poly (ether ether ketone) (PEEK)…..…………………..………..108

4.1.1.6-Poly (trimethyle terephthalate) (PTT)……………….…………..108

4.1.1.7-Poly(butylene terephthalate) (PBT).………………….………….109

4.1.2-Polymer blends…………………………………………………………….109

4.1.2.1-PHB/Polycarbolactone (PCL)..…………………………….…….109

4.1.3-Copolymers………………………………………………………………..110

4.1.3.1-PHB-co-HV copolymer………………………………………….110

4.2-Experimental Techniques………………………….…………………111

4.2.1-Temperature Modulated Differential Scanning Calorimetry

(TMDSC)………………………………………………...………………..111

4.2.1.1-Sample preparation………………………………………….……111

4.2.1.2- TMDSC measuring device………………………………….……112

4.2.1.3-The Perkin Elmer DSC-2C TMDSC

device electronic structure………………………………………..113

4.2.1.4-TMDSC measuring program…………………………………….115

4.2.1.5-TMDSC experimental techniques………………………………..116

VIII

4.2.1.6-TMDSC experimental data analysis……………….……..117

4.2.2-Dielectric spectroscopy (DS)……………………………………………122

4.2.2.1-Sample preparation………………………………………………….122

4.2.2.2-The Dielectric spectroscopy system…………………………………123

4.2.2.3-The Dielectric data analysis………………………………………....125

Chapter 5: Results and Discussion 5.A-Thermal studies…………...…………………………………………..128

Part1- DSC measurements………….…………...……………………..…129

5.1-DSC measurements……...……………………..……………………..130 5.1.1-PHB…………………………………………………………………………130

5.1.2-sPP…………………………………………………………………………..133

5.1.3-PEEK…………………………………………………………………..……138

5.1.4-PTT……………………………………………………………………….…139

5.1.5-PHB/PCL blend………………………………………………………….....140

5.1.6-PHB-coHV copolymer………………………………………………….….150

Part2-TMDSC Measurements…………………………….…………….152

5.2-TMDSC Measurements……………………………………………...153 5.2.1-Relaxation processes in semi-crystalline polymers……….………153

5.2.2-Glass transition relaxation…………………………………………156

5.2.2.1-sPP………………………………………………………….156

5.2.2.2-PHB-co-HV copolymer……………………………………157

5.2.3-Structural induced relaxation process……….……………………161

5.2.3.1-PHB…………………………………………………………161

5.2.3.2-sPP………………………………………………………….164

5.2.4-Rigid amorphous fraction (RAF) relaxation…………..………….165

5.2.4.1-PHB…………………………………………………………165

5.2.4.2-sPP……….……………………………………………….…168

5.2.5-Relaxation during iso-thermal crystallisation process……….….169

5.2.5.1-PEEK………………………………………………………..169

5.2.5.2-PBT………………………………………………………….173

5.2.5.3-PET………………………………………………………….175

5.2.5.4-PTT………………………………………………………….177

5.2.5.5-PHB………………………………………………………….180

5.2.5.6-sPP………………...…………………………………………182

IX

5.2.6-Relaxation processes after the crystallisation………………….…183

5.2.6.1-PEO…………………………………………………………183

5.2.6.2-PHB………………………………………………………....186

5.2.6.3-sPP…………………………………………………………..188

5.2.6.4-PEEK………………………………………………………..190

5.2.6.5-PBT……………………………………………………….…193

5.2.6.6-PET……………………………………………………….....195

5.2.7-Reversing melting relaxation………………………………………197

5.2.7.1-PEO…………………….……………………………………197

5.2.7.2-PEEK…………………………………………………….….200

5.2.7.3-PBT…………………………….……………………………201

5.2.7.4-PET……………………………….…………………………202

5.2.7.5-PTT………………………………….………………………203

5.2.8-Morpholological studies concerning α-relaxation………………204

5.2.8.1-PEEK………………………………….…………………….205

5.2.8.2-PBT……………………………………….………………....207

5.2.8.3-PET………………………………………….……………....208

5.2.8.4-PTT…………………………………………….…………....209

5.2.8.5-sPP………………………………………………….……..…211

5.2.8.6-PHB……………………………………………………...…..212

5.2.8.7-PHB-co-HV copolymer……………………………...…..…214

5.2.8.8-PHB/PCL blend…………………………………..…………219

5.B- Dielectric Studies………………………………………….……………230

5.3- Dielectric Spectroscopy Measurements…………….………………….231 5.3.1-Phase transition study of PHB……………………………………..231

5.3.2-Dielectric constant study of PHB and its copolymers……………233

5.3.2.1-Frequency dependence ……..…….……………………….233

5.3.2.2-Temperature dependence ……..………………………..…236

5.3.3-Dielectric loss studies of PHB and its copolymers………………..239

5.3.3.1-Frequency dependence ……..……………………………..239

5.3.3.2-Temperature dependence ……..…………………………..253

5.3.4-Dielectric loss tangent studies of PHB and its copolymers……....256

5.3.4.1-Frequency dependence ……..……………………………..256

5.3.4.2-Temerature dependence ……..……………………………259

Conclusion ……………………………………………………….…………………………… 262

References…………………………………………………………………….………………….267

Arabic Abstract

X

Acknowledgements

XI

Acknowledgements

This work was done under the Channel system between Mansoura

University, Faculty of Science, Physics Department, Polymer group, Mansoura,

Egypt and Rostock University, Faculty of Natural Science and Mathematics,

Physics Department, Polymer group, Rostock, Germany and so I gratefully

thanks:

Prof. Dr. M. D. Migahed, Physics Dept., Faculty of Science, Mansoura

University for his suggestion of this point of research and his continuous help

and support during doing this work and his fruitfull discussions, revising the

work.

Many thanks to:

Prof Dr.C.Schick, Physics Dept Mathematik und nature Wissenschaft

Fakultät, Rostock University, Germany for his help and support during doing

the experimental part of this work in Germany in the frame of the channel

system and also for his useful discussions.

And also thanks:

Ass. Prof. M. T. Ahmed, Physics Dept., Faculty of Science, Mansoura

University for his help and support during the revision of this work in Mansoura

Egypt. Many thanks to Ass. Prof. Tarek Fahmy for his help during the revision

of this work.

I would like also to thank all the PhD students and PhD’s in the polymer

group, physics department, University of Rostock, Rostock, Germany for there

cooperation.

I would like to thank his wife for her support and general help during the

preparation of this work. Finally, the author would like to thank the Egyptian

Ministry of High Education for the financial support of his mission to Germany.

Alaa El-din El-kotp Abd Elkader Mohammed

XII

Abstract

XIII

Abstract

This thesis is devoted to study the Relaxation Phenomena in Polymers

and polymer blends. The relaxation phenomena are very important because it

plays an important role in the physical properties of the polymers. Two

techniques were used in this study, namely thermal analysis techniques and

dielectric spectroscopy technique, in order to study the Relaxation processes

observed in semi-crystalline polymers.

The polymers studied in this work was semi-crystalline; polymers,

copolymer, and one polymer blend. The studied polymers are; Polyethylene

oxide (PEO), Polypropylene (PP), Poly (3-hydroxybutarate) (PHB),

Poly(ethylene terephathalate)(PET), Poly(butylene terephathalate)(PBT),

Poly(trimethyle terephathalate) (PTT), Poly(ether ether ketone)(PEEK). Beside

these pure semi-crystalline polymers one polymer blend Poly (3-

hydroxybutarate)/Polycarbolactone (PHB/PCL) was studied. The studied

copolymers are: Poly (3-hydroxybutararic acid)-co-Poly (3-hydroxyvalric acid)

PHB-co-PHV 5%, Poly (3-hydroxybutararic acid)-co-Poly (3-hydroxyvalric

acid) PHB-co-PHV 8%, Poly(3-hydroxybutararic acid)-co-Poly(3-hydroxyvalric

acid) PHB-co-PHV 12%.

A semi-crystalline polymer consists of three fractions of different

mobility: rigid crystalline fraction (RCF), mobile amorphous fraction (MAF)

and rigid amorphous fraction (RAF).

In this study, three techniques were used to study the relaxation processes

in the semi-crystalline polymers.

The differential scanning calorimetry (DSC) was used in this study to

thermally characterize the semi-crystalline polymer samples and to find the most

suitable temperatures degrees to work with the TMDSC technique.

The Temperature modulated differential scanning calorimetry (TMDSC)

which was introduced in the filed of polymer science to study the polymer

XIV

crystallisation process. However, in this study, we use it for the study of

relaxation processes.

The experimental data obtained from the TMDSC technique was first

corrected using the base curve measurements, which gives an accurate

determination of the heat flow. Then the complex heat capacity was obtained

from the corrected experimental heat flow data using a program written for

MathCAD (6) linked to Origin (7) software. Further, the complex heat capacity

was corrected using the melt data from ATHAS database, which gives an

accurate determination of the complex heat capacity.

In this study using the TMDSC technique to obtain the complex heat

capacity spectroscopy for the studied polymers in different temperature regions,

we were able to study the relaxation processes take place in the semi-crystalline

polymers.

In this study using the TMDSC technique, we be able to show that the

studied semi-crystalline polymers consists of three phases: rigid crystalline

phase or fraction (RCF), mobile amorphous phase or fraction (MAF) and rigid

amorphous phase or fraction (RAF). Therefore, the three-phase model is

applicable than the two-phase model.

The relaxation of the rigid amorphous fraction (RAF) that found in the

samples which is a rigid amorphous fraction relaxed above the glass transition

temperature of the semi-crystalline polymers was studied in details. The results

of the TMDSC technique also shows that how do the rigid amorphous fraction

formed in the crystalline polymers and how it “relaxes” again above the glass

transition (i.e., to change from glassy state to rubber state.) of these polymers.

These results also give us quantitative analysis of different components formed

in the crystalline polymers. In addition, the newly discovered relaxation process

called ‘Reversing melting relaxation’ was studied in the semi-crystalline

polymers in this study.

XV

Finally the results of the TMDSC technique indicate that the complex heat

capacity spectroscopy is very useful to investigate the different relaxation

processes take place in the semi-crystalline polymers.

In addition, the dielectric spectroscopy technique was used in the thesis to

study the dielectric relaxation in the PHB polymer and its copolymer (PHB-co-

HV), which was a very new study for this copolymer.

Using the dielectric technique the experimental results of the dielectric

loss (ε``) frequency dependence data was obtained and analyzed in the frame of

Havriliak Negami model to obtain the HN-fitting parameters.

In addition, the dielectric loss tangent (tan δ) frequency and temperature

dependence and the dielectric constant frequency and temperature dependence

were obtained too.

The dielectric results obtained for the pure PHB and its copolymers show

that there are two relaxation processes, the first is the glass transition relaxation

(α) which can be described by Vogel-Fulsher-Tamman (VFT) equation and the

second is a relaxation process (α*) take place in the free intercrystalline or

amorphous regions and can be described by the Arrhenius equation. Both

relaxation processes were analysed in the study and relaxation parameters were

calculated using the fitting by these two equations for the experimental data of

the relaxation map.

Finally the results of the TMDSC and dielectric spectroscopy techniques

indicate how is the relaxation in the semi-crystalline polymers is more complex

than the relaxation in the amorphous polymers.

XVI

جامعــه المنصوره آليه العـلـــــــــــوم قســــم الفيزيـــــاء

في دراسه ظاهره اإلسترخاء بعض البلمرات و مخاليطها

:مقدمه من

عالءالدين القطب عبدالقادر محمد

المدرس المساعد بالقسم الفيزياء/ للحصول على درجه دآتور الفلسفه في العلوم

)هالفيزياء التجريبي(

2002

المشرفون

:عنوان البحث

دراسه ظاهره اإلسترخاء في بعض البلمرات و مخاليطها

:إسم الباحث

عالءالدين القطب عبدالقادر محمد

الوظيفه اإلسمم أستاذ الفيزياء التجريبيه بقسم الفيزياء بجامعه المنصوره مصطفى دياب مجاهد 1ألمانيا -طبيقيه بقسم الفيزياء بجامعه روستوكأستاذ الفيزياء الت آريستوف شيك 2 أستاذمساعد بقسم الفيزياء بجامعه المنصوره مصطفى توفيق 3

تقرير الممتحنون

:عنوان البحث

دراسه ظاهره اإلسترخاء في بعض البلمرات و مخاليطها

:إسم الباحث

لقادر محمدعالءالدين القطب عبدا

الوظيفه اإلسمم1 2 3

تاريخ المناقشه تقديرالرساله

توقيعات لجنه الحكم

التوقيع اإلسمم1 2 3

الملخص العربي

الملخص العربي

داخل بعض البلمرات المتبلره باإلضافه الى تهدف هذه الرساله الى دراسه ظاهره اإلسترخاء التي تحدث

.بعض مخاليطها

وتنبع اهميه . و البلمرات هي مواد حديثه متعدده الخواص الفيزيقيه ولذلك تدخل في تطبيقات مختلفه

البلمرات من أنها مواد يمكن أن تخلق داخل المعمل وفي الصناعه بحيث يكون لها صفات محدده ومطلوبه

.لتطبيق بعينه

ره اإلسترخاء التي تهتم بها الدراسه تعد من الظواهر الفيزيقيه الكالسيكيه التي اهتم الفيزيقيون وظاه

ولكن الى االن لم يتم . بدراستها منذ زمن طويل بهدف الوقوف علىأسبابها والقوانين التى تحكمها

عيه تصف الظاهره الوصول الىمثل هذه القوانين ولكن ماتم التوصل اليه حتى االن هو مجرد قوانين فر

.في حاالت خاصه

وتنبع أهميه هذه الظاهره من انها تتحكم في جميع الخواص الفيزيقيه ليس للبلمرات فحسب بل لجميع

.المواد

ولقد تم خالل الدراسه دراسه البلمرات المتبلره التاليه؛ البولي إثيلين، وأآسيد البولي إثيلين، البولي

لين، ترفاثاالت البولي بيوتيلين، ترفاثاالت البولي ترمثيل، البولي إيثر إيثر بروبيلين، ترفاثاالت البولي إث

بولي (هذا باإلضافه الى مخلوطالبلمرات . آيتون، وبولي هيدروآسيدالبيوتارات

وثنائ البلمره بولي هيدروآسيدالبيوتارات مع هيدروآسيد ) بولي آربون االآتون/هيدروآسيدالبيوتارات

%.12، %8، %5وآسيد الفلريك الفلريك بنسب هيدر

:ولقداستخدم في هذه الدراسه ثالثه تقنيات هي

Uأوًال:

Uتقنيه المسح الحراري التفاضلي:

تم إستخدام هذه التقنيه في تعين الخواص الحراريه للبلمرات المتبلره هذه الخواص هي درجه الحراره

حول هذه البلمرات من الحاله الصلبه المتزججه و درجه الحراره التى يتم عندها تTcالتى يتم عندها التبلر

آماتمت . Tmelt باإلضافه الى درجه الحراره التي يتم عندها إنصهارهذه المواد Tgالى الحاله المطاطيه

وقدتم إستخدام . دراسه المدى الحراري الذي يتم فيه حدوث ظواهر اإلسترخاء الحراري داخل هذه المواد

يههذه التقنيه آدراسه تمهيد

Uثانيًا:

Uتقنيه المسح الحراري التفاضلي ذوالترددالحراري:

هذه التقنيه هي تقنيه جديده في مجال القياسات الفيزيقه فقد أدخلت الى مجال القياسات الحراريه عام

وقدأستخدمت هذه التقنيه لدراسه اإلسترخاء الحراري داخل هذه ". ريدنج" بواسطه البروفسير1993

.رهالبلمرات المتبل

وتختلف هذه التقنيه عن تقنيه المسح الحراري التفاضلي في أنه يتم تطبيق تردد حراري على العينه محل

.الدراسه ولذلك يحدث تفاعل بين الماده وهذه الحراره المتردده ويتم قياس الفيض الحراري المتردد

من ثالثه أطوار وهي الطور أآدت الدراسه بواسطه هاتان التقنياتان على أن البلمرات المتبلره تتكون

. المتبلر، الطورالغيرمتبلرالمتحرك، والطورالغيرمتبلر الثابت

.الطورالغيرمتبلر الثابت آشفت عنه األبحاث الحديثه وعن دوره في الخصائص الفيزقيه لهذه المواد

البلمرات ولقد تم خالل هذه الدراسه دراسه ظاهره اإلسترخاء الحراري التي تحدث لهذا الطور داخل

المتبلره والتي تحدث في مدى من درجات الحراره أعلى من درجه الحراره التى يتم عندها تحول هذه

Tgالبلمرات من الحاله الصلبه المتزججه الى الحاله المطاطيه

آما تم خالل الدراسه دراسه ظاهره اإلسترخاءالترآيبي التي تحدث اثناء تكون هذا الطور وهي دراسه

. ولي من نوعهاتعد األ

آما تم دراسه ظاهره اإلسترخاء الحراري التي تعد من أحدث ظواهر اإلسترخاء التي اآتشفت عام

والتي تحدث نتيجه لالنصهار العكسي الذي يحدث " إسترخاء اإلنصهار العكسي" والتي تسمى 1997

. الحراري الذي تحدث فيه هذه الظاهرهفلقدتم بواسطه هذه الدراسه تحديد المدى. داخل البلمرات المتبلره

Uثالثا:

Uتقنيه طيف ثنائ القطبيه الكهربيه:

وقدتم إستخدامه في دراسه إسترخاء ثنائ القطبيه الذي يحدث داخل البوليمر المشارك بولي

وقد تم %. 12، %8، %5هيدروآسيدالبيوتارات مع هيدروآسيد الفلريك بنسب هيدروآسيد الفلريك

ه دراسه إسترخاء ثنائ القطبيه الذي يحدث في مدى حراري حول درجه الحراره التى يتم خالل الدراس

ولقد تم ذلك عن طريق . Tgعندها تحول هذه البلمرات من الحاله الصلبه المتزججه الى الحاله المطاطيه

ليل نتائج فقد وأيضا تم تح). 'ε(وأيضا دراسه ثابت ثنائ الكهربيه) ˝ε(دراسه بارامتر فقد ثنائ الكهربيه

وقد أدت الدراسه .للحصول على بارامترات اإلنطباق" نيجامي–هافريليك "ثنائي الكهربيه بواسطه نموذج

.الى الكشف عن عمليات اإلسترخاء ثنائ القطبيه الذي يحدث داخل البوليمر المشارك

Chapter 1 Introduction and Aim of the

work

Introduction and Aim of the Work: 1.1-Introduction:

Polymers are large class of materials and they consist of a large number of

small molecules called “monomers” that can be linked together to form a very

long chain. Thus they can be called “huge molecules” or “Macromolecules “ the

word comes from the origin 'makros', which mean large and 'molecula' which

mean small mass.

Relaxation is a classical phenomena and it is about a process by which the

system goes from non-equilibrium state to equilibrium state. Relaxation

processes have different names according to their origin thus we have thermal

relaxation, dielectric relaxation or dipole relaxation and structural relaxation.

The study of relaxation processes in semi-crystalline polymers is a subject

of continuing great scientific and technological interest. A great number of

investigations have been undertaking with the purpose of characterizing the

relaxations in these materials and there has been great scientific interest in the

detailed description of the molecular processes underlying them. Molecular

interpretation of the relaxation processes is slow and conflicting that even if it is

the same process the molecular interpretation may differ. In the past view years

there have been a number of development, which clarify the nature of many of

the relaxation phenomena.

In semi-crystalline polymers in the range between liquid nitrogen

temperature (77K) and melting temperature often three or at least two processes

are commonly observed α, β, and γ or β, and (αa) in some semi-crystalline

polymers which do not show α process. Each of these processes has distinct

characteristics.

In a semi-crystalline polymer, which shows all the three processes, α-

process, which is a high temperature relaxation process, is commonly considered

2

to be connected to the amorphous phase and associated with the glass-rubber

relaxation. The β- process in such a polymer has been connected also to the

amorphous phase. The γ- processes (or β in the crystalline polymers which do

not show α- process) it is generally agreed that it has an amorphous phase

origin, but many studies consider it as it have component from a crystalline

phase. The relaxation processes studies in semi-crystalline polymers show that

these three relaxation processes (α, β, and γ) are in order of decreasing

temperature.

The mechanism of the first process known as “α-process” is related to the

main chain motions and it observed around glass transition temperature. In

addition, its intensity is increasing by increasing the degree of crystallinity. The

second process is the β-process, which related to the movement of the side

group chains or branches and it related to the amorphous regions the third

process is the γ-process, which is related to the local intermolecular relaxation at

a temperature below Tg .

3

1.2-Aim of the work: This study is concerned with polymer science in the branch of polymer

physics, it deals with semi-crystalline polymers, and their blends and

copolymers in order to study relaxation processes occur above the glass

transition region and below the melting region. These polymers were chosen for

this work to provide a complex system in which there are three different

fractions, with different kinds of mobility.

Two kinds of calorimetry were used, which is differential scanning

calorimetry (DSC), and temperature-modulated differential scanning calorimetry

(TMDSC) techniques.

Beside these techniques the Dielectric spectroscopy (DS) technique was used

in this study, which is known in the field of material physics.

This study aims to carry out investigations on the relaxation processes occur

above the glass transition region and below the melting region of the semi

crystalline polymers, copolymers and blends of the semi crystalline polymers

using these three techniques.

4

Chapter 2

Theoretical Background

2.1- Polymeric Materials: 2.1.1 General concepts:

According to the main atom in the chain, if the polymer chain is consists

of carbon atom only it called “homochain polymer” such as, polymeric sulfer

[S]n, and if it has different atoms in the main chain it is called “heterochain

polymers” such as, polyesters [OxCO]n

According to the presence of the carbon atom in the main chain, the

polymer is called “organic polymer” and if the atom is not carbon the polymer is

called “inorganic polymer”.

If the polymer contains branches connected to the sides of the main chain

it called “branched polymer”, see the figure (2.1) below.

Figure 2.1: Kinds of branched polymers (1).

Branched polymers divided into four kinds; star branched polymer, comb

branched polymer, tree-like branched polymer, and dindrimer polymer.

According to the two-dimension configuration polymers can be divided

into, “cis” polymers, and “trans” polymers. Cis polymer and trans polymer can

have the same molecular formula but not the same two-dimension configuration,

see the figure (2.2).

6

cis configuration trans configuration Figure 2.2: Cis and trans configuration both molecules have the same molecular

formula (BrCHCHBr).

According to the relative configuration around the center chain, in other

words the stereo regularity, polymers can divide into two categories isotactic

and syndiotactic

Isotactic Syndiotactic

Figure 2.3: The isotactic and syndiotactic configurations.

The classifications isotactic and syndiotactic are based on the direction in

which the same molecules are found see the figure (2.3). In isotactic polymer the

same molecule is found in the same direction but in the syndiotactic polymers

the molecule change it is position periodically.

7

2.1.2- Polymer assemblies (1*):

Assemblies of polymers may exist in the solid state in two ideal types of

assemblies. In ideal polymer crystals, macromolecules or their segments are

completely ordered. The long-range crystalline order is destroyed if a crystalline

polymer heated above its melting temperature. The resulting melt is a fluid and

in ideal case completely disordered with respect to the arrangement of polymer

segment and molecules.

Polymer molecules and segments, which completely disordered in the

solid state they are said to be amorphous. Such amorphous material resembles

silicate glass. On heating, the glass-like structure of an amorphous material is

removed to a certain temperature, the glass transition temperature. Shortly above

the glass transition temperature, high molar mass amorphous polymers resemble

chemically cross-linked rubbers whereas low molar mass polymers behave more

like liquids. The fluid state of mater is often called a “melt“, regardless of

whether it was produced by heating a crystalline polymer above its melting

temperature or by heating an amorphous polymer above its glass transition

temperature.

Crystalline and amorphous arrangements are ideal structures and their

behavior as solids or fluids constitutes ideal states. There are also arrangements

of polymer assemblies that show order similar to crystals and, at the same time,

fluidity like liquids. These materials are (in the middle) between crystals with

long-range order and liquids without any long-range order; they are therefore

called “mesomorphous”. Their most prominent representative is a liquid-

crystalline polymer that show one-dimensional (crystalline) order yet flow like

liquids in their “melts” or solutions. Other mesomorphic materials comprise

block copolymers and ionomers.

* This article was based on this reference with some modifications by the author.

8

2.1.3- Melt state of polymers (1*):

X-ray measurements of polymers melts indicate the absence of long-range

order. Small angle neutron scattering, on the other hand shows that the radius of

gyration of linear polymer molecules in melts is identical with that of polymer

coils in the unperturbed state. Since the segments density of isolated coils

decrease with increasing molar mass but the macroscopic density of melts of

true polymers does not, it follows that polymer molecules must overlap in melts.

Segments of polymer molecules are surrounded in melts by segments of the

same type. A segment cannot distinguish, however, whether an adjacent

segment is part of the same or another molecules. Polymer chains in melt thus

exhibit the same reduced radii of gyration.

Physical structures of polymers are frozen-in if melts are quenched below

their glass transition temperatures. Glassy polymers thus exhibit the same

unperturbed dimensions. Since the distribution of segments is completely at

random in the unperturbed state, it follows that neither melts nor glasses possess

long-range order. An absence of long-range order does not exclude short-range

order, however, the persistence of chains will cause short chain to pack parallel.

This local order does not exceed 1nm.

Viscosities rise from (102 -106 Pa s) in melts to ca (1012 Pa s) in glassy state,

which reduces the mobility of segments quite severely. Chains cannot pack

tightly as they would like since they have same persistence and segments are not

infinitely thin.

The polymer glass thus has same vacant sites; the density of the amorphous

polymers in the glassy state is smaller than the density of the melt. An example

is poly (methylmethacrylate)(PMMA); ρ=1.19 g/mL (glass) and ρ=1.22 g/mL

(melt).

Vacant sites are regions with the size of atoms and they generate in the glassy

polymer a free volume. * This article was based on this reference with some modifications by the author.

9

The volume fraction of the free volume can be calculate as:

φf=(νg-νm)/νg (2.1)

From the specific volumes of the glass (νg ) and the melt (νm ). At the glass

temperature, the fraction of free volume has been found as (φf) ≈0.025 for all

polymers.

2.1.4- Semi-crystalline polymers (1*):

The meaning of the word “crystal“ changed several times during the last

century. In the mid 1800´s, it denoted a material with plane surface that

intersected each other at constant angles.

At the end of 1800´s, a crystal was defined as a homogenous, an isotropic,

solid material. It is “homogenous” because physical properties do not change on

translation in the direction of crystal axis, “an isotropic” because physical

properties differ in various directions and solid because it resists deformation.

In 1900´s, crystal was redefined as materials with three-dimensional

order in a three-dimensional lattice with atomic dimension of lattice sites. For

example, Carbon atoms in Diamond occupy such lattice sites and methylene

groups in poly (methylene) [CH2]n. Perfect lattice are called “ideal”. Lattice sites

may also be taken up by larger spherical entities. Lattice with large tightly

packed spherical entities are called “superlatices”. Lattices with large spherical

domains of polymer blocks that are separated by amorphous matrices are not

considered superlatices but rather mesophases. Three-dimension lattices are

composed of smaller units whose Three-dimension repetition generates the

crystal. These units are called “unit cells”; they are the simplest parallelepipeds

that can be given with lattice sites as corners. See figure (2.4).


10

Figure 2.4: The unit cells in the crystalline polymers

All chain units must occupy crystallographic equivalent positions in ideal lattice

of chain molecules.

On crystallisation some chains units may not find their ideal positions,

however, because of the high viscosity of the melt and the fact that chain units

are dependent of each other but rather parts of the chain. The crystallised may

thus contain lattice defects or even only small crystallites besides non-crystalline

regions. Such crystallised polymers are called “semi-crystalline”. Truly, 100%

crystalline polymer is very rare. Semi-crystalline polymers are not in

thermodynamic equilibrium. Crystalline and non-crystalline regions must

therefore be interconnected: any single macromolecule passes through both

phases. The two phases of semi-crystalline polymers are therefore not separate

entities; they cannot be separated by physical means. In the crystalline or semi-

crystalline polymers, one has to distinguish between crystallisability and

crystallinity.

Crystallisability denotes the maximum theoretical crystallinity; this

thermodynamic quantity depends only on temperature and pressure.

Crystallinity is affected by kinetics and thus crystallisation conditions (i.e.,

nucleation, cooling time, etc.). It includes frozen-in non-equilibrium states and it

is always lower than the crystallisability. X-ray crystallography is the most

important method for the determination of crystal structure and crystallinity.

Most semi-crystalline polymers are however polycrystalline. Lattice layers are

ordered in each crystallite but the crystallites themselves are not. The many

small crystallites with their multitude of orientations of layer generate a system

of coaxial cones with a common tip in the centre of the sample.

11

X-ray diffractograms of semi-crystalline polymers show weak rings and a

background scattering besides the strong crystalline reflections. (See the figure

(2.5))

Semi-crystalline Amorphous Figure 2.5: The x-ray diffractogram of semi-crystalline and amorphous polymers. (1)

Weak rings are called “halos”; they are caused by short range ordering of

segments. The background scattering of polymers is always relatively strong; it

originates primarily from scattering by air and secondarily from thermal motions

in crystallites as well as from the Compton scattering.

Semi-crystalline polymers can thus have various degrees of crystallinity

and different morphologies depending on the cooling conditions for melts or

solutions. Degrees of crystallinity are usually calculated using the two-phase

model which assumes that perfect crystalline domain exist besides totally

disordered regions. The degree of crystallinity of a polymer is not an absolute

quantity since the border between crystalline and amorphous regions is not

sharp. Different experimental methods measure different degrees of order and

thus different “average” crystallinities. Degree of crystallinity can be further

calculated as mass fractions wc or volume fractions фc. They can be

interconverted by wc = фc ρc /ρ with the densities of the specimen (ρ) and 100%

crystalline polymer (ρc).

Crystallinity can be calculated using different experimental techniques as

follows:

12

Density crystallinity

)()(

,acp

apcdcw

ρρρρρρ

−

−= (2.2)

where, ρc is the density for ideal crystalline polymer, ρa is the density for the

completely amorphous .

X-ray crystallinity

)(,aac

cxc IKI

Iw

+= (2.3)

where, Ic ,Ia are the integrated intensities, Ka is a calibration factor.

Infrared crystallinity

)(log)( 10, II

Law ocic ρ= (2.4)

where, L is the thickness of the sample, Io,I are the incident and transmitted

beam at the frequency of absorption band and the absorpitivity ac of the

crystalline part.

Calorimetric crystallinity

cM

Mc h

hw

,∆∆

= (2.5)

where, ∆hM ∆hM,c are the melting enthalpies of the measured and for 100%

crystalline sample.

13

2.1.5- Polymer blends (1*):

Blending is a method of obtaining new polymer materials. Blending is

simply mixing of two polymers. A mixture of two polymers called “polymer

blend”, “polyblends”, or simply “blends”. They are prepared to improve the

property of the blend as well as to reduce the costs. Homogeneous blends are

true (molecular mixtures of two different polymers. Heterogeneous blends are

thermodynamically immiscible in the concentration range.

Hence polymer blends are homogeneous or heterogeneous mixtures of

two chemically different polymers. Some blends are prepared for economical

reasons others made to improve some property in the blend. About 10% of all

thermoplastics and 75% of all elastomers are polyblends.

Only a few commercials blends of two thermoplastics are single-phase

blends. All single-phase blends possess negative or slightly positive interaction

parameters. They are amorphous blends; their glass temperature varies

monotonically with composition. Blends can be compatible but not

thermodynamically miscible. Many blends made from amorphous and semi-

crystalline polymers. Most of these blends are compatible. Blends of two semi-

crystalline polymers are rarely used. Component of these blends are usually very

similar structure.


14

2.2-Structural Transitions in Polymers: 2.2.1-Polymer crystallization (1*):

Polymer crystallization is controlled by the micro formation of

macromolecules. Spheres arrange themselves in superlatices, for example,

spherical enzymes or latex particles. Rigid molecules with high aspects ratios

form parallel rods. Flexible molecules fold to micro lamellae and sphieriolits,

depending on crystallization conditions crystallization are initialed by nuclei

with concentrations between ca.1 nucleus per cm3 [poly (oxyethylene)] and 1012

nuclei per cm3 [poly(ethylene)]. Polymer crystallization takes place by a

mechanism called “nucleation” which is divided into two mechanisms:

(a)-Homogenous nucleation:

In the very rare homogenous nucleation, thermal activated motion causes

molecules and segments of the crystallizing polymer to cluster spontaneously

and to form unstable embryos which develop into stable nuclei up further

growth the nucleation is sporadic since nuclei are formed one after the other.

It is also “primary” (i.e., three-dimensional because surfaces of nuclei are

increased by addition of molecule segments in all three-spatial directions) see

figure (2.6).

Figure 2.6: Primary (P), Secondary (S) and tertiary (T) nucleation.


15

(b)-Heterogeneous nucleation:

Heterogeneous nucleation which is a thermal; they involve extraneous

nuclei with the diameters of at least (2-10) nm. Nuclei may be dust particles

deliberately added nucleating agents or even consist of residual nuclei of the

polymer. Melting of polymers with broad melting ranges may leave some higher

melting crystallites intact and it is these crystallites that may act as nuclei on

subsequent cooling and crystallization. Residual nuclei are also responsible for

the “memory effect” of polymer melts. Spheriolites appear on cooling of melts

at the same spots they occupied before the melting since residual nuclei where

unable to diffuse away because of high melts viscosities. Chain segments add to

surfaces of polymer nuclei in secondary nucleation and most likely to corners

and furrows of nucleating agents in tertiary nucleation. Secondary nucleation

and super cooling of the melt control chain folding and lamellae heights, see

figure (2.7).

Figure 2.7: The adding of long chain to side plane lamellae. If a chain segment of variable length Lc is added to a nucleus, the crystallites

surfaces are enlarged by the contribution 2 Lc Ld from the two side planes and

the contribution 2 Ld Lb from the two (ebd) planes. The gain of Gibbs energy by

creation of new surfaces is counteracted by a loss of Gibbs energy ∆Gcryst per

unit volume.

16

One obtains for the first segments on the surface:

∆Gi =2 Lb Ld σf+ 2 Lc Ld σs – Lc Lb Ld ∆Gcryst (2.6) Differentiating this equation with respect to Lb and equating the results with zero

delivers the critical (minimal) height Lc,0 =2 σe/ ∆Gcryst. At which the Gibbs

energy of crystallization just balances the formation an end surface, (i.e. the

addition of the first segment).

Since the change of the Gibbs energy is zero for such an addition, a nucleus thin

size can never become stable. For the nucleus to grow a stable crystal, Gibbs

energies have to be slightly negative and fold heights thus slightly larger than

Lc,0 . This additional length ∆L will be ignored.

Since the Gibbs energy of crystallization per unit volume of an extended

chain is given by ∆Gcryst = ∆HM,o – Tcryst ∆SM,o and a crystal composed of such

chain has a melting temperature of TM,o = ∆HM,o/ ∆SM,o one obtains:

)(

2

,,

,,

crystoMoM

oMeoc TTH

TL

−∆=

σ (2.7)

The critical theoretical lamellae height thus decreases with increasing super

cooling (TM,o-Tcryst.) which is confirmed by experiment.

Crystallization rate (1*):

Embryos require a critical size before they become stable nuclei and then

crystallites. At the melting temperature TM, crystallites are dissolved and the

crystallization rate is thus zero. Nuclei and crystallites can also not grow at

temperatures below the glass temperature Tg since the high viscosity prevents

the diffusion of chain segments to crystallites. The crystallization rate must

therefore run through a maximum with increasing temperature. This maximum

is found experimentally at Tcryst,max ≈(0.80-0.87) TM,o (in K) where TM,o =

melting temperature of perfect crystals.


17

Crystallization can be subdivided into a primary and secondary stage. At

the end of primary crystallization, the whole volume of the vessel is

microscopically completely filled with crystalline entities, e.g., spherulites

figure (2.8)

Figure 2.8: Schematic diagram for spherulites lamellae structures.

2.2.2-Polymer melting (1*):

Increasing vibration of the atoms on heating causes crystal lattice of linear

macromolecules to expand perpendicular to chain axes. For example, the lattice

constant (b) of poly (ethylene) enlarges by ca. 7% between 77 K and 411 K.

Monomeric units are more and more dynamically disordered around their ideal

positions at rest; even crystal defects may occur. Disorder is especially great at

the surfaces, edges and corners of crystallites at which the melting process starts.

The number of chain units involved in the melting process has been estimated as

60 to 160 from the ratio of molar activation energy to molar enthalpy (both per

mole chain unit)

Crystals of low molar mass compounds are relatively perfect. For example

crystal of C44H90 melt at Tmelt = 359 K within a temperature interval of ∆T=0.25

K. The larger chain of C94H190 crystallizes that perfectly; due to defects, some

segments are therefore somewhat more mobile in the lattice. As consequence, * This article was based on this reference with some modifications by the author.

18

segments are constantly redistributed between crystalline and non-crystalline

regions on heating and the melting of C94H190 starts at ca. 383 K and finishes at

ca. 387.6 K (∆T=3.6 K). The imperfect crystal structure produces a melting

range. The largest and most perfect crystals melt at the high-temperature end of

this range. For low molar mass materials, this transition perfect crystal-melt is

relatively sharp; it constitutes the thermodynamic melting temperature of the

specimen. Chain folds, end groups, and branch points generate additional

defects. Polymers thus have broader melting regions than oligomres, especially

if molar mass distributions are broad. The jumps of specific volumes (v) or

enthalpies (H) at TM degenerate to S-shaped curves and the sharp signals for the

first derivatives (∂v/∂T)p =ßv and (∂H/∂T)p =cp , broaden to become bell curves.

The upper end of the melting range is no longer shape and the middle of the

melting range is therefore usually taken as the melting temperature TM. The

melting temperature TM of the specimen is usually smaller than the

thermodynamic melting temperature TM,o but it may also be larger if crystals are

overheated. Melting temperatures increase with increasing degree of

polymerization to a limiting value TM,∞. Melting temperatures of high molar

mass polymers are strongly affected by the constitution of polymer.

19

2.3-Relaxation Phenomena in Polymers: 2.3.1-Relaxation phenomena (Theoretical approach) (2*): If a system is brought into a non-equilibrium state Z [T,v,ξ(0)] and then

left to itself under the condition T, V=constant, it will with increasing time,

usually strive to achieve an internal equilibrium state Z [T,v,ξe(T,v)]. This

process is called “relaxation” . In order to describe such a relaxation process:

ξτ

ξ &&&Tv

1−= (2.8)

With ( ) ( ) ( )tTvet λξξ −= 0&& ( ) ∫′

≡t

TvTv

tdt0 τ

λ (2.9)

If the process should come to stand still at a time t =te after reaching the internal

equilibrium state,

+∞=→ )(lim tTvtt eλ (2.10)

must be valid.

If the attained equilibrium state is a stable or metastable state it follows that:

(2.11) 0)(lim >=→ Tve

Tvtt te

τλMoreover in the case of an ideal, non-singular continuous function τTv, te=+∞

can theoretically be expected according to equation (2.9).

The relaxation processes to be described by equations (2.8, 2.9) are

generally non-linear processes, as the characteristic time given by:

τTv =τTv[T,v, ,ξ(t)] (2.12)

depends on the instantaneous state of the system. However, if the initial state is

not too far from the final state, one can approximately assume according to

equation (2.11) that,

( ) .0>=≈ constt Tve

Tv ττ (2.13)

20* This article was based on this reference with some modifications by the author.

Equation (2.8) thus becomes a linear differential equation. The relaxation

process is then only determined by the data of the initial and the final state, in

particular by the time constant τeTv(T,v) which is determined by the final state.

If one inserts equation (2.13) into equation (2.8) one obtains as the first integral

of the differential equation

(2.14) ( ) ( ) Tvetet τξξ /0 −= &&

and the second integral

( ) ( )[ ] eTv

eett ξ

τξξξ +

−−= )exp(0 (2.15)

The initial rate of the process is given by:

( ) ( )[ ]eTv

e ξξτ

ξ −−= 010 (2.16)

With this, one can also replace equation (2.14) by:

( ) ( )[ ]eTv

e tt ξξτ

ξ −−=1&

(2.17)

The relaxation process becomes a monotonous exponential equilibration

process. Equation (2.17) has the form of a “decay law”, as is valid for many

“naturally” proceeding processes (i.e. occurring without external disturbance).

The constant τeTv is often designated as the Debye relaxation time.

In the neighborhood of the final state, the equation s of state can be

expanded in Taylor series and the series broken off after the linear terms. Under

the condition T, v =const., one can write for the equation s of state:

( )evT

eSSS ξξξ

−⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+=, (2.18)

( )evT

ePPP ξξξ

−⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+=, (2.19)

where, S is the entropy and P is the pressure of the system.

21

Further, the relaxation represent an attenuation process during which the

internal variable monotonously drops from the initial value ξ(0) >ξe to the

equilibrium value, ξe, . 0<ξ&

Moreover, if τTv >0, equation (2.8) necessarily results in . The

attenuation curve

0>ξ&&

( )tξ then always has, the exponential function equation (2.15),

a convex curvature versus the time axes. Due to the equation (2.11), such a

curvature is essential near the final state. With a larger distance from the final

state, on the other hand, τTv can definitely assume negative values.

If τTv <0 holds together with 0<ξ& at the beginning of the process, we get

. The monotonous attenuation curve is then first concavely curved versus

the time axes. According to equation (2.8) a singularity occurs with

following the relaxation from the concave curvature ( ) to the convex

curvature ( ).

0<ξ&&

0=ξ&& 0<ξ&&

0>ξ&&

With the 0<ξ& , either τTv =0, −∞=ξ& or τTv=±∞, .finit=ξ& is valid at this

point. Two simple examples are shown in figures (2.9, 2.10).

Figure 2.9: An example of the ( )tξ function; A: 0<τTv(0)< τe

Tv , B: τTv(0)<0< τeTv

and E: linear relaxation according to equation (2.17).

22

Figure 2.10: Another example of the ( )tξ function; E: linear relaxation equation (2.17), NL: non-linear relaxation according to equation (2.21). If the entropic part predominates in the free energy, one can expect a

proportionality f~lnξ which leads to Tv~ξ2. With the formulation

(2.20) ( )[ ] 0., 22

2 >=−< constt ee

Tv τξξττ

Two cases must be distinguished: If ( )[ ]22 ee

Tv t ξξττ −< is valid,

τeTv>τTv>0 always holds for all ( )tξ > eξ . The attenuation curve, like the

exponential curve, is convexly curved versus the time axis.

Relaxation, however, occurs –especially in the first process intervals- faster than

in an exponential relaxation figure (2.9,A). On the other hand if

is valid, the process starts with τ( )[ 22 0 e

eTv ξξττ −< ] Tv <0. The attenuation

curve is at first concavely curved versus the time axis.

τTv =0 and result during the relaxation from the concave curvature to the

convex curvature figure (2.9,B). A singularity of the second case, for example,

occurs if

−∞=ξ&

)(,)(

1 oses

oTv ξξξξξ

τττ <<−

−= (2.21)

holds. In order to fulfill the conditions (2.12)

23

)(1

es

eTvo ξξ

τττ−

−= (2.22)

must be valid, so that it follows that

)()(

1e

eeTvTv ξξ

ξξτττ−−′−=

es ξξττ−

≡′ 11 (2.23)

See figure (2.10). 2.3.2-Relaxation types in polymers (4*):

A polymer may exist in a solid state (amorphous and crystalline, usually

mixed) in a viscoelastic fluid (rubber) and in a viscous fluid state. In some

polymers, e.g. in cross-linked resins, there are no viscoelastic and viscous fluid

states; the polymer does not melt at all. Polymers do not exist in the gaseous

state because they would decompose before evaporation. Polymers usually form

very poor crystals. Although it is possible to grow single crystals of many

polymers, their x-ray diffraction spectra always show the existence of a

considerable amorphous background. A real polymeric solid is usually a mixture

of crystalline and amorphous phases (i.e. its physical structure is

heterogeneous). Even in purely amorphous polymers, structural heterogeneous

has been discovered by electron microscopy and by the electron diffraction

technique (9). Polymer molecules are found to form aggregates of different forms

and size depending on the preparation and on the thermal history of the material.

This aggregate structure is also referred to as super molecular structure (10). Even

in the fluid state and in solution, aggregate structure is often found to be present.

Structural inhomogeneties in polymeric materials are formed as a consequence

of the difference of the thermodynamic behavior of macromolecules with

respect to that of small molecules. Statistical thermodynamics of polymeric


25

systems, especially of solution has been discussed in detailed by Flory (11) and

Volkenstein (12). From the peculiar thermodynamical behavior of

macromolecular systems it follows that they can exist in different crystal forms

or in different aggregate forms simultaneously. This phenomenon is known in

the physics of low-molecular-weight organic compounds as polymorphism. This

concept of polymorphism means that the system has a several states of different

configuration corresponding to approximately the same energy.

2.3.2.1-Structural relaxation (4*):

Structural relaxation can be discussed on the basis of the generalized concept

of polymorphism. Relaxation from one crystal form to another is evidently a

structural relaxation; it is often encountered in polymers. The crystalline melting

conversion is also simply regarded as structural relaxation in which the ordered

system becomes disordered or less ordered. It is possible, however, to regard the

relaxation from one aggregate form in an amorphous polymer into another as

structural relaxation because it involves large-scale rearrangement of the

structure. Such a relaxation is the glass-rubber relaxation in amorphous

polymers when the rigid glass, which has a specific super molecular structure, is

transformed to viscoelastic fluid state, which has another. A peculiarity of the

glass relaxation is that it strongly depends on the direction and speed of the

temperature variation. The disappearance of the aggregate structure observed

well above the glass-rubber relaxation is also regarded as a structural relaxation;

it is from this point of view similar to melting of semi-crystalline polymer: (i.e.

an order-disorder process). Structural relaxations will be considered here as

being characterized by the following macroscopic feature:


(a) The specific volume of the material changes abruptly at the relaxation.

This is observed by measuring the thermal dilatation at constant pressure

as a function of the temperature (13).

(b) Differential calorimetry shows enthalpy change at the relaxation (14). This

can also be explained on the basis of extension of polymorphism to

amorphous systems.

(c) The temperature depends of the mechanical or dielectric relaxation time

can not be described by simple Arrhenius equation ( ( ) ⎟⎠⎞

⎜⎝⎛=

KTEt o expττ ) as

the activation energy (enthalpy) is not constant. This means by plotting

the logarithm of the relaxation terms against reciprocal frequency no

straight line is obtained.

(d) The oscillator strength of the dielectric spectrum band (εo-ε∞) correspond

to dipoles attached to the main chain is increases as a function of the

temperature to reach a maximum value above Tg (15); the 1/T dependence

which would follow from the Kirkwood-Frölich equation;

22

32

34

23

orr

o

oo g

KTN µεπ

εεεεε ⎟

⎠⎞

⎜⎝⎛ +

+=− ∞

∞∞ (2.24)

(Where, Nr is the concentration of the repeated units, µo is the dipole moment,

(gr) is the Kirkwood equilibrium factor) is not obeyed. The reason is that the

units, which behave as rigid configurations during thermal motion, change at the

relaxation, resulting in changes in the effective dipole moment concentration.

(e) Structural relaxations are especially sensitive to the thermal

pretreatments.

26

2.3.2.2-Local motion relaxations (4*): Besides structural relaxations in polymers, relaxations may occur which

do not involve large-scale structural rearrangement; just the local motion of

some parts of the molecule is changed. Such a relaxation is, for example,

liberation (i.e., freezing of the rotation of side group is evidently different from

that of the main chain) they represent a separate subsystem in the sense of

statistical thermodynamics. This implies that the system of the side group is

characterized by a specific partial temperature and specific relaxation time (i.e.,

distribution of the relaxation times). If the side group contains polar bonds,

freezing (i.e., liberation of this rotation) is represented by a significant change in

the dielectric permittivity ε′ and loss factor ε′′. The corresponding relaxation

process is some times referred to as dipole-group relaxation (16) it illustrated in

figure (2.11).

Figure 2.11: Two different local motion (a) side group rotation, (b) isomerisation. Another possibility of rotation of short segments without involving large-scale

rearrangement of the structure is the crankshaft-type rotation of groups in the

main chain (17). Such a motion is illustrated in figure (2.11). It is a

conformational isomerisation of the main chain segments with estimated

activation energy of 13 Kcal/mol for linear hydrocarbon polymers.

A local mode relaxation also results from vibrations of short chain

segments about their equilibrium positions. Such a motion is termed local mode

process (18).


28

The following main features characterize relaxation involving local

motion of group:

(a) The specific volume of the material is not significantly changed at the

relaxation; no abrupt change of thermal dilatation versus temperature is

observed.

(b) Differential calorimetry shows no significant enthalpy change; only

changes of specific heat may be detected at such relaxations.

(c) The temperature dependence of the mechanical and dielectric relaxation

time is satisfactorily described by Arrhenius equilibrium; it is possible to

define a temperature-independent activation energy (enthalpy) for the

process.

(d) The oscillator strength of the dielectric spectrum band εο-ε∞ is

monotonous function of the temperature; at the relaxation, no maximum

is exhibited.

(e) Relaxations involving local motion are not very sensitive to thermal

pretreatments.

This specification of the relaxations in polymeric systems into main groups is

evidently not strict one. The local motion of the chain might involve some

structural rearrangement and, on the other hand, in some cases the structural

relaxation might run parallel with local motion. According to a large body of

experimental evidence (4,19) however, the relaxations involving local motion

are well separated from the structural relaxations. Correspondingly, side

group or short-chain segments can be treated as individual thermodynamic

subsystems. The situation is somewhat similar to the problem of nuclear and

electronic spin relaxation. The nuclear or electronic spin systems are

regarded as separate assemblies exhibiting their own partial temperatures,

which are quite different from that of the lattice. In real polymeric systems,

one should consider a series of assemblies formed by identical units of the

structure. Each assembly has its own statistics and its own way of

establishing equilibrium with the surroundings (i.e., with the other

29

assemblies). Classification of the system into two parts is a simplification of

this general view based on the experimental evidence.

2.3.3-Relaxation in semi-crystalline polymers: There is no 100% crystalline polymer. Even in single polymer crystals

considerable amorphous background is found by x-ray diffraction method.

Correspondingly, by studying relaxation-involving change in molecular mobility

in semi-crystalline polymers, it is difficult to separate the motions occurring in

the amorphous phase from those of the crystalline phase (3).

Therefore, the crystalline polymers are always called ”semi-crystalline”

polymer. The semi-crystalline polymers considered as “composite structure”.

This composite structure consists of crystalline phase and amorphous phase.

2.3.3.1-Relaxation in semi-crystalline polymers as composite structure (4*):

There are typically three relaxation processes observed in semi-crystalline

polymers, named α, β, γ relaxations in order of decreasing temperature. The α

relaxation may involve crystalline regions, which is supported by the

experimental data that shows that its intensity increases with increasing degree

of crystallinity. The β relaxation is usually the glass relaxation in the amorphous

regions, which really correspond to α- relaxation in totally amorphous polymers.

The γ relaxation in crystalline polymers typically corresponds to the β

relaxation in the glassy polymers, the local intermolecular relaxation at well

below Tg.


30

2.3.3.2-Crystallization dynamics and relaxation in semi-crystalline

polymer (20*):

Semi-crystalline polymers can be categorized according to their

crystallinity and crystallization dynamics as follows:

(A)-Semi-crystalline polymers with slow crystallization dynamics:

These polymers can be quenched to obtain completely amorphous form.

They are difficult to crystallize beyond 50%, so they called “low crystallinity

polymers”. These polymers show no crystalline high temperature process but

they have an amorphous fraction glass-rubber relaxation process (αa). As an

example of these polymers are the isotactic polystyrene, and aromatic

polyesters.

(B)-Semi-crystalline polymers with medium crystallization dynamics:

These polymers cannot be quenched to obtain completely amorphous

form. They are crystallizing to (30-60%) but not higher. Therefore, they called

“medium crystallinity polymers”. These polymers show (αa) relaxation process

more than β relaxation process. As an example of these polymers are; aliphatic

polyamides, and aliphatic polyesters.

(C)-Semi-crystalline polymers with fast crystallization dynamics:

These polymers can be quenched with difficulty to 50% amorphous form.

They are crystallizing to (60-80%) so they called “high crystallinity polymers”.

These polymers show both α and β relaxation processes. As an example of these

polymers are linear polyethylene (lPE), poly(oxymethylene) (POM),

poly(oxyethylene) (POE), and isotactic polypropylene (iPP).

All the three polymer categories show the low-temperature relaxation

processes γ, or β relaxation process if the α not found.


2.3.3.3-Relaxations associated with crystalline phase (4*):

Crystallinity means long-range symmetry (i.e., repeating of a unit of

specific symmetry in a microscopic range). Such a repeating produce sharp x-

ray diffraction patterns superimposed on a broad amorphous background a

typical example of this is shown in figure (2.12)

Figure 2.12: The X-ray spectrums for different polymers (21).

Figure (2.12) shows the Debye-Scherrer type of x-ray differactograms of semi-

crystalline high and low-density polyethylene in comparison with that of

amorphous polystyrene (21). The crystallinity is defined as the relative area of the

sharp maxima with respect to the broad amorphous band. No information can be

derived from x-ray diffraction measurements about how the amorphous phase is

distributed in highly crystalline polymer.

According to the two-phase model introduced by Gerngross et al (22) in

1930, the crystalline and amorphous phases are separated in space. In a polymer

in low and intermediate crystallinity, the crystallites would form separate


regions in the disordered amorphous size. This view has been modified by

Hosemann (23) in 1950, at least for polymers of high crystallinity. According to

the Para-crystalline model of Hosemann, the amorphous band observed in the X-

ray diffraction in highly crystalline polymers is due to the defects, especially at

the boundaries of the crystallites. This means that in such systems the

amorphous phase is not separated from the crystalline phase in space; it is

scattered throughout the system.

The problem has been discussed in detail by Stuart (24) in 1959. A model

experiments of Bodor (25) (1972) show that even in polymers exhibiting

relatively low crystallinity ~20% the X-ray diffraction patterns can be simulated

by introducing defects in crystalline structure rather than by separating the

amorphous disordered phases from the crystalline ordered ones in space. On the

other hand Yeh (9) (1972) showed by the electron diffraction method that such a

classically amorphous polymers as atactic polystyrene ordered regions of 20-40

A° were present.

As the amorphous and crystalline phases are not well defined in polymers

it is difficult to decide which relaxation belong to which phase. We shall

consider as belonging to the crystalline phase those relaxations, which are

applicably increased by increasing crystallinity, crystal form, or size. This does

not necessarily mean that the units, the motion of which is reflected by the

particular relaxation are actually arranged in a crystalline lattice.

Figure 2.13: The lamellae crystalline structure (26).

32

For example in figure (2.13) the lamella crystal structure of polyethylene

is shown schematically (26). The chains of the polyethylene molecule are folded

to form a lamellar configuration. The interlamellar spacing being in order of 100

A°. At the surface of the lamellar, the mobility of the chain segments is different

from that inside the lamellar (27). The relaxation corresponding to the motion of

the surface groups of the lamellar (usually referred to as α-relaxation) will be

considered here as crystalline relaxation as it is highly increased by increasing

the crystallinity. The chain segments motion which produces the relaxation, are

evidently not arranged periodically; in a strict sense the corresponding

thermodynamical subsystem should be considered as amorphous. The lamellar

configuration tends to arrange in a spherically symmetric form shown in figure

(2.14).

Figure 2.14: The spherulite lamellar structure.

This formation is refered to as spherulite and can be easily observed under light

microscope. By considering these structures of the semi-crystalline polymers,

we can find that the relaxation attributed to the crystalline phase as follows:

(αm) Crystalline-melting relaxation. This an order-disorder relaxation

involving a large enthalpy and entropy change, where the long range order

33

34

destroyed. At this relaxation the sharp x-ray diffraction, peaks vanish; an abrupt

in the thermal dilution curve and a large DSC peak are observed.

(αc) Relaxations, which are appreciably increased by increasing

crystallinity and crystal, size but are not due to the mobility of groups inside the

crystal. This relaxation usually corresponds to the mobility of the groups at the

surface or at the lattice defects.

(αcc) Relaxations of one crystal form into another. It is evidently a

structural relaxation involving long-range rearrangement of the system. A

typical crystal-crystal relaxation is observed in poly (tetrafluroethylene) at

292K, where the triclinic crystal form rearranges to hexagonal form.

(γc) Relaxations involving local motion (vibration or rotation) of groups of

the main chain arranged in the crystal lattice. These are not structural relaxations

as the equilibrium position of the vibrating or rotating unit is unchanged; the

long-range symmetry is not affected by the relaxation. The local rotations and

vibrations are in crystals collective phonon states; the spectrum of such motions

determines the specific heat of semi-crystalline polymer at low temperatures.

2.3.3.4-Mobility in ordered crystalline phase (4*):

From studies on low molecular weight inorganic and organic crystals

made by Fox et al (1964) it can be deduced that in the hypothetical perfectly

ordered phase only local vibration and rotation may occur. The spectrum of such

vibrations can be approximately calculated from the temperature dependence of

the specific heat.

In the semi-crystalline polymers, the heat capacity at low temperatures is

well described by the simple Debye theory, which predict T3-dependence. For

deducing information about the lattice vibration from specific heat data,

however, more detailed theoretical analysis is needed. This problem has


discussed in detail by Tarasov (28) (1950), Stockmayer and Hecht (29) (1953) and

Baur (30,31) (1970,1971). Only the basic approach will be outlined here.

The specific heat of a solid due to harmonic lattice vibrations is generally

expressed as:

( )

νν

ννρν d

kTh

kTh

kThkTcv ∫

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛=

max

02

2

1exp

exp)( (2.25)

Where, ν is the frequency of the lattice vibration ρ(ν) is the density of the

vibrational states.

Equation (2.25) corresponds to the harmonic lattice vibration

approximation; for a more general treatment, anharmonicity should also be

taken into account.

By approximating the density of state by a power series of modes the heat

capacity can be expressed in terms of Debye function defined as:

( )∫⎟⎠⎞

⎜⎝⎛

+

−⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎠⎞

⎜⎝⎛ T n

n

nn

n

xdxxXTn

TD

θ

θθ

02

1

1)exp()exp(

(2.26)

Where, θn =hνn /k is referred to as the characteristic temperature.

The Tarasov (28) (1950) approximation involves that the interaction along

the polymer chains through the covalent bonds is much higher than the

intermolecular interactions. Correspondingly, at elevated temperatures the one-

dimensional vibrations would dominate; the ρ(ν) spectrum is thus approximated

by a one-dimensional continuum.

At lower temperatures, when the intermolecular interactions begin to

contribute appreciably, three-dimensional vibrations are considered.

In this approximation, correspondingly, two characteristic temperatures

are introduced θ1 and θ3 corresponding to the one dimensional and three-

dimensional vibration respectively.

35

The corresponding expression is given by:

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎠⎞

⎜⎝⎛=

TD

TD

TRDcv

31

33

1

3113 θθ

θθθ

(2.27)

The vibration spectrum corresponding to the Tarasov approximation is shown in

figure (2.15.a); equation (2.27) is referred to as the Tarasov formula.

At low temperatures:

13

2

34

512

θθπ TRcv = , T≤θ3 (2.28)

Figure 2.15: The vibrational energy density of polyethylene (a) the Tarasov theory, (b) the experimental data. (5)

At higher temperatures:

1

2

23

θπ TRcv = , θ3 ≤T≤θ1 (2.29)

The Tarasov approximation thus predicts a T3 dependence of cv at low

temperature where the three-dimensional approximation is valid.

36

Figure 2.16: The temperature dependence of the specific heat at very low

temperature for amorphous and semi-crystalline polymer.(5)

As shown in figure (2.16), this approximation is valid for crystalline

polyethylene in the low temperature range below 15 K. At higher temperatures

the Tarasov approximation, which predicts linear temperature dependence, fails.

According to Baur (30,31), this disagreement with the experiment is due to

the stiffness of the polymer chains, which makes transversal acoustic waves

(phonons) effective. For a more detailed analysis the different vibratinal modes

bending, stretching are to be taken into account and also the corresponding

acoustic waves phonons which propagate in polymer isotropically.

According to the calculations of Baur (30,31), the heat capacity is expressed as:

Cv =a3 T3 (2.30)

Where a3 =2.64× 10-5 cal/mole. degree 4 for semi-crystalline polyethylene.

This T3-dependence follows also from the simple Tarasov model, and has

been experimentally observed, as shown in figure (2.16).

37

38

At somewhat elevated temperatures, between 10 K and 50 K,the specific

heat is:

Cv=a3T3 +anTn (2.31)

where (n) is between 3/2 and 3; it decreases with increasing temperature.

The dependence of the Tn term is due to contribution of the transversal phonons

(bending vibrations).

At higher temperatures between 100 K and 200 K,

Cv =a1T+ a1/2 T1/2 (2.32)

For polyethylene a1=1.08×10-2cal/mole degree2, a1/2=0.1186 cal/mole

degree1/2. The additional term T1/2 that appears in equation (2.32) with respect to

the Tarasov approximation is also attributed to the effect of transverse phonons.

Figure (2.15.b) shows the actual vibration density-spectrum of crystalline

polyethylene obtained by the best fit with the Cv data using the equation s of

Baur (equations 2.31 and 2.32). It seen that the highest contribution to the

spectrum is still due to the three dimensional vibrational modes which do not

depend on the length of the molecule; they are approximately the same for the

monomer or hydrogenated monomer and for the polymer. The rest of the

spectrum is a continuum.

From the comparison of the heat-capacity data with the lattice dynamical

calculations, it is concluded that mechanical or dielectric relaxations are not

expected to occur in perfect crystals. The experimental fact that many

relaxations are strongly dependent on the crystallinity is attributed to local

motions at dislocations and defects.

2.3.4-The glass-rubber relaxation Phenomena: 2.3.4.1-Glass-rubber relaxation in polymers (4*):

The most prominent change in the macroscopic behavior of amorphous

polymers is the glass-rubber relaxation where the rigid glassy solid material

becomes a viscoelastic fluid. At this relaxation the mechanical strength of the

material decreases rapidly, there is an abrupt change in the thermal dilation

versus temperature curve. The thermal conductivity, mechanical loss at a

periodic stress, dielectric loss, and static dielectric constant also change

appreciably by passing through this relaxation.

Figure 2.17: Thermomechanical curves at the glass-rubber relaxation of the unplastcized PVC (4).

Curve (a) in figure (2.17) represents the expansion of the sample at a constant

load recorded at a constant rate of heating. Curve (b) in figure (2.17) represents

the penetration of a cylindrical profile into the polymer at a constant load. Curve

(c) in figure (2.17) represents the mechanical loss at torsional periodic stress of

constant frequency (10Hz) (i.e., the temperature dependence of the loss modulus


39

G″(T)). It is seen that the mechanical parameters very drastic change at about

353K where the glass-rubber relaxation of this polymer is found.

The shifts of the position of the abrupt changes are due to the differences

in the effective frequency of the relaxation. This is why the mechanical loss

peak (curve c) appears at higher temperature than that corresponding to the

abrupt change in thermal expansion (dilatometeric) relaxation. The abrupt

changes observed in thermo-mechanical curves (a) and (b) are dependent on the

load; by increasing the load the relaxation temperature is shifted to lower

temperature.

A dielectric absorption curve (i.e. ε′(T)), measured by time dependent

polarization method introduced by Hamon (33) (1952) for a quenched sample has

a much lower maximum at Tg than annealed sample. As (εo- ε∞ )T is

proportional to the area under the ε′′(T) curves it is concluded that by annealing

(εo- ε∞ )T is considerably increased.

A similar effect is observed by measuring dielectric depolarization

current. By this technique the sample is polarized above the relaxation

temperature by a dc electric field, cooled down under field, and subsequently

heated up without external field to record the depolarization current.

Figure 2.18: The depolarization current spectrum for the PVC ( 4)

The curves shown in figure (2.18) have been recorded this way by using

slow 1 K/ min and fast 10 K/min cooling rates and identical heating rates.

40

41

It is seen that the area under the depolarization peak is highly increased

for the sample cooled down slowly, which roughly corresponds to the

ànnealed` case of previous measurements. The change in the mechanical,

thermal, and electrical parameters at the glass-rubber relaxation illustrated for

unplasticized PVC is generally characteristic of amorphous and semi-crystalline

polymers. From the experimental facts, it is concluded that at Tg large parts of

the polymer chain become mobile and beside change in the mobility, a structural

change also occurs. According to the structural relaxation concept, we can

consider the glass-rubber relaxation at Tg as a structural relaxation.

2.3.4.2-Classification of glass transition temperatures (1*): Glass-transition temperatures can be classified into two kinds known as

Static glass transition and Dynamic glass transition. In the following, these two

classes will be discussed in details.

Amorphous substances convert at static glass-transition temperature Tgs

from a “glassy” state to a “liquid” state (i.e., into a melt (in case of low molar

mass compounds) or a rubbery state (in case of high molar mass chains)).

Chain segment move with certain frequency (ν) at the dynamic glass

transition temperature Tgd > Tgs and the deformation time t =1/ ν.

In general, Glass-rubber transitions are rather caused by strong

intermolecular cooperative movements of chain segments. A rapid cooling of

polymeric liquid prevents monomeric units from finding their equilibrium

positions. The frozen in structure of the liquid thus contains defects of atomic

size, the free volume. These defects agglomerate similar to crystal defects if

glasses are heated. The resulting larger free volumes allow intermolecular-

cooperative movements of chain segments in which ca. 20-60 chain atoms

participate. These segments size can be deduced from the ratio of activation * This article was based on this reference with some modifications by the author.

energy for the glass transformation to the melt enthalpy of semi-crystalline

polymers and from the dependence of glass temperature of amorphous polymers

on the lengths of segments between cross-links.

To distinguish between static and dynamic glass transition temperatures,

Tgs and Tgd . The former is obtained using the DSC, DTA and

thermodialatometry, whereas, the later is obtained using the Dielectric

spectroscopy (DS), nuclear magnetic resonance (NMR) and dynamic

mechanical analysis (DMA).

Static and dynamic glass transition temperatures can be interconverted by

Willaims-Landel-Ferry equation (WLF). The glass transition is assumed to be a

relaxation process similar to viscosity; both processes depend on free volume vf.

The Doolittle equation :

( )

f

f

vvvB

A−

+= lnlnη (2.33)

which, relates viscosities (η) to the total volume (v) and free volume (vf) per

total mass. The free volume fractions are φf ≡vf/v for a temperature T and φf,0 ≡

vf,0 /v0 for the reference (To). (A) and (B) are constants.

Temperatures shift viscosities, which can be described by a shift factor:

)()(

ρηρη

TTao

ooT = (2.34)

where the densities (ρ) at temperature (T) and (ρo) at temperature (To), is correct

for thermal expansion. The shift factor (aT) corresponds to the ratio (t/to) of the

relaxation times at temperature (T) and (To).

Introduction of the Doolittle equation s for (T) and (To) into the shift factor

results in:

⎥⎥⎦

⎤

⎢⎢⎣

⎡−≈⎥

⎦

⎤⎢⎣

⎡+

⎥⎥⎦

⎤

⎢⎢⎣

⎡−=

0,0,

11303.2

log11303.2

logff

oo

ffT

BT

TBaφφρ

ρφφ (2.35)

It is further assumed that the free volume fraction φf ≡vf/v increases linearly with

temperature according to φf =φf,0+βf(T-To). The expansion factor (βf)

42

approximates the true cubic expansion factor β=(1/v) (dV/dT) for the

exponential increase of volume with temperature. Because of this

approximation, the (WLF) equation is restricted to a temperature range of To<

T< (To+100 K).

Introduction of the expansion factor βf=(φf-φf,0)/(T-To) into the equation (2.35)

gives the (WLF) equation :

( )( )

[ ][ ] o

o

o

of

f

of

T ttTTkTTk

TT

TTB

a loglog)(

303.2log

0,

0, −=−+′−−

=−+

−−

=

βφ

φ (2.36)

Equation (2.36) applies to all relaxation processes. The adjustable parameters k,

k′ and φf,0 are often assumed to be universal parameters, for example, k=17.44,

k′ =51.6 and φf,0 =0.025 for T=Tg and later as k=8.86, k′ =101.6 and φf,0

=0.025 for To=Tg+50K. For more accurate calculations different values of k, k′

and φf,0 should be used for each polymer.

2.3.4.3-Theories of the glass-rubber relaxation:

There are several approaches for a molecular interpretation of the glass-

rubber relaxation in polymers.

(a)-Kargin and Solnimsky (statistical theory approach):

One of the early approaches introduced by Kargin and Solnimsky (34,35) in

(1948,1949) is based on the statistical theory of the microbrawnian motion of

polymer chains in dilute solution. In this approach the polymer molecules are

divided into sub-molecules of lengths varying according to the gaseous

probability distribution. The motions of these “Gaussian” sub molecules are

kinetically treated; the sub molecules themselves are thought to be unchanged

during thermal motion. This approach is referred to as “normal mode theory”

based on sub-molecular model (19,36,37).

43

44

The interpretation of the dielectric glass-rubber relaxation in terms of the Normal mode theory has been discussed by Zimm et al (38), Van Beek and

Hermans (39), Kästner (40,41), Stockmyer and Baur (42).

The early theory of Kirkwood and Fuoss (43) in (1941) is also based mainly

on the normal-mode aspect. Yamafuji and Ishida (18) in (1962) extended these

theories by accounting for local motions. The normal mode theories are of little

practical use. Because of the enormous mathematical difficulties calculations

cannot be preformed exactly, so several semi-empirical parameters have been

introduced. Moreover, the normal-mode theories could not describe the non-

equilibrium behavior of the glassy state, which is its most important property.

One thing however, can be deduced from these calculations, which is of

some practical importance: at the glass relaxation, parts of the polymer

containing about 50-100 C-C bonds become mobile.

(b)-Debye, Fröhlich and Hoffman (barrier- theory approach):

Another approach originated by Debye (44) in (1945) and developed

further by Fröhlich (147) in (1949) and Hoffman (45,46,47) in (1952,1955,1965) is

referred to as the barrier-theory of the glass-rubber relaxation. In this approach,

the system is represented by a series of potential valleys. In order to change

configuration the system must overcome a certain potential barriers. The

probability for this can be described by simple kinetic equation s used in general

theory of rate processes.

The theory was first developed for describing the rotational motions.

Later Goldstein (48) (1969) proposed a generalized barrier theory to describe the

configurational changes at the glass-rubber relaxation. The barrier picture has

the advantage over the normal mode theories that non-equilibrium behavior of

the glassy state can be accounted for.

It can also be readily connected with non-equilibrium statistical

thermodynamics. Its quantitative application is hindered by our lack of

45

knowledge on the forms of the intermolecular interaction potentials by which

the potential barriers are formed.

Another difficulty is that at (Tg) the structure changes so drastically that

the potential barriers themselves are strongly temperature dependent. This is

why the barrier model is most frequently applied to describe local-mode

relaxation than glass-rubber relaxation.

(c)-Williams et al. (Free-volume theory approach):

A quite different approach has been introduced by Williams et al (49) in

(1955) based on the concept of Doolittle (50) (1951) about the free-volume theory

of the viscosity of liquids. This approach is based on the properties of liquids so

the glass-rubber relaxation is approached from high temperature side. According

to this view the viscosity of the liquids is determined nearly by their structure

which is characterized by the free-volume vf=v-v0 where (v) is the actual

specific volume, (v0) is termed as the occupied volume which would correspond

to closest packing. (v0) has been approximated in the original Doolittle concept

of free volume as the extrapolated volume to the absolute zero temperature. This

definition can be extended by requiring also infinite time of storage at zero K

(i.e., equilibrium structure) and considering only that part of the volume as free

by which the molecule can redistributed without additional energy (51).

By the free volume theory, the high temperature part of the glass-rubber

relaxation could be satisfactory explained. Below the static Tg in the glassy state

the original theory fails, because it is based on the assumption that by passing

trough Tg the free volume is frozen-in and is unchanged in the glassy state. By

accounting for time and temperature dependence of the free volume in the glass

the non-equilibrium can be qualitatively interpreted (13). The free-volume theory

has been further developed by Rusch (52) in (1968) to be able to describe the

temperature dependence of the relaxation time in the region below static Tg by

introducing non-equilibrium free volume.

46

(d)-Gibbs and DiMarzio (Thermodynamics approach):

The problem of the glass-rubber relaxation has also been approached from

the point of view of thermodynamics. Gibbs and Di Marzio (53) in (1958) treated

the glass-relaxation, as a second-order thermodynamic relaxation the way of

regarding the problem in this approach is in principle, similar to barrier theory.

The glass relaxation is approached from the high-temperature side using

equilibrium thermodynamical partion function.

At Tg the system is thought to be completely frozen; the entropy is

considered to be zero. This is an oversimplification, which makes the theory of

no use in the glassy state, when it is in a non-equilibrium thermodynamical state.

Several attempts have been made to connect the thermodynamical aspects

with some molecular theories and with the free-volume theory. A kinetic theory

based on statistical considerations has been developed by Volkenstein and

Ptytsin (54) in (1956). This theory is computationally rather complicate and does

not seem to be practically useful.

Bartenev (55,56,57,58,59) has investigated the correlation between the kinetic

and free-volume theories in a series of papers in (1951,1955,1956,1969,1970).

He found that by introducing temperature-dependent activation energy for the

kinetic process the same results are obtained as the free-volume theory.

Nose (60,61) in (1971,1972) developed further the whole theory of liquids in

order to account for the non-equilibrium behavior of the glassy state. In his

treatment configurational entropy ( Sc ) is defined in the glassy state, which is

different from zero.

It seems that at the present state of our knowledge about intra- and-inter

molecular interaction in polymeric system one should be satisfied with such

semi-phenomenological interpretations as the whole theory or the free-volume

theory, which can be easily connected with the basic aspects of non-equilibrium

thermodynamics.

47

2.3.5-Relaxation in the glassy state (4*):

(αgg) Relaxations in the glassy state, involving local molecular motion

type relaxation are easier to be handled theoretically than the glass-rubber α-

relaxation. The motion of a relatively small group of atoms to be considered in

the framework of frozen in structure a side group such as, for example, the ester

group in poly (methylmethacrylate) (PMMA), cannot rotate freely in the solid

about the C-C bond, which links to the main chain because of the large inter,

and intra molecular forces. Because of this, the side group has different energy

in different rotational positions. The problem is very similar to that of rotational

isomerism of small molecules. Below Tg the main chain is approximately rigid;

its structure determines a potential field in which the side group moves. Rotation

of the side group from one minimum to another requires energy of activation

equivalent to the height of the potential barrier to overcome.

Rotation of a side group is thus a rate process; the probability of

relaxation from one equilibrium position to another is expressed in terms of rate

constants similar to the case of the chemical reaction. Another typical possibility

of local motion in polymers is conformational relaxation in the main chain. Any

change in the sterochemical configuration of short-chain segments would results

in such relaxation.

Conformational relaxations of the main chain involve rotation and / or

relaxation. In this case, again the potential barrier picture is very useful for

interpretation of the corresponding dielectric relaxation. The general idea is to

calculate the potential between two configurations and to determine the rate

constant for the relaxation by statistical theory. The relaxations involving

rotation of side groups (β-relaxations) usually appear at low frequencies in the

temperature range from about 223 K to 323 K. The relaxations involving

conformational isomerization of the main chain appear at lower temperatures

* With some modifications made by the author.

typically near 123 K. The relaxations observed below the temperature of boiling

nitrogen down to near absolute zero are referred to as cryogenic relaxations.

They are also interpreted as being due to rotation and vibration of short-chain

segments and to hindered rotation of small side groups, such as the methyl

group. At very low temperatures, the collective vibrational phonon states of the

solid become increasingly important.

2.3.6-Thermal transition and relaxation: In thermal relaxation, compounds are in thermal equilibrium below and

above the relaxation temperature. An example is the melting temperature where

crystallites are in thermal equilibrium of the melt. Polymer may also be present

in non-equilibrium states that relax at certain temperature. Thermal relaxations

are thus kinetic phenomena that depend on the time scale (i.e., on the frequency

(a reciprocal time)). The best-known example is the glass transition relaxation.

Thermal relaxations are subdivided into those of first, second…nth order.

Classic first order relaxations are crystal→liquid (melting), liquid→ gas

(boiling). At melting temperature, heat has to be added until all ordered

monomeric unit in crystallites have been transformed into disordered units in the

melt. Enthalpy (H), volume (V), and entropy (S) all jump to higher values at

melting temperature, see figure (2.19).

Figure 2.19: The jump to a higher value at the melting temperature and glass

transition temperature.

48

49

The first derivative of (H), (V) and (S) with respect to temperature (i.e., cp

, α, cv) and to the pressure (i.e.,κ) show corresponding infinitely high signals in

the ideal case, the melting of infinitely large, perfect crystals. For imperfect

crystals, discontinuities (H, V, S) degenerate to S-shaped curves and sharp

signals (cp , α, cv) to bell curves figure (2.19). A relaxation of nth order is

defined as the transformation where the nth derivative of the Gibbs energy

shows a discontinuity. An ideal first order thermodynamic relaxation thus has

discontinuities in H, S and V at the relaxation temperature (e.g., TM).

An ideal second order thermodynamic relaxation shows discontinuities in

α, cv, and κ at the relaxation temperature Ttr . Examples of true second order

relaxation are the lambda relaxation of liquid Helium at 2.2K, the rotational

transformations of crystalline ammonium salts, and disappearance of

ferromagnetism at the Curie point.

This thermodynamical classification of the thermal relaxations

corresponds to the phase behavior. All first order relaxations exhibit two phases

at the relaxation temperatures. All second order relaxations happened in a single

phase. This classification does not correlate to the molecular processes.

2.4-Thermal Analysis: 2.4.1-Thermal analysis:

The importance of thermal analysis has increased so much in the last

twenty years (5). It based on two basic quantities heat and temperature. Heat is a

quantity that can be observed macroscopically and have its microscopic origin

which is the molecular motion. These molecular motions can be the translation,

rotation, and vibration of the molecules. These different kinds of motions give

the sensation of heat. Temperature on the other hand is more difficult to

understand. It is the intensive parameter of heat. However, to arrive to this

conclusion many aspects of temperature must be considered.

The macroscopic theories of thermal analysis are:

1. The thermodynamic or equilibrium thermodynamic theory

2. The irreversible thermodynamic theory or non-equilibrium

thermodynamic theory.

3. The kinetic theory.

The basic experimental techniques of thermal analysis are:

1. Thermometry,

2. Differential thermal analysis,

3. Calorimetry,

4. Thermomechanical analysis,

5. Dilatometry,

6. Thermogravity.

2.4.2-Theory of heat capacity (5*):

A theory of heat capacity means to find a quantitative connection between

the macroscopically observed heat capacity and the microscopic of the


50

molecules. The importance of heat capacity is clear from the following

equations:

∫=−T

po dTCHH0

Enthalpy (2.37)

Energy (2.38) ∫=−T

vo dTCUU0

∫=T

p dTTC

S0

Entropy (2.39)

G = H – TS Gibbs energy (2.40)

F = U – TS Free energy (2.41)

These equations show that the heat capacity is connected to all the

thermodynamic properties of the system, which give information about the

microscopic motions of the system. The enthalpy (H) or energy (U) gives

information about the total thermal motion and the entropy (S) gives information

about the order degree of the system and finally the Gibbs or free energy give

information about the stability of the system.

All the calorimetric techniques lead to the heat capacity at constant

pressure, (Cp). In terms of microscopic quantities, heat capacity at constant

volume, (Cv), is more accessible quantity. The relationship between (Cp) and

(Cv) is given by:

nPnT

vp TVP

VUCC

,,⎟⎠⎞

⎜⎝⎛∂∂

⎥⎦

⎤⎢⎣

⎡+⎟

⎠⎞

⎜⎝⎛∂∂

=− (2.42)

From this equation using Maxwell relations one can obtain:

Cp-Cv =TVα2 /βc (2.43)

Where, (α) is the expansivity and (βc) is the compressibility. However, the

experimental data of the expansivity and compressibility are not available over

51

the whole temperature range of interest, so one knows (Cp) but has difficulties in

evaluating (Cv). At moderate temperatures, such as those usually encountered

below the melting point of linear macromolecules, one can assume that the

expansivity is proportional to (Cp). In addition, it was found that (volume /

compressibility) does not change very much with temperature.

2.4.3-General theory of TMDSC (63*):

Temperature modulated DSC is a technique in which the conventional

heating program is modulated by some form of perturbation. The resultant heat

flow signal is then analyzed using an appropriate mathematical treatment to

deconvolute the response to the perturbation from the response to the underlying

heating programme. Since the introduction of the TMDSC technique many types

of modulation methods and mathematical analysis methods was applied to the

TMDSC technique.

To describe the origin of the different types of contributions to the heat

flow we start with the differential equation:

),( TtfdtdTC

dtdQ

pt ++= (2.44)

where, dQ/dt is the heat flow into the sample, (Cpt) is the reversing heat capacity

of the sample due to its molecular motions (vibrational, rotational and

transnational) and f(t,T) is the heat flow arising as a consequence of a kinetically

hindered event. There will be many forms of f(t,T) and they will differ with

different types of transition and different kinetic laws.

Equation (2.44) assumes that at any time and temperature there is a

process that provide a contribution to the heat flow, which is proportional to the

heating rate. This response is very fast, given the time scale of the measurement.

This is clearly a reversible process. The term “reversible” is to distinguish this

process from the processes such as melting and crystallization. The heat


52

capacity (Cpt) is a time-dependent quantity. If a molecular motion frozen it

cannot contribute to the heat capacity. However, considering a molecular motion

frozen will depend on the time scale of the measurement. As clear example of

this is the glass transition in polymer where the change in heat capacity as a

function of temperature depend on the frequency at which the observation is

made.

In TMDSC the sample is subjected to a modulated heating program:

T=To+ bt+ B sin wt (2.45)

where (To) is the start temperature, (b) is the heating rate, (B) is amplitude of the

modulation and (w) is its angular frequency. By combining equations. (2.44) and

(2.45) one obtain for many processes,

( ) wtCwtwBCTtfBCdtdQ

ptpt sincos, +++= (2.46)

In this equation the term ( )TtfBCpt ,+ represent the underlying signal and the

term represent the cyclic signal. The wtCwtwBC pt sincos + ( Ttf , ) is the

average of f(t,T) over the interval of at least one modulation and (C) is the

amplitude of the kinetically hindered response to the temperature modulation.

Both (Cpt) and (C) are vary with time and temperature but they must be

considered as effectively constant over the duration of a single modulation.

For small oscillations, heat flow depend linearly upon the temperature

modulation: heat flow as well as temperature are given by linear superposition

of the underlying signal and the cyclic signal, hence the (Cpt) is independent of

(B) while (C) is proportional to it. The term f(t,T) can also give rise to a cosine

contribution. However, for most kinetically hindered responses, which can be

modeled, at least approximately, by a low of arrhenius type, the cosine response

of f(t,T) can be made insignificantly small by ensuring that there are many

cycles over the course of the transition.

53

TMDSC normally requires that the frequency of the modulation and the

underlying heating rate be adjusted to ensure that this criterion is met, not to do

so would usually invalidate the use of this technique. Consequently, in most

cases, except in the case of melting, it can be assumed that the cosine response

derives from the reversing heat capacity. Equation (2.46) clearly implies that the

cyclic signal will have amplitude and a phase shift determined by the term

(wBCpt ) and (C) respectively.

Considering Cc=AHF/AHR which is the cyclic heat capacity = complex

heat capacity, (AHF) is the amplitude of heat flow modulation and the (AHR ) is

the amplitude of the heating rate modulation. Then:

Cpt =Cc cos δ (2.47)

C = wBCc sin δ (2.48)

where, δ is the phase shift. Consequently, there are three basic signals derived from a TMDSC

experiment; the average of the underlying signal which is equivalent to that of

conventional DSC, the in-phase cyclic signal from which (Cpt ) can be

calculated, and the out of phase signal (C).

The non-reversing heat flow can be calculated from:

Hfnon-reversing = Hfunderlying –BCc cosδ

= f(t,T) (2.49)

where, cos δ=1 if the phase-angle shift during the transition is small.

In this way, the reversing contribution can be separated from the non-

reversing contribution. This simple analysis has been applied to many transitions

in polymer systems, and founds to work well when the non-reversing process is

the loss of volatile material, a cold crystallisation or chemical reaction and (Cpt)

is the frequency–independent heat capacity.

54

The time scale dependence of (Cpt) can be expressed as:

( ) wtCwtBwCTtfbCdtdQ

pwpb sincos, +++= (2.50)

where (Cpb) is the reversing heat capacity at the frequency or distribution of

frequencies implied by heating rate (b) and (Cpw) is the reversing heat capacity

at the frequency (w) (the precise frequency w contrasts with the range associated

with (b) and different reversing heat capacities result. Equation (2.50)

generalizes equation (2.46). The term (BwC pw) is the reversing signal at

frequency (w). The term (C sin wt) is the out-of-phase term and arises from the

kinetic contribution exhibited by f in equation (2.46).

This out-of-phase i.e.,“AC component” is given by:

Out-of-phase or kinetic heat flow =bC/wB where, C/wB is an apparent

heat capacity.

By the analogy with Dynamic mechanical analysis (DMA) and Dielectric

thermal analysis (DETA) it is proposed to express the cyclic signal as a complex

quantity: (2.51) CCC ′′+′=*

and hence C2c= |C*|2=C´2+C´´2 (2.52)

where, (C*) is the complex heat capacity and (C´) is the real part and (C´´) is the

imaginary part.

The analogy with DMA and DETA must be done with care that in these

techniques mechanical work or electrical energy is lost from the sample as heat

and this is expressed as imaginary component, which is then referred to as the

loss component. In TMDSC, during an endothermic process, such as a glass

transition, energy is not lost from the sample yet there will be a measurable C´´

component. For this reason it should not referred as to loss signal we prefer the

term kinetic heat capacity.

The reversing or in-phase cyclic heat capacity =Cpw =C´

The kinetic or out-of-phase cyclic heat capacity =C/wB =C´´

Put these terms in equation (2.50) we have:

55

( ) ( wtCwtCBwTtfbCdtdQ

pb sincos, ′′+′++= ) (2.53)

( ) ( )wtCwtCBwCCbdtdQ

pwEpb sincos +++= (2.54)

where, CE =f(t,T)/b and can be referred to as the non-reversing or excess heat

capacity.

2.4.4-TMDSC as a tool to study relaxation processes in polymers:

TMDSC is a very promising technique in studying relaxation processes in

polymers. It extends the conventional DSC technique, which is a static

technique to become a dynamic technique. Since its introduction by Reading (64)

in 1993 many investigations appear to show its applicability to study relaxation

in polymers especially glass transition relaxation.

Relaxation processes are dynamic in nature so they are time or frequency

dependent processes so they can be studied by any dynamic technique. The

well-known dynamic techniques, by which the relaxation can be studied in

polymers, are Dielectric Spectroscopy (DS), Dynamic mechanical analysis

(DMA), and Nuclear magnetic resonance (NMR). The dynamic technique is

characterized by applying some perturbed kinetics, which affect the molecular

motion in the studied system and record the material response. The word

dynamic here is referred to that it can detect a dynamic process take place in the

system. A static technique such as DSC is not suitable for studying the

relaxation processes. The only process can be studied by DSC is the thermal

behavior (i.e., transition).

TMDSC has the frequency range (10-4 –10-1 Hz) this range is very limited

comparing with the other dynamic techniques DS (10-3 –107 Hz) and DMA (10-4

–102 Hz). However, it has advantage that it can detect any kind of molecular

motion and work for all polymers. The DS on the other hand detect only dipolar

56

motions so it work only on polar polymers, the DMA detect only mechanical

response and need long band of material to work with. But TMDSC work on

very small amount (ms~10mg).

Relaxation processes in semi-crystalline polymers using the TMDSC:

Studying the relaxation in the semi-crystalline polymers is a very complex

that is because the relaxation in the semi-crystalline polymers is very complex.

The subject of relaxation in semi-crystalline polymers is divided into three

different cases:

1. Glass transition relaxation (αMAF-relaxation at Tg)

2. Rigid amorphous fraction relaxation (αRAF relaxation above Tg )

3. Reversing melting relaxation (surface relaxation near the TM)

The well-studied problem of these problems is the glass transition. Many

groups work on this problem. The other problem of Rigid amorphous is also

getting more interesting now. Finally, the new discovered relaxation process of

reversing melting is getting more attention now also.

Glass transition relaxation: The glass transition is at present a main problem not only in the field of

polymer physics but also in the condensed matter physics. Until now there is no

generally accepted theory for it. It is well known now that there are two kinds of

glass transition:

• Static glass transition or thermal glass transition (vitrification)

• Dynamic glass transition or relaxation process

TMDSC allow studying glass transition in these two aspects at the same

time (i.e., simultaneously)(65). The thermal glass transition is visible in the

underlying signal, which related to the heating or cooling rate. The dynamic

glass transition can be observed in the temperature modulation frequency. From

the heat flow responses to the temperature modulation a complex heat capacity

57

can be obtained. In the glass transition region (i.e., relaxation region) a step in

the real part of the complex heat capacity and a peak in the imaginary part of the

complex heat capacity occur, see figure (2.20). This gives more information

about the glass transition in different point of view.

Figure 2.20: The real (c´) and imaginary (c´´) part of the complex heat capacity (c*).

As shown in figure (2.20) from the real part c´ and the imaginary part c´´ of the

complex heat capacity we can obtain the frequency dependent glass transition

temperature Tw with a high precision.

Another information that can be obtained from the TMDSC in the field of

glass transition is the relaxation map for the glass transition relaxation at Tg, see

figure (2.21).

Figure 2.21: A typical relaxation map, which can be obtained using the TMDSC.

58

Figure (2.21) show that the temperature dependence of (w=2πf) of the dynamic

glass transition. It also show that the temperature frequency dependence can be

described by William Landel Ferry (WLF) which is well known for the glass

transition relaxation process (α-relaxation) by other techniques such as DS.

Complex heat capacity frequency dependence:

The complex heat capacity is the main outcome from the TMDSC.

Complex heat capacity |cp*| is a function of the frequency. Frequency is

calculated from the period time tp , which is an experimental parameter of the

TMDSC. To study relaxation in the polymer at a specific temperature we make

an isothermal mode TMDSC in which we neglect any contributions from the

latent heat due to the temperature change. This lead to study only the frequency

dependent molecular motions (i.e. relaxations). To obtain information about the

relaxation we have to change the periodic time (i.e., frequency) in TMDSC

experiment and calculate the complex heat capacity |cp*|. If the complex heat

capacity |cp*| show frequency dependence this indicate the occurrence of a

relaxation process see figure (2.22).

Further, to obtain the relaxation time (τ) from the figure the following

relations is used:

fπτ

21

= (2.55)

This relation shows that the frequency is related to the relaxation time. We

consider the main relaxation time, which is the center of the curve as shown in

the figure (2.22).

59

Figure 2.22: The complex heat capacity frequency dependence obtained using the TMDSC.

60

2.4.5-Three-phase model of semi-crystalline polymers: 2.4.5.1-Introduction of the rigid amorphous fraction (RAF): Semi-crystalline polymers were described early with a model so called

“two-phase model”. This model was made by Gerngross (22) in 1930 on the basis

of the X-ray experiments. In this model the semi-crystalline polymers is divided

to crystalline phase and amorphous phase, see the figure (2.23).

Figure 2.23: Schematic diagram for the two-phase model.

When this model was made no one talk about how is the tow phases are

organized in the semi-crystalline polymer. Nothing was said about the interface

between the crystalline and amorphous phases.

Advances in measurements through the past years in the experimental

techniques especially in the calorimetry led to observe a deviations between this

simple two-phase model and the experimental results. Failure of the two-phase

model to describe morphology of semi-crystalline polymers has been a subject

of study since 1960´s (69).

H. Suzuki et al. (66) studied the heat capacities of 38 semi-crystalline

polymers of Poly (oxymethylene)´s and poly (oxethylene)´s using the

differential scanning calorimetry DSC from 205 K to the melt temperature.

61

They then, compare the experimental heat capacities with the heat

capacities calculated using the two-phase model. They found there are negative

deviations between the calculated heat capacities and the experimental one.

They found that the calculated heat capacity on the basis of two-phase model is

always larger than the measured heat capacity. Also they compare the

experimental heat capacity with two limit heat capacities, one from the super

cooled liquid and the other is for the crystal of macromolecules. They suggested

that these deviations are caused by molecules whose mobility has somehow

been hindered. These molecules located partially in the amorphous phase. They

linked these negative deviations to these molecules. Such observations

originated the term “rigid amorphous” which are molecules found in the semi-

crystalline polymer beside the normal “mobile amorphous”. So they start to put

the basis of the so-called now “three-phase model”, see figure (2.24). In this

model the semi-crystalline polymer consists of three phases; the rigid crystalline

(RCF), the mobile amorphous (MAF) and the rigid amorphous (RAF).

Nowadays this three-phase model is generally accepted as the model of

the semi-crystalline polymers.

Figure 2.24: Schematic diagram for the three-phase model.

62

Properties of the rigid amorphous fraction (RAF) (67*):

Since the introduction of the three-phase model, many researchers

interested to study the rigid amorphous fraction. The discovered properties of

this phase can be summarized as follows:

1. The RAF is a second amorphous fraction, which is different from the

mobile amorphous fraction, in that the latter is mobile while the first is

immobile.

2. The immobility of the RAF is the cause that this amorphous fraction

does not participate in the glass transition process.

3. The RAF is found with significant amounts in the crystalline polymers.

4. The RAF is constrained and immobile so it is not able to relax at the

glass transition temperature and this is supported by a sufficient

experimental data.

5. If the amount of the RAF becomes small then the three-phase model

collapses to two-phase model.

6. It is not generally accepted to call the RAF as “phase” according to the

basis of that it is not in equilibrium, as it is well known that semi-

crystalline polymers are not in equilibrium.

7. RAF is more extensive than simply tie molecules and chain folds along

the crystal boundaries.

8. RAF is in the glassy state even above the glass transition Tg .

The stability of the rigid amorphous fraction:

The stability of the RAF is depending on the polymer itself. In some

polymers such as poly (oxymethylene) (POM) the rigid amorphous fraction is

stable up to the melt. In some polymers such as, polypropylene the RAF starts

to melt above Tg (66).


63

The nature of the rigid amorphous fraction:

The nature of the RAF is not clear until now. So there is a number of

concepts and physical or morphological descriptions have been offered as the

nature of the rigid amorphous fraction including:

It is a material vitrified during the crystallization process (68), material

whose relaxation times are larger than those associated with Tg, intercrystalline

regions, nanophases and intermolecular non-crystalline regions (67).

The residual X-ray diffraction pattern for Poly (ethylene terephathalate)

(PET) suggested an oriented amorphous structure for the rigid amorphous

fraction (67).

May be the nanophases structure of the RAF distributed throughout the

semi-crystalline polymer suggested by Professor B.Wunderlich is the reasonable

phenomenological description of the RAF (67).

The effect of the rigid amorphous fraction on the glass transition:

The effect of the rigid amorphous fraction RAF on the relaxation at the

glass transition temperature is that the RAF is inhibits the relaxation at the

normal time and temperature. This means that it decrease the relaxation strength

at the glass transition temperature Tg (67).

Relaxation of the RAF (a second glass transition relaxation process) (67*):

NMR data show for semi-crystalline polymers there are three relaxation

times instead of only two. If the RAF have a glass transition temperature or not

is not clear, but it is known now that it change to rubber state above Tg of the

polymer gaining again mobility from this glass transition-like process. It is

reported also that the RAF is relaxed above Tg of the polymer little by little from


64

Tg to the Tmelt. It is found that a local movement is possible in the RAF (β-

relaxation) but not the cooperative segmental motions (α-relaxation)(67).

The extent of the rigid amorphous fraction (67*):

It is reported that the amount of rigid amorphous fraction is between 20%

to 90% depend on the polymer, the thermo mechanical history of the polymer

and the measurement technique used. RAF is detected by a lower heat capacity

value than the two-phase one.

Annealing was reported to have the effect upon the rigid amorphous

contents. Thermal treatment can be used to both reduce and restore the amount

of the rigid amorphous fraction. This indicates that we can adjust the amount of

the rigid amorphous fraction to a desired level using the thermal treatment.

It is not clear to what extent and how the rigid amorphous fraction will

affect the physical properties of the polymer. The effect of the aging on the rigid

amorphous fraction is still under study.

Figure 2.25: A schematic diagram to show how to compute Tg and RAF.


65

Calculating the rigid amorphous fraction RAF:

We can calculate the RAF in the semi-crystalline polymer using the

TMDSC curves (see figure (2.25)) and the following equations:

a

Sc

p

pa c

c∆

∆=χ (2.56)

where, χa is the amorphous content, ∆ cpsc is the change in heat capacity at the

glass transition of the semi-crystalline sample and ∆cpa is for the amorphous

sample, (see figure (2.25) line a, b, c). Line (a) represent the amorphous

polymer, line (c) represent the semi-crystalline polymer and line (b) represent

the glassy polymer. Line (a), (b) are theoretical lines obtained using the ATHAS

database (62). The crystallinity χc can be calculated from the integral of the DSC

melting peak of the semi-crystalline polymer.

χa +χc =1 (2.57)

χa = χam + χar (2.58)

χar = 1-χa - χc (2.59)

(where χa is the amorphous content, χam is the mobile amorphous content and

χar is the rigid amorphous content.)

Then using the equations (2.57, 2.58, 2.59) we can calculate the RAF contents in

the semi-crystalline polymer sample.

66

2.4.6-The reversing melting relaxation at the lamellae surface:

As mention before in the general theory of TMDSC the measured heat

capacity using the TMDSC technique consists of two main parts, the first part is

the base heat capacity cpb (i.e., base line heat capacity) and the second part is the

excess heat capacity ce.

The base line heat capacity is the heat capacity of the material without any

perturbation of any kind of external force, which is called “phonon heat

capacity”*. Base line heat capacity (i.e., phonon heat capacity) can be calculated

using the two-phase model or the three-phase model.

In the TMDSC measurement, it was hope from the first to measure only

the base line heat capacity, but in practical, it was not the case. What is really

measured is the baseline heat capacity plus some latent heat, kinetics, and effects

of the heat transfer in the sample calorimeter system.

Using the TMDSC we can do quasi-isothermal crystallisation

measurement see figure (2.26). As can be seen in the figure the quasi-isothermal

technique allows us to measure complex heat capacity as a function of time.

The measured heat capacity was expected to decrease during the

crystallization of the semi-crystalline polymer, which based on the fact that the

heat capacity of the polymer crystal is smaller than of the melt, but the

experimental measurement shows for some polymers, if crystallized at

temperatures in the melting region, that the measured complex heat capacity is

much larger than that of the heat capacity of the liquid see figure (2.27).

* One of the problems in the TMDSC is to find or calculate the base line heat capacity

67

Figure 2.26: Schematic diagram showing the quasi-isothermal crystallization

Figure 2.27: Schematic diagram showing the output of the quasi-isothermal crystallization.

68

The difference between the expected heat capacity and measured heat capacity

is so called as the “excess heat capacity”. The phenomena of excess heat

capacity have been reported since 1997 (70). This phenomenon can be observed

not only in polymers but also in low molecular weight liquid crystal compounds.

Many suggestions appear to explain this phenomenon of excess heat capacity.

I. Okazaki et al. (70) in 1997, introduced the term “reversible melting” to

explain this phenomena of excess heat capacity which related to the occurrence

of some latent heat effects during and after the quasi-isothermal crystallisation

of the polymer. This term of “reversible melting” means that, at any

temperature within the melting range of the polymer, a certain fraction of the

macromolecules can undergoes reversible melting process, which gives an

increase to the complex heat capacity measured.

C.Schick et al..(71,72,73) in (1998,1999,2000) work to investigate this

process of reversible melting using two techniques TMDSC and Temperature

modulated dynamical mechanical analysis (TMDMA). They found reversible

melting to be independent of the crystallinity rate. This means that the

crystallization and reversible melting are independent processes. It is found that

reversible melting is a local relaxation process occurs in the polymers and it is

found that, the higher the temperature, the faster the relaxation of the reversible

melting. This indicates that the relaxation process is most likely related to the

melt. It is found also that the reversible melting relaxation process is frequency

dependent. This method to explain the reversible melting relaxation process is

still need further investigations to see if the modulation amplitude related to the

reversible melting relaxation process amplitude. (71).

The microscopic origin of this phenomenon of excess heat capacity or

reversible melting is still an open question. Possible explanations are given by

Strobl´s (74) four state scheme of the polymer crystallisation and melting. In this

scheme, equilibrium between the melt and the just-developed native crystals is

assumed. Consider a polymer molecule in which a fraction is part of a crystal

and another fraction is a part of the surrounding melt. A small temperature

69

increase will remove another fraction of the molecule from the growing crystal

front to the melt and if the temperature decrease it will attached again to the

molecule to become apart of the growing crystal front. For such process, no

nucleation or molecular nucleation is necessary as long as a fraction of the

molecule is part of the crystal, see figure (2.28).

Figure 2.28: The Strobl´s idea of fluctuating molecular parts between the amorphous melt and the crystalline lamellae.

During mean crystallisation, the number of molecules in such situation is

increasing faster than the crystallinity. At the end of the main crystallisation, the

whole sample is filled with crystals and the remaining amorphous parts in-

between. From that time, the number of crystals remains practically constant and

their surfaces are practically not growing any more. The observed amplitudes of

mechanical and calorimetric excess heat capacity support this picture. If one

consider that the reversible melting occurring at the surface of all crystals. This

means that the all crystals stays in a state of a something like a “living crystals”

in the whole crystallisation process.

Another way to explain excess heat capacity starts from some fluctuations

around the local equilibrium of the segments under consideration. Now without

70

any external perturbations, the segment under consideration is some time part of

the crystal lamellae and another time it is a part of the surrounding melt. These

attachment-detachment fluctuations results in large entropy fluctuations as in the

case of glass transition (75) these fluctuations can be measured within linear

response as the heat capacity, which is given by:

kScp

2∆= (2.60)

Where, 2S∆ is the main entropy fluctuation and k is Boltzmann constant.

71

2.5-Dielectric Spectroscopy: 2.5.1- Introduction:

Dielectric spectroscopy is based on the interaction of electromagnetic

radiation with the electric dipole moment of the material under investigation; in

the frequency range 10-6 –1010 Hz. At very high frequency above 1010 Hz (i.e., in

the infrared and ultraviolet region) the absorption and the emission of the

electromagnetic radiation is due to the changes in the induced dipole moments,

which are dependent on the polarizability of the atoms or the molecules. At

lower frequencies the contribution of the induced dipole moments becomes

small in comparison with that of the permanent dipole moments of the system.

Consequently dielectric spectroscopy is useful for studying polar molecules in

the gaseous state or in solution state. In these states the absorption of the

radiation is mainly due to reorientation of permanent dipole in the system under

study.

Debye introduced this method in 1931, and it used since then to determine

molecular dipole moment and to study the structure of liquid and solid polar

materials. The study of condensed state is rather complicated since the electronic

states of the system cannot be described in terms of molecular orbitals;

collective (crystal states) excitons are to be considered. Rice and Jortner (76) in

(1967) showed that the dielectric behavior could be interpreted only in terms of

exciton states.

In polymeric solid and visco-elastic liquid systems the contributions of the

exciton states to the permanent dipole moment is not very large. This means that

one can regard polymeric solid containing certain groups of dipoles as a system

of not very interacting electrical dipoles. This why the dielectric spectroscopy

was developed originally for gases and solutions can be less accurately applied

to polymeric solids.

Since its introduction and for 30 years the dielectric spectroscopy was

used according to this to study only the gaseous and liquid states of the matter.

72

Only recently the technique is used on the basis of the effects of the

induced dipole polarization of polymers, which is directly connected to the

exciton states and correspondingly with the physical structure of the solid

polymers.

It is not possible to observe the orientation of the individual moments;

only the bulk polarization of the assembly can be measured. Therefore, the

response to the electric field is a statistical effect,

2.5.2-The dipole moment: The dielectric spectroscopy is attributed to the dipole moment. The origin

of the dipole moment is the positive and negative charge concentrations (i.e.

densities) in the material under investigation. Positive charges come from the

nuclei and they are localized. Negative charges come from the electronic system

and they are delocalised. The extent of the delocalisation depends on the

chemical structure of the material under investigation.

The total dipole moment of the molecule is given by:

( ) ( ) drrrr ne ][ ρρµ ∫ += (2.61)

where the ρe and ρn are the electrons and nuclei densities.

and the effective dipole moment is given by:

(2.62) ⎥⎦

⎤⎢⎣

⎡++= ∑ ∑

N

i

N

iz

N

iyxeff iii

222 µµµµ ∑

Where µxi , µyi µzi are the bonded moment component in the coordinates axes

Evidently, the dipole moment depends on the sterochemical structure of the

macromolecules. In the isotatic configuration the dipole moment have a large

values, whereas in the syndiotactic the dipole moment have a zero value*.

* Not all cases

73

2.5.3-Permittivity spectroscopy (theory):

The dielectric spectroscopy is based on the response of the material to the

periodic electric field given by:

)exp( tio ω+Ε=Ε (2.63)

By considering the field given by equation (2.63) then this response is expressed

in terms of complex permittivity:

εεε ′′−′== iED

*

**

(2.64)

where, D* is the displacement vector, *Ε is the electric field.

The loss tangent (tanδ) is then given by:

εεδ′′′

=tan (2.65)

where, ε′, ε′′ are the real and unreal (imaginary) part of the complex dielectric

permittivity.

The unreal part of the dielectric permittivity is related to the dielectric energy

dissipation by material (dielectric loss), see figure (2.29).

Figure 2.29: A typical dielectric spectroscopy curves.

74

The angular frequency (ω=2πf) dependence of ε′, ε′′ can be given by:

( ) ( )( )∫

∞

∞ −′′′′′′

+=′0

222

ωωωωωε

πεωε d

(2.66)

( ) ( ) ( )[ ]( )∫

∞∞

−′′−′′′

=′′0

222

ωωωεωεω

πωε d

(2.67)

The term εo- ε∞ is referred to as the oscillator strength of the transition or the

dielectric increment or dielectric relaxation strength.

Now from the Fröhlich-Kirkwood theory, the permittivity is expressed as:

22

32

34

23

orr

o

oo g

kTN µεπ

εεεεε ⎟

⎠⎞

⎜⎝⎛ +

+=− ∞

∞∞ (2.68)

where, (Nr) is the concentration of the repeat units, (µo) is their dipole moment

(gr) is Kirkwood reduction factor.

According to equation (2.68) the oscillator strength εo- ε∞ (i.e., the area under

the absorption curve) is related to the total dipole-moment concentration

involved in the relaxation.

The dipole relaxation time (τo) can be given by:

ω o τo=1 (2.69)

where, (ω o) is the relaxation angular frequency which is the maximum of (ε′′) as

shown in figure (2.29).

75

2.5.4-Arc diagrams:

When the ε′ is plotted against, ε′′ as shown in figure (2.30) for a single

relaxation time process and for real case of polyvinyl acetate (4)

Figure 2.30: The Cole-Cole plots (a) a real case of PVAc (b) obtaining the relaxation Parameters from the Cole-Cole plot (4)

In case of single relaxation time, such a plot must be a semicircle according to

the equation:

[ε′(ω)- ε′( ω o)]2+[ε′′( ω)]2=[ε′′( ω o)]2 (2.70)

However, the real experimental case is not semicircle, which mean that the

single relaxation time is not valid in the real experimental data. Empirical

corrections have been in introduced in order to fit the experimental data.

Cole and Cole (77) (1941), Fuoss and Kirkwood (78) (1941), Davidson and

Cole (79)(1950) and finally Scaife(80) (1963). In all these methods some

parameters represent the distribution of relaxation time has been introduced.

76

Cole and Cole introduced the equation:

( ) [ ao

o

i −

∞

∞ +=−− 1

*

)(1 ωτεεεωε ] (2.71)

Davidson and Cole introduced the equation:

( ) [ b

oo

i )(1*

ωτεεεωε

+=−−

∞

∞ ] (2.72)

Scaife introduced the generalized for both equations as:

( ) [ bao

o

i −

∞

∞ +=−− 1

*

)(1 ωτεεεωε ] (2.73)

Where, the parameters 0≤a≤1 and 0≤b≤1

The fit Scaife parameters for the Polyvniylacetate are a=0.09 and b=0.45.

Havriliak and Negami introduced another equation, which will be described in

details in chapter 4.

2.5.5-Dielectric spectroscopy as a tool to study the relaxation in the polymers:

During the past few decades, the dielectric spectroscopy has used to

obtain a large amount of experimental data. These data are reviewed by

McCrum et al (19) (1967) and additional data may be found in Ishida (15) (1969),

Hedvig (32) (1969) and Sazhin (81) (1970).

The outcome of the dielectric spectroscopy is the complex permitivity ε*

which have two parts the real part, which is the permitivity, (ε′) and the

imaginary part, which is the loss factor (ε′′) see figures (2.31, 2.32). These two

components are related to the dipole movements in the materials under study.

Considering the real part (ε′), its frequency dependence is a step down as

seen from figure (2.32).

77

Figure 2.31: The dielectric constant or Dielectric permitivity.

The two extreme values (εo) and (ε∞) as shown in figure are very important in

determining the oscillator strength or the dielectric relaxation strength which

equal to:

∆ε= εo- ε∞ (2.74)

Where, the parameter (εo) is so called the static relaxed permitivity and the

parameter (ε∞) is the unrelaxed permitivity. (∆ε) is also called dielectric

increment, which is also related to the area under curve.

Considering the imaginary part (ε´´) see figure (2.32) on the other hand

the relation between it and the frequency is a peak. The peak maximum

frequency (fo) is very important to draw the relaxation map.

Figure 2.32: The dielectric loss as a function of frequency.

78

The relaxation map can be used to calculate the activation energy of the

dielectric relaxation process. The other important parameter in the dielectric

spectroscopy is the electrical loss tangent (tan δ) which can be calculated using

equation (2.65).

Figure 2.33: The dielectric loss tangent frequency dependence.

The relation of the electrical loss tangent (tanδ) is also a peak. The peak

maximum frequency is the frequency at which the electric loss is maximum. The

loss tangent maximum frequency (fo) can be used to calculate the relaxation

energy.

79

Chapter 3

Literature survey

Some Previous Selected Work on Relaxation in Semi-crystalline Polymers using TMDSC

Introduction of the TMDSC: M. Reading et al. (106) (1993), reported that, Differential Scanning

Calorimetry (DSC) has been used for over twenty years to characterise physical

transformation such as melting and glass transitions as well as chemical

reactions such as epoxy-amina cross-linking in thermoset polymers. In its most

common from, called heat flux DSC, this technique consists of measuring the

temperature difference between a sample and a reference while the temperature

of the environment in which they both sit is increased linearIy with time. Once

the instrument has been properly calibrated, this temperature difference can be

equated with the difference in heat flow into the sample compared to the usually

inert reference material. This simple system can be used to measure properties

such as heat capacities, melting temperatures, heats of melting, reaction kinetic

etc.. Here we show how by modulating the usually linear rise in temperature

with a sinusoidal ripple the amount of information that can be obtained from this

type of experiment can be substantially. Increased and even that is can provide

some unique insights into the behaviour of thermally metastable systems. This

new technique is called Modulated DSC or MDSC.

M. Reading et al. (82) (1994), stated that “ Modulated differential scanning

calorimetry (MDSC) is a recently developed extension of DSC that adds a new

dimension to the conventional approach”.

81

Relaxation study using TMDSC:

The reported relaxation processes in the crystalline polymers are the glass

transition relaxation, the reversible melting relaxation, and the rigid amorphous

relaxation. The most prominent and oldest relaxation process reported is the

glass transition, but the other two processes are reported recently.

(1)-Glass transition:

S.wayer et al. (83) (1997), study the dynamic glass transition of polystyrene

PS using the TMDSC and 3w method. This allows obtaining a broadband heat

capacity spectroscopy in a frequency range of seven orders of magnitude (10-4-

103 Hz). They obtain an activation diagram close to the dielectric one.

A.Hensel and C.Schick(84) (1998), studied the relation between the

dynamic glass transition and the static glass transition using the TMDSC. They

found that the dynamic glass transition is related to the response of the polymer

to the periodic temperature perturbation and the static glass transition is related

to the vitrification due to cooling at a linear rate, which is equivalent to the

normal DSC cooling experiments. By varying the TMDSC modulation

frequency and the DSC cooling rate it was possible to compare both glass

transitions.

J. E. K.Schawe (85) (1998), showed that the glass transition can be

measured at different experimental conditions. Using spectroscopic methods at

relative high frequency the αa- relaxation is measured in the thermodynamic

equilibrium. In the caloric ease he call this phenomenon thermal relaxation

transition (TRT). With a conventional differential scanning calorimeter (DSC)

the transition of the equilibrium (the melt) into a non-equilibrium (the glassy

state) is measured. This effect is called thermal glass transition (TGT). In

contrast to the TGT, the TRT can be described using the linear response

approach. The temperature-modulated differential scanning calorimetry

82

(TIMDSC) technique superimposes a periodical temperature perturbation upon

the constant scanning rate of conventional DSC. This technique combines a

spectroscopic method with a linear temperature scan. Both the TGT and the

TRT are measured simultaneous.

J. E. K Schawe(86) (1998), showed that the temperature modulated

differential scanning calorimetry (TMDSC) technique can be used for heat

capacity spectroscopy in the low frequency range. Measured property is the

complex heat capacity C* = C' - iC ". The frequency dependent relaxation

transition measured by TMDSC occurs in the temperature range of the thermal

glass transition. Thus, the non-equilibrium of the glassy state influences the

TMDSC curves.

J. E. K. Schawe and S.Theobald (87) (1998), showed that the thermal

relaxation of polystyrene (PS) in the glass transition region is investigated with

both temperature modulated differential scanning calorimetry (TMDSC) and a

model calculation based on the dislocation concept. It is shown that the model

permits a proper description of the linear and non- linear effects of thermal

relaxation.

Z. Jiang et al. (88) (1998) showed that alternating differential scanning

calorimetry (ADSC), which is a commercial implementation (Mettler-Toledo) of

temperature- modulated differential scanning calorimetry (TMDSC), is used to

evaluate the activation energy associated with the relaxation processes in

polycarbonate in the region of the glass transition. This is achieved by varying

the frequency of the temperature modulation over a range of approximately one

decade and evaluating the mid-point of the step change in the complex heat

capacity.

Salmeron, M. et al (89) (1999), showed that the temperature dependence of

the relaxation times of the structural relaxation process of polystyrene is

determined by temperature-modulated differential scanning calorimetry

(TMDSC) and by conventional differential scanning calorimetry (DSC) in the

83

latter by modeling the experimental heat capacity curves measured in heating

scans after different thermal histories.

J. E. K Schawe (90) (2000) investigated the isothermal curing of a

thermosetting system by temperature modulated DSC (TMDSC) at different

frequencies. From the periodic component of the heat flow the amplitude and

the phase shift was determined. The amplitude mainly delivers information on

the thermal relaxation (vitrification process) whereas the phase shift also

includes information of the temperature dependence of the reaction rate and the

heat transfer conditions.

J. M. Hutchinson and S. Montserrat (91) (2001), presented an analysis of

temperature-modulated differential scanning calorimetry (TMDSC) in the glass

transition region is. It extends an earlier and simpler model by introducing a

distribution of relaxation times, characterized by a Kohlrausch-Williams-Watts

(KWW) stretched exponential parameter beta, in addition to the usual kinetic

parameters of relaxation, namely the Tool-Narayanaswamy-Moynihan (TNM)

non-linearity parameter x and the apparent activation energy ∆H*. They

presented a model describes, more realistically than did its predecessor, all the

characteristic features of TMDSC in the glass transition region, and it has been

used to examine the effects of the important experimental variables, namely the

period of modulation and the underlying cooling rate.

S.Weyer et al. (92) (2001), showed that complex heat capacity in

equilibrium can be considered as a compliance in the scheme of linear response.

Nevertheless, often the Tool-Narayanaswamy-Moynihan (TNM) or the Kovacs-

Aklonis-Hutchinson-Ramos (KAHR) models are used to describe complex as

well as total heat capacity in the glass transition region.

C.Schick et al. (93) (2001), showed that the relaxation strength at the glass

transition shows significant deviations from a two-phase model for semi-

crystalline polymers. Introduction of a rigid amorphous fraction (RAF), which is

non-crystalline but does not participate in the glass transition, allows a

description of the relaxation behavior.

84

S. Montserrat and J.M. Hutchinson (94) (2002), presented a new method

to determine the width of the distribution of relaxation times (DRT) based on

calorimetric measurements by temperature modulated differential scanning

calorimetry (TMDSC). The simulation of the glass transition by TMDSC, taking

into account a (DRT), shows that the inflectional slope of the complex heat

capacity, Cp* depends sensitively on the stretched exponential parameter beta of

the Kohlrausch-Williams-Watts equation, which is inversely related to the width

of the DRT (0 ≤β≤1).

85

(2)-Reversing melting:

K. Ishikiriyama and B. Wunderlich (95) (1997), found a small amount of

locally reversible melting in semi-crystalline poly(ethylene terephthalate)(PET)

during temperature-modulated differential scanning calorimetry (TMDSC). To

further study the reversibility of melting, poly (oxyethylene) (POE) is analyzed.

Low molar mass POE is known to be able to form extended-chain, equilibrium

crystals, while at higher molar mass and less favorable crystallization

conditions, nonequilibrium, folded-chain crystals grow. The TMDSC of POE

reveals variable amounts of reversible melting depending on crystallization

conditions and molar mass.

K. Kanari, and T.Ozawa (96) (1997), presented a computer simulations

have been applied to elucidate the response of a sample to temperature-

modulated differential scanning calorimetry (TMDSC) during transitions. Two

cases have been simulated; a latent heat without supercooling (represented by an

abrupt heat capacity pulse with perfect reversibility) and a latent heat with

perfect super-cooling or large hysteresis (an abrupt heat capacity change

without reversibility (i.e. the change in heat capacity is seen on heating) but not

on cooling). Because the simulation was applied to these well-characterized

phenomena, the results are useful to reveal actual sample thermal responses

during transitions. I.Okazaki and B. Wunderlich (97)(1997), detected a small amount of

locally reversible melting and crystallization in poly (ethylene terephthalate)

(PET) by temperature-modulated differential scanning calorimetry (TMDSC).

Extended-time TMDSC was used in the quasi-isothermal mode.

M. Merzlyakov et al. (98) (1998), found that the melting of flexible

macromolecules is an irreversible process, it was demonstrated recently by

Wunderlich et al., 1997, with temperature-modulated camorimetry that some of

the overall melting may be reversible within a fraction of a Kelvin. This was

taken as evidence for incompletely melted molecules with a remaining

molecular nucleus.”

86

C.Schick et al. (99) (1998), found that a TMDSC scan is a quite

complicated process since it contains in addition to the modulation an

underlying heating rate, and therefore may show some latent heat effect in each

period, influencing the measured heat capacity. Further, it is easier to understand

quasi-isothermal measurements with a periodic change of the temperature about

a mean temperature. In the case of quasi-isothermal measurements at successive

mean temperatures, the influence of the latent heat becomes apparent only at the

beginning of each step when the system is brought to a new mean temperature.

C.Schick et al. (100) (1998), found that to estimate the latent heat from a

common differential scanning calorimetry (DSC) run, one should know the

base-line heat capacity contribution to the total heat flow. And to estimate the

latent heat from the temperature-modulated DSC (TMDSC) scan is a quite

complicated process since it contains in addition to the modulation an

underlying heating rate, and therefore may show some latent heat effect in each

period, influencing the measured heat capacity.

F.Cser et al.(101) (1998), used (TMDSC) to study the heat flow during

melting and crystallization of some semi-crystalline polymers (i.e. different

grades of polyethylene (LDPE, LLDPE and HDPE), and polypropylene (PP)).

The heat capacities measured by TMDSC are compared with the hypothetical

complex heat capacities of Schawe and they show that numerically they are

equivalent; nevertheless, the concept of the complex heat capacity is

problematic on a thermodynamic basis. A reversing heat flow (proportional to

the experimental heat capacity of the material) was present at all conditions used

for the study.

M.C. Righetti (102) (1999), examined crystallized samples of poly(butylene

terephthalate) (PBT), in the melting region by means of temperature modulated

differential scanning calorimetry (TMDSC),which show reversible fusion. The

analysis of the complex heat capacity reveals that the fusion of poor crystallites

can follow temperature modulation more easily than perfect crystals, in

agreement with the findings recently reported in the literature, and that the

87

amount of reversible melting decreases with increasing the modulation

frequency.

A.Wurm et al. (73)(2000), found that, Quasi-isothermal temperature

modulated DSC (TMDSC) and temperature modulated DMA (TMDMA)

measurements allow for determination of heat capacity and shear modulus as a

function of time during crystallization. Non-reversible and reversible

phenomena in the crystallization region of polymers can be observed. The

combination of TMDSC and TMDMA yields new information about local

processes at the surface of polymer crystals, like reversible melting. Reversible

melting can be observed in complex heat capacity and in the amplitude of sheer

modulus in response to temperature perturbation. The fraction of material

involved in reversible melting, which is established during main crystallization,

keeps constant during secondary crystallization for PCL, PEN, PET and PEEK.

This shows that also after long crystallization times the surfaces of the

individual crystallites are in equilibrium with the surrounding melt. Simply

speaking, polymer crystals are "living crystals".

T. Albrecht et al.(103) (2001), showed that Poly(ethylene oxide) (PEO) in

the semi-crystalline state shows a reversible surface crystallization and melting;

a temperature decrease leads to a certain crystal thickening, a temperature

increase reversely to an expansion of the amorphous intercrystallite layers.

Dynamic calorimetry provides a means to investigate the kinetics of the process.

(3)-Rigid amorphous fraction:

H. Suzuki et al. (104) (1985), studied the heat capacity data of semi-

crystalline poly (oxymethylene) samples. “Delrin” and “Celcon”, are analyzed

in order to discuss the glass transition behavior of this polymer. These are two

types of non-crystalline poly(oxymethylene), the mobile and rigid amorphous

parts. The glass transition of the former occurs in a rather wider range of

88

temperature: it starts at 180 K and could end at 265 K. The latter, under restraint

due to the crystallites, remains frozen up to the melting temperature.

H. Suzuki et al. (66)(1985), found that, The heat capacities of 38 semi-

crystalline poly(oxymethylene)s and poly(oxyethylene)s were determined by

differential scanning calorimetry from 205 K through the melting transition. By

comparison with the well-known limiting heat capacities of the supercooled

liquids and the crystals of the macromolecules it was found that there are

negative and positive deviations from additivity of the heat capacities with

crystallinity between the glass transition and the melting transition. The negative

deviations are linked with "rigid amorphous" material, and the positive

deviations were previously linked to defect formation or early melting. The rigid

amorphous fraction in poly(oxymethylene) is constant up to the melting region,

in contrast to polypropylene, where it is decreasing with temperature. The

proposed mesophase transition in poly(oxymethylene) is shown to be a minor

effect. The poly(oxyethylene) heat capacity is governed by positive heat

capacity deviations within the rather short temperature range between glass

transition and melting.

S. Z. D. Cheng et al. (105) (1986), carried out thermal analysis of typical

poly (oxy-1, 4-phenyleneoxy-1, 4-phenylenecarbonyl-1,4-phenylene) (PEEK)

from 130 to 650 K for samples variously crystallized between 593 and 463 K or

quenched to the glassy state. They found that the heat capacity Cp, is

crystallinity independent between 240 K and the glass transition temperature Tg

and the RAF has a slightly higher Cp. Above Tg poorly crystallized samples

show a RAF that does not contribute to the increase in Cp at Tg. Crystallinity

reduces the heat capacity hysteresis at Tg. On crystallization three types of

crystallinity must be distinguished: wcH, wcL, and wcC. Fusion peaks at high and

low temperatures characterize wcH and wcL, respectively; wcC forms on cooling

after crystallization and causes an increase in Cp starting at about 460 K.

E. Laredo et al.(107) (1996), found that, bisphenol-A polycarbonate with

crystallinity degrees up to 21.8%, in a temperature interval covering the α and β

89

relaxations. The secondary β transition is found to be the sum of three

components whose variations in aged and annealed specimens have shown the

cooperative character of the β (1) and β (2) modes, contrary to the localized

nature of the β (3) component. A Tg decrease was observed by both TSDC and

DSC as a function of XC and has been related to the possible confinement of the

mobile amorphous phase in regions whose sizes are smaller than the correlation

lengths of the cooperative movements that characterize the motions occurring at

Tg. The relaxation intensity variations with crystallinity show the existence of an

abundant rigid amorphous phase in the semi-crystalline material. The relaxation

parameters deduced from the Direct Signal Analysis of the α relaxation for the

mobile amorphous phase do not show significant deviations from those found

for the amorphous material. The existence of the rigid amorphous phase has

been associated to the ductile-to-brittle transition experienced by the material at

low crystallinity levels.

W.Xu et al. (108) (1996), characterized the thermal behavior of the rigid

amorphous phase (RAF) of poly (ethylene naphthalene-2, 6-dicarboxylate)

(PEN) has been well by differential scanning calorimetry (DSC). The (RAF) is

supposed originating from an anisotropic interphase without lateral order

between isotropic amorphous and crystalline phase. However, there were no

direct proofs to confirm such suggestion. The kinetic mechanism of formation of

the RAF has not been studied.

S.X.Lu and P.Cebe (109) (1996), studied the relaxation behavior of

poly(phenylene sulfide) (PPS) Ryton (TM) film as a function of annealing

temperatures, Tw ranging from 30 °C to 140 °C. Previously, this type of semi-

crystalline PPS film was shown to possess a very large fraction of constrained,

or rigid, amorphous chains. They investigate relaxation of amorphous chains

using differential scanning calorimetry (DSC), dynamic mechanical analysis

(DMA), and thermally stimulated depolarization current (TSDC). DSC studies

suggest that annealing causes the as-received PPS film to relax some of its rigid

amorphous fraction and increase its crystallinity, for Ta > Tg. DMA results show

90

a corresponding increase in the temperature location of the dissipation peak and

a decrease in its amplitude when Ta increases above 100 °C. Analysis of the

TSDC ρ-peak due to injected space charges trapped at the crystal/amorphous

interphase provides additional information about amorphous phase relaxation.

S. X. Lu and P.Cebe (110) (1996), used the observation of the

disappearance and recreation of the rigid, or constrained, amorphous phase by

sequential thermal annealing. Temperature modulated differential scanning

calorimetry (TMDSC) to study the glass transition and lower melting endotherm

after annealing. They found that cold crystallization at a temperature Tcc just

above Tg creates an initial large fraction of rigid amorphous phase (RAP). Also

brief rapid annealing to a higher temperature causes the constrained amorphous

phase almost to disappear completely, a result that has never been reported

before. Further, subsequent reannealing at the original lower temperature Tcc

restores RAP to its original value.

S. X. Lu et al. (111) (1997), studied the effects of molecular weight on the

structure and properties of poly(phenylene sulfide)(PPS), crystallized from the

rubbery amorphous state at temperatures just above the glass transition. PPS

films were characterized using temperature-modulated differential scanning

calorimetry (TMDSC), small angle X-ray scattering (SAXS), and dynamic

mechanical analysis (DMA). Their results suggest that lower molecular weight

PPS contains a greater fraction of the rigid amorphous phase, probably as a

result of formation of taut tie molecules between crystals.

T. Jimbo, et al. (112) (1997), found that the three-component model is more

suitable for some semi-crystalline polymers including PPS. Further, they

assumed that the rigid amorphous component as an interfacial region between

the crystal phase and liquid-like amorphous phase, and the fraction depends

greatly on the prior thermal treatment. They focuses on the interface to

characterize the rigid amorphous component; the relationship between the rigid

amorphous fraction determined by differential scanning calorimeter (DSC) and

the one-dimensional interface fraction within two adjacent crystal lamellae

91

determined by small-angle x-ray scattering (SAXS) is estimated. The two results

showed a correlation: they revealed a similar tendency to decrease as annealing

temperature and time increase.

H.S.Lee and W. N. Kim (113) (1997), investigated Blends of poly(ether

ether ketone) (PEEK) and poly(ether imide) (PEI) prepared by screw extrusion

using a differential scanning calorimeter. The amorphous samples obtained by

quenching in the liquid nitrogen show a single glass transition temperature (Tg).

However, semi-crystalline samples cooled in DSC show double glass transition

temperatures.

S. X. Lu and P. Cebe (114) (1997), reported a thermal analysis study of the

effect of molecular weight on the amorphous phase structure of poly (phenylene

sulfide), (PPS) crystallized at temperatures just above the glass transition

temperature. Thermal properties of Fortron PPS, having viscosity average

molecular weights of 30000 to 91000, were characterized using temperature

modulated differential scanning calorimetry (TMDSC). they find that while

crystallinity varies little with molecular weight, the heat capacity increment at

the glass transition decreases as molecular weight decreases. This leads to a

smaller liquid-like amorphous phase, and a larger rigid amorphous fraction, in

the lower molecular weight (PPS). For all molecular weights, constrained

fraction decreases as the scan rate decreases.

B. Wunderlich (115) (1997), found that, polymer molecules have contour

lengths which may exceed the dimension of microphases. Especially in semi-

crystalline samples, a single molecule may traverse several phase areas, giving

rise to structures in the nanometer region. While microphases have properties

that are dominated by surface effects, nanometer-size domains are dominated by

interaction between opposing surfaces. Calorimetry can identify such size

effects by shifts in the phase-transition temperatures and shapes, as well as

changes in heat capacity. Especially restrictive phase structures exist in drawn

fibers and in mesophase structures of polymers with alternating rigid and

flexible segments. On several samples, shifts in glass and melting temperatures

92

will be documented. The proof of rigid amorphous sections at crystal interfaces

will be given by comparison with structure analyses by X-ray diffraction and

detection of motion by solid state NMR. Finally, it will be pointed out that

nanophases need special attention if they are to be studied by thermal analysis

since traditional 'phase' properties may not exist.

C.Bas and N. D. Alberola (116) (1997), preformed mechanical spectrometry

on poly(aryl ether ether ketone) (PEEK) polymer films in order to evaluate the

influence of a crystalline phase on the beta-relaxation. The Halpin-Kardos

model has been applied to describe the beta dynamic mechanical behavior of

semi-crystalline PEEK films considered as composite materials. Changes in the

low-temperature component of the beta-relaxation induced by the crystalline

phase are discussed in terms of mechanical coupling between phases. Moreover,

it is found that the pattern of the higher temperature component of the beta

transition is governed, in addition, by the rigid amorphous phase.

C. Schick et al. (117) (1997), found that, the relaxation strength at the glass

transition for semi-crystalline polymers observed by different experimental

methods shows significant deviations from a simple two-phase model.

Introduction of a rigid amorphous fraction, which is non-crystalline but does not

participate in the glass transition, allows a description of the relaxation behavior

of such systems. The question arises when does this amorphous material vitrify.

Our measurements on PET identify no separate glass transition and no

devitrification over a broad temperature range. Measurements on a low

molecular weight compound, which partly crystallizes, supports the idea that

vitrification of the rigid amorphous material occurs during formation of

crystallites. The reason for vitrification is the immobilization of co-operative

motions due to the fixation of parts of the molecules in the crystallites. Local

movements (β-relaxation) are only slightly influenced by the crystallites and

occur in the non-crystalline fraction.

S. Iannace and L. Nicolais (118) (1997), studied the isothermal melt

crystallization of poly(L-lactide) (PLLA) in the temperature range of 90 to 135

93

°C. A maximum in crystallization kinetic was observed around 105 °C. A

transition from regime II to regime III is present around 115 °C. The crystal

morphology is a function of the degree of undercooling. At crystallization

temperatures (Tc) below 105 °C, further crystallization occurs upon heating; this

behavior is not detected for Tc above 110 °C. The analysis of the heat capacity

increment at glass transition temperature (T-g) and of dielectric properties of

PLLA indicates the presence of a fraction of the amorphous phase, which does

not relax at the T-g, and the amount of this so-called rigid amorphous phase is a

function of T-c.

L. Hillebrand et al. (119) (1998), investigated several commercial and

noncommercial, high- and low-density and ultra-oriented polyethylene samples,

as well as polyethylene samples with inorganic fillers by inversion-recovery

cross- polarization magic angle spinning carbon-13 nuclear magnetic resonance

(NMR). They found in all these samples two types of all-trans chains in

orthorhombic crystalline domains are detected, which give two overlapping

carbon-13 lines with different line widths and different relaxation times. From

the NMR relaxation parameters we conclude that one type of the crystalline

chains, which composes 60-90% of the crystalline fraction in all samples, can

execute at room temperature, 180 °C flips with a frequency in the kilohertz

domain. The other crystalline chains are more rigid and probably are found in

more perfect structures in which such chain flips do not occur or occur on a

much slower time scale. Adding kaoline filler particles to polyethylene enhances

the contribution of the more mobile crystalline chains. The presence of the two

distinctly different types of crystalline environments is found in all polyethylene

samples investigated so far (more than 25 samples).

Y.S. Chun et al. (120) (2000), investigated the glass transition temperatures

(Tgs) and rigid amorphous fraction (X1) of the poly(ether ether ketone) (PEEK)

and polyaryIate (PAr) blends prepared by screw extrusion by differential

scanning calorimetry. From the measured (Tgs) of PEEK and PAr in the PEEK-

PAr blends, Flory-Huggins polymer-polymer interaction parameter (X12)

94

between PEEK and PAr was calculated and found to be 0.058 + 0.002 at 360°C.

From the measured crystallinity and specific heat increment at Tg, the X1 of

PFEK in the PEEK-Par blends was calculated and found to be 0.31, 036, and

0.39 for the pure PEEK, 5:5, and 4:6 PEEK-PAr blends, respectively. The

increase of X1 with Par composition suggests that the PEEK crystalline

becomes less perfect by the addition of PAr in the PEEK-PAr blends.

C. Schick et al. (122) (2001), reported that, temperature modulated DSC

(TMDSC) measurements at reasonably high frequencies allow for the

determination of baseline heat capacity. In this particular case, vitrification and

devitrification of the rigid amorphous fraction (RAF) can be directly observed.

0.01 Hz seems to be a reasonably high frequency for Bisphenol-A Polycarbonate

(PC). The RAF of PC is established during isothermal crystallization.

Devitrification of the RAF seems to be related to the pre-melting peak. For PC

the melting of small crystals between the lamellae is thought to yield the pre-

melting peak.

P. P. J. Chu et al. (123) (2001), described the time dependent rigid

amorphous phase growth kinetic by both linear William–Watts (WW) and non-

linear Narayanaswamy–William–Watts (NWW) stretch relaxation satisfactorily.

They tested their model upon the completely amorphous cyclic olefin

copolymers (COC, polynorbornene/polyethylene copolymer), where a large Tg

variation is detected with annealing. Increase of the rigid amorphous fraction as

reflected in the increase of Tg, is attributed to the growth of short-range ordered

phase due to the rigidity of the norbornene chain segment. The analysis shows

the growth kinetic (represented by the retardation time, and the stretch exponent)

that depends not only on the norbornene (NB) content but also on the NB

microblock structure. The kinetics for the growth of the rigid amorphous

domains follows a stretched exponential expression, similar to that given for

polymer crystallization and physical aging

C.Schick et al. (121) (2001), found that, heat capacity of semi-crystalline

polymers shows frequency dependence not only in the glass transition range but

95

also above glass transition and below melting temperature. The asymptotic value

of heat capacity at high frequencies equals base-line heat capacity while the

asymptotic value at low frequencies yield information about reversing melting.

For PC, PHB and sPP the asymptotic value at high frequencies can be measured

by TMDSC. For PCL and sPP the frequency dependence of heat capacity can be

studied in quasi-isothermal TMDSC experiments. The heat capacity spectra

were obtained from single measurements applying multi-frequency pertubations

(spikes in heating rate) like in StepScan DSC or rectangular temperature-time

profiles. Actually, the dynamic range of commercial TMDSC apparatuses is

limited and only a small part of the heat capacity spectrum can be measured by

TMDSC. Nevertheless, comparison of measured base-line heat capacity with

expected values from mixing rules for semicrystalline polymers yield

information about the formation (vitrification) and disappearance

(devitrification) of the rigid amorphous fraction (RAF). For PC and PHB the

RAF is established during isothermal crystallization while for sPP only a part of

the RAF is vitrified during crystallization. Devitrification of the RAF seems to

be related to the lowest endotherm.

M. Kattan et al. (124) (2002), performed differential scanning calorimetry

and thermally stimulated depolarisation current measurements are to quantify

various phases present in amorphous and semi-crystalline polyester samples

uniaxially drawn above their respective glass transition temperature. Their

results showed the appearance of a crystalline phase induced by stretching and

of a part of the amorphous phase which does not participate in glass transition.

The existence of this phase-called rigid amorphous phase-is enhanced by the

presence of crystallites rather than by the drawing.

96

Some Previous Selected Work on Relaxation in the Semi-crystalline Polymers using Dielectric Spectroscopy (DS)

K. Sawada and Y. Ishida (125) (1975), found that dielectric measurements

of poly(ethylene terephthalate) (PET) show a primary relaxation (αa~ relaxation)

due to segmental motions of the backbone chains in the amorphous region and a

secondary relaxation (β relaxation) due to local twisting motions of the main

chains in the amorphous region. The alpha/a relaxation is significantly affected

by crystallization in many ways, while the (β relaxation) is not. In this study, the

changes in the a. relaxation caused by isothermal crystallization from the glassy

state were traced by dielectric measurements, and on the basis of those results

the mechanism of the crystallization process is discussed.

C. R. Ashcraft and R.H. Boyd (126) (1976), studied the dielectric relaxation

in polyethylenes rendered dielectrically active through oxidation (0.5-1.7

carbonyls/1000 CH2) and chlorination (14-22 Cl/1000 CH2). Both linear and

branched polymers were studied. All of the relaxations between the melt and -

196°C were studied in the frequency range 10 Hz to 10 kHz (100 kHz in the

chlorinated samples). In the linear samples a wide range of crystallinities was

studied (55% in quenched specimens to 95% in extended-chain specimens

obtained by crystallization at 5 kbar). As is consistent with its being a crystalline

process, the α peak was found to discontinuously disappear on melting of the

samples and reappear on recrystallizing on cooling. The relaxation strength of

the α process increases with crystallinity, The measured relaxation strength is

less than that expected on the basis of direct proportionality to the crystalline

fraction with full contribution of all dipoles in the crystalline material. However,

the intensity is not sufficiently low for the process to be interpreted in terms of

reorientation of localized conformational defects in the crystal. The variation of

intensity with crystallinity is best interpreted in terms of full participation of

crystalline dipoles but with selective partitioning of both carbonyls and chlorines

favoring the amorphous domains. A strong correlation of the alpha loss peak

97

location (Tmax at constant frequency or log fmax at constant T) with crystallinity

for both carbonyl and chlorine containing polymers was found. This variation is

interpreted in terms of chain rotations in the crystal where the activation free

energy depends on crystal thickness. The dependence of log fmax and Tmax on

lamellar thickness as well as a comparison with the loss peaks of ketones

dissolved in parafins indicates that the chain rotation is not rigid and is

accompanied by twisting as the rotation propagates through the crystal. In

agreement with previous studies, the beta process is found to be strong only in

the branched polymers but can be detected in the chlorinated linear polymer.

The beta process was resolved from the alpha in the branched samples by come

fitting and its activation parameters determined. The gamma relaxation peak in

oxidized polymers including its high asymmetry (tow-temperature tail) and

increasing epsilon/max with increasing frequency and temperature when plotted

isochronally can be interpreted in terms of a simple nearly symmetrical

relaxation time spectrum that narrows with increasing temperature. No increase

in relaxation strength with temperature was found. The chlorinated polymers

behave similarly but appear to have some Boltzmann enhancement (450-750

cal/mole) of relaxation strength with temperature. The dependence of relaxation

strength on crystallinity indicates that the process is an amorphous one. Further,

no evidence of relaxation peak shape changes with crystallinity that could be

interpreted in terms of a crystalline component in addition to the amorphous one

was found. The comparison of the gamma relaxation strength with that expected

on the basis of full participation of amorphous dipoles indicates that only a small

fraction (-10% in oxidized linear polymers) of them are involved in the

relaxation. Thus it would seem that a glass-rubber transition interpretation is not

indicated but rather a localized chain motion. It is suggested that the gamma

process, including its intensity, width, and activation parameters, can be

interpreted in terms of an (unspecified) localized conformational (bond rotation)

motion that was perturbed by differing local packing environments. The thermal

expansion lessens the effects of variations in packing and leads to narrowing

98

with increasing temperature. The conformational motion itself leads to increase

in thermal expansion and hence a transition in the latter property. Some

previously proposed localized amorphous phase conformational motions appear

to be suitable candidates for the bond rotation motion. A weak relaxation peak

found at temperatures below the gamma and at 10 kHz may possibly be the

dielectric analog of the delta cryogenic peak found previously mechanically at

lower frequencies.

H. Sasabe, and C.T. Moynihan (127) (1978), studied the structural

relaxation in poly (vinyl acetate) (PVAc) in and slightly above the glass-

transition region has been studied by monitoring the time dependence of

enthalpy using differential scanning calorimetry and the frequency dependence

of electric polarization by dielectric loss measurements. The results have been

analyzed to yield the kinetic parameters characterizing the structural relaxation

and are compared with similar analyses of previously published shear

compliance and volume relaxation experiments. Relaxation of enthalpy, electric

polarization, volume, and shear stress in PVAc all appear to be characterized by

somewhat different relaxation times. The difference between the volume and

enthalpy relaxation times, coupled with the fact that PVAc exhibits a Prigogine-

Defay ratio greater than unity, is evidence for a previously proposed connection

between the thermodynamics and kinetics of structural relaxation in terms of an

order parameter model.

L.A. Dissado (128) (1982), suggested that relaxation in condensed matter

requires the cooperation of motions at several sites. This approach has been

formulated in terms of a dynamic distribution of partially correlated clusters will

be described in a manner illustrating the physical concepts involved. A brief

comparison with experimental data and empirical expressions will be given and

the potentialities of the approach summarized.

R. H. Boyd (129) (1984), found that, the dielectric measurements offer in

principle an attractive method for investigating phase anisotropy in oriented

semicrystalline polymers since relaxations can often be directly assigned

99

morphologically to one of the phases. However, crystal/amorphous composite or

form effects, as well as inherent phase anisotropy, can contribute to measured

specimen anisotropy. A recently presented theory adequately represents the

composite effects on specimen anisotropy in semicrystalline polymers whose

local structure is that of stacked lamellae (when the phase constants are not too

disparate). He extended that theory to include the presence of anisotropy within

the amorphous fraction. Under the assumption that the anisotropy in the

amorphous phase is uniform through the specimen, bounds in the dielectric

constant in an axially symmetric oriented specimen are derived that are

functions of the amorphous-phase dielectric constants, έ || (I) and έ┴ (I) (parallel

and perpendicular to the orientation direction), the crystal-phase dielectric

constant epsilon (II), the fractional crystallinity, and the orientational

distribution of the lamellar surface normals about the orientation direction.

B. Hahn et al. (130) (1985), found that, the temperature of the dielectric

beta-transition of poly (vinylidene fluoride) (PVDF), which is generally

assigned to the glass temperature of the liquidlike amorphous phase of PVDF, is

found to remain invariant in its compatible blends with poly(methyl

methacrylate) (PMMA) in which PVDF exhibits crystallinity.

G. H. Weiss et al. (131) (1985), that there are many polymeric materials

whose dielectric properties can be derived from the Williams-Watts relaxation

function Φ(t) = exp [-(t/τ)α]. He proposed a method for estimating the

parameters α, τ, and (εo- εoo), from dielectric loss data.

M.D.Migahed et al.(146) (1991), investigated the dielectric spectroscopy of

the acrylonitril-methylacrylate P(AN-MA) copolymer. They found three

relaxation processes β, α and ρ. They related the first tow processes to the

amorphous and crystalline phases. They found the origins of these processes are

attributed to the local motion of polymer backbone segments, dipole orientations

of the chain side groups and ionic space charge relaxation.

H. Schafer et al. (132) (1996), reported that, broadband dielectric spectra

are usually fitted to a superposition of contributions from one or several

100

parametrized processes (Debye, Havriliak-Negami, etc.). They proposed instead

to extract continuous distributions of relaxation times from complex dielectric

spectra by solving a Fredholm integral equation using the Tikhonov

regularization technique with a self-consistent choice of the regularization

parameter. This method is stable with respect to the noise and resolves multiple

dynamical processes.

K. Liedermann (133) (1996), presented a simple, five-parameter empirical

formula for the temperature dependence of the relaxation frequency is presented.

It is shown that this formula reduces to the Arrhenius equation at higher

temperatures and to the Vogel-Fulcher-Tamman equation at lower temperatures.

Apart from parameters, which may be obtained independently from either

equation, the proposed formula contains an additional parameter describing the

sharpness of the transition between the regions of validity of Arrhenius or

Vogel-Fulcher-Tamman equation. The applicability of the formula is tested on

dielectric relaxation data of acrylic polymers and on other dielectric data

available in the literature. The physical meaning of individual parameters is

discussed.

J. F. Bristow and D. S. Kalika (134) (1997), investigated the semi-

crystalline morphology of a series of poly(ether ether ketone) [PEEK]/poly(ether

imide) [PEI] blends as a function of blend composition and crystallization

condition by dielectric relaxation spectroscopy. Dielectric scans of the

crystallized blends revealed two glass-rubber relaxations for all specimens

corresponding to the coexistence of a mixed amorphous interlamellar phase, and

a pure PEI phase residing in interfibrillar/interspherulitic regions; no (pure

PEEK) crystal-amorphous interphase was observed. Variations in the

composition of the mixed interlamellar phase with crystallization temperature

were consistent with kinetic control of the evolving morphology: lower

crystallization temperatures led to an increase in the amount of PEI trapped

between crystal lamellae. Comparison of the relaxation characteristics of the

interfibrillar/interspherulitic phase with those of pure PEI indicated a much

101

broader spectrum of local relaxation environments for PEI in the blends,

consistent with PEI segregation across a wide range of size scales.

K. Fukao, and Y. Miyamoto (135) (1997), investigated the dielectric

measurements on samples of poly(ethylene terephthalate) (PET) during an

isothermal crystallization process. At the initial stage of the crystallization the

relaxation function, which is obtained from dielectric susceptibility, can be fitted

by a stretched exponential function (KWW). As the crystallization proceeds

however, a deviation from the KWW equation is observed and the shape of

dielectric loss versus frequency curve changes into a form described by the

Cole-Cole equation.

Y. L. Cui et al. (136) (2000), found that, a two-step kinetic crystallization

processes from the glass-like disordered state of N-(4-nitrophenyl)-(L)-prolinol

during the monitoring of the time evolution of dielectric strength and these are

discussed within steady state theory. The dynamics of structure relaxation in the

disordered state have been investigated by broadband dielectric spectroscopy.

The temperature dependence of the relaxation times is described by the Vogel-

Fulcher equation with an anomalous pre-exponential parameter. The anomaly is

discussed within the framework of the two-order parameter model of glass

formation proposed by H Tanaka.

I. Sics et.al. (137) (2000), investigated the dielectric relaxation behavior of

a series of ethylene-vinylacetate (EVA) copolymers by measuring the complex

dielectric permittivity in a broad frequency and temperature range. Crystallinity

of EVA copolymers was estimated by differential scanning calorimetry (DSC)

and wide-angle X-ray scattering (WAXS). The shape of the higher temperature

relaxation, appearing above the glass transition temperature Tg depends on the

VA content. It was found that this relaxation was asymmetric for VA

concentrations higher than 40 Wt% and changed to a symmetric shape at lower

VA values. Concurrently, as the VA content decreased, a major broadening of

the relaxation over a wide frequency range was observed. It is found that the

dielectric relaxation was preserved on going through the melting range of the

102

semicrystalline samples, although it exhibited changes of its characteristic

parameters that are typical for segmental relaxation appearing at Tg. This finding

allows one to associate this relaxation to the segmental motions at Tg in the

amorphous phase and not to the existence of interfacial regions.

E.E. Shafee (138) (2001), investigated the dielectric relaxation

characteristics of poly(3-hydroxybutyrate) (PHB) in the glass-rubber (alpha)

relaxation region. A series of cold-crystallized samples were examined, with

emphasis on the influence of semicrystalline morphology on relaxation

properties. The presence of crystallinity had a marked impact on the alpha -

relaxation characteristics of the various cold-crystallized specimens as compared

to the wholly amorphous material. The constraining influence of the crystallites

produced a progressive relaxation broadening and a positive offset in relaxation

temperature. With regard to the dielectric relaxation strength, Delta epsilon, we

found that the amorphous phase relaxation in the semicrystalline sample had a

completely different temperature dependence compared to the wholly

amorphous sample, leading to an increase in relaxation strength as the

temperature increases above the glass transition temperature (Tg). This was

explained by the existence of a rigid amorphous phase interface, which relaxes

gradually above the Tg of the mobile amorphous material. We suggest that the

mobile material is essentially located in the amorphous gaps between lamellar

stacks.

103

Chapter 4

Materials and Experimental Techniques

4.1-Materials: The materials used in this study were chosen from the semi-crystalline

polymers to provide a wide range of systems with different mobility and

different mechanisms of relaxation. Besides the pure polymers a copolymer of

crystalline polymers and polymer blends of crystalline polymers was chosen to

be a working materials to understand the relaxation phenomena in the semi-

crystalline copolymers and blends.

Many different polymeric materials have been investigated in this work as

follows;

(i)-Pure semi-crystalline polymers; Polyethylene oxide (PEO), syndiotactic

Polypropylene (sPP), Poly (3-hydroxybutyrate) PHB,

Poly (ether ether ketone) PEEK, Poly (trimethylene terephthalate) PTT,

Poly (butylene terephthalate) PBT, Poly (ethylene terephthalate) PET

(ii)-Semi-crystalline polymer blend; Poly(3-hydroxybutyrate)/ Polycrbolactone

PHB/PCL.

(iii)-Semi-crystalline copolymer Poly (3-hydroxybutyric acid-co-3-hydroxy

valeric acid) PHB-co-PHV with PHV contents 5% wt., 8% wt., and 12% wt.

Most of these materials were powders except for some of them were

granules. Some of these materials such as PHB were degraded after one

measurement so in order to overcome this problem we start our

measurements with fresh sample.

105

4.1.1-Pure polymers:

4.1.1.1-Poly (ethylene oxide) (PEO):

PEO Samples were supplied from Aldrich Chemical Company,

Milwaukee, USA. Its molecular weight was Mw≈ 300,000.

The material was provided as white granules so firstly it was heated to the

melt temperature 378K in the aluminum pan on a hot stage and then the pan led

was pressed gently and then the sample was compressed.

Polyethylene oxide (PEO) polymer belongs to the thermoplastic

polymers which mean that the polymer have low melting temperature 378 K.

The mass of Polyethylene oxide (PEO) sample used in the TMDSC was 7.906

mg.

4.1.1.2-Syndiotatic Polypropylene (sPP):

The (sPP) samples were provided by BASF, Ludwigshafen, Germany. In

this study, we use four kinds of the syndiotactic polypropylene (sPP). They have

the flowing specification see table (4.1):

Table 4.1: The specification of the sPP samples.

Sam.

name

Material rrr MW

(kg/mol)

Color&Shape Tm

(K)

KPP1 Kam sPP#368 98% 400 White Powder 428

KPP2 Kam sPP#48 95% 200 White Powder 408

KPP3 Kam sPP# ---- Low70-80% ----- White Powder 383

Fina4 Fina sPP 85% 200 Trans.granules 408

The (Kam) samples were provided as white powder so they were putted

directly in the aluminum pan then the pan led was pressed gently and then the

sample was compressed.

106

In the preparation of the FINA sPP samples used in TMDSC measurement

the same method of melting the granules before closing the pan was used to

prepare the granules FINA sPP.

These samples are thermoplastics so they have low melting temperatures as

shown in table (4.1). The mass of the samples used for the TMDSC was ~ 6.394

mg.

4.1.1.3-Poly (3-hydroxybutarate) (PHB):

Sample of PHB were supplied from Sigma-Aldrich Chemical Company,

Milwaukee, USA. The material was provided as white powder so it was putted

directly in the aluminium pan then the pan led was pressed gently and then the

sample was compressed.

Poly (3-hydroxybutarate) PHB belongs to the biopolymers. This polymer

is produced using large number of bacteria. It considered as natural optical

active saturated thermoplastic polyester. This material attracting much attention

now because of its great biological applications this because of its biodegradable

and biocompatible properties.

In the TMDSC work, 20 samples were prepared with masses from 3-5

mg. The reason of this large number of samples was to overcome the thermal

degradability so we start each measurement with a fresh prepared sample.

4.1.1.4- Poly (ethylene terephthalate) (PET):

The Poly (ethyleneterephthalate) PET material was provided from DSM,

NL. Its trade name is PET98-A8258.

The material was provided as white granules so it first heated to the melt

temperature 533 K in the aluminum pan on a hot stage and then the pan led was

pressed gently and then the sample was compressed.

107

This material is thermoset polymer so it has a high melting temperature

533 K. The sample used for TMDSC experiments has a mass 26.048 mg. PET

has many industrial applications. So it attracts a great deal of researches in order

to know more details about its properties.

4.1.1.5- Poly (ether ether ketone) (PEEK):

The Poly (ether ether ketone) PEEK material was provided from ICI chemical

co., BASF, Ludwigshafen, Germany. Its trade name is Vicrtex 381G.

The material was as brown granules so it first heated to the melt

temperature 640 K in the aluminium pan on a hot stage and then the pan led was



640 K. The sample used for TMDSC experiments was of mass 36.131mg. PEEK

has many industrial applications. So it attracts a great deal of researches in order

to know more details about its properties.

4.1.1.6-Poly(trimethyl terephathalate) (PTT):

The Poly (trimethylterephathalate) PTT material was provided by prof. M.

Dosiére, universite de Mons-Hainaut, Laboratorie de Physicochimie des

Polyméres, Belgum.





530K. The sample mass used for TMDSC experiments was 15.902 mg. PTT has

many industrial applications. So it attracts a great deal of researches in order to

know more details about its properties.

108

4.1.1.7-Poly (butylene terephthalate) (PBT):

The Poly (butyleneterephthalate) PBT material was provided from DSM,

NL. Its trade name is PBT T08200.





513 K. The material sample used for TMDSC experiments has a mass

16.928mg. PTT has many industrial applications. So it attracts a great deal of

researches in order to know more details about its properties.

4.1.2-Polymer blends: 4.1.2.1-Poly (3-hydroxybutarate)/Poly(epsilon-carbolactone) polyblend:

PHB/PCL blends material was provided from (Technology center,

Rostock, Germany).

The material was provided as dirty white films so it first cutted to small

pieces then they was putted in the aluminum pan and then the pan led was


This material is polymer blend so it has different melting temperatures.

The material sample used for TMDSC experiments are of the masses 2-6 mg.

The common solvent used in the blending process was the chloroform.

The blending ratio was PHB 95/PCL05, PHB90/PCL10, PHB80/PCL20,

PHB70/PCL30, PHB50/PCL 50 and PHB20/PCL80.

PHB/PCL has many medical applications because its biological

degradability. Therefore, it attracts a great deal of attention in order to know

more details about its properties.

109

4.1.3-Copolymers: 4.1.3.1-Poly (3-hydroxybutyrate-co-3hydroxyvalerate) PHB-co-HV:

PHB-co-HV copolymer material was supplied from (Aldrich chemical

company, Milwaukee, USA.)

In this study, we used three HV concentrations, 5%, 8% and 12% wt. The

PHB-co-HV 5% and 8% was provided as white powder so they was putted

directly in the aluminium pan then the pan led was pressed gently and then the

sample was compressed. Whereas the PHB-co-HV 12%wt. was provided as

white granules so it first heated to the melt temperature 473 K in the aluminium

pan on a hot stage and then the pan led was pressed gently and then the sample

was compressed.

This copolymer has different melting temperatures. Different samples

with varying HV content (5%, 8% and 12%wt.) were used for TMDSC

experiments with different masses; 7.704, 6.202, 33.988 mg respectively.

110

4.2-Experimental Techniques: 4.2.1-Temperature modulated differential scanning calorimetry (TMDSC):

4.2.1.1-Sample preparation:

Figure 4.1: Sample used in TMDSC experiment.

Firstly, the aluminum pan was weighted without the sample. Then the

sample was put in an aluminium pan and covered with led made of aluminium

too, see figure (4.1). The sample then pressed in the pan with the device as

shown in figure (4.2).

Figure 4.2: The compressor of the TMDSC sample.

111

After compressing, the sample is ready for the DSC and TMDSC measurements.

The sample pan has the dimensions (diameter=6.845mm, thickness = 0.820

mm). In our measurements, we used also some mass of aluminium as a

reference for our measurements.

4.2.1.2-TMDSC measuring device:

The TMDSC device used is called DSC-2C and it was produced by

( Perkin Elmer, USA). This device was controlled by computer program made

by (IFA GmbH, Germany ).

Figure (4.3) shows the DSC-2C device used through the measurements

and its controller computer.

Figure 4.3: DSC-2C device used in measuring both the DSC and TMDSC data at Rostock university, physics dept., polymer group.

112

4.2.1.3-The Perkin Elmer DSC-2C TMDSC device electronic structure:

The Perkin Elmer DSC-2C is a power compensated isoperibolic working

differential scanning calorimeter belong to the new generation which usually

equipped with computer based data acquisition system and user-friendly

software for computation of the acquired calorimetric curves. This device is a

commercially available scanning calorimeter and it consists of two parts: the

digital and the analogue part. The digital part contains the whole electronics

necessary to convert the input parameters (Tstart, Tend, heating rate, periodic time,

temperature amplitude) into a voltage (i.e., program-voltage), which is directly

proportional to the target temperature (i.e., program-temperature).

The regulation circuits of the analogue part of the DSC-2C need this

voltage as an input quantity while the output quantity is represented by the

signal-voltage which itself is proportional to the heat flux into the sample see

figure (4.4).

Figure 4.4: Show the schematic diagram of the DCS-2C used in the DSC and

TMDSC Measurements (after W.Winter and G.W.H.Höhne, 1991).

113

Sample: Sample File: Base File:

Sample Mass: Empty pan mass:

Date &time:

S.No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 w.t T1 T2 H.R Iso.1 Iso.2 T.R AT tp P.W mod

S.No 16 17 18 19 20 21 22 23 24 25 26 27 28 29 w.t T1 T2 H.R Iso.1 Iso.2 T.R AT tp P.W mod

Remarks:

Figure 4.5: Show the program sheet used during the measurements.

114

4.2.1.4-TMDSC measuring program:

The measuring program shown in figure (4.5) has the experimental parameters

as follows:

Wt: is the waiting time before start the measuring program.

T1: is the start temperature.

T2: is the end temperature.

H.R: is the heating rate.

Iso1: is the first isothermal.

Iso2: is the second isothermal.

T.R.: is the triggering rate (i.e. the no. of points per step).

AT: is the temperature amplitude.

tp: is the periodic time of the temperature signal which is related to the frequency

by the relation f = 1/tp.

Beside these experimental parameters there is a control parameters. These

parameters are:

PW: Pulse width always has the value of 8.

Mod: this parameter has two values 1 for DSC mode and 2 for the TMDSC

mode.

As shown in the figure (4.5) the program consists of 29 steps each step can has

the following diagram. See Figures (4.6, 4.7).

Figure 4.6: The program heating step component.

115

Figure 4.7: The program cooling step component.

4.2.1.5-TMDSC Experimental techniques:

The TMDSC has three basic different experimental techniques. These

techniques are as follows:

(1)-Modulated scan measurement technique:

In which the applied temperature modulated with a specified periodic time

(i.e., temperature frequency), while increasing the temperature with a specific

heating rate (i.e., underlying heating rate).

The advantage of this mode is to monitor the dynamic transition such as

dynamic glass transition (i.e., relaxation) and crystallisation and enthalpy

relaxation.

The disadvantage of this mode is the contribution of the latent heat to the

measured complex heat capacity.

(2)-Isothermal measurement technique:


(i.e., temperature frequency) at a quasi-constant temperature. (± 0.1 K).

116

The advantage of this mode is the overcome of the latent heat problems,

and monitors the temperature dependent transitions such as structural

transition and frequency dependent transitions (i.e., relaxation).

(3)-Step heating measurement technique:


(i.e., temperature frequency) while applying a ladder temperature program

with a step 1-5 K. The advantage of this mode is to monitor the change in the

complex heat capacity point by point.

4.2.1.6-TMDSC experimental data analysis:

The output of the TMDSC experiment is the heat flow versus the time and

temperature. This relation is used to obtain the heat capacity cp ,which is the

main outcome from both the DSC and TMDSC.

In the simple DSC case the heat capacity cp can be computed as:

qmHfcs

p *=

(4.1)

Where (Hf) is heat flow in (mW), (ms ) is sample mass in (mg) and (q) is the

heating or cooling rate and this equation gives cp in (J/g.K).

In the case of modulated temperature DSC or TMDSC the heat capacity,

calculation is more complicated. The complication is because of that the heat

flow is a modulated quantity. This makes the calculated heat capacity a complex

quantity not a scalar one. To calculate the complex heat capacity |cp*| from the

modulated heat flow we used Fourier transformation.

117

(a)-TMDSC mathematical background: The heat flow can be computed using the following equation: Heat flow Φ=k∆T (4.2)

The measuring program in conventional DSC is given by:

T(t)=To+ßot (4.3)

where, ßo =Heating rate, To is the starting temperature.

The heat flow measured in conventional DSC is given by:

Φm=(msCp+Cal)ßo-∆ΚCr ßo+φLoss1 (4.4)

where, (∆Κ) is calibration factor, (Cr )is the heat capacity of the reference and

the φLoss1 is the lost heat flow

For the base curve measurement we have:

Φb=CAl ßo - ∆ΚCr ßo +φLoss2 (4.5)

Subtracting both curves one get for the Heat flow

Φ=mscpßo (4.6)

which represents the measured sample curve.

118

In the TMDSC, there is an additional term, which is periodic

T(t)=To+ßot + Tasin ωot (4.7)

Where, ωo =2πf is the angular frequency and (f ) is the frequency

The temperature change is then given by:

( ) tTtdtdT

oaoo ωωββ cos+== (4.8)

Moreover, the heat flow for the measured curve is given by:

Φ(T)= Φdc(t,T)+ Ka (ωo)Ta cs cos(ωot-Φm(ω)) (4.9)

Where,

Φdc=conventional DSC curve.

Ka=Amplitude calibration factor.

cs=Heat capacity of the sample.

Φm=Phase shift between the heat flow and the temperature change.

Φ(T)= Φdc(t,T)+ Ka (ωo)Ta cs cos(ωot-Φm(ω)) (4.10)

Formula (4.10) represents the measured heat flow curve in the TMDSC.

119

(b)-TMDSC data treatment Algorithm:

To calculate the complex heat capacity from the modulated heat flow a

MathCAD (6) program was made.

The algorithm of the calculation is as the following:

The measured heat flow Φ is given by:

Φ=C*q (4.11)

Applying Fourier transform F [f] (ω)=(f(t),ei(ω,t) ) by considering this

transformation eq. (4.11) can be rewritten as:

F [Φ]= F[C*q] = F[C]*F[q] (4.12)

This equation gives:

F[C]=F [Φ]ω / F [q] ω (4.13)

If the temperature modulation given by:

T(t)=To+qot+AT sin(ωt) (4.14)

Then the total heat flow can be a superposition of the underlying heat flow

Φdc(t) and the periodic heat flow Φp (t) are given by:

( ) ( )∫

+

−

′′Φ=Φ2

2

1p

p

tt

tt

pdc tdt

tt (4.15)

( ) ( ) ( )ttt dcp Φ−Φ=Φ (4.16)

120

The periodic heating rate is given by:

)cos()cos()()( tAtAqdtdTtq qTop ωωω ==−= (4.17)

The first harmonic of the periodic heat flow Φ1 (t) is given by:

)cos()cos()sin()cos()( 221 δωδωωω −=−+=+=Φ Φ tAtbatbtat

where (a,b) are given by:

( ) ( )∫+

−

′′′Φ=2

2

)cos(2p

p

tt

tt

p

tdttt

ta ω (4.18)

( ) ( )∫+

−

′′′Φ=2

2

)sin(2p

p

tt

tt

p

tdttt

tb ω (4.19)

The phase angle δ which is the difference between the periodic heating rate qp(t)

and the first harmonic of the heat flow Φ1 (t)

δ=arctan (b/a) (4.20)

Now the complex heat capacity can be computed from the formula:

qw A

AC Φ=|| (4.21)

Then the real part (Ćw) and the imaginary part (C˝w) of the complex heat

capacity are calculated as:

δcos|| CCw =′ (4.22)

δsin|| CCw =′′ (4.23)

121

4.2.2-The dielectric spectroscopy: 4.2.2.1-Sample preparation:

Figure 4.8: The dielectric sample used through the measurements.

The sample was prepared for the dielectric measurement as thin film between

two-cupper disks shaped electrodes “sandwich”, see the figure (4.8).

The studied materials were first melted at the melting temperature on one

of the electrodes then the spacers was added to the sample then the other

electrode was added and then the whole system (i.e., the sample and the two

electrodes) was quenched to the room temperature. The sample thickness was

2x10-2 mm and the electrode thickness was 2mm each.

Spacers were added to the samples in order to be able to measure at the

samples´s melting temperatures and they were from silica, which have a very

high melting temperature.

122

4.2.2.2-The dielectric spectroscopy system:

The used dielectric device is a commercially available one and it measures

in the range (10-3-107 Hz), this called “Broad band dielectric spectroscopy”. The

device was supplied from NOVOCONTROL GmbH, Germany. The device with

its supported liquid nitrogen cryostat is shown in figure (4.9).

Figure 4.9: Dielectric spectroscopy device used in measuring at Rostock university, physics dept., polymer group.

123

The system used in the measuring dielectric data is Alpha dielectric

material analyzer see the schematic diagram shown in figure (4.10)

Figure 4.10: Schematic diagram of the system used to measure dielectric data.

The analyzer connected directly to the measuring cell as shown. The

system is controlled by a computer program. The software for measuring and

controlling called “WinDETA”.

The controlling and measuring software were provided by

NOVOCONTROL, GmbH, Germany. It capable of measuring in the frequency

range (µHz-GHz) and the temperature range (113-773 K). Figure (4.11) shows

the measuring cell.

Figure 4.11: The dielectric-measuring cell operated by the author.

124

4.2.2.3-Dielectric data analysis:

The measuring system gives the relation between frequency (f), the

dielectric constant (ε′), and the dielectric loss (ε′′) and dielectric loss tangent

(tan δ). The data is drawn on ORIGIN(7) software and the fitting for dielectric

loss ε′′ experimental data was done by the same software using the fitting

equation “2 signals Havriliak-Negami equation”. In addition, a term of the

conductivity contribution was added to the model to account for the dc

conductivity.

Data Analysis:

In order to describe the dielectric spectra quantitatively superposition of

model functions according to Havriliak and Negami (139) and a conductivity

contribution were fitted to the dielectric loss data (ε״ ). The fitting procedure was

done on the basis of the (Marquardt fitting procedures). The fitted equation was

of the form:

nHN

S)())(1(

)(ωωτ

εεωε γβ ++

∆+=∗ ∞ (4.24)

With:

ω=2πf (4.25)

ε*(ω)=ε′+iε″ (4.26)

)cos(.. 2 γϑεεεγ−

∞ ∆+=′ r (4.27)

)sin(.. 2 γϑεεγ−

∆=′′ r (4.28)

ββ ωτβπωτ 2)()2

cos(.)(21 ++=r (4.29)

125

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+=

− )2

cos()(

)2

sin(arctan

βπωτ

βπ

ϑβ

(4.30)

The term S/(ω)n is related to the conductivity. The parameter (S) is the dc-

conductivity and (n) is the power of the dc–conductivity term. For Ohmic

behavior, (n) equal unity. Deviations of (n) from unity caused by the

polarization processes. The (β) and (γ) fitting parameters are the symmetry and

asymmetry shape parameters.

126

Chapter 5

Results and Discussion

128

(A) Thermal Studies

129

Part 1

DSC measurements

130

5.1-DSC Measurements

We applied DSC in investigating the semi-crystalline polymers to have

information about the thermal changes in different temperature regions. The

results of the DSC were used to build a TMDSC programs to study these

thermal changes, which, indicate different relaxations processes.

5.1.1- Poly(3-hydroxybutarate)(PHB): (a) Thermal characteristics of the PHB polymer:

To obtain the thermal characteristics of the PHB sample a DSC program

was used. This DSC program is shown in figure (5.1). This DSC program was

repeated for the crystallisation temperatures (283, 323, 328, 333, 338, 343, 348

K).

The DSC results shown in figure (5.2) show that the PHB sample can be

crystallized at the temperature range (312-327 K). This can clearly seen from the

exothermic crystallization peak. Moreover, it melts in the temperature range

(414-443 K), which can be obtained from the melting endothermic peaks. In

addition, it is completely melt at temperature range (460-473 K), which can be

seen from the line after the large endothermic peak.

Figure 5.1: The DSC program used to investigate the thermal

characteristics of the PHB sample.

131

300 320 340 360 380 400 420 440 460-5

0

5

10

15PHB

c p in

J/g

.K

T in K

283K 323K 328K 333K 338K 343K 348K 283K

Figure 5.2: The DSC curves for different crystallization temperatures for the PHB sample with the heating rate 10 K/min.

Table 5.1: The heat of fusion and crystallinities calculated using the DSC

measurements for the PHB sample.

Tc (K) 283 323 328 333 338 343 348

∆Hf (J/g) 95.84 82.67 83.69 85.25 88.27 89.93 94.13

Xc (%) 65 56 57 58 60 61 64

The crystallinity degree was calculated using the integration of the

endothermic melting peak divided by the sample mass, which gives the heat of

fusion of the semi-crystalline sample (∆Hfsc) by dividing this value by the same

value of the 100% crystalline theoretical value from ATHAS database we can

calculate the crystallinity degree of the semi-crystalline polymer sample.

The table (5.1) shows the heat of fusion and the crystallinities obtained

from the DSC measurements of the PHB sample. From this table we can see that

132

the PHB sample crystallize at 283 K with crystallinity degree Xc =65% the same

as at 348 K.

(b) Crystallisation dynamics analysis:

The next step was to check for the slowest crystallisation mechanism in

order to follow the crystallisation process, which may lead to information about

the αc–relaxation process that is a structural induced relaxation process.

The used DSC program was of successive cooling with rate of cooling 80

K/min, see figure (5.3).

Figure 5.3: DSC temperature program used to investigate the crystallisation temperatures of the PHB sample.

10 20 30 40 50

3

4

5

388K398K408K418K428K

438K

358K

368K

378K

PHB

Hea

t Flo

w in

mW

time in min

Figure 5.4: The heat flow results obtained for the PHB sample which show different crystallisation mechanism.

133

The results shown in figure (5.4) indicate that the PHB sample have different

mechanisms of the crystallization process. The results also show that the PHB

polymer can crystallize slowly at 378 K. The idea of this measurement was to

check the possibility to follow the crystallization process in the PHB sample.

The results of these measurements were used in another study, to obtain

information about how the RAF* vitrified. This vitrification process was denoted

by αc–relaxation that is a structural induced relaxation process. This relaxation

will be studied in details in part2 of this chapter.

5.1.2- Syndiotactic polypropylene (sPP):

The idea was to study the thermal changes using the DSC for the different

samples of sPP. The DSC program was to melt the samples at 443 K then cool

down to 220 K with a fast cooling rate (i.e., quenched) and then heat the samples

to the melting temperature (443 K) with heating rate 10 K/min.

The DSC results of sPP samples show the thermal characteristics of the

samples (see figure (5.5)). We can see that the static glass transition of the sPP

samples can be found at 269 K for the KPP3 sample and 275 K for the KPP1,

KPP2, FINA4 (see Chapter 4 for the sPP samples details).

The figure also shows that the KPP3 sample can be fast crystallised in the

temperature range (303-321 K). However, before this temperature range it can

be slowly crystallised. Whereas for KPP1, KPP2, FINA4 this range changed to

(290-311 K).

*RAF is an abbreviation for Rigid Amorphous Fraction (see chapter 2 for details)

134

220 240 260 280 300 320 340 360 380 400 420 440

-3

-2

-1

0

1

2

3

4

5

6

KPP 1,2,FINA4

KPP3

c p in

J/g.

K

T in K

sPP

Figure 5.5: The DSC of the sPP samples heated with 10 K/min after it was cooled from melt 443 K.

In addition, this figure shows that the melt temperatures for these samples

are different as follows (Tm for KPP3 =390 K, KPP1= 400 K, FINA4=411K and

for KPP2=418 K). In general, it is seen that KPP3 sample has different thermal

characteristics than the other sPP samples.

The next step was to study in more details the thermal characteristics of

the different sPP samples the idea was to check the effect of repeated heating

and the effect of the cooling rate by which the polymer can be cooled from the

melt. This is to study the thermal stability of the sPP polymer samples.

Figure (5.6) shows the uncorrected heat flow for the KPP1 sample. The

figure shows that the heating for the second time produce the same curve, which

means the polymer, is stable and there is no change in the heat flow. The figure

also shows that when the cooling rate is changed to 80K/min there is no change

at the glass transition, but there is a change in the endothermic melting peak.

135

240 260 280 300 320 340 360 380 400 420 4404

6

8

10

12

14

16

18

20

after cooling with 80K/min

after cooling with 10K/min 1st and 2nd time

Tm

Tg

KPP1

Hea

t Flo

w in

mW

T in K

Figure 5.6: The uncorrected heat flow for the KPP1 sample heated from 220 K to 440 K with 10 K/min.

Figure (5.7) shows the uncorrected heat flow for the KPP2 sample. The

figure shows that the heating for the second time produce the same curve, which

means the polymer, is stable and there is no change in the heat flow. The figure

also shows when the cooling rate is changed to 80K/min there is no change at

the glass transition. But there is a crystallization peak found at 300 K and a

change in the melting peak.

136

240 260 280 300 320 340 360 380 400 420 4404

6

8

10

12

14

16

18

20

Tm

TCTg


crystallization peak after cooling with 80K/min

KPP2

Heat

Flo

w in

mW

T in K


The same results was found for the KPP3, FINA4 (see figures (5.8,5.9))

and it was found that the largest exothermic peak is that for KPP3 sample (see

the curve in the figure (5.8).

137

240 260 280 300 320 340 360 380 400 420 4402

4

6

8

10

12

14

16

18

20

TC

Tg

Tm


crystallization after cooling with 80K/min

KPP3

Heat

Flo

w in

mW

T in K


240 260 280 300 320 340 360 380 400 4202

4

6

8

10

12

14

16

18

20

22after cooling with 10K/min 1st and 2nd time

crystallization peak after cooling with 80K/min

Tm

TcTg

FINA 4

Hea

t flo

w in

mW

T in K

Figure 5.9: The uncorrected heat flow for the FINA4 sample heated from 220 K to 440 K with 10 K/min.

138

5.1.3- Poly (ether ether ketone) (PEEK):

During the PEEK investigation, the DSC heating scan was done for the

sample to have information about the thermal transitions in the PEEK polymer.

The sample was quenched first by heating it on hot stage until it was melt at 650

K then it was putted on a cold copper plate (at 298 K). The DSC program was to

heat the sample with heating rate 20 K/min from 300 K to 650 K.

350 400 450 500 550 600-50-40-30-20-10

0102030405060

Tmelt

Tc

Tg

PEEK

Hea

t flo

w in

mW

T in K

Figure 5.10: The uncorrected heat flow curve for quenched PEEK sample. The result of this heating scan is shown in figure (5.10), which shows the glass

transition (see the first arrow in figure (5.10)) at 425 K and the exothermic

crystallization peak (see the second arrow in figure (5.10)) at 453 K. At the end

of the curve, we can see the endothermic melting peak (see the third arrow in

figure (5.10)) at 616 K. Another result from figure (5.10) that the PEEK polymer

can be fast crystallized in the temperature range (444-464 K) and slowly

crystallized before and after this range. In addition, the polymer stays in the

solid glassy state in the temperature range (340-416 K).

139

5.1.4-Poly (trimethylene terephthalate) (PTT):

To start our investigations for PTT it is normal to characterize the PTT

sample using the DSC. The DSC program was to heat the sample from 300K to

520K with heating rate 20K/min. The result shown in figure (5.11) is the heat

flow curve for the PTT sample, which indicates the glass transition at 320K. In

addition, the PTT polymer can be fast crystallized in the range (344-360K) but

before this range and after this range it can be slowly crystallized.

320 340 360 380 400 420 440 460 480 500 520

-30

-20

-10

0

10

20

30

40

TC

TmTg

T in K

Heat

flow

in m

W

PTT

Figure 5.11: The heat flow curve for the PTT sample heated from 300 to 530 K with 20 K/min. In addition, the PTT polymer melt around 500 K. Further, the PTT polymer is in

glassy state in short temperature range (310-317 K). We can see also the PTT

polymer remains for a long temperature range (360-460 K) before it starts to

melt.

140

5.1.5- Polymer blend Poly (3-hydrobutarate)/Polycrbolactone (PHB/PCL):

The results of the DSC investigations for the polymer blend PHB/PCL are

shown in figure (5.12). The DSC program was to melt the sample at 470 K then

cool down to 220K with different cooling rate and then wait for 15 min then

heat with 10 K/min to 470 K, (see figure (5.12)).

Figure 5.12: The DSC program used in the PHB, PCL, PHB/PCL blend investigations. This DSC program was made to investigate the effect of cooling rate on the

PHB/PCL blend because the cooling rate affecting the crystallization of the

samples. Also to characterize the PHB/PCL blend thermally. Finally, it was

made to know the suitable crystallization conditions.

5.1.5.1- Pure PHB:

The figure (5.13) shows the DSC curves (heating scans) for heating the

sample of pure PHB that was cooled using different cooling rates. As we can see

from the figure, the PHB polymer cannot be crystallized at all if it is quenched.

The second remark on the figure is that the crystallization exothermic peak at

325 K decreases if the cooling rate is 10 K/min and it increase if the rate is 80

K/min. As a general, we can say as the cooling rate increase the crystallization

141

peak increase. In addition, it is clear that at 80 K/min rate of cooling the curve

shows a clear static glass transition at 275 K and melting temperature at 447 K.

250 300 350 400 450-4

-2

0

2

4

6

8

h e a tin g a fte r q u e n ch in g h e a tin g a fte r co o lin g w ith 1 0 K /m in h e a tin g a fte r co o lin g w ith 8 0 K /m in

c p in J

/g.K

T in K

PH B

Figure 5.13: The heating scan of the pure PHB sample with 10 K/min. 5.1.5.2- PHB95/PCL5 % wt. blend:

The DSC program for the PHB 95/ PCL 5 % wt. blend was the same as

for pure PHB. The effect of the cooling rate was investigated and the results

shown in the figure (5.14), which shows that at cooling rate 10 K/min there, is

no exothermic crystallization peak but as the cooling rate increase to 80 K/min

the peak found at 320 K. By comparing with the PHB, we can easily find that

this peak attributed to PHB. Moreover, as the sample quenched the peak

disappears again. In addition, there is no endothermic melting peak of the PCL

yet this because the ratio of the PCL is only 5% wt. The only endothermic

melting peak is for PHB. In other words the scan do not show any signature of

the PCL polymer. Finally, we can find a static glass transition at 276 K.

142

2 5 0 3 0 0 3 5 0 4 0 0 4 5 0-3

-2

-1

0

1

2

3

4

c p in J

/g.K

h e a tin g a f te r q u e n c h in g h e a tin g a f te r c o o lin g 1 0 K /m in h e a tin g a f te r c o o lin g 8 0 K /m in

T in K

P H B 9 5

Figure 5.14: The heating scan of the PHB95/PCL5 % wt. blend with 10 K/min. 5.1.5.3- PHB90/PCL10 % wt. blend:





the peak found at 320 K (PHB-peak). In addition, as the sample quenched the

peak disappears again. Moreover, there is a very small endothermic melting

peak of the PCL (see the arrow) this because the ratio of the PCL is only 10%

wt. The only endothermic melting peak is for PHB at 447 K. In this blend ratio,

the scans start to show a PCL signature. Finally, the static glass transition is

found at 277 K.

143

250 300 350 400 450-3

-2

-1

0

1

2

3

4

c p in J

/g.K

h ea tin g a fte r q u e nch ing h ea tin g a fte r co o lin g 10 K /m in h ea tin g a fte r co o lin g 80 K /m in

T in K

PHB90

Figure 5.15: The heating scan of the PHB90/PCL10 % wt. blend with 10K/min.

5.1.5.4- PHB80/PCL20 % wt. blend:




no exothermic crystallization peak but as the cooling rate increase to 80 K/min,

the peak found at 320 K (PHB) also a clear static glass transition at 275 K.

Moreover, as the sample quenched the peak disappears again. In addition, there

is a very small endothermic melting peak of the PCL (see the arrow) found at

330 K this is because the ratio of the PCL is only 20% wt. The only large

endothermic melting peak is for PHB. Here we find the PCL signature start to

appear increasingly.

144

250 300 350 400 450-4

-3

-2

-1

0

1

2

3

4

c p in J

/g.K

heating a fte r quench ing heating a fte r coo ling 10K /m in heating a fte r coo ling 80K /m in

T in K

PHB80

Figure 5.16: The heating scan of the PHB80/PCL20 %wt. blend with 10K/min. 5.1.5.5- PHB70/PCL30 % wt. blend:



shown in the figure (5.17), which shows that at cooling rate 10 K/min there is no

exothermic crystallization peak but as the cooling rate increase to 80 K/min the

peak found at 320 K (PHB) and as the sample quenched the peak disappears

again. In addition, there is a small endothermic melting peak of the PCL (see the

arrow) this because the ratio of the PCL is increased to 30% wt. The only large

endothermic melting peak is for PHB. Moreover, the exothermic crystallization

peak found at 320 K is decreased. This may be due to an interaction between the

two polymers because the ratio of the PCL is 30%wt.

145

250 300 350 400 450-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

c p in J

/g.K

heating after quenching heating after cooling 10K/m in heating after cooling 80K/m in

T in K

PHB70

Figure 5.17: The heating scan of the PHB70/PCL30 % wt. blend with 10 K/min. 5.1.5.6- PHB50/PCL50 % wt.:





the peak found at 320 K (PHB) and a clear static glass transition at 275 K. In

addition, as the sample quenched the peak disappears again. Further, there is an

equal endothermic melting peak of the PCL this because the ratio of the PCL is

50% wt. The endothermic melting peak for PHB and PCL are equal. This result

reflects that the blend is not compatible.

146

2 5 0 3 0 0 3 5 0 4 0 0 4 5 0-4-3-2-101234567

c p in J

/g.K

h e a t in g a f te r q u e n c h in g h e a tin g a f te r c o o lin g 1 0 K /m in h e a tin g a f te r c o o lin g 8 0 K /m in

T in K

P H B 5 0

Figure 5.18: The heating scan of the PHB50/PCL50 % wt. blend with 10 K/min. 5.1.5.7- PHB20/PCL80 % wt. blend: The DSC program for the PHB 20/ PCL 80 % wt. blend was the same as for

pure PHB. The effect of the cooling rate was investigated and the results shown

in the figure (5.19), which shows that at cooling rate 10 K/min there, is no

exothermic crystallization peak and if the cooling rate increased to 80 K/min

there is no peak found and as the sample quenched there is no peak. This means

that the PHB cannot be crystallized at this ratio of blending. In addition, the

endothermic melting peak of the PCL is larger than the endothermic melting

peak of the PHB this because the ratio of the PCL is 80% wt.

147

2 5 0 3 0 0 3 5 0 4 0 0 4 5 0-4-3-2-101234567

c p in J

/g.K

h e a t in g a f te r q u e n c h in g h e a t in g a f te r c o o l in g 1 0 K /m in h e a t in g a f te r c o o l in g 8 0 K /m in

T in K

P H B 2 0

Figure 5.19: The heating scan of the PHB20/PCL80 % wt. blend with 10 K/min. 5.1.5.8- Pure PCL: The DSC program for the PCL sample was the same as for pure PHB. The effect

of the cooling rate was investigated and the results shown in the figure (5.20),

which shows the endothermic melting peak of the PCL. There is no exothermic

crystallization peak for the PCL this because the crystallization temperature is

out of our measurement temperature range. The effect of the cooling rate before

heating was investigated and it show that if the cooling rate is 10 K/min and 80

K/min the endothermic melting peak of the PCL is shifted toward the higher

temperature.

148

250 300 350 400 450-4

-2

0

2

4

6

8

1 0

1 2

1 4

c p in J

/g.K

h e a tin g a fte r q u e n ch in g h e a tin g a fte r co o lin g 1 0 K /m in h e a tin g a fte r co o lin g 8 0 K /m in

T in K

PC L

Figure 5.20: The heating scan of the pure PCL sample with 10 K/min. Table 5.2: The thermal characteristics of the PHB/PCL polymer blend.

Tg PHB(K)

Tc PHB(K)

Tmelt PHB(K) Tmelt PCL(K)

Mat./ C.R 10 80 10 80 10 80 Que. 10 80 Que.PHB 276 276 322 325 445 447 449 ---- ----- ---- PHB95 302 276 --- 320 445 446 448 328 330 ---- PHB90 ----- 276 318 320 444 447 448 329 330 335 PHB80 275 276 318 320 444 446 448 329 330 335 PHB70 274 275 318 320 444 446 448 329 329 335 PHB50 ----- 276 --- 320 445 448 449 330 330 339 PHB20 275 275 316 319 444 446 448 330 329 341 PCL ----- ----- ---- ---- ---- --- ---- 330 329 341

H.R=10 K/min

149

Table 5.3: The maximum heat capacity of the endothermic melting peak of the PHB/PCL polymer blend.

Cp PCL(J/g.K) Cp PHB(J/g.K) Material/C.R 10 80 Que. 10 80 Que. PHB ------ ----- ---- 6.930 7.481 7.789 PHB95 0.220 0.115 ---- 4.106 3.342 3.379 PHB90 0.496 0.345 0.436 3.224 3.470 3.414 PHB80 1.220 1.099 1.181 4.044 4.373 3.960 PHB70 1.271 1.101 1.181 2.681 2.625 2.648 PHB50 6.585 6.702 5.538 5.980 5.562 5.100 PHB20 6.218 5.632 4.920 1.290 1.304 1.265 PCL 11.724 10.130 12.407 ------ ----- ------

Table (5.2) shows the thermal characteristics of the PHB/PCL polymer

blend. It is clear from the table that the static glass transition temperature of the

PHB polymer in the polymer blend is not much affected by the change of the

cooling rate before heating the sample. Further, the crystallization temperature

of the PHB polymer in the polymer blend is shifted by 5 K towards low

temperature side by the blending process. Further more, the melting temperature

of the PHB in the polymer blend is not much affected neither by the blending

process nor cooling rate. Finally the melting peak of the PCL polymer in the

polymer blend is affected by the blending process that it shifted towards the

lower temperature side by 3-7 K as can be seen from the table.

Table (5.3) shows how the maximum heat capacity of the PHB

endothermic melting peak and also the PCL endothermic melting peak change

according to the blending ratio.

150

5.1.6- Poly(3-Hydroxybutyric acid-co-3-Hydroxyvaleric acid) (PHB-co-HV):

PHB-co-HV copolymers was with three Hydroxyvaleric (HV) acid

contents, 5%, 8%, and 12% were investigated .The DSC program was to quench

the sample from 473 K (Tmelt) to 300 K . Then the samples were quenched to

220 K. Then melt the sample to 473 K again with 10 K/min.

Figure (5.21) shows the heat flow of the copolymer when heated in the

last part to the melt at 473 K after it was quenched. The figure show that all the

samples PHB, 5%, and 8% have a static glass transition shown in table (5.4).

Only 12% have no static glass transition temperature. In addition, from this

figure we can see that the copolymers 5%, and 8% HV contents can be fast

crystallized in the temperature range (310- 360 K) but they can be slowly

crystallized before and after this range.

250 300 350 400 450

-5

0

5

10

15

20

25

30

35

8%5%

PHB

12%

PHB-co-HV

Heat

flow

in m

W

T in K

Figure 5.21: The heating scan for the PHB-co-HV copolymer with 10 K/min.

151

Table 5.4: The thermal characteristic temperatures of the PHB-co-HV copolymer. Material Tg TC TMelt

PHB 279 324 451 PHB-co-HV5% 278 336 441 PHB-co-HV8% 277 348 434 PHB-co-HV12% ---- ----- 437

Part 2

TMDSC Studies

153

5.2 TMDSC Measurements: 5.2.1-Relaxation processes in the semi-crystalline polymers studies using TMDSC: Introductory discussion:

Semi-crystalline polymers are some kind of polymers, which can be

crystallized under different conditions. Semi-crystalline polymers cannot be

crystallised with a high degree of crystallinity; for example, the semi-crystalline

polymer such as linear polyethylene (lPE) can achieve crystallinity degree from

60-80%. According to this, these polymers are called “semi-crystalline

polymers”.

The semi-crystalline polymers are very complicated systems (i.e., their

morphology is complicated). That is because they have different components

each with different mobility, this leads to different relaxation processes. The

new* model of the semi-crystalline polymer is the three-phase model. According

to this model these polymers contain three-phases, crystalline, mobile

amorphous and rigid amorphous.

All the results are obtained using the TMDSC experimental techniques,

which is a tool for the complex heat capacity spectroscopy in different

temperature regions. This technique was used in this study because it is sensitive

to all kind of molecular motion in the semi-crystalline polymers including

relaxation. This gives it an advantage over dielectric spectroscopy techniques,

which is sensitive only to the dipolar motions. Further, dielectric spectroscopy

technique is used to study polymer materials in order to compare our TMDSC

result with standard relaxation study technique (i.e. dielectric technique).

The reported relaxation processes in semi-crystalline polymers are found

along the temperature range from glassy state to melting state. See figure (5.22).

* This model was proposed by H.Suzuki et al in 1985

154

Figure 5.22: Typical modulated heating scan TMDSC curve.

The figure shows the TMDSC scan for a polymer heated from amorphous

glassy state to the melt. Our studies of relaxation in the crystalline polymers are

attributed to this curve.

The most studied relaxation process in these polymers is the glass

transition relaxation and it is found in the amorphous polymers. By looking to

the above-sketched heating curve we can see this relaxation clearly at the glass

transition region, which is the first region and this relaxation, is called α MAF-

relaxation.

As the temperature goes to higher values we found another relaxation

process take place, which occur during the crystallisation process and this

relaxation is called αc-relaxation. This relaxation process is a structural induced

relaxation.

If the temperature is increased towards the melting region (i.e., the third

region). It is reported recently in the literatures (140,141,124) that another relaxation

process called ”rigid amorphous relaxation”, referred as αRAF-relaxation , can

take place in this region. This rigid amorphous fraction (RAF) or in some

literatures (110) it called rigid amorphous phase (RAP) starts to relax gradually as

the temperature increase above the glass transition temperature Tg.

155

Further increase in temperature (i.e. the forth region) another relaxation

process occur in this very high temperature region on the lamellae surfaces

which is called ” reversible melting “ (71). This kind of relaxation characterized

by an excess heat capacity.

We have studied many semi-crystalline polymers in order to have a clear

picture about the relaxation phenomena using the modulated temperature DSC

technique, which is a dynamic technique like the well-known technique of

dielectric spectroscopy.

156

5.2.2-Glass transition relaxation: (A relaxation process at Tg): We show in this section how the glass transition relaxation of the semi-

crystalline polymers “α MAF” can be studied using the TMDSC experimental

techniques.

5.2.2.1- Syndiotactic Polypropylene (sPP): The sPP investigation was to study the modulated scan under the

frequency 0.005Hz and heating rate 1K/min for all the samples (i.e., KPP1,

KPP2, KPP3, FINA4) to have an idea about the dynamic changes (i.e.,

relaxations) in the sPP samples in the glass transition region.

250 260 270 280 2901.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

Solid

Liquid

KPP1

FINA4

KPP3

T in K

|cp*

| in

J/g.

K

sPP

Figure 5.23: The complex heat capacity obtained from TMDSC modulated heating scans frq.=0.005, H.R.=1 K/min for the sPP samples in the glass transition region.

157

Figure (5.23) shows the modulated heating scans for the different sPP

samples. This figure shows a complex heat capacity∗ step, which is due to the

main chain relaxation in the mobile amorphous regions, αMAF-relaxation (i.e.,

the glass transition relaxation) in which the semi-crystalline polymer changes

from glassy state to rubber state.

The figure indicates also that there is a difference between the KPP3

sample and the other sPP samples in the αMAF-relaxation process. This

difference can be quantified form the relaxation strength ∆cp*. The figure shows

that the KPP3 sample has a large ∆cp* than the other sPP samples. This

quantitative analysis is displayed in table (5.5).

Table 5.5: The αMAF relaxation temperature and strength calculated using the TMDSC technique.

Material Tg

(K)

αMAF Relaxation strength

∆cp* in J/g.K

KPP1 270 0.227

KPP2 270 0.256

KPP3 267 0.378

FINA4 270 0.256

5.2.2.2-The PHB-co-HV copolymers: The investigation of the PHB-co-HV copolymers (i.e., 5%, 8%, and 12%

mw HV-content) with the TMDSC was made as a modulated heating scan for an

amorphous sample (i.e., quenched sample) and a semi-crystalline sample. To

obtain the semi-crystalline form of the copolymers the sample were crystallised

isothermally for 60 min before the modulated heating scan under frequency

0.005 and heating rate 1K/min was measured.

∗ Complex heat capacity was calculated from the modulated heat flow using a MathCAD program.

158

The two lines of crystalline and amorphous shown in the figures was

taken for the pure PHB from our PHB investigations.

Pure PHB and its copolymers:

Figures (5.24-5.27) show the modulated heating scan for the PHB and its

copolymers in the amorphous form line (1) and crystalline form line (2). As we

can see, the amorphous form gives a clear dynamic glass transition (i.e., αMAF-

relaxation) at 275, 273, 272 and 272 K for pure PHB and its copolymers

respectively. In addition, the experiments results are in a good agreement with

the two crystalline and amorphous PHB calculated lines (line (a) and (b)).

200 220 240 260 280 3000.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

b

a

2

1

(1)PHB Amorphous(2) PHB Semi-crystalline

(a)Amorphous PHB(b)crystalline PHB

PHB

T in K

|cp*|

in J

/g.K

Figure 5.24: The modulated heating scan with freq.= 0.005Hz and H.R= 1 K/min for the PHB polymer in both states amorphous and crystalline.

159

220 230 240 250 260 270 280 290 300

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2

1

b

a



PHB-co-PHV 5%

T in K

|cp*

| in

J/g.

K

Figure 5.25: The modulated heating scan with the same conditions for the PHB-co-HV5% polymer in both states amorphous and crystalline.

220 230 240 250 260 270 280 290 300

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2

1

b

a

(1) 8% Amorphous(2) 8% Semi-crystalline(a) crystalline PHB(b) Amorphous PHB

PHB-co-PHV 8%

T in K

|cp*|

in J

/g.K

Figure 5.26: The modulated heating scan with the same conditions for the PHB-co-HV8% copolymer in both states amorphous and crystalline.

160

220 240 260 280 3000.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2

1

b

a

(1) 12% Amorphous(2) 12% Semi-crystalline(a) Amorphous PHB(b) crystalline PHB

PHB-co-PHV 12%

T in K

|cp*|

in J

/g.K

Figure 5.27: The modulated heating scan with the same conditions for the PHB-co-HV 12% polymer in both states amorphous and crystalline. Table 5.6: The αMAF Relaxation temperature and strength for the PHB and its copolymers.

Material Tg αMAF Relaxation strength

∆cp* in J/g.K

PHB 275 0.578

PHB-co-HV5% 273 0.485

PHB-co-HV8% 272 0.494

PHB-co-HV12% 272 0.483

From table (5.6) one can see that the dynamic glass transition of the PHB

polymer is shifted towards lower temperature side by adding the HV contents. In

addition, the relaxation strength of the αMAF relaxation is decreased by

increasing the HV contents in the copolymer.

161

5.2.3- Structural induced relaxation process: (Relaxation during the crystallisation process)

5.2.3.1- Poly(3-hydroxybutarate) (PHB):

Since the introduction of the rigid amorphous fraction (RAF) by H.Suzuki

et al. (66) in 1985, many investigations appeared to give evidences for the

existence of this fraction (67). Our measurements of the quasi-isothermal

crystallisation of the PHB polymer at 296 K show that the crystallisation process

in the PHB could be followed to obtain information about the αc-relaxation that

takes place during the crystallisation process. Figure (5.28) shows the time

evaluation of the complex heat capacity during the crystallisation of PHB above

Tg =(273-283 K) of the polymer.

1000 10000 1000001.2

1.3

1.4

1.5

1.6

1.7

1.8

time in Sec.

PHB

a-cp measured

d- cp semi-crystalline(χc=0.64)

e-cp(χrigd=0.88 from ∆ Cp at Tg=296K)

c-cp amorph

b-cp crystal

Cp i

n J/

g.K

Figure 5.28: The crystallisation of PHB compared to the two-phase and three-phase models.

Figure (5.28) contains information about the crystallisation process of the

PHB polymer above its glass transition temperature (273-283 K). It shows that

the complex heat capacity decrease during the crystallisation process. This is

expected because the heat capacity of the crystalline polymer is less than the

heat capacity of the amorphous polymer. This also indicates the absence of the

162

contribution from the reversing melting, which reveals that heat capacity

measured is the baseline heat capacity. To confirm that the base line heat

capacity was measured we measure the frequency dependence of the heat

capacity after the crystallisation is ended. The results show no frequency

dependence (see the points at the end of the curve in figure (5.29)).

Figure (5.29) also shows that at the end of the crystallisation process the

complex heat capacity value is in agreement with the complex heat capacity

obtained using the three-phase model (line e), which take into account the RAF,

but it is less than the expected from the two-phase model (line d), which take

into account only the amorphous and crystalline phases. This indicates that the

RAF is formed during the crystallisation process itself. In other words, the

structures responsible for the RAF formation is formed or developed during the

formation of the crystalline lamellae. These structures may induce relaxation

processes (αc-relaxation) this is clear from the time dependence of the complex

heat capacity during the RAF formation process.

1000 10000 100000

t in s

-40

-20

0f - HFtotal

HF

in µ

W

1.2

1.3

1.4

1.5

1.6

1.7

d - cpb(χcrystal= 0.64)

e - cpb(χsolid(Tg) = 0.88)

c - cp liquid

b - cp solid

|cp*

| in

J g-1

K-1

Figure 5.29: The crystallisation of PHB compared to the constructed curves.

163

This result is in an agreement with pervious work (143) of the polycarbonate (PC)

polymer.

In order to analyse the crystallisation further we try to construct the

crystallisation as a function of time Xc(t) using the successive integration of the

heat flow Hf(t) during the crystallisation process (see the curve (f) in figure

(5.21) ) using the equation:

∫ ><∆Η

=Χ ∞

t

fc dttHFt

0

)(1)( (5.1)

And then applying this equation in the equation:

( ) )()( pbliquidp

cliquidpp cc

XtXctc −= −∞− (5.2)

where, (X∞) is crystalinity of 100% crystalline PHB, (Cpb) is the base line heat

capacity, ∆H∞f is the heat of fusion of 100% crystalline PHB*

We can obtain the complex heat capacity as a function of the time. See the

dashed curve and solid one in the figure. (5.29).

The difference between these two lines is that the solid curve was

calculated by considering that the RAF is formed during the crystallisation and

the dashed curve was calculated by considering that the RAF is formed after the

crystallisation.

It seen clearly that the solid is in agreement with the crystallisation

complex heat capacity which mean that the rigid amorphous is vitrified during

the crystallisation process.

* This value was taken from the X-ray measurements.

164

5.2.3.2- Syndiotactic Polypropylene (sPP):

The next was to study the quasi-isothermal crystallization to obtain the

same information about the rigid amorphous fraction (RAF). The KPP3 sample

was chosen because it yields a large exothermic crystallization peak in the DSC

study (see the results of the KPP3 sample in part1 of this chapter).

The TMDSC program was to melt the sample at 420 K then cool down to

280 K with cooling rate 80K/min and modulate at 280 K with frequency 0.005

Hz for a long isothermal time (1250 min). The complex heat capacity was

calculated during this isothermal time and the results shown in figure (5.30).

1000 100001.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1sPP

d-cpb(χsolid)=0.17)

e-cpb(χsolid)=0.51)

c-cp liquid

b-cp solid

|cp*

| in

J/g.

K

time in S

Figure 5.30: The complex heat capacity obtained from TMDSC quasi-isothermal crystallization at 280K and frequency 0.005Hz for the KPP3 samples.

Figure (5.30) shows that the crystallization process can be followed and

observed. The figure shows also that the complex heat capacity is decreased

exponentially with time and it reaches a value near the calculated value from the

165

three-phase model this indicates that the RAF is formed during the polymer

crystallization which is the same result obtained for the PHB polymer. The same

indication about the (αc-relaxation) can be found here.

5.2.4-Rigid amorphous fraction (RAF) relaxation (α RAF ):

(A relaxation process above Tg):


Until now we have information about how is the RAF is formed during

crystallisation process but we have no information about how this fraction

relaxed or changed from the glassy state to the rubber state as the mobile

amorphous changed before in the glass transition relaxation process. Is the RAF

relaxed? Moreover, how it is relaxed? These are open questions.

To answer these questions we done a TMDSC program to monitor the

relaxation of the RAF in the semi-crystalline PHB. The program was to

crystallize the PHB from the melt at 300 K crystallisation temperature for 180

min. then cooling the polymer with a very slow cooling rate (0.5 K/min) to 220

K with frequency 0.01 Hz, then wait for 10 min, then heating with a very slow

heating rate (0.5 K/min) to the melt (473 K) under the same frequency 0.01 Hz.

250 300 350 400 450

1.0

1.2

1.4

1.6

1.8

2.0

2.2

300K tw o -phase line (d ) th ree -phase line (e )

d

e

P H B

b -c p crystal

c -c p am orph

T in K

|c* p| i

n J

g-1 K

-1

Figure 5.31: Complex heat capacity of the PHB during melting under constant frequency 0.01 Hz and HR=0.5 K/min.

166

The result of the last melting curve is plotted in figure (5.31) compared to the

expected two-phase model complex heat capacity (line (d)) and three-phase

model complex heat capacity (line(e)). Moreover, the tow reference lines of

liquid (line(c)) and solid (line(b))PHB. The comparison showed that the

complex heat capacity of the PHB at the glassy state is coincident with the

reference line of the glassy PHB and it is coincident with the liquid PHB line at

the melt. This confirms that our results are accurate.

The comparison between the experimental complex heat capacity with the

one expected from the two-phase and three-phase models lines one can see how

the semi-crystalline PHB move form glassy state to the melt amorphous state by

passing two glass transition (i.e. α MAF- and α RAF relaxation processes) this is

clear from the figure (5.31). First, the system passes through the main glass

transition at 284 K. Because of this, the complex heat capacity is coincident with

the three-phase model line, which indicate the formation of the rigid amorphous

fraction. Then the system pass through a second glass transition at 316 K and as

a result the complex heat capacity coincident with the two-phase model line

which indicate that the rigid amorphous fraction is completely relaxed that is

indicated by the applicability of two-phase model at this stage. Finally, the

system starts to melt.

Effect of crystallization temperature on the α RAF relaxation processes:

By continuing our investigation of the RAF relaxation, we do the same

TMDSC program for crystallisation temperatures 340, 360, 380 K. The complex

heat capacities are plotted in figure (5.32).

The figure shows that as the crystallisation temperature increase the

complex heat capacity of the system coincidence with the two-phase model line

is much longer. In other words, the system stays for along temperature range as

a two-phase system. This may because the RAF formed at higher crystallisation

temperature is smaller than at lower crystallisation temperatures.

167

This mean that as the crystallisation temperature increase the RAF

relaxation (αRAF) starts to disappear and the system make one relaxation only in

which the system changed from the glassy state to the rubber state (αMAF). This

means that the system behaves as two-phase system when it is crystallised at

higher temperatures.

250 300 350 400 450

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

360 K340 K

380 K

e

d

PHB

Crystalline

Amorphous

|cp*

| in

J/g.

K

T in K

Figure 5.32: Complex heat capacity of the PHB during melting under constant frequency 0.01Hz for different crystallisation temperatures.

168

5.2.4.2- Syndiotactic Polypropylene (sPP): The next was to study the relaxation of the (RAF) using the TMDSC

technique in another polymer, which is the sPP. The program was to melt the

sample at 420 K and then to cool down to 363 K and stay for 180 min as an

isothermal time then heat with modulation frequency 0.0166Hz and heating rate

1 K/min to the melt again.

260 280 300 320 340 360 380 400 420

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

sPPa

Tc = 363 K

|cp*

| in

J/ g

.K

e - cpb (χsolid= 0.51)

d - cpb (χcrystal= 0.17)

b - cp solid

c - cp liquid

T in K

Figure 5.33: The complex heat capacity obtained from modulated heating scan with 0.0166Hz after TMDSC quasi-isothermal crystallization at 363K for 180 min with modulation frequency 0.0166Hz for the semi-crystalline KPP3 sample.

Figure (5.33) shows the resulted scanning curve. From the curve, we can see the

glass transition of the polymer at 275 K then the complex heat capacity is

coincident with the complex heat capacity calculated using the three-phase

model (line (e)). This indicates the formation of the rigid amorphous fraction

(RAF). Then at 300K the complex heat capacity starts to increase above the

three-phase model heat capacity until 360 K it coincident with the two-phase

model heat capacity (line (d)) which indicates that the (RAF) is relaxed along

169

this temperature range (i.e., the RAF relaxation process is slow compared to the

PHB). Moreover, the figure shows that the RAF is much stable in the sPP than

PHB (compare with figure (5.31)). This indicated by the coincident of the

complex heat capacity of the system with line (e) for a long temperature range.

5.2.5- Relaxation during Isothermal crystallization processes: 5.2.5.1- Poly(ether ether ketone) (PEEK):

The program was to melt the sample at 640K and the cool down to the

crystallization temperature then remained at this temperature for isothermal time

1500 min under frequency 0.005Hz and temperature amplitude 1K. The results

of this melt quasi-isothermal crystallization measurements for the PEEK sample

showed that the complex heat capacity increases with time instead of decrease as

expected (see figure (5.34)) because of the fact that the heat capacity of the

crystallized polymer is less than of the amorphous polymer. This increase in the

complex heat capacity was attributed to a relaxation process occurs at the

surface of the crystals in the polymer (see chapter 2 for more details about

Reversing melting). This mean that the base line heat capacity is measured plus

some other excess heat capacity.

170

100 1000 10000 100000

Liquid at 607K

2.55

2.45

2.35

2.25

2.15

2.05

1.95

1.85

1.75

564K609K605K

|cp* | i

n J/

g.K

time in Sec.

573K

530K

607K602K597K592K583K

PEEK

Figure (5.34): The complex heat capacity curves obtained by melt quasi-isothermal crystallization for quenched PEEK sample. From figure (5.34) we can see that the complex heat capacity behaves in two

ways: at the low crystallisation temperatures (i.e., 530, 564, 573, 583K) it

decreases as expected. On the other hand, at the high crystallisation temperature

(i.e., 592, 597, 602, 605, 607, 609K) it increases. This indicates that the excess

heat capacity disappears at low crystallisation temperatures, which means that

the relaxation processes may not found at the low crystallisation temperatures.

171

1000 10000

2.1

2.2

2.3

2.4

2.5

2.6

2.7PEEK

440K470K

500K

400K

432K

425K|c

p*| i

n J/

g.K

time in Sec.

Figure 5.35: The complex heat capacity curves obtained by cold quasi-isothermal crystallization for quenched PEEK sample.

Figure (5.35) shows the complex heat capacity results from the cold

crystallised PEEK samples. The idea of cold crystallisation is to crystallise the

sample starting from the glassy state not from the melt state (see figure 5.36).

Figure (5.35) indicates a very fast crystallisation processes. Therefore, we could

not obtain information about the (αc) relaxation processes occur during

crystallisation process and the (RAF) formation.

172

Figure 5.36: The melt and cold quasi-isothermal experiment.

350 400 450 500 550 600 6501.2

1.4

1.6

1.8

2.0

2.2

2.4

c

b

a

|cp* | i

n J/

g.K

T in K

PEEK

first point Lastpoint Maxmum point

(a) Liquid(b) Solid(c) 2-phase model

Figure 5.37: The complex heat capacity obtained from the melt and cold quasi- isothermal experiment for the PEEK polymer. The next step was to try to analyze the data of the two figures (5.34, 5.35) so by

taking the first, maximum, and last point in the curves shown in the figures

173

(5.34, 5.35) we plot figure (5.37), which is a relation between the complex heat

capacity obtained from the melt and cold quasi-isothermal crystallization

experiments and the temperature.

Figure (5.37) shows that as the temperature increase the complex heat

capacity increases. Line (c) indicates the complex heat capacity calculated based

on the two-phase model, which indicates the expected complex heat capacity

according to the two-phase model.

In this figure, we consider that the data points less than the two-phase

model line and the data points larger than the two-phase model line. The first

data set can give information about the rigid amorphous fraction (RAF) in the

sample; on the other hand, the second data set can give information about the

excess heat capacity. This rule will be used at the end of this chapter to study

excess heat capacity and morphology

5.2.5.2- Poly (butylene terephathalat)(PBT):

The melt quasi-isothermal crystallization experiments results are shown in

figure (5.38) for different crystallization temperatures. The program was to melt

the sample at 513 K then cool down to the crystallization temperatures and

remains at this temperature for 522 min under frequency 0.00166 Hz. The

crystallization temperatures were as shown in figure. We can see clearly that the

complex heat capacity have a large value when the sample crystallized at 493 K.

174

1000 10000

533 K513 K453 K413 K393 K

373 K 353 K333 K

493 K3.0

2.5

2.0

1.5

1.0

0.5

0.0

PBT

|cp*|

in J

/g.K

time in Sec.

Figure 5.38: The complex heat capacity obtained using the quasi- isothermal crystallization for the PBT sample.

To analyze the figure (5.38) to get more information, figure (5.39) was

plotted by taking the first and the last point in the curves shown in the figure

(5.38). Also the two-phase model expected complex heat capacity was

calculated based on the crystallinity at each crystallization temperature, see

figure (5.39). In this figure, the same rule considered in the PEEK investigation

will be used at the end of this chapter to study excess heat capacity and

morphology.

175

300 350 400 450 500 5501.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

cb

a

first point last point

(a) am orphous(b) crysta lline(c) two-phase

PBT

|cp*|

in J

/g.K

T in K

Figure 5.39: The complex heat capacity obtained using the quasi-isothermal crystallization for the PBT sample. 5.2.5.3- Poly (ethylene terephathalat) (PET):

The melt quasi-isothermal crystallization experiments for the PET

polymer revealed a great deal of information about the relaxation processes

taking place during the crystallisation of this polymer. The program was to melt

the sample at 533 K and then cool down to the crystallization temperature and

stays at the crystallization temperature for 600 min under frequency 0.00166 Hz.

The results are shown in figure (5.40).

176

1000 10000

553K533K 513K

493K

473K453K

433K

413K

373K

393K

2.289

2.098

1.906

1.714

1.523

1.331

PET

|cp*|

in J

/g.K

time in Sec.

Figure 5.40: The complex heat capacity obtained from the quasi-isothermal crystallization for the PET sample.

Then the quasi-isothermal results were analyzed by taking only the first

and the last point and the figure (5.41) was plotted. The two-phase model line

was calculated using the crystallinity degree after each crystallization

temperature. In this figure, the same rule considered in the PEEK investigation


morphology.

177

250 300 350 400 450 500 550 600 650 700

1.0

1.2

1.4

1.6

1.8

2.0

2.2

c

b

a

first point last point

(a) Amorphous(b) Crystalline(c) two-phase

T in K

|cp*

| in

J/g.

K

PET

Figure 5.41: The complex heat capacity obtained from the quasi-isothermal crystallization for the PET sample. 5.2.5.4- Poly (trimethylene terephathalat) (PTT):

The melt quasi-isothermal crystallization results are shown in figure

(5.42). The program was to melt the sample at 510 K then cool down with 10

K/min to the crystallization temperature and stays for 1000 min under frequency

0.005 Hz.

178

103 104 105 106

1.80

1.85

1.90

1.95

2.00

2.05

2.10

2.15

2.20

492K

464K

478K

484K490K

450K460K

470K

480K472K

PTT

|cp*

| in

J/g.

K

time in Sec.

Figure 5.42: The complex heat capacity curves for the PTT sample using the melt – quasi-isothermal crystallization

The cold quasi-isothermal crystallization results are shown in figure

(5.43). The sample was quenched out side the DSC-2C device by heating on a

hot stage at 510 K then cool down fast by putting it on a cold substrate. The

TMDSC program was to heat from 300 K to the crystallization temperature and

stays for 1000 min under frequency 0.005 Hz. The crystallization temperatures

were chosen just above the glass transition temperature.

179

102 103 104 1051.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

1.50

338K

330K328K

324K

PTT

|cp*|

in J

/g.K

time in Sec.

Figure 5.43: The complex heat capacity curves for the PTT sample using the cold –quasi-isothermal crystallization.

In order to analyse the two quasi-isothermal results the first, maximum,

and last point were taking and the figure (5.44) were plotted. In addition, the

crystalline line and the amorphous line were plotted. The two-phase model line

was calculated based on the crystallinity degree at each crystallization

temperature (line (c)).

Figure (5.44) shows the complex heat capacity compared to the two-phase

model expected line. In this figure, the same rule considered in the PEEK

investigation will be used at the end of this chapter to study excess heat capacity

and morphology.

180

300 350 400 450 500 5501.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

c

b

acp solid

cp liquidPTT

(c) cpb two-phase

First point max End point

|cp* | i

n J/

g.K

T in K

Figure 5.44: The complex heat capacity for the PTT sample using the melt and cold quasi-isothermal crystallization. 5.2.5.5- poly (3-hydoxybutarate)(PHB):

We have done frequency dependence measurements at different

crystallisation temperatures (240, 320, 340, 360, 380, 400, 420 K). [See the used

TMDSC program shown in figure. (5.45).]

By this program, the polymer was crystallised from the melt isothermally

for 15 min at 320K then cooled down very fast to 240 K (i.e. below Tg). Then

the frequency dependence was measured at 240 K. After that the temperature

was increased by 1 K/min to 320 K, then the frequency dependence was

measured at 320 K, afterwards the temperature was increased by (1 K/min, 20

K) step and then the frequency dependence was measured at each step until the

final stage at 420 K. The temperature amplitude was fixed along the whole

program at 0.5 K and the frequency was changed gradually from 0.0012 to 0.01

Hz.

181

Figure 5.45: The TMDSC program used in the frequency dependence measurements.

210 280 350 420

1.0

1.5

2.0

cpb

-2phase

Solid

Liquid

PHB

|cp*

| in

J/g.

K

T in K

0.04 Hz 0.02 Hz 0.01 Hz 0.005 Hz 0.0025 Hz 0.00125 Hz

Figure 5.46: The complex heat capacity of PHB compared to the constructed lines.

The results of this complicated TMDSC program is shown in figure

(5.46). This figure is plotted by taking the average complex heat capacity for

each frequency at each crystallization temperature. This gives a general picture

about the change of complex heat capacity with frequency at each crystallization

temperatures. In this figure, the same rule considered in the PEEK investigation

182


morphology.

5.2.5.6- Syndiotactic Poly propylene (sPP):

We use the same TMDSC program used in the PHB to obtain the same

results for the sPP polymer.

200 250 300 350 400 4500.60.81.01.21.41.61.82.02.22.42.62.83.0

2-Phase

Amorphous

Crystalline

0.00125 Hz 0.0025 Hz 0.005 Hz 0.01 Hz 0.02 Hz 0.04 Hz 0.083 Hz

KPP3

|cp*|

in J

/g.K

T in K

Figure 5.47: The complex heat capacity obtained from modulated TMDSC quasi- isothermal crystallisation for the semi-crystalline KPP3 sample.

Figure (5.47) shows the relation between the complex heat capacity and

the temperature at each frequency. As a direct result from this figure is the

temperature dependence of the complex heat capacity, another result is that the

frequency dependence of the complex heat capacity is that as the frequency

increases the complex heat capacity decreases.

The figure shows also that there is frequency dependence at the glassy

state but this may be due to some excess heat transfer problems occurs during

the measurements. The same rule used with the PEEK was used in figure (5.74).

183

5.2.6- Relaxation processes after the crystallization process: 5.2.6.1- Poly (ethylene oxide) (PEO):

In investigation of PEO the idea was to investigate, the relaxation

processes occur in the PEO after the crystallisation process is completed. And

this can be done by detecting the frequency dependence of the complex heat

capacity, which indicate the relaxation processes occur in the PEO, after the

crystallisation process is finished.

To overcome the problem of latent heat, which found during the modulated

scan TMDSC experiment, that affects the measured heat capacity of PEO. We

made a quasi-isothermal melt crystallisation TMDSC experiment, and then the

frequency dependence after the crystallisation process was studied [See figure

(5.48) for the time temperature program.]

Figure 5.48: The temperature-program used for PEO –isothermal melt crystallisation TMDSC measurements.

It was expected to measure the heat capacity without any contribution

from latent heat (i.e., to measure the base line heat capacity which is due to

natural vibrations of the molecules i.e., phonon heat capacity) but it was not the

case.

184

The measured (i.e., apparent) complex heat capacity frequency

dependence is shown in figure (5.49). In order to correct the measured complex

heat capacity to eliminate all errors in our results the results was corrected

according to the melt values obtained from ATHAS database.

These melt-corrected complex heat capacity data shows high values as

shown in figure (5.50). Compared to the melt line at 378K we found the values

are much greater than the value at the melt which indicate that we still have an

excess heat capacity during the quasi-iso-thermal crystallisation TMDSC

measurements due to the relaxation processes at the crystal surface which

attributed to the reversing melting relaxation process proposed in 1997 (8).

By comparing our results with the results obtained by Strobl (74) using a

light driven spectrometer technique, the comparison in figure (5.51) revealed

that Strobl results show also large value of complex heat capacity and frequency

dependence. However, indeed our data shows frequency dependence but in

limited frequency range of the TMDSC technique used. In addition, from

comparison we can see that our data show complex heat capacity values smaller

than Strobl. This may be due to that; we succeed in eliminating the latent heat

effects in the present work more than Strobl.

185

10-3 10-2 10-1

0 .8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

|cp*|

in J

/g.k

L iqu id P E O a t 3 78 K 33 1K 32 8K 32 4K 32 1K

PEO

Freq. in H z

Figure 5.49: The apparent complex heat capacity obtained from the PEO iso-thermal crystallisation TMDSC measurements frequency dependence.

10-3 10-2 10-1

1.85

1.90

1.95

2.00

2.05

2.10

2.15

2.20

2.25 PEO

Liquid PEO at 378K 331K 328K 324K 321K

|cp*

| in

J/g.

k

Freq. in Hz

Figure 5.50: The melt-corrected complex heat capacity obtained from the PEO iso-thermal crystallization TMDSC measurements frequency dependence.

186

10-3 10-2 10-1 100

2.0

2.2

2.4

2.6

2.8

3.0

3.2

321K324K

328K

331K PEO

|cp*|

in J

/g.K

Freq. in Hz

TMDSC 321K 324K 328K 331K Liquid PEO at 378K

Strobl 321K 324K 328K 331K

Figure 5.51: The comparison of the melt-corrected complex heat capacity obtained from the PEO TMDSC measurements and the results obtained by Strobl (74) light driven spectrometer experiments.


From the TMDSC program shown in figure (5.52) in which the frequency

changed as (0.04, 0.02, 0.01, 0.005, 0.0025, 0.00125 Hz), the apparent complex

heat capacity was plotted against the frequency to have information about the

complex heat capacity frequency dependence. This was done to have some

information about the relaxation processes after crystallization in the PHB

polymer.

Figure 5.52: TMDSC program used in case of PHB.

187

10-3 10-2 10-1

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2PHB

|cp*|

in J

/g.K

Freq. in Hz

240K 320K 340K 360K 380K 400K 420K

Figure 5.53: Frequency dependent apparent complex heat capacity of the PHB above and below Tg.

10-3 10-2 10-1

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2PHB

|cp*|

in J

/g.K

Freq. in Hz

240K 320K 340K 360K 380K 400K 420K

Figure 5.54: Frequency dependent complex heat capacity of the PHB above and below Tg.

Figure (5.53) shows the apparent complex heat capacity, the data was

melt-corrected. See figure (5.54), which shows no clear frequency dependence.

188

This means that our limited frequency window cannot detect the relaxation

processes take place after crystallisation and at crystallisation temperatures

above Tg.

In addition, from this figure we can see clearly the difference in the

complex heat capacity at the two-crystallisation temperatures 240 and 320 K

(see the squares and circles symbols) this is due to that the αMAF-relaxation

process takes place around 273 K.

5.2.6.3- Syndiotactic Polypropylene (sPP): The next was to study the TMDSC program shown in figure (5.55) to have

information about the complex heat capacity frequency dependence after

isothermal crystallisation of the sPP polymer at different crystallisation

temperatures, which indicates a relaxation processes take place after

crystallisation of the sPP polymer.

Figure 5.55: TMDSC program used in case of sPP.

The frequency used is (0.08, 0.04, 0.02, 0.01, 0.005, 0.0025, 0.00125 Hz). The

crystallization temperatures were as (300, 320, 340, 360, 380, 400 K).

189

10-3 10-2 10-10.20.40.60.81.01.21.41.61.82.02.22.42.6

KPP3

|cp*

| in

J/g.

K

Freq. in Hz

300K 320K 340K 360K 380K 400K 443K-melt

Figure 5.56: The apparent complex heat capacity as a function of the frequency for the KPP3 sample. Figure (5.56) shows the apparent complex heat capacity obtained from the

experiment without correction. Figure (5.57) shows the melt-corrected complex

heat capacity.

Figure (5.57) shows that there is a weak frequency dependence of the

complex heat capacity which indicate that we detect a relaxation processes after

crystallisation of the sPP polymer. In addition, the frequency dependence of

these relaxation processes increases as the crystallization temperature decrease.

This indicates that these relaxation processes are hindered increasingly as the

polymer crystallized at higher temperatures, which may be due to that the

polymer become near the melt temperature increasingly. The figure also shows

that the complex heat capacity is depending on crystallisation temperature.

190

10-3 10-2 10-10.5

1.0

1.5

2.0

2.5

3.0KPP3

340K

300K

320K

360K380K

400K

443K

|cp*

| in

J/g.

K

Freq. in Hz

Figure 5.57: The melt-corrected complex heat capacity as a function of the frequency for the KPP3 sample.


In order to study the frequency dependence of the complex heat capacity

after the crystallisation of the PEEK polymer to reveal some information about

the relaxation processes take place after the PEEK polymer crystallisation, it

was necessary to make quasi-isothermal crystallisation under frequency 0.005Hz

for time equal to 1500 min. The frequency was changed as (0.08, 0.05, 0.03,

0.025, 0.02, 0.016, 0.0142, 0.01, 0.005, 0.0025, 0.00125 Hz). The experimental

results are shown in figure (5.58). Then the experimental data was melt-

corrected using ATHAS database. The melt-corrected data is shown in figure

(5.59).

191

10-3 10-2 10-1

0.6

1.2

1.8

2.4

T640K T605K T530K T430K

PEEK

|c

p*| in

J/g

.K

Freq. in Hz

Figure 5.58: The apparent complex heat capacity obtained from frequency dependence experiments after quasi-isothermal crystallization for the PEEK sample.

192

10-3 10-2 10-1

1.0

1.5

2.0

2.5

640K 605K 530K 430K

PEEK

|c

p*| in

J/g

.K

freq. in Hz

Figure 5.59: The complex heat capacity obtained from frequency dependence experiments after quasi-isothermal crystallisation for the PEEK sample.

From figure (5.59), we can see that there is frequency dependence of the

complex heat capacity, which indicates relaxations processes occur after the

crystallisation of the PEEK polymer, is complete.

Another result from this figure one can see how the frequency dependence

is changed as the crystallization temperature increased to 605 K but it is the

same at the lower crystallization temperatures (430, 530 K). This can be

explained by that the mobility increase as the crystallization temperature

increase. In other words if the polymer is crystallized at higher temperatures it

become more mobile than if it crystallized at lower temperatures. This thermal

mobility hindered the relaxation processes take place after the crystallization of

the PEEK polymer. Further, it can be seen from the figure that there is an excess

heat capacity at 605 K, which indicates the occurrence of the reversing melting

relaxation at this crystallization temperature.

193

5.2.6.5- Poly (butylene terephathalat) (PBT):

The frequency dependence was studied after the quasi-isothermal

crystallization of the PBT sample. The TMDSC program was to melt the sample

at 513 K and then cool down to the crystallization temperature then stays for 522

min under frequency 0.00166 Hz then the frequency changed as the following:

0.00166, 0.00413, 0.0102, 0.0256, 0.0637 Hz.

The apparent complex heat capacity was plotted against the frequency in

figure (5.60). The apparent complex heat capacity was corrected using the melt

data available at ATHAS database. (See figure (5.61)).

The results in figure (5.61) show frequency dependence, which indicate

that the TMDSC frequency window is capable of detecting the relaxation

processes, which take place after the crystallization process. Another results

from the frequency dependence are that the complex heat capacity is depending

on the crystallization temperature. The complex heat capacity increase as the

crystallization temperature increase. In addition, the frequency dependence is

the of same feature. In addition, at 393K we detect an excess heat capacity

which indicate the occurrence of the reversing melting relaxation at this

crystallization temperature.

194

10-3 10-2 10-1

0.60.81.01.21.41.61.82.02.22.42.62.83.0

PBT

|cp*|

in J

/g.K

333K 353K 373K 393K 513K melt

Freq. in Hz

Figure 5.60: The apparent complex heat capacity frequency dependence obtained after the quasi-isothermal crystallization for the PBT sample.

195

10-3 10-2 10-1

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0PBT

|cp*|

in J

/g.K

333K 353K 373K 393K 513K melt

Freq. in Hz

Figure 5.61: The complex heat capacity frequency dependence obtained after the quasi-isothermal crystallisation for the PBT sample.

196

5.2.6.6- Poly (ethylene terephathalat) (PET):

The figure (5.62) shows the complex heat capacity frequency dependence

after it was crystallized near the melt at 493K for 522 min under frequency

0.00166Hz then the frequency changed as the following: 0.00166, 0.00413,

0.0102, 0.0256, 0.0637Hz.

The figure shows small frequency dependence (only 0.03 change in

complex heat capacity). This again because of the limited frequency window of

the TMDSC (0.001 to 0.1Hz)

10-3 10-2 10-1

1.94

1.96

1.98

2.00

2.02

2.04

2.06

2.08

2.10PET

493K 533K melt

|cp*

| in

J/g.

K

Freq. in Hz

Figure 5.62: The complex heat capacity obtained from the quasi- isothermal crystallization for the PET sample.

197

5.2.7-Reversing melting relaxation*: 5.2.7.1- Poly (ethylene oxide) (PEO):

In order to study the relaxation processes due to the reversing melting,

which is related to the excess heat capacity, we made an excess heat capacity

quantitative analysis. The two-phase model expected complex heat capacity line

was constructed using the crystallinity degree (Xc) obtained from the heating

scan at the end of the TMDSC crystallisation experiments (see figure (5.48)).

Using the equation:

pacccpphasetwop cXXcTc )1()( −+=− (5.3)

where the cpc and the cpa are the ATHAS values of the crystalline PEO (line (b))

and of the amorphous PEO (line(a)).The constructed two-phase model complex

heat capacity (is the line(c) in figure (5.63)).

320 325 330 335 3401.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

c

b

a

PEO

L iquid Soild 0.0666 Hz 0.0333 Hz 0.0166 Hz 0.0100 Hz 0.0083 Hz 0.0041 Hz 0.0020 Hz 0.0010 Hz cpb 2-phase

|cp*|

in J

/g.K

TC in K

Figure 5.63: The expected two-phase model complex heat capacity compared to melt- corrected complex heat capacity obtained from the PEO TMDSC measurements.

* A relaxation process in the high temperature region at the crystalline lamellae surfaces:

198

By comparing the values of the melt-corrected complex heat capacity with

the expected two-phase model complex heat capacity, we can obtain the value of

the excess heat capacity (ce) according to the equation:

)()()( TcTcTc phasetwopmeasueredpe −−− −= (5.4)

The values of the excess heat capacity (ce) calculated show a temperature

dependence and frequency dependence see figure (5.64), which indicates that

this excess heat capacity related to relaxation processes takes place at this

temperature and frequency regions. These relaxation processes are so called

“Reversing melting relaxations”. (see chapter 2 for more details.)

320 322 324 326 328 330 332 334 336 338 3400.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

Tcm

324 K328 K PEO

c e in

J/g.

K

TC in K

0.0666 Hz 0.0333 Hz 0.0166 Hz 0.0100 Hz0.0100 Hz 0.0083 Hz 0.0041 Hz 0.0020 Hz 0.0010 Hz

Figure 5.64: The calculated excess heat capacity obtained from the PEO quasi-isothermal TMDSC measurements.

199

From the Polyethylene oxide PEO results, we can conclude that this

polymer show an excess heat capacity, which make studying the base line heat

capacity somewhat difficult.

The results in figures (5.63, 5.64) indicate a frequency dependence and

crystallization temperature dependence of the complex heat capacity and it

shows also that there is an excess heat capacity and it is also frequency and

crystallization temperature dependent which indicate that it related directly to a

relaxation processes (see Wundelich et al (8)).

The results in figure (5.64) shows a peak maximum at 328 K for all

frequencies except 0.01 Hz this maximum shifts toward the low temperature

side by 6K (i.e. 324 K). This indicates that these relaxation processes are

increased as the polymer crystallized at higher temperatures until a specific

crystallisation temperature (Tcm) these relaxation processes are decrease as the

polymer crystallized at higher temperatures. That is to say, the reversing melting

relaxation processes begins to vanish when the polymer crystallized at higher

temperatures after (Tcm). This may be explained that at the (Tcm) the crystallinity

is high so there is more lamellae that these relaxation processes takes place on

their surfaces. Before and after this crystallization temperature (i.e.,Tcm) the

crystallinity is low. This explanation is true according to the crytallinity

calculations, which shows that the crystallinity at 321, 324, 328, 331 K equal to

68, 70, 75, 53% respectively.

Because of the excess heat capacity, we were not able to study the

relaxation of the rigid amorphous fraction or the interphase between the

crystalline phase and amorphous phase that was reported to be found in

polyethylene (142).

200


The next step was to study the excess heat capacity from the experimental

data points above the two-phase model expected line (see line (c) in figure

(5.37)). The excess heat capacity was calculated using the equation (5.4).

560 570 580 590 600 610

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Tcm

609K

579K

PEEK

c e in

J/g.

K

TC in K

Figure 5.65: The excess heat capacity obtained from figure (5.37) for the PEEK sample

Figure (5.65) shows that the excess heat capacity increases as the

crystallisation temperature increases, until it reaches the maximum at 579 K.

The same explanation of the PEO results is found to be true here, where the

maximum crystallinity is found at 379 K (35%).

201

5.2.7.3- Poly (butylene terephathalat)(PBT):

By considering the points above the two-phase model line in figure (5.39)

the excess heat capacity was calculated using equation (5.4). The result is

plotted in the figure (5.66), which shows that the excess heat capacity is changed

as the crystallization temperature changed in the manner that as the

crystallization temperature increase the excess heat capacity increases until its

maximum at 473K (The same explanation of the PEO results is found to be true

here, where the maximum crystallinity is found at 473K (35%)).

The excess heat capacity drops down at the melting temperature 513K.

This drop can be explained by the melt of all crystalline lamellae in the sample

so the relaxation processes disappeared.

400 420 440 460 480 500 520

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Tcm

513K

473K PBT

C e in

J/g.

K

TC in K

Figure 5.66: The excess heat capacity obtained using the quasi- isothermal crystallisation for the PBT sample.

202

5.2.7.4- Poly (ethylene terephathalat) (PET): By considering the points above the two-phase model line in figure (5.41)

one can get information about the excess heat capacity using equation (5.4)

which is related to the reversing melting that is related to a relaxation processes

occurs at the surface of the lamellae. Nevertheless, there is no microscopic

explanation about this phenomenon.

Our study reveals some information about these processes and how it

related to the crystallization temperature. (See figure (5.67)). Again, we can see

as the crystallization temperature increases the excess heat capacity increase,

which mean that the reversing melting relaxation process is temperature

dependence. In addition, the frequency 0.00166 Hz can detect these relaxation

processes. The figure shows that the excess heat capacity is maximum at 512 K

and drop at the melt at 533 K. The same previous explanations are true here

since the maximum crystallinity is 44% at 512 K. The excess heat capacity

drops down at the melting temperature 533 K. This drop can be explained by the

melt of all crystalline lamellae in the sample so the relaxation processes

disappeared.

460 480 500 520 540

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Tcm

533K

512K PET

c e in J

/g.K

TC in K

Figure 5.67: The excess heat capacity obtained from the quasi-isothermal crystallization for the PET sample.

203

5.2.7.5- Poly (trimethylene terephathalat) (PTT):

The excess heat capacity was studied using the same idea that the data

points above the two-phase model can give information about the excess heat

capacity. The results are shown in figure (5.68) which shows that the excess heat

capacity increase as the crystallization temperature increase and it reach a

maximum at 478 K then it drop down toward the melt temperature 490 K.

Excess heat capacity is related to the reversing melting relaxation processes,

which occurs on the lamellae surfaces. The same previous explanations are true

here since the maximum crystallinity is 46% at 478 K. The excess heat capacity

drops down at the melting temperature 490 K. This drop can be explained by the

melt of all crystalline lamellae in the sample so the relaxation processes

disappeared

460 470 480 490 5000.00

0.05

0.10

0.15

0.20

0.25

Tcm

490K

478K PTT

C e in

J/g.

K

TC in K

Figure 5.68: The excess heat capacity for the PTT sample using the quasi-isothermal crystallization experiments.

204

5.2.8-Morphological studies concerning α MAF relaxation: The method of calculation:

We have studied the morphology of the semi-crystalline polymers

according to three-phase model taking into consideration the rigid amorphous

fraction (RAF) which do not participate in the α-relaxation and the mobile

amorphous fraction (MAF), which participate in the αMAF-relaxation and the

rigid crystalline fraction (RCF) which do not participate in the αMAF-relaxation.

We apply the idea of the fact that the complex heat capacity values data points

below the two-phase model can give information about the morphological

fractions. Moreover, the points above the two-phase model expected line could

give information about the excess heat capacity and the related reversing

melting relaxation processes, which was studied in the pervious section.

The method used to obtain information about the morphological fractions

at different temperatures is that we take the semi-crystalline complex heat

capacity points and calculate the difference between the crystalline line value

and semi-crystalline value and this difference equal to ∆cpsc and the difference

between the crystalline line value and the amorphous line value ∆cpam then using

the following equations:

amp

scp

MAF cc

∆

∆=χ (5.5)

XRF=1-XMAF (5.6)

X RAF=XRF-XRCF (5.7)

XRF=XRCF+XRAF (5.8)

XMAF is the content of the mobile amorphous fraction, XRF is the rigid fraction

content, XRCF is the rigid crystalline fraction content, and XRAF is the rigid

amorphous fraction contents. With this method, we are able to have information

about the morphological fractions in the semi crystalline polymers.

205

5.2.8.1- Poly(ether ether ketone) (PEEK):

The experimental data below line (c) in figure (5.37) which indicates

information about the rigid amorphous fraction (RAF) was used in addition to

the equations (5.5, 5.6, 5.7, 5.8) to analyze the morphology in the PEEK

polymer.

400 420 440 460 480 500

0.00

0.20

0.40

0.60

0.80

1.00

Tg above Tgbelow Tg

MAF

RCFPEEK

Mor

phol

ogic

al fr

actio

ns

TC in K

Figure 5.69: The morphological fraction by considering two-phase model for the PEEK sample.

Figure (5.69) shows that the morphological fractions (i.e., the rigid

crystalline fraction (RCF) and the mobile amorphous fraction (MAF)) are

temperature dependent. As a result from this figure we can find that the (MAF)

dropped from 0.245 to 0.090 and (RCF) jump from 0.754 to 0.90 at glass

transition and then both (MAF) and (RCF) stay nearly constant at 0.25 and 0.75

respectively. These results of the two-phase model do not reflect the real

situation of the polymer because the MAF must be increase as the system pass

through the glass transition temperature.

206

400 420 440 460 480 500 520 540

0.0

0.2

0.4

0.6

0.8

1.0

Tg

RCF MAF RAF

below Tgabove Tg

PEEK

Mor

phol

ogic

al fr

actio

ns

TC in K

Figure 5.70: The morphological fraction by considering three-phase model for the PEEK sample.

Figure (5.70) shows the morphological fractions by considering the three-

phase model (i.e., the rigid crystalline fraction (RCF), the mobile amorphous

fraction (MAF) and the rigid amorphous fraction (RAF)). The figure shows that

the (RCF) is the same as the two-phase model, but the other two phases (MAF,

RAF) changed dramatically as seen in the figure. If the PEEK is crystallized

below Tg the (MAF) is equal to 0.82 whereas above Tg it drop to 0.28, then as

the crystallization temperature increase more MAF is found on the polymer.

On the other hand the (RAF) is jump from 0.082 to 0.488 but it relaxes

gradually above the Tg as the crystallization temperature increases (see the

triangles curve in the range 430-500 K). From this figure, we can see clearly the

glass transition effect on the three-phase model morphological fractions, where

the dashed line represents the glass transition temperature of the PEEK polymer.

207

5.2.8.2- Poly (butylene terephathalat) (PBT):

Considering the three-phase model figure (5.39), the figure (5.71) was

plotted, which shows the different fractions of the PBT polymer and how they

changed with the temperature above the glass transition temperature. The glass

transition temperature of the PBT polymer is 248 K (143). The rigid crystalline

fraction (RCF) is nearly constant as shown in the figure. On the other hand, the

other two fractions (i.e., (MAF), (RAF)) are changed dramatically with the

crystallization temperature. As a general, behaviour the (MAF) increase with

increasing crystallization temperature and the (RAF) decrease with increasing

the crystallization temperature. This indicate that if the polymer crystallized at

higher temperatures it will contain MAF content more than the RAF which may

be attributed to the increase of the mobility and the relaxation of the RAF at

higher temperatures. This means that the temperature at which the polymer is

crystallised affects the RAF content in the semi-crystalline polymer. On the

other hand, the MAF content behaviour indicates that as the crystallization takes

place at higher temperature more MAF content found in the polymer participates

in the glass transition relaxation.

33 0 3 4 0 3 50 3 60 3 70 38 0 39 0 40 00 .0

0 .2

0 .4

0 .6P B T

Mor

opho

logi

cal f

ract

ions

T C in K

M A F R A F R C F

Figure 5.71: The morphological fractions obtained using the quasi-isothermal crystallization for the PBT sample.

208

5.2.8.3- Poly (ethylene terephathalat) (PET):

We use the same method by using figure (5.41) for obtaining information

about the morphological fractions from the points below the two-phase model

line and information about the excess heat capacity from the points above the

two-phase model line. The results of morphological fractions at each

crystallization temperature are plotted in figure (5.72).

Figure (5.72) gives information about the morphological fractions above

the glass transition Tg=342K. As seen, that the (RCF) and the (MAF) increase

with increasing the crystallization temperature. On the other hand, the (RAF)

decrease as the crystallization temperature increases. This indicate that the

(RAF) relaxed at higher crystallization temperatures. Also the (MAF) is

increased because as the crystallization temperature increases the more material

become mobile amorphous which contribute to the (MAF) content. The results

give an idea about how the three-phase model can give a clear picture about

what take place in the polymer.

390 400 410 420 430 4400.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0PET

Mor

phol

ogic

al fr

actio

ns

TC in K

RCF MAF RAF

Figure 5.72: The morphological fractions obtained from the quasi-isothermal crystallization for the PET sample.

209

5.2.8.4- Poly (trimethylene terephathalat) (PTT):

Using the same method and figure (5.44) the results of the morphological

fractions and how they changed with the crystallization temperature are shown

in figure (5.73). The results show that by considering only two-phase model the

rigid crystalline fraction (RCF) and the mobile amorphous fraction (MAF) is

constant. On the other hand, by considering the three-phase model figure (5.74)

it is found that the rigid crystalline fraction (RCF) is still constant and the

mobile amorphous fraction (MAF) increases as the crystallization temperature

increase. On the other hand, the rigid amorphous phase fraction (RAF)

decreases as the crystallization temperature increase. This can be explained by

the same above explanations used with the PET It is found that the three-phase

model reflects much more information about the morphological fractions than

the two-phase model.

322 324 326 328 330 332 334 336 338 3400.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

RCF

MAF

PTT

Mor

phol

ogic

al fr

actio

ns

TC in K

Figure 5.73: The morphological fractions for the PTT sample using the quasi-isothermal crystallization experiments by considering the two-phase model.

210

322 324 326 328 330 332 334 336 338 3400.000.050.100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.850.900.951.00

PTT

Mor

phol

ogic

al fr

actio

ns

TC in K

RCF RAF MAF

Figure 5.74: The morphological fractions for the PTT sample using the quasi-isothermal crystallization experiments by considering the three-phase model.

211

5.2.8.5- Syndiotactic Polypropylene (sPP):

Using figure (5.47) and the same method figure (5.75) is obtained which

shows how are the different morphological fractions above the glass transition

temperature (i.e. mobile amorphous and rigid amorphous) changed with the

temperature and frequency. As a general behavior the mobile amorphous

fraction (MAF) increase as the temperature increase and on the other hand, the

rigid amorphous fraction (RAF) decrease as the temperature increase. This

behavior is found at all frequencies studied. These content changes of the MAF

and the RAF are frequency dependent. This may be due to the relaxation of the

RAF above the glass transition temperature.

300 310 320 330 340 350 360 370 380 390 400 410-0.2

0.0

0.2

0.4

0.6

0.8

1.0KPP3

Mor

phol

ogic

al F

ract

ions

TC in K

MAF0.0025 RAF0.0025 MAF0.005 RAF0.005 MAF0.01 RAF0.01 MAF0.02 RAF0.02 MAF0.04 RAF0.04 MAF0.083 RAF0.083

Figure 5.75: The morphological fractions obtained for the semi-crystalline KPP3 sample as a function of temperature at each frequency.

212

5.2.8.6- Poly (3-hydroxybutarate) (PHB): Considering the complex heat capacity values less than the two-phase model

line in figure (5.46) further analysis of the data can be made to obtain

information about the rigid amorphous fraction (RAF) and mobile amorphous

fraction (MAF) by assuming the rigid crystalline fraction (RCF) to be constant.

Figure (5.76) show how the RAF and the MAF content changes with the

frequency at the crystallisation temperature 240 K (i.e. below Tg ), which gives

an information about the glassy state i.e. glassy PHB.

Figure (5.77) shows the same but for a crystallisation temperature 320 K

(i.e. above Tg), which gives an information about the rubber state i.e. rubbery

PHB. From figure (5.76), we can conclude that the morphology of the PHB at

the glassy state is frequency independent (i.e., as the frequency increase the

RAF and the MAF are constant). Moreover, the RAF content is larger than the

MAF. The RAF content is larger than the MAF at the glassy state this may be

because at the glassy state, there is no mobile fraction and it is clear that the

MAF content is approaches zero.

0.00 0.01 0.02 0.03 0.040.0

0.2

0.4

0.6

0.8

1.0

RAF MAF

PHB at 240 K

Mor

phol

ogic

al F

ract

ions

Freq. in Hz

Figure 5.76: Frequency dependent morphology of the PHB below Tg.

213

0.00 0.01 0.02 0.03 0.04

0.0

0.2

0.4

0.6

0.8

1.0

RAF MAF

PHB at 320K

Mor

phol

ogic

al F

ract

ions

Freq. in Hz

Figure 5.77: Frequency dependent morphology of the PHB above Tg

From figure (5.77) it is seen that the morphology of the PHB above Tg

(i.e. rubber state at 320 K) is frequency dependent in a manner that as the

frequency increases the RAF increase and the MAF decrease exponentially and

the RAF content is smaller than the MAF.

These results can be explained by the fact that at the glassy state (i.e.

below 273 K) most of the material is rigid, which make the RAF larger than the

MAF that is because the RAF is a part of the rigid fraction. Then as the system,

pass the Tg the MAF increase in the glass-rubber relaxation process, which make

it larger than the RAF above Tg.

214

5.2.8.7- PHB-co-HV:

220 240 260 280 300 320 340 360 380 4000.0

0.5

1.0

1.5

2.0

2.5

3.0

b

a

2

1



PHB

T in K

|cp*|

in J

/g.K

Figure 5.78: The complex heat capacity obtained using the modulated scan TMDSC for the PHB polymer.

220 240 260 280 300 320 340 360 380 4000.0

0.5

1.0

1.5

2.0

2.5

3.0

2

1

b

a



PHB-co-HV 5%

T in K

|cp*|

in J

/g.K

Figure 5.79: The complex heat capacity obtained using the modulated scan TMDSC for the PHB-co-HV5% polymer.

215

220 240 260 280 300 320 340 360 380 4000.0

0.5

1.0

1.5

2.0

2.5

3.0

2

1

b

a

(1) 8% Amorphous(2) 8% Semi-crystalline(a) crystalline PHB(b) Amorphous PHB

PHB-co-PHV 8%

T in K

|cp*|

in J

/g.K

220 240 260 280 300 320 340 360 380 4000.0

0.5

1.0

1.5

2.0

2.5

3.0

2

1

b

a

(1) 12% Amorphous(2) 12% Semi-crystalline(a) Amorphous PHB(b) crystalline PHB

PHB-co-PHV 12%

T in K

|cp*|

in J

/g.K

Figure 5.81: The complex heat capacity obtained using the modulated scan TMDSC for the PHB-co-HV12% polymer.

216

290 300 310 320 330 340 350 3600

10

20

30

40

50

60

70

80

90

100 Crystalline Fraction (TMDSC) Mobile amorphous Fraction(TMDSC) Rigid amorphous Fraction(TMDSC) Crystalline Fraction (NMR) Mobile amorphous Fraction(NMR) Rigid amorphous Fraction(NMR)

Mor

phol

ogic

al fr

actio

ns (%

)

T in K

PHB

Figure 5.82: The morphological fractions change with temperature for the PHB pure polymer.

290 300 310 320 330 340 350 3600

10

20

30

40

50

60

70

80

90

100 C rys ta lline F raction (T M D S C ) M ob ile am orphous F rac tion (T M D S C ) R ig id am orphous F raction (T M D S C ) C rysta lline F raction (N M R ) M ob ile am orphous F rac tion (N M R ) R ig id am orphous F raction (N M R )

Mor

phol

ogic

al fr

actio

ns(%

)

T in K

PH B -co-PH V 5%

Figure 5.83: The morphological fractions change with temperature for the PHB-co-HV 5% copolymer.

217

290 300 310 320 330 340 350 360

0

10

20

30

40

50

60

70

80

90

100 C rystalline Fraction (TM DSC) M obile am orphous Fraction(TM DSC) R igid am orphous Fraction(TM DSC) C rystalline Fraction (NM R) M obile am orphous Fraction(NM R) R igid am orphous Fraction(NM R)

Mor

phol

ogic

al fr

actio

ns (%

)

T in K

PHB-co-PHV 8%

Figure 5.84: The morphological fractions change with temperature for the PHB-co-HV 8% copolymer.

290 300 310 320 330 340 350 360

0

10

20

30

40

50

60

70

80

90100

C rys ta lline F raction (T M D S C ) M ob ile am orphous F rac tion (T M D S C ) R ig id am orphous F raction(T M D S C ) C rys ta lline F raction (N M R ) M ob ile am orphous F rac tion (N M R ) R ig id am orphous F raction(N M R )

Mor

phol

ogic

al fr

actio

ns (%

)

T in K

PHB-co-PHV 12%

Figure 5.85: The morphological fractions change with temperature for the PHB-co-HV12% copolymer

218

Using the figures (5.78, 5.79, 5.80,5.81) and the same method and eqs.(5.5, 5.6,

5.7, 5.8) we were able to have some information about the morphological

fraction in the PHB-co-HV copolymer.

Figures (5.82-5.85) show the morphological fractions obtained using the

TMDSC and NMR (144) techniques for the PHB-co-HV copolymer. It can be seen

that our results show nearly the same behavior as the NMR technique. This

indicates that the results give the same information about the morphological

fractions as the NMR technique.

As a general conclusion from these figures, we can see from the results

that the temperature is effective on the morphological fractions. In addition, we

can see that rigid crystalline fraction (RCF) is almost constant but both the rigid

and mobile amorphous fractions (i.e., RAF and MAF) change dramatically with

temperature.

As indicated through our results the MAF increase with temperature

increasing and RAF decrease as the temperature increase. In addition, we can

see that as the temperature increase more MAF formed in the sample but less

RAF found in the sample this is because the relaxation of the RAF, which

changed to MAF as the temperature increase.

219

5.2.8.8-PHB/PCL blend:

The TMDSC experiments for studying the pure PHB, pure PCL, and the

blends of both polymers were a complicated program*. First the sample was

quenched from 300 K to 220 K without modulation and then the sample was

melted at 470 K with modulation frequency 0.01 Hz and underlying heating rate

1 K/min and temperature amplitude 1 K and then cooling down to 220 K with

the same modulation frequency and the temperature amplitude. Then remain for

15min, and afterwards melt again at 470 K under the same modulation

frequency 0.01 Hz. Then sample cooled with 80K/min to 220 K without

modulation, remain for 15 min, and finally melt again at 470 K.

5.2.8.8.1- Pure PHB:

Figure (5.86) shows the pure PHB results of the modulated heating scans

1, 2 and 3 represent heating after cooling with constant heating rate. In addition,

the curve 4 is a modulated cooling curve from 470K to 220K with underlying

cooling rate 1K/min. and frequency 0.01 Hz is shown in the figure.

Constructing the amorphous and crystalline lines:

The amorphous line and crystalline line of the PHB was used in figure

(5.86) (see PHB results on this chapter). The results were in a good agreement

with the two lines used before for the pure PHB material.

* This program was designed after a lot of tests on the pure polymers and their blend.

220

250 300 350 400 4500.0

1.0

2.0

3.0

4.0

5.0

6.0

4

3

2

1

c

b

a

|cp*|

in J

/g.K

T in K

(1) first heating with 1K/min, 0.01 Hz(2) heating after cooling with 1K/min, 0.01 Hz(3) heating after cooling with 80K/min, 0.01 Hz(4) Colling with 1K/min, 0.01 Hz(a) Amorphous(b) Crystalline (c) two-phase model

PHB

Figure 5.86: The modulated scan of pure PHB under modulation frequency 0.01 Hz and heating rate 10 K/min. Calculating of the two-phase model line:

The two-phase model was calculated, based on the crystallinity degree

calculation using the DSC melting peak of PHB sample and by applying the

equation:

cpb(T)=XcPHB*cpcPHB+(1-XcPHB)*cplPHB (5.9) The line was plotted in the figure (5.86).

Figure (5.86) shows that, at the cooling rate 80K/min the sample show a

dynamic glass transition (i.e., αMAF glass transition relaxation) at 263 K, which

is shifted from the static glass transition (273 K) (see DSC results for the PHB

sample for the static glass transition). For the other two curves, there is no clear

dynamic glass transition. This may be attributed to the sample semi-crystallinity

at these cooling rates.

221

5.2.8.8.2- PHB95 /PCL5 blend:

Figure (5.87) shows the PHB95/PCL5 %wt. blend results of the

modulated heating scans, which was cooled with two cooling rate 1K/min, 80

K/min and the first heating which was quenched form 300 K to 220 K (curves

1,2,3). Also the modulated cooling curve with 1K/min. and frequency 0.01 Hz

(curve 4).

Calculating the amorphous and crystalline lines:

The amorphous line and crystalline line of the PHB95/PCL5 %wt. blend

was calculated using these two equations: l

PCLpPHBl

PHBpPHBAp cTcTc )()()( )1()()( ξξ −+= (5.10) c

PCLpPHBc

PHBpPHBCp cTcTc )()()( )1()()( ξξ −+= (5.11) Where, ξPHB , ξPCL are the blending ratio of the PHB and PCL polymers and

clp(PHB), cl

p(PCL) are the liquid heat capacities of the PHB and PCL polymers. In

addition, the ccp PHB, cc

p PCL are the crystal heat capacities of the PHB and PCL

polymers.

Calculating of the two-phase model line:

The two-phase model was calculated on the basis of the crystallinity

degree calculated using the DSC melting peak of PHB95/PCL5 blend. The two-

phase model line was calculated at two regions of the temperature. The first

region is at TmPCL<T>TgPHB and the two-phase model line was calculated using

the equation:

[ ][ ]l

PHBpPHBsolidc

PHBpPHBsolidPHB

lPCLpPCLsolid

cPCLpPCLsolidPCLphasep

cc

ccTc

)()(

)()(2

*)1(*

*)1(*)(

−−

−−−

−++

−+=

χχξ

χχξ

(5.12)

222

The line was plotted in the figure (5.87). The second region is at T>TmPCL and

the two-phase model line were calculated using the equation:

[ ][ ]l

PHBpPHBsolidc

PHBpPHBsolidPHB

lPCLpPCLphasep

cc

cTc

)()(

)(2

*)1(*

)(

−−

−

−+

+=

χχξ

ξ (5.13)

The two-phase model line is shown in figure (5.87) (see lines (c1, c2) in the

figure).

In figure (5.87) the results show that the experimental data are in a good

agreement with the two calculated amorphous and crystalline lines (see line (a)

and (b) in the figure). The results did not show any dynamic glass transition.

Also from the curves 2, 3 it is seen that we have small peak which is attributed

to the melting of the PCL and this is because that the ratio of the PCL is only 5%

wt. In addition, the results show a large melting peak, which is attributed to the

PHB.

250 300 350 400 4500.0

1.0

2.0

3.0

4.0

c2

4

3

21

c1

b

a

PHB95

|cp*

| in

J/g.

K

T in K

Figure 5.87: The modulated scan of PHB95/PCL5%wt. blend under modulation frequency 0.01 Hz and heating rate 10 K/min.

223

5.2.8.8.3- Other PHB/PCL polymer blends:

The same TMDSC program was used for the PHB95 polymer blend

sample and the same calculating method and equations (5.10, 5.11) were used to

construct the amorphous and the crystalline line. In addition, the same equations

(5.12, 5.13) were used in constructing the two-phase model line.

In figures (5.88-5.92) the results show that the experimental data are in a

good agreement with the two calculated amorphous and crystalline lines (see

line (a) and (b) in the figure). The results showed no dynamic glass transition.

Also from the curves 1, 2, 3 it is seen that we have small peak which is

attributed to the melting peak of the PCL and this is because that the ratio of the

PCL is only 10% wt. In addition, the results showed a large melting peak, which

is attributed to the melting of the PHB.

250 300 350 400 4500.0

1.0

2.0

3.0

4.0

(1) first heating with 1K/min, 0.01 Hz(2) heating after cooling with 1K/min, 0.01 Hz(3) heating after cooling with 80K/min, 0.01 Hz(4) Colling with 1K/min, 0.01 Hz(a) Amorphous(b) Crystalline (c1, c2) two-phase model

c2

2

1

34

c1

b

a

PHB90

|cp*

| in

J/gK

T in K

Figure 5.88: The modulated scan of PHB90/PCL10 %wt. blend under modulation frequency 0.01 Hz and heating rate 10 K/min.

224

250 300 350 400 4500.0

1.0

2.0

3.0

4.0


c2

4

2

1

3

c1

b

a

PHB80

|cp*

| in

J/g.

K

T in K


250 300 350 400 4500.0

1.0

2.0

3.0

4.0


c2

24

13

c1

b

a

PHB70

|cp*

| in

J/gK

T in K

Figure 5.90: The modulated scan of PHB70/PCL30%wt. blend under modulation frequency 0.01 Hz and heating rate 10K/min.

225

250 300 350 400 4500.0

1.0

2.0

3.0

4.0


c2

42

13

c1

b

a

PHB50

|cp*|

in J

/g.K

T in K


250 300 350 400 4500.0

1.0

2.0

3.0

4.0


c24

2

1

3

c1

b

a

PHB20

|cp*|

in J

/g.K

T in K


226

5.2.8.8.4-PCL pure:

Figure (5.93) shows the pure PCL results of the modulated heating scans

which was cooled with two cooling rate 1 K/min, 80 K/min and the first heating

which was quenched form 300K to 220 K . Also the modulated cooling curve

from 470 K to 220 K with underlying cooling rate 1 K/min. and frequency 0.01

Hz.

Constructing the amorphous and crystalline lines:

The amorphous line and crystalline line of the PCL used in the figure (5.93) was

taken form the ATHAS database. The results were in a good agreement with the

two lines used before for the pure PCL material. (See DSC results for PCL). Calculating of the two-phase model:

The two-phase model was calculated on the basis of the crystallinity

degree calculated using the DSC melting peak of PCL sample, and applying the

equation:

Cpb(T)=Xc PCL*cp c PCL+(1-Xc PCL)*cp l PCL (5.14) The line was plotted in the figure (5.93).

Figure (5.93) shows that at the cooling rate 80K/min the sample show no

dynamic glass transition (i.e., glass transition Relaxation). Also for the other

two curves there is no clear dynamic glass transition. This is due to the fact that

the PCL has its glass transition at 211 K, which is beyond our measurement

temperature range.

227

250 300 350 400 4500.0

1.0

2.0

3.0

4.0


412

b

ca

3

PCL

T in K

|cp*

| in

J /g

.K

Figure 5.93: The modulated scan of PCL sample under modulation frequency 0.01 Hz and heating rate 10 K/min.

It is found that in the temperature region T>TmPCL the complex heat

capacity in the PHB coincident with the two-phase model but as the PHB

decrease in the blend the complex heat capacity is shifted towards the

amorphous liquid line (see figures (5.86-5.93) to coincident finally in the PCL

with the amorphous liquid line, see figure (5.93).

Using this two-phase model line, we can use the same idea illustrated

before (see the pervious morphology data discussions). This idea is that we can

have information about the morphological fractions at different temperatures

from the complex heat capacity, which below the two-phase model line.

228

0 20 40 60 80 100

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0 PHB/PCL blend Morphology at 245K (Tg PHB >T>Tg PCL)

Mor

phol

ogic

al fr

actio

ns

PHB %wt.

Rigid fraction (after cooling 1 K/min ) Rigid fraction (after cooling 80 K/min ) Rigid fraction (after quenching ) Mobile fraction (after cooling 1 K/min ) Mobile fraction (after cooling 80 K/min ) Mobile fraction (after quenching )

Figure 5.94: The morphological fractions of the blend as a function of the PHB ratio in the PHB/PCL blend at 245 K.

60 80 1000.20.30.40.50.60.70.80.91.01.11.21.31.41.5

PHB/PCL blend Morphology at 270K (Tg PHB >T>Tg PCL)

Mor

phol

ogic

al fr

actio

ns

PHB %wt.

Rigid fraction (after cooling 1 K/min) Rigid fraction (after cooling 80 K/min) Rigid fraction (after quenching) Mobile fraction (after cooling 1 K/min) Mobile fraction (after cooling 80 K/min) Mobile fraction (after quenching)

Figure 5.95: The morphological fractions of the blend as a function of the PHB ratio in the PHB/PCL blend at 270K.

229

70 75 80 85 90 95 1000.20.30.40.50.60.70.80.91.01.11.21.31.41.5

PHB/PCL blend Morphology at 275K (Tg PHB< T>Tg PCL)

Mor

phol

ogic

al fr

actio

ns

PHB %wt.

Rigid fraction(after cooling 1 K/min) Rigid fraction(after cooling 80 K/min) Rigid fraction(after quenching) Mobile fraction(after cooling 1 K/min) Mobile fraction(after cooling 80 K/min) Mobile fraction(after quenching)

Figure 5.96: The morphological fractions of the blend as a function of the PHB ratio in the PHB/PCL blend at 275K.

Figure (5.94-5.96) shows the morphological fractions changes as the PHB

content in the blend increase, below and above Tg of the PHB. We use the

notation RF to state for the rigid fraction in the blend. The rigid fraction in this

case state for the rigid crystalline fraction (RCF) and rigid amorphous fraction

(RAF). The temperature is fixed at 245, 270 and 275 K which is lower and

above the Tg of the PHB. The figures show that the mobile amorphous fraction

(MAF) is decrease as the PHB content increase in the PHB/PCL blend. And the

rigid fraction (RF) is increase as the PHB content increase in the PHB/PCL

blend.

The figures also show that at temperature (270 and 275 K) we cannot

obtain much information about the morphological fractions at the low PHB

contents this is because of the excess heat capacity found at this temperature.

(B)

Dielectric Studies

231

5.3-Dielectric Spectroscopy Measurements:

In recent years, copolymers have attracted the attention of the materials

researchers with increasing interest for obtaining intermediate properties with

respect to the homopolymers (146).

Dielectric spectroscopy was used in this work to study the relaxation

processes and phase transitions in relatively new copolymer namely the Poly (3-

hydroxybutaric acid-co-3-hydroxyvaleric acid ) PHB-co-HV with three

different HV contents 5%, 8%, and 12%.

5.3.1-Phase transition study of (PHB): To use the dielectric spectroscopy to investigate the phase-transition in

pure PHB, the sample was melted at 473 K and then cooled down to 223 K then

The dielectric spectra were measured during heating the sample from 220 K to

373 K at only four frequencies 100, 1000, 10,000, and 100,000 Hz

220 240 260 280 300 320 340 360 3800.0

0 .2

0 .4

0 .6

0 .8

1 .0P H B

ε''

T in K

1 0 0 H z 1 K H z 1 0 K H z 1 0 0 K H z

Figure 5.97: The dielectric loss (ε′′) versus the temperature at four frequencies for the PHB pure polymer from 220 K up to 373 K.

232

Figure (5.97) shows the dielectric loss (ε′′) versus the temperature for the

PHB pure polymer. It is seen that ε′′ shows peak, its maximum shifts as the

frequency increase to the higher temperature side. The peaks shown may be

attributed to the glass transition relaxation. In addition, the maximum of the

peak decrease with increasing the frequency. That is the dielectric loss decreases

with increasing the frequency, which, indicate a relaxation process (i.e., glass

transition-rubber transition relaxation).

It is also to be noticed that at the lowest frequency 100Hz, (ε′′) curve

shows another peak as a shoulder indicating that there is another relaxation

processes at 300K this peak may be attributed to the crystal or rigid amorphous

fraction (RAF) relaxation (140). The steep upturn at the high temperature side in

the figure indicate the ionic conduction.

In addition, relaxation of the crystal or RAF takes place at temperature

higher than glass transition temperature Tg. Another result one is that the crystal

or RAF formation hinders the main glass transition relaxation. This is clear from

the 100Hz curve that the first peak was attributed to the glass transition

relaxation and the second peak means that there is either another unresolved

relaxation process or something hindering the main relaxation process. As we go

to the high temperature side, the crystallization process of the PHB takes place

(see the dash line which indicants the DSC crystallization temperature for the

PHB).

233

5.3.2-Dielectric constant study for PHB and its copolymers: 5.3.2.1-Frequency dependence study:

10-3 10-2 10-1 100 101 102 103 104 105 106 107 108

2

4

6

8

10

12

10-3 10-2 10-1 100 101 102 103 104 105 106 107 1082.0

2.2

2.4

2.6

2.8

3.0

ε'

Freq. in Hz

PHB

ε'

Freq. in Hz

273K 278K 283K 288K 293K 298K 303K 313K 323K 328K 333K 338K 343K 348K 353K

Figure 5.98: The frequency dependence of dielectric constant ε′ for the PHB polymer

at different temperatures.

Figure (5.98) shows the dielectric constant (i.e., permitivity) as a function of

frequency for the PHB pure polymer. As shown it is clear that at lower

frequency~10-2 Hz as the temperature increases the dielectric permitivity

increases, which indicates. This indicates the “polarization” of the sample and

relaxation processes. The dramatic change in the ε′ behavior above 313 K may

be an indication of the crystallization process and confirm the DSC

measurements that the crystallization of the PHB occurs around 320 K.

234

10-3 10-2 10-1 100 101 102 103 104 105 106 107 108

101214161820222426283032343638

10-3 10-2 10-1 100 101 102 103 104 105 106 107 108

10

12

14

16

ε '

Freq. in Hz

PHB-co-HV5%

ε '

Freq. in Hz

273K 283K 293K 303K 313K 328K 333K 338K 343K 348K 353K

Figure 5.99: The frequency dependence of dielectric constant ε′ for the PHB-co-HV 5% copolymer at different temperatures.

10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 1091.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

12

34

5

6

7

8

9

10

11

12

1314

1516

1718

1920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980

A BC

DE

FG

H

I

J

K

L

M

N

O

PQ

RS

TU

VW X Y ZAAABACADAEAFAGAHAIAJAKALAMANAOAPAQARASATAUAVAWAXAYAZBABBBCBDBEBFBGBHBIBJBKBLBMBNBOBPBQBRBSBTBUBVBWBXBYBZC AC B

a bc d

ef

gh

ij

kl

m

n

o

p

q

rs

tu

vw

xy zaaabacadaeafagahaiajakalamanaoapaqarasatauavawaxayazbabbbcbdbebfbgbhbibjbkblbmbnbobpbqbrbsbtbubvbwbxbybzcacb

PHB-co-HV8% 233K 243K 253K 263K 273K 283K 293K 303K 308K 313K 323K 328K 333K 338K 343K 348K

1 353KA 358Ka 363K

368K 373K

ε '

Freq. in Hz


235

10-2 10-1 100 101 102 103 104 105 106 107 108 109

2

3

4

5

6

7 PHB-co-HV12%

353K 348K 343K 338K 333K 328K 323K 313K 303K 298K 293K 288K 283K 278K 273K

ε '

Freq. in Hz


Figures (5.99-5.101) shows the dielectric constant (i.e., permitivity) as a

function of frequency for the PHB-co-HV copolymers containing 5, 8 and 12

mol.% HV. It is clear that as the temperature increases the dielectric permitivity

increases, which indicate an “emigrational polarization” of the sample and

hence relaxation processes. . The dramatic change in the ε′ behavior above

328K can be used as an indication of the crystallization process and confirm the

DSC measurements that the crystallization of the PHB-co-HV 5%, PHB-co-

HV8% occurs around 340 and 350K respectively. On the other hand, no

indication for the crystallization process in PHB-co-HV 12% can be seen in

figure (5.101). This fact is in good agreement with the DSC measurements.

236

5.3.2.2-Temperature dependence study:

280 300 320 340 360 380 400

2.02.53.03.54.04.55.05.56.06.57.07.58.08.59.0

f in Hz 107

105

104

103

102

101

100

10-1

10-2

270 280 290 300 310 320 330 340 3502.0

2.2

2.4

2.6

2.8

3.0

ε'

T in K

PHB

ε'

T in K

Figure 5.102: The dielectric constant ε′ as a function of temperature for the PHB polymer at different frequencies.

260 280 300 320 340 360 380 400

10

15

20

25

30

35

260 280 300 320 340 36010

11

12

13

14

15

16

ε'

T in K

f in Hz 10-2

10-1

100

101

102

103

104

105

PHB-co-HV 5%

ε'

T in K

Figure 5.103: The dielectric constant ε′ as a function of temperature for the PHB-co-HV 5% copolymer at different frequencies.

237

260 280 300 320 340 360 380 400

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

f in Hz 10-2

10-1

100

101

102

103

104

105

PHB-co-HV 8%

ε'

T in K

Figure 5.104: The dielectric constant ε′ as a function of temperature for the PHB-co-HV 8% copolymer at different frequencies.

270 280 290 300 310 320 330 340 350 360 370 380 390 40005

101520253035404550556065

270 280 290 300 310 320 330 340 350 3601.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

ε'

T in K

f in Hz 107

105

104

103

102

101

100

10-1

10-2

PHB-co-HV 12%

ε'

T in K

Figure 5.105: The dielectric constant ε′ as a function of temperature for the PHB-co- HV12% polymer at different frequencies.

238

Figures (5.102-5.105) show the dependence of the dielectric constant on the

temperature for PHB and its copolymers at various fixed frequencies. From the

figures, it is clear that at low frequency and high temperature the effect of

conductivity on the spectrum becomes large. At ~1 Hz, a step in the dielectric

constant is found which decreases with increasing frequency. The change in the

dielectric constant indicate phase transition at ~310K. The temperature

dependence of the peak width may be attributed to the glass transition

relaxation, which occur in this range of temperatures.

239

5.3.3-The dielectric loss studies of PHB and its copolymers:

The dielectric loss ε’’ measurements of the PHB-co-HV copolymer were

carried directly from the glass transition temperature 273K to 353K in order to

study the relaxation processes take place in this temperature region including the

relaxation of the (RAF).

5.3.3.1-Frequency dependence study: 5.3.3.1.1-Pure PHB:

First, we start with the PHB pure polymer. The broadband dielectric

spectroscopy was used with the frequency range from 10-2 to 107 Hz to be able

to detect all the relaxation spectrum of the material.

10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 109 1010

10-1

101

PHB

273K278K283K288K293K298K303K313K323K328K333K338K343K348K353K

ε ''

Freq. in Hz

Figure 5.106: The frequency dependence of dielectric loss ε′′ for the PHB pure polymer at different temperatures.

Figure (5.106) shows the dielectric loss as a function of frequency for the

pure PHB. We can see a differences in the dielectric loss behaviors above 313K

this gives an indication of the crystallization processes that takes place in the

240

PHB sample. In addition, It is clear from the figure that the peak shifts toward

the high frequency side as the temperature increases and may be due to αMAF-

relaxation. At the low frequency, the fast decrease of the ε’’ may be due to the

conduction process or to relaxation process α* which occur in the free

amorphous and intercrystalline regions (145) (i.e., RAF).

The dielectric loss (ε``) experimental data analysis:

In order to resolve the complex spectra of the dielectric loss experimental

data an analysis was done using the Havriliak and Negami empirical equation

plus a conductivity term (See chapter 2 for more details). The result of the fitting

for the dielectric loss data gives us six parameters. The parameters (β), which

indicate for the symmetry (width of the peak), (γ) which indicate for the

asymmetry (the deviation from Debye process), (∆ε) which indicate for the

dielectric strength, (fo) which indicate for the HN-frequency value of the

dielectric loss, (S) which indicate for the conductivity related parameter and n

which is the conductivity power.

10-3 10-2 10-1 100 101 102 103 104 105 106 107 108-3

-2

-1

0 Experimental Data HN-fitt

PHB at 293K

Log ε''

Freq. in Hz

Figure 5.107: An example of the HN model fit of PHB at 293K.

241

10-3 10-2 10-1 100 101 102 103 104 105 106 107 108-4

-3

-2

-1

0

2

1

Experimental Data(1) 1st HN peak(2) 2nd HN peak

PHB at 323K

Log ε''

freq. in Hz

Figure 5.108: An example of the HN model fit of PHB at 323K.

10-3 10-2 10-1 100 101 102 103 104 105 106 107 108-5.0-4.5-4.0-3.5-3.0-2.5-2.0-1.5-1.0-0.50.00.51.0

2

1

Experimental Data(1) 1st HN peak(2 )2nd HN peak

PHB at 343K

Log ε''

Freq. in Hz

Figure 5.109: An example of the HN model fit of PHB at 343K. Figures (5.107, 5.108, 5.109) show examples of the fitting process using the Log

(ε``) to fit the Logarithm HN model plus the conductivity term. The dielectric

loss data were analyzed using (2-signal LOG HN model). In order to fit 2-peaks

242

not one peak only. (See the example figures). Table (5.7) shows the fitting

parameters for the dielectric loss data.

Table 5.7: HN fit parameters for the dielectric loss data for the pure PHB.

T(K) β1 γ1 ∆ε1 FHN1 β2 γ2 ∆ε2 FHN2 S n

273 ------ ------ ------ ------- ----- ----- ----- ------ ----- -----

278 0.39 0.59 0.4 0.0065 ----- ----- ----- ------ 0.039 0.52

283 0.41 0.63 0.4 0.118 ----- ----- ----- ----- 0.061 0.49

288 0.4 0.63 0.5 0.62 ----- ----- ----- ----- 0.08 0.5

293 0.37 0.73 0.558 5.39 ----- ----- ----- ----- 0.1 0.49

298 0.36 0.76 0.56 37 ----- ----- ----- ----- 0.14 0.48

303 0.34 0.78 0.59 167 0.93 0.75 0.4 0.0108 0.128 0.458

313 0.34 0.82 0.61 3954 0.98 0.8 0.29 0.036 0.228 0.46

323 0.337 0.838 0.578 49850 0.93 0.8 0.353 0.07 0.35 0.48

328 0.328 0.9 0.51 175100 0.9 0.8 0.36 0.109 0.43 0.49

333 0.337 0.98 0.46 502700 0.94 0.84 0.257 0.21 0.58 0.49

338 0.346 0.998 0.455 1.14x106 0.998 0.83 0.19 0.391 0.78 0.5

343 0.354 1.08 0.448 2.859x106 0.997 0.906 0.13 0.75 1.09 0.52

348 0.367 1.15 0.438 6.089x106 0.997 0.95 0.049 1.637 1.55 0.53

353 0.377 1.18 0.43 1.061x107 1.1 1 0.027 2.537 2.198 0.55

243

The relaxation map for the PHB polymer:

The final analysis was to plot the relaxation map for the PHB polymer

using the log of the frequency maximum of the dielectric loss. Our data

relaxation map in figure (5.110) shows clearly that there is the main relaxation,

which is αMAF-relaxation (that is clear because of that the squared data points

cannot be fitted with straight line). On the other hand the triangles points which

represent the β-relaxation or RAF relaxation or to the to relaxation process take

place in the crystalline region (can be fitted with straight line). Further the

circles which may due to relaxation process α* which occurs in the free

amorphous and intercrystalline regions (145) (i.e., RAF).

2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7

-2

0

2

4

6

8 PHB

log(

f max

)

1000K/T

α α* β

Figure 5.110: The relaxation map of PHB using log fmax of the dielectric loss experimental data.

244

2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7

-2

0

2

4

6

8PHB

log(

f max

)

1000K/T

Figure 5.111: The relaxation map of PHB the dielectric loss fitted using Arrhenius and Vogel Fulsher Tamman (VFT) equations.

The experimental data log(fmax=1/2πτ) versus 1000/T in figure (5.110) was fitted

using Arrhenius equation:

τ = τo exp(E/KT) (5.15)

And the Vogel-Fulsher-Tamman (VFT) equation:

τ = τo exp(E/(K(T-To))) (5.16)

in order to obtain the relaxation parameters E and τo ,see figure (5.111).

Table 5.8: The relaxation parameters for the different relaxation processes in the pure PHB polymer.

Relaxation

Process

E in kj /mol τo in sec To in K

α 113.257 3.112x10-16 206

β 7.744 2.205x10-4 -----

α* 39.904 1.984x10-15 -----

245

The dielectric relaxation spectrums of the PHB-co-HV copolymers are

shown in figures (5.112, 5.113 and 5.114). The broadband dielectric

spectroscopy was used with the frequency ranges from 10-2 to 107 Hz to be able

to detect all the relaxation spectrum of the material.

10 -3 10 -2 10 -1 10 0 1 0 1 10 2 10 3 1 0 4 10 5 10 6 1 0 7 10 8 10 9 10 1 0

1 0 -1

1 0 0

1 0 1

1 0 2

2 7 3 K 2 8 3 K 2 9 3 K 3 0 3 K 3 1 3 K 3 2 8 K 3 3 3 K 3 3 8 K 3 4 3 K 3 4 8 K 3 5 3 K

P H B -co -H V 5%

ε ''

F req . in H z

Figure 5.112: The frequency dependence of dielectric loss ε′′ for the PHB-co-HV5 % copolymer at different temperatures.

246

1 0 -3 1 0 -2 1 0 -1 1 0 0 1 0 1 1 0 2 1 0 3 1 0 4 1 0 5 1 0 6 1 0 7 1 0 8 1 0 9

1 0 -3

1 0 -2

1 0 -1

1 0 0

1 0 1

1 0 2

12

34

56

78

91 0

1 11 2

1 31 4

1 51 6

1 71 8

1 92 0

2 12 2

2 32 4

2 52 6

2 72 8

2 93 0

3 13 2

3 33 43 5

3 63 73 83 94 04 14 24 34 44 54 64 74 84 95 05 15 25 35 45 55 65 75 85 96 06 16 26 36 46 56 66 76 86 97 07 17 27 37 47 57 67 77 87 98 0

AB

CD

EF

GH

IJ

KL

MN

OP

QR

ST

UV

WX

YZA A

A BA C

A DA E

A FA G

A HA I

A JA K

A LA MA NA OA PA QA RA SA TA UA VA WA XA YA ZB AB BB CB DB EB FB GB HB IB JB KB LB MB NB OB PB QB RB SB TB UB VB WB X

B YB ZC AC B

ab

cd

ef

gh

ij

klm

no

pq

rs

tu

vw

xy

za a

a ba c

a da e

a fa g

a ha i

a ja k

a la m

a na o

a pa qa ra sa ta ua va wa xa ya zb ab bb cb db eb fb gb hb ib jb kb lb mb nb ob pb qb rb sb tb ub vb wb x

b yb zc ac b

P H B -c o -H V 8 % 2 3 3 K 2 4 3 K 2 5 3 K 2 6 3 K 2 7 3 K 2 8 3 K 2 9 3 K 3 0 3 K 3 0 8 K 3 1 3 K 3 2 3 K 3 2 8 K 3 3 3 K 3 3 8 K 3 4 3 K 3 4 8 K

1 3 5 3 KA 3 5 8 Ka 3 6 3 K

3 6 8 K 3 7 3 K

ε ' '

F re q . in H z


10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 109 101010-2

10-1

100

101

102 353K 348K 343K 338K 333K 328K 323K 313K 303K 298K 293K 288K 283K 278K 273K

PHB-co-HV12%

ε''

Freq. in Hz


247

The figures ((5.112, 5.113 and 5.114) show the dielectric loss as a function of

frequency for the PHB-co-HV copolymers. We can see that there is a behavior

above 328 K gives an indication of the crystallization processes that take place

in the PHB-co-HV samples. In addition, it is clear from the figures that peak

shifts toward the high frequency as the temperature increases, which indicate

that this peak is due to αMAF-relaxation. In addition, at the high temperature and

low frequency a fast decrease is observed in the spectrum which is due to the

conduction process or to the same above mentioned relaxation process α*.

The experimental data analysis:

The experimental data analysis was done using the Havriliak and Negami

model plus the conductivity term for the dielectric loss data. Representative

examples of HN fits for the copolymers are given in figures (5.115 –5.117).

10-3 10-2 10-1 100 101 102 103 104 105 106 107 108

-2

-1

0

Experimental Data HN-Fitt

PHB-co-HV 5%

Log ε''

Freq. in Hz

Figure 5.115: An example of the HN model fit of PHB-co-HV 5% at 293 K

248

10-3 10-2 10-1 100 101 102 103 104 105 106 107 108-3.0-2.9-2.8-2.7-2.6-2.5-2.4-2.3-2.2-2.1-2.0-1.9-1.8-1.7-1.6

Experimental Data HN-fitt

Log ε''

Freq. in Hz

Figure 5.116: An example of the HN model fit of PHB-co-HV 8% at 293 K.

10-3 10-2 10-1 100 101 102 103 104 105 106 107 108-2.5

-2.0

-1.5

-1.0

-0.5

0.0

Experimental Data HN-Fitt

Log ε''

Freq. in Hz

Figure 5.117: An example of the HN model fit of PHB-co-HV 12% at 293 K.

249

Tables (5.9-5.11) show the fitting parameters for the dielectric loss data of the

different copolymers.

Table 5.9: The HN-fitting parameters for the dielectric loss data for the PHB-co-HV5%.

T(K) β γ ∆ε fHN S n

283 0.36 0.76 3.5 0.32 0.13 0.38 293 0.35 0.87 3.82 32.15 0.27 0.38 303 0.32 0.94 3.95 927 0.51 0.46 313 0.33 0.95 3.95 15950 0.94 0.52 323 0.34 0.96 3.95 753400 2.16 0.556 333 0.35 0.96 3.95 1.766x106 3.02 0.58 338 0.36 1.906 3.35 1.422x107 4.49 0.6 343 0.33 0.715 29.75 2.35 x109 6.7 0.71

Table 5.10: The HN-fitting parameters for the dielectric loss data for the PHB-co-HV 8%.

T(K) β γ ∆ε fHN S n

283 0.27 1 0.155 1.08 -- --

293 0.3086 1 0.159 98.12 -- --

303 0.35 0.95 0.248 1548 0.019 0.507

313 0.359 1.108 0.216 30700 0.034 0.516

323 0.389 0.946 0.206 145200 0.064 0.536

328 0.402 0.946 0.203 342800 0.0916 0.55

333 0.408 1.37 0.184 1.606x106 0.138 0.57

338 0.406 9.45 0.1456 2.466x108 0.217 0.595

343 0.414 13.92 0.146 1.188 x109 0.355 0.62

250

Table 5.11: The HN-fitting parameters for the PHB-co-HV 12% copolymer.

T(K) β1 γ1 ∆ε1 fHN1 β2 γ2 ∆ε2 f HN2 S n 273 0.29 0.089 0.62 15.34 ---- ---- ---- ---- 0.04 0.278 278 0.308 0.116 0.72 21.38 ---- ---- ---- ---- 0.05 0.31 283 0.32 0.127 0.71 27.6 ---- ---- ---- ---- 0.064 0.34 288 0.35 0.14 0.71 64.3 ---- ---- ---- ---- 0.089 0.38 293 0.397 0.15 0.73 199 ---- ---- ---- ---- 0.125 0.408 298 0.409 0.177 0.72 830 ---- ---- ---- ---- 0.178 0.437 303 0.44 0.182 0.7 2530 ---- ---- ---- ---- 0.26 0.46 313 0.442 0.19 0.7 24570 0.9994 0.508 0.72 0.014 0.42 0.52 323 0.5 0.198 0.71 91910 1 0.555 0.8 0.025 0.97 0.55 328 0.56 0.209 0.73 107500 0.999 0.58 1.29 0.0339 1.398 0.56 333 0.56 0.21 0.83 302300 0.998 0.585 3.27 0.035 1.79 0.583 338 0.56 0.215 0.9 616400 0.997 0.6 7.56 0.038 2.178 0.606 343 0.58 0.216 1 899000 0.9975 0.616 12.85 0.0427 3.13 0.617 348 0.59 0.225 1.137 1.491x106 0.9974 0.657 19.13 0.058 6.43 0.622 353 0.609 0.228 1.41 2.777x106 0.996 0.68 26.21 0.081 15.95 0.66

The relaxation map for the PHB-co-HV copolymer:

The final analysis was to plot the relaxation map for the PHB-co-HV 5%

copolymers using the log of the frequency maximum of the dielectric loss data.

The activation diagram in figures (5.118, 5.119) show clearly the existence of

the main relaxation, α-relaxation (that is clear because of that the data points

(see the squared data points) cannot be fit with straight line) and we cannot find

any relaxation due to the (RAF) relaxation or to relaxation process take place in

the crystalline region.

251

3.0 3.1 3.2 3.3 3.4 3.5 3.6

0

1

2

3

4

5

6

log(

f max

)

1000K/T

Figure 5.118: The VFT fitting of the PHB-co-HV 5% copolymer using the dielectric loss experimental data.

2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6-0.50.00.51.01.52.02.53.03.54.04.55.05.56.06.57.0

log(

f max

)

1000K/T

Figure 5.119: The VFT fitting of the PHB-co-HV 8% copolymer using the dielectric loss experimental data.

252

Table 5.12: The αMAF –relaxation parameters. Copolymer E in kj/mol τo in sec To (K) PHB-co-HV 5% 99.398 1.33x10-15 209 PHB-co-HV 8% 59.40 3.638x10-13 229

2.6 2.8 3.0 3.2 3.4 3.6 3.8

-1

0

1

2

3

4

5

6

7

8

lo

g(f m

ax )

1000K/T

Figure 5.120: The Arrhenius fitting of the PHB-co-HV 12% copolymer using the dielectric loss experimental data. The relaxation map for the PHB-co-HV12% copolymer:

Figure (5.120) shows clearly the existence of the main relaxation (which

is not α). In addition, we found a sub process, which may be attributed to the α*-

relaxation that takes place in the free amorphous region and intercrystalline

region (145). Table 5.12: The relaxation parameters for the PHB-co-HV 12% copolymer.

Relaxation process

E in kj/mol τo in sec.

Main process 39.605 4.968x10-22 Sub process 13.620 3.897x10-5

253

5.3.3.2-Temperature dependence study:

260 280 300 320 340 360 380

0

2

4

6

8

10

260 280 300 320 340 3600.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

ε''

T in K

PHB

ε''

T in K

f in Hz 10-2

10-1

100

101

102

103

104

105

107

Figure 5.121: The dielectric loss as a function of temperature for the pure PHB at different frequencies. Figures (5.121-5.124) show the dielectric loss as a function of temperature for

the PHB and its copolymers we can see how the conduction process affects the

relaxation process. It is clear that as the frequency increases the peak maximum

shifts towards the high temperature side (see the inset in the figure (5.121)).

which reveals that this relaxation process is αMAF. The dielectric loss upturn to a

very high value at 10-2 Hz. This upturn is due to conduction process, and hence

that the conductivity affects the relaxation process at the low frequencies.

254

260 280 300 320 340 360 380-20

0

20

40

60

80

100

120

140

260 280 300 320 340 3600.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

ε''

T in K

PHB-co-HV 5%

ε''

T in K

f in Hz 10-2

10-1

100

101

102

103

104

105

Figure 5.122: The dielectric loss as a function of temperature for the PHB-co-HV 5% at different frequencies.

260 280 300 320 340 360 380 400-20

0

20

40

60

80

100

120

140

160

260 280 300 320 340 360 3800.00

0.01

0.02

0.03

0.04

0.05

ε''

T in K

f in Hz 10-2

10-1

100

101

102

103

104

105

107

PHB-co-HV 8%

ε''

T in K

Figure 5.123: The dielectric loss as a function of temperature for the PHB-co-HV 8% at different frequencis.

255

260 280 300 320 340 360 380

0

20

40

60

80

100

120

260 280 300 320 340 3600.0

0.1

0.2

ε''

T in K

f in Hz 107

106

105

104

102

101

100

10-1

10-2

PHB-co-HV 12%

ε''

T in K

Figure 5.124: The dielectric loss as a function of temperature for the PHB-co-HV 12% at different frequencies.

256

5.3.4-Dielectric loss tangent studies of PHB and its copolymers: 5.3.4.1-Frequency dependence study:

In order to complete our study for the dielectric loss study the results are

represented by tan δ (=ε’’/ ε’) to obtain more information about the relaxation

processes in the four samples of the pure PHB and its three copolymers.

10-2 10-1 100 101 102 103 104 105 106 107 108 109 10100.00

0.01

0.02

0.03

0.04

0.05

T in K 273 278 283 288 293 298 303 313 323 328 333 338 343 348 353

PHB

tan δ

Freq. in Hz

Figure 5.125: The (tan δ) as a function of frequency for the PHB at different temperatures. Figures (5.125-5.128) show the frequency dependence of the (tan δ) for the pure

PHB and its copolymers, at various fixed temperatures. It is clear from the

figures that there is no common characteristic behavior of tan δ occurs at 273 K.

As the temperature increases the decay become slower and slower as shown in

the figures. At intermediate temperatures (283-293 K) a shoulder starts to appear

in the spectra. As the temperature increases, the shoulder becomes a peak. As

the temperature further, increase the peak maximum shifted to the high

frequency side (101 to 105 Hz). This peak was due to αMAF-relaxation processes,

257

which occurs around the glass transition temperature (273 K). As the

temperature further increases above 333 K the peak, disappear again.

10-2 10-1 100 101 102 103 104 105 106 1070.00

0.01

0.02

0.03

0.04

0.05

0.06

PHB-co-HV 5%ta

n δ

Freq. in Hz

T in K 273 283 293 303 313 328 333 338 343 348 353

Figure 5.126: The (tan δ) as a function of frequency for the PHB-co-HV 5% at different temperatures.

258

10-2 10-1 100 101 102 103 104 105 106 107 1080.00

0.01

0.02

0.03

0.04

PHB-co-HV 8%

tan δ

Freq. in Hz

T in K 273 283 293 303 313 323 333 343 353 363 373


10-2 10-1 100 101 102 103 104 105 106 1070.00

0.01

0.02

0.03

0.04

PHB-co-HV 12%

tan δ

Freq. in Hz

T in K 273 283 293 303 313 323 333 343 353


259

5.3.4.2-Temperature dependence study: Figures, (5.129, 5.130, 5.131, 5.132) show the dielectric loss tangent as a

function of temperature for pure PHB and its copolymers for various fixed

frequency. As a general trend in these figurers, is that the peak maximum is

shifted towards the high temperature as the frequency increase. (See the figures

below). The upturn at the high temperature region is due to the conductivity in

the sample.

260 280 300 320 340 360 3800.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

260 280 300 320 340 3600.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

tan δ

T in K

f in Hz 10-2

10-1

100

101

102

103

104

105

107

PHB

tan δ

T in K

Figure 5.129: The (tan δ) as a function of temperature for the PHB at different frequencies.

260

260 280 300 320 340 360 380-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

260 280 300 320 340 3600.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

tan δ

T in K

PHB-co-HV 5%

tan δ

T in K

f in Hz 10-2

10-1

100

101

102

103

104

105

Figure 5.130: The (tan δ) as a function of temperature for the PHB-co-HV 5% at different frequencies.

260 280 300 320 340 360 380 400

0

10

20

30

40

50

60

260 280 300 320 340 360 3800.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

tan δ

T in K

f in Hz 10-2

10-1

100

101

102

103

104

105

PHB-co-HV 8%

tan δ

T in K


261

260 280 300 320 340 360 380

0.0

0.5

1.0

1.5

2.0

260 280 300 320 340 3600.00

0.01

0.02

0.03

0.04

0.05

tan

δ

T in K

f in Hz 10-2

10-1

100

101

102

103

104

105

PHB-co-HV 12%

tan δ

T in K


Conclusion

263

Conclusion: 1-DSC results: 1- It was able to determine the static glass transition temperature Tg and the

crystallization temperature Tc, and the melting temperature (T melt).

2- DSC results reveal the thermal behavior of the pure semi-crystalline

polymers.

3- The crystallinity Хc and the heat of fusion ∆Ηf was calculated for the

PHB sample at different crystallization temperatures.

4- Using the DSC it was able to know the thermal behavior of different

syndiotatic polypropylene, which explored that the KPP1 do not

show any exothermic peak while the KPP2, KPP3, and FINA 4 show

crystallization peak.

5- Investigations of the PEEK sample reveal that it has the static glass

transition at 425K and crystallized at 453K and melt at 616K.

6- Investigations of the PTT sample reveal that it has the static glass

transition at 320K and crystallized at 350K and melt at 510K.

7- Investigations of the PHB/PCL polymer blend revealed that The static

glass transition temperature of the PHB polymer in the polymer blend is

not much affected by the change of the cooling rate.

8- Also the crystallization temperature of the PHB polymer in the polymer

blend is shifted by 5K towards higher temperature side by the blending

process.

9 – The melting temperature of the PHB in the polymer blend is not much

affected neither by the blending process nor cooling rate.

10- The investigations of PHB-co-HV copolymer with 5%, 8%, 12% HV

contents revealed that the thermal behavior is different with the HV

contents.

264

11- The static glass transition is shifted 1K towards the lower temperature when

5% HV content added to the PHB pure, while, it is shifted by 2K when 8%

HV content, only 12% have no static glass transition temperature.

12 – The copolymers 5%, and 8% HV contents can be fast crystallized in the

temperature range (310- 360K) while they can be slowly crystallized

before and after this range.

2- TMDSC results: 1. -The TMDSC is a new experimental technique (introduced in 1993),

which is sensitive to all kinds of molecular motions, either polar or not

polar which makes it a promising relaxation technique.

2. -The only disadvantage of this technique is that it is limited in the

frequency range (10-1 to 10-3 Hz), but it still in the developing stage

compared to other relaxation study techniques.

3. Using the TMDSC were able to study the α-relaxation in the syndiotactic

poly propylene and PHB-co-HV copolymer samples by calculating the

dynamic glass transition temperatures and relaxation strength.

4. Using TMDSC, we able to investigate the RAF formation process, which

is found to be a structure induced relaxation process occur during the

isothermal crystallization of the PHB and sPP pure polymers.

5. Using the TMDSC we investigated the αRAF -relaxation of the RAF in

PHB and sPP pure polymers and found that αRAF –relaxation take place

above Tg of the semi-crystalline polymer.

6. Using TMDSC, it is found that there are two relaxation processes which

take place during the isothermal crystallization of the semi-crystalline

polymers the αC –relaxation and reversing melting relaxation. These

processes were investigated in PEEK, PBT, PET, PTT, PHB, sPP Pure

semi-crystalline polymers.

265

7. Using the TMDSC, we were able to determine the temperature ranges in

which these relaxation processes can occur were investigated in PEEK,

PBT, PET, PTT, PHB, sPP pure semi-crystalline polymers.

8. . Relaxation processes take place after the crystallization of the semi-

crystalline polymers in the regions between crystalline lamellae and the

amorphous melt.

9. Invistegation of the reversing melting relaxation in the semi crystalline

polymers revealed that this process is related to the melting of the

crystals.

10. In the investigation of morphology for semi-crystalline polymers we

achieved experimental data comparable to the NMR technique.

11. Investigating the PHB/PCL polymer blend we can conclude that the

experimental data are in agreement with the two calculated amorphous

and crystalline lines for all the studied blend. Also, the results did not

show any dynamic glass transition. Further, the endothermic melting

peaks appeared in the TMDSC curves are affected by both the PHB and

PCL blending ratios. Further more it is found that in the temperature

range T>Tm PCL the complex heat capacity in the PHB coincident with the

two-phase model but as the PHB decrease in the blend the complex heat

capacity is shifted towards the amorphous liquid line to coincident finally

with the amorphous liquid line in the PCL.

12. From the blend morphology study concerning α-relaxation in the

PHB/PCL blend it is found that the MAF decrease as the PHB content

increase in the blend, on the other hand the RF increases as the PHB

content increase in the blend.

13. PHB-co-HV copolymer morphology studies for the α-relaxation was

comparable with the NMR study.

266

2- Dielectric spectroscopy results: From the dielectric results, we conclude that

1. Dielectric spectroscopy is useful technique to investigate the relaxation

processes in the semi-crystalline polymers and copolymers.

2. The major relaxation modes found in the PHB and PHB-co-HV

copolymer

are αMAF-relaxation and α* relaxation processes. these two processes were

distinctly separated.

3. The dielectric loss data were analysed using the Havriliak –Negami

model and the fitting parameters were achieved. The main relaxation

mode αMAF-relaxation was characterized by the Arrhenius or VFT

expressions from which the activation energy E and the preexponential

factor τo were evaluated.

---------------------------

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Relaxation Phenomena studies on Some Polymers and polymer ... · EL-Mansoura University Faculty of Science Physics Department Relaxation Phenomena studies on Some Polymers and polymer