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 اﷲ اﻟﺮﺣﻤﻦ اﻟﺮﺣﻴﻢ )وﻣﺎ اوﺗﻴﺘﻢ ﻣﻦ اﻟﻌﻠﻢ اﻻ ﻗﻠﻴﻼ ( ﺻﺪق اﷲ 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 Prof.Dr.M.D.Migahed Prof.Dr.Christoph Schick Ass.Prof.M.T.Ahmed Position Signature Prof. of Experimental Physics at Mansoura University, Mansoura, Egypt. Prof. of Applied Physics at Rostock University, Rostock, Germany. 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 Name Signature Date of discussion: Degree of dissertation: Referee Signature: No. 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), Poly(ethylene Polypropylene (PP), terephathalate)(PET), Poly (3-hydroxybutarate) Poly(butylene (PHB), 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-coHV), 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 دراﺳﻪ ﻇﺎهﺮﻩ اﻹﺳﺘﺮﺧﺎء ﻓﻲ ﺑﻌﺾ اﻟﺒﻠﻤﺮات و ﻣﺨﺎﻟﻴﻄﻬﺎ ﻣﻘﺪﻣﻪ ﻣﻦ: ﻋﻼءاﻟﺪﻳﻦ اﻟﻘﻄﺐ ﻋﺒﺪاﻟﻘﺎدر ﻣﺤﻤﺪ اﻟﻤﺪرس اﻟﻤﺴﺎﻋﺪ ﺑﺎﻟﻘﺴﻢ ﻟﻠﺤﺼﻮل ﻋﻠﻰ درﺟﻪ دآﺘﻮر اﻟﻔﻠﺴﻔﻪ ﻓﻲ اﻟﻌﻠﻮم /اﻟﻔﻴﺰﻳﺎء )اﻟﻔﻴﺰﻳﺎء اﻟﺘﺠﺮﻳﺒﻴﻪ( 2002 اﻟﻤﺸﺮﻓﻮن ﻋﻨﻮان اﻟﺒﺤﺚ: دراﺳﻪ ﻇﺎهﺮﻩ اﻹﺳﺘﺮﺧﺎء ﻓﻲ ﺑﻌﺾ اﻟﺒﻠﻤﺮات و ﻣﺨﺎﻟﻴﻄﻬﺎ إﺳﻢ اﻟﺒﺎﺣﺚ: ﻋﻼءاﻟﺪﻳﻦ اﻟﻘﻄﺐ ﻋﺒﺪاﻟﻘﺎدر ﻣﺤﻤﺪ م اﻹﺳﻢ 1ﻣﺼﻄﻔﻰ دﻳﺎب ﻣﺠﺎهﺪ 2آﺮﻳﺴﺘﻮف ﺷﻴﻚ 3ﻣﺼﻄﻔﻰ ﺗﻮﻓﻴﻖ اﻟﻮﻇﻴﻔﻪ أﺳﺘﺎذ اﻟﻔﻴﺰﻳﺎء اﻟﺘﺠﺮﻳﺒﻴﻪ ﺑﻘﺴﻢ اﻟﻔﻴﺰﻳﺎء ﺑﺠﺎﻣﻌﻪ اﻟﻤﻨﺼﻮرﻩ أﺳﺘﺎذ اﻟﻔﻴﺰﻳﺎء اﻟﺘﻄﺒﻴﻘﻴﻪ ﺑﻘﺴﻢ اﻟﻔﻴﺰﻳﺎء ﺑﺠﺎﻣﻌﻪ روﺳﺘﻮك-أﻟﻤﺎﻧﻴﺎ أﺳﺘﺎذﻣﺴﺎﻋﺪ ﺑﻘﺴﻢ اﻟﻔﻴﺰﻳﺎء ﺑﺠﺎﻣﻌﻪ اﻟﻤﻨﺼﻮرﻩ ﺗﻘﺮﻳﺮ اﻟﻤﻤﺘﺤﻨﻮن ﻋﻨﻮان اﻟﺒﺤﺚ: دراﺳﻪ ﻇﺎهﺮﻩ اﻹﺳﺘﺮﺧﺎء ﻓﻲ ﺑﻌﺾ اﻟﺒﻠﻤﺮات و ﻣﺨﺎﻟﻴﻄﻬﺎ إﺳﻢ اﻟﺒﺎﺣﺚ: ﻋﻼءاﻟﺪﻳﻦ اﻟﻘﻄﺐ ﻋﺒﺪاﻟﻘﺎدر ﻣﺤﻤﺪ م اﻹﺳﻢ اﻟﻮﻇﻴﻔﻪ 1 2 3 ﺗﺎرﻳﺦ اﻟﻤﻨﺎﻗﺸﻪ ﺗﻘﺪﻳﺮاﻟﺮﺳﺎﻟﻪ ﺗﻮﻗﻴﻌﺎت ﻟﺠﻨﻪ اﻟﺤﻜﻢ م اﻹﺳﻢ 1 2 3 اﻟﺘﻮﻗﻴﻊ اﻟﻤﻠﺨﺺ اﻟﻌﺮﺑﻲ اﻟﻤﻠﺨﺺ اﻟﻌﺮﺑﻲ ﺗﻬﺪف هﺬﻩ اﻟﺮﺳﺎﻟﻪ اﻟﻰ دراﺳﻪ ﻇﺎهﺮﻩ اﻹﺳﺘﺮﺧﺎء اﻟﺘﻲ ﺗﺤﺪث داﺧﻞ ﺑﻌﺾ اﻟﺒﻠﻤﺮات اﻟﻤﺘﺒﻠﺮﻩ ﺑﺎﻹﺿﺎﻓﻪ اﻟﻰ ﺑﻌﺾ ﻣﺨﺎﻟﻴﻄﻬﺎ. و اﻟﺒﻠﻤﺮات هﻲ ﻣﻮاد ﺣﺪﻳﺜﻪ ﻣﺘﻌﺪدﻩ اﻟﺨﻮاص اﻟﻔﻴﺰﻳﻘﻴﻪ وﻟﺬﻟﻚ ﺗﺪﺧﻞ ﻓﻲ ﺗﻄﺒﻴﻘﺎت ﻣﺨﺘﻠﻔﻪ .وﺗﻨﺒﻊ اهﻤﻴﻪ اﻟﺒﻠﻤﺮات ﻣﻦ أﻧﻬﺎ ﻣﻮاد ﻳﻤﻜﻦ أن ﺗﺨﻠﻖ داﺧﻞ اﻟﻤﻌﻤﻞ وﻓﻲ اﻟﺼﻨﺎﻋﻪ ﺑﺤﻴﺚ ﻳﻜﻮن ﻟﻬﺎ ﺻﻔﺎت ﻣﺤﺪدﻩ وﻣﻄﻠﻮﺑﻪ ﻟﺘﻄﺒﻴﻖ ﺑﻌﻴﻨﻪ. وﻇﺎهﺮﻩ اﻹﺳﺘﺮﺧﺎء اﻟﺘﻲ ﺗﻬﺘﻢ ﺑﻬﺎ اﻟﺪراﺳﻪ ﺗﻌﺪ ﻣﻦ اﻟﻈﻮاهﺮ اﻟﻔﻴﺰﻳﻘﻴﻪ اﻟﻜﻼﺳﻴﻜﻴﻪ اﻟﺘﻲ اهﺘﻢ اﻟﻔﻴﺰﻳﻘﻴﻮن ﺑﺪراﺳﺘﻬﺎ ﻣﻨﺬ زﻣﻦ ﻃﻮﻳﻞ ﺑﻬﺪف اﻟﻮﻗﻮف ﻋﻠىﺄﺳﺒﺎﺑﻬﺎ واﻟﻘﻮاﻧﻴﻦ اﻟﺘﻰ ﺗﺤﻜﻤﻬﺎ .وﻟﻜﻦ اﻟﻰ اﻻن ﻟﻢ ﻳﺘﻢ اﻟﻮﺻﻮل اﻟىﻤﺜﻞ هﺬﻩ اﻟﻘﻮاﻧﻴﻦ وﻟﻜﻦ ﻣﺎﺗﻢ اﻟﺘﻮﺻﻞ اﻟﻴﻪ ﺣﺘﻰ اﻻن هﻮ ﻣﺠﺮد ﻗﻮاﻧﻴﻦ ﻓﺮﻋﻴﻪ ﺗﺼﻒ اﻟﻈﺎهﺮﻩ ﻓﻲ ﺣﺎﻻت ﺧﺎﺻﻪ. وﺗﻨﺒﻊ أهﻤﻴﻪ هﺬﻩ اﻟﻈﺎهﺮﻩ ﻣﻦ اﻧﻬﺎ ﺗﺘﺤﻜﻢ ﻓﻲ ﺟﻤﻴﻊ اﻟﺨﻮاص اﻟﻔﻴﺰﻳﻘﻴﻪ ﻟﻴﺲ ﻟﻠﺒﻠﻤﺮات ﻓﺤﺴﺐ ﺑﻞ ﻟﺠﻤﻴﻊ اﻟﻤﻮاد. وﻟﻘﺪ ﺗﻢ ﺧﻼل اﻟﺪراﺳﻪ دراﺳﻪ اﻟﺒﻠﻤﺮات اﻟﻤﺘﺒﻠﺮﻩ اﻟﺘﺎﻟﻴﻪ؛ اﻟﺒﻮﻟﻲ إﺛﻴﻠﻴﻦ ،وأآﺴﻴﺪ اﻟﺒﻮﻟﻲ إﺛﻴﻠﻴﻦ ،اﻟﺒﻮﻟﻲ ﺑﺮوﺑﻴﻠﻴﻦ ،ﺗﺮﻓﺎﺛﺎﻻت اﻟﺒﻮﻟﻲ إﺛﻠﻴﻦ ،ﺗﺮﻓﺎﺛﺎﻻت اﻟﺒﻮﻟﻲ ﺑﻴﻮﺗﻴﻠﻴﻦ ،ﺗﺮﻓﺎﺛﺎﻻت اﻟﺒﻮﻟﻲ ﺗﺮﻣﺜﻴﻞ ،اﻟﺒﻮﻟﻲ إﻳﺜﺮ إﻳﺜﺮ آﻴﺘﻮن، وﺑﻮﻟﻲ هﻴﺪروآﺴﻴﺪاﻟﺒﻴﻮﺗﺎرات. هﺬا ﺑﺎﻹﺿﺎﻓﻪ اﻟﻰ ﻣﺨﻠﻮﻃﺎﻟﺒﻠﻤﺮات )ﺑﻮﻟﻲ هﻴﺪروآﺴﻴﺪاﻟﺒﻴﻮﺗﺎرات/ﺑﻮﻟﻲ آﺮﺑﻮن اﻻآﺘﻮن( وﺛﻨﺎئ اﻟﺒﻠﻤﺮﻩ ﺑﻮﻟﻲ هﻴﺪروآﺴﻴﺪاﻟﺒﻴﻮﺗﺎرات ﻣﻊ هﻴﺪروآﺴﻴﺪ اﻟﻔﻠﺮﻳﻚ ﺑﻨﺴﺐ هﻴﺪروآﺴﻴﺪ اﻟﻔﻠﺮﻳﻚ .%12 ،%8 ،%5 وﻟﻘﺪاﺳﺘﺨﺪم ﻓﻲ هﺬﻩ اﻟﺪراﺳﻪ ﺛﻼﺛﻪ ﺗﻘﻨﻴﺎت هﻲ: ﻻ: Uأو ً Uﺗﻘﻨﻴﻪ اﻟﻤﺴﺢ اﻟﺤﺮاري اﻟﺘﻔﺎﺿﻠﻲ: ﺗﻢ إﺳﺘﺨﺪام هﺬﻩ اﻟﺘﻘﻨﻴﻪ ﻓﻲ ﺗﻌﻴﻦ اﻟﺨﻮاص اﻟﺤﺮارﻳﻪ ﻟﻠﺒﻠﻤﺮات اﻟﻤﺘﺒﻠﺮﻩ هﺬﻩ اﻟﺨﻮاص هﻲ درﺟﻪ اﻟﺤﺮارﻩ اﻟﺘﻰ ﻳﺘﻢ ﻋﻨﺪهﺎ اﻟﺘﺒﻠﺮ Tcو درﺟﻪ اﻟﺤﺮارﻩ اﻟﺘﻰ ﻳﺘﻢ ﻋﻨﺪهﺎ ﺗﺤﻮل هﺬﻩ اﻟﺒﻠﻤﺮات ﻣﻦ اﻟﺤﺎﻟﻪ اﻟﺼﻠﺒﻪ اﻟﻤﺘﺰﺟﺠﻪ اﻟﻰ اﻟﺤﺎﻟﻪ اﻟﻤﻄﺎﻃﻴﻪ Tgﺑﺎﻹﺿﺎﻓﻪ اﻟﻰ درﺟﻪ اﻟﺤﺮارﻩ اﻟﺘﻲ ﻳﺘﻢ ﻋﻨﺪهﺎ إﻧﺼﻬﺎرهﺬﻩ اﻟﻤﻮاد . Tmeltآﻤﺎﺗﻤﺖ دراﺳﻪ اﻟﻤﺪى اﻟﺤﺮاري اﻟﺬي ﻳﺘﻢ ﻓﻴﻪ ﺣﺪوث ﻇﻮاهﺮ اﻹﺳﺘﺮﺧﺎء اﻟﺤﺮاري داﺧﻞ هﺬﻩ اﻟﻤﻮاد .وﻗﺪﺗﻢ إﺳﺘﺨﺪام هﺬﻩ اﻟﺘﻘﻨﻴﻪ آﺪراﺳﻪ ﺗﻤﻬﻴﺪﻳﻪ Uﺛﺎﻧﻴًﺎ: Uﺗﻘﻨﻴﻪ اﻟﻤﺴﺢ اﻟﺤﺮاري اﻟﺘﻔﺎﺿﻠﻲ ذواﻟﺘﺮدداﻟﺤﺮاري: هﺬﻩ اﻟﺘﻘﻨﻴﻪ هﻲ ﺗﻘﻨﻴﻪ ﺟﺪﻳﺪﻩ ﻓﻲ ﻣﺠﺎل اﻟﻘﻴﺎﺳﺎت اﻟﻔﻴﺰﻳﻘﻪ ﻓﻘﺪ أدﺧﻠﺖ اﻟﻰ ﻣﺠﺎل اﻟﻘﻴﺎﺳﺎت اﻟﺤﺮارﻳﻪ ﻋﺎم 1993ﺑﻮاﺳﻄﻪ اﻟﺒﺮوﻓﺴﻴﺮ" رﻳﺪﻧﺞ" .وﻗﺪأﺳﺘﺨﺪﻣﺖ هﺬﻩ اﻟﺘﻘﻨﻴﻪ ﻟﺪراﺳﻪ اﻹﺳﺘﺮﺧﺎء اﻟﺤﺮاري داﺧﻞ هﺬﻩ اﻟﺒﻠﻤﺮات اﻟﻤﺘﺒﻠﺮﻩ. 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. أآﺪت اﻟﺪراﺳﻪ ﺑﻮاﺳﻄﻪ هﺎﺗﺎن اﻟﺘﻘﻨﻴﺎﺗﺎن ﻋﻠﻰ أن اﻟﺒﻠﻤﺮات اﻟﻤﺘﺒﻠﺮﻩ ﺗﺘﻜﻮن ﻣﻦ ﺛﻼﺛﻪ أﻃﻮار وهﻲ اﻟﻄﻮر اﻟﻤﺘﺒﻠﺮ ،اﻟﻄﻮراﻟﻐﻴﺮﻣﺘﺒﻠﺮاﻟﻤﺘﺤﺮك ،واﻟﻄﻮراﻟﻐﻴﺮﻣﺘﺒﻠﺮ اﻟﺜﺎﺑﺖ. اﻟﻄﻮراﻟﻐﻴﺮﻣﺘﺒﻠﺮ اﻟﺜﺎﺑﺖ آﺸﻔﺖ ﻋﻨﻪ اﻷﺑﺤﺎث اﻟﺤﺪﻳﺜﻪ وﻋﻦ دورﻩ ﻓﻲ اﻟﺨﺼﺎﺋﺺ اﻟﻔﻴﺰﻗﻴﻪ ﻟﻬﺬﻩ اﻟﻤﻮاد. وﻟﻘﺪ ﺗﻢ ﺧﻼل هﺬﻩ اﻟﺪراﺳﻪ دراﺳﻪ ﻇﺎهﺮﻩ اﻹﺳﺘﺮﺧﺎء اﻟﺤﺮاري اﻟﺘﻲ ﺗﺤﺪث ﻟﻬﺬا اﻟﻄﻮر داﺧﻞ اﻟﺒﻠﻤﺮات اﻟﻤﺘﺒﻠﺮﻩ واﻟﺘﻲ ﺗﺤﺪث ﻓﻲ ﻣﺪى ﻣﻦ درﺟﺎت اﻟﺤﺮارﻩ أﻋﻠﻰ ﻣﻦ درﺟﻪ اﻟﺤﺮارﻩ اﻟﺘﻰ ﻳﺘﻢ ﻋﻨﺪهﺎ ﺗﺤﻮل هﺬﻩ اﻟﺒﻠﻤﺮات ﻣﻦ اﻟﺤﺎﻟﻪ اﻟﺼﻠﺒﻪ اﻟﻤﺘﺰﺟﺠﻪ اﻟﻰ اﻟﺤﺎﻟﻪ اﻟﻤﻄﺎﻃﻴﻪ Tg آﻤﺎ ﺗﻢ ﺧﻼل اﻟﺪراﺳﻪ دراﺳﻪ ﻇﺎهﺮﻩ اﻹﺳﺘﺮﺧﺎءاﻟﺘﺮآﻴﺒﻲ اﻟﺘﻲ ﺗﺤﺪث اﺛﻨﺎء ﺗﻜﻮن هﺬا اﻟﻄﻮر وهﻲ دراﺳﻪ ﺗﻌﺪ اﻷوﻟﻲ ﻣﻦ ﻧﻮﻋﻬﺎ. آﻤﺎ ﺗﻢ دراﺳﻪ ﻇﺎهﺮﻩ اﻹﺳﺘﺮﺧﺎء اﻟﺤﺮاري اﻟﺘﻲ ﺗﻌﺪ ﻣﻦ أﺣﺪث ﻇﻮاهﺮ اﻹﺳﺘﺮﺧﺎء اﻟﺘﻲ اآﺘﺸﻔﺖ ﻋﺎم 1997واﻟﺘﻲ ﺗﺴﻤﻰ "إﺳﺘﺮﺧﺎء اﻹﻧﺼﻬﺎر اﻟﻌﻜﺴﻲ" واﻟﺘﻲ ﺗﺤﺪث ﻧﺘﻴﺠﻪ ﻟﻼﻧﺼﻬﺎر اﻟﻌﻜﺴﻲ اﻟﺬي ﻳﺤﺪث داﺧﻞ اﻟﺒﻠﻤﺮات اﻟﻤﺘﺒﻠﺮﻩ .ﻓﻠﻘﺪﺗﻢ ﺑﻮاﺳﻄﻪ هﺬﻩ اﻟﺪراﺳﻪ ﺗﺤﺪﻳﺪ اﻟﻤﺪى اﻟﺤﺮاري اﻟﺬي ﺗﺤﺪث ﻓﻴﻪ هﺬﻩ اﻟﻈﺎهﺮﻩ. Uﺛﺎﻟﺜﺎ: Uﺗﻘﻨﻴﻪ ﻃﻴﻒ ﺛﻨﺎئ اﻟﻘﻄﺒﻴﻪ اﻟﻜﻬﺮﺑﻴﻪ: وﻗﺪﺗﻢ إﺳﺘﺨﺪاﻣﻪ ﻓﻲ دراﺳﻪ إﺳﺘﺮﺧﺎء ﺛﻨﺎئ اﻟﻘﻄﺒﻴﻪ اﻟﺬي ﻳﺤﺪث داﺧﻞ اﻟﺒﻮﻟﻴﻤﺮ اﻟﻤﺸﺎرك ﺑﻮﻟﻲ هﻴﺪروآﺴﻴﺪاﻟﺒﻴﻮﺗﺎرات ﻣﻊ هﻴﺪروآﺴﻴﺪ اﻟﻔﻠﺮﻳﻚ ﺑﻨﺴﺐ هﻴﺪروآﺴﻴﺪ اﻟﻔﻠﺮﻳﻚ .%12 ،%8 ،%5وﻗﺪ ﺗﻢ ﺧﻼل اﻟﺪراﺳﻪ دراﺳﻪ إﺳﺘﺮﺧﺎء ﺛﻨﺎئ اﻟﻘﻄﺒﻴﻪ اﻟﺬي ﻳﺤﺪث ﻓﻲ ﻣﺪى ﺣﺮاري ﺣﻮل درﺟﻪ اﻟﺤﺮارﻩ اﻟﺘﻰ ﻳﺘﻢ ﻋﻨﺪهﺎ ﺗﺤﻮل هﺬﻩ اﻟﺒﻠﻤﺮات ﻣﻦ اﻟﺤﺎﻟﻪ اﻟﺼﻠﺒﻪ اﻟﻤﺘﺰﺟﺠﻪ اﻟﻰ اﻟﺤﺎﻟﻪ اﻟﻤﻄﺎﻃﻴﻪ .Tgوﻟﻘﺪ ﺗﻢ ذﻟﻚ ﻋﻦ ﻃﺮﻳﻖ دراﺳﻪ ﺑﺎراﻣﺘﺮ ﻓﻘﺪ ﺛﻨﺎئ اﻟﻜﻬﺮﺑﻴﻪ )˝ (εوأﻳﻀﺎ دراﺳﻪ ﺛﺎﺑﺖ ﺛﻨﺎئ اﻟﻜﻬﺮﺑﻴﻪ)' .(εوأﻳﻀﺎ ﺗﻢ ﺗﺤﻠﻴﻞ ﻧﺘﺎﺋﺞ ﻓﻘﺪ ﺛﻨﺎﺋﻲ اﻟﻜﻬﺮﺑﻴﻪ ﺑﻮاﺳﻄﻪ ﻧﻤﻮذج "هﺎﻓﺮﻳﻠﻴﻚ –ﻧﻴﺠﺎﻣﻲ" ﻟﻠﺤﺼﻮل ﻋﻠﻰ ﺑﺎراﻣﺘﺮات اﻹﻧﻄﺒﺎق.وﻗﺪ أدت اﻟﺪراﺳﻪ اﻟﻰ اﻟﻜﺸﻒ ﻋﻦ ﻋﻤﻠﻴﺎت اﻹﺳﺘﺮﺧﺎء 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, αprocess, 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 liquidcrystalline 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). * This article was based on this reference with some modifications by the author. 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 semicrystalline 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 wc , d = ρc (ρ p − ρa ) ρ p (ρc − ρa ) (2.2) where, ρc is the density for ideal crystalline polymer, ρa is the density for the completely amorphous . X-ray crystallinity wc , x = Ic (I c + K a I a ) (2.3) where, Ic ,Ia are the integrated intensities, Ka is a calibration factor. Infrared crystallinity wc ,i = (ac ρL) log10 ( Io ) I (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 wc = ∆h M ∆h M , c (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 semicrystalline polymers. Most of these blends are compatible. Blends of two semicrystalline polymers are rarely used. Component of these blends are usually very similar structure. * This article was based on this reference with some modifications by the author. 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. * This article was based on this reference with some modifications by the author. 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: Lc ,o = 2σ eTM ,o ∆H M ,o (TM ,o − Tcryst ) (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. * This article was based on this reference with some modifications by the author. 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: &= − ξ& 1 & ξ (2.8) τ Tv ξ&(t ) = ξ&(0)e− λTv (t ) With t λTv (t ) ≡ ∫ 0 dt ′ τ Tv (2.9) If the process should come to stand still at a time t =te after reaching the internal equilibrium state, lim t → t e λTv (t ) = +∞ (2.10) must be valid. If the attained equilibrium state is a stable or metastable state it follows that: lim t → t e λTv (t ) = τ eTv > 0 (2.11) Moreover 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, τ Tv (t ) ≈ τ eTv = const > 0. * (2.13) This article was based on this reference with some modifications by the author. 20 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 ξ&(t ) = ξ&(0 )e −t / τ and the second integral ξ (t ) = [ξ (0 ) − ξ e ] exp( −t τ e Tv e Tv (2.14) ) + ξe (2.15) The initial rate of the process is given by: ξ (0) = − 1 τ e [ξ (0) − ξe ] (2.16) Tv With this, one can also replace equation (2.14) by: ξ&(t ) = − 1 τ e [ξ (t ) − ξe ] (2.17) Tv 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: ⎛ ∂S ⎞ S = S e + ⎜⎜ ⎟⎟ (ξ − ξ e ) ⎝ ∂ξ ⎠T ,v (2.18) ⎛ ∂P ⎞ P = Pe + ⎜⎜ ⎟⎟ (ξ − ξ e ) ⎝ ∂ξ ⎠T ,v (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, ξ&< 0 . Moreover, if τTv >0, equation (2.8) necessarily results in ξ&&> 0 . The attenuation curve ξ (t ) 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 ξ&< 0 at the beginning of the process, we get &< 0 . The monotonous attenuation curve is then first concavely curved versus ξ& the time axes. According to equation (2.8) a singularity occurs with &= 0 following the relaxation from the concave curvature ( ξ& &< 0 ) to the convex ξ& curvature ( ξ&&> 0 ). With the ξ&< 0 , either τTv =0, ξ&= −∞ or τTv=±∞, ξ&= finit. is valid at this point. Two simple examples are shown in figures (2.9, 2.10). Figure 2.9: An example of the ξ (t ) function; A: 0<τTv(0)< τeTv , B: τTv(0)<0< τeTv and E: linear relaxation according to equation (2.17). 22 Figure 2.10: Another example of the ξ (t ) 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~ξ 2 . With τ Tv e < τ 2 [ξ (t ) − ξ e ]2 ,τ 2 = const. > 0 the formulation (2.20) Two cases must be distinguished: If τ Tv e < τ 2 [ξ (t ) − ξ e ]2 is valid, τeTv>τTv>0 always holds for all ξ (t ) > ξ e . 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 τ Tv e < τ 2 [ξ (0) − ξ e ]2 is valid, the process starts with τTv <0. The attenuation curve is at first concavely curved versus the time axis. τTv =0 and ξ&= −∞ 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 τ Tv = τ o − τ1 , ξ e < ξ s < ξ (o ) (ξ − ξ s ) (2.21) holds. In order to fulfill the conditions (2.12) 23 τ o = τ Tv e − τ1 (2.22) (ξ s − ξ e ) must be valid, so that it follows that τ Tv = τ Tv e − τ 1′ τ 1′ ≡ τ1 (ξ − ξ e ) (ξ − ξ e ) (2.23) ξs −ξe 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 * This article was based on this reference with some modifications by the author. 24 systems, especially of solution has been discussed in detailed by Flory Volkenstein (12) . From the peculiar thermodynamical (11) behavior and 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: * This article was based on this reference with some modifications by the author. 25 (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 ( τ (t ) = τ o exp⎛⎜ E ⎞ ⎟ ) as ⎝ KT ⎠ 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 which would follow from the (15) ; the 1/T dependence Kirkwood-Frölich equation; 2 3ε o 4πN r ⎛ ε ∞ + 2 ⎞ 2 εo − ε∞ = ⎜ ⎟ g r µo 2ε o + ε ∞ 3KT ⎝ 3 ⎠ (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). * This article was based on this reference with some modifications by the author. 27 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 28 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. * This article was based on this reference with some modifications by the author. 29 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. * This article was based on this reference with some modifications by the author. 30 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 xray 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 semicrystalline 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 * This article was based on this reference with some modifications by the author. 31 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 Xray 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 experiments of Bodor (25) (24) in 1959. A model (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 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 * This article was based on this reference with some modifications by the author. 34 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: ⎛ hν ⎞ ⎟ kT ⎠ ⎛ hν ⎞ ⎝ dν cv (T ) = k ∫ ⎜ ⎟ (2.25) kT ⎠ ⎡ ⎛ hν ⎞⎤ 2 0 ⎝ ⎢exp⎜ kT − 1⎟⎥ ⎠⎦ ⎣ ⎝ Where, ν is the frequency of the lattice vibration ρ(ν) is the density of the 2 max ρ (ν )exp⎜ 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 ⎞ ⎛θ ⎞ Dn ⎜ n ⎟ = n⎜⎜ ⎟⎟ ⎝T ⎠ ⎝θn ⎠ ⎛ θn ⎞ ⎜ ⎟ ⎝T ⎠ ∫ 0 X n+1 exp( x)dx (exp( x) − 1)2 (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 onedimensional 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 threedimensional vibration respectively. 35 The corresponding expression is given by: ⎛ θ ⎞⎤ ⎛ θ ⎞ ⎛ θ ⎞⎡ ⎛ θ ⎞ cv = 3RD1 ⎜ 1 ⎟ + ⎜⎜ 3 ⎟⎟ ⎢ D3 ⎜ 3 ⎟ − D1 ⎜ 3 ⎟⎥ ⎝ T ⎠ ⎝ θ1 ⎠⎣ ⎝ T ⎠ ⎝ T ⎠⎦ (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: cv = 12π 4 R T 3 5 θ 2 3θ 1 , 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: 3π 2 R T cv = , θ3 ≤T≤θ1 (2.29) 2 θ1 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 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. 38 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 * This article was based on this reference with some modifications by the author. 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 It is seen that the area under the depolarization peak is highly increased for the sample cooled down slowly, which roughly corresponds to the `annealed` 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 intermolecularcooperative 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. 41 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 : ln η = ln A + B(v − v f ) vf (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: aT = (ηTo ρo ) (ηoTρ ) (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: log aT = ⎡ To ρ o ⎤ B ⎡1 1 ⎤ B ⎡1 1 ⎤ ≈ − ⎢ − ⎥ + log ⎢ ⎢ ⎥ ⎥ 2.303 ⎢⎣φ f φ f , 0 ⎥⎦ ⎣ Tρ ⎦ 2.303 ⎢⎣ φ f φ f , 0 ⎥⎦ (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 : log aT = −B (2.303φ f ,0 ) (T − To ) φ f ,0 + (T − To ) βf = − k [T − To ] = log t − log t o k ′ + [T − To ] (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 glassrubber 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 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 nonequilibrium 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 further by Fröhlich (147) in (1949) and Hoffman (44) in (45,46,47) (1945) and developed 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 44 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. 45 (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. 46 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 αrelaxation. 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. 47 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 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. 49 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 * This article was based on this reference with some modifications by the author. 50 molecules. The importance of heat capacity is clear from the following equations: T H − H o = ∫ C p dT Enthalpy (2.37) Energy (2.38) Entropy (2.39) G = H – TS Gibbs energy (2.40) F = U – TS Free energy (2.41) 0 T U − U o = ∫ C v dT 0 T S=∫ 0 Cp T dT 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: ⎤ ⎛ ∂V ⎞ ⎡⎛ ∂U ⎞ C p − C v = ⎢⎜ ⎟ ⎟ + P ⎥⎜ ⎦ ⎝ ∂T ⎠ P ,n ⎣⎝ ∂V ⎠ T ,n (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: dQ dT = C pt + + f (t , T ) dt dt (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. * This article was based on this reference with some modifications by the author. 52 The heat 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, dQ = BC pt + f (t , T ) + wBC pt cos wt + C sin wt (2.46) dt In this equation the term BC pt + f (t , T ) represent the underlying signal and the term wBC pt cos wt + C sin wt represent the cyclic signal. The f (t , T ) 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 nonreversing 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: dQ = bC pb + f (t , T ) + BwC pw cos wt + C sin wt dt (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: and hence C * = C ′ + C ′′ C2c= |C*|2=C´2+C´´2 (2.51) (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 dQ = bC pb + f (t , T ) + Bw(C ′ cos wt + C ′′ sin wt ) dt (2.53) dQ = b(C pb + C E ) + Bw(C pw cos wt + C sin wt ) dt (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: τ= 1 2πf (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 semicrystalline 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 semicrystalline 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) . This article was based on this reference with some modifications by the author. 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 * This article was based on this reference with some modifications by the author. 64 Tg to the Tmelt. It is found that a local movement is possible in the RAF (βrelaxation) 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. * This article was based on this reference with some modifications by the author. 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: χa = ∆c pSc ∆c pa (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. (where χa +χc =1 (2.57) χa = χam + χar (2.58) χar = 1-χa - χc (2.59) 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 inbetween. 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: cp = ∆S 2 k (2.60) Where, ∆S 2 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: µ = ∫ r[ ρ e (r ) +ρ n (r )]dr (2.61) where the ρe and ρn are the electrons and nuclei densities. and the effective dipole moment is given by: ⎡ N N ⎤ N µ eff = ⎢∑ µ 2 x + ∑ µ 2 y + ∑ µ 2 z ⎥ ⎣ i i i i i i (2.62) ⎦ 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: Ε = Ε o + exp(iωt ) (2.63) By considering the field given by equation (2.63) then this response is expressed in terms of complex permittivity: D* ε = * = ε ′ − iε ′′ E * (2.64) where, D* is the displacement vector, Ε is the electric field. * The loss tangent (tanδ) is then given by: tan δ = ε ′′ ε′ (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: 2 ε ′′(ω ′)ω ′dω ′ ε ′(ω ) = ε ∞ + ∫ π 0 (ω ′)2 − ω 2 ∞ ε ′′(ω ) = (2.66) (ω ′)[ε ′(ω ′) − ε ∞ ]dω ′ π ∫0 (ω ′)2 − ω 2 2 ∞ (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: 3ε o 4πN r εo − ε∞ = 2ε o + ε ∞ 3kT 2 ⎛ ε∞ + 2 ⎞ 2 ⎜ ⎟ g r µo ⎝ 3 ⎠ (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: ε * (ω ) − ε ∞ = [1 + (iωτ o )1−a ] εo − ε∞ (2.71) Davidson and Cole introduced the equation: ε * (ω ) − ε ∞ b = [1 + (iωτ o )] εo − ε∞ (2.72) Scaife introduced the generalized for both equations as: b ε * (ω ) − ε ∞ = [1 + (iωτ o )1− a ] εo − ε∞ (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 Semicrystalline 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 (10-4103 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 82 differential scanning calorimetry (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. (90) J. E. K Schawe (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 KovacsAklonis-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 semicrystalline 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 temperaturemodulated 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 semicrystalline 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 semicrystalline 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 PEEKPAr 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 premelting 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 nonlinear 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 Semicrystalline 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 glasstransition 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 PrigogineDefay 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 VogelFulcher 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 semicrystalline 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. Material rrr MW name (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% Trans.granules 408 200 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 pressed gently and then the sample was compressed. This material is thermoset polymer so it has a high melting temperature 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. Dosi´ere, universite de Mons-Hainaut, Laboratorie de Physicochimie des Polym´eres, Belgum. The material was provided as white granules so it first heated to the melt temperature 530 K in the aluminium pan on a hot stage and then the pan led was pressed gently and then the sample was compressed. This material is thermoset polymer so it has a high melting temperature 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. The material was provided as white granules so it first heated to the melt temperature 513 K in the aluminium pan on a hot stage and then the pan led was pressed gently and then the sample was compressed. This material is thermoset polymer so it has a high melting temperature 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 pressed gently and then the sample was compressed. 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 w.t T1 T2 H.R Iso.1 Iso.2 T.R AT tp P.W mod 1 2 3 4 5 6 7 8 9 10 11 12 13 14 S.No w.t T1 T2 H.R Iso.1 Iso.2 T.R AT tp P.W mod 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Remarks: Figure 4.5: Show the program sheet used during the measurements. 114 15 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: In which the applied temperature modulated with a specified periodic time (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: In which the applied temperature modulated with a specified periodic time (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: cp = Hf ms * q (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 where, (4.3) 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: dT = β (t ) = β o + ω oTa cos ω ot dt (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)) Formula (4.10) represents the measured heat flow curve in the TMDSC. 119 (4.10) (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 (t )dc 1 = tp t+ tp 2 ∫ Φ(t′)dt′ t− (4.15) tp 2 Φ (t ) p = Φ (t ) − Φ dc (t ) (4.16) 120 The periodic heating rate is given by: q p (t ) = ( dT ) − qo = AT ω cos(ωt ) = Aq cos(ωt ) dt (4.17) The first harmonic of the periodic heat flow Φ1 (t) is given by: Φ1 (t ) = a cos(ωt ) + b sin(ωt ) = a 2 + b 2 cos(ωt − δ ) = AΦ cos(ωt − δ ) where (a,b) are given by: 2 tp a(t ) = b(t ) = 2 tp t+ tp 2 ∫ Φ(t ′) cos(ωt ′)dt ′ t− t+ (4.18) tp 2 tp 2 ∫ Φ (t ′)sin(ωt ′)dt ′ t− (4.19) tp 2 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: | C w |= AΦ Aq (4.21) Then the real part (Ćw) and the imaginary part (C˝w) of the complex heat capacity are calculated as: C w′ =| C | cosδ (4.22) Cw′′ =| C | sin δ (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: ε ∗ (ω ) = ε ∞ + ∆ε (1 + (ωτ HN ) β )γ + S (ω ) n (4.24) With: ω=2πf (4.25) ε*(ω)=ε′+iε″ (4.26) −γ 2 ε ′ = ε ∞ + ∆ε .r . cos(γϑ ) (4.27) −γ 2 ε ′′ = ∆ε .r .sin(γϑ ) r = 1 + 2(ωτ ) β . cos( π 2 (4.28) β ) + (ωτ ) 2 β (4.29) 125 π ⎤ ⎡ sin( β) ⎥ ⎢ 2 ϑ = arctan⎢ ⎥ π −β ⎢ (ωτ ) + cos( β ) ⎥ 2 ⎦ ⎣ (4.30) The term S/(ω)n is related to the conductivity. The parameter (S) is the dcconductivity 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 (A) Thermal Studies 128 Part 1 DSC measurements 129 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. 130 PHB 15 283K 323K 328K 333K 338K 343K 348K 283K cp in J/g.K 10 5 0 -5 300 320 340 360 380 400 420 440 460 T in K 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) ∆Hf (J/g) Xc (%) 283 323 328 333 338 343 348 95.84 82.67 83.69 85.25 88.27 89.93 94.13 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 131 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. 5 PHB 438K Heat Flow in mW 428K 418K 408K 398K 388K 4 378K 368K 3 358K 10 20 30 40 50 time in min Figure 5.4: The heat flow results obtained for the PHB sample which show different crystallisation mechanism. 132 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) 133 6 5 sPP 4 cp in J/g.K 3 KPP3 2 1 0 KPP 1,2,FINA4 -1 -2 -3 220 240 260 280 300 320 340 360 380 400 420 440 T in K 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. 134 20 KPP1 after cooling with 10K/min 1st and 2nd time 18 Heat Flow in mW 16 after cooling with 80K/min 14 12 Tm 10 8 6 Tg 4 240 260 280 300 320 340 360 380 400 420 440 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. 135 20 KPP2 after cooling with 10K/min 1st and 2nd time 18 Heat Flow in mW 16 14 12 Tm 10 8 6 Tg TC crystallization peak after cooling with 80K/min 4 240 260 280 300 320 340 360 380 400 420 440 T in K Figure 5.7: The uncorrected heat flow for the KPP2 sample heated from 220 K to 440 K with 10 K/min. 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). 136 20 KPP3 after cooling with 10K/min 1st and 2nd time 18 Heat Flow in mW 16 14 12 10 Tm 8 6 crystallization after cooling with 80K/min Tg 4 TC 2 240 260 280 300 320 340 360 380 400 420 440 T in K Figure 5.8: The uncorrected heat flow for the KPP3 sample heated from 220 K to 440 K with 10 K/min. FINA 4 22 20 after cooling with 10K/min 1st and 2nd time Heat flow in mW 18 16 14 Tm 12 10 8 crystallization peak after cooling with 80K/min 6 Tg 4 Tc 2 240 260 280 300 320 340 360 380 400 420 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. 137 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. 60 PEEK 50 40 Heat flow in mW 30 20 10 Tmelt 0 -10 -20 Tg -30 -40 -50 Tc 350 400 450 500 T in K 550 600 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). 138 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. 40 PTT Heat flow in mW 30 20 10 0 -10 Tg Tm -20 -30 TC 320 340 360 380 400 420 440 460 480 500 520 T in K 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. 139 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 140 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. 8 cp in J/g.K 6 PHB h e a tin g a fte r q u e n c h in g h e a tin g a fte r c o o lin g w ith 1 0 K /m in h e a tin g a fte r c o o lin g w ith 8 0 K /m in 4 2 0 -2 -4 250 300 350 T in K 400 450 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. 141 4 PH B 95 3 p c in J/g.K 2 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 1 0 -1 -2 -3 250 300 350 400 450 T in K 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 DSC program for the PHB 90/ PCL 10 % wt. blend was the same as for pure PHB. The effect of the cooling rate was investigated and the results shown in the figure (5.15), 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-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. 142 4 P H B 90 h e a tin g a fte r q u e n c h in g h e a tin g a fte r c o o lin g 1 0 K /m in h e a tin g a fte r c o o lin g 8 0 K /m in 3 cp in J/g.K 2 1 0 -1 -2 -3 250 300 350 400 450 T in K Figure 5.15: The heating scan of the PHB90/PCL10 % wt. blend with 10K/min. 5.1.5.4- PHB80/PCL20 % wt. blend: The DSC program for the PHB 80/ PCL 20 % wt. blend was the same as for pure PHB. The effect of the cooling rate was investigated and the results shown in the figure (5.16), 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) 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. 143 4 3 cp in J/g.K 2 PH B 80 h e a tin g a fte r q u e n c h in g h e a tin g a fte r c o o lin g 1 0 K /m in h e a tin g a fte r c o o lin g 8 0 K /m in 1 0 -1 -2 -3 -4 250 300 350 400 450 T in K Figure 5.16: The heating scan of the PHB80/PCL20 %wt. blend with 10K/min. 5.1.5.5- PHB70/PCL30 % wt. blend: The DSC program for the PHB 70/ PCL 30 % wt. blend was the same as for pure PHB. The effect of the cooling rate was investigated and the results shown in the figure (5.17), 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. 144 4.0 3.5 3.0 cp in J/g.K 2.5 PHB70 heating after quenching heating after cooling 10K /m in heating after cooling 80K /m in 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 250 300 350 400 450 T in K Figure 5.17: The heating scan of the PHB70/PCL30 % wt. blend with 10 K/min. 5.1.5.6- PHB50/PCL50 % wt.: The DSC program for the PHB 50/ PCL 50 % wt. blend was the same as for pure PHB. The effect of the cooling rate was investigated and the results shown in the figure (5.18), 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 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. 145 7 6 PH B 50 5 p c in J/g.K 4 3 2 1 0 -1 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 -2 -3 -4 250 300 350 400 450 T in K 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. 146 7 6 PH B 20 5 4 2 1 p c in J/g.K 3 0 h e a t in g a f t e r q u e n c h in g h e a t in g a f t e r c o o lin g 1 0 K /m in h e a t in g a f t e r c o o lin g 8 0 K /m in -1 -2 -3 -4 250 300 350 400 450 T in K 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. 147 14 12 PCL 10 cp in J/g.K 8 6 4 2 0 h e a tin g a fte r q u e n c h in g h e a tin g a fte r c o o lin g 1 0 K /m in h e a tin g a fte r c o o lin g 8 0 K /m in -2 -4 250 300 350 400 450 T in K 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. Mat./ C.R PHB PHB95 PHB90 PHB80 PHB70 PHB50 PHB20 PCL Tg PHB(K) 10 80 276 276 302 276 ----- 276 275 276 274 275 ----- 276 275 275 ----- ----- Tc PHB(K) 10 80 322 325 --- 320 318 320 318 320 318 320 --- 320 316 319 ---- ---- Tmelt PHB(K) 10 445 445 444 444 444 445 444 ---- H.R=10 K/min 148 80 447 446 447 446 446 448 446 --- Que. 449 448 448 448 448 449 448 ---- Tmelt PCL(K) 10 ---328 329 329 329 330 330 330 80 ----330 330 330 329 330 329 329 Que. ------335 335 335 339 341 341 Table 5.3: The maximum heat capacity of the endothermic melting peak of the PHB/PCL polymer blend. Cp PCL(J/g.K) Material/C.R 10 80 Que. PHB ------------PHB95 0.220 0.115 ---PHB90 0.496 0.345 0.436 PHB80 1.220 1.099 1.181 PHB70 1.271 1.101 1.181 PHB50 6.585 6.702 5.538 PHB20 6.218 5.632 4.920 PCL 11.724 10.130 12.407 Cp PHB(J/g.K) 10 80 Que. 6.930 7.481 7.789 4.106 3.342 3.379 3.224 3.470 3.414 4.044 4.373 3.960 2.681 2.625 2.648 5.980 5.562 5.100 1.290 1.304 1.265 ------ ----- ------ 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. 149 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. 35 30 PHB-co-HV Heat flow in mW 25 12% 20 15 10 5 8% 5% 0 PHB -5 250 300 350 400 450 T in K Figure 5.21: The heating scan for the PHB-co-HV copolymer with 10 K/min. 150 Table 5.4: The thermal characteristic temperatures of the PHB-co-HV copolymer. Material PHB PHB-co-HV5% PHB-co-HV8% PHB-co-HV12% Tg 279 278 277 ---- TC 324 336 348 ----- 151 TMelt 451 441 434 437 Part 2 TMDSC Studies 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 153 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. 154 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. 155 5.2.2-Glass transition relaxation: (A relaxation process at Tg): We show in this section how the glass transition relaxation of the semicrystalline 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. 2.2 2.1 sPP Liquid KPP3 2.0 |cp*| in J/g.K 1.9 FINA4 1.8 KPP1 1.7 1.6 Solid 1.5 1.4 1.3 250 260 270 280 290 T in K 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. 156 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. Tg αMAF Relaxation strength (K) ∆cp* KPP1 270 0.227 KPP2 270 0.256 KPP3 267 0.378 FINA4 270 0.256 Material in J/g.K 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. 157 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., αMAFrelaxation) 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)). 2.2 PHB 2.0 1.8 |cp*| in J/g.K a 1 1.6 1.4 2 1.2 (1)PHB Amorphous (2) PHB Semi-crystalline 1.0 0.8 b (a)Amorphous PHB (b)crystalline PHB 0.6 200 220 240 260 280 T in 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. 158 300 2.0 PHB-co-PHV 5% 1.8 a |cp*| in J/g.K 1.6 1 1.4 2 1.2 1.0 (1)PHB Amorphous (2) PHB Semi-crystalline b 0.8 (a)Amorphous PHB (b)crystalline PHB 0.6 220 230 240 250 260 270 280 290 300 T in K Figure 5.25: The modulated heating scan with the same conditions for the PHB-co-HV5% polymer in both states amorphous and crystalline. 2.0 PHB-co-PHV 8% 1.8 a |cp*| in J/g.K 1.6 1 1.4 2 1.2 (1) 8% Amorphous (2) 8% Semi-crystalline (a) crystalline PHB (b) Amorphous PHB 1.0 b 0.8 220 230 240 250 260 270 280 290 300 T in K Figure 5.26: The modulated heating scan with the same conditions for the PHB-co-HV8% copolymer in both states amorphous and crystalline. 159 2.0 PHB-co-PHV 12% 1.8 |cp*| in J/g.K 1.6 a 1 1.4 2 1.2 1.0 b (1) 12% Amorphous (2) 12% Semi-crystalline (a) Amorphous PHB (b) crystalline PHB 0.8 0.6 220 240 260 280 300 T in 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. 160 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. 1.8 PHB Cp in J/g.K 1.7 c-cp amorph 1.6 1.5 1.4 1.3 1.2 a-cp measured d- cp semi-crystalline(χc=0.64) e-cp(χrigd=0.88 from ∆ Cp at Tg=296K) b-cp crystal 1000 10000 100000 time in Sec. 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 161 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. c - cp liquid 1.6 -1 |cp*| in J g K -1 1.7 1.5 1.4 1.3 HF in µW 1.2 d - cpb(χcrystal= 0.64) e - cpb(χsolid(Tg) = 0.88) b - cp solid 0 f - HFtotal -20 -40 1000 10000 100000 t in s Figure 5.29: The crystallisation of PHB compared to the constructed curves. 162 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: t 1 Χ c (t ) = < HF (t ) > dt ∆Η ∞ f ∫0 (5.1) And then applying this equation in the equation: c p (t ) = c p −liquid X c (t ) (c p −liquid − c pb ) X∞ (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. 163 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). 2.1 sPP c-cp liquid 2.0 |cp*| in J/g.K 1.9 d-cpb(χsolid)=0.17) 1.8 e-c (χ )=0.51) pb solid 1.7 1.6 1.5 b-cp solid 1.4 1000 10000 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 164 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): 5.2.4.1- Poly(3-hydroxybutarate) (PHB): 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. 2 .2 PHB 1 .8 c -c p am * -1 |c p| in J g K -1 2 .0 orp h 1 .6 1 .4 d 300K tw o -p h a s e lin e (d ) th re e -p h a s e lin e (e ) 1 .2 e 1 .0 b -c ry p c 250 s ta l 300 350 T in K 400 450 Figure 5.31: Complex heat capacity of the PHB during melting under constant frequency 0.01 Hz and HR=0.5 K/min. 165 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. 166 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. 2.4 PHB 2.2 |cp*| in J/g.K 2.0 1.8 1.6 380 K Amorphous 340 K 360 K 1.4 d 1.2 1.0 e Crystalline 250 300 350 400 450 T in K Figure 5.32: Complex heat capacity of the PHB during melting under constant frequency 0.01Hz for different crystallisation temperatures. 167 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. 2.8 sPP 2.6 |cp*| in J/ g.K 2.4 a d - cpb (χcrystal= 0.17) 2.2 c - c p liquid olid b - cps 2.0 1.8 e - cpb (χsolid= 0.51) 1.6 Tc = 363 K 1.4 260 280 300 320 340 360 380 400 420 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 168 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. 169 2.55 PEEK 2.45 2.35 2.25 2.15 592K 597K 602K Liquid at 607K 2.05 1.95 607K 605K 609K 573K 564K * |cp | in J/g.K 583K 530K 1.85 1.75 100 1000 10000 100000 time in Sec. 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. 170 2.7 500K PEEK 2.6 |cp*| in J/g.K 2.5 425K 470K 440K 2.4 432K 2.3 2.2 400K 2.1 1000 10000 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. 171 Figure 5.36: The melt and cold quasi-isothermal experiment. 2.4 PEEK first point Lastpoint Maxmum point * |cp | in J/g.K 2.2 2.0 1.8 (a) Liquid (b) Solid (c) 2-phase model a 1.6 c b 1.4 1.2 350 400 450 500 550 600 650 T in K Figure 5.37: The complex heat capacity obtained from the melt and cold quasiisothermal 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 172 (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. 173 3.0 PBT 493 K 2.5 533 K 513 K 453 K 413 K 353 K |cp*| in J/g.K 2.0 1.5 393 K 373 K 333 K 1.0 0.5 0.0 1000 10000 time in Sec. Figure 5.38: The complex heat capacity obtained using the quasiisothermal 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. 174 5.5 5.0 |cp*| in J/g.K 4.5 4.0 3.5 PBT first po int la st poin t (a) a m orp hou s (b) crysta lline (c) tw o-pha se 3.0 2.5 2.0 a c 1.5 1.0 300 350 b 400 450 500 550 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). 175 2.289 PET 493K 2.098 |cp*| in J/g.K 553K 1.906 533K 513K 473K 453K 433K 1.714 373K 1.523 393K 413K 1.331 1000 10000 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 will be used at the end of this chapter to study excess heat capacity and morphology. 176 2.2 PET 2.0 |cp*| in J/g.K a 1.8 c 1.6 1.4 b first point last point (a) Amorphous (b) Crystalline (c) two-phase 1.2 1.0 250 300 350 400 450 500 550 600 650 700 T in K 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. 177 2.20 PTT 2.15 2.10 |cp*| in J/g.K 2.05 2.00 492K 1.95 490K 484K 480K 478K 472K 470K 464K 460K 450K 1.90 1.85 1.80 3 10 4 10 time in Sec. 5 10 6 10 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. 178 1.50 PTT 1.45 1.40 324K |cp*| in J/g.K 1.35 330K 328K 1.30 1.25 338K 1.20 1.15 1.10 1.05 2 10 3 10 time in Sec. 4 10 5 10 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. 179 2.1 2.0 PTT cp liquid 1.9 a cp solid c 1.7 1.6 (c) cpb two-phase * |cp | in J/g.K 1.8 1.5 First point max End point b 1.4 1.3 1.2 300 350 400 450 500 550 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. 180 Figure 5.45: The TMDSC program used in the frequency dependence measurements. PHB 2.0 |cp*| in J/g.K Liquid 1.5 cpb-2phase 0.04 Hz 0.02 Hz 0.01 Hz 0.005 Hz 0.0025 Hz 0.00125 Hz Solid 1.0 210 280 350 420 T in K 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 181 will be used at the end of this chapter to study excess heat capacity and 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. 3.0 2.8 KPP3 2.6 2.4 |cp*| in J/g.K 2.2 Amorphous 2.0 2-Phase 1.8 1.6 0.00125 Hz 0.0025 Hz 0.005 Hz 0.01 Hz 0.02 Hz 0.04 Hz 0.083 Hz 1.4 1.2 Crystalline 1.0 0.8 0.6 200 250 300 T in K 350 400 450 Figure 5.47: The complex heat capacity obtained from modulated TMDSC quasiisothermal 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). 182 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. 183 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. 184 2 .4 PEO 2 .2 |cp*| in J/g.k 2 .0 1 .8 1 .6 1 .4 L iq u id P E O a t 3 7 8 K 331K 328K 324K 321K 1 .2 1 .0 0 .8 10 -3 10 -2 10 -1 F re q . in H z Figure 5.49: The apparent complex heat capacity obtained from the PEO iso-thermal crystallisation TMDSC measurements frequency dependence. PEO 2.25 2.20 |cp*| in J/g.k 2.15 2.10 2.05 2.00 1.95 Liquid PEO at 378K 331K 328K 324K 321K 1.90 1.85 -3 10 -2 -1 10 10 Freq. in Hz Figure 5.50: The melt-corrected complex heat capacity obtained from the PEO iso-thermal crystallization TMDSC measurements frequency dependence. 185 3.2 |cp*| in J/g.K 3.0 2.8 PEO 33 1K TMDSC 321K 324K 328K 3 28K 331K Liquid P E O at 378K S trobl 321K 324K 328K 331K 2.6 2.4 324K 32 1K 2.2 2.0 10 -3 10 -2 10 -1 10 0 Freq. in Hz 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. 5.2.6.2- Poly(3-hydroxybutarate) (PHB): 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. 186 2.2 PH B 2.0 240K 320K 340K 360K 380K 400K 420K 1.8 |cp*| in J/g.K 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 10 -3 10 -2 10 -1 Freq. in H z Figure 5.53: Frequency dependent apparent complex heat capacity of the PHB above and below Tg. 2.2 PH B 2.0 1.8 240K 320K 340K 360K 380K 400K 420K |cp*| in J/g.K 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 10 -3 10 -2 10 -1 Freq . in H z 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. 187 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). 188 2.6 KPP3 2.4 2.2 300K 320K 340K 360K 380K 400K 443K-melt |cp*| in J/g.K 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 -3 10 -2 -1 10 10 Freq. in Hz 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. 189 3.0 KPP3 |cp*| in J/g.K 443K 2.5 400K 2.0 380K 360K 340K 320K 1.5 300K 1.0 0.5 -3 10 -2 -1 10 10 Freq. in Hz Figure 5.57: The melt-corrected complex heat capacity as a function of the frequency for the KPP3 sample. 5.2.6.4- Poly (ether ether ketone) (PEEK): 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 meltcorrected using ATHAS database. The melt-corrected data is shown in figure (5.59). 190 PEEK |cp*| in J/g.K 2.4 1.8 1.2 T640K T605K T530K T430K 0.6 10 -3 10 -2 10 -1 Freq. in Hz Figure 5.58: The apparent complex heat capacity obtained from frequency dependence experiments after quasi-isothermal crystallization for the PEEK sample. 191 2.5 PEEK |cp*| in J/g.K 2.0 1.5 640K 605K 530K 430K 1.0 -3 10 -2 10 freq. in Hz -1 10 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. 192 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. 193 |cp*| in J/g.K 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 PBT 333K 353K 373K 393K 513K melt -3 10 -2 10 Freq. in Hz -1 10 Figure 5.60: The apparent complex heat capacity frequency dependence obtained after the quasi-isothermal crystallization for the PBT sample. 194 3.0 PBT 2.8 2.6 |cp*| in J/g.K 2.4 2.2 2.0 1.8 333K 353K 373K 393K 513K melt 1.6 1.4 1.2 -3 10 -2 10 Freq. in Hz -1 10 Figure 5.61: The complex heat capacity frequency dependence obtained after the quasi-isothermal crystallisation for the PBT sample. 195 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) 2.10 2.08 PET |cp*| in J/g.K 2.06 493K 533K melt 2.04 2.02 2.00 1.98 1.96 1.94 -3 10 -2 10 Freq. in Hz -1 10 Figure 5.62: The complex heat capacity obtained from the quasi- isothermal crystallization for the PET sample. 196 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: c p (T )two − phase = c p c X c + (1 − X c )c pa (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)). 2.2 PEO 2.1 a 2.0 L iquid S oild 0 .0666 H z 0 .0333 H z 0 .0166 H z 0 .0100 H z 0 .0083 H z 0 .0041 H z 0 .0020 H z 0 .0010 H z c p b 2 -ph ase |cp*| in J/g.K 1.9 1.8 1.7 1.6 c 1.5 1.4 b 1.3 1.2 320 325 330 335 340 T C 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: 197 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: ce (T ) = c p − measuered (T ) − c p − two − phase (T ) (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.) 0.75 328 K 0.70 PEO 324 K 0.65 ce in J/g.K 0.60 0.55 0.50 0.0666 Hz 0.0333 Hz 0.0166 Hz 0.0100 Hz 0.0100 Hz 0.0083 Hz 0.0041 Hz 0.0020 Hz 0.0010 Hz 0.45 0.40 0.35 Tcm 0.30 0.25 320 322 324 326 328 330 332 334 336 338 340 TC in K Figure 5.64: The calculated excess heat capacity obtained from the PEO quasi-isothermal TMDSC measurements. 198 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). 199 5.2.7.2- Poly (ether ether ketone) (PEEK): 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). 0.30 PEEK 579K 0.25 ce in J/g.K 0.20 0.15 609K 0.10 0.05 Tcm 0.00 560 570 580 590 600 610 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%). 200 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. 473K 0.09 PBT 0.08 Ce in J/g.K 0.07 0.06 0.05 0.04 Tcm 513K 0.03 400 420 440 460 480 500 520 TC in K Figure 5.66: The excess heat capacity obtained using the quasiisothermal crystallisation for the PBT sample. 201 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. 0.07 PET 512K 0.06 ce in J/g.K 0.05 533K 0.04 0.03 0.02 Tcm 0.01 460 480 500 520 540 TC in K Figure 5.67: The excess heat capacity obtained from the quasi-isothermal crystallization for the PET sample. 202 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 0.25 PTT 478K Ce in J/g.K 0.20 0.15 490K 0.10 0.05 Tcm 0.00 460 470 480 490 500 TC in K Figure 5.68: The excess heat capacity for the PTT sample using the quasi-isothermal crystallization experiments. 203 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: χ MAF = ∆c scp ∆c am p (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. 204 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. 1.00 PEEK RCF Morphological fractions 0.80 0.60 0.40 0.20 0.00 below Tg 400 Tg 420 MAF above T g 440 460 480 500 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. 205 1.0 PEEK RCF MAF RAF Morphological fractions 0.8 0.6 0.4 0.2 Tg 0.0 above Tg below Tg 400 420 440 460 480 500 520 540 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 threephase 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. 206 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. PBT Morophological fractions 0 .6 0 .4 0 .2 MAF RAF RCF 0 .0 330 340 350 360 370 380 390 400 T C in K Figure 5.71: The morphological fractions obtained using the quasi-isothermal crystallization for the PBT sample. 207 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. 1.0 Morphological fractions 0.9 RCF MAF RAF PET 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 390 400 410 420 430 440 TC in K Figure 5.72: The morphological fractions obtained from the quasi-isothermal crystallization for the PET sample. 208 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. 1.0 PTT 0.9 Morphological fractions 0.8 0.7 0.6 MAF 0.5 0.4 0.3 RCF 0.2 0.1 0.0 322 324 326 328 330 332 334 336 338 340 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. 209 Morphological fractions 1.00 0.95 PTT 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 322 324 RCF RAF MAF 326 328 330 332 334 336 338 340 TC in K Figure 5.74: The morphological fractions for the PTT sample using the quasi-isothermal crystallization experiments by considering the three-phase model. 210 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. 1.0 MAF0.0025 RAF0.0025 MAF0.005 RAF0.005 MAF0.01 RAF0.01 MAF0.02 RAF0.02 MAF0.04 RAF0.04 MAF0.083 RAF0.083 KPP3 Morphological Fractions 0.8 0.6 0.4 0.2 0.0 -0.2 300 310 320 330 340 350 360 370 380 390 400 410 TC in K Figure 5.75: The morphological fractions obtained for the semi-crystalline KPP3 sample as a function of temperature at each frequency. 211 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. 1.0 PHB at 240 K RAF MAF Morphological Fractions 0.8 0.6 0.4 0.2 0.0 0.00 0.01 0.02 0.03 0.04 Freq. in Hz Figure 5.76: Frequency dependent morphology of the PHB below Tg. 212 1.0 PHB at 320K RAF MAF Morphological Fractions 0.8 0.6 0.4 0.2 0.0 0.00 0.01 0.02 0.03 0.04 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. 213 5.2.8.7- PHB-co-HV: 3.0 PHB 2.5 |cp*| in J/g.K 2.0 1 a 1.5 2 1.0 (1)PHB Amorphous (2) PHB Semi-crystalline b 0.5 (a)Amorphous PHB (b)crystalline PHB 0.0 220 240 260 280 300 320 340 360 380 400 T in K Figure 5.78: The complex heat capacity obtained using the modulated scan TMDSC for the PHB polymer. 3.0 PHB-co-HV 5% 2.5 |cp*| in J/g.K 2.0 1 a 1.5 2 (1)PHB Amorphous (2) PHB Semi-crystalline 1.0 b (a)Amorphous PHB (b)crystalline PHB 0.5 0.0 220 240 260 280 300 320 340 360 380 400 T in K Figure 5.79: The complex heat capacity obtained using the modulated scan TMDSC for the PHB-co-HV5% polymer. 214 3.0 PHB-co-PHV 8% 2.5 |cp*| in J/g.K 2.0 1 a 1.5 2 1.0 b (1) (2) (a) (b) 0.5 0.0 220 240 260 280 300 320 8% Amorphous 8% Semi-crystalline crystalline PHB Amorphous PHB 340 360 380 400 T in K 3.0 PHB-co-PHV 12% 2.5 |cp*| in J/g.K 2.0 1 a 1.5 2 1.0 (1) 12% Amorphous (2) 12% Semi-crystalline (a) Amorphous PHB (b) crystalline PHB b 0.5 0.0 220 240 260 280 300 320 340 360 380 400 T in K Figure 5.81: The complex heat capacity obtained using the modulated scan TMDSC for the PHB-co-HV12% polymer. 215 100 Morphological fractions (%) 90 PHB C rystalline Fraction (TMDSC) Mobile amorphous Fraction(TMDSC) R igid amorphous Fraction(TMDSC) C rystalline Fraction (NMR) Mobile amorphous Fraction(NMR) R igid amorphous Fraction(NMR) 80 70 60 50 40 30 20 10 0 290 300 310 320 330 340 350 360 T in K Figure 5.82: The morphological fractions change with temperature for the PHB pure polymer. 100 Morphological fractions(%) 90 C ry s ta llin e F ra c tio n (T M D S C ) M o b ile a m o rp h o u s F ra c tio n (T M D S C ) R ig id a m o rp h o u s F ra c tio n (T M D S C ) C ry s ta llin e F ra c tio n (N M R ) M o b ile a m o rp h o u s F ra c tio n (N M R ) R ig id a m o rp h o u s F ra c tio n (N M R ) P H B -c o -P H V 5% 80 70 60 50 40 30 20 10 0 290 300 310 320 330 340 350 360 T in K Figure 5.83: The morphological fractions change with temperature for the PHB-co-HV 5% copolymer. 216 100 PH B -co-PH V 8% C rysta lline Fraction (T M D S C ) M obile am orpho us F raction (T M D S C ) R igid am orphou s Fraction(T M D S C ) C rysta lline Fraction (N M R ) M obile am orpho us F raction (N M R ) R igid am orphou s Fraction(N M R ) Morphological fractions (%) 90 80 70 60 50 40 30 20 10 0 290 300 310 320 330 340 350 360 T in K Figure 5.84: The morphological fractions change with temperature for the PHB-co-HV 8% copolymer. 100 P H B -co -P H V 12% C rys ta llin e F ra c tio n (T M D S C ) M o b ile a m o rp h o u s F ra c tio n (T M D S C ) R ig id a m o rp h o u s F ra c tio n (T M D S C ) C rys ta llin e F ra c tio n (N M R ) M o b ile a m o rp h o u s F ra c tio n (N M R ) R ig id a m o rp h o u s F ra c tio n (N M R ) Morphological fractions (%) 90 80 70 60 50 40 30 20 10 0 290 300 310 320 330 340 350 360 T in K Figure 5.85: The morphological fractions change with temperature for the PHB-co-HV12% copolymer 217 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. 218 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. 219 6.0 PHB 5.0 |cp*| in J/g.K 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 (c) two-phase model 3.0 1 2 3 4 2.0 a c 1.0 0.0 b 250 300 350 400 450 T in K 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. 220 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: c p ( A) (T ) = ξ PHB c lp ( PHB ) (T ) + (1 − ξ PHB )c lp ( PCL ) (5.10) c p ( C ) (T ) = ξ PHB c cp ( PHB ) (T ) + (1 − ξ PHB )c cp ( PCL ) (5.11) Where, ξPHB , ξPCL are the blending ratio of the PHB and PCL polymers and clp(PHB), clp(PCL) are the liquid heat capacities of the PHB and PCL polymers. In addition, the ccp PHB, ccp 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 twophase 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: [ c p−2 phase (T ) = ξ PCL χ solid −PCL * c cp ( PCL ) + (1 − χ solid −PCL ) * c lp ( PCL) [ + ξ PHB χ solid −PHB * c cp ( PHB ) + (1 − χ solid −PHB ) * c lp ( PHB ) ] ] (5.12) 221 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: [ ] c p−2 phase (T ) = ξ PCL c lp ( PCL) + ξ PHB [χ solid −PHB * c cp ( PHB) + (1 − χ solid −PHB ) * c lp ( PHB) ] (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. 4.0 PHB95 3 1 |cp*| in J/g.K 3.0 2 4 2.0 a c2 c1 1.0 0.0 b 250 300 350 400 450 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. 222 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. 4.0 PHB90 |cp*| in J/gK 3.0 (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 1 2 4 3 2.0 a c2 c1 1.0 b 0.0 250 300 350 400 450 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. 223 4.0 PHB80 1 |cp*| in J/g.K 3.0 2 3 4 2.0 a c2 c1 1.0 (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 b 0.0 250 300 350 400 450 T in K Figure 5.89: The modulated scan of PHB80/PCL20 %wt. blend under modulation frequency 0.01 Hz and heating rate 10 K/min. 4.0 PHB70 |cp*| in J/gK 3.0 1 3 2 4 2.0 a c2 c1 (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 1.0 b 0.0 250 300 350 400 450 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. 224 4.0 PHB50 3 |cp*| in J/g.K 3.0 1 2 4 2.0 a c2 c1 1.0 (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 b 0.0 250 300 350 400 450 T in K Figure 5.91: The modulated scan of PHB50/PCL50 %wt. blend under modulation frequency 0.01 Hz and heating rate 10 K/min. 4.0 PHB20 |cp*| in J/g.K 3.0 32 2.0 4 1 a c2 c1 1.0 0.0 (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 b 250 300 350 400 450 T in K Figure 5.92: The modulated scan of PHB20/PCL80 %wt. blend under modulation frequency 0.01 Hz and heating rate 10 K/min. 225 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. 226 4.0 PCL |cp*| in J /g.K 3.0 3 2 4 1 2.0 a c 1.0 0.0 (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 b 250 300 350 400 450 T in 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. 227 PHB/PCL blend Morphology at 245K (Tg PHB >T>Tg PCL) 1.0 0.9 Morphological fractions 0.8 0.7 0.6 0.5 0.4 0.3 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 ) 0.2 0.1 0.0 0 20 40 60 80 100 PHB %wt. Morphological fractions Figure 5.94: The morphological fractions of the blend as a function of the PHB ratio in the PHB/PCL blend at 245 K. 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 60 PHB/PCL blend Morphology at 270K (Tg PHB >T>Tg PCL) 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) 80 100 PHB %wt. Figure 5.95: The morphological fractions of the blend as a function of the PHB ratio in the PHB/PCL blend at 270K. 228 1.5 1.4 PHB/PCL blend Morphology at 275K (Tg PHB< T>Tg PCL) 1.3 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) Morphological fractions 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 70 75 80 85 90 95 100 PHB %wt. 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. 229 (B) Dielectric Studies 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 (3hydroxybutaric 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 1 .0 PHB 100Hz 1KHz 10KHz 100KHz 0 .8 ε '' 0 .6 0 .4 0 .2 0 .0 220 240 260 280 300 320 340 360 380 T in K 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. 231 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). 232 5.3.2-Dielectric constant study for PHB and its copolymers: 5.3.2.1-Frequency dependence study: 12 PHB 273K 278K 283K 288K 293K 298K 303K 313K 323K 328K 333K 338K 343K 348K 353K 3.0 10 2.8 2.6 ε' 8 ε' 2.4 6 2.2 2.0 -3 -2 -1 0 1 2 10 10 10 10 10 10 4 3 4 10 5 6 10 10 3 10 7 8 10 10 10 4 10 Freq. in Hz 2 -3 10 -2 10 -1 10 0 10 1 10 2 10 10 5 6 10 7 10 8 10 Freq. in Hz 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. 233 38 36 PHB -co-H V5% 273K 283K 293K 303K 313K 328K 333K 338K 343K 348K 353K 16 34 32 14 30 28 26 ε' 12 24 ε ' 22 10 20 10 18 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 Freq. in Hz 16 14 12 10 10 -3 10 -2 -1 10 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 Freq. in Hz Figure 5.99: The frequency dependence of dielectric constant ε′ for the PHB-co-HV 5% copolymer at different temperatures. 3.0 P H B -co -H V 8% 233K 243K 253K 263K 273K 283K 293K 303K 308K 313K 323K 328K 333K 338K 343K 348K 353K 358K 363K 368K 373K 2.8 2.6 ab A 1Bc 2Cd e 3DE f 4 Fg 5 G 2.4 h i H 6 j k I 7 10 2.2 m K 9 ε' l J 8 n L 11 o M 12 p N 13 14 2.0 1.8 q O r P s 15 R t 16 u 17 S v 18 T w 19 U V x 20 W y 21 2 22 3X Y z aa 2 42 5ZAAa bac a dae 2 627A B AC aFfaga hai 28 29A 3D 0AE A33 G 31A ja K A 32 ka AIA 3H 435 A a an A Ll3m o 3a6J M ap AN 37 qar 3A 8 Aa aS sat 9 Aa a u 40 av w 4O 1AP x5a Y 42 A T A 4Q 3AR Aa4W a2 zB ba 44A 4 5 b b bc 46 4U 7AV Z A b d beb 48 9AX 5a 0A B C g 1yA B b hbib 5 53 Ffb j6 5B 455 G 5D 6BE B bK kb 57B BIB 5B 8 b 59 bn B 6H 061 B Ll6m oBP 6 2J M BN 3 q Bb 6B 4 brb S 5 sbtb ubv 66 Bb 6O 7bp BR 68 6Q 9 70B bxb yb z w B 7 1BT 72 BX Bb7W c ac b 7U 3BV YC 74 576B A 7 7BZ 7 87 9 CB 80 Q 1 A 1.6 1.4 -3 -2 -1 10 10 10 a 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 F req . in H z Figure 5.100: The frequency dependence of dielectric constant ε′ for the PHB-co-HV 8% copolymer at different temperatures. 234 7 PH B-co-HV12% 353K 348K 343K 338K 333K 328K 323K 313K 303K 298K 293K 288K 283K 278K 273K 6 5 ε' 4 3 2 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 Freq. in H z Figure 5.101: The frequency dependence of dielectric constant ε′ for the PHB-co-HV 12% copolymer at different temperatures. 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-coHV8% 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. 235 5.3.2.2-Temperature dependence study: 9.0 8.5 8.0 7.5 7.0 6.5 6.0 ' ε 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 PHB 3.0 f in Hz 7 10 5 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2 10 2.8 2.6 ' ε 2.4 2.2 2.0 270 280 290 300 310 320 330 340 350 T in K 280 300 320 340 360 380 400 T in K Figure 5.102: The dielectric constant ε′ as a function of temperature for the PHB polymer at different frequencies. 16 35 PHB-co-HV 5% 15 f in Hz -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 14 30 ε' 13 12 25 ε' 11 10 260 280 300 320 340 360 T in K 20 15 10 260 280 300 320 340 360 380 400 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. 236 3.0 PHB-co-HV 8% 2.8 f in Hz -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 2.6 2.4 ε' 2.2 2.0 1.8 1.6 260 280 300 320 340 360 380 400 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. 65 PHB-co-HV 12% 60 5.0 55 4.5 50 4.0 45 40 35 ε' 30 25 f in Hz 7 10 5 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2 10 3.5 ε' 3.0 2.5 2.0 1.5 270 280 290 300 310 320 330 340 350 360 T in K 20 15 10 5 0 270 280 290 300 310 320 330 340 350 360 370 380 390 400 T in K Figure 5.105: The dielectric constant ε′ as a function of temperature for the PHB-coHV12% polymer at different frequencies. 237 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. 238 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 1 PH B 273K 278K 283K 288K 293K 298K 303K 313K 323K 328K 333K 338K 343K 348K 353K ε '' 10 -1 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 Freq . in H z 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 239 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 αMAFrelaxation. 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. 0 PHB at 293K Experimental Data HN-fitt Log ε'' -1 -2 -3 -3 -2 -1 10 10 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 Freq. in Hz Figure 5.107: An example of the HN model fit of PHB at 293K. 240 PHB at 323K 0 Log ε'' -1 1 -2 Experimental Data (1) 1st HN peak (2) 2nd HN peak 2 -3 -4 -3 -2 -1 10 10 10 0 10 1 2 10 3 10 4 10 5 10 6 10 7 10 8 10 10 freq. in Hz Figure 5.108: An example of the HN model fit of PHB at 323K. 1.0 PHB at 343K 0.5 0.0 -0.5 -1.0 Log ε'' -1.5 1 -2.0 -2.5 -3.0 -3.5 Experimental Data (1) 1st HN peak (2 )2nd HN peak 2 -4.0 -4.5 -5.0 -3 -2 -1 0 10 10 10 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 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 241 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 0.998 0.83 0.19 0.391 0.78 0.5 0.906 0.13 0.75 1.09 0.52 6 338 0.346 0.998 0.455 1.14x10 343 0.354 1.08 0.448 2.859x106 0.997 348 353 0.367 0.377 1.15 1.18 0.438 0.43 6.089x10 6 0.997 0.95 0.049 1.637 1.55 0.53 1.061x10 7 1.1 1 0.027 2.537 2.198 0.55 242 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). 8 PHB 6 log(fmax) 4 α * α β 2 0 -2 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 1000K/T Figure 5.110: The relaxation map of PHB using log fmax of the dielectric loss experimental data. 243 8 PHB 6 log(fmax ) 4 2 0 -2 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 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 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 ----- Process 244 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 P H B -c o -H V 5 % 2 10 1 10 0 273K 283K 293K 303K 313K 328K 333K 338K 343K 348K 353K ε '' 10 -1 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 F r e q . in H z Figure 5.112: The frequency dependence of dielectric loss ε′′ for the PHB-co-HV5 % copolymer at different temperatures. 245 10 10 P H B -c o - H V 8 % 10 2 a b c A 10 d B 1 e C 1 f D 2 g E 3 h F 4 i G 5 j H 6 I 7 10 9 0 ε '' 10 -1 10 -2 k l m K n L 10 M op 11 N 12 O q r 13 P 14 Q s t 15 16 R S u v 17 18 T U w x 19 2 0 VW y z 21 22 X Y aa ab 23 2 4 ZA A a c 25 AB ad 26 AC ae 27 AD af B cb 8 0 28 AE ag C A 7 9 cC a 7 B Z 29 AF ah b8 z 77 B Y 30 AG ai 7X 6b y 7 5B 7B4 31 AH aj bx 3B V 72 bW w 32 B7 U 7 1B 7 0B I ak S Tb ub v 3 3 AA 9 BR 6B 86 Q J al b sb t 34 A 6 7B b r P 6 6 3 5 K a ma n B Ob pb q 5 BN 6 46 M 36 AL ao 37 AM ap 6 26 3B B L b nb o 38 AN 6 06 1B B J Kbbl m 39 AO aq 40 AP ar 5 85 9 B HB I b k 41 AQ as G b ib j AR 4 24 3 5 65 7B B at AS a ua v B E Fb gb h 5 45 5 44 T B D b f 4 5A 5 3 A4 U BC be 5 2B A w 46 V BB 5a Y 1yA 7A 4A 8a4W xA 9A 5a 0 X aZ zb ab bb cb d J 8 1 A a 10 -3 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 233K 243K 253K 263K 273K 283K 293K 303K 308K 313K 323K 328K 333K 338K 343K 348K 353K 358K 363K 368K 373K 8 10 9 F r e q . in H z Figure 5.113: The frequency dependence of dielectric loss ε′′ for the PHB-co-HV8 % copolymer at different temperatures. PHB-co-HV12% 10 2 10 1 353K 348K 343K 338K 333K 328K 323K 313K 303K 298K 293K 288K 283K 278K 273K ε '' 100 10 -1 10 -2 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 Freq. in Hz Figure 5.114: The frequency dependence of dielectric loss ε′′ for the PHB-co-HV12 % copolymer at different temperatures. 246 10 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). PHB-co-HV 5% Log ε'' 0 -1 Experimental Data HN-Fitt -2 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 Freq. in Hz Figure 5.115: An example of the HN model fit of PHB-co-HV 5% at 293 K 247 -1.6 -1.7 -1.8 -1.9 -2.0 -2.1 Log ε'' -2.2 -2.3 -2.4 -2.5 -2.6 -2.7 -2.8 -2.9 Experimental Data HN-fitt -3.0 -3 -2 -1 10 10 10 0 10 1 10 2 10 3 4 10 10 5 10 6 10 7 10 8 10 Freq. in Hz Figure 5.116: An example of the HN model fit of PHB-co-HV 8% at 293 K. 0.0 Log ε'' -0.5 -1.0 -1.5 Experimental Data HN-Fitt -2.0 -2.5 -3 -2 -1 0 10 10 10 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 Freq. in Hz Figure 5.117: An example of the HN model fit of PHB-co-HV 12% at 293 K. 248 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 283 293 303 313 323 333 338 343 γ 0.36 0.35 0.32 0.33 0.34 0.35 0.36 0.33 ∆ε fHN 0.76 0.87 0.94 0.95 0.96 0.96 1.906 0.715 3.5 3.82 3.95 3.95 3.95 3.95 3.35 29.75 S 0.32 32.15 927 15950 753400 1.766x106 1.422x107 2.35 x109 0.13 0.27 0.51 0.94 2.16 3.02 4.49 6.7 Table 5.10: The HN-fitting parameters for the dielectric loss data for the PHB-co-HV 8%. T(K) β 283 0.27 293 γ ∆ε fHN S n 1 0.155 1.08 -- -- 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 8 338 0.406 9.45 0.1456 2.466x10 0.217 0.595 343 0.414 13.92 0.146 1.188 x109 0.355 0.62 249 n 0.38 0.38 0.46 0.52 0.556 0.58 0.6 0.71 Table 5.11: The HN-fitting parameters for the PHB-co-HV 12% copolymer. T(K) 273 278 283 288 293 298 303 313 323 328 333 338 343 348 353 β1 0.29 0.308 0.32 0.35 0.397 0.409 0.44 0.442 0.5 0.56 0.56 0.56 0.58 0.59 0.609 γ1 0.089 0.116 0.127 0.14 0.15 0.177 0.182 0.19 0.198 0.209 0.21 0.215 0.216 0.225 0.228 ∆ε1 0.62 0.72 0.71 0.71 0.73 0.72 0.7 0.7 0.71 0.73 0.83 0.9 1 1.137 1.41 fHN1 15.34 21.38 27.6 64.3 199 830 2530 24570 91910 107500 302300 616400 899000 1.491x106 2.777x106 β2 ---------------------0.9994 1 0.999 0.998 0.997 0.9975 0.9974 0.996 γ2 ---------------------0.508 0.555 0.58 0.585 0.6 0.616 0.657 0.68 ∆ε2 ---------------------0.72 0.8 1.29 3.27 7.56 12.85 19.13 26.21 f HN2 ---------------------0.014 0.025 0.0339 0.035 0.038 0.0427 0.058 0.081 S 0.04 0.05 0.064 0.089 0.125 0.178 0.26 0.42 0.97 1.398 1.79 2.178 3.13 6.43 15.95 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. 250 n 0.278 0.31 0.34 0.38 0.408 0.437 0.46 0.52 0.55 0.56 0.583 0.606 0.617 0.622 0.66 6 5 log(fmax ) 4 3 2 1 0 3.0 3.1 3.2 3.3 3.4 3.5 3.6 1000K/T log(fmax) Figure 5.118: The VFT fitting of the PHB-co-HV 5% copolymer using the dielectric loss experimental data. 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 1000K/T Figure 5.119: The VFT fitting of the PHB-co-HV 8% copolymer using the dielectric loss experimental data. 251 Table 5.12: The αMAF –relaxation parameters. Copolymer PHB-co-HV 5% PHB-co-HV 8% E in kj/mol 99.398 59.40 τo in sec 1.33x10-15 3.638x10-13 To (K) 209 229 8 7 6 5 log(fmax ) 4 3 2 1 0 -1 2.6 2.8 3.0 3.2 3.4 3.6 3.8 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 Main process Sub process E in kj/mol τo in sec. 39.605 13.620 4.968x10-22 3.897x10-5 252 5.3.3.2-Temperature dependence study: 10 PHB 0.20 0.18 0.16 8 f in Hz 0.14 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 7 10 0.12 '' 6 ε 0.10 0.08 0.06 ε 0.04 '' 4 0.02 0.00 260 280 300 320 340 360 T in K 2 0 260 280 300 320 340 360 380 T in K 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. 253 PHB-co-HV 5% 140 0.7 0.6 120 f in Hz -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 0.5 100 80 0.4 ε'' 0.3 0.2 ε'' 60 0.1 40 0.0 260 280 300 320 340 360 T in K 20 0 -20 260 280 300 320 340 360 380 T in K Figure 5.122: The dielectric loss as a function of temperature for the PHB-co-HV 5% at different frequencies. PHB-co-HV 8% 160 140 0.05 120 0.04 f in Hz -2 100 80 ε '' 60 40 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 7 10 0.03 ε '' 0.02 0.01 0.00 260 280 300 20 320 340 360 380 T in K 0 -20 260 280 300 320 340 360 380 400 T in K Figure 5.123: The dielectric loss as a function of temperature for the PHB-co-HV 8% at different frequencis. 254 120 PHB-co-HV 12% 100 0.2 80 60 ε'' 0.1 ε'' 40 0.0 260 280 300 20 320 340 360 T in K f in Hz 7 10 6 10 5 10 4 10 2 10 1 10 0 10 -1 10 -2 10 0 260 280 300 320 340 360 380 T in K Figure 5.124: The dielectric loss as a function of temperature for the PHB-co-HV 12% at different frequencies. 255 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. 0.05 PHB T in K 273 278 283 288 293 298 303 313 323 328 333 338 343 348 353 0.04 tan δ 0.03 0.02 0.01 0.00 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 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, 256 which occurs around the glass transition temperature (273 K). As the temperature further increases above 333 K the peak, disappear again. 0.06 PHB-co-HV 5% 0.05 T in K 273 283 293 303 313 328 333 338 343 348 353 tan δ 0.04 0.03 0.02 0.01 0.00 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 Freq. in Hz Figure 5.126: The (tan δ) as a function of frequency for the PHB-co-HV 5% at different temperatures. 257 7 10 0.04 PHB-co-HV 8% T in K tan δ 0.03 273 283 293 303 313 323 333 343 353 363 373 0.02 0.01 0.00 -2 10 -1 10 0 10 1 2 10 3 10 4 10 5 10 6 10 7 10 10 Freq. in Hz Figure 5.127: The (tan δ) as a function of frequency for the PHB-co-HV 8% at different temperatures. 0.04 PHB-co-HV 12% T in K 273 283 293 303 313 323 333 343 353 tan δ 0.03 0.02 0.01 0.00 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 Freq. in Hz Figure 5.128: The (tan δ) as a function of frequency for the PHB-co-HV 12% at different temperatures. 258 8 10 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. 0.9 PHB 0.10 0.09 0.8 0.08 f in Hz -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 7 10 0.07 0.06 tan δ 0.6 tan δ 0.7 0.5 0.4 0.05 0.04 0.03 0.02 0.01 0.00 260 280 300 320 340 360 T in K 0.3 0.2 0.1 0.0 260 280 300 320 340 360 T in K Figure 5.129: The (tan δ) as a function of temperature for the PHB at different frequencies. 259 380 PHB-co-HV 5% 4.0 0.20 3.5 0.18 f in Hz -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 0.16 3.0 0.14 0.12 tan δ tan δ 2.5 2.0 0.10 0.08 0.06 0.04 1.5 0.02 0.00 260 1.0 280 300 320 340 360 T in K 0.5 0.0 -0.5 260 280 300 320 340 360 380 T in K Figure 5.130: The (tan δ) as a function of temperature for the PHB-co-HV 5% at different frequencies. 60 PHB-co-HV 8% 0.040 50 0.035 f in Hz -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 0.030 tan δ 40 tan δ 30 0.025 0.020 0.015 0.010 20 0.005 0.000 260 280 300 320 340 360 380 T in K 10 0 260 280 300 320 340 360 380 400 T in K Figure 5.131: The (tan δ) as a function of temperature for the PHB-co-HV 8% at different frequencies. 260 2.0 PHB-co-HV 12% 0.05 0.04 1.5 tan δ tan δ 0.03 1.0 0.02 0.01 0.00 260 280 300 320 340 360 T in K 0.5 f in Hz -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 0.0 260 280 300 320 340 360 380 T in K Figure 5.132: The (tan δ) as a function of temperature for the PHB-co-HV 12% at different frequencies. 261 Conclusion 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. 263 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. 264 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 semicrystalline 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. 265 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. 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