Thermal Analysis of Polymeric Materials Part 11 pot

5 Structure and Properties of Materials ___________________________________________________________________ 586 References General References Sect. 5.1. The fundamental tabular summary of crystallography is:. Henry NFM, Lonsdale K, eds (1969) International Tables for X-Ray Crystallography, Vol I. The International Union of Crystallography, Publ Kynoch Press, Birmingham, see also later reprints. Specific books treating the crystal structures of linear macromolecules are: Wunderlich B (1973) MacromolecularPhysics, Vol I, Crystal Structure, Morphology, Defects. Academic Press, New York; Alexander LE (1969) X-Ray Diffraction Methods in Polymer Science. Wiley-Interscience. New York; Tadokoro H (1979) Structure of Crystalline Polymers. Wiley, New York; Miller RL (1989) Crystallographic Data for Various Polymers. In Brandrup J, Immergut EH, Polymer Handbook, 3 rd edn. Wiley, New York, Sect VI, pp 1–277. Proteins are special macromolecules. For their crystal structure see, for example,: Blundell TL, Johnson, LN (1976) Protein Crystallography. Academic Press, New York. Specific books of interest to the history of crystallography are: Burke JG (1966) Origins of the Science of Crystals. University of California Press, Berkeley; Kepler J (1611) Strenua seu, de nive sexangula. Frankfurt. Reprint in English (1966) The Six-cornered Snowflake. Oxford Univ Press (Clarendon), London; Hooke R (1665) Micrographia, or some Physiologi- cal Descriptions of Minute Bodies Made by Magnifying Glasses with Observations and Inquiries Thereupon. London. The firstenumerations ofthe 14 translation lattices, 32 point groups,and 230space groups can be found in: Bravais A (1850) Mémoire sur les systèmes formès par des points distribués regulièrement sur un plan ou dans l’espace. J Ecole Polytech 19: 1 128, English translation by Shaler A (1949) Cryst Soc Amer Memoir, Vol 1; Hessel JFC (1831) Kristallometrie oder Kristallonomie und Kristallographie. Leipzig; Schoenflies A (1891) Kristallsysteme und Kriststallstruktur. Leipzig. A general text on symmetry groups is: Flurry RL, Jr (1980) Symmetry Groups, Theory and Chemical Applications. Prentice Hall, Englewood Cliffs. Sect. 5.2. The main reference on which this Sect was developed is: Wunderlich B (1973) Macromolecular Physics,Vol I, CrystalStructure, Morphology, Defects. Academic Press,New York. A more recent source of excellentpictures andbrief discussionsof polymer morphology is given by Woodward AE (1988) Atlas of Polymer Morphology. Hanser, München. The first major treatise on polymer crystallization is the three volume series: Stuart HA, ed (1955) Die Physik der Hochpolymeren. See Vol 3 Ordnungserscheinungen und Umwand- lungserscheinungen in festen hochpolymeren Stoffen. Springer, Berlin. General books on optical microscopy, a technique often sufficient to evaluate the morphology of polymers and general crystal morphology are: Hemsley DA (1989) Applied Polymer Light Microscopy. Elsevier, New York; Sawyer L, Grubb DT (1987) Polymer Microscopy. Chapman and Hall (Methuen), New York. Discussions ofthe problems of chain foldingare publishedin the followingplaces: (1979) Special issue of the Farad Disc Chem Soc 68; Dosiére M, ed (1993) Crystallization of Polymers. NATO ASI Series C, Volume 405, Kluver, Dordrecht; (2002) Proceedings of the International Symposium on Polymer Crystallization in Mishima, Japan, June 9–12, also published in part in a special issue (2003) J Macromolecular Science B42. References for Chap. 5 ___________________________________________________________________ 587 Sect. 5.3. The main referenceon which thissection was developedwith updates is: Wunderlich B (1973) Macromolecular Physics, Vol I, Crystal Structure, Morphology, Defects, Chap 4. Academic Press, New York. For a summary of the history and development of defect concepts of non-polymeric defects see: Nabarro FRN (1967) Theory of Crystal Dislocations. Oxford University Press (Clarendon), London; FriedelJ (1964) Dislocations. Pergamon, Oxford [translationof (1956) Les Dislocations. Gauthiers-Villars, Paris]; Frank FC (1949) Disc Farad Soc 5: 48–54; Frank FC, Read WT, Jr (1950) Phys Rev 70: 722–723. Discussion of dislocations in polymers is given by: Keith HD, Passaglia E (1964) J Res Natl Bur Stand 68A: 513–518; Predecki P, Statton WO (1966) J Appl Phys 37: 4053–4059; (1967) Appl Polymer Symp 6: 165–181; (1967) J Appl Phys 38: 4140–4144; Lindenmeyer PH (1966) J Polymer Sci, Part C 15: 109–127; Peterson JM, Lindenmeyer PH (1966) J Appl Phys 37: 4051–4053. Early discussions of polymer point defects are given by: Holland VF, Lindenmeyer PH (1965) J Applied Phys 36: 3049–3056; Science 147: 1296–1297; Pechhold W (1968) Kolloid Z Z Polym 228: 1–38; Reneker DH (1962) J Polymer Sci 59: S39–42. For updates on defects by molecular dynamics simulations see the Refs to Sects 1.3 and 2.1 and: Wunderlich B, Kreitmeier SN (1995) MRS Bulletin, September issue, pp 17 27; Suter U, Monnerie L, eds (1994) Atomistic Modeling of Physical Properties of Polymers, Springer, Berlin (Adv Polymer Sci, Vol 116). Early ideas about deformation of polymers are found in: Frank FC, Keller A, O’Connor A (1958) Phil Mag 3: 64–74; Bonart R (1969) Kolloid Z Z Polym 231: 438–458; Hay IL, Keller A (1965) Kolloid Z Z Polym 204: 43–74. Sect. 5.4. The main references with which this section was developed are: Wunderlich B (1980) Macromolecular Physics, Vol 3, Crystal Melting. Academic Press, New York; (1990) Thermal Analysis. Academic Press, Boston; (1997) The Basis of Thermal Analysis. In Turi E ed, Thermal Characterization of Polymeric Materials 2 nd edn. Academic Press, New York, pp 205 482; Ubbelohde, AR (1965) Melting and Crystal Structure. Oxford University Press, London, and also (1978) The Molten State of Matter, Melting and Crystal Structure. Wiley, New York. For a larger summary of melting data see, for example: Wunderlich B, Pyda, M (2004) Thermodynamic Properties of Polymers, in Kroschwitz JI, ed, Encyclopedia of Polymer Science and Engineering, 3 rd edn, John Wiley & Sons, New York; see also (1990) 2 nd ed, Vol 16, pp 1188–1192. Also available via: www.mrw.interscience.wiley.com/epst. Sect. 5.5. For general literature on the discussions of mesophases and their transitions see also Sect 2.5. Many of the here discussed examples are reviewed in: Gordon M, ed (18983/84) Liquid Crystal Polymers I–III. Springer, Berlin (Adv Polymer Sci, Vols 59–61). Specific references to the materials discussed in some detail are as follows: DDA, MBPE, PEIM, and HPX: Chen W, Wunderlich B (1999) Macromol Chem Phys 200, 283–311. DDA-12: Yandrasits MA, Cheng SZD, Zhang A, Cheng J, Wunderlich B, Percec V (1992) Macromolecules 25: 2112–2121; Cheng SZD, Yandrasits MA, Percec V (1991) Polymer 32: 1284–1292; Blumstein RB, Thomas O, Gauthier MM, Asrar J, Blumstein A (1985) in Blumstein A, ed Polymeric Liquid Crystals. Plenum Press, New York p 239. PDES: Varma-Nair M, Wesson JP, Wunderlich B (1989) J Thermal Anal 35: 1913–1939. OOBPD: Cheng J, Chen W, Jin Y, Wunderlich B (1994) Mol Cryst Liq Cryst 241: 299–314; Cheng J. Jin Y, Liang G, Wunderlich B, Wiedemann HG (1992) Mol Cryst Liq Cryst 213: 237–258; Wiedemann HG, Grebowicz J, Wunderlich B (1986) Mol Cryst Liq Cryst: 140: 219–230. 5 Structure and Properties of Materials ___________________________________________________________________ 588 PP: See the extensive list of references and summary of the properties in [46] pp 57 and 58. TlX: Lindau J, Diele S, Krüger H, Dörfler HD (1981) Z phys Chem (Leipzig) 262: 775–784; Lindau J, König HJ, Dörfler HD (1983) Colloid Polymer Sci 261: 236–240. PE: Hu W, Buzin A, Lin JS, Wunderlich B (2003) J Polymer Sci, Part B: Polymer Phys 41: 403–417; Kwon YK, Boller A, Pyda M, Wunderlich B (2000) Polymer 41: 6237–6249; Boller A, Wunderlich B (1997) J Thermal Analysis 49: 343–349; Fu Y, Chen Y,Pyda M, Londono D, Annis B, Boller A, Habenschuss A, Cheng J, Wunderlich B (1996) J Macromol Sci, Phys B35: 37–87; Chen W, Fu Y, Wunderlich B, Cheng J (1994) J Polymer Sci, Part B: Polymer Phys 32: 2661–2666 (1994). Sect. 5.6. The basic references for the description of polymer melts are: Flory PJ (1953) Principles of Polymer Chemistry. Cornell University Press, Ithaca, NY; Bueche F (1962) Physical Properties of Polymers. Wiley, New York; de Gennes PG (1979) Scaling Concepts in Polymer Physics. Cornell University Press, Ithaca, NY; Doi M, Edwards SF (1988) The Theory of Polymer Dynamics. Oxford University Press, New York; de Gennes PG (1990) Introduction to Polymer Physics. Cambridge University Press, Cambridge. More details about physical properties of amorphous polymers can be found in: Ferry JD (1980) Viscoelastic Properties of Polymers, 3 rd edn. Wiley, New York; Ward IM (1983) Mechanical Properties of Solid Polymers, 2 nd edn. Wiley, New York; Matsuoka S (1992) Relaxation Phenomena in Polymers. Hanser, München. Specific References 1. See, for example the collections of beautiful crystals in: DeMichele V (1969) Kristalle; ein farbenfrohes Bild geheimnisvoller und gesetzmäßiger Kunstformen der Natur. Südwest Verlag, München (125 color reproductions); Roberts WL, Rapp GR, Jr, Weber J (1974) Encyclopedia of Minerals. Van Nostrand, New York. 2. Klug A, Crick FHC, Wyckoff HW (1958) Diffraction by Helical Structures. Acta Cryst 11: 199–213. 3. Shimanouchi T, Mizushima S (1955) On the Helical Configuration of a Polymer Chain. J Chem Phys 23: 707–711. 4. G. Natta G, Corradini P (1960) General Considerations on the Structure of Crystalline Polyhydrocarbons. Nuovo Cimento, Suppl 15: 9–39. 5. McCoullough RL (1962) Representation of Ordered Systems . Polymer Preprints 3(2): 53–57. 6. The classical book dealing with the packing of motifs in crystals is: Kitaigorodskii AI (1955) Organicheskaya Kristallokhimiya. Press of theAcad SciUSSR. Moscow; revised English translation (1961) by the Consultants Bureau, New York. 7. Bunn CW (1939) The Crystal Structure of Long Chain Normal Hydrocarbons. The Shape of the >CH 2 -group. Trans Farad Soc 35: 482–491. 8. Hajduk DA, Harper PE, Gruner SM, Honeker CC, Kim G, Thomas EL, Fetters LJ (1994) The Gyroid: A New Equilibrium MorphologyinWeaklySegregated Diblock Copolymers. Macromolecules 27: 4063–4075. 9. Matsen MW, Bates FS (1996) Unifying Weak-and Strong-segregationBlock Copolymer Theories. Macromolecules 29: 1091–1098; and Matsen MW, Bates FS (1997) Block Copolymer Microstructures in the Intermediate-segregation Regime. J Chem Phys 106: 2436–2448. 10. Hikosaka M (1987) Unified Theory of Nucleation of Folded-chain and Extended-chain Crystals of Linear-chain Polymers. Polymer 28: 1257–1264. 11. Wunderlich B, Shu HC (1980) The Crystallization and Melting of Selenium. J Crystal Growth 48: 227–239; see also: Crystallization during Polymerization of Selenium from the Vapour Phase. Polymer 21: 521–524. References for Chap. 5 ___________________________________________________________________ 589 12. Staudinger H, Johner H, Signer R, Mie G, Hengstenberg J (1927) Der polymere Formaldehyd, ein Modell der Zellulose. Z phys Chem 126: 425–448; see also: Staudinger H, Signer R (1929) Über den Kristallbau hochmolekularer Verbindungen. Z Krist 70: 193–210; Sauter, E. (1932) Röntgenographische Untersuchungen an hochmolekularen Polyoxymethylenen. Z Phys Chem B18: 417–435. 13. Storks KH (1938) An Electron Diffraction Examination of Some Linear High Polymers. J Am Chem Soc 60: 1753–1761. 14. Keller A (1957) A Note on Single Crystals in Polymers: Evidence of a Folded Chain Conformation. Phil Mag 2: 1171–1175. 15. Fischer, EW (1957) Stufen und spiralförmiges Kristallwachstum bei Hochpolymeren. Z Naturforsch 12a: 753–754. 16. Geil PH (1958) Polyhedral Structures in Polymers Grown from the Melt. In Doremus, RH, Roberts BW, Turnbull DW, eds. Growth and Perfection of Crystals. Wiley, New York, p 579. 17. Till PH, Jr (1957) The Growth of Single Crystals of Polyethylene. J Polymer Sci 24: 301–306. 18. Kobayashi K (1958) Fourth Int Congress for Electron Microscopy in Berlin, Germany. Published in(1962) Properties andStructure of Polymers. Kagaku (Chem) 8:203, Kagaku Dojin, Kyoto. 19. Herrmann K, Gerngross O, Abitz W (1930) Zur röntgenographischen Strukturerfor- schung des Gelantinemicells. Z phys Chem 10: 371–394. 20. Bassett DC, Olley RH, Sutton SJ, Vaughan AS (1966) On Sperulite Growth in a Monodisperse Paraffin. Macromolecules 29: 1852–1853; On Chain Conformations and Sperulitic Growth in Monodisperse n-C 294 H 590 . Polymer 37: 4993–4997. 21. A first and quite comprehensive discussion of chain-folded crystals was given by Geil PH (1963) Polymer Single Crystals. Interscience, New York. 22. Popoff B (1927) Die Erscheinung der Strahlungskrystallisation. Fortschr Mineal Krist Petr 11: 320–321. 23. Fu Y, Busing WR, Jin Y, Affholter KA, Wunderlich B (1993) Poly(ethylene Tereph- thalate) Fibers 1. Crystal Structure and Morphology Studies with Full-pattern X-ray Diffraction Refinement. Macromolecules 26: 2187–2193. 24. Fu Y, Busing WR, Jin Y, Affholter KA, Wunderlich B (1994) Structure Analysis of the Noncrystalline Material in Poly(ethylene Terephthalate) Fibers. Macromol Chem Phys 195: 803–822. 25. Fu Y, Annis B, Boller A, Jin Y, Wunderlich B (1994) Analysis of Structure and Properties of Poly(ethylene Terephthalate) Fibers. J Polymer Sci, Part B: Polymer Phys 32: 2289–2306. 26. Busing WR (1990) X-ray Diffraction Study of Disorder in Allied Spectra-1000 Polyethylene Fibers. Macromolecules 23: 4608–4610. 27. Bu H, Pang Y, Song D, Yu Y, Voll T, Czornyj G, Wunderlich B (1991) Single Molecule Single Crystals. J Polymer Sci, Part B: Polymer Phys 29: 139–152. 28. Bu H, Shi S, Chen E, Hu H, Zhang Z, Wunderlich B (1996) Single-molecule Single Crystals of Poly(ethylene Oxide). J Macromol Sci, Phys B35: 731–747. 29. Geil PH, Anderson FR, Wunderlich B, Arakawa T (1964) Morphology of Polyethylene Crystallized from the Melt under Pressure. J Polymer Sci, Part A 2: 3707–3720. 30. Wunderlich B, Melillo L, Cormier CM, Davidson T, Snyder G (1967) Surface Melting and Crystallization of Polyethylene. J Macromol Sci B1: 485–516. 31. Wunderlich B, Melillo L (1968) Morphology and Growth of Extended Chain Crystals of Polyethylene. Makromolekulare Chemie 118: 250–264. 32. Sumpter BG, Noid DW, Liang GL, Wunderlich B (1994) Atomistic Dynamics of Macromolecular Crystals. Adv Polymer Sci 116: 27–72. 5 Structure and Properties of Materials ___________________________________________________________________ 590 33. Sumpter BG, Noid DW, Wunderlich B (1992) Computational Experiments on the Motion and Generation of Defects in Polymer Crystals. Macromolecules 25: 7247–7255. 34. Peterlin A (1971) Molecular Model of Drawing Polyethylene and Polypropylene. J Mater Sci 6: 490–508. 35. Takayanagi M, Imada K, Kajiyama T (1966) Mechanical Properties and Fine Structure of Drawn Polymers. J Polymer Sci Part C 15: 263–280. 36. Kamezawa M, Yamada K, Takayanagi M (1979) Preparation of Ultrahigh Modulus Isotactic Polypropylene by Means of Zone Drawing. J Appl Polymer Sci 24:1227–1236. 37. Wunderlich B (1958) Theory of Cold Crystallization of High Polymers. J Chem Phys 29: 1395–1404. 38. Hirschfelder J, Stevenson D, Eyring, H (1937) A Theory of Liquid Structure. J Chem Phys 5: 896–912. 39. Lennard-Jones, JE Devonshire AF (1939) Critical and Cooperative Phenomena. III. A Theory of Melting and the Structure of Liquids. IV: A Theory of Disorder in Solids and Liquids and the Process of Melting. A Proc Roy Soc, London, Ser A 169: 317–338; 170: 464–484. 40. Richards JW (1897) Relations between the Melting Pointsand the Latent Heats of Fusion of the Metals. Chem News 75: 278–279. 41. Xenopoulos A, Cheng J, Yasuniva M, Wunderlich B (1992) Mesophases of Alkyl- ammonium Salts. I. First-order Transitions. Molecular Crystals and Liquid Crystals 214: 63–79. 42. Walden P (1908) Über die Schmelzwärme, spezifisch Kohäsion und die Molekulargröße bei der Schmelztemperature. Z Elektrochem 14: 713–724. 43. Wunderlich B, Grebowicz, J (1984) Thermotropic Mesophases and Mesophase Transitions of Linear, Flexible Macromolecules. Adv Polymer Sci 60 61: 1–59. 44. Androsch R (2001) Reversibility of the Low-temperature Transition of Polytetra- fluoroethylene asRevealedby Temperature-modulated DifferentialScanningCalorimetry. J Polymer Sci, Part B: Polym Phys 39: 750–756. 45. Fyfe CA (1983) Solid State NMR for Chemists. C.F.C Press, Guelph, CN. 46. Wunderlich B, Möller M, Grebowicz J, Baur H (1988) Conformational Motion and Disorder in Low and High Molecular Mass Crystals. Springer, Berlin (Adv Polymer Sci, Vol 87). 47. de Gennes PG (1971) Reptation of a Polymer Chain in the Presence of Fixed Obstacles. J Chem Phys 55: 572–579 (1971). 48. Festag R, Alexandratos SD, Cook KD, Joy DC, Annis B, Wunderlich B (1997) Single- and Few-chain Polystyrene Particles by Electrospray. Macromolecules 30: 6238–6242. 49. van Krevelen DW ed (1997) Properties of Polymers: Their Correlation with Chemical Structure; Their Numerical Estimation and Predictionfrom Additive Group Contributions, 3 rd edn. Elsevier, Amsterdam. 50. Roberts AD, ed (1988) Natural Rubber Science and Technology. Oxford University Press, New York. 51. Boyd RH (1985) Relaxation Processes in Crystalline Polymers: Experimental Behavior; Molecular Interpretation—A Review. Polymer 26: 323–347 and 1123–1133. 52. Wunderlich, B (1997) The Basis of Thermal Analysis. In Turi E ed, Thermal Character- ization of Polymeric Materials 2 nd edn. Academic Press, New York, pp 387–389. 53. Wunderlich B (1962) Motion in Polyethylene. III. The Amorphous Polymer. J Chem Phys 37: 2429–2432. 54. Wunderlich B (1963) Motion in the Solid State of High Polymers. J Polymer Sci, Part C 1: 41–64. CHAPTER 6 ___________________________________________________________________ Single Component Materials In the last two chapters of the book on Thermal Analysis of Polymeric Materials the link between microscopic and macroscopic descriptions of macromolecules will be discussed with a number of examples based on the thermal analysis techniques which are described in the prior chapters. Chapter 6 deals with single-component systems, Chap. 7 with multiple-component systems. It is shown in Sect. 6.2, as suggested throughout the book, that practically all partially crystalline polymers represent nonequilibrium systems, andthat thermodynamics canestablish theequilibrium limits for the description. It was found, however, more recently, that equilibrium thermody- namics may be applied to local areas, often small enough to be called nanophases [1]. These local subsystems are arrested and cannot establish global equilibrium. Amorphous polymers are easier to treat as equilibrium systems as long as they consist of single components above their glass transition temperature and are without extensive surfaces that introduce significant local stresses, as shown in Sect. 6.3. For macromolecules, in general, the meaning of the term component was relaxed to account for the fact that macromolecules are sufficiently large, so that small changes in their length do not affect their properties significantly, i.e., all macromolecules in a distribution are considered to be one component. Note, that this is not true for distributions that contain oligomers, defined in Sect. 3.1 as molecules below 1,000 atoms in size. Similarly, decoupled segments of a polymer chain may change the accounting for components, as is shown in Sect. 6.2. Section 6.1 is a review and extension of the prior, basic thermodynamic description of phases and transitions. 6.1 The Order of Transitions 6.1.1 Review of Thermodynamics, Motion, and Reversibility A concise review of the relative order, mobility, density, and possible types of phase transitions of one-component systems is presented by the schematic of Fig. 2.115, along withthe dictionarydefinition ofthe word transition. This schematic isdiscussed in Sect. 2.5 in connection with an initial description of phases and their transitions. More details of the structure and properties of crystals, mesophases, and amorphous phases are given in Chap. 5. Some characteristics of the three types of mesophases are given in Fig. 2.107. Quantitative information on the thermodynamic parameters of the transitions between the condensed phases is summarized in Fig. 2.103 and described in more detail in Sect. 5.5. The dilute phases in Fig. 2.115, the gases, are of lesser interest forthe present description, although the ideal gas law in Figs. 2.8 and 6 Single Component Materials ___________________________________________________________________ 592 2.9 and the extension to nonideal gases in Figs.2.99 and 2.100 are the basic equations to which the thermodynamics of most systems is based. The link of the various glasses in Fig. 2.103 goes only to their corresponding mobile, condensed phases. The omission of the connections of the glassy areas to the phases of higher order indicates that such direct transitions are not possible. This point needs some elaboration, in particular, since a definition of devitrification as a transition from a glass to the crystal is still popular. Polymeric glasses crystallize frequently by cold crystallization, i.e., above the glass transition, as shown in Fig. 5.116, i.e., they change first to a supercooled liquid before crystallization. A typical example is the well-known cold crystallization of amorphous poly(ethylene terephthalate) on heating, as shown in Figs. 4.122, 4.136, 4.138 and 4.139. For more symmetricand flexible macromolecules, suchas polyethyleneor poly(oxymethylene), the motion needed to crystallize is so little, that crystallization can occur at the very beginning of the glass transition so that glass transition and cold crystallization overlap. The glass transition is then masked by the big exotherm of crystallization, and the increase in heat capacity, characteristic of a glass transition, is missing, because the sample is solid again after it gained temporarily enough mobility for crystallization. Similarly, metals andminerals withclose to sphericalmotifs needonly minor rearrangements to crystallize and can often do so at the beginning of large- amplitude, cooperative motion. To describe all the mentioned cases, it is suggested with Fig. 2.103 that the devitrification to the states of higher order or the crystal is always a two-step transition, step one is the glass transition to gain mobility, to be followed by step two, the ordering or ultimate crystallization. Straight-forward definitions oftransitions are available only forthe first-order and glass transitions. The basic definitions of both transitions are given in Sect. 2.5 and experimental information is summarized in Sects. 5.4 6. As the dictionary definition of Fig. 2.115 indicates, even subtle changes may be, and have been, called transitions. The observation of gradual changes without transitions have been documented with some examples in Sect. 5.5 (see Fig. 2.108 and 5.143). The definition of the order of thermodynamic transitions, finally is discussed with Fig. 2.119 [2]. Any thermodynamic definition needs special caution before being applied to polymeric systems. It is shown in Sect. 2.5 with the free enthalpy diagram of Fig. 2.118 that the glass transition, although superficially similar to a second-order transition, is time- and frequency-dependent, and thus, is not a thermodynamic transition. Many of the polymer transitions that exhibit a heat of transition, and thus fit the criterion for a first-order transition ( S g 0), are also not equilibrium transitions because of the chain-folding principle and semicrystalline behavior described in Chap. 5. Before discussing the transitions in polymeric single-component systems, in Sect. 6.2, it is necessary to look at the large increase in number of phase areas caused by irreversibility, as shown schematically in Fig. 2.120. Figure 6.1 shows schematically a diagram of phase areas of different degrees of metastability [3]. The diagram is drawn under the assumption of a one-component polymeric system which is limited to one crystal polymorph and one mesophase in addition to the liquid and glassy phases. Different sequences of transition occur on heating the seven possible low-temperature structures represented by areas #3, #10, #14, #8, #15, #6, and #11. The transitions are indicated by the densely dotted, narrow 6.1 The Order of Transitions ___________________________________________________________________ 593 Fig. 6.1 boxes. All one-phase areas are marked by the remaining dotted boxes. The boxes without shading represent two- and three-phase areas. Only the left side of the diagram, structures #1 #3, can be in equilibrium. This is judged from the phase rule which permits at constant pressure only one phase in a given phase area, and two at the boundaries, as pointed out in Sect. 2.5.7, and from the frozen-in nature of the single-phase areas of the glasses discussed in Sect. 2.5.6. The importance of this phase-diagram lies in the illustration of the large variety of metastable phase structures. Increasing the number ofpossible polymorphs of crystalsand mesophases, naturally, increases the number of combinations and the analysis becomes more complicated. All of the 15 different phase-combinations in Fig. 6.1 have been observed. Examples of several polymer systems will be discussed next. 6.1.2 First-Order Phase Transitions For polyethylene, themost studied polymer, all of the 15 phase areasshown in Fig. 6.1 seem to be possible, and most have, indeed, been realized. The sequence of phases seen on heating of extended chain crystals, represented by the phase area #3 in Fig. 6.1, to mesophase, area #2, and melt #1 is seen in the equilibrium phase diagram of linear polyethylene under high hydrostatic pressure in the upper left of Fig. 6.2. Condis crystals of close to 100% crystallinity havebeen grown onisobaric crystalliza- tion above the triple point. The hexagonal condis-crystal phase is sufficiently mobile to permit chain extension after folding on initial crystallization, as required by the chain-folding principle described in Sect. 5.2.2. On cooling from the melt, however, the transitions do not occur at the equilibrium temperatures because of the need of crystal and molecular nucleation described in Sect. 3.5. Other examples of the possibility of equilibrium melting of extended-chain equilibrium crystals that were 6 Single Component Materials ___________________________________________________________________ 594 Fig. 6.2 grown after chain extension of the crystals in the condis phase are polytetra- fluoroethylene, asillustrated inthe upperright ofFig. 6.2,andtrans-1,4-polybutadiene and polydiethylsiloxane. For the latter two polymers DSC traces are shown in Figs. 2.112 and 5.129, respectively. For polytetrafluoroethylene the phase IV in Fig. 6.2 disappears at somewhat higher pressure (for the phase-diagram, see Fig. 5.130). For trans-1,4-polybutadiene and polydiethylsiloxane the DSC traces indicate partial crystallinity. A glass transition is easily detected, arising from the amorphous fractions of trans-1,4-polybutadiene and polydiethylsiloxane. The phase sequence is, thus, better described by the sequence #14 #13#12#4#1. On better crystallization, this non-equilibrium sequence approaches the equilibrium sequence #3 #2#1, with a possible intermediate of #10#9#2#1. Just as partial crystallization of the condis crystals of trans-1,4-polybutadiene and polydiethylsiloxane from the melt results in the metastable phase area #4, sufficiently quick cooling of phase area #4 may yield areas #5 and #6 which contain the corresponding glasses. It must be observed, however, that the glass-transition temperatures of mesophase and melt are not necessarily fixed in the sequence given in Fig. 6.1. If the mesophase permits easier large-amplitude motion than the melt, as observed in some liquid crystals, the mesophase glass transition temperature, T g ,may be lower than the glass transition of the melt. The existence of a metastable mesophase together with melt or glass, is also found in quenched polypropylene, as seen in Fig. 5.146. The metastable mesophase of polypropylene has been known for many years, but no condition of elevated pressure was found that stabilizes the conformationally disorderedcrystals. The conformational disorder consists mainly of helix reversals. When the CD glass of polypropylene reaches its glass transition temperature, at about 350 K, the condis crystal orders to the monoclinic crystal with an exotherm of about 600 J mol 1 . 6.1 The Order of Transitions ___________________________________________________________________ 595 Fig. 6.3 The phase area #4 in Fig. 6.1 is less likely for liquid crystals than for condis crystals since the small increase in order that is needed to change a mobile melt into a mobile liquid crystal occurs fast and is usually completely reversible as seen in the reversible transition shown in TMDSC of Fig. 5.144 for a small molecule and the upper curves of Fig.5.154 for a macromolecule. Once in phase area #2, the polymeric liquid crystals will, however, not crystallize completely on cooling, but rather become a semicrystalline material. In the present scheme, they will produce metastable phase areas #9, followed by #10. On crystallizationof polyethylene atatmospheric pressure,the structure typicalfor a semicrystalline polymer results. It usually consists of nanophase-separated crystalline/amorphous phase structures, as described in Chap. 5, and is represented by phase areas #7 and #8 of Fig. 6.1. A zero-entropy production path on heating, discussed inSect. 2.4, permits to evaluatethe freeenthalpy distribution inareas #7 and #8, as shown in Fig. 6.3 [4] (see also schematics of G in Figs. 2.88 and 2.120). The glass transition of the amorphous phase can be used to estimate the strain introduced into the metastable, amorphous nanophases by the interfaces with the crystals. The local strain manifests itself in an increase of the glass-transition temperature and the possible presence of a rigid amorphous fraction that does not show a contribution to the increase in heat capacity at T g , as is discussed in Sect. 6.1.3. Most bulk-crystallized macromolecules which do not exhibit intervening mesophases are described by the phase areas #7 and #8 of Fig. 6.1. The lowerleft TMDSCtraces inFig. 6.2illustrate thespecial case of poly(ethylene terephthalate) as also documented with Figs. 4.122, 4.136–139, and 5.116. At low temperature, this quenched sample is fully glassy-amorphous, i.e., it is represented by area #11. At the glass transition, it changes simply to area #1, as a supercooled, [...]... specific heat capacity gives a measure of the crystallization kinetics by showing the drop of the heat capacity from the supercooled melt to the value of the solid as a function of time, while the total heat-flow rate is a direct measure of the evolution of the latent heat of crystallization From the heat of fusion, one expects a crystallinity of 64%, the total amount of solid material, however, when estimated... Sect 6.2.6 Proof of such structures is given in Figs 5.68–72 and 5 .113 115 for fibers of poly(ethylene terephthalate) and Figs 5.157, 5.158, and 6.4 for gel-spun, ultra-high-molar-mass polyethylene The reversing heat capacity and the total heat-flow rate of an initially amorphous poly(3-hydroxybutyrate), PHB, are illustrated in Fig 6.18 [21] The quasi-isothermal study of the development of the crystallinity... approaching the limit of the microphase size of one micrometer, the broadening of the glass transition to lower temperature becomes negligible 606 6 Single Component Materials _ A quantitative analysis of the data of Fig 6.13 is attempted in Fig 6.14 [20] Extrapolating the increase in heat capacity to Tg, suggests that 1/3 of the total beads of 85 nm contribute to... distribution as illustrated in Fig 5.76 The crystals of Curve F have a chain extension of up to 2 m Curve E, in contrast, was generated from crystals with an extension of up to 10 m The superheating of the crystals of F is less than the crystals of E, and in addition, the melting range on slow dilatometry is broader because of the presence of molecules of lower molar mass which melt at a lower temperature,... 357 K and the end of the glass transition reaches up to about 375 K Between 380 and 420 K a second Tg seems to exist, attributed to a RAF (for Te, see also Fig 4.137) The first quantitative analysis of RAF was carried out by analysis of the heat capacity of semicrystalline poly(oxymethylene), POM, as shown in Fig 6.16 [20] Clearly, the 67% of crystallinity computed from the heat of fusion, which would... that of the liquid can be based on the differential equation of Fig 6.5 The number of holes refers then not to the equilibrium number of holes, N*, which changes only with temperature, but to the actual change of holes, N, with time during heating or cooling with rate q The solution of this equation is given in Sect 4.4.6 with Fig 4.131 under the assumption of first-order kinetics, and applied to the analysis. .. illustrated by curve 9 of Fig 3.67 Crystallizing a melt during cooling, as is often the case in industrial applications, leads to an even broader distribution of crystals of different degrees of perfection, as can be surmised from the curves on the right of Fig 6.23 and seen from fast calorimetry of Fig A.10.6 Once produced, the metastable crystal distributions must be analyzed under conditions of zero-entropy-production... reversible, above, a need of molecular nucleation introduces supercooling (see Sect 3.5.6) Changing from pure paraffins to narrow fractions of similarly low-molar-mass fractions of PE, the reversibility is largely retained, as seen from Fig 6.25 which illustrates the melting of fraction PE560 of a weight average molar mass of 560 Da and polydispersity of 1.06 The melting temperature of 354.5 K for C40H82... approximates the melting end of the quasi-isothermal data, as well as the beginning of crystallization on quasi-isothermal TMDSC on cooling The low-temperature melting peak at 332.6 K is most likely the eutectic 616 6 Single Component Materials _ Fig 6.25 temperature of the distribution of molecular lengths discussed in detail in Chap 7 and may contain some of the transitions... that of C40H82 The apparent reversing heat capacity shows a sizeable contribution to the melting, but not as much as seen for the pure C50H102 in Fig 6.24 where all fusion is complete within 1.0 K, i.e., with a modulation amplitude of 0.5 K, the melting of C50H102 would be fully reversing The width of the melting region of PE560 is about 30 K The broadening of the melting of PE560 in the quasi-isothermal . Academic Press, New York; (1990) Thermal Analysis. Academic Press, Boston; (1997) The Basis of Thermal Analysis. In Turi E ed, Thermal Characterization of Polymeric Materials 2 nd edn. Academic Press,. Interpretation—A Review. Polymer 26: 323–347 and 112 3 113 3. 52. Wunderlich, B (1997) The Basis of Thermal Analysis. In Turi E ed, Thermal Character- ization of Polymeric Materials 2 nd edn. Academic Press,. book on Thermal Analysis of Polymeric Materials the link between microscopic and macroscopic descriptions of macromolecules will be discussed with a number of examples based on the thermal analysis