Thermal Analysis of Polymeric Materials Part 14 pptx

7 Multiple Component Materials ___________________________________________________________________ 766 Fig. 7.75 in Fig. 7.73 [33]. The straight-forward interpretation is that some, but not all of the low-molar-mass polystyrene is dissolved inthepoly( -methylstyrene). The solubility can be reduced by increasing the molar mass of the polystyrene component. The higher glass transition is then much sharper and approaches the proper C p . With even higher molar mass, one can reach complete immiscibility, as shown. 7.3.3. Glass Transitions of Copolymers While for solutions of homopolymers the mixing of the chain segments may be incomplete when compared to the intermolecular mixing, the distribution of the chain segments of the copolymers are fixed by the polymerization reaction, as described in Sect. 3.4, i.e., the same concentration can yield different segment distributions and glass transitions. The change of the glass transition with composition and randomness of the repeating units along the chain is demonstrated in Fig. 7.71 for poly(styrene-co- acrylonitrile) based on the Barton equation. Two further examples are given in Figs. 7.76 and 7.77 for poly(acrylonitrile-co-1,4-butadiene) and poly(styrene-co- methyl methacrylate) [34], respectively. As expected, the average T g of the two homopolymers, the T g for the critical run number R* (= 81.8, see Fig. 7.70), and the alternating copolymers (R = 100) lie on a straight line. The usually inaccessible region between the alternating copolymer and the value for R* was achieved with special control of the sequence regularity. The data in Fig. 7.77 exhibit a minimum in T g at an R-value of 65.2, corresponding to a styrene mole fraction of 0.57. Special complications arise whenthestereospecific homopolymers show different glass transitions for isotactic (I), syndiotactic (S), and heterotactic (H) chains. An example is the poly(methyl methacrylate). The iso- and syndiotactic stereoisomers of PMMA have glass transition temperatures of 315 and 400 K, respectively. Treating the stereoisomers as copolymers with a modified Barton equation of Fig. 7.70: 7.3 Glass Transitions of Copolymers, Solutions, and Blends ___________________________________________________________________ 767 Fig. 7.76 Fig. 7.77 T g =m I T gI +m S T gS +m H T gH , the heterotactic glass transition was estimated as 391 K. The different possible PMMA polymers should thus be found in a triangle defined by these three limiting glass transitions. The truly atactic polymer is specified by the parameters m I =m S = 0.25 and m H = 0.5, at 374 K. 7 Multiple Component Materials ___________________________________________________________________ 768 Another aspect of thermal analysis concerns the thermodynamic functions based on heat capacity. Obviously, the number of possible copolymers is so large, that complete measurements for all copolymers are not possible. Fortunately, the heat capacity of glassy and liquid copolymers over wide temperature ranges are not structure sensitive (for a discussion of structure-sensitive properties see Sect. 5.3.1). A simple additivity rule based on the molar composition of the components is suggested in Fig. 2.70 for the copolymers of styrene and butadiene (see also the addition scheme of heat capacities in Fig. 2.77). Improvements beyond the empirical, direct additivity of heat capacities is needed at low temperatures, where skeletal vibrations govern the heat capacities. With only few measured points it is possible to establish the functional relationship of the  1 and  3 temperatures with concentration for the inter- and intramolecular vibrations (see Sect. 2.3). The group-vibration frequencies are strictly additive, so that heatcapacities of complete copolymer systems can be calculated using the ATHAS, as discussed in Sect. 2.3.7. In Fig. 2.70 the glass transition changes with concentration, to reach 373 K for the pure polystyrene, as for the previously discussed copolymer systems with polystyrene. Below T g , the solid C p of both components needs to be added for the heat capacity of the copolymer, above, the liquid C p must be used. The glass transition retains the same shape and width as seen in Fig. 7.68 on the example of brominated poly(oxy-2,6-dimethyl-1,4-phenylene) [29]. To summarize the basic information of the first three sections of this chapter, one recognizes that the glass transitions for multicomponent systems must take into account the mixing between and within the macromolecules. The first is described by one of the equations in Fig. 7.69, the latter by combination of contributions of dyads or triads which affect the chain stiffness with the intermolecular effects as by the Barton equation in Fig. 7,70. The broadening of the glass-transition region in case of solutions in Fig. 7.73, in contrast to random copolymers of Figs. 2.70 and 7.68, is taken as an indication of nanophase separation. The change in the sharpness of the glass-transition region is an important, often neglected tool for the characterization of polymeric materials and will be further explored in the discussion of the next two sections. 7.3.4. Glass Transitions of Block Copolymers The chemical structure of block copolymers is given by the number of blocks, their sequence, and their length, as discussed in Sect. 3.4.1 and Fig. 1.19. A diblock copolymerpoly(styrene-block- -methylstyrene)(S/MS) ofmolar masses 312,000, and 354,500 Da, for example, has the following approximate chemical structure: [CH 2 CH(C 6 H 5 )] 3,000 [CH 2 C(CH 3 )(C 6 H 5 )] 3,000 . For such large molar masses,thesegments will separate into microphases, with the junctions between the different repeating unit sequences defining the interfaces, as is described in Sect. 5.1.11. The liquid-liquid phase diagram is discussed in Sect. 7.1.6 (see Fig. 7.21). The phase areas of such diblock copolymers are often sufficiently large to allow independent, large-amplitude molecular mobility on both sides of the point of decoupling of the components. Depending on the nature of the components, 7.3 Glass Transitions of Copolymers, Solutions, and Blends ___________________________________________________________________ 769 Fig. 7.78 glass transitions and ordering are possible within the separate phases. The crystalliza- tion of the block copolymers is described in Sect. 7.1.6, the glass transitions are discussed next. Figure 7.78 represents the heat capacities of the homopolymers polystyrene and poly( -methyl styrene) with sharp glass transitions at 375 and 443 K, respectively [35]. On copolymerization to a triblock molecule, MS SMS(45), a much broader glass transition results. It stretches from the polystyrene to the poly( -methylstyrene) glass transition and could indicate a solution, but the molar mass seems too high for solubility when compared to Fig. 7.75 in Sect. 7.3.2 (M w  10 6 Da). Similarly, the figure indicates broad transition regions for the other copolymers. The interpretation of these data becomes clearer when introducing an entropy relaxation by slow cooling before an analysis with a faster heating rate (see Sect. 6.1.3). Figure 7.79 documents that the enthalpy relaxation centers at the glass transitions of the homopolymers with a reduction in peak amplitude on copoly- merization that is larger than expected fromthe reduction in concentration. This is the typical behavior of phase-separated polymers. Even more conclusive is that electron microscopy on the same samples reveals that all these high-molar-mass S/MS block copolymers are microphase-separated. Separate experiments on small spheres of polystyrene indicate that the glass transition broadens as the radius of the spheres decreases as shown in Figs. 6.13–15 [35]. The broadening of the glass transitions in Fig. 7.79 results, thus, from the smallness of the phase areas. Figure 7.80 combines the data of Figs. 13–15 together with information on two of the block copolymers of Fig. 7.78 which have an overall lamellar structure. The plot shows that the broadening of the glass transition is related to the specific surface area of the phases. The indicated temperature difference is then 7 Multiple Component Materials ___________________________________________________________________ 770 Fig. 7.79 Fig. 7.80 T=T g  T b or T e T g ,whereT b and T e are the beginning and the end of the glass transition regions, respectively, defined in Fig. 2.117. The value of T increases sharply with the surface area of the microphase. For the transition of the phases surrounded by a surface that connects to a phase of lower glass transition, the glass transition starts atlowertemperature (spheres ofpolystyreneinairandMSsurrounded 7.3 Glass Transitions of Copolymers, Solutions, and Blends ___________________________________________________________________ 771 Fig. 7.81 by S), while a surrounding surface coupled strongly to a phase of higher glass transition extends to higher temperatures (S surrounded by MS). In the block copolymers of Fig. 7.78, this effect broadens the glass transition to such a degree that the two transitions practically fuse. It is of interest to note that the broadening in solutions of polymers, which was linked to the inability to completely mix the homopolymer chains with the solvent, extends symmetrically to both sides (see Sect. 7.3.2) rather than to one side, as in the surface effect of Fig. 7.78. Thermal analysis is, thus, able to distinguish incomplete mixing from surface effects. Comparing the block copolymers of high molar mass to solutions of the same polymers described, as in Sect. 7.3.2, one expects solubility at lower block lengths. Indeed, Fig. 7.81 shows that this is so, and that Barton’s equation describes the data for the bock copolymer solutions (run number R = 0), blocky copolymers (indicated run numbers R = 6 and 30), as well as random copolymers (   ) [36]. A quantitative thermal analysis ofaseriesoftaperedblockcopolymerswascarried outwithpoly(n-butyl acrylate-block-gradient-n-butylacylate-co-methylmethacrylate) [37], i.e., one of the blocks was copolymerized from both components with changing composition from one end to the other. Such block copolymers show, in addition to the size and strain effects, a partial solubility. A third phase due to the gradient in concentration was not discovered for the analyzed samples. To summarize all copolymers, Fig. 7.82 reproduces a three-dimensional plotofthe Barton equation, as it was used throughout this chapter. This graph allows the correlation between the three types of projections possible and shown in various parts of this chapter. The two effects that must be added for a full description are the specific interactions (see Fig. 7.69, Schneider equation) and the broadening of the glass transition, available from heat capacity analysis. 7 Multiple Component Materials ___________________________________________________________________ 772 Fig. 7.82 7.3.5. Glass Transitions of Multi-phase Systems Multi-phase systems have been discussed throughout the last two chapters and it became increasingly clear that thermal analysis of the glass transition region gives important information for the description of materials. Every one of the seven characteristics of the glass transition of Fig. 2.117 contains information on the nature of the phase to be analyzed. Copolymers, solutions, and blends can be classified as solutions or as macro-, micro-, or nanophase-separated systems by measuring T g , C p and the broadness of the glass transition region. The broadening of the glass transition, prominently featured in this section, is qualitatively linked to the loss of cooperativity of the large-amplitude motion. Without cooperative behavior, the torsional oscillationsaboutflexible bonds gradually lead at sufficiently high temperature to motions of larger amplitude, ultimately reaching rotational isomers of higher internal energy, E. This motion leads to an endothermic contribution to the heat capacity, as discussed in Fig. 2.33. Interactions between the molecules hinder this motion and force a narrower glass transition range with a T 2  T 1 in Fig. 2.117 of typically 3 to 10 K. The early initiation of such molecular isomerism as a gradual endotherm of little cooperativity is seen for polyethylene in Fig. 2.65 for the glass as well as the crystal, and is discussed in Sects. 2.3.10, 2.1.6, and 5.3.4. The main reason for the gradual initiation of conformational isomerism in polyethylene is the rather small volume requirement for internal rotation which decreases the cooperativity of neighboring segments. The broadening of glass transitions in polymer solutions, as in Fig. 7.73, and on partial ordering, as in Fig. 2.64, reaches the 50 and 100 K range of T g  T b or T e  T g of Fig. 2.117. It certainly is not a negligible effect. In this case, one again assumes, 7.3 Glass Transitions of Copolymers, Solutions, and Blends ___________________________________________________________________ 773 that nanophases of different structure increase or decrease their glass transitions from the average value. Onlyifsufficientlylargephasesoffullyintra-andintermolecularly randomized mobile repeating units (beads) are present, does the glass transition get sharper. This size-effect is illustrated in Fig. 7.80 and is expected to change with the nature of the system. Besides calorimetry, one has several other, quite sensitive thermal analysis techniques for the analysis of the glass transition, such as dilatometry, TMA, DMA, and DETA, all described in Chap. 4. A detailed analysis of the DMA of polyethylene is given in Sect. 5.6.6 by means of Fig. 5.171. The so-called -transition is linked to the gradual increase of heat capacity that leads ultimately to the glass transition. The DMA is very sensitive to this early softening in the glassy region, but up to the present, only DSC data have seen a quantitative description, as discussed above. The (broadened) glass transition is only poorly recognized in Fig. 5.171 by DMA as the -transition and by DSC it is only obvious in the heat capacity. Quantitative analysis is possible after extrapolation to fully amorphous polyethylene (see Fig. 2.46). The polyethylenes of lower crystallinity are commonly copolymerized, as demonstrated in Figs. 7.37 and 7.38. An additional observation is that melting can begin within the glass transition region. Finally, the -transition in Fig. 5.171 is most likely linked to the gauche-trans equilibrium in the crystal and on the interface of the crystals which could be studied in more detail in gel-spun polyethylenes, described in Sect. 6.2.6, Figs. 5.157, 5.158, and 6.4. Most recently the glass transition of these fibers could be analyzed by quantitative DSC, as documented in Fig. 6.105 and 6.106. The glass transition must belong to the metastable mesophase of the polyethylene fibers and is broadened considerably to higher temperatures. The glass transitions of crystals that can be treated as two-phase structures with at least one phase being a mesophase are illustrated by OOBPD, treated in Sect. 5.5.4 (see Fig. 5.143). The mesophase glass transition is broadened because of lack in cooperativity (dotted area). A similar, but macromolecular mesophase is shown in Fig. 2.68. In this case one can describe the sample as a multi-block copolymer. A normal, only slightly broadened amorphous glass transition occurs at about 275 K and is decreased in C p by the presence of some rigid amorphous fraction (see Sect. 6.1.3). This is followed by the shaded area which is the mesophase glass transition. As discussed in Sect. 5.5, many of such two-part repeating units can be considered nanophase-separated (Figs. 2.106 and 5.135). The broadening of glass transitions, thus, is an important characteristic for the description of polymers. 7 Multiple Component Materials ___________________________________________________________________ 774 References General References Sect. 7.1. The general references for the equilibrium thermodynamics of polymers are as follows: Flory PJ (1953) Principles of Polymer Chemistry. Cornell University Press, Ithaca (and later reprints); Billmeyer FW (1984) Textbook of Polymer Science, Chaps 7 and 8. Wiley-Interscience, New York; Morawetz H (1979) Macromolecules in Solution. Wiley, New York. References to many interaction parameters 3 are given in: Barton AFM (1990) Handbook of Polymer–Liquid Interaction Parameters and Solubility Parameters. CRC Press, Boca Raton. Sect. 7.2. The main reference for this part of the course is: Wunderlich B (1976,1980) Macromolecular Physics, Volume II, Crystal Nucleation, Growth, Annealing, and Volume III, Crystal Melting. Academic Press, New York (look for the chapters on copolymer crystallization and melting). A general summary of the topic phase diagrams of polymers is given by: Porter RS, Jonza JM, Kimura M, Desper CR, George ER (1989) A Review of Phase Behavior inBinary Blends: Amorphous, Crystalline, Liquid Crystalline, and On Transreaction. Polymer Eng Sci: 29: 55–62. For the description of the eutectic phase diagram with and without the interaction parameter 3, see: Flory PJ (1949) Thermodynamics of Crystallization in High Polymers. IV. A Theory of Crystalline States and Fusion in Polymers, Copolymers, and their Mixtures with Diluents. J Chem Phys 17: 223–240; and (1955) Theory of Crystallization in Copolymers. Trans Farad Soc 51: 848–857. The details on the time dependence of the eutectic crystallization are given by: Baur H (1965) Zur Theorie der Kristallisation von Copolymeren. Kolloid Z Z Polymere 203: 97–107; (1966) Zur Frage nach der geordneten Selektion von Sequenzen bei der Kristallisation von Kopolymeren. Ibid 212: 97–112; (1968) Bemerkungen zur Kinetik der Kristallisation von Polymeren. Ibid 224: 36–46; (1967) Zur Dynamik des Schmelzens und Kristallisierens in Mischungen (Teil I). Ber Bunsenges 71: 703–711. The solid solution crystallization is first described by: Sanchez IC, Eby RK (1975) Thermodynamics and Crystallization of Random Copolymers. Macromolecules 8: 638–642. The theory of cold crystallization is derived on the basis of copolymers by: Wunderlich B (1958) Theory of Cold Crystallization of High Polymers. J Chem Phys 29: 1395–1404. Further applications of such computer-generated matching of chemical structure and crystals were shown by: Hanna S, Windle AH (1988) Geometrical Limits to Order in Liquid- crystalline Random Copolymers. Polymer 29: 207–223. Sect. 7.3. 7.3 For general discussions of the glass transitions of polymer solutions and copolymers see: Turi E, ed (1997) Thermal Characterization of Polymeric Materials, 2 nd ed. Academic Press, San Diego. A Summary of solubility data for polymers is given by: Krause S, in Brandrup J, Immergut EH, Grulke GA, eds (1999) Polymer Handbook, 4 th ed. Wiley, New York. References for Chap. 7 ___________________________________________________________________ 775 A discussion of the “hole volume” and the rule of constant C p at T g can be found in: Wunderlich B (1960) Study of the Change in Specific Heat of Monomeric and Polymeric Glasses During the Glass Transition. J Phys Chem 64: 1052–1056. The description of the historic Gordon-Taylor and Wood equations for the glass transition of solutions and copolymers can be found in: Gordon M, Taylor JS (1952) Ideal Copolymers and the Second-order Transitions of Synthetic Rubbers. I. Noncrystalline Copolymers. J Appl Chem 2:493–500; Wood LA(1958)Glass TransitionTemperatures ofCopolymers. J Polymer Sci 28: 319–330; for the relationship to the volume changes, see Kovacs AJ (1964) Glass Transition in Amorphous Polymers. Phenomenological Study. Fortschr Hochpolym Forsch 3: 394–508. Specific References 1. Wunderlich B (1971) Differential Thermal Analysis. In Weissberger A, Rossiter BW, eds Physical Methods of Chemistry, Vol 1, Part V, Chapter 8, pp 427–500. Wiley, New York. 2. Debye P, Hückel E (1923) The Theory of Electrolytes. I. Lowering of Freezing Point and Related Phenomena. Physikal. Z 24: 185–206; see also your favorite Physical Chemistry texts, such as are listed on pg VIII. 3. Hildebrand JH (1947) The Entropy of Solution of Molecules of Different Sizes. J Chem Phys 15: 225–228. 4. Huggins ML (1942) Some Properties of Solutions of Long-chain Compounds. J Phys Chem 46: 151–158; Thermodynamic Properties of Solutions of Long-chain Compounds. Ann NY Acad Sci 43:1–32; Theory of Solution of High Polymers. J Am Chem Soc 64: 1712–1719. 5. Flory P (1942) Thermodynamics of High-polymer Solutions. J Chem Phys 10: 51–61. 6. Quinn FA, Jr, Mandelkern L (1958) Thermodynamics of Crystallization in High Polymers: Polyethylene. J Am Chem Soc 80: 3178–3182. 7. Quinn FA, Jr, Mandelkern L (1959) Thermodynamics of Crystallization in High Polymers: Polyethylene, (correctionof the ofTable 1 forthe heat offusion of polyethylene by the diluent method). J Am Chem Soc 81: 6533. 8. Prime RB,Wunderlich B (1969) Extended-chain Crystals.IV. Meltingunder Equilibrium Conditions. J Polymer Sci, Part A-2 7: 2073–2089. 9. Pak J,Wunderlich B (2002) Reversible Melting of Polyethylene Extended-chainCrystals Detected by Temperature-modulated Calorimetry. J Polymer Sci, Part B: Polymer Phys 40: 2219–2227. 10. Wunderlich B, Melillo L (1968) Morphology and Growth of Extended Chain Crystals of Polyethylene. Makromol Chem 118: 250–264. 11. Prime RB, Wunderlich B, Melillo L (1969) Extended-Chain Crystals. V. Thermal Analysis and Electron Microscopy of the MeltingProcess in Polyethylene. JPolymer Sci, Part A-2 7: 2091–2097. 12. Prime RB, Wunderlich B (1969) Extended-Chain Crystals. III. Size Distribution of Polyethylene Crystals Grown under Elevated Pressure. J Polymer Sci, Part A-2 7: 2061–2072. 13. Chen W, Wunderlich B (1999) Nanophase Separation of Small And Large Molecules. Macromol Chem Phys 200: 283–311. 14. Androsch R, Wunderlich B (1998) Melting and Crystallization of Poly(ethylene-co- octene) Measured by Modulated DSC and Temperature-resolved X-ray Diffraction. Proc 26 th NATAS Conf in Cleveland, OH. Williams KR, ed 26: 469–474. 15. Androsch R, Wunderlich B (1999) A Study of the Annealing of Poly(ethylene-co- octene)s by Temperature-modulated and Standard Differential Scanning Calorimetry. Macromolecules 32: 7238–7247. [...]... a heat of transition of 0.1 kJ mol 1 and the other at 432.5 K with a heat of transition of 0.56 kJ mol 1 is probably a transition from one crystal form to another [59] v The PDPSi shows a disordering transition from condis crystal I to condis crystal II at 338.3 K with a heat of transition of 1.4 kJ mol 1 [59] w The PDHSi shows a disordering transition at 323.2 K with a heat of transition of 14. 84 kJ/mol... discussions of the glass transitions of polymer solutions and copolymers see: Turi E, ed (1997) Thermal Characterization of Polymeric Materials, 2nd ed Academic Press, San Diego A Summary of solubility data for polymers is given by: Krause S, in Brandrup J, Immergut EH, Grulke GA, eds (1999) Polymer Handbook, 4th ed Wiley, New York References for Chap 7 775 _ A discussion of. .. Theory of Electrolytes I Lowering of Freezing Point and Related Phenomena Physikal Z 24: 185–206; see also your favorite Physical Chemistry texts, such as are listed on pg VIII 3 Hildebrand JH (1947) The Entropy of Solution of Molecules of Different Sizes J Chem Phys 15: 225–228 4 Huggins ML (1942) Some Properties of Solutions of Long-chain Compounds J Phys Chem 46: 151–158; Thermodynamic Properties of. .. by: Sanchez IC, Eby RK (1975) Thermodynamics and Crystallization of Random Copolymers Macromolecules 8: 638–642 The theory of cold crystallization is derived on the basis of copolymers by: Wunderlich B (1958) Theory of Cold Crystallization of High Polymers J Chem Phys 29: 1395 140 4 Further applications of such computer-generated matching of chemical structure and crystals were shown by: Hanna S, Windle... cooperativity of neighboring segments The broadening of glass transitions in polymer solutions, as in Fig 7.73, and on partial ordering, as in Fig 2.64, reaches the 50 and 100 K range of Tg Tb or Te Tg of Fig 2.117 It certainly is not a negligible effect In this case, one again assumes, 7.3 Glass Transitions of Copolymers, Solutions, and Blends 773 _ that nanophases of different... (correction of the of Table 1 for the heat of fusion of polyethylene by the diluent method) J Am Chem Soc 81: 6533 8 Prime RB, Wunderlich B (1969) Extended-chain Crystals IV Melting under Equilibrium Conditions J Polymer Sci, Part A-2 7: 2073–2089 9 Pak J, Wunderlich B (2002) Reversible Melting of Polyethylene Extended-chain Crystals Detected by Temperature-modulated Calorimetry J Polymer Sci, Part B:... Melillo L (1968) Morphology and Growth of Extended Chain Crystals of Polyethylene Makromol Chem 118: 250–264 11 Prime RB, Wunderlich B, Melillo L (1969) Extended-Chain Crystals V Thermal Analysis and Electron Microscopy of the Melting Process in Polyethylene J Polymer Sci, Part A-2 7: 2091–2097 12 Prime RB, Wunderlich B (1969) Extended-Chain Crystals III Size Distribution of Polyethylene Crystals Grown under... Contents J Thermal Anal 46: 681–718 17 Mathot VBF, ed (1993) Calorimetry and Thermal Analysis of Polymers Hanser Publishers, Munich, 1993 18 Androsch R, Wunderlich B (2003) Specific Reversible Melting of Polyethylene J Polymer Sci, Part B: Polymer Phys 41: 2157–2173 19 Cao M-Y, Varma-Nair M, Wunderlich B (1990) The Thermal Properties of Poly(oxy-1,4benzoyl), Poly(oxy-1,4-naphthoyl) and its Copolymers Polymers... polymers of similar backbone structure The group vibration frequencies are usually tabulated in the listed references g Temperature range of the ATHAS recommended experimental heat capacity data The computations of heat capacities of solids are based on these data and are usually carried out from 0.1 to 1,000 K, to provide sufficiently broad ranges of temperature for the addition schemes and for analysis of. .. transition is at 206.7 K; its heat of transition is 2.72 kJ mol 1 [52,55] n The POB shows a disordering transition at 616.5 K with a heat of transition of 3.8 kJ mol 1 [51] o The PON shows a disordering transition at 614. 5 K with a heat of transition of 0.4 kJ mol [51] 1 Appendix 1–The ATHAS Data Bank 779 p The glass transition temperature of semicrystalline PBT is seen . discussions of the glass transitions of polymer solutions and copolymers see: Turi E, ed (1997) Thermal Characterization of Polymeric Materials, 2 nd ed. Academic Press, San Diego. A Summary of solubility. information for the description of materials. Every one of the seven characteristics of the glass transition of Fig. 2.117 contains information on the nature of the phase to be analyzed. Copolymers,. the sharpness of the glass-transition region is an important, often neglected tool for the characterization of polymeric materials and will be further explored in the discussion of the next two sections. 7.3.4.