Thermal Analysis of Polymeric Materials

___________________________________________________________________

Fig. 7.76

Fig. 7.77

Tg = mI TgI + mS TgS + mH TgH ,

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 mI = mS = 0.25 and mH = 0.5, at 374 K.

768 7 Multiple Component Materials

___________________________________________________________________

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 and3 temperatures with concentration for the interand intramolecular vibrations (see Sect. 2.3). The group-vibration frequencies are strictly additive, so that heat capacities 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 Tg, the solid Cp of both components needs to be added for the heat capacity of the copolymer, above, the liquid Cp 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 copolymer poly(styrene-block- -methylstyrene) (S/MS) of molar masses 312,000, and 354,500 Da, for example, has the following approximate chemical structure:

[CH2 CH(C6H5) ] 3,000 [CH2 C(CH3)(C6H5) ] 3,000 .

For such large molar masses, the segments 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,

___________________________________________________________________

glass transitions and ordering are possible within the separate phases. The crystallization 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 (Mw 106 Da). Similarly, the figure indicates broad transition regions for the other copolymers.

Fig. 7.78

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 copolymerization that is larger than expected from the 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

770 7 Multiple Component Materials

___________________________________________________________________

Fig. 7.79

Fig. 7.80

T = Tg Tb or Te Tg, where Tb and Te 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 at lower temperature (spheres of polystyrene in air and MS surrounded

___________________________________________________________________

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].

Fig. 7.81

A quantitative thermal analysis of a series of tapered block copolymers was carried out with poly(n-butyl acrylate-block-gradient-n-butyl acylate-co-methyl methacrylate) [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 plot of the 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.

772 7 Multiple Component Materials

___________________________________________________________________

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 Tg, Cp 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 oscillations about flexible 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 T2 T1 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 Tg Tb or Te Tg of Fig. 2.117. It certainly is not a negligible effect. In this case, one again assumes,

___________________________________________________________________

that nanophases of different structure increase or decrease their glass transitions from the average value. Only if sufficiently large phases of fully intraand intermolecularly 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 Cp 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.

774 7 Multiple Component Materials

___________________________________________________________________

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 0 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 in Binary 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 0, 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 Liquidcrystalline 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, 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.

___________________________________________________________________

A discussion of the “hole volume” and the rule of constant Cp at Tg 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 Transition Temperatures of Copolymers. 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, (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: 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 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 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 26th 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.

776 7 Multiple Component Materials

___________________________________________________________________

16.Mathot VBF, Scherrenberg RL, Pijpers MFJ, Bras W (1996) Dynamic DSC, SAXS and WAXS on Homogeneous Ethylene-propylene and Ethylene-octene Copolymers with High Comonomer 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.

19Cao M-Y, Varma-Nair M, Wunderlich B (1990) The Thermal Properties of Poly(oxy-1,4- benzoyl), Poly(oxy-1,4-naphthoyl) and its Copolymers. Polymers for Adv Technol 1: 151–170.

20.Hanna S, Lemmon T, Spontak RJ, Windle AH (1992) Dimensions of Crystallites in a Thermotropic Random Copolyester. Polymer 33: 3–10.

21.Langelaan HC, Posthuma de Boer A (1996) Crystallization of Thermotropic Liquid Crystalline HBA/HNA Copolymers. Polymer 37: 5667–5680.

22.Biswas A, Blackwell J (1988) Three-dimensional Structure of Main-chain Liquidcrystalline Copolymers, Parts 1–3. Macromolecules 21: 3146–3164.

23.Blackwell J, Biswas A, Cheng HM, Cageao RA (1988) X-ray Analysis of Liquid Crystalline Copolyesters and Copolyamides. Molecular Cryst Liq Cryst 155: 299–312.

24.Varma-Nair M, Habenschuss A, Wunderlich B (1992) Phase Transitions in

Poly(4-hydroxybenzoic acid), Poly(2,6-hydroxynaphthoic acid) and their Copolymers. Proc 21st NATAS Conf in Atlanta GA, 21: 343–348.

25.Ashman PC, Booth C (1975) Crystallinity and Fusion of Ethylene Oxide–Propylene Oxide Block Copolymers. 1. Type PE Copolymers. Polymer 16: 889–896.

26.Di Lorenzo ML, Pyda M, Wunderlich B (2001) Calorimetry of Nanophase-separated Poly(oligoamide-alt-oligoethers). J Polymer Sci, Part B: Polymer Phys 39: 1594–1604.

27.Di Lorenzo ML, Pyda M, Wunderlich B (2001) Reversible Melting in Nanophaseseparated Poly(oligoamide-alt-oligoether)s and its Dependence on Sequence Length, Crystal Perfection, and Molecular Mobility. J Polymer Sci, Part B: Polymer Phys 39: 2969–2981.

28.Wunderlich B (2003) Reversible Crystallization and the Rigid Amorphous Phase in Semicrystalline Macromolecules. Progress in Polymer Sci 28: 383–450.

29.Bopp RC, Gaur U, Kambour RP, Wunderlich B (1982) Effect of Bromination on the Thermal Properties of Poly(2,6-dimethyl-1,4-phenylene Oxide). J Thermal Anal 25: 243–258.

30.Schneider HA, Di Marzio EA (1992) The Glass Temperature of Polymer Blends: Comparison of Both the Free Volume and the Entropy Predictions with Data. Polymer 33: 3453–3461.

31.Suzuki H, Mathot VBF (1989) An Insight into the Barton Equation for Copolymer Glass Transition. Macromolecules 22: 1380–1384.

32.Suzuki H, Kimura N, Nishio Y (1994) A Note on Analysis of Glass Transition Temperature Data of Steric Copolymers. Polymer 35: 5555–5559.

33.Lau S-F, Pathak J, Wunderlich B (1982) Study of Phase Separation in Blends of Polystyrene and Poly- -methylstyrene in the Glass Transition Region.

Macromolecules 15: 1278–1283.

34.Suzuki H, Nishio Y, Kimura N, Mathot VBF, Pijpers MFJ, Murakami Y (1994) Effects of Sequence Length Distribution on Heat Capacity and Glass Transition Temperature of Styrene–Methyl Methacrylate Copolymers. Polymer 35: 3698–3702.

35.Gaur U, Wunderlich B (1980) Study of Microphase Separation in Block Copolymers of Styrene and -Methylstyrene in the Glass Transition Region using Quantitative Thermal Analysis. Macromolecules 13: 1618–1625.

36.H. Suzuki H, Miyamoto T (1990) Glass Transition Temperatures of Compatible Block Copolymers. Macromolecules 23: 1877–1879.

37.Buzin AI, Pyda M, Matyjaszewski K, Wunderlich B (2002) Calorimetric Study of Blockcopolymers of Poly(n-butyl Acrylate) and Gradient Poly(n-butyl Acrylate-co-methyl Methacrylate). Polymer 43: 5563–5569.