Thermal Analysis of Polymeric Materials

___________________________________________________________________

A similar comparison of DSC and quasi-isothermal TMDSC for poly(ethylene terephthalate) is given in Fig. 3.92. The reversible melting is substantial and seems to contradict the schematic of melting developed with Fig. 3.76. More will be said about this topic in Chaps. 4–7 in connection with the description of temperature modulation in the melting range. The picture that has developed from this thermal analysis is that the globally metastable, semicrystalline, and flexible polymers in their

Fig. 3.92

chain-folded macroconformation have a nanophase structure which supports local equilibria [1]. A condition for such a picture is that the long molecules must have decoupled molecular segments at the phase boundary which can crystallize and melt independently of the rest of the molecule.

Thermal analysis experiments, which prove the existence of molecular segments which melt independently of the rest of the molecule, are shown in Fig. 3.93. A double melting peak is seen in the identical reference DSC traces ‘a’ after crystallization at 400 K. Next, the samples were extracted at different temperatures ‘b’ to ‘d’, cooled quickly, dried, and then analyzed by DSC again. The extractions should have removed all molecules that were above their dissolution temperature which changes with molar mass parallel to the melting temperature (see Fig. 3.73). The weights of material removed are listed in parentheses. At low temperature, only molecules of low molar mass are extracted and the corresponding low-temperature peak in ‘a’ has disappeared. On extractions ‘c’ and ‘d’, increasing amounts of unextractable segments are proven. These segments melt at lower temperature because of the poorer crystallization after extraction, compared to the melt crystallization at 400 K.

The melting and crystallization rates of oligomers and polymers were first measured by microscopy in the presence of remaining crystal, to eliminate nucleation effects. Figure 3.94 illustrates data for poly(oxyethylene) as a function of molar mass. On extrapolation to monomer dimensions, the metastability gap disappears and one

268 3 Dynamics of Chemical and Phase Changes

___________________________________________________________________

Fig. 3.93

Fig. 3.94

reaches the same behavior as shown schematically in Fig. 3.76, and observed for crystals of small, rigid motifs and oligomers below the critical length of Fig. 3.91.

Fast optical microscopy can also be used for the study of reorganization during melting. Figure 3.95 illustrates an electrically-conducting, fast-heatable, tin-oxide- coated slide on which a folded-chain polyethylene growth spiral is deposited (left).

___________________________________________________________________

Fig. 3.95

On melting, it forms the droplet shown below the divide on the right. Plotting the temperatures of melting as a function of heating-rate gives the results of the graph at the bottom right. Only on heating faster than 75 K min 1, the melting temperature is constant, signaling that then the crystals melt without reorganization, while on slower heating, they perfect and give a higher Tm. Although no quantitative reorganization rates were obtained, one can identify the zero-entropy-production case, where imperfect crystals melt without change in metastability (see Sects. 2.5 and 6.2).

A direct study of the melting of small regions has recently become available as a microcalorimeter, based on an atomic force microscope, AFM, as shown schematically in Fig. 3.96. For more details about the operating principle see also Appendix 10 (Fig. A.10.5). The platinum wire tip serves as a heater and simultaneously as a thermometer. Together with an identical reference tip it can serve as a DTA (see Sect. 4.3). At the same time the AFM can produce a topographical image. Figure 3.97 illustrates how it is possible to image the melting produced by setting the AFM tip at a preselected point of a growth spiral of solution-grown polyethylene and heating to melt. Further development of this special instrumentation may give direct information on the thermal behavior of microphase and nanophase structures as was proposed in a general discussion of modern thermal analysis [35].

A quantitative, isothermal measurement of the crystallization kinetics, usable for analysis by the Avrami method, is illustrated in Fig. 3.98 by the upper left curve. Similar curves can be generated by dilatometry or adiabatic calorimetry as described in Sects. 4.1 and 4.2. At time zero, one assumes that the isothermal condition has been reached. The dotted segments of the heat-flow response are then proportional to the heat of crystallization evolved in the given time intervals and can be converted directly into the changes of the mass fraction of crystallinity after calibration or normalization to the total heat evolved. An independent crystallinity determination

270 3 Dynamics of Chemical and Phase Changes

___________________________________________________________________

Fig. 3.96

Fig. 3.97

is possible for the completely crystallized sample. A detailed development of the calculation of crystallinity from DSC data is given in Sect. 4.4.7.

The curves in the lower right of Fig. 3.98 illustrate a point-by-point determination of not only the crystallinity, but also the nature of the crystallization as a function of time. The example polymer is a poly(oxy-1,4-phenylene-oxy-1,4-phenylene carbonyl- 1,4-phenylene) or simply poly(ether ether ketone), PEEK. After the given time at the

___________________________________________________________________

Fig. 3.98

crystallization temperature, the sample is heated directly under DSC conditions and the heat of fusion is used for crystallinity evaluation. The changing curve-shape indicates that reorganization is possible at the crystallization temperature. The initial crystals have a melting temperature of about 600 K, but increase quickly in perfection. Only after about 10 min does a secondary crystallization of poorer crystals develop with a peak which moves to a higher Tm with time.

Data on the development of crystallinity, obtained by adiabatic calorimetry are depicted in Fig. 3.99. Note, that for the Avrami analysis the crystallinity must be calculated in volume fraction, vc, while the heat of fusion is usually expressed in weight-fraction, wc, as displayed in Figs. 3.84 and derived in Fig. 5.80, respectively. The correlation between the two crystallinities is given by:

where , a, and c are the densities of the sample, amorphous phase, and crystal. Since copolymers do not crystallize completely, one normalizes the data, as shown in the right graph of Fig. 3.99. This normalization corresponds to the assumption that the spherulites are of the same low crystallinity throughout their volume, and the space between the spherulites is filled with pure amorphous phase. This is a postulate that must be verified, for example by electron microscopy and X-ray diffraction. Especially later crystallization stages may involve new growth within the lamellar stacks of the spherulite or creation of whole new stacks changing the structure [36].

From the slope on the right graph of Fig. 99 an Avrami exponent of 3.2 results, close to the value expected for athermal nucleation followed by spherulitic growth, but because of the many assumptions that went into the derivation of the Avrami equation still not proven without a detailed structural analysis.

___________________________________________________________________

It is interesting to note that the deviations from the Avrami expression occur at a level that is given by the limit of applicability of the free growth approximation in Fig. 3.55. Similar data for a single molar mass, but at different temperatures, are shown in Fig. 3.101. All crystallizations seem to approach a common limit, but deviate at different temperatures from the Avrami equation.

Fig. 3.101

Linear growth rates for polyethylene gained from microscopy are shown in Fig. 3.102. The break in the curve is attributed to a change in the secondary or molecular nucleation mechanism. At low temperature, one assumes multiple nucleations to occur during the growth of a given patch on the surface (regime 2), while at high temperature, nucleation occurs only once for the same patch (regime 1) [37]. The observed slopes correspond to the expected changes in growth-rate, the absolute values, however, do not [38].

Dilatometric data by measurement of stress decay on fibers are shown in Fig. 3.103 for extension ratios from one (no extension) to six. Besides the increase in rate of crystallization on stretching, one finds a decrease of the Avrami exponents from 3.5 to 1.3 with increasing extension ratio. The nature of the crystal morphology is changing from spherulitic to fibrillar as increases.

A final crystallization mechanism concerns, as in the earlier described LiPO3 case, crystallization coupled with polymerization. The example is the change of trioxane rings to poly(oxymethylene) chains within single crystals of the cyclic monomer trioxane:

x (CH2 O )3 (O CH2)3x

Electron microscopy permitted the detailed study of this process. Figure 3.104 illustrates the dynamics of the polymerization. Note that the density of the growing

274 3 Dynamics of Chemical and Phase Changes

___________________________________________________________________

Fig. 3.102

Fig. 3.103

polymer within the trioxane crystal is larger than the monomer. As a result, cavities are produced, which permit easy mass transport to the growing chain end. Once nucleated, the fibrillar polymer crystals may grow to the end of the monomer crystal. The nucleation was achieved at liquid nitrogen temperature by irradiation with X-rays. At this temperature further chemical reaction does not occur. On warming to 323 K,

___________________________________________________________________

Fig. 3.104

Fig. 3.105

it demonstrates the special nature of flexible macromolecules. Finally, the nucleation process was shown to be of importance for the initiation of a crystal, as well as the addition of a new macromolecule to a crystal when accepting the concept of molecular nucleation. This summary of data demonstrates the utility of the various forms of thermal analysis for the analysis of the crystallization and melting of polymers.

276 3 Dynamics of Chemical and Phase Changes

___________________________________________________________________

References

General References

Sect. 3.1–3. For general texts on the chemistry of synthesis of polymers see: Lenz RW (1967) Organic Chemical Synthesis of High Polymers. Interscience, New York; Odian G (1991) Principles of Polymerization. Wiley, New York, 3rd edn; Saunders JK (1973) Organic Polymer Chemistry. Chapman and Hall, London; Allcock H R, Lampe FW (1980) Contemporary Polymer Chemistry. Prentice-Hall, Englewood Cliffs; Rempp P, Merrill EW (1990) Polymer Synthesis. Hüthig and Wepf, Heidelberg. Also, use your introductory polymer science texts and the reference books listed in the General References in the Preface.

Specific books on reaction kinetics of small molecules are: Gardiner WC (1969) Rates and Mechanics of Chemical Reactions. Benjamin, New York; Bamford CH, Tipper CF (1969–1986) Comprehensive Chemical Kinetics, Vols 1 26. Elsevier, Amsterdam; Laidler KL, Keith J (1987) Chemical Kinetics, 3rd edn. Harper and Row, New York.

The problems of interaction of crystallization and polymerization of Sect. 3.2.2 are reviewed in Wunderlich B (1976) Macromolecular Physics, Vol 2, Crystal Nucleation, Growth, Annealing. Academic Press, New York, Chap VI.

The matrix control is treated, for example, in: Ingram, VM (1965) The Biosyntheses of Macromolecules. Benjamin, New York; and information on ribonuclease can be found in: Spakman DH, Stein WH, Moore S (1960) J Biol Chem 235: 648.

Specific sources on molecular mass distributions are: Flory PJ (1953) Principles of Polymer Chemistry, Chaps 3, 8 and 9. Cornell University Press, Ithaca; Peebles LH (1971) Molecular Weight Distributions in Polymers. Wiley-Interscience, New York. The problem of ring formation is treated by: Jacobson H, Stockmeyer WH (1950) Intramolecular Reaction in Polycondensation. I. The Theory of Linear Systems. J Chem Phys: 18: 1600–1606; and Jacobson H, Beckmann CO, Stockmeyer WH (1950) , II. Ring-chain Equilibria in Polydecamethylene Adipate. J Chem Phys 18: 1607–1612.

More recent experiments proving the presence of very large rings in step reactions and a discussion of the role of ring formation in step polymerization are summarized by: Kricheldorf HR (2003) The Role of Ring-ring Equilibria in Thermodynamically Controlled Polycondensation, Macromol Symp 199: 15–22; see also other papers in the same issue and the introduction: What Does Polycondensation Mean? Ibid pp 1–13.

The recently developed living polymerization in polycondensation is reviewed by: Yokozawa T, Yokoyama A (2004) Chain-growth Polycondensation: Living Polymerization Nature in Polycondensation and Approach to Condensation Polymer Architecture. Polymer J (Japan) 36: 65–83 (in English). Examples are found for polyamides (2000) J Am Chem Soc 122: 8313–2314. Polyesters: (2003) Macromolecules 36: 4328–4336. Polyethers (2001) J Am Chem Soc 123: 9902–9903. Polythiophenes (2004) Macromolecules 37: 1169–1171. Several block copolymers can be found in the publications (2002) J Am Chem Soc 124: 15158–15159; and (2003) J Polymer Sci, Part A: Polymer Chem 41: 1341–1346.

Use your basic reference books on mathematics and vector analysis to support the reading on molar mass distributions. Some examples are the (1960–) International Dictionary of Applied Mathematics. Van Nostrand, Princeton, NJ; Feller W (1950–) An Introduction to Probability Theory and Its Applications. Wiley, New York; Mood AM (1950) Introduction to the Theory of Statistics. McGraw-Hill, New York; Hamming RW (1962–) Numerical Methods for Scientists and Engineers. Dover, New York.

Sect. 3.4. The references are to be supplemented with those listed for Sects. 3.1–3. Check there for examples of many polymer reactions.

More information on copolymerization is available through: Ham GE, ed (1964) Copolymerization. Wiley-Interscience, New York; Nashay A, McGrath JE (1977) Block