Thermal Analysis of Polymeric Materials

References for Chap277.3

___________________________________________________________________

Copolymers: Overview and Critical Survey. Academic Press, New York; Cowie JMG, ed (1985) Alternating Copolymerization. Plenum Press, New York.

Three specific sources for information on pyrolysis are: Madorsky SL (1964) Thermal Degradation of Organic Polymers. Wiley-Interscience, New York; Kelen T (1983) Polymer Degradation. Van Nostrand Reinhold, New York; Halim HS, ed (2000) Handbook of Polymer Degradation, 2nd edn. Dekker, New York.

For polymer reactions, see: Carraher, Jr. CE, Moore JA, eds (1983) Chemical Reactions on Polymers. American Chem. Soc. Symposium Series, Plenum Press, New York; Hodge P, Sherrington DC, eds (1980) Polymer-supported Reactions in Organic Synthesis. WileyInterscience, New York.

Sect. 3.5 and 6. The lecture follows closely the ideas which are described in much greater detail in: Wunderlich B (1976 and 1980), Macromolecular Physics, Vol. 2, Crystal Nucleation, Growth, Annealing, and Vol. 3, Crystal Melting. Academic Press, New York.

Some more specific articles on unsolved problems in polymer crystallization can be found in the proceedings of three international discussion meetings: (1979) Special issue of the Farad Disc Chem Soc 68; Dosiére M, ed (1993) Crystallization of Polymers. NATO ASI Series, C, Vol 405, Kluver Academic Publishers, Dordrecht, Netherlands; (2002) Proceedings of the International Symposium on Polymer Crystallization in Mishima, Japan, June 9–12, partially published (2003) Journal of Macromolecular Science, Physics Ed, vol B42.

Additional sources for information on crystallization and nucleation are: Hoffman JD, Davies GT, Lauritzen, Jr. JI (1976) The Rate of Crystallization of Linear Polymers with Chain Folding. In Hannay, NB, Treatise on Solid State Chemistry. Plenum, New York; Mark JE, Eisenberg A, Graessley WW, Mandelkern, L, Samulski, ET, Koenig, JL, Wignal, GD (1993) Physical Properties of Polymers, 2nd ed. ACS Washington DC. Also, look up the Polymer Handbook, and the Enc Polymer Sci and Eng listed in the Preface.

Specific References

1.Wunderlich B (968) Crystallization During Polymerization. Fortschr Hochpolymeren Forsch (Adv Polymer Sci) 5: 568–619.

2.Stuart JM, Young JD (1969) Solid Phase Peptide Synthesis. Freeman, San Francisco.

3.Atherton R, Sheppard RC (1989) Solid Phase Peptide Synthesis: A Practical Approach. IRL Press, Oxford.

4.Rothe M, Dunkel W (1967) Linear Cyclic Oligomers. XXIII. Synthesis of Monodisperse Oligomers of -Aminocaproic Acid up to a Degree of Polymerization of 25 by the Merrifield Method. J Polymer Sci, Letters 5: 589–593.

5.Heitz W, Wirth Th, Peters W, Strobl G, Fischer EW (1972) Synthesis and Properties of Monodisperse n-Paraffins up to C140H282. Macromol Chem 162: 63–79.

6.Bidd I, Whiting, MC (1985) The Synthesis of Pure n-Paraffins with Chain-lengths between One and Four Hundred. J Chem Soc, Chem Comm 9: 543–44.

7.Dröscher M, Wegner G (1978) Poly(ethylene Terephthalate). A Solid State Condensation Process. Polymer 19: 43–47.

8.Kovacs AJ, Buckley CP (1975,1976) Melting Behavior of Low Molecular Weight Poly(ethylene oxide). I Extended Chain Crystals. Prog Colloid Polymer Sci 58: 44–52; II. Folded Chain Crystals, Colloid Polymer Sci 254: 695–715.

9.Keller A, Udagawa Y (1970) Preparation of Long-chain Paraffins from Nitric Acid Degradation Products of Polyethylene; Consequences for Polymer Crystal Studies. J. Polymer Sci., Part A2, 8: 19–34.

10.Battista OA (1975) Microcrystal Polymer Science. McGraw-Hill, New York.

11.Ungar G, Stejny J, Keller A, Bidd I Whiting MC (1985) The Crystallization of Ultralong Paraffins: The Onset of Chain Folding. Science 229: 386–389.

12.O’Gara JE, Wagener KB, Hahn SF (1993) Acyclic Diene Metathesis (ADMET) Polymerization. Synthesis of Perfectly Linear Polyethylene. Makromol Chem Rapid Commun 14: 657–662.

13.Smith JA, Brzezinska KR, Valenti DJ, Wagener KB (2000) Precisely Controlled Methyl Branching in Polyethylene via Acyclic Diene Metathesis (ADMET) Polymerization. Macromolecules 33: 3781–3784.

14.Benkhoucha R, Wunderlich B (1978) Crystallization During Polymerization of Lithium Dihydrogen Phosphate. Part I. Nucleation of the Macromolecular Crystal from the

278 3 Dynamics of Chemical and Phase Changes

___________________________________________________________________

Oligomer Melt. Part II. Crystal Growth by Dimer Addition. Z allgem anorg Chem 444: 256–276.

15.Benkhoucha R, Wunderlich CC, Wunderlich B (1979) Melting and Crystallization of a Polyphosphate. J Polymer Sci, Polymer Phys Ed, 17: 2151–2162.

16.Ewen JA, Jones RL, Razawi AJ, Ferrara JD (1988) Syndiospecific Propylene Polymerization with Group IVB Metallocenes J Am Chem Soc 110: 6255–6256.

17.Coates GW (2000) Precise Control of Polyolefin Stereochemistry Using Single-site Metal Catalysts. Chem Rev 100: 1223–1252.

18.Boor J, Jr (1979) Ziegler-Natta Catalysts and Polymerization. Academic Press, New York.

19.Szwarc M (1968) Carbanions, Living Polymers, and Electron Transfer Processes. Interscience, New York; see also: (1983) Living Polymers and Mechanisms of Anionic Polymerization. Adv Polymer Sci 49: 1–175.

20.Bianchi JP, Price FP, Zimm BH (1957) Monodisperse Polystyrene. J Polymer Sci 26: 27–38.

21.van Krevelen DW ed (1997) Properties of Polymers: Their Correlation with Chemical Structure; Their Numerical Estimation and Prediction from Additive Group Contributions, 3rd edn. Elsevier, Amsterdam.

22.Wasserman PD (1989) Neural Computing. Van Nostrand-Reinhold, New York

23.Hect-Nielson R (1990) Neurocomputing. Addison-Wiley, New York.

24.Sumpter BG, Noid DW (1996) On the Design, Analysis, and Characterization of Materials Using Computational Neural Networks. Ann Rev Mater Sci 26: 223 277.

25.Turnbull D, Fisher JC (1949) Rate of Nucleation in Condensed Systems. J Chem Phys 17: 71–73.

26.Keller A, Willmouth FM (1970) Self-seeded Crystallization and its Potential for Molecular Weight Characterization. I. Experimentation on Broad Distributions. J. Polymer Sci, Part A2 8: 1443–1456.

27.Armistead K, Goldbeck-Wood G (1992) Polymer Crystallization Theories. Adv Polymer Sci Vol 100: 219–312.

28.Photograph, courtesy of Kovacs A (1973).

29.Wunderlich B, Mehta A (1974) Macromolecular Nucleation. J Polymer Sci, Polymer Phys Ed 12: 255–263.

30.Mehta A, Wunderlich B (1975) A Study of Molecular Fractionation during the Crystallization of Polymers. Colloid and Polymer Sci 253: 193–205.

31.Hellmuth E, Wunderlich B (1965) Superheating of Linear High-Polymer Polyethylene Crystals. J Appl Phys 36: 3039–3044.

32.Bassett DC (2003) Polymer Spherulites: A Modern Assessment. J Macromol Sci, Physics B42: 227–256.

33.Freeman ES, Carroll B (1958) The Application of Thermoanalytical Techniques to Reaction Kinetics. The Thermogravimetric Evaluation of the Decomposition of Calcium Oxalate Monohydrate. J Chem Phys 62: 394–397.

34.The results on reversible crystallization and melting are reviewed in: Wunderlich B (2003) Reversible Crystallization and the Rigid Amorphous Phase in Semicrystalline Macromolecules. Progress in Polymer Science 28/3: 383–450.

35.Wunderlich B (2000) Temperature-modulated Calorimetry in the 21st Century. Thermochim Acta 355: 43–57.

36.Zachman HG, Wutz, C (1993) Studies of the Mechanism of Crystallization by Means of WAXS and SAXS Employing Sychrotron Radiation, in Dosiére M, ed. Crystallization of Polymers. NATO ASI Series, C, Vol 405, Kluver Academic Publishers, Dordrecht, Netherlands pp 403–414.

37.Armistead JP, Hoffman JD (2002) Direct Evidence of Regimes I, II, and III in Linear Polyethylene Fractions as Revealed by Spherulitic Growth Rates. Macromolecules 35: 3895–3913.

38.Point JJ, Janimak JJ (1993) An Evaluation of the Theories of Regimes of Nucleation Controlled Crystal Growth as Applied to Polymers. J Cryst Growth 131: 502–517.

CHAPTER 4

___________________________________________________________________

Thermal Analysis Tools

All basic techniques of thermal analysis treated in this chapter are already mentioned in Sect. 2.1.3, together with a number of further, less basic techniques. The thermal analysis tools are grouped according to the variables they are designed to determine, as is summarized in Fig. 2.4. The International Confederation for Thermal Analysis and Calorimetry, ICTAC, and the regional North American Thermal Analysis Society, NATAS, are the scientific organizations concerned with this field of science (see Figs. 2.5 and 6) and their proceedings contain a continuous record of thermal analysis [1,2]. Thermometry and dilatometry are treated in Sect. 4.1. They are the techniques most prominently represented by the mercury-in-glass thermometer, shown in Fig. 2.7 and the measurement of length, shown in Fig. 4.12, below. Section 4.2 contains a general description of calorimetry. Thermometry can be coupled, next, with the measurement of time by taking heating and cooling curves as seen, for example, in Fig. 4.9, below, and Fig. 1.67. These simple thermal analyses are the forerunners of DTA and DSC, popular techniques of thermal analysis, treated in Sects. 4.3 and 4.4. The measurement of length leads in Sect. 4.5 under conditions of changing temperature and a fixed force is thermomechanical analysis, TMA, which on adding force modulation leads to dynamic mechanical analysis, DMA. Also treated in Sect. 4.5 is DETA. Section 4.6 deals, finally, with measurement of mass with changing temperature and time.

4.1 Thermometry and Dilatometry

4.1.1. Principle and History of Thermometry

The most common method of temperature measurement is contact thermometry, as demonstrated in Fig. 4.1. One brings a thermometer, C, a system with a known thermal property, into intimate contact with the to be measured system, A. Next, thermal equilibration is awaited. When reached, the temperatures of A and C are equal. The use of C as a contact thermometer is based on the fact that if the two systems A and B are in thermal equilibrium with C they must also be in thermal equilibrium with each other. This statement is sometimes called the zeroth law of thermodynamics. It permits to use B with a known temperature to calibrate C, and then use C for measurement of the temperature of system A. A calibration with B can be made at a fixed temperature of a phase transition without degree of freedom, as given by the phase rule of Sect. 2.5.7. Less common are methods of temperature measurement without a separate thermometer system. They make use of the sample itself. For example, the temperature of the sample can be determined from its length, the speed of sound within the sample, or the frequency of light emitted.

280 4 Thermal Analysis Tools

___________________________________________________________________

Fig. 4.1

Everyone is born with the ability to recognize temperature by contact through the degree of pain. No pain feels comfortable. This is the zero of the physiological temperature scale of Fig. 4.1. Cold and ice-cold show increasing degrees of pain in one direction, warm, hot, and red-hot, in the other. This temperature scale is, however, not very precise and has, in addition, no direction: It is impossible to distinguish pain caused by low temperature from pain caused by high temperature.

The first accurate temperature measurements were made in the 17th century in Florence, Italy. The thermometers capable of such precision measurement consisted of a partially liquid-filled, closed capillary and bulb, as indicated in the sketch in the lower right of Fig. 4.1. The change in length of the liquid thread in the capillary is proportional to the change in temperature. The equation in the figure gives a linear scale of temperature in terms of length. The constants a and b must be determined by calibration with systems B. All other temperatures are then given by interpolation.

Further historical development of thermometry was seen during the 18th century with the invention of various temperature scales. In principle, one can choose any function of length for a definition of temperature, but certainly, one wants to make it as easy as possible, and transferable from one thermometer type to another. The first significant suggestion for a temperature scale was made by Newton1. He said, the freezing point of water should be given the temperature zero degrees and body temperature should be 12 degrees higher. The interval of 12 degrees was thought to be useful because it can easily be subdivided into whole parts.

1 Sir Isaac Newton, 1642–1727, English physicist and mathematician at Cambridge University 1669–1701, the central figure of the scientific revolution of the 17th century. Most well known for his exploration of light (Opticks, 1704), forces, gravity and motion (Philosophiae Naturalis Principia Mathematica, 1687), and mathematics (Arithmetica Universalis, 1707).

___________________________________________________________________

The next important scale was developed in 1714 by Fahrenheit1. He found freezing of pure water difficult to reproduce. The water frequently becomes undercooled. A saturated solution of a salt, such as NH4Cl, has much more constant freezing temperature. So, Fahrenheit chose this lower temperature as his zero. He then chose body temperature to be 96°, which resulted in a more convenient, eight times finer division than proposed by Newton. Fahrenheit was a famous instrument maker and also introduced mercury as a liquid with reproducible, simple thermal properties. On further experimentation with the freezing of ice, he found that if the water was seeded with crystals, the freezing point was reproducible. So it was not very much later that Fahrenheit’s scale was actually based on the freezing of water. At the same time, the upper value of the scale was also changed, namely to the boiling point of water, a more reproducible fixed point than body temperature. Since the old scale had already been adopted, the freezing point of water was given the value 32° and the boiling point of water the value 212°, giving the well-known scale with a fundamental interval of 180°F. The scale found wide acceptance, especially in English-speaking countries. The advantage of the Fahrenheit scale is its convenient subdivision for the description of the weather, the feel of water for washing and bathing, in cooking and baking, refrigeration, and for the evaluation of the body temperature, the most important uses of thermometry in daily life. We still like to give weather information in Fahrenheit’s degrees because the scale is fine enough that there is no need of any decimals, and also because the values of negative temperatures are not very important, they just signify extreme cold.

Another scale was developed in France by Réaumur in 1730. It was based on experiments that showed the even expansion of an 80/20 wt-% mixture of water and ethyl alcohol. Réaumur found that this mixture expands exactly 80 parts per thousand between the ice and steam points. Thus, he invented the scale which showed the freezing of water at zero and boiling 80°.

A fourth scale was developed in 1742 by Celsius2. He chose the freezing of water as 0° and boiling as 100°. The celsius scale, finally won out among the over 30 empirical temperature scales because of the general change to the decimal system. For many years now, it has been accepted internationally as the mercury-in-glass scale of temperature, designated as °C. Today it is also part of the International Temperature Scale, ITS 1990 [3], described in Appendix 8, the most precise empirical temperature scale. The sometimes used name of centigrade is not internationally recognized and should be avoided, just as the term micron for micrometer or the abbreviation cc for cm3 are not accepted.

All empirical Hg-based temperature scales have limitations. First, they are only usable within the range where mercury is liquid, from a low temperature of 39°C to

1 Daniel Gabriel Fahrenheit, 1686–1736, German physicist and instrument maker, best known for inventing the mercury-in-glass thermometer (1714) and developing the Fahrenheit temperature scale. Born in Danzig, Pol. Gdansk, he spent most of his life in the Netherlands.

2 Aders Celsius, 1701–1744, Professor of astronomy at the University of Uppsala, Sweden. In 1742 he described his thermometer in a paper read before the Swedish Academy of Sciences.

___________________________________________________________________

thermodynamic temperature scale is independent not only of any materials’ property, but also of the state of matter. The zero of the thermodynamic temperature fixes the zero of thermal motion of the molecules, as illustrated in Fig. 2.9. Through the connection of temperature with radiation laws, it is easily possible to measure temperatures of millions of kelvins, as pointed out in Appendix 8. The easy correlation between the celsius and kelvin scales comes from the accidental fact that the mercury-in-glass scale is practically linear in terms of the kelvin scale from 0 to 100°C. At higher temperatures, this accidental linearity does not hold. At 300°C, for example, the deviation is close to 30 degrees.

4.1.2 Liquid-in-glass Thermometers

A typical liquid-in-glass thermometer, capable of high precision thermometry is the mercury thermometer shown in Fig. 2.7. The variables of state needed for thermometry are temperature and time. The SI unit of temperature is the kelvin (K) or the degree celsius (°C), as summarized in Figs. 2.3 and Appendix 8. At the bottom of Fig. 4.2 a further concise connection of temperature to the second law of thermodynamics is given. Finally, time, the other variable often used in thermometry is listed in the figure. The unit of time is the second, and its abbreviation is s, not sec. For all practical purposes the unit is the well-known ephemeris second (from Gk. *"- , for the day), representing the proper fraction of the year 1900. The SI unit of time is chosen to match this time interval as closely as possible with the cesium-133 clock, described in Fig. 4.3 (atomic clock). The second is, thus, independent of astronomical time. Common combinations of time-temperature measurements are the cooling and heating curves illustrated in Fig. 1.67, above, and 4.8, below, respectively.

Only for low-temperature and inexpensive thermometers does one use other liquids than mercury in liquid-in-glass thermometers, such as alcohol or petroleum distillates. The mercury-in-glass thermometer has a useful range from about 240 to 800 K. With thermometers of smaller range, as are used in calorimetry, a precision of ±0.0001 K has been reported. For many applications the precision required is, however, less than ±0.01 K. The highest precision in Hg-in-glass thermometers was reached between the years of 1880 and 1920 when these thermometers were used to maintain the standard of temperature. Note, the scale of a thermometer can be read to one tenth of the markings, if need be, by using a magnifier for estimating the position of the meniscus.

The basic technique of temperature measurement with the liquid-in-glass thermometer is to provide intimate contact with the to-be-measured system, wait until the exponential approach to thermal equilibrium has reached an acceptable error, and if needed, make corrections for the heat flow from the to-be-measured system.

A number of errors in the mercury-in-glass thermometer need to be considered. Most are connected with irreversible or slowly reversing bulb contractions and are coupled with time and immersion effects. From the differential expansivity of mercury and glass, one can calculate that the volume within the capillary corresponding to one kelvin on the scale of the thermometer must communicate with 6,000 times this volume in the bulb of the thermometer to register the proper change of temperature. The most important limitation of the absolute accuracy of a thermometer, thus, resides in the precision to which the volume of the bulb can be maintained.

284 4 Thermal Analysis Tools

___________________________________________________________________

Fig. 4.3

The most bothersome effect is the irreversible contraction of the glass after the bulb is blown. It continues for many years and may cause effects of 1 2 scale divisions. To eliminate this effect, all liquid-in-glass thermometers must be calibrated from time to time at one temperature, usually the ice point. The same correction is then added to all measured temperatures (see Fig. 2.7).

A shorter time effect is the hysteresis of the thermometer. On heating it takes a thermometer bulb several minutes to reach its final volume, but on cooling, it may take many hours. The slow hysteresis effect involves 1 2 scale divisions for every 100 K of temperature change. It is best avoided by using the thermometer only in the heating mode. When cooling is necessary, temperature changes should be kept as small as possible.

Finally, every contact thermometer has a thermometer lag due to the time for heat conduction. It takes a certain time for the heat to flow into or out of the thermometer. For a typical laboratory thermometer with a bulb of size 4.9 × 25 mm, filled with mercury, this effect has a time constant of 1 2 s to reach half of the initial temperature difference. Thus, if one wants an accuracy of 0.001 times the initial temperature difference, one must wait for a period of 10 such half-times.

Since the temperature measurement is dependent on the volume of the bulb, pressure differentials across the bulb walls must be kept constant. Typically the indicated temperature changes by one scale division when the pressure differential across the bulb changes by one atmosphere (0.1 MPa). One should thus always use the thermometer in the same position since the mercury inside the thermometer is a major pressure source for the bulb. Changing a thermometer with a 350-mm-long mercury thread from the horizontal to the vertical position, changes the pressure by 0.05 MPa or 0.5 scale divisions. Naturally, special precautions are needed, for example, when measuring water temperatures at great depths, as in oceanography.

___________________________________________________________________

The immersion effect is the largest and most common of all the causes of error, one which always must be corrected for. The drawing on the left in Fig. 4.4 illustrates a thermometer immersed only partially and the use of the correction equation. A length of n degrees on the scale of the mercury column is outside of the bath. The

Fig. 4.4

bath temperature itself is t, k is the differential glass and mercury expansion coefficient, which can usually be set to be equal to 1.6×10 4 K 1, and is the temperature of the stem, usually room temperature. The correction that must be added to the thermometer reading because of only partial immersion is shown in the example to be more than one degree! Obviously such a big error must always be corrected for.

In some thermometers, the so-called partial immersion thermometers, these corrections have been made at the factory. A partial immersion thermometer can be recognized by an engraved mark 76 mm from the bottom of the bulb. Such thermometers must always be immersed to this mark, and the stem must be kept at room temperature in order to have a precise reading. A partial immersion thermometer which is not immersed to its immersion mark, or which does not have the emerging stem at room temperature, still needs to be corrected by an expression analogous to that shown for total immersion thermometers. A final note of caution: no temperature measurement is possible if the bulb is not safely immersed to the beginning of the constant-diameter capillary.

4.1.3 Resistance Thermometers and Thermocouples

Metals, as well as semiconductors have been used as resistance thermometers. As given in Fig. 4.5, the conductivity depends upon the number of charge carriers n, their charge e, and their mobility . The mobility of the electrons is impeded by the

286 4 Thermal Analysis Tools

___________________________________________________________________

Fig. 4.5

increasing atomic vibration amplitudes at higher temperatures. The resistance increases almost linearly with temperature. The best-known resistance thermometers are made of platinum. They are also used for the maintenance of the international temperature scale, ITS 90, as shown in Appendix 8. Over a wide temperature range, the change of its resistance is 0.4% per degree. In order to make a platinum resistance thermometer, a wire is wound noninductively. Most conveniently, the total resistance is made to be 25.5 + at 273.15 K. Under this condition, the resistance of the thermometer will change by about 0.1 + K 1. The best precision that has been achieved with platinum resistance thermometers is ±0.04 K at 530 K and ±0.0001 K at 273.15 K. It decreases to ±0.1 K at 1700 K.

Semiconductor properties are also summarized in Fig. 4.5. The conduction mechanism of semiconductors is more complicated. At low temperatures, semiconductors have a very high resistance because their conductance band is empty of electrons. As the temperature increases, electrons are promoted out of the relatively low-lying valence band into the conductance band, or they may also be promoted from impurity levels into the conductance band. It is also possible that positive holes, created by the electrons promoted out of the valence band, carry part or all of the current. All these effects increase the conductance with increasing temperature by creating mobile charge carriers that more than compensate the decrease in mobility with increasing temperature. Semiconductors, thus, have over a wide temperature range the opposite dependence of resistance of metals on temperature. Typically, one may have as many at 1017 charge carriers per cubic centimeter at room temperature, and the specific resistance may vary from 10 2 to 10+9 + cm. The temperature coefficient of the resistivity may be ten times greater than that of a metal resistance thermometer. Semiconductor thermometers can be built in many shapes. Frequently they are very small beads, so that their heat capacity and thermal lag are small. They