Thermal Analysis of Polymeric Materials

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rests with the quality of the membrane. It must not let small polymer molecules pass, but have free exchange of solvent. Best results have been obtained with molar masses above 50,000 Da.

1.4.7 Other Characterization Techniques

A series of additional characterization techniques for macromolecules is available. All should be familiar to the polymer scientist. Ultracentrifugation is a special technique, although in principle well understood, it is more difficult to make absolute measurements on synthetic polymers than for the more compact globular proteins for which the method was originally developed.

The scattering of neutrons is in several aspects similar to the earlier discussed light scattering, as is summarized together with the scattering of electrons in Fig. 1.72. It can be used to find molar mass, the shape of the molecule, and the interaction with the solvent. Of particular interest is the neutron scattering of polymers in solutions of their deuterated counterparts since the scattering diameter of hydrogen for neutrons is particularly large. With such experiments it could be shown that in

Fig. 1.72

the melt polymer molecules assume, indeed, shapes close to those calculated in Sect. 3 and found in solution at the -temperature, i.e., they are unaffected by the excluded volume.

The end-group determination can be done with many analytical tools, such as infrared analysis, nuclear magnetic resonance, or the detection of radioactive end groups which were included during the synthesis. The end-group determination for the purpose of measurement of the molar mass of macromolecules, great precision is necessary.

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Calorimetry and dilatometry were used to estimate super-high molar masses for some crystallizable polymers. For such high molar masses, crystallization is increasingly impeded and the fraction of the molecules able to crystallize has been calibrated with respect to molar mass for polytetrafluoroethylene [25,26].

Melt viscosity can also be used for molar mass estimates. The measurements are, however, somewhat less precise because of the high viscosities due to entanglements of the molecules, and it is inconvenient to work at the higher temperatures needed to melt the polymer. A frequent measurement is that of the melt index. A basic extrusion-capillary is used to determine the (mass) rate of flow of the polymer through a specified capillary under controlled conditions of temperature and pressure. Similarly, the Mooney viscometer gives a measure of the torque to revolve a rotor at constant speed in a polymer at constant speed, which is linked ultimately to molar mass. The Mooney viscometer has found application in the rubber industry as an empirical measure of molar mass. Somewhat more information on melt viscosity is given in Sect. 5.6.6.

A final tool is electron microscopy and atomic force microscopy. Both tools can image isolated molecules and an estimate of their volume can be made, which in turn, can be converted to molar mass with knowledge of the density. Both amorphous polymers as well as crystalline polymers have been analyzed. The main problem of this technique is the separation of the sample into single-molecule droplets or crystals [27] (see also Figs. 5.160 and 5.74, respectively).

This summary of the experimental evaluation of molecular sizes, interactions and shapes concludes the discussion of Atoms, Small, and Large Molecules. The major topics of this first chapter of the book were the identification of all types of molecules, the naming of macromolecules, and their characterization via molecular mass and chain statistics, as well as experimental molar mass and distribution determination. Several of the instruments described are classified as thermal analysis equipment and belong into the large field of thermometry, which will be treated in more detail in Sect. 4.1.

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References

General References

Sect. 1.1. For the section on the microscopic description of matter, review your physical chemistry references. Examples are given in the General References of the Preface.

The book by Dalton J (1808) “A New System of Chemical Philosophy” is available in many reprints, for example, (1964) The Science Classics Library. The Citadel Press, New York.

A useful reference to the state of science at the beginning of the modern science era is: Lavoisier AL (1789) Elements of Chemistry. Paris. Frequently reprinted, for example, found in a Dover Publication as a paperback facsimile reprint (1965) New York (translation by Kerr R, 1790, Edinburgh).

A typical source of bibliographic information is Farber E, ed (1961) Great Chemists. Interscience Publ. New York. Much information can also be found in the electronically searchable Encyclopædia Britannica.

The history of polymer science can be followed best with the books: Morawetz H (1985) Polymers, The Origin and Growth of a Science. Wiley, New York; and Furukawa Y (1998) Inventing Polymer Science: Staudinger, Carothers, and the Emergence of Macromolecular Chemistry. University of Pennsylvania Press.

Sect. 1.2. A sufficiently detailed description of the IUPAC rules for naming polymers is given in: Brandrup J, Immergut, EH, Grulke EA, eds (1999) Polymer Handbook. Wiley, 3rd edn, New York. See also: International Union of Pure and Applied Chemistry (1991) Compendium of Macromolecular Nomenclature. Blackwell, Oxford; a summary of the nomenclature of inorganic and organic small and large molecules is given also in Lide DR, ed (2002/3) Handbook of Chemistry and Physics, 83rd edn. CRC Press, Boca Raton.

Collections of threeand four-letter abbreviations of polymers have been made by many organizations. IUPAC Division of Applied Chemistry, Plastics and High Polymer Section (1969) Recommendations for Abbreviations for Terms relating to Plastics and Elastomers. Pure Appl Chem 18: 583–589. Commission on Macromolecular Nomenclature (1974) List of Standard Abbreviations (Symbols) for Synthetic Polymer Materials. Pure Appl Chem 40: 475–476. For a collection of abbreviations accepted internationally by many organizations see also Elias HG, Pethrick RA (1984) Polymer Yearbook. Harwood Acad Publ, Chur, Switzerland.

To find out about extensive details for a polymer which is new to you, check: Mark HF, Gaylord, NG Bikales NM (1985 89) Encyclopedia of Polymer Science and Engineering. Interscience Publ., 2nd edn, New York. (A 12-volume 3rd edn is in preparation, Kroschwitz, ed (2003–2004) Wiley, New York.) It may also be sufficient to check your introductory polymer science text (see examples in the Preface).

Sect. 1.3. Use your basic reference books on mathematics, statistics, and vector analysis to support the concepts and derivations developed. Some examples are: (1960 and later) International Dictionary of Applied Mathematics. Van Nostrand, Princeton. Feller W (1950 and later) An Introduction to Probability Theory and Its Applications. Wiley, New York.

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Mood AM (1959) Introduction to the Theory of Statistics. McGraw-Hill, New York. Hamming RW (1962 and later) Numerical Methods for Scientists and Engineers. Dover, New York. Coffin JG (1911 and later) Vector Analysis. Wiley, New York.

The early ideas about molecular mass distributions are well displayed in Flory PJ (1953) Principles of Polymer Chemistry. Cornell University Press, Ithaca.

A specially detailed book about molecular chain dimensions and rubber elasticity is by: Bueche F. (1962) Physical Properties of Polymers. Interscience, New York.

A Specialized book on molecular mass distributions is Peebles LH (1971) Molecular Weight Distribution in Polymers. Wiley Interscience, New York.

The classical texts on rotational isomers and the calculation of chain conformations are: Flory PJ (1966) Statistical Mechanics of Chain Molecules. Interscience, New York. Volkenstein, MV (1963) Configurational Statistics of Polymeric Chains. Engl translation, Interscience, New York.

For a general review of the molecular dynamics method see, for example: Klein ML (1985) Computer Simulation Studies of Solids. Ann Rev Phys Chem 36: 525–548. Suter U, Monnerie L eds (1994) Atomistic Modelling of Physical Properties of Polymers. Springer, Berlin (Adv Polymer Sci, vol 116).

A general collection of papers on simulations is given in: Roe RJ, ed (1991) Computer Simulation of Polymers. Prentice Hall, Englewood Cliffs.

Sect. 1.4. A number of books specializing on the techniques of polymer characterization are: White JR (1989) Polymer Characterization. Chapman and Hall, New York. Barth HG, Mays JW (1991) Modern Methods of Polymer Characterization. Wiley-Interscience, New York. Compton TR (1989) Analysis of Polymers: An Introduction. Pergamon Press, New York. Craver CD (1983) Polymer Characterization. Am Chem Soc Washington DC (Advances in Chemistry Series 203).

Specific References

1.Pauling L (1960) The Nature of the Chemical Bond.. Cornell University Press, 3rd edn, Ithaca, NY.

2.Kroto HW, Heath JR, O’Brien SC, Curl RF, Smalley RE (1985) C60: Buckminsterfullerene. Nature 318: 162–163.

3.The first write-up of the suggested classification of molecules including macromolecules was given in: Wunderlich B. (1980) Macromolecular Physics, Vol. III, Sect. 8.1.2. Academic Press, New York. See also a recent summary: Wunderlich B (1999) A Classification of Molecules and Transitions as Recognized by Thermal Analysis. Thermochim Acta 340/41: 37–52.

4.Staudinger H (1920) Über Polymerisation. Ber 53: 1073–1085.

5.IUPAC Commission on Macromolecular Nomenclature: (1976) Nomenclature of Regular Single-stranded Organic Polymers. Pure Appl Chem 48: 375–385; (1985) Source-based Nomenclature for Copolymers. Ibid 57: 1427–1440.

6.Newkome GR; Morefield CN; Vogtle F (2001) Dendrimers. Wiley, Chichester, UK, second edn.

7.Raymo, FM, Stoddart JF (1999) Interlocked Macromolecules. Chem Rev 99: 1643–1663.

8.Sperling LH, Fay JJ, Murphy CJ, Thomas DA (1990) Interpenetrating Polymer Networks, The State of the Art. Makromol Chem Makromol Symp 38: 99–113.

9.Lowry GG (1970) Markov Chains and Monte Carlo Calculations in Polymers. Marcel Dekker, New York.

10.Wall FT, Erpenbeck JJ (1959) Statistical Computation of Radii of Gyration and Mean Internal Dimensions of Polymer Molecules. J Chem Phys 30: 637–640.

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11.Cheng SZD, Noid DW, Wunderlich B (1989) Molecular Segregation and Nucleation of Poly(ethylene oxide) Crystallized from the Melt. IV. Computer Modeling. J Polymer Sci Part B Polymer Phys 27: 1149–1160.

12.Miller KJ, Hollinger HB Grebowicz J, Wunderlich B (1990) On the Conformations of Poly(p-xylylene) and its Mesophase Transitions. Macromolecules 23: 3855–3859.

13.Noid DW, Sumpter BG, Wunderlich B (1990) Molecular Dynamics Simulation of the Condis State of Polyethylene. Macromolecules 23: 664–669.

14.Sumpter BG, Noid DW Wunderlich B (1990) Computer Experiments on the Internal Dynamics of Crystalline Polyethylene: Mechanistic Details of Conformational Disorder. J Chem Phys 93: 6875–6889.

15.Noid DW, Sumpter BG, Wunderlich B, Pfeffer GA (1990) Molecular Dynamics Simulations of Polymers: Methods for Optimal Fortran Programming. J Comp Chem 11: 236–241.

16.Kuhn W (1936) The Relationship Between Molecular Size, Statistical Molecular Shape, and Elastic Properties of Highly Polymerized Substances. Kolloid Z 76: 258–271.

17.Hughlin MB (1972) Light Scattering from Polymer Solutions. Academic Press, London.

18.Stacey KA (1956) Light Scattering in Physical Chemistry. Academic Press, New York.

19.Strutt JW (Lord Rayleigh) (1914) Diffraction of Light by Spheres of Small Relative Index. Proc Roy Soc London (A) 90: 219–225.

20.Zimm BH (1948) The Scattering of Light and the Radial Distribution Function of Highpolymer Solutions. J Chem Phys 16: 1093–1099.

21.Zimm BH (1948) Apparatus and Methods for Measurement and Interpretation of the Angular Variation of Light Scattering; Preliminary Results on Polystyren Solutions. J Chem Phys 16: 1099–1116.

22.Data by Billmeyer, Jr. FW, Kokle, V (1964) The Molecular Structure of Polyethylene. XV. Comparison of Number-average Molecular Weights. J Am Chem Soc 86: 3544–3546.

23.Einstein A (1906) Eine neue Bestimmung der Moleküldimensionen. Ann Phys 19:

289–306 [correction Ann Phys (1911) 34: 591–592].

23.Debye P (1944) Light Scattering in Solutions. J Appl Phys 15: 338–342.

24.Debye P (1947) Molecular-weight Determination by Light Scattering. J Phys Colloid Chem 51: 18–32.

25.Suwa T, Takehisa M, Machi S (1973) Melting and Crystallization Behavior of Poly(tetrafluoroethylene). New Method for Molecular Weight Measurement of Poly(tetrafluoroethylene) Using a Differential Scanning Calorimeter. J Appl Polymer Sci 17: 3253–3257.

26.Sperati CA, Starkweather, Jr. HW (1961) Fluorine-containing Polymers. II. Polytetrafluoroethylene. Adv Polymer Sci 2: 465–495.

27.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 B 35: 731–747.

CHAPTER 2

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Basics of Thermal Analysis

The basic, macroscopic theories of matter are equilibrium thermodynamics, irreversible thermodynamics, and kinetics. Of these, kinetics provides an easy link to the microscopic description via its molecular models. The thermodynamic theories are also connected to a microscopic interpretation through statistical thermodynamics or direct molecular dynamics simulation. Statistical thermodynamics is also outlined in this section when discussing heat capacities, and molecular dynamics simulations are introduced in Sect. 1.3.8 and applied to thermal analysis in Sect. 2.1.6. The basics, discussed in this chapter are designed to form the foundation for the later chapters. After the introductory Sect. 2.1, equilibrium thermodynamics is discussed in Sect. 2.2, followed in Sect. 2.3 by a detailed treatment of the most fundamental thermodynamic function, the heat capacity. Section 2.4 contains an introduction into irreversible thermodynamics, and Sect. 2.5 closes this chapter with an initial description of the different phases. The kinetics is closely linked to the synthesis of macromolecules, crystal nucleation and growth, as well as melting. These topics are described in the separate Chap. 3.

2.1 Heat, Temperature, and Thermal Analysis

The introductory discussion on thermal analysis begins with a brief outline of the history of the understanding of heat and temperature. Heat is obviously a macroscopic quantity. One can feel its effect directly with one’s senses. The microscopic origin of heat, the origin on a molecular scale, rests with the motion of the molecules of matter discussed in Sect. 2.3. The translation, rotation, internal rotation, and vibration of molecules are the cause of heat. Temperature, in turn, is more difficult to comprehend. It is the intensive parameter of heat. Before we can arrive at this conclusion, several aspects of heat and temperature must be considered. A short description based on experiments is given in Sects. 2.1.5 and 2.1.4 and more details are found in Sects. 4.2 and 4.1.

2.1.1 History

The scheme of the elements of the ancient Greek philosophers of some 2500 years ago contained heat (fire) as one of the four basic elements. The other three elements were the phases, gas (air), liquid (water), and solid (earth) as discussed in Sect. 2.5 and Chap. 5. Figure 2.1 is an illustration of this ancient scheme. It is interesting that the logo of the International Confederation for Thermal Analysis and Calorimetry,

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paragraphs are reprinted in Fig. 2.2. In the first paragraph, Lavoisier1 states the difficulties with respect to the word heat. Without knowledge about the origin of heat, he suggests the solution, copied in Fig. 2.2. He points out that after the introduction of the word caloric for the substance of heat, one can go ahead and investigate the effects of heat without inconsistency of nomenclature. Indeed, the calorimetric theory was well developed before full knowledge of heat as molecular motion was gained.

It is interesting that today one would not accept the ultimate experiments which at the end of the 19th century supposedly disproved the theory of the caloric. The main difficulty in the caloric theory was the explanation of friction. Friction seemed to be an inexhaustible source of caloric. For measurement Count Rumford in 1798 used a blunt drill “to boil 26.5 pounds of water.” The only effect on the metal was to shave off 4.145 grams. Next, he could prove that the capacity of heat of this powder, meaning the amount of heat to raise its temperature by a fixed amount, was identical to that of the uncut material. He argued that the fact that the powder had the same capacity for heat also proved that there was no caloric lost in shaving off the metal. This obviously is insufficient proof. The powder may have had the same capacity for heat, but it was not proven to have a smaller heat content. For a complete proof, one would have to reconvert the powder into solid metal and show that in this process there was no need to absorb caloric, a more difficult task. Count Rumford himself probably felt that his experiments were not all that convincing, because at the end of his paper he said, in a more offhand analysis: “In any case, so small a quantity of powder could not possibly account for all the heat generated, . . . the supply of heat appeared inexhaustible.” Finally, he stated, “Heat could under no circumstances be a material substance, but it must be something of the nature of motion.” So, one has the suspicion that Count Rumford knew his conclusions before he did the experiment.

The other experiments usually quoted in this connection were conducted by Humphry Davy2 in 1799. He supposedly took two pieces of ice and rubbed them together. During this rubbing, he produced large quantities of water. Ice could, thus, be melted by just rubbing two pieces of ice together. Since everyone knows that one must use heat to melt ice, this was in his eyes proof that caloric could not be the reason for fusion and the “work of rubbing” had to be the cause of melting. The unfortunate part of this otherwise decisive experiment is that one could not repeat it under precise conditions. It is not possible to rub two pieces of ice together to produce water. The friction is too little. If one increases the friction by using pressure, the melting temperature is reduced, so that melting occurs by conduction of heat. One must again conclude that Davy got results he was expecting and did not analyze his experiment properly for conduction of heat, the probable cause of the melting. The experiments, however, were accepted by the scientific community, and since the conclusions seemed correct, there was little effort for further experiments.

1 Antoine-Laurent Lavoisier, 1743–1794. Leading French Chemist of the 18th century. Well known for his development of the understanding of the reactions of oxygen. As a public administrator before the French Revolution, he was executed during the revolutionary terror.

2 Sir Humphry Davy, 1778–1829. English Chemist and Fellow of the Royal Society who discovered sodium, potassium, and iodine and is known for his early work on electrolysis.

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A mathematical theory of the caloric, seemingly in contrast to these experiments, was given by Carnot1, based on the efficiency of a reversible heat engine, which seemed to rest on the assumption of a conserved material of heat (the caloric). The qualitative arguments of Count Rumford and Davy, however, could finally be proven by the quantitative experiments of Joule2 in the 1840s. From these experiments he inferred properly that heat was a state of motion, not a material. In the early 1850s this conflict to Carnot’s findings was finally resolved by Kelvin3 and Clausius4. Joule had correctly asserted that heat could be created and destroyed proportionally to the exchanged amount of mechanical, electrical, or chemical energy (first law of thermodynamics, the total energy of a system is conserved, see Sects. 2.1.5 and 2.2.2), but Carnot’s result also holds, it rests not on the conservation of heat, but of entropy (under reversible conditions, the change in entropy is zero, second law of thermodynamics, see Sect. 2.2.3).

Since language is rarely corrected after scientific discovery of old errors, some of this confusion about heat is maintained in present-day languages. Several different meanings can be found in any dictionary for the noun “heat.” A good number of these have a metaphorical meaning and can be eliminated immediately for scientific applications. Eliminating duplications and separating the occasionally overlapping meanings, one finds that there remain four principally different uses of the word heat. The first and primary meaning of heat describes the heat as a physical entity, energy, and derives it from the quality of being hot which, in turn, describes a state of matter. An early, fundamental observation was that in this primary meaning, heat describes an entity in equilibrium. Heat is passed from hot to cold bodies, to equilibrate finally at a common, intermediate, degree of hotness. In the seventeenth and the eighteenth century, this observation was the basis of the theory of the caloric, as described above. Heat was assumed to be an indestructible fluid that occupies spaces between the molecules of matter as sketched in Figure 1.2.

Turning to the other meanings of the word heat listed in most dictionaries, one finds that a degree of hotness is implied. This indicates that heat is still confused with its intensive parameter temperature. The example “the heat of this room is unbearable” is expressed correctly by saying “the temperature of this room is unbearable.” The improper use of heat in this case becomes clear on recognizing that,

1 Sadi Carnot, 1824, lived 1796–1832, French army officer and “constructor of steam engines.”

2 James P. Joule, 1818–1889, English physicist. He found that the energy of an electric current can produce either heat or mechanical work, each with a constant conversion factor.

3 William Thomson, 1st Baron Kelvin of Largs, 1824–1907, Scottish engineer, mathematician, and physicist. Professor at the University of Glasgow, England. His major contributions to thermal analysis concern the development of the second law of thermodynamics, the absolute temperature scale (measured in kelvins) and the dynamic theory of heat.

4 Rudolf Clausius, 1822–1888, Professor at the University of Bonn. German mathematical physicist who independently formulated the second law of thermodynamics and is credited with making thermodynamics a science.

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depending on the matter inside the room, the same temperature can be produced by different amounts of heat. A more detailed description of the term temperature will be given in Sects. 2.1.4 and 4.1.

The third meaning of heat involves the quantity of heat. This reveals that heat actually is an extensive quantity, meaning that it doubles if one doubles the amount of material talked about. Doubling the size of an object will take twice the amount of heat to reach the same degree of hotness (temperature).

Finally, a fourth meaning connects heat with radiation. This meaning is not clearly expressed in most dictionaries. Again, turning to Lavoisier’s “Elements of Chemistry,” he wrote there: “In the present state of our knowledge we are not able to determine whether light be a modification of caloric, or caloric be, on the contrary, a modification of light.” Very early, people experienced that the sun had something to do with heat, as expressed in terms like “the heat of the sun.” The inference of a connection between heat and color also indicates a link between heat and radiation through expressions like red-hot and white-hot, as expressed in the physiological temperature scale described in Sect. 4.1. Today, one should have none of these difficulties since we know that heat is just one of the many forms of energy. The radiant energy of the sun, felt as heat, is the infrared, electromagnetic radiation. By absorption into matter, it is converted to heat, the energy of molecular motion.

As a result of not changing the use of language during the last 200 years, today each child is still first exposed to the same wrong and confusing meanings based on the centuries-old misconceptions. Only later and with considerable effort do some acquire an understanding of heat as the extensive, macroscopic manifestation of the microscopic molecular motion and temperature as its intensive parameter, perhaps best expressed by the ideal gas theory, described in Figs. 2.8 and 9.

2.1.2 The Variables of State

Six physical quantities are commonly used for the description of the state of matter, hence they are called variables of state. They are, with their SI units given in parentheses, the total energy, U (J), temperature, T (K), volume, V (m3), pressure, p (Pa), number of moles, n (mol), and mass, M (kg). The SI units are summarized in some more detail in Fig. 2.3 [1].1 Of these variables of state, the quantities whose magnitudes are additive when increasing the system are called extensive, i.e., they double with doubling of the system. Quantities whose magnitudes are independent of the extent of the system are called intensive. Of the listed functions, T and p are intensive, all others are extensive. Furthermore, infinitesimal changes of the variables of state are indicated by the letter “d.” For partial infinitesimal changes, as arise when restrictions are placed on the variables, one writes the symbol “ ” instead of “d.” It signifies that in this case all but one variable of state are kept constant. When necessary, the variables kept constant are identified by subscripts.

1 There are four simple rules to satisfy the SI rules: 1.) Use only SI units. 2.) Use only numerical values from 0.1 to 999. 3.) Scale other values by using prefixes such as k = 1,000, M = 1,000,000, m = 1/1,000, = 1/1,000,000. 4.) Use only one scaling prefix and use it only in the numerator.

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Fig. 2.3

The first law of thermodynamics states simply that the total energy U is conserved, i.e., there can be no production or loss of energy, as discussed in more detail in Sects. 2.1.5 and 2.2.2. An identical conservation law exists for mass M. Both of these conservation laws must, however, be combined if the velocity of the described matter approaches the speed of light or during nuclear reactions. In these cases the ratio of U to M may change, but in a fixed ratio, given by: U/ M = c2, the Einstein equation, where c is the speed of light, a constant, and U and M signify the changes in energy and mass, respectively. For all topics of this book such speeds and nuclear processes are of no concern and one can use the independent laws of energy and mass conservation.

Heat, Q, and work, w, are two forms of energy that appear when energy is exchanged between systems. The heat and work are not stored as such in the system, i.e., one cannot allot definite parts of the energy content of a system to heat and work. Their infinitesimal changes depend on the path taken to accomplish the change, and are thus marked by a Greek “ ” instead of d or which represent infinitesimal changes of state. The change is used to express the overall change in total energy dU = Q + w. This equation represents the first law of thermodynamics. In words, it can be said that the sum of heat and work exchanged must equal the change in total energy U, the parts exchanged as heat and work may, however, be much different for different paths. The only condition is that their sum (= dU) is the same for all paths.

2.1.3 Techniques of Thermal Analysis

Thermal analysis is the analytical technique that establishes the experimental data for the variables of state. Details about the definition of thermal analysis are given in Fig. 2.4. The six most basic thermal analysis techniques which allow the determina-