Thermal Analysis of Polymeric Materials

__________________________________________________________________

3.Wasserman PD (1989) Neural Computing, Theory and Practice, Van Nostrand Reinhold, New York.

4.The application of neural networks to are described by Noid DW, Varma-Nair M, Wunderlich B, Darsey, JA (1991) Neural Network Inversion of the Tarasov Function Used for the Computation of Polymer Heat Capacities. J Thermal Anal 37: 2295–2300.

5.Darsey JA, Noid DW, Wunderlich B, Tsoukalas L (1991) Neural-Net Extrapolations of Heat Capacities of Polymers to Low Temperatures. Makromol Chem Rapid Commun 12: 325–330.

6.Moore WG (1972) Physical Chemistry. Fourth Ed, p vi, Prentice-Hall, Englewood Cliffs, NJ.

7.Bumstead HA, Gibbs Van Name R (1906) The Scientific Papers of J. Willard Gibbs. Longmans, Green and Co. Reprinted by Dover Publications, New York, 1961.

8.Lewis GN, Randall M (1923) Thermodynamics, p 448. McGraw–Hill, New York; revised second ed by Pitzer KS, Brewer L (1961) p 130.

9.A modern adiabatic calorimeter is described by: Gmelin E, Rödhammer P (1981) Automatic Low Temperature Calorimetry for the Range 0.3 320 K. J Phys E, Instrument.

14:223–238.

10.Höhne GWH, Hemminger WF, Flammersheim H-J (2003) Differential Scanning Calorimetry. 2nd edn, Springer, Berlin.

11.Reading M (1993) Modulated Differential Scanning Calorimetry–A New Way Forward in Materials Characterization. Trends in Polymer Sci 1(8): 248–253.

12.For the original paper on the Nernst-Lindemann approximation see: Nernst W, Lindemann FA (1911) Spezifische Wärmen und die Theorie der Energieeinheiten. Z Electrochem 17: 817–827.

13.For the original paper on the Dulong-Petit rule see: Petit AT, Dulong PL (1819) Recherches de la Théorie de la Chaleur. Ann Chim Phys 10: 395–413.

14.Pan R, Varma M, Wunderlich B (1989) On the Cp to Cv Conversion for Solid Linear Macromolecules II. J Thermal Anal 35: 955–966.

15.Einstein A (1907) Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme. Ann Physik 22: 180–190 (corrections p 800).

16.Debye P (1912) Zur Theorie der spezifischen Wärme. Ann Physik 39: 789–839.

17.Schrödinger E (1926) in Geiger H, Scheel K, eds, Handbuch der Physik. Springer, Berlin, Vol 10, p 275.

18.Gaur U, Pultz G, Wiedemeier H, Wunderlich B (1981) Analysis of the Heat Capacities of Group IV Chalcogenides using Debye Temperatures. J Thermal Anal 21: 309–326.

19.Baur H, Wunderlich B (1998) About Complex Heat Capacities and Temperaturemodulated Calorimetry. J Thermal Anal and Calorimetry 54: 437–465.

20.See for example: Hirschfelder JO, Curtis CF, Bird RB (1954) Molecular Theory of Gases and Liquids. Wiley, New York (§11.4b).

21.The experimental data of the ATHAS Data Bank are published under the title: Heat Capacity and Other Thermodynamic Properties of Linear Macromolecules. Gaur U, Shu H-C, Mehta A, Wunderlich B (1981) I. Selenium. J Phys Chem Ref Data 10: 89–117; Gaur U, Wunderlich B (1981) II. Polyethylene. Ibid 10: 119–152; III. Polyoxides. Ibid

10:1001–1049; IV. Polypropylene. Ibid 10: 1051–1064; Gaur U, Wunderlich B (1982) V. Polystyrene. Ibid 11: 313–325; Gaur U, Lau S-F, Wunderlich BB, Wunderlich B (1982) VI. Acrylic Polymers. Ibid 11: 1065–1089; Gaur U, Wunderlich BB, Wunderlich B (1983). VII. Other Carbon Backbone Polymers. Ibid 12: 29–63; Gaur U, Lau, S-F, Wunderlich BB, Wunderlich B (1983) VIII. Polyesters and Polyamides. Ibid 12: 65–89; Gaur U, Lau S-F, Wunderlich B (1983) IX. Aromatic and Inorganic Polymers. Ibid 12: 91–108; Varma-Nair M, Wunderlich B (1991) X. Update of the ATHAS 1980 Data Bank. Ibid 20: 349–404.

188 2 Basics of Thermal Analysis

__________________________________________________________________

22.Barnes J, Fanconi B (1978) Critical Review of Vibrational Data and Force Field Constants for Polyethylene. J Phys Chem Ref Data 7: 1309–1321.

23.Zhang G, Gerdes S, Wunderlich B (1996) Heat Capacities of Solid Globular Proteins. Macromolecular Chem Phys 197: 3791–3806.

24.Wunderlich B (1964) A Thermodynamic Description of the Defect Solid State of Linear High Polymers. Polymer 5: 125–134; The Melting of Defect Polymer Crystals. Ibid 5: 611–624.

25.Ehrenfest P (1933) Phase Changes in the Ordinary and Extended Sense Classified According to the Corresponding Singularities of the Thermodynamic Potential. Proc Acad Sci, Amsterdam 36: 153–157, Suppl 75b, Mitt Kammerlingh Onnes Inst, Leiden.

26.Hosemann, R (1963) Crystalline and Paracrystalline Order in High Polymers. J Appl Phys 34: 25–41.

27.Chen W, Wunderlich B (1999) Nanophase Separation of Small and Large Molecules. Invited feature article Macromol Chem Phys 200: 283–311.

28.Glasses obtained on cooling of liquid crystalline mesophases were first described by: Vorlaender, D (1933) Remarks on Liquocrystalline Resins and Laquers. Trans Farad Soc 29: 907–910.

CHAPTER 3

___________________________________________________________________

Dynamics of Chemical and Phase Changes

The field of dynamics belongs into physical chemistry and deals with the kinetics of making and breaking of bonds in molecules and changes in phases. For macromolecules the basic processes are the syntheses, alteration, and decompositions of polymers and the crystallization and melting. To some degree the kinetics of the glass transition is also of interest. The polymerization kinetics is divided into four major types, as described in Sects. 3.1 and 3.2 (stepwise, step, matrix, and chain reactions). These syntheses lead to different molecular mass distributions, as described in Sect. 3.3. Once a macromolecule is made, its decomposition and its modification by polymer reactions can also be studied in Sect. 3.4 using kinetics, along with facts about polymerization, copolymerization, and cross-linking. Crystal nucleation, molecular nucleation, crystal growth and melting are used to illustrate the kinetics of phase changes in Sects. 3.5 and 3.6. Information on the time-dependence of the glass transition is given in Sects. 5.6, 6.1, and 6.3. Crystallization and melting of flexible macromolecules are often, but not always, free of reorganization of strong bonds. Crystallization during polymerization [1] and decomposition during melting provides connections between flexible and rigid macromolecules (see Sect. 1.1).

3.1 Stepwise and Step Reactions

3.1.1 Stepwise Reactions

Syntheses of pure macromolecules are common in biochemistry, but rare for synthetic polymers. In a pure substance all molecules have the same composition and structure. Most syntheses of polymers, however, give a rather broad range of molecular lengths and may also introduce randomly placed isomers and comonomers, as described in Chap. 1 and discussed in more detail in this chapter. The biological molecule ribonuclease, as a well-studied example, is from a class of proteins that functions as an enzyme to control catalytically the transfer of phosphorus containing groups to cleave ribonucleic acids. Its chemical structure is written as C575H901O193N171S12, making it a rather small macromolecule. The structure consists of a chain of 17 different amino acids from the 20 commonly found in nature. Of these, none occur in blocks longer than three identical amino acids. The general structure is H2N–(CRiH–CO–NH–)123 CRjH–CO–OH, where i and j represent the side-groups of the different amino acids. All of its different amino acids are arranged in an identical sequence within each ribonuclease molecule, so that all molecules are of identical length and have a a molar mass of 13,682 Da. Figure 3.1 displays the sequence

190 3 Dynamics of Chemical and Phase Changes

___________________________________________________________________

Fig. 3.1

distribution of the polymer with the three-letter codes representing the amino acid repeating units (ala = alanine, val = valine, leu = leucine, etc.). The number of different proteins that could be made of the 20 naturally occurring amino acids with the same length as ribonuclease is practically unlimited. One can imagine 20124 (or 10161) different pure molecules with 124 repeating units! On this example one can see the importance to predict the one molecule that gives the most ideal properties for the problem on hand. It would be an impossible task to make the different molecules and then search for the most suitable application.

A straight-forward approach to the synthesis of pure substances, which can be extended to pure copolymers such as the ribonuclease, is the stepwise addition of one monomer, A, to a monomer, B, followed by separation from the excess chemicals. A third step can then add the next monomer. Again, separation from the excess chemicals has to follow this reaction step. This separation becomes more difficult as the chain gets longer, since the differences in properties between the successively made molecules become smaller as one approaches the length of polymer molecules. A yield of 90% for each of the 123 steps needed to make ribonuclease, for example, would produce only 0.002% of the polymer. In order to make a reasonable amount, the enormous, practically impossible yield of 99% must be achieved for each combined reaction and separation step. Only then can one count on converting 29% of the monomers into the proper polymer.

Considerable help became available through the Merrifield method [2,3], as is illustrated in the sequence of reactions in Fig. 3.2. A gel consisting of an open polymeric network is first produced (see Fig. 3.48, below), for example, of polystyrene, cross-linked with 2% divinylbenzene. The first step of the synthesis is the activation of some of the phenyl groups of the polystyrene by a Friedel-Crafts reaction with methylchloromethylether in the presence of tin tetrachloride. The reaction

___________________________________________________________________

Fig. 3.2

produces methyl alcohol and attaches the methylene chloride group onto a styrene repeating unit of the gel, as shown. In step 2, the active group reacts with a blocked amino acid. The blocking hinders the addition of additional amino acids in the polymerization step 2 and stops the reaction at point 3. After each step of the reaction, the separation of the reactants is rather simple. The product of interest is attached to the network, and all excess reactants and side-products can be flushed by rinsing the gel. After rinsing of all excess chemicals, step 4 in Fig. 3.2 shows how deblocking produces the reactive, attached amino acid. Extension by one additional amino acid is now possible in step 5. Repeating the deblocking, step 4, and extension, step 5 for (x – 2) times, produces a polymer with the designed sequence of x amino acids, shown as the equation in step 6. The final step consists of the recovery of the polymer by cleaving it off the gel with HBr. The Merrifield reaction scheme permits automation of the stepwise reactions with computer control of each step and switching to preselected, different amino acids. Still, a limited yield remains, but can be helped by using longer sequences as starting material or reactant. This technique and related methods are used today for generating unique, short polyamino acids [4].

An oligomer is a molecule made of a number of repeating units, too short to be called a macromolecule which needs to have more than 1000 atoms (Gk. & = few, = part). In Fig. 3.3 several methods for the synthesis of oligomers are suggested. The illustrated example has been used to make longer paraffins as model compounds for polyethylene [5,6], several other series of oligomers have also been prepared [7–9]. As the chain-length increases, the initial monomers change to higherboiling oligomers, and finally become solid.

A specially interesting method for making oligomers is the etching of lamellar crystals with well-defined thickness, as mentioned in Fig. 3.3. Chain-folded crystals of polymers are described in Sect. 5.2. Their lamellar surfaces consist of folds, loose

192 3 Dynamics of Chemical and Phase Changes

___________________________________________________________________

Fig. 3.3

ends, and ties to other crystals and the remaining amorphous phase. All these materials etch faster than the crystal interior. It is, thus, possible by etching to get oligomers with lengths of the crystal thickness in the chain direction [9]. Applications have been, for example, the production of microcrystalline powders [10] and the study of the length for beginning of chain folding in polymer crystals [11].

Oligomers are too short to have typical polymer properties, but they establish the important relationship of the properties as a function of molecular length when going from a small molecule to its corresponding macromolecule. As long as the oligomer is rather short, it can still form, for example, equilibrium crystals and give, thus, a reliable extrapolation of the equilibrium melting temperature that otherwise may not always be available. For example, Fig. 3.4 shows schematically how the melting temperatures of paraffin crystals approach that of polyethylene. The crystal structure changes little in the basic lateral packing of the chains, but there is a decreasing effect from the chain ends. Note that little change occurs after one reaches the polymer molecular mass range (> 10,000 Da). The equation listed gives a good empirical fit to the experimental data.

Quite different is the change of viscosity, , plotted in Fig. 3.5. As soon as a length of about 1,000 mobile backbone units, z, designated as number of beads, is reached, increases faster with molar mass. This is due to entanglements of the molecules, a typical polymer property. The viscosity is a property which does not reach a limiting value when macromolecular dimensions are reached. A similar dependence on length as for the melting exists for the glass transition temperature, Tg, displayed in the bottom half of Fig. 3.5 for the example of polystyrene. At Tg, the large-amplitude molecular motion of the viscous liquid stops. Macroscopically, the liquid becomes a solid with mainly vibrational motion, as is discussed in Sect. 2.5. More details about the entanglements and glass transition are given in Chaps. 5–7.

___________________________________________________________________

Fig. 3.4

Fig. 3.5

3.1.2 Mechanism of Step Reactions

In Sect. 3.1.1 it was established that polymerization reactions must have high precision in repetition in order to yield macromolecules. The two most common reactions for such high-yield polymerizations are step-growth and chain-growth polymerizations.

194 3 Dynamics of Chemical and Phase Changes

___________________________________________________________________

These two reactions have largely different reaction paths and lead to different molarmass distributions which are often rather broad and must be described using the techniques derived in Sect. 1.3. Step-growth polymerization is treated in the remaining part of this Sect. 3.1, chain-growth polymerization is covered in Sect. 3.2.

Figure 3.6 illustrates an idealized, kinetic reaction scheme of a step reaction. Molecules of all lengths are at all times able to extend. In reality, the forward reaction is usually able to reverse and to depolymerize or to connect the chain ends to rings.

Fig. 3.6

Assuming a chemical group A can react only with a second group B, as for an alcohol and an acid on esterification, one can think of two types of such polymerizations. One occurs with identical monomers with oppositely reacting groups on the ends of each molecule, as in A B, shown in the top two reaction schemes of Fig. 3.6, the other occurs between two different monomers, each with two identical groups on its ends, as shown in the second three reactions of Fig. 3.6. The five major characteristics of step-reaction polymerizations are listed at the bottom of Fig. 3.6 and will be detailed next. Point 5 is particularly troublesome since it will lead to an inactive molecule.

A simple example of the beginning of a step-growth polymerization is outlined in Fig. 3.7. A purely kinetics-controlled reaction is assumed, as in Fig. 3.6. The scheme of Fig. 3.6 allows no reverse reaction, and for Fig. 3.7, ring formation is also excluded, so that only oligomer chains are produced. Under these conditions, the indicated 16 monomer molecules can be connected with 15 bonds to each other, i.e., they do not polymerize completely. The sequence of steps is indicated by the different shadings of the bonds. After step 1, 25% of the reaction is completed (solid bonds). Only few dimer molecules have been produced, but the monomer weight fraction is already cut in half, as shown in the first column of the table. There is no indication of oligomers or polymers in the distribution of mers listed in the figure.

___________________________________________________________________

Fig. 3.7

Step 2 is shown after half of the reaction is over. Larger molecules have now appeared, and the weight fraction of monomers is less than 0.2. Still, one is far from having made polymer molecules. The early decrease in monomer concentration and the late appearance of polymers is typical for the step-growth mechanism.

Step 3 of the schematic of Fig. 3.7 has the reaction completed to 75%. Monomer molecules have now disappeared, and all molecules are different, i.e., a broad molarmass distribution has developed, again typical of step-growth polymerization. Larger oligomers are still absent. In the last step of this simple example, 14 of the 16 possible bonds are made (87.5%). Now, larger oligomer molecules appear, illustrating the importance to drive step-growth reactions almost to completion. In the above mentioned esterification, completion is forced by removing the produced water:

R OH + H OCO R' R OCO R' + H2O

The statistics of the step-growth polymerizations in Fig. 3.6 is rather easy to develop. If type A B monomers are the reactants, one sets their initial number equal to No. To use the same No for the reaction of A A with B B, one must begin the reaction in the second case with precisely equal numbers of No/2 of each monomer. The number of molecules in the reaction mixture, N, is then always the number of A- units that remain unreacted. The fractional conversion, p, and the degree of polymerization, DP, can then be calculated as shown in Fig. 3.8. The number-average molar mass can also be calculated using the formalism of Fig. 1.25.

The table in Fig. 3.8 is calculated for a relatively large repeating unit, ethylene terephthalate (Mo = 192.16 Da, 22 atoms) and illustrates that at least 99% completion is necessary to drive the reaction to a range of lengths required for linear macromolecules. A DP of 100 is a macromolecule of 2,200 atoms and a molar mass of about 20,000 Da, both values typical for a polyester which is industrially useful.