Thermal Analysis of Polymeric Materials Part 14 pptx

Glass Transitions of Block Copolymers The chemical structure of block copolymers is given by the number of blocks, theirsequence, and their length, as discussed in Sect.. crystalliza-Fig

Fig 7.75

in Fig 7.73 [33] The straight-forward interpretation is that some, but not all of thelow-molar-mass polystyrene is dissolved in the poly(-methylstyrene) The solubilitycan be reduced by increasing the molar mass of the polystyrene component Thehigher glass transition is then much sharper and approaches the proper Cp Witheven higher molar mass, one can reach complete immiscibility, as shown

7.3.3 Glass Transitions of Copolymers

While for solutions of homopolymers the mixing of the chain segments may beincomplete when compared to the intermolecular mixing, the distribution of the chainsegments of the copolymers are fixed by the polymerization reaction, as described inSect 3.4, i.e., the same concentration can yield different segment distributions andglass transitions The change of the glass transition with composition and randomness

of the repeating units along the chain is demonstrated in Fig 7.71 for

poly(styrene-co-acrylonitrile) based on the Barton equation Two further examples are given in

Figs 7.76 and 7.77 for poly(acrylonitrile-co-1,4-butadiene) and

poly(styrene-co-methyl methacrylate) [34], respectively As expected, the average Tg of the twohomopolymers, the Tgfor the critical run number R* (= 81.8, see Fig 7.70), and thealternating copolymers (R = 100) lie on a straight line The usually inaccessibleregion between the alternating copolymer and the value for R* was achieved withspecial control of the sequence regularity The data in Fig 7.77 exhibit a minimum

in Tgat an R-value of 65.2, corresponding to a styrene mole fraction of 0.57.Special complications arise when the stereospecific homopolymers show differentglass transitions for isotactic (I), syndiotactic (S), and heterotactic (H) chains Anexample is the poly(methyl methacrylate) The iso- and syndiotactic stereoisomers ofPMMA have glass transition temperatures of 315 and 400 K, respectively Treatingthe stereoisomers as copolymers with a modified Barton equation of Fig 7.70:

Fig 7.76

Fig 7.77

Tg = mITgI + mSTgS + mHTgH,the heterotactic glass transition was estimated as 391 K The different possiblePMMA polymers should thus be found in a triangle defined by these three limitingglass transitions The truly atactic polymer is specified by the parameters mI= mS=0.25 and m = 0.5, at 374 K

Another aspect of thermal analysis concerns the thermodynamic functions based

on heat capacity Obviously, the number of possible copolymers is so large, thatcomplete measurements for all copolymers are not possible Fortunately, the heatcapacity of glassy and liquid copolymers over wide temperature ranges are notstructure 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 issuggested in Fig 2.70 for the copolymers of styrene and butadiene (see also theaddition 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 onlyfew measured points it is possible to establish the functional relationship of the1and

3temperatures with concentration for the inter- and intramolecular vibrations (seeSect 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 inSect 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 systemswith polystyrene Below Tg, the solid Cpof both components needs to be added forthe heat capacity of the copolymer, above, the liquid Cp must be used The glasstransition retains the same shape and width as seen in Fig 7.68 on the example ofbrominated poly(oxy-2,6-dimethyl-1,4-phenylene) [29]

To summarize the basic information of the first three sections of this chapter, onerecognizes that the glass transitions for multicomponent systems must take intoaccount the mixing between and within the macromolecules The first is described byone 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 theBarton equation in Fig 7,70 The broadening of the glass-transition region in case ofsolutions in Fig 7.73, in contrast to random copolymers of Figs 2.70 and 7.68, istaken as an indication of nanophase separation The change in the sharpness of theglass-transition region is an important, often neglected tool for the characterization ofpolymeric materials and will be further explored in the discussion of the next twosections

7.3.4 Glass Transitions of Block Copolymers

The chemical structure of block copolymers is given by the number of blocks, theirsequence, 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, and354,500 Da, for example, has the following approximate chemical structure:

[CH2CH(C6H5)]3,000[CH2C(CH3)(C6H5)]3,000

For such large molar masses, the segments will separate into microphases, with thejunctions between the different repeating unit sequences defining the interfaces, as isdescribed 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 sufficientlylarge to allow independent, large-amplitude molecular mobility on both sides of thepoint of decoupling of the components Depending on the nature of the components,

Fig 7.78

glass transitions and ordering are possible within the separate phases The tion of the block copolymers is described in Sect 7.1.6, the glass transitions arediscussed next

crystalliza-Figure 7.78 represents the heat capacities of the homopolymers polystyrene andpoly(-methyl styrene) with sharp glass transitions at 375 and 443 K, respectively[35] On copolymerization to a triblock molecule, MSSMS(45), a much broaderglass 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 forsolubility when compared to Fig 7.75 in Sect 7.3.2 (Mw 106

Da) Similarly, thefigure indicates broad transition regions for the other copolymers

The interpretation of these data becomes clearer when introducing an entropyrelaxation by slow cooling before an analysis with a faster heating rate (seeSect 6.1.3) Figure 7.79 documents that the enthalpy relaxation centers at the glasstransitions of the homopolymers with a reduction in peak amplitude on copoly-merization that is larger than expected from the reduction in concentration This is thetypical behavior of phase-separated polymers Even more conclusive is that electronmicroscopy on the same samples reveals that all these high-molar-mass S/MS blockcopolymers are microphase-separated

Separate experiments on small spheres of polystyrene indicate that the glasstransition 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 thesmallness of the phase areas Figure 7.80 combines the data of Figs 13–15 togetherwith information on two of the block copolymers of Fig 7.78 which have an overalllamellar 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

Fig 7.79

Fig 7.80

T = Tg Tbor TeTg, where Tband Teare the beginning and the end of the glasstransition regions, respectively, defined in Fig 2.117 The value of T increasessharply with the surface area of the microphase For the transition of the phasessurrounded by a surface that connects to a phase of lower glass transition, the glasstransition starts at lower temperature (spheres of polystyrene in air and MS surrounded

Fig 7.81

by S), while a surrounding surface coupled strongly to a phase of higher glasstransition extends to higher temperatures (S surrounded by MS) In the blockcopolymers of Fig 7.78, this effect broadens the glass transition to such a degree thatthe two transitions practically fuse It is of interest to note that the broadening insolutions of polymers, which was linked to the inability to completely mix thehomopolymer chains with the solvent, extends symmetrically to both sides (seeSect 7.3.2) rather than to one side, as in the surface effect of Fig 7.78 Thermalanalysis is, thus, able to distinguish incomplete mixing from surface effects.Comparing the block copolymers of high molar mass to solutions of the samepolymers 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 datafor the bock copolymer solutions (run number R = 0), blocky copolymers (indicatedrun numbers R = 6 and 30), as well as random copolymers () [36]

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 changingcomposition from one end to the other Such block copolymers show, in addition tothe size and strain effects, a partial solubility A third phase due to the gradient inconcentration was not discovered for the analyzed samples

To summarize all copolymers, Fig 7.82 reproduces a three-dimensional plot of theBarton equation, as it was used throughout this chapter This graph allows thecorrelation 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 thespecific interactions (see Fig 7.69, Schneider equation) and the broadening of theglass transition, available from heat capacity analysis

Fig 7.82

7.3.5 Glass Transitions of Multi-phase Systems

Multi-phase systems have been discussed throughout the last two chapters and itbecame increasingly clear that thermal analysis of the glass transition region givesimportant information for the description of materials Every one of the sevencharacteristics 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 assolutions or as macro-, micro-, or nanophase-separated systems by measuring Tg, Cpand the broadness of the glass transition region

The broadening of the glass transition, prominently featured in this section, isqualitatively linked to the loss of cooperativity of the large-amplitude motion.Without cooperative behavior, the torsional oscillations about flexible bonds graduallylead at sufficiently high temperature to motions of larger amplitude, ultimatelyreaching rotational isomers of higher internal energy, E This motion leads to anendothermic contribution to the heat capacity, as discussed in Fig 2.33 Interactionsbetween the molecules hinder this motion and force a narrower glass transition rangewith a T2  T1 in Fig 2.117 of typically 3 to 10 K The early initiation of suchmolecular isomerism as a gradual endotherm of little cooperativity is seen forpolyethylene in Fig 2.65 for the glass as well as the crystal, and is discussed inSects 2.3.10, 2.1.6, and 5.3.4 The main reason for the gradual initiation ofconformational isomerism in polyethylene is the rather small volume requirement forinternal rotation which decreases the cooperativity of neighboring segments.The broadening of glass transitions in polymer solutions, as in Fig 7.73, and onpartial ordering, as in Fig 2.64, reaches the 50 and 100 K range of Tg Tbor 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 fromthe average value Only if sufficiently large phases of fully intra- and intermolecularlyrandomized mobile repeating units (beads) are present, does the glass transition getsharper This size-effect is illustrated in Fig 7.80 and is expected to change with thenature of the system.

Besides calorimetry, one has several other, quite sensitive thermal analysistechniques 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 tothe gradual increase of heat capacity that leads ultimately to the glass transition TheDMA is very sensitive to this early softening in the glassy region, but up to thepresent, 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) Thepolyethylenes of lower crystallinity are commonly copolymerized, as demonstrated

in Figs 7.37 and 7.38 An additional observation is that melting can begin within theglass 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 beanalyzed by quantitative DSC, as documented in Fig 6.105 and 6.106 The glasstransition must belong to the metastable mesophase of the polyethylene fibers and isbroadened considerably to higher temperatures

The glass transitions of crystals that can be treated as two-phase structures with atleast 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 incooperativity (dotted area) A similar, but macromolecular mesophase is shown inFig 2.68 In this case one can describe the sample as a multi-block copolymer Anormal, only slightly broadened amorphous glass transition occurs at about 275 K and

is decreased in Cpby 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 Asdiscussed in Sect 5.5, many of such two-part repeating units can be considerednanophase-separated (Figs 2.106 and 5.135) The broadening of glass transitions,thus, is an important characteristic for the description of polymers

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 3 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 copolymercrystallization 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 interactionparameter3, see: Flory PJ (1949) Thermodynamics of Crystallization in High Polymers IV

A Theory of Crystalline States and Fusion in Polymers, Copolymers, and their Mixtures withDiluents 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 vonKopolymeren Ibid 212: 97–112; (1968) Bemerkungen zur Kinetik der Kristallisation vonPolymeren Ibid 224: 36–46; (1967) Zur Dynamik des Schmelzens und Kristallisierens inMischungen (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 crystalswere shown by: Hanna S, Windle AH (1988) Geometrical Limits to Order in Liquid-crystalline 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, 4thed Wiley, New York

Cp gWunderlich B (1960) Study of the Change in Specific Heat of Monomeric and PolymericGlasses 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 Copolymersand the Second-order Transitions of Synthetic Rubbers I Noncrystalline Copolymers J ApplChem 2: 493–500; Wood LA (1958) Glass Transition Temperatures of Copolymers J PolymerSci 28: 319–330; for the relationship to the volume changes, see Kovacs AJ (1964) GlassTransition in Amorphous Polymers Phenomenological Study Fortschr Hochpolym Forsch 3:394–508

3 Hildebrand JH (1947) The Entropy of Solution of Molecules of Different Sizes J ChemPhys 15: 225–228

4 Huggins ML (1942) Some Properties of Solutions of Long-chain Compounds J PhysChem 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 HighPolymers: Polyethylene J Am Chem Soc 80: 3178–3182

7 Quinn FA, Jr, Mandelkern L (1959) Thermodynamics of Crystallization in HighPolymers: 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 EquilibriumConditions J Polymer Sci, Part A-2 7: 2073–2089

9 Pak J, Wunderlich B (2002) Reversible Melting of Polyethylene Extended-chain CrystalsDetected by Temperature-modulated Calorimetry J Polymer Sci, Part B: Polymer Phys40: 2219–2227

10 Wunderlich B, Melillo L (1968) Morphology and Growth of Extended Chain Crystals ofPolyethylene Makromol Chem 118: 250–264

11 Prime RB, Wunderlich B, Melillo L (1969) Extended-Chain Crystals V ThermalAnalysis 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 ofPolyethylene 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

26thNATAS 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

WAXS on Homogeneous Ethylene-propylene and Ethylene-octene Copolymers with HighComonomer Contents J Thermal Anal 46: 681–718.

17 Mathot VBF, ed (1993) Calorimetry and Thermal Analysis of Polymers HanserPublishers, Munich, 1993

18 Androsch R, Wunderlich B (2003) Specific Reversible Melting of Polyethylene JPolymer Sci, Part B: Polymer Phys 41: 2157–2173

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

Poly(oxy-1,4-20 Hanna S, Lemmon T, Spontak RJ, Windle AH (1992) Dimensions of Crystallites in aThermotropic Random Copolyester Polymer 33: 3–10

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

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

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

24 Varma-Nair M, Habenschuss A, Wunderlich B (1992) Phase Transitions inPoly(4-hydroxybenzoic acid), Poly(2,6-hydroxynaphthoic acid) and their Copolymers.Proc 21stNATAS Conf in Atlanta GA, 21: 343–348

25 Ashman PC, Booth C (1975) Crystallinity and Fusion of Ethylene Oxide–PropyleneOxide 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

Nanophase-separated 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 inSemicrystalline Macromolecules Progress in Polymer Sci 28: 383–450

29 Bopp RC, Gaur U, Kambour RP, Wunderlich B (1982) Effect of Bromination on theThermal 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 GlassTransition Macromolecules 22: 1380–1384

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

33 Lau S-F, Pathak J, Wunderlich B (1982) Study of Phase Separation in Blends ofPolystyrene 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 ofStyrene–Methyl Methacrylate Copolymers Polymer 35: 3698–3702

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

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

37 Buzin AI, Pyda M, Matyjaszewski K, Wunderlich B (2002) Calorimetric Study of

Block-copolymers of Poly(n-butyl Acrylate) and Gradient Poly(n-butyl Acrylate-co-methyl

Methacrylate) Polymer 43: 5563–5569

Table of Thermal Properties of Linear Macromolecules and Related Small Molecules—The ATHAS Data Bank a

1 Poly(alkene)s 780

2 Poly(vinyl)s and Related Polymers 781

3 Aliphatic Poly(oxide)s 783

4 Poly(acrylate)s and (methacrylate)s 784

5 Aliphatic Poly(ester)s 785

6 Poly(itaconate)s 786

7 Aliphatic Poly(amide)s 787

8 Poly(amino Acid)s 787

9 Phenylene-containing Polymers 789

10 Poly(silylene)s 792

11 Poly(siloxane)s 792

12 Aliphatic and Aromatic Poly(sulfone)s 793

13 Inorganic Polymers 793

14 Paraffins and Perfluoroparaffins 793

15 Tetraalkylammonium Salts 797

16 Other Small Molecules 798

17 References 799

In the table the following symbols are used: The glass transition temperature is

listed as Tg; Cp is the change of the heat capacity at Tg for the fully amorphous sample; Tm is the equilibrum melting temperature; Hf, the heat of fusion for the 100% crystalline sample; S, H, and G are the entropy, enthalpy, and free enthalpy (Gibbs function), respectively; So represents the residual entropy at absolute zero based on the presented data; 3 and 1 are the characteristic temperatures for the contributions of the skeletal vibrations to the heat capacity; N represents the number

of skeletal vibrations per repeating unit (the total number of vibrations is given by the number of degrees of freedom = three times the number of atoms in the repeating unit); Cp denotes the heat capacity at constant pressure The last line of each entry (in italics) gives the filename and the references, starting at p 799.

Footnotes for the Table

a This table includes all data collected, measured, and updated as of November 1994 Please

correspond with us about improvements, new data, errors, etc In the column of the table labeled #, (a) represents the amorphous sample, and (c) represents the 100% crystalline sample; the mark ** represents heat capacities for semicrystalline polymers; the mark * next

to the reference numbers, given in italics, indicates that an update is available only in the ATHAS Data Bank The last line for each entry lists the abbreviation under which data can

be retrieved in the computer version of the data bank, available in our web-site, and also listed the reference number to the last update on the given entry At this reference, information on the source of the experimental data can be found

b The change in the heat capacity at Tg, listed in J K1 mol1, as derived from the ATHAS recommended, experimental data A * in this column indicates that the data were derived

p pfirst numeral in parentheses refers to the number of small, mobile beads in the repeating unit(like CH2, O, or CHCH3) The average increase in Cp at Tg of all listed molecules persmall bead is 11.5 ± 1.7 J K1 mol1 The second numeral refers to large beads (like C6H4).The increase in Cp of a large bead at Tg is double or triple that of a small bead.

c The melting temperature is an estimate of the equilibrium melting temperature, and the heat

of fusion in kJ mol1 of repeating unit is computed for 100% crystallinity

d An X in this column indicates that enthalpy, entropy, and free enthalpy are available, based

on the ATHAS recommended data

e Residual entropy in the glassy state at zero temperature, in J K1 mol1

f The number of skeletal vibrational modes used in the Tarasov equation with the theta

tem-peratures of the previous two columns Values of theta temtem-peratures in parentheses areestimates based on data from polymers of similar backbone structure The group vibrationfrequencies are usually tabulated in the listed references

g Temperature range of the ATHAS recommended experimental heat capacity data The

computations of heat capacities of solids are based on these data and are usually carried outfrom 0.1 to 1,000 K, to provide sufficiently broad ranges of temperature for the additionschemes and for analysis of superheated polymers, as in laser ablation studies For the

references, in italics, see the list starting on p 799.

h The PTFE has additional crystal-crystal-condis crystal transitions at 292 K and 303 K; their

combined heats of transition are 850 J mol1 [13]

i Properties of the metastable, monoclinic selenium are also analyzed and described in detail

in [3,39]

j The trans-PBUT has an additional condis state at lower temperature The crystal-condis

crystal transition is at 356 K, and the heat of transition is 7.8 kJ mol1 [18, 41]

k The PPX has two lower first-order transitions, leading to condis crystals at 504 K and 560 K

with heats of transition of 5.0 and 1.5 kJ mol1 [32]

l For deuterated, amorphous, solid polystyrene and ring-only deuterated polystyrene, heat

capacities lead to Tarasov 3 and 1 temperatures of 55, 244 K and 49, 278 K, respectively.The thermodynamic functions S, H, and G are in [22] For other data, see [23]

m The PDES has an additional condis state at a lower temperature The crystal-condis crystal

transition is at 206.7 K; its heat of transition is 2.72 kJ mol1 [52,55]

n The POB shows a disordering transition at 616.5 K with a heat of transition of 3.8 kJ mol1[51]

o The PON shows a disordering transition at 614.5 K with a heat of transition of 0.4 kJ mol1[51]

gaddition, it shows the existence of a rigid-amorphous fraction [53] The quenched sampleshows some small transition at 248 K which is probably not the Tg, as assumed earlier [72].

q The listed glass transition temperature has been assigned to relaxation processes of the

n-alkyl/cycloalkyl side groups Another, Tg

U has been assigned to the backbone [29]

r Semicrystalline PPO shows the existence of a rigid-amorphous phase which governs the

thermal properties from Tg to Tm Fusion, superheating and annealing are directly affected bythe rigid-amorphous phase [42]

s Above Tg, poorly crystallized samples show a rigid-amorphous fraction that does notcontribute to the increase in heat capacity at Tg [35]

t Between Tg and Tm, the Cp of the liquid cannot be extrapolated from melt since the liquidheat capacities of the fluorinated polymers are nonlinear [19]

u The PDMSi shows two small transitions One is at 240 K with a heat of transition of

0.1 kJ mol1 and the other at 432.5 K with a heat of transition of 0.56 kJ mol1 is probably atransition from one crystal form to another [59]

v The PDPSi shows a disordering transition from condis crystal I to condis crystal II at

338.3 K with a heat of transition of 1.4 kJ mol1 [59]

w The PDHSi shows a disordering transition at 323.2 K with a heat of transition of

14.84 kJ/mol [59]

x Estimated glass transition temperature and change in heat capacity at Tg for PTDSi [59]

y The PTDSI shows a disordering transition at 329 K with a heat of transition of 39.2 kJ/mol

[59]

z All these paraffins and perfluoroparaffins have additional crystal-mesophase transitions [57],

[62] and [66]

aa For ammonium salts, the temperature listed is the isotropization temperature TA3Br and

TA3I decompose immediately after isotropization All the tetra-n-alkylammonium salts have

additional crystal-mesophase transitions In addition, no heat capacities for the liquid could

be measured due to decomposition [67]

ab The transition temperature listed corresponds to a change of a nematic liquid crystal to the

melt; OOBPD has several mesophase transitions below this temperature [68]

ac The glass transition and ... the sharpness of theglass-transition region is an important, often neglected tool for the characterization ofpolymeric materials and will be further explored in the discussion of the next twosections... information for the description of materials Every one of the sevencharacteristics of the glass transition of Fig 2.117 contains information on the nature

of the phase to be analyzed Copolymers,... 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