Thermal Analysis of Polymeric Materials

coupled with TGA 439–443 development from DTA 820–823,

820–822 difference from DTA 821 dual 334, 335

extreme conditions, see: DTA, extreme condition

fingerprinting 350–354, 350–354 glass transition, measurement

354–355

calculation 835, 836, 836 heat capacity measurement

102–104, 103, 349–350 heat-flow-rate equation 835, 836,

835, 836

heat-flux 331–335, 820, 820 modern 332–335, 332, 335

mathematical treatment 340–348,

341–348

conditions for 341, 342

348

steady state 341–343, 341, 343, 841, 841

with temperature gradient 341–343, 341, 343

without temperature gradient 344–348, 344

melting, see: melting, by DSC online baseline correction

831–834, 831–833

power compensation 335–338, 336 principle of operation 337, 338

principle 329

standard, used for TMDSC with sawtooth modulation 837–839, 837–839

signals, standard and modulated

333

steady state 333, 333, 342, 841,

841

temperature gradient 343 DTA, and DTGA, data 439–443,

440–443 difference from DSC 821

early equipment 330, 821, 822 extreme conditions 824–829, 824,

825, 828, 829

fast measurement 826–828 low temperature 824

high temperature and pressure

825

see also: microcalorimetry ICTAC rules 438, 822, 823

fast, melting without reorganization, 268, 269, 612

see also: DSC 79 schematic 820

DTGA 439

Dulong-Petit’s rule 106, 110 dynamic mechanical analysis, see:

DMA

E

ebulliometer 60 Einstein 64

approximation of Cv 111 function 110, 110, 125 temperature 110, 110, 111, 111

elasticity, coefficient, isothermal, see: modulus

energy 578, 579, 579 thermodynamics 579, 579

entropy 579–583, 580 comparison to gas expansion

581, 581

fusion diagram 581–583, 582,

583

rubber, data 580 thermodynamics 580, 580, 581

Hookean 415, 416, 579 perfect 415

Poisson’s ratio 405, 405, 579, 580, 580, 581

see also: viscoelasticity electron, affinity 3

valence 3, 3 electronegativity 3, 3 elements, ancient 72 emanation thermal analysis 79

emulsion polymerization 217, 217 enantiomorph 463

end-group, determination 66 nomenclature 14, 16, 16

end-to-end distance 31, 31 restrictions 33

energy 75, 76, 76 bond 3, 4

table of 324 conservation of 76

Clausius-Clapeyron 300, 581, 582, 690

Debye, for heat capacity, see: function, Debye

835, 835, 836

Gibbs, for partial molar quantities

157

Gibbs-Di Marzio 760, 761 Gibbs-Duham 98, 98 Gibbs-Thomson 154, 155 Gordon-Taylor 760, 761 Johnston 762

Maxwell, relation of polarizability and refractive index 424, 808, 809

Nernst-Lindemann 105–106, 105 for organic molecules and

macromolecules 105, 106 Poisson 261, 261

Schneider 761, 761

Tarasov 125, 126 Tool-Narayanaswamy 683 van der Waals 51, 163 van’t Hoff 817

virial 55

Williams-Landel-Ferry 419, 577, 578

Wood 760 equipartition 107 esterification, energetics 201

rate 200

etching, by hydrolysis 236 chemical 191, 192, 236

Euler reciprocity relationship 813 evolved gas analysis 79 expansivity 105, 292

conversion, linear-to-volume 292 linear 292

table of, for solids 295

extensive thermodynamic quantities 75 extension, of flexible macromolecules

580

of rigid macromolecules 405, 479

F

Fahrenheit 281 temperature scale 281

fiber 503–507, 504–507 carbon 235

formation 530–533, 531–533 gel-spun, of polyethylene 569–571,

570, 571, 674–677, 674–677 of PET 409–411, 409–411, 505,

506, 505–507, 534, 535, 535, 677–670, 678, 679

see also: melting, of fibers shish-kebab morphology 503, 504 X-ray diffraction, of PET 504–506,

505–507

of polyethylene 513, 596, 596, 674, 674, 675

fingerprinting of materials by DTA or DSC 350–354, 350–354

flight, random 31, 31–32, 487, 487 Flory 9

flux of extensive thermodynamic quantities 88, 147, 148,

148

fold-length, in crystals 488–493 force-times-length term in enthalpy

expressions 304, 305,

579–582

Fourier series 840, 841, 841 freedom, degree of 106, 112

slowly responding 117 freely-jointed chain, equivalent 47, 48 Freeman-Carroll method 263–264, 263

445, 445

freezing point lowering 58–62, 59, 99,

99, 100, 711, 711 solvents for 60

function, Debye 113

one-dimensional 111, 112, 113,

125

three-dimensional 113, 113, 114

two-dimensional 112, 113 for chalcogenides, 2 and 3

116

gel 230–231, 231, 237 gel-permeation chromatography, see:

size exclusion chromatography

Gibbs 92

free energy or function, see: enthalpy, free

glass 6, 7, 165, 167

behavior of 180, 389–391, 391 motion in 572, 573

structure 572, 573 ordering of 592

pressure densified 690, 690 transition, see: transition, glass

glide plane 462, 463, 462 Goodyear 234

grafting 235, 235

gravity, center of 32, 32–33 Gimm’s tetrahedron 5, 5 group theory 460, 848 Gay-Lussac 282

H

heat 76, 81–84, 83 capacity 82, 83

additions scheme 131–133,

132, 133, 139, 140, 145 apparent 355, 356

apparent, contributions to 742 at arrested equilibrium 157 by DSC 349–350

by molecular mechanics calculation on cooling 86

heat, capacity, by TMDSC 364–369,

365–368, 385–388, 385–388 calculation, using the ATHAS

system 121–145, 123,

124–143, 144, 145 comparison to expansivity 303 complex 117–118, 118, 382,

384

crystallinity dependence 118–121, 119–121

determination of Cp Cv 104–106, 105

dissipative 117 equations for 101

for two energy levels 108 for harmonic oscillators 109,

110, 109, 110 imaginary 117

measurement 101–104, 103 missing, in case of symmetric

jump motion 555–558,

556, 557

of a liquid 131–133 of a solid 111–116

of copolymers 139, 768

of homologous series 128–133, 129, 132, 133

of liquid selenium 138–139,

139

of MBPE-9 137–138, 138 heat capacity of solid paraffins

327–329, 327, 328

of polyethylene, large-amplitude motion 136, 136

of polymethionine 136, 137 relation to the thermodynamic

functions 95

of polyoxides 128–131,

129–132

of poly(oxybenzoate-co- oxynaphthoate) 134, 135

of poly(styrene-co-butadiene) 139–140, 140

of polytetrafluoroethylene 134,

134, 135

of starch 142–144, 142, 143 on fast heating 157, 158 quantum mechanics 106–111,

107 thermodynamic theory

104–106

heat, content, see: enthalpy (H) development of the understanding of

71–75, 72

flow rate 147, 342, 343

as an example of a transport process 158, 158

derivation of the equation for 835, 836, 835, 836

difference between reversible and reversing 358

latent 84, 291

measurement of 304, 305, 305 see also: calorimetry

of combustion 309 of formation 322

of fusion, by DSC 355, 356, 356 diluent method 100, 100, 715,

715

of reaction, for organic compounds 323, 324, 324

pump 581

reference temperature for the (enthalpy) 304, 322

specific 82

unit of 304, 305 heating curve 290, 290, 291 helix 463

anticlined 474 axes 463, 464 class of 463, 464 enantiomorphs 463 handedness 463 irrational 463 isoclined 474 lattice 463–468

packing in crystals 471–473, 472 projection 464

Heller 801

Helmholtz free energy, see: energy, free Henry’s law 708, 708

Hildebrand, entropy of mixing of macromolecules 709, 709

hindrance, steric 37, 38

history of, calorimetry 304–307, 305 chemistry 1, 2, 1, 2

covalent structures 9, 10 crystals 165, 166, 455–457, 456 dilatometry 291–293, 293

DSC and DTA 329–331, 330 heat and temperature 71–75, 72 natural polymers 9–10, 11

synthetic polymers 11–12, 12 TGA 429, 429, 430 thermometry 279–283, 280

Hooke’s law 404, 405, 415, 416, 579 hydrodynamics 415

I

ICTAC 77, 78, 331 logo 72, 73, 77, 78

impingement, of crystals 239, 239, 240, 261

lines of 239, 240, 242 induction time 239, 241, 241 infinitesimal changes 75, 76 interference effects 52, 851

International Confederation for Thermal Analysis and Calorimetry, see: ICTAC

international temperature standard, see: ITS 1990

intensive thermodynamic quantities 75 inversion, axes 461, 462, 461

center of 461, 461 ionomer 236, 236 irradiation, with 60Co 234 irreversibility 94

Ising model, 122, 554, 555, 554, 555 isometric crystal, see: crystal, isometric isomer 17, 23

conformational 39 model 122

head-to-head 23 head-to-tail 23 rotational 37–40, 38, 39 positional 23

stereo 23, 848 structural 23

isomorphism, see: crystals, isomorphism

isotacticity 24

ITS 1990 281, 818, 818, 819 IUPAC 13

J

Joule 74

Journal of Thermal Analysis and Calorimetry 77, 331

jump-motion in crystals 555–558, 556,

557

K

Kauzmann paradox 142 Kauzmann temperature 140 Kekulé 9

Kelvin 74 kinetics 189, 817

nonisothermal 263–264, 263 Kossel crystal 249, 250

Kuhn 47

length 47, 48, 48, 49 kurtosis 28, 28

L

Laplacian operator 835 Lavoisier 73

LC, see: liquid, crystal Le Chatelier 330

Legendre transformation 93, 813 length, comparison 293–295, 294, 295

measurement, 291–295, 292–295 by interference microscopy

294, 819 standard 291

krypton-86 819 scale, macroscopic V,

microscopic V, 37 lifetime, determination by TGA

446–449, 447, 449 linearly variable differential

transformer, see: LVDT liquid, definition 164, 165, 575

crystal 167, 169, 170, 171, 172 amphiphilic, block copolymer,

structure of 484, 485, 484, 485, 724, 724, 725

cold crystallization 547, 548 examples 171, 172, 172, 547,

548

glass transition, see: transition, glass

gradual change of order 560 macromolecular 553, 553 nematic 169, 552, 553, 552,

553

nematic, macromolecular 553,

553

nematic, one-phase structure of 553, 553

see also: mesophase

smectic 169, 552, 552, 553,

553

soap, transitions 562, 562 thermotropic 724, 724

glass transition, see: transition, glass phase, see: phase, amorphous

liquidus line 100

Lissajous figure 379, 380, 380, 381, 386, 386, 397, 397

LVDT 294, 295, 295, 407

M

macroconformation 32, 486–489, 487 of molecules in crystals 486–488

macromolecule 6–7, 6 see: polymer

macrophase 162 mass 428, 429 material property 512

Maxwell, model, see: viscoelasticity, models

relations 93, 813 Maxwell-Boltzmann distribution of the

speeds of molecules of a gas

815

mean, arithmetic 28, 28 melting 6, 165

broadening of range of 400, 597 by DSC 339, 355–358, 356–358 by TMDSC 396–401, 397, 399,

401 equilibrium 151 experiments 264–275

free enthalpy diagrams 152–154 kinetics 238

mechanism 538 temperature, change with

crystallization temperature

613, 635, 661–663 extrapolation to equilibrium

154, 155, 537, 660, 661 odd-even effect 327–329, 329, 543,

757

of alkali halides, table of 540, 541,

541

of copolymers 725–758, 734–748,

750–753, 755–758

block 723–725, 747–755, 748,

750–753, 755, 756 alternating 751–754, 751–753

LLDPE 733–742, 735–742 PETcoOB 743, 743, 744 POBcoON 743–747, 744–747 regular 756–758, 757, 758 theory 725–733, 726, 727–733 with long long and short side-

chains 755, 756

of crystals of linear hydrocarbons 542–544, 543

of fibers 672–681, 673–681 of lamellae 148–155, 149, 150

of macromolecules 544–547, 544,

545

of nonspherical motifs 541–542,

542

of PEEK 668–672, 669–672

of polyethylene 611–623, 612, 613,

616–623

of polymers with long side chains 754, 755, 755, 756

of poly(oxymethylene) 666–668,

666, 667

of polypropylenes 644–649,

644–649

of poor crystals 652–654, 652–654 of spherical motifs 538–541,

538–541

of the fold surface of polyethylene 623, 623

of the growth face of polypropylene 646, 647, 647

prediction of 536–547, 537–545 rate 255–256, 256, 268 reorganization during 400, 401,

401

reversible, decoupling of segments of polymer chains 649–651, 651

of poly( -caprolactone) 641–643, 642–644

of polycarbonate 637–639,

637–639

of polynaphthoate 634–637,

635, 636

of poly(oxyethylene) 264–265,

264, 265, 624–627, 624–627 of poly(phenylene oxide)

639–641, 640, 641

of polyterephthalates 628–634,

628–634 reversing, table 650

surface melting 529, 530, 623, 623, 646, 647, 647

under strain 581–583, 582, 583 zero-entropy-production 151, 153,

154, 154 mer 13, 191 mesogen 169

mainand side-chain 26 mesophase 165, 167, 169–175, 547–571

characteristics of the three 171 classes of 165, 166, 551–555,

552–554

cold crystallization 547, 548 examples 561–571, 561–565,

567–571

glass 166, 167, 175, 176 transition, see: transition, glass

gradual change of order 560 motion in 551, 552, 552 summary 572

metal, heavy, density 5 microcalorimeter, based on AFM 269,

270, 331 principle of 829, 829

for small amounts of heat, based on a design of Tian and Calvet 314, 315

data and loss calculation 315–317, 316

microcrystalline powder 236 micrometer screw 293 microphase 162, 167 microscopy, polarizing 850 Miller index 458–460, 459 mirror plane 461, 462 mixing, entropy of 97, 97

free enthalpy of 97 ideal 97, 97

solids, liquids, and gases 96 modulus 404

bulk 404, 404 table 405

comparison to heat capacity 418,

419 complex 418, 418 dynamic 413 shear 404, 404

tensile 404, 404, 405, 406, 406 rubber elastic plateau 406 viscous flow

three-phase model 534, 534 Moiré pattern, optical analog 522,

852–853

molar quantities, partial 98, 98, 712,

712

mole 428

molecular mass, determination, by AFM 67

by boiling point elevation 58–62, 59, 60

by calorimetry 67 by dilatometry 67

by electron microscopy 67 by freezing point lowering

58–62, 59

by light scattering 54, 54 by melt viscosity 67

by membrane osmometry 65 by solution viscosity 63–65

distribution 27, 27–30, 33–37 examples 30

Gaussian 33, 34, 35 number average 29, 29 polydispersity 30

see also: reaction, chain and reaction, step

weight average 29, 30 molecule 2, 2

amphiphilic 170, 563, 563, 724 classification scheme 6–8, 6, 8 pseudo 3

size unit of, compared to the humansize unit V

small, definition 6, 6 structure 3–5

compared to motion V moment 27–28

calculation of 28, 28 monomer 13

motion, compared to structure V molecular, types of 121, 122 large-amplitude 121, 122

N

nanophase 162, 162, 168, 169 NATAS, 77, 77, 331

Natta 209

Nernst 94

network, interpenetrating 26 neural 84, 88, 811–812

Newton 280 Newton’s law 290

normal mode analysis 121, 123, 816 North American Thermal Analysis

Society, see: NATAS nucleation, athermal 241

critical 243, 243

table of dimensions 244 heterogeneous 240, 246–249, 246,

248, 249

homogeneous, 240, 244–246, 244,

245 rate of 244

induction time 238, 241, 241 molecular 253–255, 254, 398

critical length for 254, 255 evidence for 253

observation of 238, 239, 240–242,

241

primary 240, 242–246, 252 thermodynamics of 242, 243

rate, evaluation 240–242, 240 secondary 249–253, 250, 251, 252 tertiary 253

thermal 240 numbers, types of 849

complex 117, 816, 849 rational and irrational 463, 849

O

oligomer 191 properties 192, 193

synthesis 191–192, 192 oscillation, see: vibration osmometry, membrane 65–66, 65

vapor phase 61 Ostwald 664

ripening 664

rule of successive states 564

P

packing fraction 302, 302, 303 of rods 469

in polymer crystals 468–471,

469–472, 474–482 544, 544, 545

partial changes, infinitesimal 75, 76 partition function 107, 107, 108 PC, see: plastic crystal

Peltier effect 314, 315 permittivity 425

complex 426–428, 427 phase 162

amorphous 165

fraction, rigid, see: RAF model, 573

property, structure sensitive or insensitive 574, 575 structure 572–574, 573, 574

property 574, 575

viscosity 575–578, 575–577 areas of single-component systems

593, 593–597 condensed 167, 177

description V, 162–171, 163, 167, 168, 170, 171, 176–178, 177, 178, 706–709, 708

diagram 706–725, 706–722, 724 by DSC 706, 706, 707

by thermometry 290 eutectic 100, 290, 291

for many polymeric components 718–723, 719–722

irreversible, macromolecule with small molecules 715, 716, 716–717, 720, 722

of block copolymers 723–725,

724

of small molecules 99–101,

100

polymer and low-mass components 714–717, 715,

716

polymer and low-mass homologs 717–723, 717–722

pVT 298–301, 300, 301 thermodynamics 706–708,

706–708

equilibrium, of macromolecules with macromolecules 710, 717, 717, 718

of macromolecules with its homologous oligomers 718–723, 718, 719–722

of macromolecules with small molecules 708, 708, 709–715, 709–715

of small molecules 99–101, 99, 100, 708, 708

modulus for three 534, 534 rule 181, 707

separation, liquid-liquid 712–714,

712–714

sizes 162, 167–169, 168 solid 6, 7, 176

see also: glass or crystal transition, see: transition, phase

pipette 295, 296 plasma V

plastic crystal 167, 170, 170, 171 examples 172–174, 172, 173, 539,

540, 540 see also: mesophase

motion in 551, 552, 552 plastics, 7, 24, 234

colloquialism for the easily shaped polymeric (macromolecular) materials, for details, see: polymer

plateau, rubber-elastic 406, 406 point group 460

mumber of 462 polarization 424, 425, 425 polydispersity 30, 224 polymer 6, 6, 7, 13

branched 24–26, 25, 197, 733–735,

734, 735 brushes 25, 25

characterization of 50–67, 51–57,

58–66 flexible 6

identification, with TGA 439

by DTA, DSC 350, 351, 351 ladder 24–25, 24

living, see: reaction, chain, without termination

molecule, differences to small molecules VI, VII

chain structure, polar and nonpolar 480

macroconformations, linear 486–488, 487

network 24–26, 25, 26 nomenclature, abbreviations 16, 17

copolymers, isomers 22–24,

22, 23 seniority list 14

source based 13–22, 13, 18–21 structure based 13–22, 14, 15,

18–21

reaction 233–238, 233–237 rigid 6, 7

semicrystalline 488 transitions 536, 537, 537

ultimate strength 533–535, 534,

535

polymerization, degree of 27 emulsion 217, 217

living, see: reaction, chain, without termination

Merrifield method 190–192, 192, 237

of lithium phosphate 201–206,

202–206 see also: reaction

stereo-specific 207, 209 topotactic 510, 511 Ziegler-Natta 209–211, 210, 211

potentiometer 288

production, of extensive thermodynamic quantities 88, 147, 148,

148 sign of 88

properties, colligative 51, 58, 65, 96 prediction of 226, 227

purity analysis 319–320, 320, 321 pycnometer 295, 296, 296 pyrolysis 232

see also: decomposition pyrometer 289, 819 pyrosynthesis by DTA 354, 354

R

radiation, scattering 801–805 electromagnetic 50 electron 66

neutron 66 radius, atomic 3, 302

van der Waals 37, 301, 302 RAF 138, 605, 607–609, 607–609, 693, 694, 694

formation on crystallization 608,

609

disappearance on melting 641, 641 glass transition, see: transition,

glass Raoult’s law 708, 708 Rayleigh 51

ratio 54, 54, 809, 809, 810 derivation 806–810, 807–809

reaction, chain, copolymer 227–229,

227, 228

emulsion polymerization, 217,