Modern Polymer Spect..

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3.17 Ferini Re.sonrriire.s 169 a Figure 3-40. (a) Calculated Raman spectra in the CHZ-bending region of single-chain polyethylene. The BZ was divided into 72 intervals of 5". Each Lorentzian function has AI~,/~ = 5 cn-': (b) Calculated Ranian spectrum in the CHz-bending region of crystalline polyethylene as n convolution of Lorentzian lines as in case (a).
15 Figure 3-41. Calculated Raman spectrum for crystalline polyethylene in the CH-stretching region. The spectrum is a convolution of numerous combination and overtone levels in Ferini resonance with the nonresonant CH2 antisyinmetric stretchings. This spectrum should be compared with the experimental one of Figure 3-37. levels; moreover, in addition to the overtone levels, we should also consider their combinations. For the space group we can use the observed experimental frequencies: (2P-)-, B3u x B3,, = A,, 2 x 731 = 1462 an-'; 2(P-)+, B?,, x Bzu = A,, 2 x 719 = 1438 cm-'; (P-)- + (P-)', B3u x B?, = Bl,, 731 + 719 = 1450 cn-'. It follows that for the space group the mode (af)+ can couple with 2(P-)- and 2(P-)+ while (6')- can interact with the combination (P-)- + (P-)'. Raman spectra of stretch-oriented (extruded rods) in various polarization directions 128, 1231 show that the symmetry species of the lines at 1464 and 1440 cm-' is certainly Big, while the line at 1416 cm-' is certainly A,. The full treatment needs to consider in addition to the k 40 modes also the k # 0 modes (throughout the whole BZ) due to either the finiteness of the chain, or to the whole continuous dispersion curve for an infinite chain. The population of overtones and combinations becomes extremely large and many of these levels can enter Fermi resonances with a large transfer of intensity from the fundamental strong modes. Once the bending region has been understood the same approach must be taken by considering all line-group or space-group overtones and combinations of the d modes which are in Fermi resonance with the CH2-stretching modes. All details of the calculations are provided in [140]. Figure 3-41 gives the result for crystalline polyethylene. The most important and useful feature in the Raman spectra of polymethylene chains is that reported in Figure 3-37, which is easily observed every time a sequence of CH2 units occurs in a molecule. If the system forms an orthorhombic lattice, generally one observes a broad and strong line near 2850 cn-' with a broad wing which extends towards higher frequencies foiming a broad background scattering that reaches -2950 cm-'. Broad and sometimes ill-defined bands appear near 2930 and 2900 cin-l. For the orthorhoinbic system, such a background scat-
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Modern Polymer Spectroscopy Edited
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Modern Polymer Spectroscopy Edited
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Preface For unfortunate reasons the
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However, theory and calculations yi
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Contents 1 Two-Dimensional Infrared
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Con ten t~ xi Index 5.2 Force Field
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Contributors M. Del Zoppo Dipartime
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1 Two-Dimensional Infrared (2D IR)
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1.2 Brick~qrorrnrl 3 . Figure 1-3.
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1.0 , Figure 1-6. The in-phtrse and
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1.2 Bcrckgroinizd 7 where AA (i~) i
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1.2 Background 9 1.2.5 Two-Dimensio
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1.3 Bnsic Properties of 20 IR Corre
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2D IR spectrometer coupled with a d
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1.5 Applirtrtions 15 Unlike a dispe
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\ '\ Melliyleiie 1'7- -3000 Posiliv
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11 Amorphous Crystalline ,...." I F
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1.5 Applications 21 / I 1430 Figure
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1.5 Appliccitioiis 23 Methylene Fig
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1.5 Ajqdicrrtions 25 3024 Figure 1-
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1.5 Applicutions 27 Furthermore. th
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1.7 Coizclirsions 29 derived in a s
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1.9 References 31 [9] Colthup, N. B
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2 Segmental Mobility of Liquid Crys
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SRMPLE/DETECTOR e3 ‘retardation
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2.4 Srvuc me-Dependenr Alignment 37
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2.5 Electric Field-Innductid Orirnt
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2.5 Electric Field-nclticetl Orient
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a -@ COWER SRHPLE ._ 2.5 Elec tric
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2.5 Electric Field-Itzduced Orienta
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2.5 Electric Field-IwrElrced Orient
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2.5 Electric Field-Im/irced Orientu
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2.5 Electric Field-Induced Orientli
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2.5 Electric Field-Induced Orientat
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2.5 Electric Field-Induced Orienfat
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2.5 Elrc tric Field-Iiidircwl Orim
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2500 2008 I s00 WRVtNdMRtR CM-I Fig
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-3.6 Aligmient OJ' Side- Clinin Liy
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~ polyester 2.6 Alignnient qf Side-
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I." 0.9 0.8 Figure 2-34. FTlR 0.7 p
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induced alignment of the investigat
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2.7 Orientation oj Liquid Ci:i,stal
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2.7 Orieritation of Liquid Ciysttrl
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0 8 18 16 1 a W u z a m a 0 Ln m Q
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2.7 Orientation oj Liquid Crystals
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2.7 Orientation of Liquid Crjvtals
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2.7 Orientatioiz of Liquid Crystals
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2.8 Conclusions 81 strain. As A0 is
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3. I0 Refcreiice.r 83 [I 71 Hoffina
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2.10 References 85 [92] Wiesner, U.
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t Order/Disorder in Chain Molecules
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onds which hold atoms together thro
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3.2 The Dyriamical Case qf Simll ar
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3.2 The Dyrinniical Case of Sinnll
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3.4 S11or.f- and Loizg-Rcrizye Vibr
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3.4 Slzort- and Loiig-Range Vibrati
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eyularity), e.g., 2. During the pol
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3.5 Towards Lnrger Molecules: From
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3.5 TOIIYW~ Laiyer Molertiles: Fvoi
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3.5 Towmu" Larger Molecules: F~om O
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1700 - CIO --- ca c 22 _- c 12 l l
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3.6 From Dynamics to Vibrational Sp
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3.6 Froin Dynaiiiics to T’ihratio
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3.7 The Case of Isotactic Polypropy
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3.7 The Cuse of Isotactic Polypvop.
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3.8 Density of Vibrational States a
Page 134 and 135: 3.8 Dtvz.sit,v of L’ihrntioizal S
Page 136 and 137: 3.8 Driisity of Vibratioiid StLitrs
Page 138 and 139: 3 9 Mouiiiq ToIvmds Rerrlitv: From
Page 140 and 141: 3.9 Moving Towards Reality: From Or
Page 142 and 143: 3.9 Moving Towards Reality: Froin O
Page 144 and 145: 3.10 Wlmt Do We Learn from Cnlcailc
Page 146 and 147: + 3.11 A Very Siriiple Ccrse: Latti
Page 148 and 149: 3 I1 A Yey) Siiiiple Case: LLittice
Page 150 and 151: 3.11 A Vq> Siiiiplc Crrw: Luttice D
Page 152 and 153: Figure 3-22. Sample eigenvectors in
Page 154 and 155: 3.12 CIS-trans Opening @the Double
Page 156 and 157: 3.13 Defect Modes cis Structtrr.al
Page 158 and 159: 3.13 Defect Mo&s cis Structurcil Pr
Page 160 and 161: 0 3.14 Case Studies N 0 d - Y N o m
Page 162 and 163: 3.14 Case Studies 147 OC 60 58 57.
Page 164 and 165: 3.14 Case Studies 149 GI A V E N U
Page 166 and 167: 3.14 Case Studies 15 1 correspond t
Page 168 and 169: 3.14 Case Studies 153 (I10 + 200) +
Page 170 and 171: 3.14 Case Studies 155 1500 1480 146
Page 172 and 173: 3.14 Case Studies 157 the molecular
Page 174 and 175: 17E (ir 1, R): (iii) z = 4, t = 1,
Page 176 and 177: 3.16 Stnictural Znlioi~zogeneity an
Page 178 and 179: 3.1 7 Fermi Resonancrs 163 stants.
Page 180 and 181: 3.1 7 Femi Resorinnces 165 2 L 1 29
Page 182 and 183: lowing. The CHl-bending mode 6 [cer
Page 186 and 187: 3. I7 Fernii Resoiiances 17 1 terin
Page 188 and 189: 3.18 Band Broadening and Confonnati
Page 190 and 191: 3.18 Bmd Brourleiziriy md Cmforrnat
Page 192 and 193: 3.18 Band Bvoaderiing arid Conjonna
Page 194 and 195: 3.18 Band Broadening and Confornmti
Page 196 and 197: 3.19 A Worked E.utinple 181 pre-mel
Page 198 and 199: 3.19 A Wovh-ecl E.uanzple 183
Page 200 and 201: 3.19 A Worked Example 185 19 5°C 2
Page 202 and 203: 3.19 A Workrd Example 187 Figure 3-
Page 204 and 205: 3.19 A Worked E.rcnniplr 189 LAM I
Page 206 and 207: 3.19 A Worked E.xuniple 191 Figure
Page 208 and 209: 3.19 A Worked E.vnn~yle 193 Figure
Page 210 and 211: 3.19 A Worked E.vnrqde 195 009.1 00
Page 212 and 213: 3.19 A Worked Example 197 existence
Page 214 and 215: 3.1 9 A Worked Example 199 The soli
Page 216 and 217: 3.20 References 201 very important,
Page 218 and 219: 3.20 References 203 [41] M. Gussoni
Page 220 and 221: 3.20 Refeeveiicrs 205 [I 171 P. Jon
Page 222 and 223: 4 Vibrational Spectroscopy of Intac
Page 224 and 225: 4.3 Georrietvy oj Intuct Po1vniev.r
Page 226 and 227: 1'45 4.4 Geometric Chunges I?zditce
Page 228 and 229: 4.4 Geometric Chmges Iiid~lrcecl bj
Page 230 and 231: 4 5 Mer1iodolog.v of Raiii~11 Studi
Page 232 and 233: 4.7 Poly(p-pheiq.lene) 217 with an
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4.7 Pol)~(p-pheiz~~lene) 219 ENERGY
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is worthwhile pointing out that the
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~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 801 Table 4-3
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4.7 Poly(y-phenylene) 225 Figure 4-
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Table 4-4. Observed Raman frequenci
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4.8 Other Polwieys 229 Table 4-5. T
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under various models. According to
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4. I0 Mechnriism oj Charge. Transpo
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4.12 Reftrences 235 [ 131 Kuzmany,
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4.12 References 237 [98j Matsunuma,
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5 Vibrational Spectroscopy of Polyp
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5.2 FOYCC Fields 241 such calculati
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5.2 Force Fields 243 accounts for o
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5.2 Force Fields 245 centers of the
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5.2 Force Fields 247 ture with conf
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5.3 Amide Modes 249 to the nh initi
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5.3 Ainide Modes 251 Table 5-1. Ami
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Table 5-2. Some amide modes of four
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5.3 Amidc Modes 255 Figure 5-1. Opt
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5.4 Polypeptides 257 nonhydrogen-bo
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5.4 Polvpeptida 259 Figure 5-2. Ant
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I 5.4 Polypeptides 261 )I .- + $ 80
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1226M 1222s (1 1165W 1167s (1 1120V
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135s 9 1 Ms1i 122Wbr 147 NH ob(37)
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5.4 Polypeptides 267 glycine residu
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5.4 Polypeptides 269 Raman bands in
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5.4 Polypeptides 271 Figure 5-7. St
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Frequency (cm-'1 100% b 700 500 300
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5.4 Polypptidt~s 215 Table 5-9. Obs
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~~ ~~ ~~~ ~ ~ ~~ 5.4 Polypeptides 2
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5.4 Poliyeptides 219 Table 5-11. Co
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Table 5-12. Aniide mode frequencies
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1351 Lifson, S., Stern, P. S., J. C
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5.6 Refeverices 285 [130] Tiffany,
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Index Amide modes 249 Amorphous pol
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Step-scan FTIR spectroscopy 14,34 -
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