Modern Polymer Spect..

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lowing. The CHl-bending mode 6 [certainly of A1 symmetry ( 1 1 ) ) 3.17 Fermi Resonaiices 167 (Figure 3-37b) observed at 1460 cm-~' should have its first overtone 126 : 2 x 1460 = 2920 cni-', A1 x A1 = Al) which can enter Fermi resonance with the d+ mode of A1 symmetry. Eigenstates mix, frequencies are split apart with intensity borrowing froin the fundamental to the overtone producing two strong lines at 2876 and 2942 cni- ' (Figure 3-38a-c'i. It should be remembered that the first overtone 26 should generally have vanishing intensity, but because of Fernii resonance its frequency is pushed upward and it borrows a lot of intensity from the fundamental d+ observed at 2876 cm-' . A similar, but seemingly more complex case, occurs for polymethylene chains. Let us consider the dispersion curve of polyethylene or the corresponding vibrations of finite polymethylene chains (Figure 3-39 j whose frequencies lie on these dispersion curves at finite values of the phase coupling (Section 3.5). The vibrations of the lower portion of the dispersion branch of CH2 rocking have their first overtone levels ( - 720 x 2 zz 1440 cnrl) close to the fundamental levels of the CHZ-bending motions. On their turn, the first overtones of the levels along the dispersion curve of the CH2-bendings occur just in the frequency region where the fhdaniental CH stretching modes occur (2 x -1440 z 2880 cnirl). When symmetry allows, Fernii resonances occur and levels repel each other with drastic intensity changes. The issue becomes formally more complex since (Section 3.6) when molecules crystallize in an orthorhonibic lattice (with two molecule per unit cell) the number of frequency branches doubles, thus doubling the number of levels which can generate both overtones and combinations which may produce Fermi resonances in the proper frequency ranges, as just indicated. These Fernii resonance phenomena have found detailed mathematical treatment first tackled by Snyder et al. [138, 1391 for single all-tram chains and later reformulated by Abbate et al. for ii) single chains, (ii) an orthorhombic lattice [140], (iii) all-trans, and (iv) conformationally distorted chains [ 141, 1421. The most interesting features to be accounted for are the Raman scattering of polymethylene chains in the frequency regions centered near 1450 and 2900 cnirl. For the sake of simplicity in the discussion which follows we label with (+) and (-) the symmetric and antisymnietric combinations respectively either of internal coordinates (e.g., C-H stretches within a CH? group) or of 'group coordinates' between two CH2 units within the 'chemical repeat unit' made up by two CH? groups. First, we discuss the case of true k = 0 modes for an infinite chain (or the case of k 4 0 for finite long chains). Let us, for the sake of simplicity, consider the spectrum of traiis polyethylene both as a single chain and crystallized in an orthorhombic lattice with two molecules per unit cell. Since the spectrum of polyethylene as single chain is not available for this discussion we necessarily use the calculated spectra as simulation of reality [140]. Let us first compare the general features of the calculated Raman spectra in the CHz-bending centered near 1435 cm-' for a single chain and for crystalline polyethylene (Figures 3-40a, b) (point group D?!,). The single very strong line near 1435 cm-' (Figure 3-39) is to be assigned to the limiting k = 0 totally symmetric in-phase CH?S+ mode of A, species. For the crystalline material, such a mode splits into two levels near 1420 (Ag) and 1435 an-' (BI?); an additional broad scattering (with a wing towards higher frequencies) is calculated
168 3 Vibrational <strong>Spect</strong>ra as u Probe oj. Strurtrrrcil Ordu 30( V cm -1 I 25C 15C 1oc Figure 3-39. Dispersion curves of single-chain polyethylene, indicating the scheme of Fermi resonances which can occur between phonon of different branches. near 1464 cm-'. Following the previous procedure we look first at the first overtone of the infrared active CH? rocking P- mode for a single chain (line group symmetry) (2P-), BzU x Bzu =A,. For the line-group, Fermi resonance can take place between 2P- of A, species and the A&+ flindamental, giving rise to the weaker line near 1445 an-'. Extension of the treatment to the case of the orthorhombic lattice with two molecules per unit cell needs to consider that each level splits into two
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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.
Page 132 and 133: 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 184 and 185: 3.17 Ferini Re.sonrriire.s 169 a Fi
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
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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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