Modern Polymer Spect..

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3.18 Band Bvoaderiing arid Conjonnationril Flexibility 177 tional relaxation contribution can be easily evaluated. For all antisymmetric modes a = 0 and p = $; only the contribution from coupled vibrational-reorientational motions can then be obtained from Raman experiments. The evaluation of the pure reorientational contribution can be obtained by suitably subtracting the contribution from vibrational relaxations (Eq. (3-59)). 3.18.2 Short and long n-alkanes The Raman spectra of a series of n-alkane suitably chosen have been studied [137] with the precise aim of extracting from d- (antisymmetric, - depolarized) and d' (symmetric - polarized) modes of the CH2 group information of general validity on intra- and intermolecular dynamics using the techniques discussed in Section 3. IS. 1. The following molecules have been studied [ 1371 in the solid and liquid states: propane-d6 (CD3CH2CD3) butane-d6 (CD3CH2CH2CD3), and pentane-dlo (CD~CH~CHZCH~CD~) and n-nonadecane. The following conclusions, which may be of general interest, have been derived: 1. For d+ p = 0, thus allowing us to distinguish the contribution by vibrational relaxation processes; for d- CI = 0 and p = %, thus the coupled vibrationalreorientational processes are active simultaneously. The reorientational contribution was derived by suitable deconvolution methods (Eq. (3-59)). 2. The temperature independence of the band width of d+ modes has been verified and provides an average value of T(VIBR) - 1.3 x 10l2 s for the three small deuterated molecules. An amplitude-dependent vibrational dephasiiig process (inhomogeneous broadening) best accounts for the observed temperatureindependent broadening. 3. A ~ J of ~ / d- ~ is strongly teniperature-dependent and increases rapidly with increasing temperature (Figure 3-41); correspondingly, r(RE0RIENT) decreases by at least one order of magnitude from low to higher temperatures (see Table 3-3). It is found that, at a given temperature, identical for the three deuterated molecules, the band width increases with increasing chain length. Moreover, at a constant temperature, the reorientational relaxation time increases with increasing chain length. This trend is consistent with the view that the contribution of reorientational relaxation decreases with increasing chain length, as might be expected based on inertial and frictional effect. Indeed, it is conceivable that while the molecule of propane in the liquid phase may easily tumble in all directions about its axes, for longer molecules the end-over-end tumbling becomes progressively less likely while some sort of rotation about the long molecular axis may still occur even for longer n-alkanes. 4. For chains larger than propane (for which no torsional motion about (CHl)-(CH?) bonds exists) it is quite conceivable that the increasing hinderance to molecular reorientation which broadens d- mode comes from torsional motions of the molecular skeleton, i.e., its overall torsional flexibility. In other words, when a flexible molecule tries to tumble it necessarily drives the motions of the torsional angles. We expect these contributions to increase with iiicrcasing
178 3 Vihmtional <strong>Spect</strong>ra ITS CI Probe of Structural Order Table 3-3. Frequencies, bandwidths (full widths at half inaxiriiumi and reorieiitntioiiizl-rel~ixalion times of d- of propane-dh, butane-d6 and pentane-dl,] as a function of temperature. Temperature A1'1,2(d-) s(RE0RIENT) d- iK) (cm-') (cm-l) x 1012 s CD3CH:CD? 101 177 235 288 300 CD1 CHzCH2 CD3 135 185 231 300 CD3CD2CH2CD2CD3 143 191 240 300 2919.0 15.7 3920.5 24.8 2925.0 70.0 2923.5 79.0 2896.5 15.0 2896.5 24.2 2899.5 40.0 2898.0 65.0 2896.5 18.1 2898.0 20.1 2899.5 24,s 2901.0 30.9 1.3 0.58 0. I7 0.15 1.7 0.66 0 33 0.1s 1.2 0.93 0.67 0.48 temperature and chain length. The threshold temperature at which for a given chain length coupled rotations and torsion are able to generate conformational kinks in a more or less nonequilibrium structure (either pinned at a given site or mobile along the chain) remains an unsolved problem faced by many authors who tackled the problem by numerical simulations [ 1481. 5. For the short-chain models it has been found that, by increasing the temperature (i.e., when the coupling between rotations and torsions increases), the frequency of d- increases consistently by a few wavenumbers (see Table 3-3); this suggests that either the diagonal or off-diagonal force constants within each CH2 unit change when the niolecule is (even slightly) conformationally distorted or the onset of torsional distortions activates iiitraniolecular coupliiig which extends at an unknown distance s at either side of the CH2 group (see Eq. (3-45)). 3.18.3 Collective Chain Flexibility In this section our attention is focused on attempts to describe in molecular terms the broadening and the upward shift of d- mode as discussed in Sections 3.18.1 and 3.18.2. Let us first consider the case of a long 11-alkane molecule in the solid crystalline phase. Froin lattice dynainical calculations it is known that collective librational phonons (about the chain axis) exist in the lattice, some giving rise to scattering and/or absorption in infrared [70]. Let us take a n-alkane molecule with an even number of carbon atom which belongs to the C?h point group. The rigid rotation about its axis is of B, species, the same as the Raman active d- mode. When the
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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
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3.8 Dtvz.sit,v of L’ihrntioizal S
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3.8 Driisity of Vibratioiid StLitrs
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3 9 Mouiiiq ToIvmds Rerrlitv: From
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3.9 Moving Towards Reality: From Or
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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 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 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
Page 234 and 235: 4.7 Pol)~(p-pheiz~~lene) 219 ENERGY
Page 236 and 237: is worthwhile pointing out that the
Page 238 and 239: ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 801 Table 4-3
Page 240 and 241: 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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