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  • Journal of the Korean Physical Society, Vol. 32, No. 4, April 1998, pp. 505512

    FTIR and Polarised Raman Spectra of Acrylamide and Polyacrylamide

    R. MuruganDepartment of Physics, Pondicherry Engineering College, Pondicherry 605 104, India

    S. MohanDepartment of Physics, Pondicherry University, Pondicherry, 605 104, India

    A. BigottoDipartimento Di Scienze Chimiche, Universita Degli Studi Di Trieste, Trieste, Via Valerio, 22, Italy

    (Received 2 March 1998)

    The Fourier Transform Infrared (FTIR) and Laser Raman spectra of acrylamide and polyacry-lamide are presented. The frequencies were assigned to various fundamental modes on the basis ofnormal coordinate calculations. The agreement between the observed and calculated frequencieswas good, and the assignment of the normal modes was satisfactorily realized.

    I. INTRODUCTION

    In the last two decades, the industrial use of acry-lamide and acrylamide polymer have grown enormously.In view of the increasing importance, the structure andconformation of polyacrylamide (PA) have received con-siderable attention in the recent literature. Vibrationalspectroscopy is potentially useful tool for structural anal-ysis and deriving conformational variations. There areseveral discrepancies in the assignments proposed foracrylamide and polyacrylamide. Therefore, in an at-tempt to put them on a more firm basis, a through inves-tigation on the Raman and infrared spectra have beenundertaken in the present work.

    While, normal coordinate analysis of acrylamide [1,2]and vinyl polymers [3] have been the subject of numerousresearch paper, these analyses and a satisfactory inter-pretation of the vibrational spectra of PA are still miss-ing. Normal coordinate treatment of PA is very essen-tial to elucidate the relationship between the molecularstructure and vibrational spectra of this polymer. Withthe aim of gaining more complete knowledge on the vi-brational spectra of PA, the infrared and Raman spectraof single crystal acrylamide, acrylamide in nujol mull,polyacrylamide solutions, polyacrylamide gel and solidpolyacrylamide were recorded.

    II. EXPERIMENTAL

    Spectroscopically pure white crystalline solid acry-lamide and polyacrylamide were obtained commercially,

    the former from Kodak Chemicals, USA and the latterfrom Aldrich Chemicals, USA. PA gels are prepared byco-polymerization technique and aqueous PA solutionsare prepared following Gupta et al. [2].

    Unoriented sample of acrylamide was prepared asmulls and KBr disk, N-deuteration was achieved by re-peated exchanges with D2O. The removal of D2O wascarried out at room temperature in order to minimizea possible sample deterioration which was reported inliterature [3]. Single crystals in the form of thin sheetscontaining the a and b axes were obtained by slow evap-oration of chloroform solutions.

    The infrared spectra of acrylamide and acrylamidefrom D2O were recorded using Perkin-Elmer 983 G dou-ble beam grating spectrometer. The polarized infraredspectra were measured using a wire-grid polarizer and re-flecting beam-condenser. The Raman spectrum of acry-lamide was obtained with a SPEX Ramalog Spectrom-eters using Spectra-Physics Model 171 argon ion laseroperating on the 514.5 nm line. The measurements werecarried out using standard SPEX accessories.

    The FTIR spectra of PA and partially deuterated PAfilm were recorded using Shimadzu 8101 Spectropho-tometer. The Raman spectra of PA gel, PA solution andsolid PA were recorded using Dilor Z24 Raman Spec-trometer equipped with a Spectra-Physics Model 165 ar-gon ion laser source and the calibrated wave numbers areaccurate to within 2 cm1.

    III. NORMAL COORDINATE TREATMENT

    -505-

  • -506- Journal of the Korean Physical Society, Vol. 32, No. 4, April 1998

    Fig. 1. Internal coordinates for acrylamide.

    Fig. 2. Internal coordinates for polyacrylamide.

    The molecular model and internal coordinates of acry-lamide and polyacrylamide adopted for the normal coor-dinate calculation is shown in figure 1 and 2. From thestructural point of view, the acrylamide belongs to Csstructure and the 24 fundamental vibrations fall into 17in-plane (A) and 7 out-of plane (A) type. The selectionrule for acrylamide are shown in Table 1. The structuralparameters of acrylamide used in this present investiga-tions are: C-N=1.315 A; C=O=1.243 A; C-C=1.47 A;C=C=1.337 A; N-H=1.02 A and C-H=1.07 A. All thebond angles were assumed to be 120.

    Earlier spectroscopic studies on PA suggests that thepreferred chain confirmation is in the form of 31 isotac-

    Table 1. Selection rule for acrylamide.

    Molecule Site Unit cellCs C1 C2h

    A 17 (i.r., R) Ag 30 (6L) (R)Bg 30 (6L) (R)

    A 24 (i.r., R)Au 29 (5L) + Tb (i.r.)

    A 7 (i.r., R) Bu 28 (4L) + Ta,c (i.r.)

    L=Lattice modes

    tic helical structure. Three chemical repeat units areinvolved in the translational repeat unit and the 86 opti-cally active normal vibrations are classified under the linegroup isomorphous to the point group C3 and are bothinfrared and Raman active. The 28 A modes exhibitparallel dichroism in the infrared while the 29 doublydegenerate E modes exhibit perpendicular dichroism.

    The structural parameters of polyacrylamide em-ployed in this calculation were transferred from acry-lamide, polyacrylic acid and other related structure [46].The factor group analysis of PA is shown in Table 2.The local symmetry coordinates of PA obtained fromthe internal coordinates are shown in Table 3. Follow-ing, Tadokoro et al. [7] the symmetry coordinates wereconstructed from the local symmetry coordinates.

    The normal coordinate calculations were performedusing Wilsons FG matrix method using the program de-scribed previously [8] for polymers. The modifications ofthe original program is based on the method detailedby Hanon et al. [9]. The initial set of force constantsused in the normal coordinate calculations of PA weretransferred from acrylamide, polyacrylic acid and othervinyl polymers [46] and were adjusted to obtain a goodagreement between the calculated and the observed fre-quencies.

    IV. RESULTS AND DISCUSSION

    1. Acrylamide

    The recorded infrared spectra of acrylamide in KBr,

    Table 2. Number of normal modes and selection rule for Polyacrylamide.

    E C13 C23 No. of normal modes Raman active Infrared active

    A 1 1 1 30-2 (T, R) A A()1 2 30-1 (T)

    E1 1 2 30-1 (T)

    A A()

    =exp i(2pi/3)T and T: pure translations parallel and perpendicular to the helix axisR: pure rotation about the helix axisA() and A(): electric vector parallel or perpendicular to the helix axis.

  • FTIR and Polarised Raman Spectra of Acrylamide and Polyacrylamide - R. Murugan et al. -507-

    Table 3. Local symmetry coordinates for polyacrylamide.

    S1 21/2 (r1 r2) a NH2

    S2 21/2 (r1 + r2) s NH2

    S3 21/2 (r3 r4) a CH2

    S4 21/2 (r3 + r4) s CH2

    S5 r5 C-HS6 r6 C-O

    S7 61/2 (21 2 3) NH2

    S8 201/2 (41 2 6 5 7) CH2

    S9 d1 CNS10 2

    1 (2 + 6 5 7) CH2S11 6

    1/2 (22 5 6) CHS12 2

    1/2 (3 2) NH2S13 2

    1/2 (d3 d4) b C-CS14 6

    1/2 (2d2 d3 d4) a C-CS15 2

    1/2 (3 + 2) NH2S16 2

    1/2 (3 1) (C-NH2)S17 3

    1/2 (d2 + d3 + d4) s C-CS18 2

    1/2 (2 6 + 5 7) CH2S19 2

    1/2 (5 6) C-HS20 2

    1 (2 6 5 + 7) CH2S21 2

    1/2 (3 2) (C-O)S22 2

    1/2 (1 3) C-CS23 6

    1/2 (22 1 3) b C-CS24 6

    1/2 (22 1 3) (O-C-N)S25 30

    1/2 (54 1 2 6 5 7) a C-CS26 6

    1/2 (5 + 6 + 4 1 2 3) a C-CS27 1 C-CS28 2 C-N

    S29S30S31S32

    61/2(1 + 2 + 4 + 5 + 6 + 7) = 061/2(1 + 2 + 3 + 4 + 5 + 6) = 031/2(1 + 2 + 3) = 031/2(1 + 2 + 3) = 0

    redundantcoordinatesa and b - asymmetric stretching, b and a - asymmetric bending s - symmetric bending, s, symmetric stretching, -

    wagging, t - twisting, - torsion and - rocking.

    acrylamide in Nujol mull, deuterated acrylamide, sin-gle crystal acrylamide, polarised infrared spectrum ofacrylamide, infrared spectrum of acrylamide at 157Cand Laser Raman spectrum of acrylamide are shown infigures 38. The observed, calculated frequencies andPotential energy Distribution (PED) for acrylamide areshown in Table 4. The relative cartesian displacementscalculated for the out-of-plane fundamentals are shown

    Fig. 3. Infrared spectrum of acrylamide in KBr.

    in Fig. 9.The assignments for the vibrational bands of acry-

    lamide are made on the basis of the dichorism of theinfrared bands and of Raman depolarization data. Crys-tals of acrylamide are monoclinic, space group P21/c[C52h]with four molecules in the unit cell [10]. From the Ta-

    Fig. 4. Infrared spectrum of acrylamide in Nujol mull(from D2O twice).

  • -508- Journal of the Korean Physical Society, Vol. 32, No. 4, April 1998

    Fig. 5. Infrared spectrum of single crystal acrylamide.

    ble 1 it is clear that each molecular fundamental shouldgive four components in the crystal spectrum, two beinginfrared (IR) active and two Raman active. One of theinfrared (IR) active components is polarized along the baxis, the other in the ac plane. The A and A molec-ular fundamentals can be discriminated on the basis ofthe Raman polarization measurements of solutions. Thedicroism of the infrared bands can also give informationsabout the assignment to the symmetry species, using theoriented gas model to predict the behaviour in polarizedlight. For the free molecule only the direction of thetransition moment of the A vibrations is fixed by sym-metry and for these modes, using the atomic coordinatesgiven by Isakov [10], the proportionality factors for theabsorption are.

    a b c ( ab)I(A) 0.542 0.269 0.189

    From these values it appears that, in the polarisedinfrared spectra of the ab crystal plane, the A modeshould give the strongest component with the electricvector of the light perpendicular to the b axis. Someof the A modes can also show the same dichroism asthe A vibrations, since the direction of the transitionmoment is only fixed in the molecular plane. However,bands with a prevailing component polarized along the baxis or with components of comparable intensity in bothpolarizations can be confidently assigned to A modes.

    On these grounds, the most part of the absorptionbands appearing below 1000 cm1, which show a pre-vailing polarization along the a-axis, could be associatedto A vibrations. However, the polarized character of theRaman lines found at 831,626 and 303 cm1 in solutionplaces totally symmetric modes at these wavenumbers

    Fig. 6. Polarised Infrared spectrum of acrylamide.

    Fig. 7. Infrared spectrum of acrylamide at 157C.

    and therefore only the bands at 991, 963, 819, 708, 665,490 and 215 cm1 are plausible candidates for the as-signment to A modes. Deuteration strongly affects thegroup of bands between 820 and 650 cm1, thus indi-cating that the NH2 wagging and twisting motions con-siderably contribute to the corresponding normal modes.This interpretation is also supported by the observationthat these bands undergo a strong positive shift (819830, 665682 and 708733 cm1) and a noticable sharp-ening on cooling to 157C.

    The remaining infrared bands show a dichroism con-sistent with the attribution to the A symmetry and, inmost cases this attribution is confirmed by the polarisedcharacter of the corresponding Raman lines. The re-maining vibrational assignments are shown in Table 4.On the whole, the fit between the calculated and ob-served frequencies shown in Table 4 is good and the ex-perimental facts are satisfactorily accounted for by theforce field, indicating that the force constants obtainedare reasonable.

    2. Polyacrylamide

    The recorded Fourier Transform infrared spectra ofpolyacrylamide, deuterated polyacrylamide and Raman

    Fig. 8. Laser Raman spectrum of acrylamide.

  • FTIR and Polarised Raman Spectra of Acrylamide and Polyacrylamide - R. Murugan et al. -509-

    Table 4. Calculated and observed frequencies (cm1) and approximate potential energy of acrylamide.

    Infrared frequency Laser Raman frequency Calculated frequency Vibrational assignment PED %A SPECIES

    3352 W 3342 W 3341 a NH2 S1(99)3180 W 3163 VS 3227 s NH2 S2(100)3105 VS 3103 VW 3126 a CH2 S3(99)3030 MS 3030 MS(P) 3022 s CH2 S4(98)3011 W 3006 CH S5(100)1675 W 1685 MS(P) 1690 C=O S6(50), S7(21), S13(11)1650 W 1639 VS(P) 1648 C=C S7(62), S6(10), S16(10)1612 MS 1595 VS(P) 1626 C-C S8(60), S7(15), S15(10)1430 VS 1432 VS(P) 1426 C-N S9(100)1353 S 1350 W 1330 $ NH2 S10(60), S17(17)1282 S 1280 S(P) 1268 NH2 S11(45), S13(30), S16(15)1138 VS 1149 S(P) 1129 $ CH2 S12(55), S14(30), S15(15)1053 S 1052 S(P) 1062 CH2 S13(54), S15(28), S14(12)831 M 831 S(P) 838 C-H S14(60), S11(28)626 W 626 S(P) 629 C-C S15(40), S6(10)510 VS 492 MS 495 O=C-N S16(33), S13(20)

    S10(20), S17(10)303 MS 303 MS(P) 310 C=C-C S17(40), S6(10)

    A SPECIES991 S 990 W 1031 NH2 S18(42), S22(46)963 VS 963 W 960 CH2 S19(100)816 M 819 W 822 CH2 S20(50), S18(33)708 W 708 W 699 NH2 S21(97)660 W 665 W 644 CH2 S22(49), S18(12), S23(22)490 VS 490 MS 491 C=O S23(41), S22(23)225 W 215 W 218 C-C S24(80), S22(15)

    a and s - asymmetric and symmetric stretching, - bending, - wagging, - twisting, - torsion and $ - sciscoring.

    spectra of solid polyacrylamide, polyacrylamide solutionand polyacrylamide gel are shown in figures 10 and 11.The calculated and observed frequencies along with thepotential energy distribution for PA is presented in Table5. No remarkable differences are observed in the Ramanspectra of solid PA and the aqueous solutions, but ingel phase, one new band appears around 1295 cm1. Asthe complete PED matrix is very complex, only the pre-dominant terms are listed in Table 5. The assignmentsfor the vibrational bands of PA are made by comparisonwith the infrared and Raman spectra of acrylamide andother related polymers.

    In the infrared spectrum of PA, the two strong inten-sity bands appearing around 3335 and 3198 cm1 areundoubtedly associated with the N-H stretching vibra-tions since they are shifted to around 2550 and 2395cm1 upon deuteration. The normal coordinate anal-ysis on PA predicts the calculated values 3338 and 3171cm1 corresponding to the infrared bands 3335 cm1and 3198 cm1 are due to the asymmetric and symmet-ric NH2 stretching vibrations and also, these modes arepure stretching modes as expected. The correspondingmodes in acrylamide are found at 3352 and 3180 cm1.

    The methylene group vibrations are useful to monitorthe extent of polymerization. The calculated values 2965

    and 2912 cm1 corresponding to the medium intensityRaman bands at 2958 and 2930 cm1 are assigned toboth A and E asymmetric and symmetric CH2 stretch-ing vibrations. In MA, these modes are observed at 3105and 3030 cm1. The lowering of the above frequenciesin PA compared to MA is mainly due to the unsatu-rated linkage in MA. The weak intensity infrared bandobserved at 2860 cm1 in PA and its Raman counterpartat 2871 cm1 has been assigned to CH stretching modeof A species.

    The information about the overall structure of PA canbe obtained by closely monitoring the vibrations of amidegroups. The vibrational modes of amide groups are con-siderably affected by the involvement of these groups inhydrogen bonding. The C-O stretching (amide I) vibra-tions occurs at 1660 cm1 in the infrared spectrum ofsolid PA, the corresponding band in PA solutions is at1670 cm1 and in MA it is observed at 1675 cm1. Ac-cording to the PED data, for this amide I band in PA,there is a considerable contribution from C-C stretchingand NH2 deformational vibration. The difference in theamide I band in MA and PA are due to the differencein the strengths of intermolecular and intramolecular hy-drogen bonds.

    The most obvious spectral changes in the infrared

  • -510- Journal of the Korean Physical Society, Vol. 32, No. 4, April 1998

    Fig. 9. Out-of-plane vibrations of acrylamide.

    spectra upon deuteration in PA is mainly due to thevibrations involving amide hydrogen atoms. The normalcoordinate analysis on PA predicts the infrared bands ob-served at 1620 and 1600 cm1 are due to the NH2 bend-ing (amide II band) in A and E species respectively. Amedium intensity infrared band observed at 1465 cm1,is the characteristic frequency for the CH2 bending vi-brations and is in close agreement with the calculatedvalues at 1452 cm1 for A species.

    The medium intensity band observed at 1436 cm1 inRaman and 1426 cm1 in infrared has been assigned toC-N stretching (amide III) vibrations of the A species.The corresponding amide III band in MA is found around1430 cm1. The medium intensity infrared band ob-served at 1375 and 1367 cm1 have been assigned toCH2 wagging vibrations in A and E species respectively.The PED obtained for this mode shows that there is aconsiderable contribution from (CH)2 stretching and C-C stretching to this mode.

    The Raman spectrum of PA shows several bands ofmedium or weak intensity in the range 1200800 cm1.Bands observed at 1182, 1121, 1172, 1104 and 1022 cm1

    Fig. 10. Infrared spectra of polyacrylamide and deuteratedpolyacrylamide.

    Fig. 11. Laser Raman spectrum of A. Polyacrylamidesolution B. Polyacrylamide Gel and C. Solid polyacrylamide.

    in the Raman spectrum of PA are particularly interest-ing in view of their large variation in intensity attributedto differences in the degree of crystallinity, tacticity orproportion of helical structure. There are two fundamen-tal C-C stretching vibration for a MA at 1650 and 1612cm1. In PA, the calculated values 1171 and 1120 cm1corresponding to 1176 and 1125 cm1 infrared bands aredue to C-C stretching in A species.

    The weak intensity infrared bands observed at 998 and987 cm1 have been assigned to rocking mode of NH2group in A and E species respectively. The medium in-tensity infrared band observed at 974 cm1 has been as-signed to C-NH2 wagging mode and this mode remainsessentially unchanged from going to solid polymer toaqueous solution to cross linked gel. Proceeding towardsthe lower frequencies, C-C and C-N torsional modes arecalculated at 99 and 201 cm1 in A species and 101 and195 cm1 in E species respectively.

    Thus, the vibrational assignments for the Raman andinfrared spectra of PA, its aqueous solution and its cova-lently cross linked gel in the region 4000200 cm1 arediscussed on the basis of a comparison with the spectraof related polymer structure and MA. On the basis ofisotactic helical structure, the 86 normal modes of PAare assigned satisfactorily with the help of normal coor-dinate analysis.

    ACKNOWLEDGMENTS

    One of the authors (R. M.) expresses his thanks toCSIR and DST, NEW DELHI and PEC,PONDICHERRY for providing financial assistance topresent this work at 3rd AISAMP.

    REFERENCES

    [1] G. Raman Rao and K. Venkata Ramiah, Indian J. Pureand Appl. Phys. 19, 593 (1981).

    [2] Y. Anjaneyulu, Krishnan Lal and H. L. Bhatnagar, J.Indian Chem. Soc. 65, 400 (1988).

    [3] V. J. Schurz, H. Bayzer and H. Stubchen, Makromo.Chem. 23, 152 (1957).

  • FTIR and Polarised Raman Spectra of Acrylamide and Polyacrylamide - R. Murugan et al. -511-

    Table 5. Calculated and observed frequencies (cm1) and approximate potential energy distribution of polyacrylamide.

    Calculated Observed frequency Type offrequency Raman Infrared vibration

    % PED

    A SPECIES3338 3325 W 3335 VS a NH2 81S13171 3182 VS 3198 VS s NH2 85S22965 2958 M 2950 M a CH2 88S32912 2930 M 2910 W s CH2 79S4, 12S102856 2871 W 2860 VW CH 86S51651 1658 M 1660 VS C-O 59S6, 16S7, 10S131614 1622 MS 1620 S NH2 62S7, 12S11452 1456 M 1465 M CH2 68S8, 18S21422 1436 M 1426 M C-N 65S9, 20S131340 1346 M 1375 W CH2 55S10, 16S13, 10S171321 1331 W 1325 W CH 61S11, 24S5, 11S81208 1210 W 1225 W NH2 48S12, 28S9, 18S171171 1182 M 1176 M b CC 87S131120 1121 M 1125 M a CC 92S14984 990 W 998 M NH2 48S15, 22S1, 16S7968 971 W 974 M (C-NH2) 38S16, 24S7, 21S8902 906 M 900 VW s C-C 84S17821 834 W 825 M (CH2) 41S18, 22S4, 21S8780 795 W 798 VW (C-H) 39S19, 30S8, 18S4651 658 W 660 VW (C-H2) 31S20, 28S4, 19S18626 640 M 630 M (C-O) 39S21, 30S8, 18S4614 620 W 622 S C-C 42S22, 26S3, 20S13471 479 S 486 M b C-C 35S23, 27S13441 456 W 452 W a (O-C-N) 31S24, 30S14311 320 W 318 VW a C-C 42S25, 28S5, 11S8242 253 W 259 M b C-C 44S26, 30S8201 C-N 42S27, 19S999 111 W C-C 41S28, 26S17, 15S6

    E SPECIES3338 3325 W 3335 VS a NH2 78S13171 3182 VS 3198 VS s NH2 82S22962 2958 M 2950 M a CH2 88S32918 2930 M 2910 W s CH2 94S42855 2871 W 2860 VW CH 92S51651 1658 M 1660 VS C-O 88S6, 20S7, 12S131590 1599 M 1600 W NH2 64S7, 15S11442 1456 M 1465 M CH2 66S8, 22S21416 1433 M 1420 W C-N 85S91352 1367 M CH2 51S10, 24S5, 20S41321 1331 W 1325 M CH 44S11, 28S8, 22S51204 1215 W NH2 42S12, 29S4, 20S91161 1172 VW b CC 84S131092 1104 S 1095 W b CC 86S141017 1022 VW 1029 VVW a CC 88S15980 987 VW NH2 61S16, 32S7942 951 W 954 M (C-NH2) 41S17, 15S7, 20S12869 886 VW 878 M s CC 84S18802 810 W 812 W CH2 44S19, 24S3, 20S13758 764 M 775 W C-H 31S20, 18S4, 24S15641 650 VW CH2 32S21, 20S11, 28S13619 630 VVW 635 W C-O 36S22, 22S9, 24S14602 620 M C-C 38S23, 29S5, 22S13458 472 M b C-C 32S24, 28S19, 28S14402 412 W a O-C-N 30S25, 25S4, 20S15282 290 VVW 296 VW a C-C 38S26, 30S11, 25S13262 275 VW 265 W a C-C 32S27, 28S8, 24S15195 176 VVW C-N 45S28, 16S9101 111 W C-C 30S29, 26S7, 20S13

    Abbreviations used: S, strong; M, medium; W, weak; VW, very weak; VVW, very very weak; MS, medium strong; VS,

    very strong; a, asym. stretch; s, sym. stretch; , deformation; , wagging and , torsion.

    [4] M. K. Gupta and Rama Bansil, J. Polymer Sci.: Polymer Phys. Edn. 19, 353 (1981).

  • -512- Journal of the Korean Physical Society, Vol. 32, No. 4, April 1998

    [5] R. A. Kydd and A. R. C. Dunham, J. Mol. Struct. 69,79 (1980).

    [6] J. Jonathan, J. Mol. Spectrosc. 6, 205 (1961).[7] L. Bardet, G. Cassanas-Fabre and M. Alain, J. Mol.

    Struct. 24, 153 (1975).[8] K. Holland-Moritz, E. Sausen, P. Djudovic, M. M. Cole-

    man and P. C. Painter, J. Polymer Sci. Polymer Phys.Edn. 17, 25 (1979).

    [9] H. Tadokoro, M. Kobayashi, M. Ukita, K. Yasufuku and

    S. Murahashi, J. Chem. Phys. 42, 1482 (1965).[10] D. J. Christen, J. Mol. Struct. 48, 101 (1978).[11] M. J. Hanon, F. J. Boerio and J. L. Koenig, J. Chem.

    Phys. 50, 2829 (1969).[12] I. V. Isakov, Z. Stukt. Khim. 7, 898 (1966).[13] N. B. Colthup, L. H. Daly and S. E. Wilberly, Intro-

    duction to Infrared and Raman Spectroscopy (Academicpress, Boston, 1988), p. 250.