Journal of Polymer Science Macromolecular Reviews, Volume 4, Issue 1 (p 67-90)

7/27/2019 Journal of Polymer Science Macromolecular Reviews, Volume 4, Issue 1 (p 67-90)

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Laser-Vibrational Scattering by PolymersR . F. SCHAUFELE*

Esso Research and Engineering Co.

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6711. Scattering Sources . . . . . . . . . . . . . . . . . . . . . . 69

111. Laser Excitat ion an d Physical Fo rm .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71IV. Polymethylene Ch ains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77A. Solid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77B. Liquid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87V. Fu tu re Progress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90I. INTRODUCTION

Vibrational characterization of polymers has been utilized exten-sively as an approach towards the elucidation of their moleculargeometry. Most experiments, however, have involved the absorp-tion of infrared energy, owing to difficulties which, in the past, haveplagued workers attempting Raman scattering studies (1). Althoughother complementary, direct, structural approaches, such as magneticresonance and X-ray diffraction may be utilized, reliance solely uponthe absorption of infrared energy for structural information limitsthe number and types of vibrational modes observable to those whichare infrared active.A number of intrinsic, complementary differences exist betweenRaman scattering and infrared absorption spectroscopy, arising frombasic dissimilarities in the participating physical processes. Theabsorption of infrared energy by a molecule requires a change in itselectric dipole moment to occur during the transition if this processis to take place. Quantum mechanically this requires that the dipoletransition moment integral M = $\k, < re > \kl dv # 0, where \ k 2 and\Elare the upper and lower vibrational state functions and < re > =p d ip is the dipole moment operator a t any instant of time, i.e.,

* Present address: Owens-Illinois Inc., Red Cedar Research Park, Okemos,Michigan.67


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68 R . F. SCHAUFELEp d i p PO I- ( d p / @ k ) o Q k , Q k being a normal molecular coordinateand the subscript referring to values for nuclei in their equilibriumpositions. The time-dependent differential term determines whetheror not the transition occurs, its probability (intensity) being propor-tional to MZ. n contrast a vibrational transition via Raman scatter-ing depends upon the dipole moment induced in a molecule,pind~dipupon interaction with the oscillating electric field vector, E , of inci-dent light. In the first order pind-dip = (Y El where the polarizabilitytensor (YN (Y O + ( d ( ~ / d Q k ) ~ Q k , the subscript refers to values whenthe nuclei are a t their equilibrium positions, and Q k is a normal molec-ular coordinate. Again the time-dependent differential term deter-mines whether or not the Raman transition moment integral M = $9, 9 1 dv # 0. Since the operators < p j n d - d i p > and< p d i p > are respectively symmetric and antisymmetric, they connectthe zeroth vibrational state to upper states which are also respectivelysymmetric and antisymmetric. In molecules with high effectivesymmetry, such as a center of inversion, this selectivity is such that

k

k

MOLECULAR S Y M M E TRY AND VIBRATIONAL ACT IV ITY

&I-W2s>v,CT430w-I0

Uv,WCT0w0

25a

INFRAREDACTIVITY

&I-W2s>v,CT42 INTERMEDIATEw-I02U SHADED AREAS DENOTE5 MUTUAL OVERLAP O F

RAMA N AND INFRAREDACTIVITYg v LOWESTv,WCT0

SHADED AREAS DENOTEMUTUAL OVERLAP O F

IFig. 1. Moleciilar symmetry and vibrational activit.y.


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LASER VIBRATIONAL SCATTERING 69infrared and Raman transitions are mutually exclusive. Relatingthis result to hydrocarbon polymers, infrared-active modes are pri-marily C-H motions, whereas Raman-active modes include theskeletal motions of the C-C backbone. With a progressive decreaseof molecular symmetry, however, increasing mutual activity occurs,as shown schematically in Figure 1. Experimentally, Raman scat-tering occurs as emission sidebands of the incident frequency, havinga typical intensity - 1 O V that of the incident light and with adisplacement frequency equal to the interval between participatingstates.

11. SCATTERING SOURCESBefore the advent of the laser, observation of Raman scatteringby polymers was hampered, if not prevented, by a combination offactors including low source intensity, interference by other line andcontinuum source frequencies, and competition by various pro-cesses for the incident excitation energy. The latter include absorp-tion by the scattering specimen, with subsequent radiationlessdissipation or its emission as fluorescence at other frequencies, photo-decomposition of the molecule into other species, and elastic (Rayl-eigh or Tyndall) scattering. These disadvantages are particularlypronounced for the low preossure mercury (Toronto) arc lamp, gener-ally utilized for its 4358 A emission line. Although the electronicabsorption bands of pure synthetic polymers generally lie above25,000 cm-', impurities and degradation products may absorb a t-23,000 cm-l (4358 A) or lower, hampering or preventing scatteringstudies in many instances (1). Although some improvement hasbeen made towards increasing the intensity of mercury arcs byutilizing a geometry in which the luminus flux is localized in a small

volume, increasing its directionality and facilitating its focusing to asmall spot (2,3), the other aforementioned disadvantages associatedwith this frequency remain. Studies have been reported (4), whichutilized lower excitation frequencies with sources such as cesium,rubidium, and helium, but lacked the intensity and simplicity ofmercury arc emission.The laser was conceived in the mid-1950's (5,6)and first reduced topractice with the stimulated emission by ruby (7) (6943A) which wassoon followed by the He-Ne gas laser (8) (6328A) and has since beenextended to hundreds of other lasering frequencies in other systems.


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70 R . F. SCHAUFELETABLE I

Selected Laser Lines Suitable for Raman ExcitationPowers

GQ (watts)Ar+ 4880, 5145Kr+Xe+He-Ne 6328

-208, 5309, 5682, 6471, 67645419, 5971, 6271- 10 . 80 . 1

0 . 1GaAs 8400-9000 (depends upon temperature) 5YAG: bNd3+ 10,650 5

8 Output power refers to the strongest individual line which, for multiplelines, is underlined.The laser's monochromaticity, intensity, directionality, and linearpolarization provide an ideal exciting source for Raman scatteringspectroscopy. Also, the large range of laser frequencies now availablepermit considerable flexibility in the selection of a laser frequency toeliminate the disadvantages of mercury arcs. A partial list of laserfrequencies particularly suitable for continuous Raman scattering aregiven in Table I. These have been chosen on the basis of theirintensity, their reliability as practical devices, and also for spanning afrequency range in which the probabilities for absorption, fluores-cence, and photodecomposition are reduced, while remaining in thespectral region for which the photocathodes of available photoelectricdetectors retain adequate response. Together, S-20 and S-1 photo-cathodes encompass this range of frequencies. The laser's high degreeof directionality permits several orders of magnitude enhancement ofthe exciting intensity by focusing or reduction of the beam diameter.However, since the intensity of a spontaneously scattered Ramanband, IR, s proportional to (G4/A'i;) l o , where 'i; is the exciting sourcefrequency of intensity I 0 and A'i; is the mode frequency, the scatteredintensity of a given band is reduced by aofactor of -23 in changingthe exciiation frequency from Ar+ (4880 A), -20,500 cm-', to Nd3+(10,650A), -9,400 cm-'. Detector response, as well as grating andreflector efficiencies, introduce additional factors to the overall re-sponse so that the selection of a particular excitation frequency is abalance of all these considerations.


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LASER VIBRATIONAL S C A T T E R I N G 71LASER-EXCITED RAMAN SPECTROMETER

RECORDER

POLARI 6 3 2 8 i He-Ne LASER LO C K- NA MP L I F I E RBAND- PA SSF I L T E R 5 - 2 0 PHOTOMULTIPL IER

7 RATING DOUBLE IMONOCHROMATORSCATTERING CELL

ANALYZING PRISM

Fig. 2. Schematic diagram of her-excited Raman spectrometer system.The first successful application of a laser to induce Raman scatter-ing by a polymer was reported by Schaufele (9) for isotactic poly-proplene, utilizing a continuous He-Ne laser together with photo-electric detection. An excellent Raman-Rayleigh intensity ratio wasobserved with little or no fluorescence or photodecomposition, per-mitting the definitive characterization of even the lowest frequencyRaman vibrational modes to within -50 ern-' of the laser frequency.Information of similar high quality has been observed and reported(10) in a survey of polymers having various physical forms. The

instrumental arrangement is represented schematically in Figure 2.Specific experimental details have been described elsewhere (11,12).111. LASER EXCITATION AND PHYSICAL F O R M

Several different experimental arrangements are required to maxi-mize the Raman-Rayleigh scattering intensity ratio, depending uponthe physical form of the polymer. For a translucent solid this is bestaccomplished by focusing the laser beam into a conical cavity cuteither into a cast piece or a pellet formed by compression of


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L

ETOA

ME

FOVO

P

CS

L

BM

L

.TU

SD

L

BM

+ 1OO

b.T

SD

LQD f

CL T

cLQD

L BM LE O V

O

1LBM MRP q

MUP

WE

P

C

MR

ISUO

Fg3E

menaa

menoraeaoospmennvaouspcoms


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LASER VIBRATIONAL SCATTERING 73powder (9), as shown in Figure 3a. The cavity functions as a lighttrap, producing multiple scattering of the incident photons via theintrinsic reflectivity and transmittance of the specimen to the laserfrequency. By suitably adjusting the thickness from the cavity wallto the front surface (generally 1 mm or less) an optimum Raman-Rayleigh intensity ratio is reached which is superior to either front orback surface illumination. Schrader and Bergmann (13) have sinceindependently verified this theoretically. The resulting Ramanbands are depolarized by subsequent Rayleigh scattering. Anillustration of a result utilizing this approach is shown in Figure 4 orpoly(viny1 chloride). X-ray diffraction studies (14) have shown theunit cell to contain 2 helical chains, each of which has 4 skeletalatoms and 1 turn per repeat period. A normal coordinate analysis

c0I

3000 2800 1400 1200 loo0 800 600 400 200 0A'v ( cm- '1

Fig. 4. Laser-excited Raman scattering by translucent, helicalCH3 [CHzCHCI], CH3 (300K).

3000 2800A'v ( cm- '1

Fig. 4. Laser-excited Raman scattering by translucent, helicalCH3 [CHzCHCI], CH3 (300K).


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74 R . F. SCHAUFELEof the vibrational modes of this sytem has been reported (15) , andfurther analysis is presently in progress (16).When the specimen is a transparent, solid polymer, directionality ofthe laser beam is preserved in passing through, producing a scatteringimage which is colinear with the monochromator slit aperature forscattering observed at 90" to the direction of incidence, as shown inFigure 3b. Reduction of the incident laser beam diameter, togetherwith collimation over the active specimen volume, results in either ahigher spectroscopic resolution or a higher signal/noise ratio thanthat occurring with a larger beam diameter. This technique also per-mits small spatial regions within the scattering specimen to be selec-tively studied. Alternatively, a second or multiple passes may beproduced through the scattering specimen by suitable reflection of theexit beam. The study of polarization characteristics of polymerRaman bands is facilitated by the utilization of laser excitation to-gether with a transparent specimen. This is attributable to the highdegree of linear polarization of the former and the low probability ofdepolarization of Raman light via Rayleigh scattering in the latter.An illustration of results from this approach is shown in Figure 5 forsolid, transparent polyisobutylene. Linear band polarizations par-allel and perpendicular to the experimental scattering plane (definedby the laser and observation directions) have been separated intotheir components by means of an analyzing prism. Largest degreesof polarization occur for bands a t -720 cm-' and in the -2900 cm-lC-H stretching region, reflecting their totally symmetric type dis-placements (factors of 0.56 and 1.6 are necessary to correct polariza-tion intensity ratios, I t / /II, or instrumental interactions with linearlypolarized light in these respective frequency regions). Normal co-ordinate analysis for this polymer has not, as yet, been reported.Band polarization characteristics of polymers nominally translucentmay be studied either in the molten state of the infinite chain, orcorrelated with bands of the low molecular weight liquids (oligomers).One of the differences between transparent liquids and solids isthat the former generally requires a scattering cell to prevent flowduring measurement. By a suitable reduction of the laser beamdiameter, thereby decreasing the active scattering volume, specimensize can be reduced to 5 p1 or less as, for example by utilizing a capil-lary cell, as shown in Figure 3c. The liquid state often has a greaternumber of active degrees of motion than the solid, which may be


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L A S E R V I B R A T IO N A L S C A T T E R I N G 75indicated by a broadening in the half-widths of Raman scatteredbands of liquids, above values for the solid. An illustration of thiseffect, utilizing a 5 pl specimen of CH30(CHzCHz0)4H3, an oligo-mer of helical polyoxyethylene, is given in Figure 6. Although apreliminary study has been reported (17) for scattering by this

!


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76 R . F. SCHAUFELE

rAMAN W T l E R I f f i BI c n p ( w h C yLIOUID - 3JO.KFUARIZATION II TO StATTERING RA NE

LIWID - 300.KPOLARIZATIONI O SCATTERING PLA NE

W I D 77%POLARIZATIONI O SCeiTTERlff iR A N Ef

-1' I ' I I 1 ' ' I I t ' ) 1 I I '3000 2000 1600 1200 000 400 CA i ; ( c m - ' )

Polarized, laser-excited Raman scattering by liquid and solidig. 6.CH,O(CH&HzO)rCH, (300 and 77K).


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LASER V I B R A T I O N A L SCATTERING 77material at room temperature, the present study provides informa-tion regarding polarized scattering by the liquid a t 300K anddepolarized scattering by the solid at 77K. The helix of the infinitechain is known (18) to contain '/* chemical units (CH2CH20) perturn. The 300K polarized study shows that bands a t 279 cm-' andin the 2800-2900 cm-' C-H stretching region have a high degree oflinear polarization. At 77K sharpening of bands and the disappear-ance of diffuse structure occurs for the solid, probably indicating areduction in number of those rotational isomers present in the liquid.For example, the localized CH2 twisting mode a t 1283 cm-' (300K)undergoes a reduction in half-width from 39 to 12 cm-'. Morestriking, however, is the apparent disappearance of the broad banda t 279 cm-' (300"K),whose half-width at 300K is 85 cm-', revealinga number of sharp bands for the 77K solid above and below thisfrequency, with band half-widths of 9-13 cm-' (experimental resolu-tion 8 cm-l). The la tt er series of bands are skeletal deformationmodes for which further analysis is presently in progress (19).

The intensity of Raman scattering by polymers in solution isattenuated by a factor proportional to the solute volume fraction.This reduction can be offset by the higher intensity and directionalityof lasers over their mercury arc counterpart. Exploitation of thelatter characteristic is illustrated in Figure 3 4 in which the laserbeam is repeatedly reflected within a scattering cell to multiply theRaman intensity. The polarized scattering by sodium polyphos-phate (Z 'v 200; 5 w t %) in water solution, utilizing this technique,is shown in Figure 7 . The sharp, polarized band at 1156 cm-' ischaracteristic of a localized vibration, probably a symmetric P-0stretching mode. Certain of the broader bands arise from morehighly delocalized modes, whose half-widths reflect a large number ofconformational configurations. This information, which is unattain-able via infrared absorption experiments due t o solvent absorption,suggests many areas for further development.

IV . POLYMETHYLENE CHAINSA. Solid

A series of bands in the Raman scattering spectra of short-chainpolymethylenes is observed to occur below 600 cm-' (see Fig. 8 ) , heirfrequency varying inversely with the chain length. These bands


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78 R . F. SCHAUFELE

Polar izat ion II to sca t te r ing p loneolar izat ion II to sca t te r ing p lone

1 ' 1 - 1 I - I _L - i 1 - _ 1 - _ 1 I 1 1 I I I2000 1000 1600 1400 1200 1000 800 600 400 200A; (cm- )

Fig. 7. Polarized, laser-excited Raman scattering by HO [Na+P03-],H inwater (300K).

were found to persist in the monoclinic modification, which containstwo chains per unit cell, characteristic of pure even-numbered poly-methylenes above C26H64 at room temperature, as well as for thetriclinic form, containing only one chain for even-numbered membersbelow C28H68 (20,21). This la tter observation precluded their assign-ment to intermolecular modes and indicated tha t they result primarilyfrom intramolecular transitions. Early Raman studies by severalworkers (22) reported a number of low frequency bands for shortchain polymethylenes in the liquid state, i.e., below C18H38. At lowtemperatures where these materials solidify only one sharp band wasreported below 800 cm-l, it s frequency being inversely proportional


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LASER VIBRATIONAL SCATTERING 79

2883

>

1132

8 X

303I

67 4

0

I I I I I I I I I I3000 2000 1400 1200 1000 800 600 400 200 0

AZ (crn)Fig. 8. Raman scattering by crystalline C W H ~ ,300K).

to the chain length. Mizushima and Shimanouchi (22) showed thatthis band could be simply explained by assignment to the symmetric,longitudinal, accordionlike motion characteristic of an extended,planar zig-zag carbon backbone, as shown schematically in Figure 9.The additional bands of the liquid were attributed to rotationalisomers within the chain. Using a semiemperical approach theyshowed that the low temperature frequencies could be fitted to thelinear approximation for the longitudinal fundamental frequency of alinear chain of identical harmonic oscillators

A; N ( E / ~ ) l ~ ( 2d) - l (m/n) , for m >> n (1)where E is Youngs elastic modulus, p is the density, c is the speedof light, d refers to the distance between chain units, m is the vibra-tion order, and n is the number of chain units. This approximation


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80 R. F. S C H A U F E L E

Fig. 9. Longitudinal accordion mode of an ext,endednormal hydrocarbon molecule.

results from the basic relationship derived by Born and von Karman(23) for the finite chain given byA; = ( E / P ) ' / ~ ( ~d r)-l sin (rmln) (2)

Utilizing E = 3.4 x 10l2 ynes/cm2 as a first approximation (22),together with the X-ray density of the polyethylene crystal (24),p = 0.9834 g/cm3, and fully extended intermethylene distance,d = 1.275 x lo-* cm, longitudinal fundamental frequencies (m = 1)were calculated for Eq. (2). Excellent agreement occurs with thelowest frequency polymethylene bands observed here (as),as shownin Table 11. Perdeuteration of C36H74hifts the observed funda-mental longitudinal frequency to values predicted by the ratio ofdensities, as shown in Table 111. The observed high intensity ofthis fundamental results from a large change of polarizability for thismode, together with its low Av. This suggested that overtones ofthis vibration were, perhaps, also observed. Longitudinal, funda-mental, and overtone displacements are shown in Figure 10 as a func-tion of chain length. In this instance even values of m give nochange of polarizability so that only odd values are predicted (25).Utilizing Eq. (2) as an approximation to verify specific assignmentsfor m, band frequencies were plotted versus m/n, as shown in Figure11. The resulting function differs somewhat from Eq. (a), as mightbe expected for the actual planar zig-zag geometry of the poly-methylene chain, with methyl end groups. Allowance for these per-


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L A S E R V I B R A T I O N A L S C A T T E R I N G 81TABLE I1

Longitudinal Accordion Mode Frequencies of Polymethylene ChainsUtilizing Eq. (1) and (2)

Number of Order Calc Eq. (1) Calc Eq. (2) Obscarbon atoms m A? (cm-l) A9 (cm-') A; (cm-I)~~ ~

1820242832364494

1351221018776685526

1341211018776685526

132.5120.09 7 . 884.77 5 . 86 7 . 45 6 . 526

m = l(accordion I

m = 2u)

rn33

v,0m = 4

0zs

m = 5

Fig. 10. Longitudinal displacements of a linear chain.


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82 R . F. SCHAUFELETABLE 111

Longitudinal Acoustical Frequencies of Polymethylene ChainsUtilizing Eq. (3)n m A$ Calc (cm-I) A? Obs (crn-')CnHzn+z18 1

35

20 135

24 135

28 135

32 135

36 13579

44 135

94 13579

11131517192 12 325272931

128.335850 1116.032747327842324137821233918930640347315625426.075

123170216261305345382414443467489510531557

97.4

84.0

73.8

65.9

54.3

132.5355493113.6324475279422241377211337189303403475155259

2671

121168216265305346386417444467491512536556

97.8

84.7

75.8

67.4

56.5


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LASER VIBRATIONAL SCATTERING 83TABLE 111 (continued)

n

36 1 63 .Oa 62 .03 177" 1755 283* 281

a Frequencies were calculated utilizing Eq. ( l ) , i.e.,= ( P D / P H ) ~ "A: (CnH2n+dAi (CnDzn+z)

turbations was taken by means of a least-squares fit of the observedfrequencies to a (m/n) eries expansion of Eq. (2). Best agreementoccurred when even powers of (m/n)were also included, as given byEq. (3).

where A = 2495 f 86 cm-1B = - (5 .867 2.855) x lo3cm-'C = (6.253 f 3.537) x lo4cm-'D = - (3 .485 f 2.058) x lo5cm-'E = (7.329 f 5.676) x lo5cm-lF = - (4 .724 f 5.964) x lo5cm-'

Frequencies calculated from Eq. (3) are compared with the observedvalues in Table 111. For the infinite chain Eq. (3) reduces to Eq.(1) . From the value of A in Eq. (3 ) the elastic modulus of the fullyextended polyethylene chain was calculated, showing that E =(3.58 f .25) x 10l2 dyn/cm2. This is comparable with that ob-tained experimentally by X-ray diffraction techniques in the direc-tion of the polyethylene fiber axis (as ) , although the value obtainedfrom dynamical mechanical measurements is an order of magnitudelower (27). Young's modulus, estimated theoretically from the bondstretching and bending force constants, is also in agreement withthis value, if the molecular force field is adequate (28).


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84 R. F. SCHAUFELE

0 I 10.1 0.2 0.3

I0 m/n

Fig. 11. Lo w frequency Raman bands plotted as a function of m/n andtheir assignmentsn-m.


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LASER VIBRATIONAL SCATTERING 85It is also instructive to relate the longitudinal frequencies observedfor finite chains to those calculated by means of normal coordinateanalysis of the infinite chain. Such calculations have been carried

out by Tasumi and Shimanouchi (29), and by Tasumi and Krimm(30), for vibrational branch frequencies as a function of 6,, the phasedifference between neighboring CH2 groups, taking into accountinteractions between internal and lattice vibrations of polyethylene.From the Born-von Karman theory of a linear chain with n identicalunits6, = 7r(m/n) (4)

Comparing Tasumi and Krimms theoretical values with the longi-tudinal frequencies reported here (25), excellent agreement occursbetween infinite chain theory and the finite chain observables, asshown in Figure 12. For an isolated polymethylene chain, v 5 and v gcorrespond to the CCC skeletal deformation and the CC torsionalvibrational modes respectively. In the polyethylene unit cell, whichcontains two chains, a and b, these modes undergo admixture. Forthe infinite chain the longitudinal vibration becomes the longitudinalacoustical branch.It is interesting that the long chain, C94H190, takes the extendedplanar zig-zag form in crystals, since the 26 cm- accordion vibrationwould be frequency shifted if the chain were folded. Accordion-typevibrations are also predicted to occur for folded polyethylene. For aclamped-clamped chain, vibrational frequencies and mode symmetriesmatch those for the free-free configuration. Whether the longitudi-nal mode frequency is characteristic of the folded segment length orof the total chain length, however, depends upon how well the nodea t the fold decouples motions between adjacent fold segments. Thisquestion has been partially resolved by utilizing a prototype mole-cule for a folded polymethylene chain, namely the (C&)34 ring. Itscrystal and molecular structure have been determined by Newmanand Kay (31,32), employing X-ray diffraction. Its triclinic unitcell contains one molecule which consists, approximately, of twoparallel, planar zig-zag chains of 15 methylenes each, linked on eachend by two closure methylenes. A schematic representation of theactual structure is shown in Figure 13. A series of Raman-scatteredlongitudinal mode bands were observed for (CH2)34 from whose fre-quencies its chain segments are observed to move individually, but


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86 R . F. SCHAUFELE

40C

3001A

Y2WUwIA

5

200

100

0 1 1 I0 0.1 0.2 0.3

m/nFig. 12. Low frequency Raman bands and theoretical (7 ) dispersion curvesof v 6 th e CCC bending, and vg, the CC torsional, vibrations for each of the twopolymethylene chains, a and b, in the polyethylene unit cell.


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LASER VIBRATIONAL SCATTERING 87

G T T T T T T T T T T T T G 'G G 'T TG G'G T T T T T T T T T T T T G '

Fig. 13. Schematic representation of the molecular structure for the(CHd34 ring.with a degree of coupling interaction. These results and a study offolded polyethylene will be reported elsewhere.

Longitudinal fundamental modes of decoupled polyethylene foldsegments, -100 methylene units or less, or overtones, for chainsseveral times longer, may be observed via Raman scattering. How-ever, the mode fundamental of an extended chain or strongly coupledsegments, lo5methylene units long, for example, occurs at 10-2cm-1,in the region accessible to Fabry-Perot interferometers and opticalheterodyning experiments. A distribution of effective chain lengthsfor a particular specimen results in a longtidudinal mode distributionfunction characteristic of each sequence length and its abundance.The utilization of Raman scattering for the study of short or foldedchains and the latter approaches for extended infinite chains are alsoapplicable to the longitudinal branches of polymers in helical or coilconfigurations.

B. LiquidIt is interesting to compare the behavior of polymethylene chains

in the liquid and solid states by means of the Raman scatteredlongitudinal vibrational mode. Such a comparison is shown inFigure 14 for CH3(CH2)12CH3, for example, an oligomer of poly-


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88 R . F. SCHAUFELE

X 1/3

RAMAN SCATTERING BY C H ~ I C H $ I ~ C H ~L I O U I D - 3OO-KP O L A R I Z A T I O N I I TO SCATTERINGPLANE1 r-m

LumX 1/3

lD0fLlOUlD - X 0 - KPOLARIZATION 1

IcmN

TO SCATTERING PLANE

r-P-mjLc

--000 2600

SOLID - 77OKPOCARIZATIONI O SCATTERING

L0A i ; ( c m - ' )

CH3(CH2)&H, (300 and 77K).Fig. 14. Polarized, laser-excited liamari scattering by liquid and solid


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LASER VIBRATIONAL SCATTERING 89ethylene. At 300"K, this mode occurs at 219 cm-I with a bandhalf-width of 50 cm-'. For the solid a t 77K this mode frequencyhas shifted to 159 cm-' with a half-width of 11 cm-' (experimentalresolution 9 cm-I). Utilizing Eq. 3, its calculated value for the fullyextended chain at 300K is 164 cm-'. The 60 cm-I upward fre-quency shift and 5-fold band half-width increase in going from thesolid to the liquid indicate an increased distribution of effective chainlengths for the liquid, with values considerably less than the fullyextended configuration. Considering the various parts of the chainto be planar zig-zag segments, as a first approximation, utilizing Eq.(3) , a 219 cm-' longitudinal mode frequency occurs for a segment of10 methylene units. The longitudinal band for the shorter (4)methylene segment is predicted to occur in the vicinity of 400 cm-l,where the observed broad structure may also include the first over-tone of the 219 cm-' fundamental. This effect is consistent with atype of chain folding in which the segments are vibrationally de-coupled by a gauche bond and have a distribution of lengths, themost likely segment pair being -10 and 4 methylene units. Forband half-width frequencies of 194 and 244 cm-I this corresponds to- ( l l ; 3 ) and -(9.5;4.5) methylene segment pairs, respectively. Amore detailed study of this effect will be reported elsewhere.

V. FUTURE PROGRESSCurrent areas of study in the vibrational analysis of polymersreflect the progress made during recent years. Theoretical studieshave begun on the interactions (29,30) between polymer chains andalso for specific nonregular structures (16,33). These advances havebeen facilitated by improved theoretical techniques leading to accu-rate values for hydrocarbon polymer force fields, the advent of large,high speed computers, and the regenerative interaction betweenexperiment and theory. Future developments will probably includeimproved force fields for heteronuclear polymers (eventually extend-ing to biopolymers) relating band intensities to specific structures, andimproved predictability of physical properties. Structural studies ofpolymer liquids and solutions will receive increased emphasis.Certain of the observables should be related to statitical configura-tional distributions for which theoretical studies show considerable

progress, (34,35,36).


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90 R . F. SCHAUFELEReferences

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Journal of Polymer Science Macromolecular Reviews, Volume 4, Issue 1 (p 67-90)

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