- Email: [email protected]
Conformational dependence of Raman frequencies and intensities in alkanes and polyethylene
VI SI ELSEVIER
ONAL PY
Vibrational Spectroscopy 14 (1997) 159-170
Conformational dependence of Raman frequencies and intensities in alkanes and polyethylene Antulio Tarazona a, Eckhard Koglin a, Betty B. Coussens b, Robert J. Meier b, * a Institute of Applied Physical Chemistry (IPC), Research Center Jiilich, D-52425 Jiilich, Germany b DSM Research, P.O. Box 18, 6160 MD Geleen, The Netherlands
Received 7 November 1996; accepted 24 February 1997
Abstract
Raman vibrational frequencies and intensities of several octane conformers, taken as models for corresponding conformational sequences in polyethylene, were calculated using quantum mechanical ab initio methods. Wherever direct comparison with experimental data for polyethylene was possible, agreement was very satisfactory. The present data suggest that ab initio calculated Raman data on relatively short oligomers may provide valuable information regarding the interpretation of polymer Raman spectra, in particular concerning issues where interpretation based on experimental verification is not possible. Keywords: Infrared; Raman; PE; Polymers; Alkane; Ab initio; Intensities
1. Introduction Vibrational spectroscopy is known to be able to provide detailed information on polymeric structures, e.g., provide information on quantities such as configuration, conformation, chemical composition and orientation [1-3]. A major contribution to the analysis of vibrational spectra, in particular the conformational dependence for alkanes and polyethylene (PE), was presented by Snyder and Schachtschneider [4-6]. Several of the issues we want to address in the present paper originate from the observation that the interpretation of the vibrational spectrum of poly-
* Corresponding author.
ethylene, as of many other polymers, is based on early force field methods [7]. It was very common for these early force fields that the force field parameters were fitted to represent the observed frequencies in the best possible way, i.e., the force fields parameters were fitted on the experimental frequencies [5,6]. Intensities were usually not considered by computation. The most advanced results seem to have been presented by Snyder and Kim [8,9] while using an early force field and a bond polarisability approach for calculating the Raman spectra of liquid n-alkanes. With current ab initio quantum mechanical calculations it has become possible to calculate vibrational frequencies and the corresponding intensities when the molecules are not too large. Results from such calculations provide us with more objective data than was possible from the fitted force field
0924-2031/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PII S0924-2031(97)00013-1
160
A. Tarazona et al. / Vibrational Spectroscopy 14 (1997) 159-170
calculations in which the results were biased by the input of experimental frequencies. Also inherent limiting features of bond polarisability methodology are absent. Ab initio studies have hardly, as far as we are aware of, been pursued with respect to the vibrational spectrum of polyethylene. Gough [10] has presented a few polarisability and polarisability derivative data on alkanes up to hexane, mostly in the all-trans conformation. The discussion regarding vibrational spectra in that work was rather limited and needs further exploration. We also believe that independent ab initio calculations are necessary to provide the required evidence for the correctness of some well-known procedures employed in analysing polymer vibrational spectra, e.g., the common assumption that the Raman scattering cross-section is constant as a function of molecular strain and molecular conformation. Although even a polymer like polyethylene has been extensively studied using vibrational spectroscopy, there are still many items of significant interest which have either not been resolved yet or which require further examination. For example, although numerous experimental studies (see Ref. [11] and references therein) have been undertaken on thin polymer fibres using microRaman spectroscopy in order to reveal the molecular strain, with the final intention to relate this to macroscopic mechanical properties, quantification of the strained fraction seems only justifiable when dependence of the Raman intensities on the applied molecular strain is known. It has been commonly assumed, most likely in view of the small absolute experimental strains applied (0-4%), that the strain dependence of the Raman intensities is small. With only ab initio quantum mechanical calculations being able to provide the independent information, it was recently shown [12] that the strain dependence of the intensity of the C - C stretching bands in polyethylene can not be assumed negligible even at the mentioned strain levels. Another example concerns the interpretation of the vibrational spectrum of semi-crystalline polyethylene involving the part of the Raman spectrum covering the C - C stretching range from 1000-1150 cm -1. Raman spectra in this range typically show three features: two sharp bands centered at 1060 and 1130 cm -~, representing the asymmetric and the
symmetric C - C stretching of all-trans polyethylene chains, respectively, and a broad band centered around 1080 cm -1. Because crystalline polyethylene consists of all-trans polyethylene chains (neglecting chain folds), in a semi-crystalline polyethylene the former two bands primarily probe the level of crystallinity. The 1080 cm- 1 band is characteristic of the conformationally disordered chain and is therefore characteristic for the amorphous phase and the melt of polyethylene and (long) alkanes. The ratio of the 1080 cm-1 band intensity over the overall intensity in this C - C stretching range is one of the often practised ways to calculate the crystallinity of semicrystalline polyethylene. When calculating Raman crystallinities, however, it is generally assumed that it is allowed to use integrated intensities as a measure of the total amount of material in a certain phase. More explicitly, in the procedure to calculate the Raman crystallinity of polyethylene it is implicitly assumed that the integrated intensity for a polyethylene chain of given length is the same for that chain in the orthorhombic phase and in the amorphous phase, respectively. A further argument which makes it necessary to explore the validity of current procedures to analyse experimental spectra is taken from Snyder [5]. He suggested long ago that and we think the issue has not lost its importance meanwhile, "the best argument for rejecting the 1080 cm-~ as directly attributable to gauche bond stretching is found in the fact that there does not exist an acceptable correlation between the shape of the observed band and that expected from the distribution of those modes in which gauche bond stretching coordinates are involved to the greatest extent." In addition, Snyder noted in the same paper that "the 1080 cm -1 band of polyethylene whose potential energy is largely from asymmetric C - C stretching and whose intensity is largely from methylene wagging." Different basic character of vibrations will, at least in principle, lead to different scattering crosssections and thus to different Raman cross-sections. We thus see that part of the unknown information relates to the fact that Raman intensities are rarely evaluated theoretically. The currently only feasible way to accomplish this by independent means seems to rely on results obtained from ab initio quantum mechanical calculations. Such calculations are currently computationally unfeasible on large segments
A. Tarazonaet al. / Vibrational Spectroscopy 14 (1997) 159-170
of a polymer chain. Therefore we need to rely on data obtained on relatively short alkanes. We will see from the present study, however, that such results may be favourably compared to experimental vibrational data on polyethylene. The above formulated questions concerning the interpretation of Raman intensities, however, require an independent reliable method. Because in those cases direct comparison to experimental data is not possible, the first goal in our study is to present ab initio calculated data, which were obtained from calculations on various conformers of octane, for which directly comparable experimental data are available. Finally, we wish to emphasize that the current study, with octane taken as a model for certain aspects of the full polyethylene chain, is intended as a first exploratory investigation regarding some of the Raman intensities in polyethylene. By comparing calculated and experimental data at a quantitative level, we hope to be able to put forward qualitative statements on the issues addressed in the above. For clarity, it may be noted that results presented in the present study refer to isotropic Raman scattering only.
2. Computational details As a model for (parts of) the polyethylene chain, we have studied several conformers of octane. The size of this molecule still allows for ab initio calculation of the vibrational frequencies and intensities. Recently, the strain dependence of the Rarnan C - C stretching bands in polyethylene was simulated with ab initio calculations using octane as a model and satisfactory agreement was obtained between calculated and experimentally frequency shifts [12]. We have therefore adopted the same model and the same level of calculations in the present study. Most of the calculations were performed with the Gaussian 92 suite of programs [13]. All geometries were fully optirnised within Cl-symmetry using the 6-31G* basis set. Because we also intended to study the effect of the C - C torsional bond or conformational angle on frequencies and intensities, for all systems torsional bonds with the torsional or conformational angle deliberately selected set different from 180 °, the trans case, were constrained. This implies that
161
the torsional or conformational bond angle z, illustrated by
is stepwise varied while fixed (constrained) at each step. When we look at the calculated energies for each of these conformations this leads to a rotational energy profile or, using alternatively naming, a conformational energy function. Correspondingly, when one or more gauche bonds were present in the octane each of these bonds was constrained to + 60 °. For a single gauche bond the state with the torsional angle set at + 60 ° is a local minimum on the energy surface. Consequently either or not constraining this angle will essentially make no difference. Electron correlation effects were not considered, but have been shown to be small at the MP2 level as revealed from calculations on the polarisability derivatives for the C - C stretch and CCC bending vibration in alkanes reported by Gough [10]. Geometries were optimised until individual gradients were less than 10 - 4 hartree/bohr and the root-mean-force less than 10 - 7 hartree/bohr. At the time we ran the ggggg, gtggt and ttggt conformers, Gaussian 94 [14] had been locally installed and was employed and geometries were optimised until individual gradients were less than 10 -5 hartree/bohr and the root-mean-force less than 10 -8 hartree/bohr. In any sequence containing more than one gauche bond, all gauche bonds are g÷ or, equivalently, they are all g - , unless explicitly indicated otherwise as for the case tg÷tg-t. Geometry optimisations were followed by a force constant calculation to obtain Raman frequencies and the Raman intensities. No scaling of vibrational frequencies was applied.
3. Results and discussion The calculated modes can be identified with the experimentally observed modes by enumeration of the total number of observed Raman active modes and considering the symmetry of the modes and by making reference to the octane frequencies published
162
A. Tarazonaet al. / VibrationalSpectroscopy 14 (1997) 159-170
by Snyder [5]. The fact that three of the calculated frequencies of octane exhibiting Raman activity are identified with the single 1060 cm -1 band in polyethylene is in accordance with the splitting observed when shortening the length of the alkane, viz., Table V in Ref. [6]. In more detail, the calculated Raman bands positioned at 972, 1084, 1125, 1142, 1254, 1449 and the broad feature around 1640 cm -~ were identified with the experimental Raman bands reported for solid n-octane [15] at 899, 1045, 1062, 1138, 1297 and the 1384, 1449-1469 cm -1 range, respectively. The difference between calculated and experimental frequencies is typically of the order of 10%, which is a well-known deviation of HartreeFock calculated vibrational frequencies from experimental values. The calculated octane bands at 1084, 1125 and 1142 cm -1 correspond, in the long chain limit, to the asymmetric C - C stretch vibration in polyethylene, whereas the 1254 c m - I is related to the symmetric C - C stretching in polyethylene (see also Table 1 in Ref. [12]). We first discuss calculated data which can be compared to directly measurable experimental quantities. We feel such comparison is required for validating the use of octane as a model for polyethylene as far as vibrational spectra are concerned. We have already mentioned the known deviation of some 10% in the absolute values of calculated frequencies when calculating vibrational frequencies in the 500-3500 cm-1 range using Hartree-Fock methods. 3.1. Effect o f strain on vibrational frequencies
Very satisfactory agreement was found [12] between calculated and experimental Raman shifts/% molecular strain 1 for the 1060 cm -1 and the 1130 cm -1 bands (calculated values 16.8 c m - 1 / % strain and 8.0 c m - 1 / % strain versus the experimental [16,17] values 14 c m - i / % strain and 8.7 c m - 1 / % strain). In addition, the quoted [12] frequencies corresponding to the 1296 c m - ~ polyethylene band lead to a Raman shift of 1.3 c m - 1 / % strain. This is a small shift only when one realizes that even for the
1Molecular swain is here defined as the strain applied in the direction of the extended chain and must be distinguished from macroscopic strain.
high-modulus polyethylene fibres, for which macroscopic strain is most directly converted into molecular strain, the maximum applicable strain before failure is about 4%. This small calculated strain dependence agrees with experimental data reported by Wool and Bretzlaff [18] who did not find any perceptible shift of the experimental 1296 cm -1 mode. The latter data have been obtained on normal stressed polyethylene films rather than ultra-high modulus fibres and therefore it can not be expected that the macroscopically applied strain is close to the molecular strain as was shown to be the case for the named fibres [16]. Consequently the shift/% strain values presented by Wool and Bretzlaff are underestimates of the shift/% molecular strain which is the calculated value. This is also revealed when we compare the shift upon strain of the (experimental) 720-730 cm-1 band shape to the calculated values. Our ab initio data reveal that this A u-type mode in octane is at 780 cm -1 whereas for 10% strained octane the band has shifted down to 707 cm-1, from which a shift/% strain of 7.3 c m - 1 is corroborated. This value is to be compared to the Wool and Bretzlaff value of 2 - 3 c m - 1 / % strain. The feature that normal polyethylene will not allow for a full transformation of macroscopic strain to molecular strain, which subsequently leads to an underestimate of experimentally determined shift/% strain values for such samples, is most likely the cause of the apparent discrepancy between the calculated and experimental values for compressed polyethylene recently reported by Lacks [19] 2 Experimental data on other Raman (and IR) shifts for polyethylene under stress have also been presented by Wool and Bretzlaff [18]. The calculated Raman bands in the 3000 c m - l range, viz., Table 1, exhibit shifts/% strain up to 4 cm-1 (upward fre-
2 It may be worthwhile noting that all calculated frequencies reported in the present study were all obtained within the harmonic approximation.Still, agreementwith experimentis satisfactory. This contrasts the results presented by Wool and Bretzlaff [18] who used a simple force field approach to compute the frequencies and reported that the calculated harmonic frequencies led to the wrong sign of the frequency shifts for the C-C stretching bands. Anharmonic contributions were assumed very substantial and even dominating for many of the IR and Raman bands.
A. Tarazona et al. / Vibrational Spectroscopy 14 (1997) 159-170 Table 1 Ab initio (6-31G * basis) calculated Raman frequencies and intensities for 0 and 10% molecular strain in all-trans n-octane 0% strain Frequency 3175 3181 3190 3192 3198 3201 3226 3259 3260 Sum Ramanin~nsities
10% strain Intensity 2.4 129.0 94.0 219.0 391.0 97.0 60.0 58.0 190.0 1240.4
Frequency 3189 3196 3199 3213 3218 3220 3246 3294 3304
Intensity 6.5 248.0 75.0 294.0 288.0 52.0 2.9 110.0 185.0 1261.4
Frequencies are given in cm-1 and Raman intensities in ~4. For S.I. units the values should be multiplied by 4~'~o (in j - i C 2 m-l).
quency shift) when individual frequencies in Table 1 are considered. It is corroborated from the data presented in Table 1 that the Raman frequencies and the integrated intensities in this range are practically constant as a function of strain, at least for realistic strains in polyethylene (up to 5% molecular strain as obtained for high-modulus fibres). Thus, the 3000 cm-1 range seems relatively insensitive to molecular strain.
3.2. Conformational dependence: Raman spectrum in the range 0-600 cm- l
results for octane are compared in Fig. 1. The data plotted from our calculations refer to single conformers of octane. The data points from Snyder and Kim are energy-weighted sums over all conformations. It is possible to obtain a similar weighted curve based on ab initio data, but this requires substantial computational demands. Nevertheless, based on the presently available data, the current ab initio results seem to confirm the applicability of the previously reported data based on a force field and the bond polarisability scheme. Moreover, we believe that the ab initio calculated vibrational intensities provide a more sound basis as they do not involve assumptions like additivity of bond polarisability. Snyder [6] has noted that " S o m e modes of the n-paraffins have frequencies which are quite insensifive (say, within the normal half-width of a band) as to whether the molecule is planar or has one or two or perhaps even several gauche bonds. Notable examples are the totally symmetric C - C stretching and < CCC bending modes. Thus the presence of a band
10 • "~
A
8~-
~6 ¢/) t"
,-.
4
t~
t~
Snyder and Kim [8] have studied the Raman spectra of the liquid n-alkanes C4-C 9 and presented the overall Raman intensity in the given frequency range as a function of gauche content (viz., Fig. 11 in Ref. [8]). The analysis of the data was performed by employing a dedicated alkane force field [6] in conjunction with a simple bond polarisability model. The data showed a small increase in overall intensity when going from 0 to 20% gauche content, whereas a significant decrease by some 80% was computed for the 100% gauche isomers. Using our ab initio calculated frequencies and intensities we were able to calculate the Raman intensity of octane in the 0-600 c m - 1 range from first principles. Our calculations rather nicely confh'rn the results from Snyder and Kim. The results from Snyder and Kim and our
163
2 0
i
0
0.2
i
0.4 0.6 gauche content
I
0.8
Fig. 1. Integrated Raman intensity for the 0-600 cm-1 range for octane as a function of gauche content. The diamonds indicate the data taken from Snyder and Kim [8], while the triangles are the ab initio calculated values for each individual conformer as corroborated from the present study. The squares are the ab initio calculated values with the two values with gauche content 0.2 (ttgtt and tgttt) and the two values with gauche content 0.4 (ttggt and tg ÷ t g - t ) averaged. Because the energy difference between the conformers within each of these two sets is very small (much less than 1 kcal/mol), arithmetic averaging is equal to Boltzmann weighted summation. The drawn lines are intended as a guide to the eye. Note the qualitative agreement between experiment and theory concerning a small, but discernible, increase of intensity at low gauche content.
164
A. Tarazona et al. / Vibrational Spectroscopy 14 (1997) 159-170
Table 2 Ab initio (6-31G * basis) calculated Raman frequencies for the < CCC bending region near 300 cm- l Rotamer
Force field calculated frequency a
Calculated frequency present work, ab initio
~t~ tgttt ugu tgtgt
274 285 300
291 296 303 303
fully extended chain in the melt. For the totally symmetric < C C C b e n d i n g m o d e our calculations c o n f i r m S n y d e r ' s c o n c l u s i o n and we find an e v e n smaller spacing b e t w e e n the frequencies for the various conformers as can be corroborated from the data collected in Table 2.
3.3. Conformational dependence: Raman spectrum around 1300 c m - 1
Various octane conformers. Values are frequencies given in cm- 1. For S.I. units the values should be multiplied by 4zr% (in j-1 C 2 m-l). a Data from Snyder [6].
in the R a m a n spectrum of the liquid n-paraffins, associated with this latter m o d e c a n n o t be interpreted to indicate the presence o f fully extended molecules as has b e e n suggested." S n y d e r ' s statement disagreed with other views [20] advocating that the presence of the l o w - f r e q u e n c y b a n d a r o u n d 300 c m - 1 in the melt, and which is associated with the < C C C b e n d i n g mode, is indicative of the persistence of the
A further confirmation of the applicability o f the results as obtained from the simulations o n octane can be obtained w h e n we inspect the intensity in the 1300 c m -1 range. Strobl a n d H a g e d o m [21] have experimentally verified that the overall intensity in this spectral range for polyethylene does not change as a function of temperature b y calibration to the carbonyl stretch vibration in e t h y l e n e - v i n y l acetate copolymer. Because o f the highly localised character of this vibration, Strobl and H a g e d o m argued that the R a m a n intensity o f this b a n d should be i n d e p e n dent on chain conformation. For polyethylene the
Table 3 Ab initio (6-31G * basis) calculated Raman frequencies and intensities for various octane conformers in the experimental 1300 cm- l range Angle ~" a
60° ttgtt
100°
140°
180° all trans
60° tgttt
1441 (0.35) 1455 (5.75) 1458 (12.4) 1462 (37.4)
1421 (0.3) 1443 (0.3) 1449 (3.0) 1455 (22.6) 1461 (32.0)
1442 (1.5) 1452 (45.5) 1454 (0.4) 1462 (10.2) 1485 (0.1)
1449(60.6)
1422 (7.2) 1448 (5.6) 1454 (9.9) 1457 (28.6) 1471 (2.7) 1485 (12.4)
Total intensity
55.9
58.2
57.7
60.6
66.4
Conformer
tg + tg- t
ttggt
gtggt
ggggg
1410 (3.2) 1422 (1.4) 1445 (2.3) 1452 (4.4) 1458 (33.5) 1468 (15.7)
1407 (2.9) 1430 (7.3) 1442 (2.8) 1455 (29.6) 1460 (7.8) 1484 (7.0)
1406 (7.4) 1423 (3.7) 1447 (1.5)
60.5
57.4
72.8
1423 (13.4) 1446 (1.6) 1453 (23.2) 1466 (5.9) 1468 (1.3) 1489 (15.0) Total intensity
60.4
1472 (60.2)
The values are frequencies given in cm- 1. The values in parentheses are the Raman intensifies given in ~4. For S.I. units the values should be multiplied by 4~r% (in j - i C 2 m-l). a The angle r is the backbone C-C torsional angle as defined in Section 2.
A. Tarazona et al. / Vibrational Spectroscopy 14 (1997) 159-170
165
main (conformational) effect of an increase of temperature is an increase in the overall gauche content in the alkane or polyethylene. When we now inspect the total Raman intensity in this spectral range as deduced from the currently presented calculations, viz., Table 3, we conclude that the dependence on conformation is very weak. In more detail, the (calculated) integrated Raman intensity in the 1300 cm-~ range is practically identical for the ttttt, the tg+tg+t, the ttggt and the gtggt conformers. For a single gauche defect we need to average tgttt and ttgtt, which leads again to practically the same value of about 60 ,~4 (the energy difference between these conformers was calculated to be 2 . 1 0 -3 kcal/mol and therefore averaging is equivalent to Boltzmann weighted summation). Only for the ~ggggg conformer a relatively high value of 72.8 ,~4 is calculated. However, the likelihood (Boltzmann weighted) to have a ggggg sequence is of the order of 3% only, and therefore this conformer will hardly contribute to the overall Raman intensity in this frequency range. Thus, from the point of view of intensities the calculated data are in good agreement with the experimental evidence presented by Strobl and Hagedorn, i.e., for polyethylene the Raman intensity in the (experimental) 1300 cm -1 range is practically conformer and thus temperature, independent. Most importantly, our data therefore confirm the result presented by Strobl and Hagedorn and implies that the integrated intensity over the experimental 1300 cm -I range may be used as a reference for studying intensity changes in other parts of the polyethylene Raman spectrum.
wise lead to good relative intensities. However, we have meanwhile seen that the 1300 cm -1 cluster (experimental frequency range) can be considered constant as a function of temperature. Taking this as a gauge, we still observe a considerable increase in Raman intensity in the 700-950 cm-1 range with increasing temperature, i.e., with increasing gauche content. The calculated integrated intensities in the calculated frequency range 700-1000 cm -1 have been collected in Table 4. It is clear from those data that at high temperatures, i.e., in the melt, when the trans-gauche ratio approaches l, the integrated Raman intensity roughly doubles, whereas a tail develops towards lower frequencies. The calculated results seem in qualitative agreement with the experimental observations, albeit that the calculated increase of intensity is underestimating the experimental increase which corresponds to about a factor of 3-4, assuming a constant integrated intensity in the 1300 cm-~ range which was taken as the reference intensity. Extended-chain-polyethylene, however, which is virtually 100% crystalline, does not show Raman intensity in this spectral range [23]. This suggests that our octane model may not be appropriate to describe the intensity changes in this spectral range correctly for polyethylene. Alternatively, the relative Raman intensity for the all-trans chain might decrease upon lengthening of the alkane. Additional calculations on long alkanes are required to further elucidate on these matters.
3.4. Raman spectrum in the range 700-1000 cm - 1
One of the most intriguing spectral ranges for polyethylene is the experimental 1060-1130 cm -~ region which comprises the C - C stretching bands arising from crystalline (1060 and 1130 cm -1) and amorphous (1080 cm -1, broad) bands, viz., the discussion on Raman crystallinity in the Introduction. When we inspect the data in Table 5 two observations may be made. Firstly, the total intensity in the calculated range 1030-1305 cm -1, which corresponds to experimental C - C stretching region in polyethylene, is some 20% lower for the gauche conformer (ttgtt) and the gtggt conformer compared to the trans conformer (ttttt). For the tgttt and ggggg conformers the difference is only 5%. The difference
We now turn to quantities that can not be directly compared to presently available experimental data. Experimentally a considerable increase in Raman intensity upon melting has been observed for long alkanes and polyethylene in the frequency range 700-950 cm -~. The experimental spectra for a sample of C36H74 w e r e shown in Fig. 4 of Ref. [22] and for a polyethylene in Fig. 5 of Ref. [22]. The spectra shown in Ref. [22] do not necessarily show the correct relative intensities as it is very difficult to measure Raman spectra while fully retaining the net sensitivity of the measurement, which would other-
3.5. Conformational dependence: Raman spectrum in the range 1000-1200 c m - z ( C - C stretching)
A. Tarazona et al. / Vibrational Spectroscopy 14 (1997) 159-170
166
between the all-trans conformer on the one hand and the ttgtt or the gtggt conformer on the other hand is practically entirely due to the intensity change of the group of frequencies in the range 1230-1305 cm -1 (primarily corresponding to the intense symmetric C - C stretching range in polyethylene, see assignments above) with a calculated increase in Raman intensity of 5.5 ~4 to 16.9 ,~4 when going from ~-= 60 ° (gauche conformation ttgtt) to r = 180° (all-trans conformation). These results indicate that
whereas the calculated integrated Raman intensity in the (calculated) range 1140-1300 cm-1 (experimental range 1060-1130 cm -1 for polyethylene) varies between 0 and 20% between conformers, there is a relatively large effect, according to the present calculations up to a factor of 3, regarding the calculated range 1230-1305 cm -1 (experimental range 1130 cm-1 for polyethylene). The effect of conformation on the Raman spectrum is more apparent from the simulated spectra shown in Fig. 2. The spectra have
Table 4 Ab initio (6-31G * basis) calculated integrated Raman intensities in the calculated frequency range 700-1000 c m - l Conformer
Frequency
Intensity
Conformer
Frequency
Intensity
ttttt
971 870 997 978 956 953 967 954 916 883 818 794 780 956 946 890 884 828 786 977 956 900 889 831 794 773
16.5 0.2 1.1 1.7 20.9 2.2 13.4 1.1 5.3 3.9 0.4 0.5 0.35 8.8 1.1 2.9 17.3 3.7 1.4 2.8 10.9 8.4 4.0 1.7 0.4 0.8
gtggt
996 973 929 903 875 840 808 773 991 946 910 867 839 786 779
2.5 4.1 7.9 11.8 4.1 2.6 1.5 1.75 12.4 1.1 4.4 25.4 1.0 10.8 0.2
ttgtt
tgttt
tg+tg-t
ttggt
Conformer ttttt ttgtt tgttt tg + t g - t ttggt gtggt ggggg
ggggg
Integrated intensity 16.7 25.9 25.0 35.2 29.0 36.3 55.3
Raman intensities are given in ~4. For S.I. units the values should be multiplied by 4~r¢o (in J - 1 C 2 m - 1 ) .
167
A. Tarazona et al. / Vibrational Spectroscopy 14 (1997) 159-170 Table 5 Ab initio (6-31G * basis) calculated Raman frequencies and intensities for various octane conformers in the C-C stretching range Conformer ttttt
ttgtt
tgttt
tg + tg + t
ttggt
gtggt
ggggg
1084 (4.5) 1125 (8.2)
1 0 4 9 (0.7) 1125 (6.7) 1127 (10.8)
1 0 3 2 (2.3) 1099 (10.8)
1142 (24.1)
1 1 5 2 (1.6) 1165 (13.6) 1188 (5.3)
1048 (3.7) 1088 (1.1) 1107 (7.7) 1136 (3.2) 1139 (11.9) 1166 (12.6) 1191 (3.2)
1135 (4.6) 1 1 4 9 (6.6) 1179 (17.7) 1185 (1.2)
1 0 5 0 (0.4) 1083 (0.2) 1111 (8.2) 1130 (14.3) 1158 (1.7) 1177 (5.4) 1181 (5.0)
1 0 5 4 (2.2) 1 0 7 0 (2.5) 1107 (6.7) 1147 (12.0) 1 1 6 0 (1.2) 1173 (0.8) 1 1 8 3 (8.1)
1 0 6 4 (3.3) 1088 (2.9) 1 1 1 2 (2.9) 1 1 4 6 (3.5) 1183 (0.7) 1195 (1.1) 1204(11.4)
Total intensity 1030-1230
36.8 1254 (16.9)
38.7 1 2 5 3 (3.1) 1305 (2.4)
43.4 1253 (4.8) 1305 (3.1)
43.2 1258 (2.3) 1 2 8 6 (2.8)
35.2 1265 (4.2) 1275 (0.8)
33.5 1263 (1.3) 1271 (2.7)
25.8 1275 (0.4) 1283 (0.6)
Total intensity 1230-1305
16.9
5.5
7.9
5.1
5.0
4.0
1.0
Total intensity
53.7
44.2
51.3
48.3
44.2
44.2
51.3
The values are frequencies given in cm-1. The values in parentheses are the Raman intensities given in/~4. For S.I. units the values should be multiplied by 4~r% (in j - i C 2 m-l).
b e e n simulated using the ab initio calculated freq u e n c i e s and by fixing the line-width at 8 c m -~ . The results obtained i m p l y that the R a m a n intensity varies differently in different parts o f the R a m a n s p e c t r u m in the 1 0 3 0 - 1 3 0 5 c m -1 range w h e n c h a n g i n g conformation. T h e s e changes do not s e e m to vary simply linearly with the fraction o f g a u c h e bonds.
B e c a u s e the largest difference b e t w e e n integrated intensity b e t w e e n c o n f o r m e r s is 20%, the net effect on calculated crystallinity levels using the 1 0 6 0 - 1 1 3 0 c m -~ range in p o l y e t h y l e n e is small. O n the other hand the large intensity change in the calculated range 1 2 3 0 - 1 3 0 5 c m - 1 (primarily c o r r e s p o n d i n g to the intense s y m m e t r i c C - C stretching band near
Table 6 Ab initio (6-31G * basis) calculated Raman frequencies and intensities for various octane conformers Angle ~" a
Total intensity 1030-1250
Total intensity 1250-1305 Total intensity
60° (ttgtt)
80°
100°
120°
140°
160°
180° (all-trans)
1049 (0.7) 1125 (6.7) 1127 (10.8)
1 0 5 6 (1.5) 1 1 2 4 (7.2) 1129 (11.4)
1060 (3.1) 1123 (8.7) 1132 (10.9)
1060 (5.4) 1123 (10.1) 1134 (8.9)
1067 (6.1) 1121 (10.3) 1136 (5.4)
1084 (4.5) 1125 (8.2)
1152 (1.6) 1165 (13.6) 1188 (5.3)
1156 (12.7)
1149 (12.3)
1147 (12.1)
1147 (5.1) 1152 (12.4)
1078 (5.1) 1120 (5.7) 1134 (5.6) 1139 (1.7) 1145 (19.3)
1187 (5.2)
1186 (5.4)
1175 (4.4)
38.7 1253 (3.1) 1305 (2.4)
38.0 1259 (4.1) 1294 (4.1)
40.4 1272 (3.5) 1278 (6.9)
40.9 1261 (11.3) 1292 (1.8)
39.3 1253 (15.1)
37.4 1253 (16.5)
36.8 1254 (16.9)
1142 (24.1)
5.5
8.2
10.4
13.1
15.1
16.5
16.9
44.2
46.2
50.8
54.0
54.4
53.9
53.7
The values are frequencies given in cm -1 . The values in parentheses are Raman intensities given in ~4. For S.I. units the values should be multiplied by 47r% (in j-1 C 2 m-l). a The angle ~- is the backbone C-C torsional angle as defined in Section 2.
A. Tarazona et al. / Vibrational Spectroscopy 14 (1997) 159-170
168
1130 cm -1 in polyethylene, see assignments above) can be seen reflected in the observed drop in intensity in this range when melting the sample (e.g., see Fig. 4 in Ref. [22]), whereas the retained intensity in the calculated range 1030-1230 cm-1 is reflected in the experimental observation that the amorphous or melt band is practically symmetric around 1080 c m with a band width of some 40 c m - l . In order to be able to describe the Raman spectrum of polyethylene in the 1060-1130 cm-1 quantitatively, we need various type input data. This particularly applies to the 1080 cm -1 band which arises due to the amorphous or the melt phase. A complication which arises in this range is the persistence of residual all-trans intensity in the melt, i.e., at spectral positions 1060 and 1130 cm -1, as shown in Fig.
1 of Ref. [22]. In fact, a detailed examination of the Raman spectra of polyethylene presented by Strobl and Hagedorn [20] reveals a similar observation. In order to elucidate these phenomena, it is necessary to further investigate the conformational dependence of the Raman intensities. Because in a real experimental system the dihedral angles within the main chain will never exactly equal 180° (trans conformation) or 60 ° (gauche conformation), the Raman intensities as a function of torsional angle are required as part of the computed input parameters required to elucidate the observed experimental spectra. Ab initio calculated values for the C - C stretching range have been collected in Table 6. According to Snyder [6] " A deviation of 10° away from an exactly staggered conformation has a relatively small effect on calcu-
ttgtt
4J .-I W
tg~
4J H
tt~
ggggg
1000
loso
11oo
11so
Wavenumber
lz~o
1~o
laoo
13~0
(cm -I)
Fig. 2. Calculated Raman spectra in the C - C stretching spectral range for various octane conformers. The envelopes were constructed using reasonable line-widths (as observed from experimental data). The line width was fixed at 8 c m - 1 for all Raman bands. Intensities are based on the data presented in Table 5.
A. Tarazona et al. /Vibrational Spectroscopy 14 (1997) 159-170
lated frequencies in the important spectral region 1500-700 cm-1; for gauche n-C4Hlo the average frequency change is less than 2 cm-1. '' Furthermore, Snyder has noted that for pentane the effect is even smaller. Snyder's statements are all based on early force field calculations. From the present data collected in Table 6 we corroborate that for the Raman bands in the (calculated) range 1030-1305 cm-1 the band shifts are less than 6 cm-~ for a 20 ° change in torsional angle. When we compare calculated data for the ttxtt conformer with the torsional angle x = 180° ( = trans) and 160°, respectively, within the 700-1500 cm -1 spectral range we find a maximum frequency shift of 4 cm-1 with the sole exception of the (calculated) 1125 cm -1 Raman frequency which shifts by 8 cm -1. The findings by Snyder are thus confirmed by the present ab initio calculated data. From Table 6 it is corroborated that the overall intensity does not show any dramatic variation upon torsional angle. These data may be subsequently employed to interpret the melt and amorphous spectra of polyethylene. Since a full study involves a complete analysis of the conformational distribution in a bulk polymer, a full report on this issue will be presented elsewhere (R.J. Meier, data not shown).
169
using the vibrational frequencies. Although our ab initio work primarily supports the interpretations previously reported, the ab initio methodology provides independent and in this respect unbiased information. Moreover, the ab initio calculations provide frequencies and intensities. The latter can not be directly obtained from force field simulations, but can only be estimated using models based on, e.g., additivity of bond polarisabilities. The ab initio calculated data might subsequently be used to study experimentally inaccessible problems, e.g., the precise description of the character of the 1080 cm - l band and the persistence of Raman intensity in the 'crystalline' 1060 cm-1 and 1130 cm-1 bands in the melt. Although the present study is but a first semiquantitative attempt, we hope to have demonstrated the applicability and usefulness of ab initio calculated Raman spectra for elucidating the Raman spectra of polyethylene.
Acknowledgements Mr. J.P.C. van Heel is gratefully acknowledged for preparing the envelope spectra. The management of DSM Research is acknowledged for permission to publish this work.
4. Conclusions We have investigated the applicability of ab initio calculated Raman frequencies and intensities using octane as a model molecule to describe part of the Raman spectra of polyethylene. The effect of strain on the all-trans conformer and conformational changes were studied. In all cases where a pretty direct comparison to experimental data could be pursued (more precisely, calculated data on octane compared to experimental data on polyethylene), agreement was definitely very satisfactory. Many of the earlier interpretations presented by Snyder and others which often relied on more simple models, e.g., the assumption of additive bond polarisability and its appropriateness to describe the Raman spectra, were now confirmed on basis of ab initio calculated data. Furthermore previous studies involving interpretation have often relied on 'biased' force fields, i.e., force fields which were parametrised
References [1] D.I. Bower, W.F. Maddams, The Vibrational Spectroscopy of Polymers, Cambridge University Press, Cambridge, 1989. [2] P.C. Painter, M.M. Coleman, J.L. Koenig, The Theory of Vibrational Spectroscopy and its Application to Polymeric Materials, John Wiley and Sons, New York, NY, 1982. [3] H.W. Siesler, K. Holland-Moritz, Infrared and Raman Spectroscopy of Polymers, Marcel Dekker, New York, NY, 1980. [4] R.G. Snyder, J.H. Schachtschneider, Spectrochim. Acta 19 (1963) 85. [5] J.H. Schachtschneider, R.G. Snyder, Spectrochim. Acta 19 (1963) 117. [6] R.G. Snyder, J. Chem. Phys. 47 (1967) 1316. [7] J. Dechant, Ultrarot Spektroskopische Untersuchungen an Polymeren, Akademie Verlag, Berlin, 1972. [8] R.G. Snyder, Y. Kid, J. Phys. Chem. 95 (1991) 602. [9] R.G. Snyder, J. Chem. Soc. Faraday Trans. 88 (1992) 1823. [10] K.M. Gough, J. Chem. Phys. 91 (1989) 2424. [11] R.J. Meier, B.J. Kip, Microbeam Anal. 3 (1994) 61. [12] R.J. Meier, H. Vansweevelt, Polymer 36 (1995) 3825. [13] M.J. Frisch, G.W. Trucks, M. Head-Gordon, P.M.W. Gill,
170
A. Tarazonaet aL/VibrationalSpectroscopy 14 (1997) 159-170
M.W. Wong, J.B. Foresman, B.G. Johnson, H.B. Schlegel, M.A. Robb, E.S. Replogle, R. Gomperts, J.L. Andres, K. Raghavachari, J.S. Binkley, C. Gonzalez, R.L. Martin, D.J. Fox, D.J. Defrees, J. Baker, J.J.P. Stewart, J.A. Pople, Ganssian '92, Revision B, Gaussian, Pittsburgh, PA, 1992. [14] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. A1-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, Gaussian '94, Gaussian, Pittsburgh, PA, 1994. [15] T. Simanouti, S.-I. Mizushima, J. Chem. Phys. 17 (1949) 1102.
[16] J.A.H.M. Moonen, W.A.C. Roovers, R.J. Meier, B.J. Kip, J. Polym. Sci. Polym. Phys. B 30 (1992) 361.
[17] B.J. Kip, M.C.P. Van Eijk, R.J. Meier, J. Polym. Sci. B 29 (1991) 99, also appeared in: CHEMTRACTS-Macromolecular Chemistry 2 (1991) 282 (condensation and commentary by D.C. Prevorsek). [18] R.P. Wool, R.S. Bretzlaf, J. Polym. Sci. Polym. Phys. Ed. 24 (1986) 1039. [19] D.J. Lacks, J. Phys. Chem. 99 (1995) 14430. [20] S. Mizushima, Structure of Molecules and Internal Rotation, Part I, Academic Press, New York, NY, 1954, ch. 5. [21] G.R. Strobl, W. Hagedom, J. Polym. Sci., Polym. Phys. 16 (1978) 1181. [22] C.C. Naylor, R.J. Meier, B.J. Kip, K.P,J. Williams, S.M. Mason, N. Conroy, D.L. Gerrard, Macromolecules 28 (1995) 2969. [23] D. Haarer, H.W. Spiess (Eds.), Spektroskopie Amorpher und Kristalliner Festk~rper, Steinkopf, Darmstadt, 1995, Fig. 5.13.
ONAL PY
Vibrational Spectroscopy 14 (1997) 159-170
Conformational dependence of Raman frequencies and intensities in alkanes and polyethylene Antulio Tarazona a, Eckhard Koglin a, Betty B. Coussens b, Robert J. Meier b, * a Institute of Applied Physical Chemistry (IPC), Research Center Jiilich, D-52425 Jiilich, Germany b DSM Research, P.O. Box 18, 6160 MD Geleen, The Netherlands
Received 7 November 1996; accepted 24 February 1997
Abstract
Raman vibrational frequencies and intensities of several octane conformers, taken as models for corresponding conformational sequences in polyethylene, were calculated using quantum mechanical ab initio methods. Wherever direct comparison with experimental data for polyethylene was possible, agreement was very satisfactory. The present data suggest that ab initio calculated Raman data on relatively short oligomers may provide valuable information regarding the interpretation of polymer Raman spectra, in particular concerning issues where interpretation based on experimental verification is not possible. Keywords: Infrared; Raman; PE; Polymers; Alkane; Ab initio; Intensities
1. Introduction Vibrational spectroscopy is known to be able to provide detailed information on polymeric structures, e.g., provide information on quantities such as configuration, conformation, chemical composition and orientation [1-3]. A major contribution to the analysis of vibrational spectra, in particular the conformational dependence for alkanes and polyethylene (PE), was presented by Snyder and Schachtschneider [4-6]. Several of the issues we want to address in the present paper originate from the observation that the interpretation of the vibrational spectrum of poly-
* Corresponding author.
ethylene, as of many other polymers, is based on early force field methods [7]. It was very common for these early force fields that the force field parameters were fitted to represent the observed frequencies in the best possible way, i.e., the force fields parameters were fitted on the experimental frequencies [5,6]. Intensities were usually not considered by computation. The most advanced results seem to have been presented by Snyder and Kim [8,9] while using an early force field and a bond polarisability approach for calculating the Raman spectra of liquid n-alkanes. With current ab initio quantum mechanical calculations it has become possible to calculate vibrational frequencies and the corresponding intensities when the molecules are not too large. Results from such calculations provide us with more objective data than was possible from the fitted force field
0924-2031/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PII S0924-2031(97)00013-1
160
A. Tarazona et al. / Vibrational Spectroscopy 14 (1997) 159-170
calculations in which the results were biased by the input of experimental frequencies. Also inherent limiting features of bond polarisability methodology are absent. Ab initio studies have hardly, as far as we are aware of, been pursued with respect to the vibrational spectrum of polyethylene. Gough [10] has presented a few polarisability and polarisability derivative data on alkanes up to hexane, mostly in the all-trans conformation. The discussion regarding vibrational spectra in that work was rather limited and needs further exploration. We also believe that independent ab initio calculations are necessary to provide the required evidence for the correctness of some well-known procedures employed in analysing polymer vibrational spectra, e.g., the common assumption that the Raman scattering cross-section is constant as a function of molecular strain and molecular conformation. Although even a polymer like polyethylene has been extensively studied using vibrational spectroscopy, there are still many items of significant interest which have either not been resolved yet or which require further examination. For example, although numerous experimental studies (see Ref. [11] and references therein) have been undertaken on thin polymer fibres using microRaman spectroscopy in order to reveal the molecular strain, with the final intention to relate this to macroscopic mechanical properties, quantification of the strained fraction seems only justifiable when dependence of the Raman intensities on the applied molecular strain is known. It has been commonly assumed, most likely in view of the small absolute experimental strains applied (0-4%), that the strain dependence of the Raman intensities is small. With only ab initio quantum mechanical calculations being able to provide the independent information, it was recently shown [12] that the strain dependence of the intensity of the C - C stretching bands in polyethylene can not be assumed negligible even at the mentioned strain levels. Another example concerns the interpretation of the vibrational spectrum of semi-crystalline polyethylene involving the part of the Raman spectrum covering the C - C stretching range from 1000-1150 cm -1. Raman spectra in this range typically show three features: two sharp bands centered at 1060 and 1130 cm -~, representing the asymmetric and the
symmetric C - C stretching of all-trans polyethylene chains, respectively, and a broad band centered around 1080 cm -1. Because crystalline polyethylene consists of all-trans polyethylene chains (neglecting chain folds), in a semi-crystalline polyethylene the former two bands primarily probe the level of crystallinity. The 1080 cm- 1 band is characteristic of the conformationally disordered chain and is therefore characteristic for the amorphous phase and the melt of polyethylene and (long) alkanes. The ratio of the 1080 cm-1 band intensity over the overall intensity in this C - C stretching range is one of the often practised ways to calculate the crystallinity of semicrystalline polyethylene. When calculating Raman crystallinities, however, it is generally assumed that it is allowed to use integrated intensities as a measure of the total amount of material in a certain phase. More explicitly, in the procedure to calculate the Raman crystallinity of polyethylene it is implicitly assumed that the integrated intensity for a polyethylene chain of given length is the same for that chain in the orthorhombic phase and in the amorphous phase, respectively. A further argument which makes it necessary to explore the validity of current procedures to analyse experimental spectra is taken from Snyder [5]. He suggested long ago that and we think the issue has not lost its importance meanwhile, "the best argument for rejecting the 1080 cm-~ as directly attributable to gauche bond stretching is found in the fact that there does not exist an acceptable correlation between the shape of the observed band and that expected from the distribution of those modes in which gauche bond stretching coordinates are involved to the greatest extent." In addition, Snyder noted in the same paper that "the 1080 cm -1 band of polyethylene whose potential energy is largely from asymmetric C - C stretching and whose intensity is largely from methylene wagging." Different basic character of vibrations will, at least in principle, lead to different scattering crosssections and thus to different Raman cross-sections. We thus see that part of the unknown information relates to the fact that Raman intensities are rarely evaluated theoretically. The currently only feasible way to accomplish this by independent means seems to rely on results obtained from ab initio quantum mechanical calculations. Such calculations are currently computationally unfeasible on large segments
A. Tarazonaet al. / Vibrational Spectroscopy 14 (1997) 159-170
of a polymer chain. Therefore we need to rely on data obtained on relatively short alkanes. We will see from the present study, however, that such results may be favourably compared to experimental vibrational data on polyethylene. The above formulated questions concerning the interpretation of Raman intensities, however, require an independent reliable method. Because in those cases direct comparison to experimental data is not possible, the first goal in our study is to present ab initio calculated data, which were obtained from calculations on various conformers of octane, for which directly comparable experimental data are available. Finally, we wish to emphasize that the current study, with octane taken as a model for certain aspects of the full polyethylene chain, is intended as a first exploratory investigation regarding some of the Raman intensities in polyethylene. By comparing calculated and experimental data at a quantitative level, we hope to be able to put forward qualitative statements on the issues addressed in the above. For clarity, it may be noted that results presented in the present study refer to isotropic Raman scattering only.
2. Computational details As a model for (parts of) the polyethylene chain, we have studied several conformers of octane. The size of this molecule still allows for ab initio calculation of the vibrational frequencies and intensities. Recently, the strain dependence of the Rarnan C - C stretching bands in polyethylene was simulated with ab initio calculations using octane as a model and satisfactory agreement was obtained between calculated and experimentally frequency shifts [12]. We have therefore adopted the same model and the same level of calculations in the present study. Most of the calculations were performed with the Gaussian 92 suite of programs [13]. All geometries were fully optirnised within Cl-symmetry using the 6-31G* basis set. Because we also intended to study the effect of the C - C torsional bond or conformational angle on frequencies and intensities, for all systems torsional bonds with the torsional or conformational angle deliberately selected set different from 180 °, the trans case, were constrained. This implies that
161
the torsional or conformational bond angle z, illustrated by
is stepwise varied while fixed (constrained) at each step. When we look at the calculated energies for each of these conformations this leads to a rotational energy profile or, using alternatively naming, a conformational energy function. Correspondingly, when one or more gauche bonds were present in the octane each of these bonds was constrained to + 60 °. For a single gauche bond the state with the torsional angle set at + 60 ° is a local minimum on the energy surface. Consequently either or not constraining this angle will essentially make no difference. Electron correlation effects were not considered, but have been shown to be small at the MP2 level as revealed from calculations on the polarisability derivatives for the C - C stretch and CCC bending vibration in alkanes reported by Gough [10]. Geometries were optimised until individual gradients were less than 10 - 4 hartree/bohr and the root-mean-force less than 10 - 7 hartree/bohr. At the time we ran the ggggg, gtggt and ttggt conformers, Gaussian 94 [14] had been locally installed and was employed and geometries were optimised until individual gradients were less than 10 -5 hartree/bohr and the root-mean-force less than 10 -8 hartree/bohr. In any sequence containing more than one gauche bond, all gauche bonds are g÷ or, equivalently, they are all g - , unless explicitly indicated otherwise as for the case tg÷tg-t. Geometry optimisations were followed by a force constant calculation to obtain Raman frequencies and the Raman intensities. No scaling of vibrational frequencies was applied.
3. Results and discussion The calculated modes can be identified with the experimentally observed modes by enumeration of the total number of observed Raman active modes and considering the symmetry of the modes and by making reference to the octane frequencies published
162
A. Tarazonaet al. / VibrationalSpectroscopy 14 (1997) 159-170
by Snyder [5]. The fact that three of the calculated frequencies of octane exhibiting Raman activity are identified with the single 1060 cm -1 band in polyethylene is in accordance with the splitting observed when shortening the length of the alkane, viz., Table V in Ref. [6]. In more detail, the calculated Raman bands positioned at 972, 1084, 1125, 1142, 1254, 1449 and the broad feature around 1640 cm -~ were identified with the experimental Raman bands reported for solid n-octane [15] at 899, 1045, 1062, 1138, 1297 and the 1384, 1449-1469 cm -1 range, respectively. The difference between calculated and experimental frequencies is typically of the order of 10%, which is a well-known deviation of HartreeFock calculated vibrational frequencies from experimental values. The calculated octane bands at 1084, 1125 and 1142 cm -1 correspond, in the long chain limit, to the asymmetric C - C stretch vibration in polyethylene, whereas the 1254 c m - I is related to the symmetric C - C stretching in polyethylene (see also Table 1 in Ref. [12]). We first discuss calculated data which can be compared to directly measurable experimental quantities. We feel such comparison is required for validating the use of octane as a model for polyethylene as far as vibrational spectra are concerned. We have already mentioned the known deviation of some 10% in the absolute values of calculated frequencies when calculating vibrational frequencies in the 500-3500 cm-1 range using Hartree-Fock methods. 3.1. Effect o f strain on vibrational frequencies
Very satisfactory agreement was found [12] between calculated and experimental Raman shifts/% molecular strain 1 for the 1060 cm -1 and the 1130 cm -1 bands (calculated values 16.8 c m - 1 / % strain and 8.0 c m - 1 / % strain versus the experimental [16,17] values 14 c m - i / % strain and 8.7 c m - 1 / % strain). In addition, the quoted [12] frequencies corresponding to the 1296 c m - ~ polyethylene band lead to a Raman shift of 1.3 c m - 1 / % strain. This is a small shift only when one realizes that even for the
1Molecular swain is here defined as the strain applied in the direction of the extended chain and must be distinguished from macroscopic strain.
high-modulus polyethylene fibres, for which macroscopic strain is most directly converted into molecular strain, the maximum applicable strain before failure is about 4%. This small calculated strain dependence agrees with experimental data reported by Wool and Bretzlaff [18] who did not find any perceptible shift of the experimental 1296 cm -1 mode. The latter data have been obtained on normal stressed polyethylene films rather than ultra-high modulus fibres and therefore it can not be expected that the macroscopically applied strain is close to the molecular strain as was shown to be the case for the named fibres [16]. Consequently the shift/% strain values presented by Wool and Bretzlaff are underestimates of the shift/% molecular strain which is the calculated value. This is also revealed when we compare the shift upon strain of the (experimental) 720-730 cm-1 band shape to the calculated values. Our ab initio data reveal that this A u-type mode in octane is at 780 cm -1 whereas for 10% strained octane the band has shifted down to 707 cm-1, from which a shift/% strain of 7.3 c m - 1 is corroborated. This value is to be compared to the Wool and Bretzlaff value of 2 - 3 c m - 1 / % strain. The feature that normal polyethylene will not allow for a full transformation of macroscopic strain to molecular strain, which subsequently leads to an underestimate of experimentally determined shift/% strain values for such samples, is most likely the cause of the apparent discrepancy between the calculated and experimental values for compressed polyethylene recently reported by Lacks [19] 2 Experimental data on other Raman (and IR) shifts for polyethylene under stress have also been presented by Wool and Bretzlaff [18]. The calculated Raman bands in the 3000 c m - l range, viz., Table 1, exhibit shifts/% strain up to 4 cm-1 (upward fre-
2 It may be worthwhile noting that all calculated frequencies reported in the present study were all obtained within the harmonic approximation.Still, agreementwith experimentis satisfactory. This contrasts the results presented by Wool and Bretzlaff [18] who used a simple force field approach to compute the frequencies and reported that the calculated harmonic frequencies led to the wrong sign of the frequency shifts for the C-C stretching bands. Anharmonic contributions were assumed very substantial and even dominating for many of the IR and Raman bands.
A. Tarazona et al. / Vibrational Spectroscopy 14 (1997) 159-170 Table 1 Ab initio (6-31G * basis) calculated Raman frequencies and intensities for 0 and 10% molecular strain in all-trans n-octane 0% strain Frequency 3175 3181 3190 3192 3198 3201 3226 3259 3260 Sum Ramanin~nsities
10% strain Intensity 2.4 129.0 94.0 219.0 391.0 97.0 60.0 58.0 190.0 1240.4
Frequency 3189 3196 3199 3213 3218 3220 3246 3294 3304
Intensity 6.5 248.0 75.0 294.0 288.0 52.0 2.9 110.0 185.0 1261.4
Frequencies are given in cm-1 and Raman intensities in ~4. For S.I. units the values should be multiplied by 4~'~o (in j - i C 2 m-l).
quency shift) when individual frequencies in Table 1 are considered. It is corroborated from the data presented in Table 1 that the Raman frequencies and the integrated intensities in this range are practically constant as a function of strain, at least for realistic strains in polyethylene (up to 5% molecular strain as obtained for high-modulus fibres). Thus, the 3000 cm-1 range seems relatively insensitive to molecular strain.
3.2. Conformational dependence: Raman spectrum in the range 0-600 cm- l
results for octane are compared in Fig. 1. The data plotted from our calculations refer to single conformers of octane. The data points from Snyder and Kim are energy-weighted sums over all conformations. It is possible to obtain a similar weighted curve based on ab initio data, but this requires substantial computational demands. Nevertheless, based on the presently available data, the current ab initio results seem to confirm the applicability of the previously reported data based on a force field and the bond polarisability scheme. Moreover, we believe that the ab initio calculated vibrational intensities provide a more sound basis as they do not involve assumptions like additivity of bond polarisability. Snyder [6] has noted that " S o m e modes of the n-paraffins have frequencies which are quite insensifive (say, within the normal half-width of a band) as to whether the molecule is planar or has one or two or perhaps even several gauche bonds. Notable examples are the totally symmetric C - C stretching and < CCC bending modes. Thus the presence of a band
10 • "~
A
8~-
~6 ¢/) t"
,-.
4
t~
t~
Snyder and Kim [8] have studied the Raman spectra of the liquid n-alkanes C4-C 9 and presented the overall Raman intensity in the given frequency range as a function of gauche content (viz., Fig. 11 in Ref. [8]). The analysis of the data was performed by employing a dedicated alkane force field [6] in conjunction with a simple bond polarisability model. The data showed a small increase in overall intensity when going from 0 to 20% gauche content, whereas a significant decrease by some 80% was computed for the 100% gauche isomers. Using our ab initio calculated frequencies and intensities we were able to calculate the Raman intensity of octane in the 0-600 c m - 1 range from first principles. Our calculations rather nicely confh'rn the results from Snyder and Kim. The results from Snyder and Kim and our
163
2 0
i
0
0.2
i
0.4 0.6 gauche content
I
0.8
Fig. 1. Integrated Raman intensity for the 0-600 cm-1 range for octane as a function of gauche content. The diamonds indicate the data taken from Snyder and Kim [8], while the triangles are the ab initio calculated values for each individual conformer as corroborated from the present study. The squares are the ab initio calculated values with the two values with gauche content 0.2 (ttgtt and tgttt) and the two values with gauche content 0.4 (ttggt and tg ÷ t g - t ) averaged. Because the energy difference between the conformers within each of these two sets is very small (much less than 1 kcal/mol), arithmetic averaging is equal to Boltzmann weighted summation. The drawn lines are intended as a guide to the eye. Note the qualitative agreement between experiment and theory concerning a small, but discernible, increase of intensity at low gauche content.
164
A. Tarazona et al. / Vibrational Spectroscopy 14 (1997) 159-170
Table 2 Ab initio (6-31G * basis) calculated Raman frequencies for the < CCC bending region near 300 cm- l Rotamer
Force field calculated frequency a
Calculated frequency present work, ab initio
~t~ tgttt ugu tgtgt
274 285 300
291 296 303 303
fully extended chain in the melt. For the totally symmetric < C C C b e n d i n g m o d e our calculations c o n f i r m S n y d e r ' s c o n c l u s i o n and we find an e v e n smaller spacing b e t w e e n the frequencies for the various conformers as can be corroborated from the data collected in Table 2.
3.3. Conformational dependence: Raman spectrum around 1300 c m - 1
Various octane conformers. Values are frequencies given in cm- 1. For S.I. units the values should be multiplied by 4zr% (in j-1 C 2 m-l). a Data from Snyder [6].
in the R a m a n spectrum of the liquid n-paraffins, associated with this latter m o d e c a n n o t be interpreted to indicate the presence o f fully extended molecules as has b e e n suggested." S n y d e r ' s statement disagreed with other views [20] advocating that the presence of the l o w - f r e q u e n c y b a n d a r o u n d 300 c m - 1 in the melt, and which is associated with the < C C C b e n d i n g mode, is indicative of the persistence of the
A further confirmation of the applicability o f the results as obtained from the simulations o n octane can be obtained w h e n we inspect the intensity in the 1300 c m -1 range. Strobl a n d H a g e d o m [21] have experimentally verified that the overall intensity in this spectral range for polyethylene does not change as a function of temperature b y calibration to the carbonyl stretch vibration in e t h y l e n e - v i n y l acetate copolymer. Because o f the highly localised character of this vibration, Strobl and H a g e d o m argued that the R a m a n intensity o f this b a n d should be i n d e p e n dent on chain conformation. For polyethylene the
Table 3 Ab initio (6-31G * basis) calculated Raman frequencies and intensities for various octane conformers in the experimental 1300 cm- l range Angle ~" a
60° ttgtt
100°
140°
180° all trans
60° tgttt
1441 (0.35) 1455 (5.75) 1458 (12.4) 1462 (37.4)
1421 (0.3) 1443 (0.3) 1449 (3.0) 1455 (22.6) 1461 (32.0)
1442 (1.5) 1452 (45.5) 1454 (0.4) 1462 (10.2) 1485 (0.1)
1449(60.6)
1422 (7.2) 1448 (5.6) 1454 (9.9) 1457 (28.6) 1471 (2.7) 1485 (12.4)
Total intensity
55.9
58.2
57.7
60.6
66.4
Conformer
tg + tg- t
ttggt
gtggt
ggggg
1410 (3.2) 1422 (1.4) 1445 (2.3) 1452 (4.4) 1458 (33.5) 1468 (15.7)
1407 (2.9) 1430 (7.3) 1442 (2.8) 1455 (29.6) 1460 (7.8) 1484 (7.0)
1406 (7.4) 1423 (3.7) 1447 (1.5)
60.5
57.4
72.8
1423 (13.4) 1446 (1.6) 1453 (23.2) 1466 (5.9) 1468 (1.3) 1489 (15.0) Total intensity
60.4
1472 (60.2)
The values are frequencies given in cm- 1. The values in parentheses are the Raman intensifies given in ~4. For S.I. units the values should be multiplied by 4~r% (in j - i C 2 m-l). a The angle r is the backbone C-C torsional angle as defined in Section 2.
A. Tarazona et al. / Vibrational Spectroscopy 14 (1997) 159-170
165
main (conformational) effect of an increase of temperature is an increase in the overall gauche content in the alkane or polyethylene. When we now inspect the total Raman intensity in this spectral range as deduced from the currently presented calculations, viz., Table 3, we conclude that the dependence on conformation is very weak. In more detail, the (calculated) integrated Raman intensity in the 1300 cm-~ range is practically identical for the ttttt, the tg+tg+t, the ttggt and the gtggt conformers. For a single gauche defect we need to average tgttt and ttgtt, which leads again to practically the same value of about 60 ,~4 (the energy difference between these conformers was calculated to be 2 . 1 0 -3 kcal/mol and therefore averaging is equivalent to Boltzmann weighted summation). Only for the ~ggggg conformer a relatively high value of 72.8 ,~4 is calculated. However, the likelihood (Boltzmann weighted) to have a ggggg sequence is of the order of 3% only, and therefore this conformer will hardly contribute to the overall Raman intensity in this frequency range. Thus, from the point of view of intensities the calculated data are in good agreement with the experimental evidence presented by Strobl and Hagedorn, i.e., for polyethylene the Raman intensity in the (experimental) 1300 cm -1 range is practically conformer and thus temperature, independent. Most importantly, our data therefore confirm the result presented by Strobl and Hagedorn and implies that the integrated intensity over the experimental 1300 cm -I range may be used as a reference for studying intensity changes in other parts of the polyethylene Raman spectrum.
wise lead to good relative intensities. However, we have meanwhile seen that the 1300 cm -1 cluster (experimental frequency range) can be considered constant as a function of temperature. Taking this as a gauge, we still observe a considerable increase in Raman intensity in the 700-950 cm-1 range with increasing temperature, i.e., with increasing gauche content. The calculated integrated intensities in the calculated frequency range 700-1000 cm -1 have been collected in Table 4. It is clear from those data that at high temperatures, i.e., in the melt, when the trans-gauche ratio approaches l, the integrated Raman intensity roughly doubles, whereas a tail develops towards lower frequencies. The calculated results seem in qualitative agreement with the experimental observations, albeit that the calculated increase of intensity is underestimating the experimental increase which corresponds to about a factor of 3-4, assuming a constant integrated intensity in the 1300 cm-~ range which was taken as the reference intensity. Extended-chain-polyethylene, however, which is virtually 100% crystalline, does not show Raman intensity in this spectral range [23]. This suggests that our octane model may not be appropriate to describe the intensity changes in this spectral range correctly for polyethylene. Alternatively, the relative Raman intensity for the all-trans chain might decrease upon lengthening of the alkane. Additional calculations on long alkanes are required to further elucidate on these matters.
3.4. Raman spectrum in the range 700-1000 cm - 1
One of the most intriguing spectral ranges for polyethylene is the experimental 1060-1130 cm -~ region which comprises the C - C stretching bands arising from crystalline (1060 and 1130 cm -1) and amorphous (1080 cm -1, broad) bands, viz., the discussion on Raman crystallinity in the Introduction. When we inspect the data in Table 5 two observations may be made. Firstly, the total intensity in the calculated range 1030-1305 cm -1, which corresponds to experimental C - C stretching region in polyethylene, is some 20% lower for the gauche conformer (ttgtt) and the gtggt conformer compared to the trans conformer (ttttt). For the tgttt and ggggg conformers the difference is only 5%. The difference
We now turn to quantities that can not be directly compared to presently available experimental data. Experimentally a considerable increase in Raman intensity upon melting has been observed for long alkanes and polyethylene in the frequency range 700-950 cm -~. The experimental spectra for a sample of C36H74 w e r e shown in Fig. 4 of Ref. [22] and for a polyethylene in Fig. 5 of Ref. [22]. The spectra shown in Ref. [22] do not necessarily show the correct relative intensities as it is very difficult to measure Raman spectra while fully retaining the net sensitivity of the measurement, which would other-
3.5. Conformational dependence: Raman spectrum in the range 1000-1200 c m - z ( C - C stretching)
A. Tarazona et al. / Vibrational Spectroscopy 14 (1997) 159-170
166
between the all-trans conformer on the one hand and the ttgtt or the gtggt conformer on the other hand is practically entirely due to the intensity change of the group of frequencies in the range 1230-1305 cm -1 (primarily corresponding to the intense symmetric C - C stretching range in polyethylene, see assignments above) with a calculated increase in Raman intensity of 5.5 ~4 to 16.9 ,~4 when going from ~-= 60 ° (gauche conformation ttgtt) to r = 180° (all-trans conformation). These results indicate that
whereas the calculated integrated Raman intensity in the (calculated) range 1140-1300 cm-1 (experimental range 1060-1130 cm -1 for polyethylene) varies between 0 and 20% between conformers, there is a relatively large effect, according to the present calculations up to a factor of 3, regarding the calculated range 1230-1305 cm -1 (experimental range 1130 cm-1 for polyethylene). The effect of conformation on the Raman spectrum is more apparent from the simulated spectra shown in Fig. 2. The spectra have
Table 4 Ab initio (6-31G * basis) calculated integrated Raman intensities in the calculated frequency range 700-1000 c m - l Conformer
Frequency
Intensity
Conformer
Frequency
Intensity
ttttt
971 870 997 978 956 953 967 954 916 883 818 794 780 956 946 890 884 828 786 977 956 900 889 831 794 773
16.5 0.2 1.1 1.7 20.9 2.2 13.4 1.1 5.3 3.9 0.4 0.5 0.35 8.8 1.1 2.9 17.3 3.7 1.4 2.8 10.9 8.4 4.0 1.7 0.4 0.8
gtggt
996 973 929 903 875 840 808 773 991 946 910 867 839 786 779
2.5 4.1 7.9 11.8 4.1 2.6 1.5 1.75 12.4 1.1 4.4 25.4 1.0 10.8 0.2
ttgtt
tgttt
tg+tg-t
ttggt
Conformer ttttt ttgtt tgttt tg + t g - t ttggt gtggt ggggg
ggggg
Integrated intensity 16.7 25.9 25.0 35.2 29.0 36.3 55.3
Raman intensities are given in ~4. For S.I. units the values should be multiplied by 4~r¢o (in J - 1 C 2 m - 1 ) .
167
A. Tarazona et al. / Vibrational Spectroscopy 14 (1997) 159-170 Table 5 Ab initio (6-31G * basis) calculated Raman frequencies and intensities for various octane conformers in the C-C stretching range Conformer ttttt
ttgtt
tgttt
tg + tg + t
ttggt
gtggt
ggggg
1084 (4.5) 1125 (8.2)
1 0 4 9 (0.7) 1125 (6.7) 1127 (10.8)
1 0 3 2 (2.3) 1099 (10.8)
1142 (24.1)
1 1 5 2 (1.6) 1165 (13.6) 1188 (5.3)
1048 (3.7) 1088 (1.1) 1107 (7.7) 1136 (3.2) 1139 (11.9) 1166 (12.6) 1191 (3.2)
1135 (4.6) 1 1 4 9 (6.6) 1179 (17.7) 1185 (1.2)
1 0 5 0 (0.4) 1083 (0.2) 1111 (8.2) 1130 (14.3) 1158 (1.7) 1177 (5.4) 1181 (5.0)
1 0 5 4 (2.2) 1 0 7 0 (2.5) 1107 (6.7) 1147 (12.0) 1 1 6 0 (1.2) 1173 (0.8) 1 1 8 3 (8.1)
1 0 6 4 (3.3) 1088 (2.9) 1 1 1 2 (2.9) 1 1 4 6 (3.5) 1183 (0.7) 1195 (1.1) 1204(11.4)
Total intensity 1030-1230
36.8 1254 (16.9)
38.7 1 2 5 3 (3.1) 1305 (2.4)
43.4 1253 (4.8) 1305 (3.1)
43.2 1258 (2.3) 1 2 8 6 (2.8)
35.2 1265 (4.2) 1275 (0.8)
33.5 1263 (1.3) 1271 (2.7)
25.8 1275 (0.4) 1283 (0.6)
Total intensity 1230-1305
16.9
5.5
7.9
5.1
5.0
4.0
1.0
Total intensity
53.7
44.2
51.3
48.3
44.2
44.2
51.3
The values are frequencies given in cm-1. The values in parentheses are the Raman intensities given in/~4. For S.I. units the values should be multiplied by 4~r% (in j - i C 2 m-l).
b e e n simulated using the ab initio calculated freq u e n c i e s and by fixing the line-width at 8 c m -~ . The results obtained i m p l y that the R a m a n intensity varies differently in different parts o f the R a m a n s p e c t r u m in the 1 0 3 0 - 1 3 0 5 c m -1 range w h e n c h a n g i n g conformation. T h e s e changes do not s e e m to vary simply linearly with the fraction o f g a u c h e bonds.
B e c a u s e the largest difference b e t w e e n integrated intensity b e t w e e n c o n f o r m e r s is 20%, the net effect on calculated crystallinity levels using the 1 0 6 0 - 1 1 3 0 c m -~ range in p o l y e t h y l e n e is small. O n the other hand the large intensity change in the calculated range 1 2 3 0 - 1 3 0 5 c m - 1 (primarily c o r r e s p o n d i n g to the intense s y m m e t r i c C - C stretching band near
Table 6 Ab initio (6-31G * basis) calculated Raman frequencies and intensities for various octane conformers Angle ~" a
Total intensity 1030-1250
Total intensity 1250-1305 Total intensity
60° (ttgtt)
80°
100°
120°
140°
160°
180° (all-trans)
1049 (0.7) 1125 (6.7) 1127 (10.8)
1 0 5 6 (1.5) 1 1 2 4 (7.2) 1129 (11.4)
1060 (3.1) 1123 (8.7) 1132 (10.9)
1060 (5.4) 1123 (10.1) 1134 (8.9)
1067 (6.1) 1121 (10.3) 1136 (5.4)
1084 (4.5) 1125 (8.2)
1152 (1.6) 1165 (13.6) 1188 (5.3)
1156 (12.7)
1149 (12.3)
1147 (12.1)
1147 (5.1) 1152 (12.4)
1078 (5.1) 1120 (5.7) 1134 (5.6) 1139 (1.7) 1145 (19.3)
1187 (5.2)
1186 (5.4)
1175 (4.4)
38.7 1253 (3.1) 1305 (2.4)
38.0 1259 (4.1) 1294 (4.1)
40.4 1272 (3.5) 1278 (6.9)
40.9 1261 (11.3) 1292 (1.8)
39.3 1253 (15.1)
37.4 1253 (16.5)
36.8 1254 (16.9)
1142 (24.1)
5.5
8.2
10.4
13.1
15.1
16.5
16.9
44.2
46.2
50.8
54.0
54.4
53.9
53.7
The values are frequencies given in cm -1 . The values in parentheses are Raman intensities given in ~4. For S.I. units the values should be multiplied by 47r% (in j-1 C 2 m-l). a The angle ~- is the backbone C-C torsional angle as defined in Section 2.
A. Tarazona et al. / Vibrational Spectroscopy 14 (1997) 159-170
168
1130 cm -1 in polyethylene, see assignments above) can be seen reflected in the observed drop in intensity in this range when melting the sample (e.g., see Fig. 4 in Ref. [22]), whereas the retained intensity in the calculated range 1030-1230 cm-1 is reflected in the experimental observation that the amorphous or melt band is practically symmetric around 1080 c m with a band width of some 40 c m - l . In order to be able to describe the Raman spectrum of polyethylene in the 1060-1130 cm-1 quantitatively, we need various type input data. This particularly applies to the 1080 cm -1 band which arises due to the amorphous or the melt phase. A complication which arises in this range is the persistence of residual all-trans intensity in the melt, i.e., at spectral positions 1060 and 1130 cm -1, as shown in Fig.
1 of Ref. [22]. In fact, a detailed examination of the Raman spectra of polyethylene presented by Strobl and Hagedorn [20] reveals a similar observation. In order to elucidate these phenomena, it is necessary to further investigate the conformational dependence of the Raman intensities. Because in a real experimental system the dihedral angles within the main chain will never exactly equal 180° (trans conformation) or 60 ° (gauche conformation), the Raman intensities as a function of torsional angle are required as part of the computed input parameters required to elucidate the observed experimental spectra. Ab initio calculated values for the C - C stretching range have been collected in Table 6. According to Snyder [6] " A deviation of 10° away from an exactly staggered conformation has a relatively small effect on calcu-
ttgtt
4J .-I W
tg~
4J H
tt~
ggggg
1000
loso
11oo
11so
Wavenumber
lz~o
1~o
laoo
13~0
(cm -I)
Fig. 2. Calculated Raman spectra in the C - C stretching spectral range for various octane conformers. The envelopes were constructed using reasonable line-widths (as observed from experimental data). The line width was fixed at 8 c m - 1 for all Raman bands. Intensities are based on the data presented in Table 5.
A. Tarazona et al. /Vibrational Spectroscopy 14 (1997) 159-170
lated frequencies in the important spectral region 1500-700 cm-1; for gauche n-C4Hlo the average frequency change is less than 2 cm-1. '' Furthermore, Snyder has noted that for pentane the effect is even smaller. Snyder's statements are all based on early force field calculations. From the present data collected in Table 6 we corroborate that for the Raman bands in the (calculated) range 1030-1305 cm-1 the band shifts are less than 6 cm-~ for a 20 ° change in torsional angle. When we compare calculated data for the ttxtt conformer with the torsional angle x = 180° ( = trans) and 160°, respectively, within the 700-1500 cm -1 spectral range we find a maximum frequency shift of 4 cm-1 with the sole exception of the (calculated) 1125 cm -1 Raman frequency which shifts by 8 cm -1. The findings by Snyder are thus confirmed by the present ab initio calculated data. From Table 6 it is corroborated that the overall intensity does not show any dramatic variation upon torsional angle. These data may be subsequently employed to interpret the melt and amorphous spectra of polyethylene. Since a full study involves a complete analysis of the conformational distribution in a bulk polymer, a full report on this issue will be presented elsewhere (R.J. Meier, data not shown).
169
using the vibrational frequencies. Although our ab initio work primarily supports the interpretations previously reported, the ab initio methodology provides independent and in this respect unbiased information. Moreover, the ab initio calculations provide frequencies and intensities. The latter can not be directly obtained from force field simulations, but can only be estimated using models based on, e.g., additivity of bond polarisabilities. The ab initio calculated data might subsequently be used to study experimentally inaccessible problems, e.g., the precise description of the character of the 1080 cm - l band and the persistence of Raman intensity in the 'crystalline' 1060 cm-1 and 1130 cm-1 bands in the melt. Although the present study is but a first semiquantitative attempt, we hope to have demonstrated the applicability and usefulness of ab initio calculated Raman spectra for elucidating the Raman spectra of polyethylene.
Acknowledgements Mr. J.P.C. van Heel is gratefully acknowledged for preparing the envelope spectra. The management of DSM Research is acknowledged for permission to publish this work.
4. Conclusions We have investigated the applicability of ab initio calculated Raman frequencies and intensities using octane as a model molecule to describe part of the Raman spectra of polyethylene. The effect of strain on the all-trans conformer and conformational changes were studied. In all cases where a pretty direct comparison to experimental data could be pursued (more precisely, calculated data on octane compared to experimental data on polyethylene), agreement was definitely very satisfactory. Many of the earlier interpretations presented by Snyder and others which often relied on more simple models, e.g., the assumption of additive bond polarisability and its appropriateness to describe the Raman spectra, were now confirmed on basis of ab initio calculated data. Furthermore previous studies involving interpretation have often relied on 'biased' force fields, i.e., force fields which were parametrised
References [1] D.I. Bower, W.F. Maddams, The Vibrational Spectroscopy of Polymers, Cambridge University Press, Cambridge, 1989. [2] P.C. Painter, M.M. Coleman, J.L. Koenig, The Theory of Vibrational Spectroscopy and its Application to Polymeric Materials, John Wiley and Sons, New York, NY, 1982. [3] H.W. Siesler, K. Holland-Moritz, Infrared and Raman Spectroscopy of Polymers, Marcel Dekker, New York, NY, 1980. [4] R.G. Snyder, J.H. Schachtschneider, Spectrochim. Acta 19 (1963) 85. [5] J.H. Schachtschneider, R.G. Snyder, Spectrochim. Acta 19 (1963) 117. [6] R.G. Snyder, J. Chem. Phys. 47 (1967) 1316. [7] J. Dechant, Ultrarot Spektroskopische Untersuchungen an Polymeren, Akademie Verlag, Berlin, 1972. [8] R.G. Snyder, Y. Kid, J. Phys. Chem. 95 (1991) 602. [9] R.G. Snyder, J. Chem. Soc. Faraday Trans. 88 (1992) 1823. [10] K.M. Gough, J. Chem. Phys. 91 (1989) 2424. [11] R.J. Meier, B.J. Kip, Microbeam Anal. 3 (1994) 61. [12] R.J. Meier, H. Vansweevelt, Polymer 36 (1995) 3825. [13] M.J. Frisch, G.W. Trucks, M. Head-Gordon, P.M.W. Gill,
170
A. Tarazonaet aL/VibrationalSpectroscopy 14 (1997) 159-170
M.W. Wong, J.B. Foresman, B.G. Johnson, H.B. Schlegel, M.A. Robb, E.S. Replogle, R. Gomperts, J.L. Andres, K. Raghavachari, J.S. Binkley, C. Gonzalez, R.L. Martin, D.J. Fox, D.J. Defrees, J. Baker, J.J.P. Stewart, J.A. Pople, Ganssian '92, Revision B, Gaussian, Pittsburgh, PA, 1992. [14] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. A1-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, Gaussian '94, Gaussian, Pittsburgh, PA, 1994. [15] T. Simanouti, S.-I. Mizushima, J. Chem. Phys. 17 (1949) 1102.
[16] J.A.H.M. Moonen, W.A.C. Roovers, R.J. Meier, B.J. Kip, J. Polym. Sci. Polym. Phys. B 30 (1992) 361.
[17] B.J. Kip, M.C.P. Van Eijk, R.J. Meier, J. Polym. Sci. B 29 (1991) 99, also appeared in: CHEMTRACTS-Macromolecular Chemistry 2 (1991) 282 (condensation and commentary by D.C. Prevorsek). [18] R.P. Wool, R.S. Bretzlaf, J. Polym. Sci. Polym. Phys. Ed. 24 (1986) 1039. [19] D.J. Lacks, J. Phys. Chem. 99 (1995) 14430. [20] S. Mizushima, Structure of Molecules and Internal Rotation, Part I, Academic Press, New York, NY, 1954, ch. 5. [21] G.R. Strobl, W. Hagedom, J. Polym. Sci., Polym. Phys. 16 (1978) 1181. [22] C.C. Naylor, R.J. Meier, B.J. Kip, K.P,J. Williams, S.M. Mason, N. Conroy, D.L. Gerrard, Macromolecules 28 (1995) 2969. [23] D. Haarer, H.W. Spiess (Eds.), Spektroskopie Amorpher und Kristalliner Festk~rper, Steinkopf, Darmstadt, 1995, Fig. 5.13.