J. Phys. Chem. B 2007, 111, 6327-6335
6327
Normal Vibrational Analysis of a trans-Planar Syndiotactic Polystyrene Chain F. Javier Torres,† Bartolomeo Civalleri,*,† Cesare Pisani,† Pellegrino Musto,‡ Alexandra R. Albunia,§ and Gaetano Guerra§ Dipartimento di Chimica IFM and NIS Centre of Excellence, UniVersita` di Torino, Via Pietro Giuria 7, 10125 Torino, Italia, Institute of Chemistry and Technology of Polymers (ICTP), National Research Council of Italy, Via Campi Flegrei, 34, OliVetti Building, 80078 Pozzuoli (Napoli), Italy, and Dipartimento di Chimica, UniVersita` di Salerno, Via Ponte don Melillo, 84084 Fisciano (SA), Italia ReceiVed: March 21, 2007; In Final Form: April 12, 2007
The full vibrational spectra of R and β crystalline phases of syndiotactic polystyrene (sPS), that is, phases presenting the trans-planar conformation, have been experimentally determined and compared with that calculated at the B3LYP/6-31G(d,p) level of theory for an infinite trans-planar chain. The normal vibrational analysis of most representative modes of the periodic model allowed us to give a general description of each one, which was further confirmed by the direct inspection of mode animations. An assignment of the different modes was performed in terms of frequency, relative intensity, and direction of the transition-moment vector of the observed IR peaks as well as Raman vibrational frequencies.
I. Introduction Syndiotactic polystyrene (sPS) is a polymeric material with well-known properties such as high melting point, high chemical stability, and high crystallization rate. Since its synthesis was reported several years ago,1,2 it has been the object of intensive research due to its complex polymorphic behavior, which, making some simplifications, can be described in terms of two crystalline forms, R and β, containing planar zigzag chains and two forms, γ and δ, containing s(2/1)2 helical chains generated by TTGG conformational sequences.3 Several Fourier transform infrared (FTIR) studies of the different crystalline phases of sPS have been reported in the literature.4-19 These studies have clearly established characteristic absorption peaks of the trans-planar conformation, which occurs for R and β, as well as of the s(2/1)2 helical conformation, which occurs for the γ and δ crystalline phases. In particular, experimental studies have allowed isolation of the IR spectra of the pure hexagonal R20-23 and orthorhombic β24-26 crystalline phases. As discussed in detail in ref 11, spectral subtraction procedures are made straightforward by the presence of the low absorption peak centered at 841 cm-1 that, upon crystallization, is shifted to higher frequencies. In fact, its exact position was found to depend on the crystalline phase R or β as well as on the degree of perfection of the crystallites (that is, on the occurrence of R′ or R′′ modifications3), and the shifts are large enough (from 11 up to 17 cm-1) to afford spectroscopic resolution of the amorphous and the crystalline components. Less information is available in the literature on the Raman spectra of the various crystalline modifications of sPS. The spectra of the trans-planar form were first reported by Reynolds and Hsu17 and, subsequently, by Nyquist et al.18 who attempted a partial assignment of the prominent peaks on a correlative basis. Later, Kellar et al.27,28 reported a detailed study aimed at identifying peaks characteristic of the crystalline phase, with the goal of developing a method for the quantitative evaluation * Corresponding author. E-mail:
[email protected]. † Universita ` di Torino. ‡ National Research Council of Italy. § Universita ` di Salerno.
of the crystallinity degree. Their analysis was however limited to the 850-600 cm-1 range. The development of such methods appears highly desirable, in view of the sensitivity and quantitative accuracy of Raman spectroscopy. Further advantages arise from the nondestructive nature of the technique, the absence of any sample preparation requirement, and the possibility to analyze, with the same degree of confidence, samples in the form of powders or films of any thickness. For quantitative purposes, therefore, Raman spectroscopy displays an enhanced versatility with respect to IR spectroscopy, the latter being confined to the sampling of films with a thickness of few microns. Although vibrational spectroscopy represents a powerful technique that allows the description of the sPS different crystalline forms, a complete normal-mode analysis is essential to further understand the structural dynamics of the material and to clearly distinguish the conformationally sensitive modes. Such normal-mode analysis was attempted with molecular models consisting of small chains of variable lengths and phenyl rings as substituents.29-31 Two studies were also reported in which a vibrational analysis of an infinite periodic chain of sPS was performed.17,19 In those works, the normal modes were computed using the Wilson GF matrix method with force constants taken from molecular calculations and adapted to the corresponding structure; furthermore, the simulated spectra were compared only with vibrational spectra of the crystalline R phase and without subtraction of the spectrum of the amorphous phase. In this paper, experimental spectra of films presenting both R and β crystalline phases, after subtraction of the amorphous phase contribution, are compared with vibrational frequencies and relative IR intensities of peaks of ab initio-simulated spectra of a trans-planar sPS chain, as obtained at the B3LYP/6-31G(d,p) by using the CRYSTAL06 code.32 The purpose is to take advantage of both approaches, in particular, of the ab initio simulation, to obtain a full vibrational analysis of trans-planar sPS. By using a periodic treatment of the polymer, long-range effects of the infinite structure on vibrational frequencies, the intensity of the infrared active modes, and the dipole moment direction are fully taken into account. Moreover, animations of all of the normal modes are generated to confirm the results of
10.1021/jp072257q CCC: $37.00 © 2007 American Chemical Society Published on Web 05/23/2007
6328 J. Phys. Chem. B, Vol. 111, No. 23, 2007 the performed normal vibrational analysis by direct inspection of the modes. II. Experimental and Computational Methods A. Experimental Section. a. Materials. Syndiotactic polystyrene was supplied by Dow Chemical under the trademark Questra 101. 13C nuclear magnetic resonance characterization showed that the content of syndiotactic polystyrene triads was over 98%. The weight-average molar mass obtained by gel permeation chromatography (GPC) in trichlorobenzene at 135 °C was found to be Mw ) 3.2 × 105 with the polydispersity index Mw/Mn ) 3.9. Amorphous films, 20-100 µm thick, have been obtained by melt extrusion. Uniaxially oriented films were obtained by monoaxial stretching of extruded sPS films, at draw ratios of λ ∼ 3 and at a constant deformation rate of 0.1 s-1, in the temperature range of 105-110 °C with a Brukner stretching machine. The R-form semicrystalline films were obtained by increasing the temperature (∼2 °C/min) from room temperature up to 220 °C and then maintaining the samples at that temperature for 30 min. The β-form semicrystalline films were obtained by a sudden heating at 220 °C for 30 min of films presenting a clathrate phase with 1,2-dibromoethane. b. Techniques. Infrared spectra were obtained at a resolution of 2.0 cm-1 with a Vector 22 Bruker spectrometer and/or with a Perkin Elmer System 2000 spectrometer. Both instruments were equipped with a deuterated triglycine sulfate (DTGS) detector and a Ge/KBr beam splitter. The frequency scale was internally calibrated to 0.01 cm-1 using a He-Ne reference laser. Thirty-two scans were signal averaged to reduce the noise. The thickness of the films used for infrared measurements was always between 20 and 40 µm in order to keep the peaks of interest in the range of absorbance-concentration linearity. Polarized infrared spectra were recorded by the use of a SPECAC 12500 wire grid polarizer. The degree of axial orientation relative to the crystalline phase has been formalized on a quantitative numerical basis using the Hermans’s orientation function. In particular, the order parameter of the 1222 cm-1 bands has been directly used as a measure of the axial orientation function (fcIR, which is equal to unity for perfect alignment and null for random orientation)33 for trans-planar crystalline phases. For the used R and β semicrystalline uniaxially stretched films, fcIR ∼ 0.96. The degree of crystallinity of the used unoriented R and β sPS films was 45% and 42%, respectively, as evaluated according to the IR procedure described in refs 11 and 15. Raman spectra were collected with a Nexus FT-Raman spectrometer from Nicolet (Madison, WI) equipped with a CaF2 beam splitter and an indium-gallium-arsenide (InGaAs) photoelectric detector. Collection was performed on the 180° backscattered radiation. The excitation source was a diodepumped Nd:YAG laser (λ ) 1064 nm) operating at a laser power of 750 mW. The spectra were collected in a Ramanshift range between 100 and 3700 cm-1 at a resolution of 4 cm-1. Signal averaging over at least 500 consecutive scans was performed to improve the signal-to-noise ratio. B. Computational Section. The model employed for the present study was an infinite one-dimensional chain of the transplanar sPS, which was constructed by the application of the symmetry operators of the Pm2a rod group to its irreducible part and the repetition of the resulting unit in the chain axis direction. Even if calculations could be performed on the crystalline structures of the trans-planar sPS phases, the adopted level of
Torres et al. theory does not include dispersive effects needed for a correct description of the crystal packing. Therefore, for consistency, we decided to concentrate on the isolated infinite chain model that includes all of the most relevant vibrational modes and describes both R and β phases of sPS. The ab initio quantum mechanical calculations were performed with the periodic CRYSTAL06 code.32 The B3LYP Hamiltonian34 together with a Gaussian-type all-electron 6-31G(d,p) basis set were used as the level of theory. The DFT exchange-correlation contribution was evaluated by numerical integration over the cell volume.35 Radial and angular points of the atomic grid were generated through Gauss-Legendre and Lebedev quadrature schemes. A grid pruning was adopted, as discussed in ref 35. In the present study, a (75,974)p grid was used, which contained 75 radial points and a variable number of angular points, with a maximum of 974 on the Lebedev surface in the most accurate integration region. The atomic positions and the lattice constant were fully relaxed. Default optimization algorithms and convergence criteria were adopted.32,36 Once the equilibrium geometry was determined, the normal frequencies at the Γ point were computed, within the harmonic approximation, by diagonalizing the mass-weighted Hessian matrix. CRYSTAL analytically calculated the potential energy first derivatives with respect to the atomic displacements from the equilibrium positions, whereas second derivatives were calculated numerically.35,37 The energy tolerance for the SCF process was set to 10-10 hartree. To compare the computed and the experimental data, the calculated frequencies were scaled by a factor of 0.9614, as proposed by Scott and Radom38 for the adopted level of theory. The IR intensity Ai of the ith mode is defined as follows
A i ∝ di |
∂µ 2 | ∂Qi
It is proportional to the degeneracy di of the ith mode that multiplies the square of the first derivative of the cell dipole moment with respect to the normal mode coordinate Qi. The latter was computed numerically by using localized Wannier functions in the unit cell.39,40 At present, a Raman activity calculation is still not available in the current release of the CRYSTAL code. III. Results and Discussion A. Vibrational Spectra of r and β trans-Planar Crystalline Phases. FTIR spectra for the spectral range of 3150-400 cm-1 of sPS semicrystalline films that present the trans-planar crystalline phases (R and β), after subtraction of the contribution of the amorphous phase (am),13 are shown in Figure 1, spectra (R) and (β), respectively. The most conformationally sensitive spectral regions4-8 are shown in more detail in three inset figures. Several conformationally sensitive peaks, that is, peaks whose positions are different for amorphous and crystalline phases, are clearly apparent. Particularly relevant is the intense 1223 cm-1 peak (central inset of Figure 1), which corresponds to a weak amorphous peak at 1196 cm-1 and is absent for helical crystalline structures (γ and δ).4-8 Between conformationally sensitive bands, a distinction is to be made between regularity peaks associated with stereoregular chain segments of variable length and true crystallinity bands due to the crystal force field which manifests itself as a splitting of a single peak into two components.11 The occurrence of crystal field splitting can be suggested for the peaks observed at 1452 (left inset of Figure 1) and 1379 cm-1 (middle inset of
Normal Vibrational Analysis of a trans-Planar sPS Chain
J. Phys. Chem. B, Vol. 111, No. 23, 2007 6329
Figure 1. FTIR spectra of sPS for the spectral range of 3150-400 cm-1; from bottom to top: amorphous phase (am); R form (R) and β form (β) semicrystalline films after subtraction of the contribution of the amorphous phase, calculated (calc) infrared spectrum of a trans-planar sPS chain. The frequencies of the calculated spectrum were scaled by a factor equal to 0.9614. A Lorentzian profile was used with a fwhm of 10 cm-1. The experimental and the calculated intensities of the peaks were scaled with respect to their corresponding maximum value. The inset figures (experimental spectra only) allow visualization of the most relevant conformationally sensitive peaks (inset 1460-1200 cm-1) as well as the conformationally and packing-sensitive peaks (inset 920-830 cm-1).
Figure 1) for fully amorphous films, split at 1454-1444 and 1390-1375 cm-1 for the R form or at 1454-1442 and 13921373 cm-1 for β form. The occurrence of crystal field splittings has been also observed for helical sPS crystalline phases, mainly by using two-dimensional FTIR spectroscopy.14 It is also worth adding that some of the conformationally sensitive peaks are also packing-sensitive peaks since they present different positions for the R and β crystalline forms. Particularly packing-sensitive are the peaks located at 902 and 852 cm-1 for the R form and at 911 and 858 cm-1 for the β form (see right inset of Figure 1),6,11 which have been widely used in the literature to quantify the relative amounts of the R and β phases in melt-crystallized sPS samples. Polarized FTIR spectra of the R and β crystalline forms of sPS are reported for the wavenumber range of 3150-400 cm-1 in Figure 2. These spectra have been obtained by subtraction of the amorphous phase contribution from FTIR spectra of uniaxially oriented (for λ ≈ 3) sPS films including R and β phases. The spectra of Figure 2 clearly show that, for both crystalline phases, all absorbance peaks can be easily divided in two classes, those which are present in the spectra taken with the polarization plane parallel (thin lines) or perpendicular (thick lines) to the draw direction. Of course, the thin-line and thickline peaks correspond to vibrational modes parallel and perpendicular to the chain axis and are indicated as || and ⊥ in Table 3. The Raman spectra of an amorphous sPS film and of a semicrystalline film in the R form are reported in Figure 3, traces A and B, respectively. It is observed that the occurrence of a regular trans-planar arrangement of the polymer chains induces significant changes in the Raman spectrum. These changes are localized in the wavenumber ranges of 1410-1250, 870-700, and 560-160 cm-1, as highlighted in the insets of Figure 3. In particular, it is apparent that several peaks develop upon crystallization, which are absent in the amorphous phase. These are located at 1374, 525, and 401 cm-1 and appear to be well suited for the development of quantitative methods for the assessment of the crystallinity degree. In fact, as opposed to
Figure 2. FTIR spectra for the wavenumber range of 3150-400 cm-1 taken with the polarization plane parallel (||, thin lines) and perpendicular (⊥, thick lines) to the draw direction for uniaxially oriented (for λ ≈ 3) sPS films including R and β crystalline phases after subtraction of the amorphous phase contribution. Peaks corresponding to vibrational modes being parallel (thin lines) and perpendicular to the chain axis (thick lines) are clearly apparent.
the 772 cm-1 crystalline peak proposed by Kellar et al.,27,28 the above peaks do not overlap with components of the amorphous phase and, therefore, do not need complex deconvolution procedures to yield the required information. No detectable differences are observed between the Raman spectra of the two trans-planar modifications R and β. B. Calculated Vibrational Spectrum of a trans-Planar sPS Chain. The factor group of the Pm2a rod group is an isomorphic C2V point group; according to this symmetry, the calculated frequencies are classified automatically by the code. The resulting irreducible representation of the normal modes at the Γ point is as follows
Γ ) 29A1 x 17A2 x 17B1 x 29B2
6330 J. Phys. Chem. B, Vol. 111, No. 23, 2007
Torres et al.
Figure 3. FT-Raman spectra in the wavenumber range of 3700-100 cm-1 of an amorphous sPS films (trace A) and a semicrystalline film presenting the R phase (trace B). The insets display a comparison between the amorphous spectrum (thin line) and the semicrystalline spectrum (thick line) in the wavenumber regions most sensitive to the presence of the crystalline phase.
In this set, the three acoustic modes and the one associated with the rotation of the polymer about the periodic direction have already been subtracted; therefore, a total of 92 modes remain. According to the selection rules, all of the 92 modes are Raman active, but only 75 modes (A1, B1, and B2 symmetries) are IR active. The whole set of calculated modes is reported in Table 1 together with the computed IR intensity of each mode. The latter are expressed as the percentage of the maximum value equal to 89 km/mol obtained for ω ) 681 cm-1. These scaled IR intensities are used to produce a simulated spectrum (spectrum (calc) of Figure 1), which can be compared with the experimental ones for the R and β crystalline phases (spectra (R) and (β) of Figure 1). The position of the peaks practically coincides in the zone from 400 to 1600 cm-1, while in the zone of the higher frequencies from 2800 to 3150 cm-1, the computed values are overestimated due to the anharmonic character of the C-H stretching that dominates this part of the spectrum. Additionally, Table 1 lists the direction of the transition-moment vector with respect to the chain axis of each computed frequency. In agreement with the experimental results obtained in the polarized FTIR spectra (see Figure 2), two possible orientations are identified, parallel or perpendicular. These directions together with the frequency values and the relative intensities can be used to determine a correspondence between the calculated and the experimental sets, as reported in Table 3. In Table 1, a description of each vibration in terms of internal coordinates is also given. The adopted internal coordinates are reported in Table 2 and shown in Figures 4 and 5. Normal modes are therefore described in terms of the atomic displacements along one or more internal coordinates. The nomenclature adopted for each internal coordinate is the same as that used by Reynolds and Hsu.17 Although we consider Reynolds-Hsu’s set quite descriptive, three internal coordinates were added by us, namely, F, χ, and Ψ′, which correspond to the wagging of the chain hydrogen atoms and the phenyl group along the periodic direction. They are highlighted with red color in Figure 4. In addition to these, various modes of the phenyl group, which cannot be defined in terms of the adopted internal modes, were considered, as shown in Figure 5.
From inspection of Figures 1-3 and computed results in Table 1, Table 3 reports a comparison between experimental peak positions, from both IR and Raman spectra, and calculated vibrational frequencies. The agreement is good and allows one to confidently assign experimental results to the normal modes listed in Table 1. Different zones of the infrared spectrum can be characterized by analyzing the mode description reported in the last column of Table 1 and by direct inspection of the animations of the frequencies.41 The higher part of the spectrum ranging from 3200 to 2800 cm-1 represents the region of the C-H stretching. By observing the experimental and the calculated IR spectra in Figure 1, it is possible to note that the simulated one contains almost all of the features of the experimental spectrum, with the exception of the observed peaks at the highest frequencies, that is, 3104 cm-1. Also, for data from the Raman spectra, the highest observed frequencies (i.e., 3166 and 3200 cm-1) are far from the computed ones. Furthermore, a quite big difference is observed if the spectral band widths are compared. In the calculated IR spectrum, the C-H stretching modes span the 3083-2913 cm-1 range with a spread of 173 cm-1, while in the experimental ones, these modes are in the range of 32002844 cm-1 with a spread of 316 cm-1. Despite these two incongruities, namely, (i) the missing computed frequency corresponding to the highest experimental peak positions and (ii) the difference between the band widths, the four main peaks of the observed spectrum are clearly identified in the computed set, with the two higher C-H stretching modes being associated with the phenyl rings, while the two lower ones belong to the C-H stretching of the alkyl CH and CH2 groups. The large deviations of the calculated frequencies from the experimental one make the comparison and the assignment of the peaks more complicated. As stated above, this spectral region is markedly effected by anharmonic effects, and also, overtones and combinations are present. For instance, modes at 3200 (Raman), 3166 (Raman), and 3104 (IR) cm-1 correspond to two overtones (i.e., 2 × 1602 and 2 × 1583 cm-1) and a combination (i.e., 1602 + 1493 cm-1), respectively. Similarly, the frequency at 3002 cm-1 can tentatively be assigned to the second overtone of the intense Raman peak at 1002 cm-1 (i.e., 3 × 1002 cm-1). Moreover, comparison between theory and experiment is
Normal Vibrational Analysis of a trans-Planar sPS Chain
J. Phys. Chem. B, Vol. 111, No. 23, 2007 6331
TABLE 1: The Whole Set of Calculated Normal Modesa ω
IR intensity (%)
TMV direction
symmetry
assignment
ω
IR intensity (%)
TMV direction
symmetry
assignment
3087 3086 3075 3072 3067 3064 3057 3056 3050 3050 2962 2951 2941 2936 2913 2904 1596 1595 1575 1574 1479 1479 1460 1440 1438 1436 1361 1341 1329 1325 1310 1309 1296 1286 1269 1199 1176 1164 1164 1161 1158 1144 1140 1140 1074 1072
22 29 12 35 18 10 2 3 3 6 72 10 1 5 48
⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ || ⊥ ⊥
1 0
⊥ ⊥
1 3
|| ⊥
0
||
15 2
|| ||
0 0
|| ⊥
51 2
|| ⊥
9 3 6 1 10 16 0 0 0
⊥ ⊥ ⊥ ⊥ ⊥ || ⊥ ⊥ ⊥
100 0 0 0
|| ⊥ ⊥ ⊥
1 40 0
⊥ || ⊥
3 7 0 0 0 0 2
⊥ || ⊥ ⊥ ⊥ ⊥ ⊥
0 0 0 0
|| ⊥ || ⊥
0 3 0
⊥ || ⊥
0 0 0 2
⊥ ⊥ ⊥ ⊥
1057 1037 1020 1015 1007 978 976 976 956 955 949 935 928 887 879 839 826 813 756 751 743 723 692 681 611 611 571 563 549 531 522 446 410 403 388 340 281 221 215 208 165 70 36 36 35 31
⊥ || ⊥ ⊥ ⊥
⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥
r r r r r r r r r r s, d s d s, d s, d d T, σ, R T, σ, R T, σ T, σ T, σ, R T, σ, R δ δ ζ, σ ζ, σ ζ, σ, χ, R ζ, σ χ, σ, S F, χ, S σ, T, ζ σ, T, ζ, χ σ, T, ζ, χ F, χ σ, T, r F, χ, S ζ, R, σ, T σ ζ, R, σ, T ζ, R, σ, T χ, σ, φ F, χ σ σ σ, τ, T γ, ω, φ, σ, ζ
2 1 1 1 10
0 6 2 1 5 11 4
A1 B2 A1 B2 A1 B2 A1 B2 A1 B2 B2 A1 B1 B2 A1 A2 A1 B2 A1 B2 A1 B2 A1 A2 A1 B2 A1 B2 B2 B1 A1 B2 A1 A2 B2 B1 A1 A1 B2 B2 A1 A2 A1 B2 B2 A1
0 0 0
⊥ || ||
A1 B1 B2 A1 B2 A2 B2 A1 A2 B1 B2 A2 B1 A2 B1 B1 A2 B1 A1 A2 B1 B2 A2 B1 B2 A1 A1 A2 B2 B1 B2 A2 A2 B1 A1 B1 B2 A2 B2 B1 A1 A2 A2 A1 B1 B1
ω, φ, σ, ζ, T ω, φ, τ, S σ, ζ, T, τ, D1 σ, T, D1 τ, ζ, S ω, φ, S, F, χ D2 D2 µ µ S, σ, D2 µ, D4 µ, D4 µ, D5 µ, D6 µ, τ, F µ, Ψ µ, Ψ, τ χ, D2 µ, D5 µ, τ, D5 τ, D2 µ, D6 µ, τ, D6 D3 D3 χ, D3 F, ω, D6 τ, φ τ, F, D5 τ, φ, D3 F, ω, D6 D4 D4 φ, ω τ, D5 τ D5 τ, φ, ω τ, F, D5 χ, φ, ω Ψ Ψ′ φ, ω Ψ′, τ Ψ, τ
a Reported frequencies (in cm-1) are scaled by a factor equal to 0.9614.36 The infrared intensities of each mode are expressed as percentage fraction of the maximum computed intensity of 89 km/mol (ω ) 681 cm-1). The direction of the transition-moment vector (TMV) for each mode is referred to the chain axis. Normal mode symmetry refers to the Pm2a rod group. Assignment is given in terms of internal coordinates, as defined in Table 2.
complicated because of the Fermi mixing for both phenyl and alkyl CH stretching vibrations with CH bending modes. We hypothesize a Fermi resonance to exist between the in-phase alkyl CH2 symmetric stretching fundamental (i.e., estimated to be at 2890 cm-1, in agreement with the calculated mode at 2913 cm-1) and the overtone of the CH2 bending modes at 14541444 cm-1. For a splitting of some 35 cm-1, this would lead to a doublet around 2925 and 2855 cm-1, close to the bands observed in the IR spectra. Such a hypothesis is also confirmed by the inspection of the Raman spectra, where a broad band is observed at 2900 cm-1. A similar explanation can be attempted for the computed mode at 2962 cm-1, which is very intense and falls markedly off with respect to observed bands in the IR spectra (see Figure 1). In that case, if we consider the Raman peak at 2976 cm-1 as a fundamental, in good agreement with the computed frequency, a Fermi mixing can be hypothesized with the overtone of the intense IR peak at 1493 cm-1 (i.e., 2986 cm-1) that leads to the band at 3027 cm-1, not present in the Raman spectra, and a peak around 2930 cm-1 that would
fall below the intense and broad IR band at 2920 cm-1. In the Raman spectra, this Fermi resonance would not take place because of the very weak intensity of the peak at 1493 cm-1. By taking all of those aspects into account, an attempt to assign computed CH stretching frequencies to experimental peaks is reported in Table 3. At difference with the CH stretching bands, a better match between experimental and calculated frequencies is observed in the region from 1600 to 1493 cm-1. This part of the spectrum is strictly associated to the phenyl groups; therefore, they are expected to not be sensitive to the chain conformation. Motion along internal coordinates T, R, and σ are observed; therefore, these modes are principally characterized by C-C stretching of the atoms that link the aromatic group with the chain and the carbon atoms that form the ring with an additional contribution of the in-plane bending of the ring hydrogen atoms. In the zone of the spectrum below the experimental peak at 1493 cm-1, vibrations involving atoms that belong to the chain as well to the aromatic ring are identified. For example, the
6332 J. Phys. Chem. B, Vol. 111, No. 23, 2007 TABLE 2: Description of the Internal Coordinates Employed for the Mode Assignment Reported in Table 1a internal coordinate
description
d s r S R T
stretching Cch-Hch stretching Cch-Hch stretching Cph-Hph stretching Cch-Cch stretching Cch-Cph stretching Cph-Cph
δ γ ζ σ ω φ
bending Hch-Cch-Hch bending Hch-Cch-Cch bending Hch-Cch-Cph bending Hph-Cph-Cph bending Cch-Cch-Cch bending Cch-Cch-Cch
τ Ψ Ψ′b
torsion CH2 group torsion phenyl group phenyl group wagging along the periodic direction Hch wagging along the periodic direction (for CH) Hch wagging along the periodic direction (for CH2) Hph out of the plane
Fb χb µ
a The superscripts ph and ch are used to discriminate atoms belonging to the phenyl groups and the chain, respectively. b Shown with red color in Figure 4.
Torres et al. TABLE 3: Comparison between Observed IR and Raman Peak Positions (νexp) for the Amorphous Phase and r/β Crystalline Forms of sPS and Calculated Frequencies for an All-trans sPS Infinite Chain (ωcalc) νexpa am
computed frequencies at 1460 and 1440 correspond to the CH2 bending vibrations (δ), while the modes at 1438 and 1361 cm-1 are mainly characterized by the coupling between ζ and σ internal coordinates (see Table 2), which are CCH bendings of the CH in the chain and the phenyl groups, respectively. As reported in Table 3, these computed frequencies are assigned to two experimental peaks of the R and β crystalline forms. This is justified by considering that the model, adopted for the calculations, does not allow one to take into account the interactions between the chains in the crystalline form which cause the splitting of these modes, and it is therefore more reasonable to compare them with the experimental peaks obtained in the amorphous films. The other modes in this region, with lower frequencies, are more complex than the previous ones. According with the assignment in Table 1, they are the result of the coupling of several and different internal coordinates, and their description is therefore more complicated; however, the assignment task can be enormously simplified by a direct visualization of the normal modes through graphical animations available at the CRYSTAL website.41 For example, the animations of the frequencies computed at 1361, 1310, 1309, and 1296 cm-1 permit us to observe that, in addition to the hydrogen bendings, a modest contribution of the C-C stretchings is also present in these cases, rendering the mode description more complete. Additionally, mode animations can also be useful to understand the nature of some peculiar cases. The modes computed at 1325 and 1199 cm-1 have B1 symmetry, and according to their animations, they can be classified as pure backbone vibrations. Both frequencies are the result of the wagging of the chain hydrogen atoms along the periodic direction together with C-C backbone stretchings. The difference of 136 cm-1 between them can be attributed to their symmetric and antisymmetric character. In the case of the former, the H displacement of the CH2 and the CH groups occurs in the same direction, while for the latter, the atomic displacement occurs in opposite directions. The next two modes below the frequency at 1199 cm-1 are similar to those computed at 1310 and 1309 cm-1; therefore, they will not be further
R
Raman β
R/β
am 3200c 3162c
3104c 3083 3061
3002c 2976 2928d 2919d ∼2890e 2903-2900
2920d
1452
1345 1329 1279 1196 1181 1029
906 840
540
2856d 2844d 1602 1583 1493 1454 1444 1442 1390 1392 1375 1373 1350 (||) 1334 1336 1313 1293 1276 1223 (||) 1183 1172 1155 1094 1092 1085 1069 1030 1004 989 977 964 902 (||) 911(||) 852 (||) 858 (||) 750 (||) 698 (||) 621 538 (||)
3086 3072 3050
3062 3052 3037d
3027d 3002c
1379
cm-1
ωcalca
IRb
2849d
1451 1438
1453 1446 1374 1352
1330-1320 1300
1319 1294
1222-1203 1182
1203
1155 1072 1028 1002 990
235 173
1595 1575 1479 1460 1438-1440f 1361 1325 (||) -1329 (⊥) 1310-1309 1296-1286f 1269 1199 (||) 1176 1164 1158 1074 1072 1057 1020 1007 978 976 949 879 (||) 839 (||) 813
772
620 405
2913 2904f
2845d 1602 1583 1493
901 840 796 769 756
2962
526 452 400 351 230 178
743 (||) 681 (||) 611 531 (||) 446 410 340 221 165
a Data in cm-1. b Unless otherwise explicitly indicated, all IR peaks have transition-moment vectors oriented perpendicularly to the chain axis. c Overtone or combination. d Possible Fermi resonance (see text for details). e Estimated fundamental. f IR inactive mode.
discussed. The lowest part of this region, formed by the modes at 1074, 1072, and 1057 cm-1, is characterized by the presence of CCC backbone bendings and torsions of the CH2 groups coupled with CCH bendings of the CH, CH2, and phenyl groups. The lowest region of the spectrum, ranging from 1020 to 538 cm-1, contains modes related mainly to the aromatic groups, and they can be described in terms of the ring deformations shown in Figure 5. Although most of these frequencies are not
Normal Vibrational Analysis of a trans-Planar sPS Chain
J. Phys. Chem. B, Vol. 111, No. 23, 2007 6333
Figure 4. Schematic representation of the internal modes in a part of the periodic polymer. The adopted nomenclature corresponds to that adopted by Reynolds and Hsu in ref 17.
Figure 5. Schematic representation of the phenyl ring deformations associated with the modes in the range from 1020 to 611 cm-1 of the calculated infrared spectrum.
coupled with any backbone mode, some exceptions are identified by analyzing the mode animations. The computed frequency at 1007 cm-1 involves a D1-type ring deformation together with CCC backbone bendings and the torsion of the CH2 groups. Additionally, the frequency at 949 cm-1 can be also described as a mixed mode because it is the result of a mixing among D2-type ring deformation, C-C backbone stretching, and CCH backbone bendings. Both modes are produced by the coupling between ring vibrations and chain modes and are therefore expected to be sensitive to the chain conformation. In the part below 949 cm-1, many modes of B1 symmetry are found. The direction of the transition-moment vectors associated with these modes is parallel to the chain axis, making their assignment to the corresponding experimental features easy. It is interesting to note that, although most of them are pure ring modes characterized by CH out-of-plane bending, conformationalsensitive frequencies are also identified. That is the case of the ones calculated at 839 and 531 cm-1. As reported in Table 1,
the former one corresponds to τ and F internal coordinates together with a CH out-of-plane bending of the phenyl groups, whereas the latter involves the same chain modes and a D5type ring deformation. Frequencies below 400 cm-1 involve complex modes, usually torsions, where groups of atoms are involved in the vibration. For instance, the lowest observed Raman peak at 178 cm-1 corresponds to a torsion of the phenyl rings around the C-C backbone. For assignment and description of low-frequency vibrations, we refer to Tables 1 and 2 and to the graphical animation of the vibrations.41 C. Additional Considerations Based on Comparison between Experimental and Calculated Spectra. The good agreement between calculated and experimental results (Figure 1 and Table 3) suggests some additional considerations, which contribute to identify and rationalize the occurrence of conformationally sensitive, packing-sensitive, and crystal field-split peaks.
6334 J. Phys. Chem. B, Vol. 111, No. 23, 2007 First of all, the occurrence of crystal field splittings (e.g., at 1454-1444 and 1390-1375 cm-1 for the R form) suggested by the experimental analysis is confirmed by the presence of single normal modes (with suitable intensity) for the isolatedchain calculations (at 1438 and 1361 cm-1, respectively). It is also worth noting that the spectral region between 1454 and 1029 cm-1, which includes peaks which are generally conformationally sensitive, as well as the conformationally sensitive peaks located at 858-852 and 838 cm-1 correspond to vibrational modes with the participation of atoms that belong to the chain as well as to the aromatic ring. The packing-sensitive peaks located at 902 and 852 cm-1 for the R form and at 911 and 858 cm-1 for the β form (right inset of Figure 1) correspond to vibrational modes mainly including the bending of aromatic hydrogens (µ). This result is easy to rationalize since, in both crystalline phases,20-26 these hydrogen atoms, being external to the chain, experience the largest nonbonded interactions with neighboring chains. IV. Conclusions The vibrational spectra of R and β crystalline phases of syndiotactic polystyrene (sPS), that is, phases presenting the trans-planar conformation, have been experimentally determined and compared with vibrational frequencies as computed at the B3LYP/6-31G(d,p) level of theory for an infinite trans-planar chain. The comparison between experimental (IR and Raman) and calculated results has allowed us to perform a full vibrational analysis with the assignment of the different vibrations in terms of frequency, relative intensity, and direction of the transitionmoment vector of the observed IR peaks. The comparison between infrared spectra of both crystalline phases, as obtained from spectra of semicrystalline films after subtraction of the contribution of the amorphous phase, and the infrared spectrum of a fully amorphous sPS film has allowed us to establish the occurrence of conformationally sensitive, packing-sensitive, and crystal field-split peaks. In particular, the occurrence of crystal field splitting can be suggested for the peaks observed at 1452 and 1379 cm-1 for fully amorphous films, split at 1454-1444 and 1390-1375 cm-1 for the R form, or at 1454-1442 and 1392-1373 cm-1 for β form. Each infrared peak of the R and β crystalline forms is present in only one of the two polarized spectra, taken with the polarization plane parallel or perpendicular to the draw direction of uniaxially oriented sPS films, after subtraction of the amorphous phase contribution (Figure 2). On this basis, for all infrared peaks of both crystalline forms, the orientation of the transition-moment vector of the corresponding vibrational modes (parallel or perpendicular to the chain axis) has been clearly established. The Raman spectra of the crystalline forms display very characteristic and sharp signals which can be especially useful for quantifying the crystalline phase in a sample. Raman spectroscopy appears to be less sensitive to chain packing than infrared, insofar as the spectra of the R and β phases are essentially coincident. The simulated B3LYP/6-31G(d,p) infrared spectrum of an infinite trans-planar sPS chain nicely agrees with the experimental ones for the R and β crystalline forms, and the comparison confirms the effect of the crystal packing on vibrational spectra. The normal vibrational analysis of the most representative modes of the periodic model allowed us to give a general description of each one, which was further confirmed by the direct inspection of mode animations.
Torres et al. The combination of experiment and theory is shown to be a very useful tool to characterize polystyrene, and in perspective, it can fruitfully be applied to other polymers. Acknowledgment. Work was performed for Regione Piemonte in the frame of the research project “Innovative Materials for Hydrogen Storage”. Financial support of the “Ministero dell’Istruzione, dell’Universita` e della Ricerca” (PRIN 2004) of “Regione Campania” (Legge 5 and Centro di Competenza per le Attivita` Produttive) is gratefully acknowledged. We thank Dr. Christophe Daniel and Dr. Giuseppe Milano of the University of Salerno for useful discussions. References and Notes (1) Ishihara, N.; Kuramoto, M.; Uoi, M. Macromolecules 1986, 19, 2035. (2) Zambelli, A.; Longo, P.; Pellecchia, C.; Grassi, A. Macromolecules 1987, 20, 2035. (3) Guerra, G.; Vitagliano, V. M.; De Rosa, C.; Petraccone, V.; Corradini, P. Macromolecules 1990, 23, 1539. (4) Niquist, R. A. Appl. Spectrosc. 1989, 43, 440. (5) Reynolds, N. M.; Savage, J. D.; Hsu, S. L. Macromolecules 1989, 22, 2867. (6) Guerra, G.; Musto, P.; Karasz, F. E.; MacKnight, W. J. Makromol. Chem. 1990, 191, 2111. (7) Vittoria, V. Polym. Commun. 1990, 31, 263. (8) Filho, A. R.; Vittoria, V. Makromol. Chem., Rapid Commun. 1990, 11, 199. (9) Reynolds, N. M.; Stidham, H. D.; Hsu, S. L. Macromolecules 1991, 24, 3662. (10) Nakaoki, T.; Kobayashi, M. J. Mol. Struct. 1991, 242, 315. (11) Musto, P.; Tavone, S.; Guerra, G.; De Rosa, C. J. Polym. Sci., Part B: Polym. Phys. 1997, 35, 1055. (12) Tashiro, K.; Useno, Y.; Yoshioka, A.; Kobayashi, M. Macromolecules 2001, 34, 310. (13) Yoshioka, A.; Tashiro, K. Macromolecules 2003, 36, 3001. (14) Musto, P.; Rizzo, P.; Guerra, G. Macromolecules 2005, 38, 6079. (15) Albunia, A.; Musto, P.; Guerra, G. Polymer 2006, 47, 234. (16) Kobayashi, M.; Nakaoki, T.; Ishihara, N. Macromolecules 1990, 23, 7836. (17) Reynolds, N. M.; Hsu, S. L. Macromolecules 1990, 23, 3463. (18) Niquist, R. A.; Putzig, C. L.; Leugers, C. L.; McLachlan, R. D.; Thrill, B. Appl. Spectrosc. 1992, 46, 981. (19) Rastogi, S.; Gupta, V. D. J. Macromol. Sci., Phys. 1994, B33, 129. (20) De Rosa, C.; Guerra, G.; Petraccone, V.; Corradini, P. Polym. J. 1991, 23, 1435. (21) Corradini, P.; De Rosa, C.; Guerra, G.; Napolitano, R.; Petraccone, V.; Pirozzi, B. Eur. Polym. J. 1994, 30, 1173. (22) De Rosa, C. Macromolecules 1996, 29, 8460. (23) Cartier, L.; Okihara, T.; Lotz, B. Macromolecules 1998, 31, 3303. (24) De Rosa, C.; Rapacciuolo, M.; Guerra, G.; Petraccone, B.; Corradini, P. Polymer 1992, 33, 1423. (25) De Rosa, C.; Guerra, G.; Corradini, P. Rend. Fis. Acc. Lincei. 1991, 2, 227. (26) Chatani, Y.; Shimane, Y.; Ijitsu, T.; Yukinari, T. Polymer 1993, 34, 1625. (27) Kellar, E. J. C.; Galiotis, C.; Andrews, E. H. Macromolecules 1996, 29, 3515. (28) Kellar, E. J. C.; Evans, A. M.; Knowles, J.; Galiotis, C.; Andrews, E. H. Macromolecules 1997, 30, 2400. (29) Jasse, B.; Monnerie, I. J. Mol. Struct. 1977, 39, 165. (30) Kim, P. K.; Hsu, S. L.; Ishida, H. Macromolecules 1985, 18, 1905. (31) Kim, P. K.; Hsu, S. L.; Ishida, H. Polymer 1986, 27, 34. (32) Dovesi, R.; Saunders, V. R.; Roetti, C.; Orlando, R.; ZicovichWilson, C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I. J.; D’Arco, P.; Llunell, M. CRYSTAL06 User’s Manual; Universita` di Torino: Torino, Italy, 2006. (33) Albunia, A.; Di Masi, S.; Rizzo, P.; Milano, G.; Musto, P.; Guerra, G. Macromolecules 2003, 36, 8695. (34) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (35) Pascale, F.; Zicovich-Wilson, C. M.; Gejo, F. L.; Civalleri, B.; Orlando, R.; Dovesi, R. J. Comput. Chem. 2004, 25, 888.
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J. Phys. Chem. B, Vol. 111, No. 23, 2007 6335 (40) Zicovich-Wilson, C. M.; Bert, A.; Dovesi, R.; Saunders, V. R. J. Chem. Phys. 2002, 116, 1120. (41) Graphical animation of vibrational frequencies are available at the web site: www.crystal.unito.it/vibs/alpha-ps. Animations were generated by using Noel Y. WEBVIB, release 1.04; 2005; A Perl script to prepare CRYSTAL06 vibrational frequencies for the JMOL (www.jmol.org) graphic engine.
