- Email: [email protected]
Spectroscopic determination of the average content of gauche structures in organic molecules containing polymethylene chains
Volume
80, number
CHEMJCAL
3
SPECTROSCOPIC
DETERMINATION
IN ORGANIC MOLECULES
PHYSICS
15 June1981
LETTERS
OF THE AVERAGE
CONTENT OF GAUCHE STRUCTURES
CONTAINING POLYMETHYLENE
CHAINS *
Giuseppe ZERBI and S. ABBATE Ishkto di ChimicaUniversitydi Dfeste, Tkieste,Italy and CNR, Istituto chimicaIndustriale,Politecnico, Milan,Italy Received
23 March 1981
From the analysis of Fermi resonances in the CH-stretching and HCH-bending regions of the Raman spectra of transpolymethylene chains and CDaCHaCDa, it is proposed that when gauche structures are present additional spectral features occur. A method for the determination of the relative concentration of gauche structures is proposed.
With this short paper we hope to take a step forward in the interpretation of the Raman spectrum of polymethylene molecules, with the desire to derive information for the elucidation of the structure of these types of molecules which are found in several molecular systems as polymers (polyethylene, polyalkenamers, nylons, etc.), organic molecules (n-alkanes, fatty acids) and biological materials (phospholipids and membranes) We focus our attention on a few spectroscopic signals in the Raman spectrum which may be related to the existence of gauche structures. A quantitative analysis of these signals may provide a way to estimate the relative concentration of gauche conformers in an otherwise all-tram medium. In 1972 Iavalley and Sheppard [1] from the analysis of the infrared and Raman spectra of 1 ,1,1,3,3,3hexadeuteropropane have clearly shown that in the spectral region of the CH-stretching vibrations a strong Fermi resonance occurs. In particular the first overtone of the scissoring CH2 motion (&CH2) (2 X 1466 $= 2932 cm-l, A1 X A, = A1) is shown to couple through Fermi resonance with the fundamental level of the CH2 symmetric stretching of species A1 occurring in the same frequency range. The two perturbed A1 states show two strong totally symmetric Raman lines near 2876 and 2942 cm-l. The depolarized weak * Presented at the March Meeting of the American Physical Society,
New York (1980).
0 009-2614/81/0000-0000/$02.50
line near 2925 cm-l is assigned to the antisymmetric B, CH2 stretching which is free from resonance perturbations- The unusually large observed intensity of the first overtone, 26-CHz, near 2942 cm-l, is the result of Fermi resonance which allows for the intensity borrowing from the fundamental level. When a polymethylene chain molecule is formed, the intramolecular dynamics of the chain may somehow modify the intra-CH2 Fermi resonance scheme seen in CD3CH2CD3. This may occur as the result of some additional dynamical factors directly related to the existence of a sequence of CH2 units in a given conformational state. Let us, for the time being, consider the case of an all-tram-polymethylene chain either as an isolated molecule (one-dimensional crystal) or packed in a three-dimensional orthorhombic or monoclinic lattice (these lattices are found in polyethylene, n-alkanes, fatty acids, etc.). By considering the lattice dynamics of inftite onedimensional alI-tram-polymethylene chains (like in polyethylene) the infinite number of normal-mode frequencies is organized along branches in the phonon dispersion curves. Phonon dispersion curves for the one-dimensional lattice in the harmonic approximation have been calculated [2] and their shape can be considered approximately known. The experimental verification of the phonon dispersion curves has been carried out by Snyder and Schachtschneider [3] from
0 North-Holland Publishing Company
455
Volume 80, number 3
CHEMICAL PHYSICS LETTERS
the analysis of the infrared spectra of n-alkanes in the sohd state. The frequency versus phase plots obtained, clearly define the dispersion curves for t&kanes. The evtrema of these curves coincide with rhe k = 0 modes of an infinite one-dlmennonal cry&a1 of polyethyIene. Some of these limiting modes are infrared or Raman actwe and have been unquestionabiy observed in the infixed and Raman spectra [3]. The very large amount of spectroscopic work [4]
based on theory and calculations on polyethylene and trans-planar-poiymethylene chains puts the interpretatlon of the spectra (infrared and Raman) on a somew!lat firm basis. in terms of the dynamics and structure of these kinds of molecules. We wish to focus our attention in this paper on the Raman spectrum of polymethylene chains m the CH2scissoring region near 1460 cm-’ and in the CHstretching region near 3000 tin-1_ In these frequency ranges the observed features in the Raman spectrum reveal the existence of additional resonances. First, It has been qualitatively pointed out [s] and Iater quantitatively shown [6,7] that the two-phonon states (first overtone states) of the dispersion curves of the CHz-rocking modes occur in the frequency range of the CHZ-scissoring modes. thus entering m Fermi resonance through some anharmomc coupling_ Analogcusly, the two-phonon states of the dispersion curve of the CH, modes near 1440 cm-l generate Fermi resonances with the CH-stretching levels [G--8]. The present interpretation of the observed spectrum of trans-polymethylene chains is basically the following [6]. The Raman band centered near 1460 cm-1 arises from the superposition of rocking two-pho:on states which interact with the B,, and Ag fundamerr:aIs of the factor group splitting due to the orthorhombic lattlce near 1440 and 1416 cm-l respectively. In the CH-stretching region, calculations assess [6] that in the Raman spectrum the broad bands observed at 2930 and 2900 cm-l are essentially due to an envelope of overtone modes which interact via Fermi coupling with the fundamental symmetric CH-stretching normal mode of the single chain associated with the band near 2850 cm-l. The interrnoIecuIar packing gives rise to an additional Raman scattering between the two funda-
mentals near 2850 and 2883 cm-l- The Raman line near 2883 cm-ldue to the antisymmetric CH2 stretching, floats on top of a broad, strong background of Ag species. 456
15 June 1981
We wish to discuss in this paper the fact that when gauche structures are introduced in the trans host lattice, the number of two-phonon states arising from the complicated Fermi resonance of the trans chain decreases, the intramolecular coupling of CH-stretching modes changes and new spectral features due to the uncoupled or partially decoupIed CH, groups in gauche conformation shouId appear. For such dynamicalIy uncoupled gauche-CH2 groups the only Fermi resonance still existing is that which takes place in the starting model molecule CD,CH,CD,. In fig. 1 we report the co.woluted Raman spectrum of antisyrnrnetic and symmetnc stretching modes for an isolated CH, group. We would exps*t that for a totally gauche-polymethylene chain the Raman spectrum in the CH-stretching region should be smilar to that depicted in fig. 1, namely the overtone of the bending mode should occur near 2940 cm-l and a very close strong doublet of practically equal intensity should occur near 2880 cm-l due to the antisymmetric and symmetric CH,stretching modes. When the concentration of trans bonds increases, the previously discussed Fermi resonance schemes are activated and the symmetric CH2stretching fundamental of the trans section shouId appear near 2850 cm-l _ The intensity of the CH2 symmetric mode for the all-trans molecule seems weaker than the corresponding mode in the isolated CH2 group since the former lends intensity to a manifold of overtone states toward higher frequencies_ The 2940 cm-l band weakens considerably more than the 2850 cm-l band does in going from the totally gauche- to the totally tram-polyethylene, due to the same mechanism acting on the 2850 cm-l band (see figs. 1 and 2).
75 I
cm-’
Fig- 1. Convoluted calculated Raman spectrum of antisymmetric and symmetric CHz-stretching modes in CDsCHzCD3. Fermi resonance is only active within the isolated CH2 group (2&CH, in Fermi resonance with CH1 symmetric stretch).
Volume
80, number
3
CHEMICAL
PHYSICS
average concentration 75= = 50=‘
c 2z 250
2950 Fig. 2. Convoluted polymethylene
2wo calculated
singlechain
Raman
2850 spectrum
cm-’
of an all-trans-
molecule.
15 June 1981
LETTERS
and changes in concentration
of
gauche structure in the sample studied. We feel that the method presented in this paper makes E&man spectroscopy one of the unique tools for a direct qualitative and quantitative study of gauche structures in polymethylene systems in the various phases. It should be equally useful for the study of the conformational changes in phospholipids, membrane systems, etc. Ome the overall structures have been determined,
more detailed information on local gauche structures can be obtained in the infrared by selective deuteration [7-l 31 and in infrared and Raman spectra, where markers for local structures have been identified ]E4]_
We then propose that the ratio of the intensities 1(2850)/1(2940) should be proportional to the relative concentration of gauche and trans structures in a conformationally disordered polymethylene chain. Such a ratio should decrease wi*Lhan increase of the population of gauche structures. With similar arguments we also propose that when gauche structures are introduced in a trans host lattice the Fermi resonance peak near 1464 cm-l should decrease in intensity and slowly disappear along with the increase of the conformational disorder of the polymethylene chain. These predictions are nicely confirmed qualitatively by the Raman spectrum of liquid polyethylene and of long-chain n-hydrocarbons 173 _ Recent Raman spectra in the CH2-bending region of samples of polyethylene with an increase in concentration of amorphous content [9] also support our views. Strong support of our interpretation comes from the recent sets of experiments published by Wunder and co-workers, on the Raman spectra of various polymethylene samples. These authors have actually measured the ratio 1(2850)/(2940) for: (I) molten nhexadecane at various temperatures and in solution at various concentrations and temperatures [9] ; (ii) moIten polyethylene at different temperatures [lo] ; (iii) solid polyethylene at various concentrations of amorphous material [ 111. All these experiments support the proposal presented in this paper and fully discussed in ref. [6]_ Wunder and co-workers also propose some methods for the actual quantitative estimate of the
References [ 11 J.LavaBey and N. Sheppard, Spectrochim. Acta 28A (1972) 2091. [21 G. Zerbr and L. Piseri, J. Chem. Phys. 43 (1965) 3840; hf. Tasumi and S. Krimm, J. Chem. Phys. 46 (1967) 755. and R.G. Snyder, Spectrochim. i31 J.H. Schachtschneider Acta 19 (1963) 85; R-G. Snyder and J.H. Schachtschneider, Spectrochim. Acta 19 (1963) 117. modern trends, [41 M. Tasumi, in: Vrbmtional spectroscopy, eds. A.J. Barnes and W-J. Ch-viBe-Thomas (Elsevier, Amsterdam, 1977). [51 R-G. Snyder, S-L. Hsu and 8 Krimm, Spectrochim. Actz 34A (1978) 395.
161 S. Abbate and G. Zerbi, Meeting of the Italian Physic0
Chemical Society, Bologna (1979);
r71 PI PI [lOI 1111 1121 r131 P41
J. Phys. Chem., submitted for publication. G. Zerbi, R. Magni, M. Gussoni, K. HoBand Moritz, A. Bigotto and S. Dirlikov, J. Chem. Phys, to be pubhshed. R.G. Snyder and J.R. Scherer, J. Chem Phys. 71 (1979) 3221. G.R. Strobl and W. Hagedom, J. Polym. Sci. 16 (1978) 1181. S.L. Wunder and SD. Merajiver, J. Chem. Phys., to be published. S.L. Wunder and SD. Merajiver, Macromolecules, to be pttblishedS.L. Wunder, private communication. G. Zerbi and M. Gussoni, Chem. Phys Letters 74 (1980) 24. G. Zerbi, R. Magni and M. Gussoni, J. Mol. Struct., to be published.
457
80, number
CHEMJCAL
3
SPECTROSCOPIC
DETERMINATION
IN ORGANIC MOLECULES
PHYSICS
15 June1981
LETTERS
OF THE AVERAGE
CONTENT OF GAUCHE STRUCTURES
CONTAINING POLYMETHYLENE
CHAINS *
Giuseppe ZERBI and S. ABBATE Ishkto di ChimicaUniversitydi Dfeste, Tkieste,Italy and CNR, Istituto chimicaIndustriale,Politecnico, Milan,Italy Received
23 March 1981
From the analysis of Fermi resonances in the CH-stretching and HCH-bending regions of the Raman spectra of transpolymethylene chains and CDaCHaCDa, it is proposed that when gauche structures are present additional spectral features occur. A method for the determination of the relative concentration of gauche structures is proposed.
With this short paper we hope to take a step forward in the interpretation of the Raman spectrum of polymethylene molecules, with the desire to derive information for the elucidation of the structure of these types of molecules which are found in several molecular systems as polymers (polyethylene, polyalkenamers, nylons, etc.), organic molecules (n-alkanes, fatty acids) and biological materials (phospholipids and membranes) We focus our attention on a few spectroscopic signals in the Raman spectrum which may be related to the existence of gauche structures. A quantitative analysis of these signals may provide a way to estimate the relative concentration of gauche conformers in an otherwise all-tram medium. In 1972 Iavalley and Sheppard [1] from the analysis of the infrared and Raman spectra of 1 ,1,1,3,3,3hexadeuteropropane have clearly shown that in the spectral region of the CH-stretching vibrations a strong Fermi resonance occurs. In particular the first overtone of the scissoring CH2 motion (&CH2) (2 X 1466 $= 2932 cm-l, A1 X A, = A1) is shown to couple through Fermi resonance with the fundamental level of the CH2 symmetric stretching of species A1 occurring in the same frequency range. The two perturbed A1 states show two strong totally symmetric Raman lines near 2876 and 2942 cm-l. The depolarized weak * Presented at the March Meeting of the American Physical Society,
New York (1980).
0 009-2614/81/0000-0000/$02.50
line near 2925 cm-l is assigned to the antisymmetric B, CH2 stretching which is free from resonance perturbations- The unusually large observed intensity of the first overtone, 26-CHz, near 2942 cm-l, is the result of Fermi resonance which allows for the intensity borrowing from the fundamental level. When a polymethylene chain molecule is formed, the intramolecular dynamics of the chain may somehow modify the intra-CH2 Fermi resonance scheme seen in CD3CH2CD3. This may occur as the result of some additional dynamical factors directly related to the existence of a sequence of CH2 units in a given conformational state. Let us, for the time being, consider the case of an all-tram-polymethylene chain either as an isolated molecule (one-dimensional crystal) or packed in a three-dimensional orthorhombic or monoclinic lattice (these lattices are found in polyethylene, n-alkanes, fatty acids, etc.). By considering the lattice dynamics of inftite onedimensional alI-tram-polymethylene chains (like in polyethylene) the infinite number of normal-mode frequencies is organized along branches in the phonon dispersion curves. Phonon dispersion curves for the one-dimensional lattice in the harmonic approximation have been calculated [2] and their shape can be considered approximately known. The experimental verification of the phonon dispersion curves has been carried out by Snyder and Schachtschneider [3] from
0 North-Holland Publishing Company
455
Volume 80, number 3
CHEMICAL PHYSICS LETTERS
the analysis of the infrared spectra of n-alkanes in the sohd state. The frequency versus phase plots obtained, clearly define the dispersion curves for t&kanes. The evtrema of these curves coincide with rhe k = 0 modes of an infinite one-dlmennonal cry&a1 of polyethyIene. Some of these limiting modes are infrared or Raman actwe and have been unquestionabiy observed in the infixed and Raman spectra [3]. The very large amount of spectroscopic work [4]
based on theory and calculations on polyethylene and trans-planar-poiymethylene chains puts the interpretatlon of the spectra (infrared and Raman) on a somew!lat firm basis. in terms of the dynamics and structure of these kinds of molecules. We wish to focus our attention in this paper on the Raman spectrum of polymethylene chains m the CH2scissoring region near 1460 cm-’ and in the CHstretching region near 3000 tin-1_ In these frequency ranges the observed features in the Raman spectrum reveal the existence of additional resonances. First, It has been qualitatively pointed out [s] and Iater quantitatively shown [6,7] that the two-phonon states (first overtone states) of the dispersion curves of the CHz-rocking modes occur in the frequency range of the CHZ-scissoring modes. thus entering m Fermi resonance through some anharmomc coupling_ Analogcusly, the two-phonon states of the dispersion curve of the CH, modes near 1440 cm-l generate Fermi resonances with the CH-stretching levels [G--8]. The present interpretation of the observed spectrum of trans-polymethylene chains is basically the following [6]. The Raman band centered near 1460 cm-1 arises from the superposition of rocking two-pho:on states which interact with the B,, and Ag fundamerr:aIs of the factor group splitting due to the orthorhombic lattlce near 1440 and 1416 cm-l respectively. In the CH-stretching region, calculations assess [6] that in the Raman spectrum the broad bands observed at 2930 and 2900 cm-l are essentially due to an envelope of overtone modes which interact via Fermi coupling with the fundamental symmetric CH-stretching normal mode of the single chain associated with the band near 2850 cm-l. The interrnoIecuIar packing gives rise to an additional Raman scattering between the two funda-
mentals near 2850 and 2883 cm-l- The Raman line near 2883 cm-ldue to the antisymmetric CH2 stretching, floats on top of a broad, strong background of Ag species. 456
15 June 1981
We wish to discuss in this paper the fact that when gauche structures are introduced in the trans host lattice, the number of two-phonon states arising from the complicated Fermi resonance of the trans chain decreases, the intramolecular coupling of CH-stretching modes changes and new spectral features due to the uncoupled or partially decoupIed CH, groups in gauche conformation shouId appear. For such dynamicalIy uncoupled gauche-CH2 groups the only Fermi resonance still existing is that which takes place in the starting model molecule CD,CH,CD,. In fig. 1 we report the co.woluted Raman spectrum of antisyrnrnetic and symmetnc stretching modes for an isolated CH, group. We would exps*t that for a totally gauche-polymethylene chain the Raman spectrum in the CH-stretching region should be smilar to that depicted in fig. 1, namely the overtone of the bending mode should occur near 2940 cm-l and a very close strong doublet of practically equal intensity should occur near 2880 cm-l due to the antisymmetric and symmetric CH,stretching modes. When the concentration of trans bonds increases, the previously discussed Fermi resonance schemes are activated and the symmetric CH2stretching fundamental of the trans section shouId appear near 2850 cm-l _ The intensity of the CH2 symmetric mode for the all-trans molecule seems weaker than the corresponding mode in the isolated CH2 group since the former lends intensity to a manifold of overtone states toward higher frequencies_ The 2940 cm-l band weakens considerably more than the 2850 cm-l band does in going from the totally gauche- to the totally tram-polyethylene, due to the same mechanism acting on the 2850 cm-l band (see figs. 1 and 2).
75 I
cm-’
Fig- 1. Convoluted calculated Raman spectrum of antisymmetric and symmetric CHz-stretching modes in CDsCHzCD3. Fermi resonance is only active within the isolated CH2 group (2&CH, in Fermi resonance with CH1 symmetric stretch).
Volume
80, number
3
CHEMICAL
PHYSICS
average concentration 75= = 50=‘
c 2z 250
2950 Fig. 2. Convoluted polymethylene
2wo calculated
singlechain
Raman
2850 spectrum
cm-’
of an all-trans-
molecule.
15 June 1981
LETTERS
and changes in concentration
of
gauche structure in the sample studied. We feel that the method presented in this paper makes E&man spectroscopy one of the unique tools for a direct qualitative and quantitative study of gauche structures in polymethylene systems in the various phases. It should be equally useful for the study of the conformational changes in phospholipids, membrane systems, etc. Ome the overall structures have been determined,
more detailed information on local gauche structures can be obtained in the infrared by selective deuteration [7-l 31 and in infrared and Raman spectra, where markers for local structures have been identified ]E4]_
We then propose that the ratio of the intensities 1(2850)/1(2940) should be proportional to the relative concentration of gauche and trans structures in a conformationally disordered polymethylene chain. Such a ratio should decrease wi*Lhan increase of the population of gauche structures. With similar arguments we also propose that when gauche structures are introduced in a trans host lattice the Fermi resonance peak near 1464 cm-l should decrease in intensity and slowly disappear along with the increase of the conformational disorder of the polymethylene chain. These predictions are nicely confirmed qualitatively by the Raman spectrum of liquid polyethylene and of long-chain n-hydrocarbons 173 _ Recent Raman spectra in the CH2-bending region of samples of polyethylene with an increase in concentration of amorphous content [9] also support our views. Strong support of our interpretation comes from the recent sets of experiments published by Wunder and co-workers, on the Raman spectra of various polymethylene samples. These authors have actually measured the ratio 1(2850)/(2940) for: (I) molten nhexadecane at various temperatures and in solution at various concentrations and temperatures [9] ; (ii) moIten polyethylene at different temperatures [lo] ; (iii) solid polyethylene at various concentrations of amorphous material [ 111. All these experiments support the proposal presented in this paper and fully discussed in ref. [6]_ Wunder and co-workers also propose some methods for the actual quantitative estimate of the
References [ 11 J.LavaBey and N. Sheppard, Spectrochim. Acta 28A (1972) 2091. [21 G. Zerbr and L. Piseri, J. Chem. Phys. 43 (1965) 3840; hf. Tasumi and S. Krimm, J. Chem. Phys. 46 (1967) 755. and R.G. Snyder, Spectrochim. i31 J.H. Schachtschneider Acta 19 (1963) 85; R-G. Snyder and J.H. Schachtschneider, Spectrochim. Acta 19 (1963) 117. modern trends, [41 M. Tasumi, in: Vrbmtional spectroscopy, eds. A.J. Barnes and W-J. Ch-viBe-Thomas (Elsevier, Amsterdam, 1977). [51 R-G. Snyder, S-L. Hsu and 8 Krimm, Spectrochim. Actz 34A (1978) 395.
161 S. Abbate and G. Zerbi, Meeting of the Italian Physic0
Chemical Society, Bologna (1979);
r71 PI PI [lOI 1111 1121 r131 P41
J. Phys. Chem., submitted for publication. G. Zerbi, R. Magni, M. Gussoni, K. HoBand Moritz, A. Bigotto and S. Dirlikov, J. Chem. Phys, to be pubhshed. R.G. Snyder and J.R. Scherer, J. Chem Phys. 71 (1979) 3221. G.R. Strobl and W. Hagedom, J. Polym. Sci. 16 (1978) 1181. S.L. Wunder and SD. Merajiver, J. Chem. Phys., to be published. S.L. Wunder and SD. Merajiver, Macromolecules, to be pttblishedS.L. Wunder, private communication. G. Zerbi and M. Gussoni, Chem. Phys Letters 74 (1980) 24. G. Zerbi, R. Magni and M. Gussoni, J. Mol. Struct., to be published.
457