Laser-Raman study of the longitudinal acoustic mode in polyethylene

A Raman band of low frequency, arising from an accordionlike vibration of all-trans \documentclass{article}\pagestyle{empty}\begin{document}$ \rlap{‐‐} ({\rm CH}_2 \rlap{‐‐})_n $\end{document} segments and previously observed in normal paraffins and in polyethylene single crystals, has now also been found in bulk and in cold-drawn polyethylene, both linear and branched. The accordionlike vibration, or longitudinal acoustic mode (LAM), in polyethylene is compared with the LAM in normal paraffins. Whereas the Raman bands corresponding to the third (LAM-3) and higher modes are quite intense in a long-chain paraffin such as n-C₉₄H₁₉₀, they are so weak in polyethylene as to be unobservable with the apparatus used. This is attributed to the presence of the chain fold in polyethylene. Of the two extreme structural models of the fold here discussed, namely the models of “tight folds” and of “loose loops,” only the latter seems capable of accounting for the weakness of LAM-3 and higher modes in polyethylene. A quantity called “nominal Raman length” is defined as the length of that all-trans n-paraffin that would have the same LAM-1 frequency as the polyethylene sample under consideration. The nominal Raman length is always greater than the average long spacing, deduced from discrete x-ray scattering at small angles after applying a Lorentz correction, and, after allowing for chain tilt, is found equal to the segment length between folds. This can be accounted for by both of the models mentioned. As a test of the theory of surface melting the frequency of the accordion vibration of annealed polyethylene single crystals was measured as a function of temperature up to the melting point; no frequency change with temperature was observable. On the basis of the naive idea that there is complete decoupling of the vibrations in the all-trans chain segment from the disordered (molten) surface layer, one would predict that upon surface melting and the concomitant shortening of the all-trans segment, the LAM-1 frequency should increase. A more careful analysis, taking into account the existence of coupling of the LAM to the surface layer, shows that the outcome of this experiment does not necessarily invalidate the idea of surface melting. Bulk polyethylene samples exposed to ⁶⁰Co γ-radiation for doses up to 100 Mrad show a slight shift of the Raman band to lower frequencies, whereas no such shift was observed upon absorption of a swelling agent. A search, without success, was made for a longitudinal acoustic mode in polypropylene, poly(vinylidene fluoride), nylon 66, and polyoxymethylene.     

The effect of interlamellar forces on the longitudinal acoustic mode of polyethylene crystals

The fold periods and longitudinal acoustic modes [LAMs] for isothermally crystallized polyethylene (PE) single crystals were determined in the dried state and in the presence of decalin and silicone oil. Upon swelling with decalin, the fold period increased by 7% while the LAM peak frequency decreased by approximately 1 cm^?1. Several possible explanations for the change in LAM frequency are discussed but the exact interpretation is open to question. No change in fold period was observed upon soaking a dried crystal mat in silicone oil. This fold period invariance along with the fact that silicone oil has no effect on the melting point of PE crystals indicates that there is no significant interaction between the oil and the methylene groups on the crystal surface. The effect of suspending crystals (which have never been dried down) in silicone oil should only be to increase the average interlamellar distance and, therefore, to reduce any interlamellar forces. It is shown that the LAM peak frequency for crystals suspended in silicone oil is the same as that for the dried crystals, indicating that interlamellar forces do not exert a significant perturbing influence on the LAM of polyethylene crystals.     

Longitudinal acoustic mode in polymers. VII. Surface structure from swelling studies of freeze-dried polyethylene single crystals

Raman longitudinal acoustic mode (LAM) spectra have been obtained from freeze-dried polyethylene single-crystal samples swollen in decalin. The changes in ν(LAM) have been studied as a function of molecular weight, temperature of crystallization, and temperature of measurement. These data, together with knowledge of how terminal “defects” influence ν(LAM) of the trans stems, lead to the conclusion that surface folds and cilia are the components responding to the swelling agent. The analysis also shows what the relative effects of these structures are as a function of molecular weight and crystallization temperature. This study indicates that cilia are primarily responsible for the large increases in x-ray long period observed for swollen single-crystal mats.     

Stress-induced straightening of tie chains in oriented PE films as revealed by Raman (LAM) study

The Raman longitude acoustical mode (LAM) study of axially stressed polyethylene-made microfilms gave evidence of the formation of the straight tie molecules localized in two neighboring crystals and in an amorphous layer situated between them. The samples were bicomponent blends composed of polyethylenes with different MW (7 × 10⁴ and 2 × 10⁶). Each MW fraction exhibits an individual LAM band responding to crystals with the size specific to a given fraction. Under tensile stress, the bands shift insignificantly towards an exciting laser line. In addition, the LAM localized on all-trans sequencies with the length exceeding the mean crystallite size appear in the spectrum of a stressed sample. The reversibility of these spectral changes depends on the draw ratio of samples. We conclude the effect is due to stress-induced gauch-to-trans transformations taking place in the amorphous layers. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2829–2833, 1998     

A raman LAM study of lamellar thickness of virgin polyethylene powder

The lamellar thickness of polyethylene virgin reactor powder has been successfully measured using the Raman longitudinal acoustic mode (LAM). Relatively high lamellar thicknesses have been found. These values change with polymerization temperature in an unusual way, with lamellar thickness being larger for lower polymerization temperature, i.e., at higher undercooling for crystallization. Agreement within an experimental error of 10% has been obtained between values from LAM and those calculated by the Thompson—Gibbs equation from the melting point measured by differential scanning calorimetry.     

A new look at the crystallization of polyethylene. II. Crystallization from the melt at low supercoolings

This article is part of the general project laid out in Part I (ref. 9) and is concerned with obtaining information on primary (unthickened) crystals of polyethylene formed at low supercoolings. For this, a technique had to be devised by which crystallization could be speeded up so as to eliminate or at least reduce lamellar thickening. Indeed we were able to increase the rate of crystallization by an order of magnitude using a technique which we have called enhanced self-nucleation. Using this technique we find that when viewed under an optical microscope, spherulites crystallize uniformly over the field of view, and not, as is usual, by a radial growth process. Isothermal crystallization in bulk linear polyethylene has been studied by means of the enhanced self-nucleation technique as a function of crystallization time by using Raman LAM and melting points to assess variations of fold length Data have been obtained at very much shorter times than before. At short times, we find a constant fold length; at longer times the crystals thicken linearly with the logarithm of time. Values of the initial fold length for crystallization temperatures between 118 and 130°C are presented. Associated with the thickening at short times we find an induction time which increases with temperature.     

Micro-Raman study of the longitudinal acoustic modes (LAM) evolution along the transition front in uniaxially stretched HDPE

Low-frequency Raman spectra were recorded along the transition front of uniaxially cold drawn High Density Polyethylene (HDPE) samples with a Raman microscope instrument. The high spatial resolution capacity of the technique allows to analyze the variation of the Longitudinal Acoustic Mode (LAM) along the transition zone between the isotropic structure and the oriented one. The evolution of the LAM over the transition zone was followed by measuring the LAM intensity, bandwidth and position as a function of the distance along the transition front. The LAMs are affected by the stretching process before the transition zone is reached and the lamellar structure was found to be totally disrupted before the fibrillar structure is formed. Whereas the LAM intensity decreases gradually along the transition region, the bandshape and peak frequency do not change significantly, indicating that the distribution of fully planar zigzag segments in the remaining lamella, structure is not really affected during the deformation process. The concentration of lamella, which still remain dimensionally intact, decreases gradually along the transition zone up to the stage where the structure is getting fibrillar.     

Theory of second-order Raman scattering from a zigzag chain with application to polyethylene

The extinction coefficient for acoustic branch, second-order (two-phonon) Raman scattering from a zigzag chain, using force constants and polarizabilities appropriate to polyethylene is computed. As a consequence of the computation, we propose identification of a line at 890 cm^?1 in the published Raman spectrum of polyethylene as a second-order Raman line.     

Longitudinal acoustic mode in polymers. VIII. Nature of mass perturbations in terminally brominated paraffins

Raman spectra have been obtained of the longitudinal acoustic mode (LAM) in α-BrC₂₀H₄₁ and α, ω-BrC₂₀H₄₀Br, and compared with such spectra for n-C₂₀H₄₂. Normal coordinate analyses of these three molecules clearly account for (i) the frequency decreases on Br substitution; (ii) the presence of doublet LAM modes in both brominated molecules; and (iii) the decrease in the total intensity of the LAM mode resulting from the added masses, as distinct from the increase predicted by the elastic rod model. These results thus provide experimental support for predictions made from normal coordinate and intensity analyses regarding the influence on LAM bands of mass perturbations at the ends of paraffinic chains.     

Regularity modes in Raman spectra of polyolefins: Part II. Polyethylene and ethylene copolymers

In this work, the thermal behavior of the regularity modes in Raman spectra of polyethylene with different densities and random ethylene/1-hexene copolymers with varying content of comonomer are studied. We demonstrate especially that the vibrational modes at 1062 and 2850 cm^↙1 are related to a critical sequence length of trans-conformers of 6⬜8 CH₂ groups, while the modes at 1130, 1170, 1295, and 2883 cm^↙1 indicate a critical sequence length of trans-conformers of 18 CH₂ groups. Upon increasing the 1-hexene content in the ethylene/1-hexene copolymers, the evolution of the intensities of the Raman modes at 1062, 1130, 1170, 1295, and 1417 cm^↙1, normalized to the intensity of the band at 2850 cm^↙1, is similar to the evolution of the intensities of the same modes in the Raman spectra of low density polyethylene at increasing temperature. This observation however contrasts with that in the Raman spectra of polyethylenes with middle and high densities. We suppose that these results can be explained by similarities in the structure of non-crystalline areas of low density polyethylene and the ethylene/1-hexene copolymers, which contain significant amounts of short sequences of trans-conformers.     

Comparison of near-infrared and Raman spectroscopy for the determination of the density of polyethylene pellets

In this study, we compare near-infrared (NIR) and Raman spectroscopy for the determination of the density of linear low density polyethylene (PE) (in a pellet form). As generally known, Raman spectral features are more selective than those of NIR for most chemical samples. NIR spectroscopy has been more extensively used for the quantitative analysis of polymers, but Raman spectroscopy is the better choice as long as the problem of reproducibility of Raman measurements (especially for solid samples), mostly resulting from insufficient sample representation due to probing only localized chemical information and the sensitivity of sample placement with regard to the focal plane, can be overcome. To improve sample representation and reproducibility of Raman measurements, we have employed the wide area illumination (WAI) Raman scheme, capable of illuminating a laser onto a large sample area (28.3 mm²) for Raman spectral collection (a 6-mm laser spot with a focal length of 248 mm). Diffuse reflectance NIR spectra of PE pellets were collected using a sample moving system which allowed for the scanning of large areas. The prediction error was 0.0008 g cm⁻³ for Raman spectroscopy and 0.0011 g cm⁻³ for NIR spectroscopy. The harmonization of inherently selective Raman features and a reproducible spectral collection with correct sample representations using the WAI scheme led to an accurate determination of the density of the PE pellets.     

Hydrogen bonding effects on the skeletal optical and the longitudinal acoustical modes in long chain molecules and polymers

Raman spectra of stearyl alcohol (n-C₁₈H₃₇OH) indicate that vibrational bands in both the skeletal optical (1000-1200 cm^?1) and longitudinal acoustical (0–500 cm^?1) regions are considerably perturbed by intermolecular hydrogen bonding. The zone interior skeletal stretching mode reflecting phonon dispersion in the v₄ branch of the infinite polyethylene chain is found at 1105 cm^?1, approximately 20 cm^?1 higher than in the corresponding n-alkane. Similarly the single nodal longitudinal acoustical mode (LAM-1) is found shifted by 12 cm^?1 to higher frequency when the expected “mass effect” produced by the ? OH group is considered. This shift is further increased to 16 cm^?1 at ?100°C indicating a further perturbation on this accordion mode due to the increased strength of the hydrogen bond at the low temperatures. The positions of the higher multinodal vibrations, LAM-3 and LAM-5, are also perturbed by the hydrogen bond but by differing amounts. The observation of a low-frequency Raman-active LAM in polytetrahydrofuran [(? CH₂CH₂CH₂CH₂O? )_n] is discussed in conjunction with the expected effects of hydrogen bonding at the lamellar surface.     

Some simulations on crystallinity in a typical linear low-density polyethylene

Crystallinity in ethylene/1-hexene copolymers, a type of linear low-density polyethylene, was investigated by Monte Carlo simulations. The comonomer distributions generated in the simulated chains and the melting temperatures of real chains were used to estimate the minimum crystallite thickness, which is the critical quantity for simulating crystallization in any type of polymer. Simulated values of this thickness were in good agreement with values calculated from Raman longitudinal acoustic mode (LAM) spectroscopy, except for very low 1-hexene mole fractions, where there were presumably complications from high melt viscosities and chain entanglements. The use of this information in estimating properties of these copolymers is illustrated by some preliminary results on the effects of varying amounts of this comonomer on the sizes and numbers of the polyethylene crystallites.     

Direct on-line Raman measurement of flying solid samples: determination of polyethylene pellet density

We demonstrated an on-line Raman measurement of polyethylene (PE) pellet density when it is flying in a sample line. While in flight, pellets are sparsely populated at spectral collection, a spectral collection strategy covering a large spatial volume (larger number of pellets simultaneously) is necessary to acquire reasonable Raman intensity. In addition, the Raman measurement must be less sensitive to pellet position, because position and distribution are uncontrollable in a flying condition. To fulfill these requirements, a wide area illumination (WAI) scheme capable of covering a large sample volume (illumination volume: 0.7 cm³) was used when the pellets were flying in a 2.5-cm-diameter sample line. In addition, a long focal length (250 mm) was used so that minor changes in pellet position would not significantly affect the resulting Raman spectral feature. Although Raman intensity substantially decreased due to the large void space among flying pellets, a correct spectral feature representing PE was successfully obtained without any significant spectral distortion. Using partial least squares (PLS) regression, the prediction error under flying conditions was 0.0009 g cm⁻³, which was comparable to that acquired when the pellets were packed (0.0008 g cm⁻³). When a conventional Raman scheme covering a smaller sample volume with a short focal length was used, the PE intensity decreased dramatically, and the resulting signal-to-noise ratio was not proper for quantitative analysis.     

Raman longitudinal acoustic mode (LAM) studies of folded-chain morphology in poly(ethylene oxide) (PEO). II. Normal mode analysis of folded-chain structures of PEO

Normal mode calculations were carried out on model folded-chain molecules to determine the effect of a fold on the LAM of PEO. The presence of a chain fold results in a decrease in the LAM frequency and intensity, the change in frequency being very much smaller than the change in intensity. End interactions do not seem to have much effect on the LAM when a fold is present at the chain ends. The effective chain length for determining the LAM frequency was found to be that part of the chain experiencing interchain interactions.     

A comparison of the Raman LAM and electron microscopy in determining crystallite thickness distributions: Polyethylenes with narrow size distributions

A detailed quantitative comparison between thin section electron microscopy, utilizing the chlorosulfonation technique, and the Raman low-frequency acoustical mode (LAM) in determining the crystallite size distribution in polyethylenes having narrow distributions is made. Three different polyethylene systems have been analyzed, one of which was specifically prepared for this work. Very good quantitative agreement is obtained between these two analytical methods when account is taken of the chain tilt and the distribution is restrained to be narrow. Systems having broad crystallite size distributions introduce complexities into this comparison.     

Chain elastic modulus of polyethylene: A spectroscopically determined force field (SDFF) study

Our SDFF for linear saturated hydrocarbon chains has been used to calculate the chain modulus of isolated and crystalline chains of n-alkanes of varying lengths. This has been done for static deformations and for the dynamic deformation in the longitudinal acoustic mode (LAM). Extrapolation to infinite chain length gives a common value of the room-temperature crystal modulus of 303 GPa (also obtained in an infinite chain calculation). Experimental Raman LAM measurements, corrected for chain-end interactions, give a modulus of 305 GPa, in excellent agreement. Problems with the experimental values obtained by inelastic neutron scattering and x-ray diffraction are discussed. © 1996 John Wiley & Sons, Inc.     

Raman spectroscopic investigations of the structure and phase transitions of liquid crystalline lead(II) alkanoates

Lead(II) alkanoates with even chain lengths from octanoate to octadecanoate have been investigated by Raman spectroscopy. In the low frequency region, transverse and longitudinal acoustical modes (TAM, LAM) have been assigned. It was shown that LAM-1 is the vibration of the double chain with the node of the vibration in the Pb²⁺ layer. A fully extended conformation of the chains in the low temperature phase was confirmed. The frequencies and intensities of the LAMs as compared with those of the alkanes and the fatty acids led to an estimate of the force constant and polarizability of the Pb²⁺ -COO^- bond relative to the C-C bond. The defects at the chain ends were investigated in the ρ(CH₃) and v(CC) region. For the intermediate (CM) phase, both the Pb²⁺ layer distance reduction and the chain length independent enthalpy contributions can be attributed mainly to defects at the chain ends.     

Chain direction elastic modulus of PE crystal and interlamellar force constant of n-alkane crystals from RAMAN measurements

Spectroscopic data can deliver force constants only if the exact chain conformation is known. For the longitudinal acoustic modes (LAM), however, simple linear chain models can be used to yield the effective longitudinal chain modulus from spectroscopic data of oligomer crystals. The model of p-coupled linear chain molecules with N masses and only nearest neighbor interactions was used to investigate the longitudinal acoustic modes with s nodes. The frequencies plotted versus s/N fall onto different branches for different s. The intermolecular coupling and the heavier endmasses shift the LAM branches to higher and lower frequencies, respectively. There exists a value x₀ depending on the masses and force constants, where the branches cut the dispersion curve of the infinite molecule. For s/N ≥ x₀ the effect of endmasses dominates. Low-frequency RAMAN spectra of n-alkanes (N = 20, …, 40 C atoms) were recorded and analyzed. The LAM1 branch runs clearly above a smooth fit through all other LAM data and the origin. This fit approximates to first order the dispersion curve of the infinite PE molecule in an ideal crystal. Its curvature exceeds that of the dispersion curve of the simple linear chain, but is somewhat smaller than that of the dispersion curve of the planar zig-zag chain with rigid bonds. The slope at the origin yields the limiting elastic modulus E_c = 315 GPa in chain direction of crystalline polyethylene. From our measurements on n-alkanes we obtained the frequency shift of LAM1 due to the interlayer coupling and the heavier endmasses. Calculation of the intermolecular coupling constant of the model of a long row of linear chain molecules with the same frequency shift yield the mean value f_l = 2.5 N/m. This value decreases with increasing chain length. The relevance and applicability of the model is discussed. © 1997 John Wiley & Sons, Inc.     

Study of oriented polyethylene structures using a Raman longwave acoustic mode

This paper concerns the basics of using longwave (low-frequency) Raman spectroscopy in the region of a longitudinal acoustic mode for the study of structural features of polymers. Using ultrahighmolecular- weight polyethylene (UHMW PE)-based reactor powders, gels, and oriented fibers obtained by the gel technology, the length distribution of straight-chain segments and its relation to the morphology of the sample were analyzed. An important role of the low-frequency Raman spectroscopy in creating domestic gel technology for preparing ultrahigh-strength threads from polyethylene was demonstrated.