Band structures polyethylene results

Results of photoemission studies of polyethylene have shown definite evidence for wide energy bands among deep valence orbitals ( ), but the nature of the fundamental absorption edge has not been resolved. Band structure calculations predict direct interband excitations to occur above 12.6 eV (.8) whereas the absorption threshold is at 7.2 eV and a strong peak in e occurs at 9.0 eV. The momentum dependence of the absorption threshold indicates that the threshold is of excitonic origin, i.e. the excitation is localized by the strong electron-hole or configuration inter-... 

Polymer Conformation and Crystallinity. Beyond the stereoregularity and tacticity, the geometrical conformation of the polymer chain in the solid material could influence its electronic structure, through a modification of its valence band molecular orbitals. Indeed, a few years ago, very characteristic band structures were calculated for T, G, TG, and TGTG polyethylenes ( ). More recently. Extended Huckel crystal orbital calculations showed that for isotactic polypropylene, a zig-zag planar or a helical conformation resulted in significant changes in the theoretical valence band spectra, supporting the idea that conformation effects could be detected experimentally by the XPS method ( ). 

Figure 2 shows the HF, two DFT variants (LDA and gradient corrected BLYP), and MBPT(2) band structures of polyethylene calculated with the 6-31G basis set [66]. The MBPT(2) bands are above the HF and below the DFT ones. The correlation shift is different at different points in the bands, being around 2 eV for the first two bands. For the third band, the shift is about 5 eV at 0 and 3 eV at n/a. Table 3 list the calculated and measured peaks, the positions of which are not sensitive to the distribution of the incident radiation in the spectra [66]. The HF values are much larger than the measured data while DFT results are too small. As expected, MBPT(2) greatly reduces the... 

Finally, we show in Figure 12 the experimental band structures together with the calculated ones for polyethylene.62 These density-functional results (with a local-density approximation) demonstrate a very good agreement between theory and experiment, but it should be stressed that the experimental data have been shifted rigidly about 2 eV upwards in energy, which is consistent with the results above. We add that band structures from Hartree-Fock calculations were in general too wide,63 which is a common deficiency of Hartree-Fock calculations. 

Most polymers (typified by polystyrene and polyethylene) are electrically insulating and have conductivities doped with iodine to become electrically conducting (values have now been reported up to olO Scm ) represented a pivotal discovery in polymer science that ultimately resulted in the award of the Nobel Prize for Chemistry in 2000 [4]. The study of electrically conducting polymers is now well advanced and two extremes in the continuum of transport mechanisms exist. If the charge carriers are present in delocalized orbitals that form a band structure along the polymer backbone, they conduct by a delocalization mechanism. In contrast, isolated groups in a polymer can function as acceptors or donors of electrons and can permit... 

Experimental results on the band dispersion in o-bond polymers are very limited due to difficulty in preparing thin films with oriented chains [20, 31, 32, 62]. Here, we introduce the band dispersion of quasi-one-dimensional polymer polyethylene. Early work on the band structure study was carried out on systems with alkyl chains and was aimed at understanding the electronic structure of polyethylene, in particular, the possible existence of one-dimensional band structure in thin films where molecular chains assemble via weak interchain interactions. There is renewed interest in the band dispersions as they determine carrier transport properties in nanoscale molecular electronics [63]. 

The third part of Chapter 10 describes the calculation of various mechanical properties (such as bulk modules and shear modules) of some simple polymers based on their band structure but corrected for correlation. In the case of polyethylene and some of its halogenated derivatives the theoretical results are compared with available experimental data. 

The first pioneering ab initio crystal orbital studies on polyethylene have been presented by Andre et al. 139-41] and were devoted to an analysis of the valence band structure. We have recently performed similar calculations with the aim to obtain the equilibrium structure of the all-trans conformation of polyethylene 113,42,43]. Results obtained with a 7s3p/3s basis are shown in table 3 together with those of X-ray and neutron investigations. 

Polyethylene has been studied spectroscopically in greater detail than any other polymer. This is primarily a result of its (supposedly) simple structure and the hope that its simple spectrum could be understood in detail. Yet as simple as this structure and spectrum are, a satisfactory analysis had not been made until relatively recently, and even then significant problems of interpretation still remained. The main reason for this is that this polymer in fact generally contains structures other than the simple planar zig-zag implied by (CH2CH2) there are not only impurities of various kinds that differ chemically from the above, but the polymer always contains some amorphous material. In the latter portion of the material the chain no longer assumes an extended planar zig-zag conformation, and as we have noted earlier, such ro-tationally isomeric forms of a molecule usually have different spectra. Furthermore, the molecule has a center of symmetry, which as we have seen implies that some modes will be infrared inactive but Raman active, so that until Raman spectra became available recently it was difficult to be certain of the interpretation of some aspects of the spectrum. As a result of this work, and of detailed studies on the spectra of n-paraffins, it now seems possible to present a quite detailed assignment of bands in the vibrational spectrum of polyethylene. 

In polypropylene, one methyl group replaces an hydrogen atom in the polyethylene repetitive unit this results in an intense structure located in the middle of the C-C (C2s) band. In isotactic polypropylene moreover, the bonding and antibonding structures of this band are split in accordance with theoretical calculations performed on isotactic polypropylene in an helical conformation (1, A4). 

The molecular structure of naphthazarin (44) has been a subject of considerable interest, particularly because of the rapid intramolecular proton transfer effects observed for this species . Andersen recently investigated naphthazarin and its 2,3-dichloro derivative (68) by means of IR LD spectroscopy on samples aligned in stretched polyethylene. Unfortunately, no useful LD was observed for naphthazarin (partly because of low solubility), but the dichloro derivative was readily dissolved and aligned in stretched polyethylene . The observed wavenumbers, IR intensities and polarization directions were well reproduced by the results of B3LYP/6-31G calculations. Two strong, differently in-plane polarized bands at 1230 and 1204 cm were assigned to transitions with... 

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