Molecular orbitals polymer chains

We will first sketch briefly how the electronic stmcture of a perfect one-dimensional polymer chain is perceived in a molecular picture before drawing the comparison to a semiconductor band picture. For our molecular based approach, we consider, say, a perfect PPP chain as a sequence of molecular repeat units such as phenylenes that are coupled by a covalent bond. As a result of the coupling, the molecular orbitals of adjacent units can interact and split. Due to the perfect order and symmetry, this process takes place across the entire chain leading to the... 

The optical and electronic functions of polysilanes owe to their delocalized highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) that are occupied by holes and conduction electrons, respectively. The polymer does not show high conductivity or optical nonlinearity if the electrons or holes are localized on a small part of the polymer chain. To elucidate the structure of HOMO and LUMO is therefore important for the molecular design of polysilanes as functional materials. 

Unfortunately there seems to be no way at present absolutely to characterize the behavior of a plasticizer in terms of some fundamental property. The reason is that the behavior of the plasticizer is intimately tied up with the polymer to which it is added, and the polymer, in turn, depends greatly on its previous history. For example, one can prepare two samples of film from the same batch of polymer yet, by drawing one to a greater extent, it will increase in crystallinity owing to better orientation of the chains, and the effect of the plasticizer will, therefore, be quite different. Whereas one can use molecular orbital calculations to predict, for in-... 

Two theoretical approaches for calculating NMR chemical shift of polymers and its application to structural characterization have been described. One is that model molecules such as dimer, trimer, etc., as a local structure of polymer chains, are in the calculation by combining quantum chemistry and statistical mechanics. This approach has been applied to polymer systems in the solution, amorphous and solid states. Another approach is to employ the tight-binding molecular orbital theory to describe the NMR chemical shift and electronic structure of infinite polymer chains with periodic structure. This approach has been applied to polymer systems in the solid state. These approaches have been successfully applied to structural characterization of polymers... 

Sometimes the estimation of the electronic structures of polymer chains necessitates the inclusion of long-range interactions and intermolecular interactions in the chemical shift calculations. To do so, it is necessary to use a sophisticated theoretical method which can take account of the characteristics of polymers. In this context, the tight-binding molecular orbital(TB MO) theory from the field of solid state physics is used, in the same sense in which it is employed in the LCAO approximation in molecular quantum chemistry to describe the electronic structures of infinite polymers with a periodical structure -11,36). In a polymer chain with linearly bonded monomer units, the potential energy if an electron varies periodically along the chain. In such a system, the wave function vj/ (k) for electrons at a position r can be obtained from Bloch s theorem as follows(36,37) ... 

Molecular models show that rotation about the Ca—Gp bond is strongly hindered and that the least strained conformation is that in which Ha and H6, the two /J-protons, each have 0=30°, and with the polymer chain, R, at 90° to the nodal plane of the 2p-orbital. We expect that eq. (18)... 

Estimations [21] give / [ 3.7 eV and /i2 2.8 eV. In view of these estimations according to expression (10) the difference AEX— AE reaches value 0.1 eV at decrease of the polymer chain length (IV- - oo) down to value N0A equal, 40 dimer units or 80 bonds C-C. At the same time, experimental data for polyenes give the value A0.i 20 bonds C-C [22]. Thus, the model of noninteracting molecular orbitals delocalized along the whole chain overestimates increase AE with reduction of length of a chain. 

The number of bands in a band structure is equal to the number of molecular orbitals in the unit cell. So if the unit cell contains 17 times as many atoms as the basic unit, it will contain 17 times as many bands. The band structure may look messy. The chemist s feeling that the 17-mer is a small perturbation on the basic electronic unit can be used to simplify a complex calculation. Let s see how this goes, first for the polyene chain, then for the PtH42- polymer. 

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