Polyacetylenes electronic effects

While Section 4.4 considers electron transport in the framework of a single-charge tunneling problem, such a theory would not explain the conductivity of polyacetylene. It turns out that the conductivity of many ID conductors often involves many-electron effects, and to study ID electronic systems with path integral simulations, one has to first solve the fermion sign problem. 

In the weak-coupling limit unit cell a (, 0 7a for fra/u-polyacetylene) and the Peierls gap has a strong effect only on the electron states close to the Fermi energy eF-0, i.e., stales with wave vectors close to . The interaction of these electronic states with the lattice may then be described by a continuum, model [5, 6]. In this description, the electron Hamiltonian (Eq. (3.3)) takes the form ... 

Since the discovery of doped polyacetylene, a range of polymer-intense semiconductor devices have been studied including normal transistors and field-effect transistors (FETs), and photodiodes and light-emitting diodes (LEDs). Like conductive polymers, these materials obtain their properties due to their electronic nature, specifically the presence of conjugated pi-bonding systems. 

A particularly interesting property of Durham polyacetylene is that it can be stretched to draw ratios of up to 20 during the transformation, to yield a polyacetylene sample with high levels of orientation. This effect was reported by Bott et al. 378) for thin films in the electron microscope and then by Leising et al. 379), who drew single fibres of polyacetylene to a highly oriented /rani-state with a density of 1.06 g cm-3. 

The structure/property relationships that govern third-order NLO polarization are not well understood. Like second-order effects, third-order effects seem to scale with the linear polarizability. As a result, most research to date has been on highly polarizable molecules and materials such as polyacetylene, polythiophene and various semiconductors. To optimize third- order NLO response, a quartic, anharmonic term must be introduced into the electronic potential of the material. However, an understanding of the relationship between chemical structure and quartic anharmonicity must also be developed. Tutorials by P. Prasad and D. Eaton discuss some of the issues relating to third-order NLO materials. 

We choose as model system the simplest conjugated polymers - the trans-polyacetylene. This compound shows a. dimerized structure with an altemance between double bond (1.35A) and single bond (1.45A) the monomer is then simply a double bond (see figure (8)). The tt electrons are assumed to be effectively describe not by the full PPP Hamiltonian but by the Extended Peierls-Hubbardmodel (EPH) [17, 14], a short version of it) for simplicity... 

The exact relative locations of the lowest excited Bu and Ag states are difficult to predict on a theoretical basis. Indeed, they sensitively depend on the interplay between electron correlation effects and bond-length alternation effects, as shown for instance by Soos and his co-workers23. Strong effective bond alternations favour the 1BU state as the S, state this is the case in polyparaphenylene and PPV due to the presence of phenylene rings. The effective bond alternation is much weaker in polyacetylene while it is intermediate in polythiophene where the 2Ag state is found to lie slightly above the 1BU state. 

Impurity and Aperiodicity Effects in Polymers.—The presence of various impurity centres (cations and water in DNA, halogens in polyacetylenes, etc.) contributes basically to the physics of polymeric materials. Many polymers (like proteins or DNA) are, however, by their very nature aperiodic. The inclusion of these effects considerably complicates the electronic structure investigations both from the conceptual and computational points of view. We briefly mentioned earlier the theoretical possibilities of accounting for such effects. Apart from the simplest ones, periodic cluster calculations, virtual crystal approximation, and Dean s method in its simplest form, the application of these theoretical methods [the coherent potential approximation (CPA),103 Dean s method in its SCF form,51 the Hartree-Fock Green s matrix (resolvent) method, etc.] is a tedious work, usually necessitating more computational effort than the periodic calculations... 

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