Non-Linear Excitations and the Electronic Structure of Conjugated Polymers

Macromolecular Systems Microscopic Interactions and Macroscopic Properties Deutsche Forschungsgemeinschaft (DFG) 

Copyright 2000 WILEY-VCH Verlag GmbH, Wdnheim. ISBN 978-3-527-27726-1 

So far we have only mentioned the construction of adequate models for the investigation of physical properties. However, there are competing approaches to address the same set of questions. One of these approaehes uses sophistieated quantum-chemieal eodes [lc,d] to calculate structure and electronie states of these materials. Although sueh a proeedure may be able to reproduee the observed properties of a specific material quite well it is very difficult to obtain information about general trends and physical mechanisms. Therefore we did not follow this route. Another weU-estahhshed method for calculating ground-state properties, namely the local density functional, has been used to some extent [3]. The drawback of this method, however, is the finite size of the system which can be calculated within a reasonable amount of computer resources. Therefore only a few questions have been addressed via this approach. 

Therefore, we shall argue in favor of a simple model which is capable to include the most essential physics. Assuming the sp -hybridisation of the carbon atom leaves one 7t-elec-tron per atom the others being incorporated into the bonds as cr-electrons. It is the physical behaviour of this single rt-electron which is responsible for all the interesting effects. 

It turns out that there is a typical length scale in this model Vp/A (with the Fermi velocity vp and the electronic gap 2 A) which is considerably larger than the interatomic spacing a. Thus for most physical properties of interest a continuum approximation is valid. This stresses the generic aspects of the whole class of these materials even more. 

---

Non-Linear Excitations and the Electronic Structure of Conjugated Polymers... 

---