Disordered quasi-one-dimensional systems

In the case of disordered quasi-one-dimensional systems the NFC method can also be applied to the case of an arbitrary number of orbitals per site either in an ab initio form > or in a semiempirical, for instance, extended Huckel form. In the ab initio case one has the secular determinant instead of a tridiagonal in a triblock-diagonal form... 

CALCULATIONAL METHODS FOR DISORDERED QUASI-ONE-DIMENSIONAL SYSTEMS... 

In this contribution, we discussed effects of disorder on the electronic properties of quasi-one-dimensional Peierls systems, like the conjugated polymer fraus-poly-acetylene. Since polymer materials generally are rather disordered and the effect of disorder on any quasi-one-dimensional system is strong, a proper description of these materials requires consideration of such effects. 

This model, which is sometimes referred to as the Fluctuating Gap Model (FGM) [42], has been used to study various aspects of quasi-one-dimensional systems. Examples arc the thermodynamic properties of quasi-one-dimensional organic compounds (NMP-TCNQ, TTF-TCNQ) [271, the effect of disorder on the Peierls transition [43, 44, and the effect of quantum lattice fluctuations on the optical spectrum of Peierls materials [41, 45, 46]. 

There is a well-known review article by Ishii that contains a proof that the particular solutions in a disordered one-dimensional system grow exponentially with probability approaching 1 as a function of the size of the system. The proof should also hold in a polymer or quasi-one-dimensional system. With this result in mind, we compare the first and last components of (p ), that is, the ends of our finite polymer chain. 

Fig. 3.4 (a) Schematic picture of the temperature dependence of the various scattering times in the inhomogeneous disorder model and the respective localization domains, (b) The corresponding diffusion constant expected for the inhomogeneous quasi-one-dimensional system. (From Ref. 87.)... 

When we deal with the real polymer systems, disorder effects have to be taken into consideration. This is because in the (quasi) one-dimensional system the disorder tends to make the electronic states localized in cooperation with the electron-lattice coupling [12]. If the disorder is severe, the charges will be transported via hopping among the localized states accompanied by disorder potential as in the case of classical amorphous or non-crystalline media. This will be discussed in sections 2.3.2 and 2.3.3 in relation to the charge transport and recombination in the materials. 

This makes the system very robust with respect to energetic disorder, again in contrast to the purple bacterial system which is quasi-one-dimensional. 

---