Polaron lattice model

Another experimental evidence against the polaron lattice model for the metallic state of heavily doped trans-(CH)j comes from Electron-Energy-Loss Spectroscopy (EELS) data [21]. These data show levels spread well across the gap, which is more in agreement with the disordered incommensurate state than with the picture of narrow polaron bands in the gap. Band structure calculations using the Valence Effective Hamiltonian (VEH) technique [22] support this conclusion since it is shown that a large energy gap exists between the polaron bands in the band structure of the polaron lattice. On the other hand, experimental and theoretical results have been presented that support the polaronic metal state for doped polyaniline (emeraldine salt) [23]. 

Another mechanism that has been proposed is that the carriers move as small polarons20. A small polaron is a carrier that is self trapped in a well created by the lattice distortion. This lattice distortion is formed when a carrier stays sufficiently long in a position to polarize the medium around it. The applied field can lower the polaron barrier in a PF fashion and increase the mobility. The polaron transport model is attractive in that the mobilities in this mechanism are not critically dependent on the sample preparation. 

In band theory considerations, electrons are strictly delocalized, however, in many materials, it is better to view electronic defects as located at particular sites. The additional electron from the phosphorus donor atom in silicon, for example, could be viewed as not completely delocalized but located on the Si atom according to p/.-I- Si j. In such cases, the electronic model moves from band-type to polaronic-type model (a polaron is an electronic point defect and is formed when an electron has a bound state in the potential created by a distorted lattice). 

The dimensional structure of these materials. If we consider that there is no reticulation, these materials can appear one-dimensional in relation to both charge transfer and vibrational energy. This apparent anisotropy should be considered only local (at a short distance) because the study of conduction phenomena shows an isotropy of transport properties, which is quite well explained with the theory of interchain hopping mechanisms (Kivelson model [22] for solitons polaron lattice introduced by Bredas and coworkers [23,24]). 1 will show that the heterogeneous polymers model may also be used. 

Unfortunately, neither the results presented in this article, nor any previously reported model are able to present an undisputable explanation for the behavior of heavily doped trans-(CH) at and above the critical doping concentration. We have pointed out here, that it is essential to include three-dimensional interactions into the Hamiltonian, since calculations with this interaction included will provide information concerning the stability of the polaron lattice vs, the soliton lattice. An extension of the method presented in this article to include inter-chain interactions is under development and we hope to report results from calculations based on this method in the near future. 

Choi, H.-Y. and Mele, E. J. (1986) "Dynamical Conductivity of Sohton Lattice and Polaron lattice in the Continuum Model of Polyacetylene" Phys. Rev. B 34, 8750-8757. 

There are two different temperature regimes of diffusive behavior they are analogous to those described by Holstein [1959] for polaron motion. At the lowest temperatures, coherent motion takes place in which the lattice oscillations are not excited transitions in which the phonon occupation numbers are not changed are dominant. The Frank-Condon factor is described by (2.51), and for the resonant case one has in the Debye model ... 

The addition of Li20 to NiO leads to an increase in conductivity, as illustrated in Fig. 2.16. The lithium ion Li+ (74 pm) substitutes for the nickel ion Ni2+ (69 pm) and, if the mixture is fired under oxidizing conditions, for every added Li+ one Ni2+ is promoted to the Ni3+ state, the lost electron filling a state in the oxygen 2p valence band. The lattice now contains Ni2+ and Ni3+ ions on equivalent sites and is the model situation for conduction by polaron hopping , which is more often referred to simply as electron hopping . 

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