Localized and extended states in doped polyaniline: The effect of bond-length alternation

Abstract

We present numerical studies of localization properties of oxidized and protonated disordered polyaniline. The calculations are performed on the single electron level, using Hiickel theory for~electrons. The spatial extension of the eigenstates at the Fermi energy is determined by a fast and accurate transfer-matrix scheme. The spatial extension of eigenstates diverges for a large degree of protonation, provided all bonds within the benzoid and quinoid can be described with the same set of tight-binding parameters. Localization effects become important for small degrees of protonation and in systems that show bond-length alternation in quinoid rings and aromatic bonds in benzoid rings.

Tight-Binding Effective Hamiltonians for the Electronic States of Polyaniline Chains

“…Parts (a-1) and (a-2) refer to the ordered lattice where protonation is randomly distributed in 25% and 100%, respectively, of the imine nitrogens. In parts (b-1) and (b-2) the same concentrations of protonated imine nitrogens are distributed over a completely disordered bipolaronic lattice rings [16][17][18] (we do not consider here any other kind of disorder such as ring torsion or bond length disorder). A distinctive sign of disorder is the fragmentation of the electronic spectrum, a broadening of the density of states and the presence of states in energy regions otherwise forbidden to the electron in the corresponding ordered system.…”

“…Existing tight-binding (TB) parameterizations of polyanilines are often deduced from Streitweiser [15] with some slight modification [16][17][18], and are used as ingredients of TB Hamiltonians even if the overall band structure generated from them has poor agreement with the band structures obtained from more sophisticated methods; other parameterizations in the literature [19], also introduced in a renormalization approach [20,21], have allowed a better reproduction of the band structures (at least in the energy region around the fundamental gap). Other studies [22,23] have proposed simplified model cells which somehow summarize the content of the true polymer cell; the scope is to use them for the evaluation of the transport properties of the polymeric structure, even if this use has to be taken with caution due to the high sensitivity of the band structures and the densities of states to the parameterization of the original polymeric Hamiltonian.…”

Renormalization approach for transport and electronic properties of conducting polymers

“…A great impulse to the solution of the problem has been given by introducing the alternative idea to consider as decisive the role of the disorder due to the random distribution of quinoid and benzoid rings in the chain. [8][9][10][11] In this approach the system has been generally studied in the frame of the Hückel theory, by assigning to the atoms appropriate site energies and hopping interactions according to the type of bonds. To expect electronic transport in a system dominated by disorder may appear surprising; however, this hypothesis is corroborated by the fact that in certain systems with correlated disorder, or in the presence of internal symmetries of the defects, a part of the eigenstates of the spectrum tends to be delocalized, determining an increase of the conductivity of the system; the simplest form of correlated disorder which is worth mentioning for its consequences on the study of conducting polymers, is the random dimer model; [12][13][14][15] it has been deeply studied in the case of binary lattice, but also in more general situations.…”

Three-dimensional effects on extended states in disordered models of polymers

“…In fact, it is very tempting to relate all this to the known fact that polyaniline shows a metal-insulator transition, with the concentration of dopant acting as a control parameter (see Ref. 38 and references therein). Another important consequence of this work is that other experimental procedures we have proposed to find out whether delocalization can be measured or not, such as disordered superlattices, 17 are likely to be correct even if 3D effects have not been taken into account.…”