Two-polaron state

Scheme 13. A schematic picture of a ferromagnetic coupling unit between two polaronic states aax>rding to the Fukotome model...

Poly(3-octylthiophene) has been doped with LiAsFg in a benzonitrile solution or iodine in a methylene chloride solution [70]. In the visible-near IR spectra, the interband absorption was suppressed and new absorption peaks appeared due to the transition between the two polaron states and from the valence band to the lower polaron state. The spin density increased with increasing concentration of iodine, indicating the... 

Fig. 10. Formation of the bipolaron (= diion) state in poly-p-phenylene upon reduction In the model it is assumed that the ionized states are stabilized by a local geometric distortion from a benzoid-like to a chinoid-Iike structure. Hereby one bipolaron should thermodynamically become more stable than two polarons despite the coulomb repulsion between two similar charges...

At higher doping levels the polaron states interact the authors calculated that a bipolaron level is 0.49 eV more stable than two polaron levels so unfavourable polaron interactions are avoided via the formation of a more stable bipolaron, in agreement with the epr data of Scott and colleagues (1983). 

On the basis of their results the authors concluded that the crossover from the neutral to oxidised form of poly pyrrole, and vice versa, requires the number of spins to pass through a maximum, i.e. the creation and anihilation of bipolarons involves the passage through the polaron state. They expressed this as a two-step redox reaction ... 

Two lower states of the frans-(CH) are energetically degenerated as follows from symmetry conditions. Theory shows that electron excitation invariably includes the lattice distortion leading to polaron or soliton formations. If polarons have analogs in the three dimensional (3D) semiconductors, the solitons are nonlinear excited states inherent only to ID systems. This excitation may travel as a solitary wave without dissipation of the energy. So the 1-D lattice defines the electronic properties of the polyacetylene and polyconjugated polymers. 

Fig. 6. Magnetic polarons (big shaded regions) for different values of electron concentration p in the interval 1 ln< p <21 n. The small ellipses correspond to the two-electron states of the segments.

Bipolaron — Bipolarons are double-charged, spinless quasiparticles introduced in solid state physics [i]. A bipolaron is formed from two -> polarons (charged defects in the solid). For chemists the double-charged states mean dications or dianions, however, bipolarons are not localized sites, they alter and move together with their environment. By the help of the polaron-bipolaron model the high conductivity of -> conducting polymers can be explained. 

Two recent and detailed three-dimensional band calculations on trans-PA [93] and on PPV [94] yield similar results tjtn is at least 3 x 10 2, so three-dimensional behavior should be observed and no polaron state should... 

The case U = 0 is of special interest. In such a case, making one bipolaron from two polarons does not cost energy. The maximum spin concentration is i, which means that 50% of the boxes possess unpaired spins. This result can be explained as follows. Since (1) at the maximum spin concentration one has q = 1, and (2) placing one or two balls in the box is equivalent, there are four equiprobable cases (1) neutral site (no ball), (2) polaron up, (3) polaron down, and (4) bipolaron (two balls). Two among four of these states are magnetic, which gives for the spin concentration. The room-temperature data for polypyrrole and poly aniline can almost be fitted with U 0, which means that in these compounds polarons and bipolarons would be degenerate. 

Fig. 28.1. In a genetic switch, the total state of the system depends on two variables whether the DNA site is occupied or not and the number of copies of the transcription factor. In the left panel, the logarithm of the steady state probability for the occupancy state and protein number is plotted. This probability acts like an effective potential. In the right panel, the effective potential for a charge transfer or two site polaron is plotted as a function of the enviromnent polarization for the two electronic states. The governing time-dependent eqnations for the two problems share many similarities...

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