Bipolarons poly

Eig. 2. Lattice distortions associated with the neutral, polaron, and bipolaron states in poly(p-phenylene). 

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...

The electronic band structure of a neutral polyacetylene is characterized by an empty band gap, like in other intrinsic semiconductors. Defect sites (solitons, polarons, bipolarons) can be regarded as electronic states within the band gap. The conduction in low-doped poly acetylene is attributed mainly to the transport of solitons within and between chains, as described by the intersoliton-hopping model (IHM) . Polarons and bipolarons are important charge carriers at higher doping levels and with polymers other than polyacetylene. 

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 ... 

Fig. 2 Schematic representation of the doping of poly(p-phenylene ethynylene) (PPE) under formation of polarons (radical cations, radical anions) and bipolarons (dications, dianions). Note that multiple carriers can coexist on each macromolecule...

During the past three years we have been studying the chemical (SbCl5) oxidation of well-characterized oligomers of polyacetylene, poly[p-phenylene vinylene] (PPV) and poly[2,5-thienylene vinylene] (PTV) in order to determine how polaron and bipolaron states can be preferentially formed and stabilized. 

Figure 1. Examples of conducting polymers and species responsible for charge storage. Top, poly(acetylene) and soliton 2nd, poly-p-phenylene and bipolaron 3rd, poly- -phenylene sulfide 4th, poly(heterocycles) and bipolaron. Bipolarons in poly(furan) have not yet been established.

Fig. 4.3 The bipolaron state in poly(p -phenylenevinylene) is shown schematically.

Aida and coworkers developed poly(pyrrole)-containing mesoporous silica films in both hexagonal and lamellar phases.34 The polypyrrole chains are highly constrained and insulated when incorporated within hexagonal mesoscopic channels and the possibility of the polarons recombining into bipolarons is significantly suppressed. In contrast, the two-dimensional lamellar phase affords spatial freedom for electron recombination. 

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. 9.14 Two alternative bonding structures (a) and (b), polaron (c) and bipolaron (d) for poly(p-phenylene) and polythiophene.

Figure 4.8-1 Electronic structure and chemical structure of hole and electron polarons (a), hole and electron bipolarons (b), and hole and electron solitons (c). Examples of chemical structures refer to poly(thiophene) and poly(acetylene), respectively.

Poly(phenylene vinylene), PPV, and its soluble derivatives have emerged as the prototypical luminescent semiconducting polymers. Since PPV has a nondegenerate ground state, structural relaxation in the excited state leads to the formation of polarons, bipolarons, and neutral excitons. However, prior to treating the structural relaxation in the excited state, one needs to develop a satisfactory description of the electronic excited states. 

Scheme 5.J. The oxidation (doping) of poly p-phenylene). The bipolaron is the final oxidation product in poly(p-phenylene) and other polymers with nondegenerate ground states.

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