Polyacetylene soliton structures

In real tran -polyacetylene, the structure is dimerized with two carbon atoms in the repeat unit. Thus the tt band is divided into occupied tt and unoccupied n bands. The bond-alternated structure of polyacetylene is characterishc of conjugated polymers. Consequently, since there are no partially filled bands, conjugated polymers are expected to be semiconductors, as pointed out earlier. However, for conducting polymers the interconnection of chemical and electronic structure is much more complex because of the relevance of non-linear excitations such as solitons (Heeger, 2001). 

FIGURE 1.22. (a) Schematic representation of soliton structures in polyacetylene, (b) Schematic band structure for neutral, positive, and negative solitons. 

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. 

Fig. 1. Possible structures for polyacetylene chains showing the two degenerate trans-structures (a) and (b), and the two non-degenerate cis-structures, (c) cis-transoid and (d) trans-cisoid and (e), a soliton defect at a phase boundary between the two degenerate trans-phases of polyacetylene, where the bond alternation has been reversed.

Many phenomena such as dislocations, electronic structures of polyacetylenes and other solids, Josephson junctions, spin dynamics and charge density waves in low-dimensional solids, fast ion conduction and phase transitions are being explained by invoking the concept of solitons. Solitons are exact analytical solutions of non-linear wave equations corresponding to bell-shaped or step-like changes in the variable (Ogurtani, 1983). They can move through a material with constant amplitude and velocity or remain stationary when two of them collide they are unmodified. The soliton concept has been employed in solid state chemistry to explain diverse phenomena. 

Fig. 9.11 Spatially extended soliton (f = 7) on a polyacetylene chain centred on the 30th carbon atom, (a) variation in bond alternation parameter, (b) the electronic wavefunction and (c) bonding structure.

These solitons are illustrated in Fig. 9.12. The mobility of the soliton along the polyacetylene chain means that the charged solitons (ii) and (iii) can behave as spin-less charge carriers. These are distinctly different objects from the electrons and holes found in conventional semiconductors, which carry charge and spin. Thus, while bond-alternated polyacetylene has the band structure of... 

Questions that had been of fundamental importance to quantum chemistry for many decades were addressed. When the existence of bond alternation in trans-polyacetylene was been demonstrated [14,15], a fundamental issue that dates to the beginnings of quantum chemistry was resolved. The relative importance of the electron-electron and electron-lattice interactions in Ti-electron macromolecules quickly emerged as an issue and continues to be vigorously debated even today. Aspects of the theory of one-dimensional electronic structures were applied to these real systems. The important role of disorder on the electronic structure and properties of these low dimensional metals and semiconductors was immediately evident. The importance of structural relaxation in the excited state (solitons, polarons and bipolarons) quickly emerged. 

The work of Su Shrieffer and Heeger (11) focussed on conjugated polymers having two valence bond structures, say A and B. In the case of trans polyacetylene, where A and B are degenerate, they showed intrinsic defects can occur, in which A phase goes continuously over to B phase, forming a soliton kink. 

Some photoelectron spectroscopy studies of /rani -polyacetylene in the pristine [28, 46], p-type doped [47-52] and -type doped [52] forms, can be found in the literature. Although no new well defined structure is detected upon doping, which would correspond to doping induced soliton levels, the density of states... 

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