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where A is a constant and e is the activation energy of hopping. The exponent n is usually 1/4 or 1/3 (it is the reciprocal of the effective dimensionality of the space in which the charge transport occurs). The charge transport in a conjugated chain and the interchain hopping is explained in terms of conjugation defects (radical or ionic sites), called solitons and polarons. Several possible conjugation defects are demonstrated in Fig. 5.33 on the example of trans -polyacetylene. A soliton is an electroneutral radical site with a spin equal to 1/2 connected to the rest of the chain by somewhat longer bonds; the charge and the bond lengths are, however, disturbed also in the close surroundings of the defect, hence the soliton extends over about 15 ( CH ) units. If we remove or add an electron to the soliton, a zero spin and the corresponding charge appears (charged soliton). Two neutral solitons can recombine and the chain defect is cancelled. On the other hand, charged and neutral solitons in neighbouring sites form a stable pair called polaron. Both the solitons and polarons are mobile along the chain, but a soliton, unlike a polaron, moves virtually without overcoming energy barriers. If the number
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trans- polyacetylene
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Fig. 5.33 Conjugation defects in trans -polyacetylene
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of polarons in the chain increases, they can interact basically in two ways: two polarons can either form two charged solitons or a new stable zero-spin defect called bipolaron. 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 polyacetylene 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. There exist numerous conjugated macromolecules showing high electronic conductivities after doping. Materials thus prepared are also termed 'synthetic metals' (their significance is documented, for example, by the existence of a journal of the same name). This section presents only a very brief summary of this constantly growing field. Further information can be found in numerous reviews and monographs; the most representative ones are listed below. All important electronically conducting polymers, except perhaps for polyacetylene, can be prepared electrochemically by anodic oxidation of the monomers. The reaction is initiated by splitting off two hydrogen atoms from the monomer molecule (H M H), which subsequently polymerizes by interconnecting thus activated sites: nH M H-+ H (M)* H + {In - 2)H + + (2w - 2)e" (5.5.39) According to this scheme, the consumption of positive charge should be close to 2F/mol of monomer. Experimental values for various monomers are considerably higher, in the range from 2.1 to 2.7. This is due to the fact that the dehydrogenation of the monomer generally occurs at more positive potentials than the p-doping of the polymer thus prepared. Therefore, the produced polymer is oxidized immediately after its formation (p-doped) with the consumption of a non-stoichiometric, additional positive charge: H (M)n H + nyAT-+ H (M)7+ W-nyAT + nye~ (5.5.40) where y is the so-called doping level (y 0.1-0.7). Both the mentioned reactions proceed in parallel. The mechanism of electrochemical polymerization is not completely elucidated, but obviously the first step of the polymerization, i.e. the formation of a dimer, H M M H, is rate-determining. As soon as the dimer is formed, it further oxidizes more easily to the trimer and higher oligomers, since the oxidation potential of the oligomer gradually decreases with increasing polymerization degree, n. The polymerization reaction is, therefore, accelerated at a constant electrode potential as the polymer chain grows. Several examples of conducting polymers that can be electrochemically doped are quoted in Table 5.3.
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Table 5.3 Examples of electronically conducting polymers, y is the level of electrochemical doping and K is the maximum electrical conductivity. Except for polyacetylene and polyparaphenylene, only p-doping is considered Polymer Polyacetylene n-doped p-doped Polyparaphenylene n-doped p-doped Polypyrrole Repeat unit CH=CH 0.09 0.05 ~\ 7~ 0.44 0.1 0.4 100 1000 100 100 500 y K (S/cm)
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