Interchain hopping

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. 

Fig. 21 A schematic view of the hierarchy of charge carrier hopping in a network of disordered conjugated polymer chains. 1 depicts ultra-fast motion within an ordered segment of the chain while 2 and 3 illustrate intra-and interchain hopping processes...

The transverse charge motion is incoherent for a quasi-one-dimensional conductor as long as the condition h hiT is fulfilled (where the intrachain scattering time provides a broadening to the quasi-one-dimensional Fermi surface). This situation is encountered at high temperature. The interchain hopping rate is thus determined by the one-dimensional Fermi golden rule [60] ... 

PDAs A Model of CPs Without Disorder In PDAs one would expect to have only two processes to consider transport along a really periodic chain, and all similar interchain hopping events. The case of PDAs illustrates the ambiguities of transport studies on CPs. Early time-of-flight experiments yielded mobilities ==5 cm2/V s along the chains, and 10 3 along the perpendicular directions [217]. A mobility of a few cm2/V s is typical of a molecular crystal, and the polymer character was not apparent. 

More recent work [221-225] has not yet resolved the puzzle. It seems, however, that the small mobilities obtained initially were influenced by trapping, and the intrinsic value should be larger. Evidence for a sublinear increase in drift velocity with electric field and a tendency toward saturation has been found [224], but at a much higher field than proposed earlier. The lower limit of the low-field mobility would be about 103 cm2/V s. But since the chain length in the PDAs investigated to date is not known, the relative influence of intrachain transport and interchain hopping in this value is uncertain. It will be some time before values to be compared to a theory of transport in a CP are available. The high electron mobilities... 

Similar studies with dilute and semidilute suspensions of luminescent libers in organogels should be possible, but none to our knowledge has been conducted w ith the same level of detail. It is most probable that interchain hopping between gelator fibers will be much less efficient than transfer within and along the long axis of a fiber. 

The interchain hopping transport can be described by the probability Ql(x) -where x is the effective conjugation or delocalization length-of finding a comparable mean free path on another chain weighted by the Frank-Condon factor FC. The conductivity a can then be described as a function of the concentration C of polarons, multiplied by the integral over the interchain hopping probability Pp(x) [96, 97]. 

It is known that the polymer chains are lying in the plane of the surface.34 In a typical polymer device structure anode/polymer/cathode, the charge carriers are traveling across the polymer film, which is perpendicular to the plane of the film. Therefore, the conductivity of the film will, to a large extent, depend on the rate for interchain hopping of the carriers or on the rate for the interchain electron transfer. If a polymer film is dominated by the Ar-type aggregation style shown in Fig. 6.4, where the bulky side chains (the insulators) are trapped inside the aggregate and... 

An alternative interpretation for the activated behavior of the photocurrent and the PIA-decrease with temperature was proposed by Townsend et al. [35]. They assigned their experiment results to a thermally activated interchain-hopping mechanism for bipolaron-like charged soliton pairs, the experiments of which were carried out on Durham frany-polyacetylene. 

In the quasi one-dimensional systems these fluctuations are suppressed to some extent by the interchain hopping of electrons (see e.g. and this makes the transitions possible. However... 

Peierls transitions and this produces a principle way to change the properties of materials The influence of impurities on the interchain hopping probability is also essential since the hopping is necessary to suppress the fluctuations of the order parameter [6],... 

With the objective to inve.stigate the dependence of carrier transport on the interchain separation. Riihe et al [252,253] have synthesized doped (C104 ,PF5 ) poly(3,4-cycloalkylpyrrole)s having 3, 4, 5 or 10 methylene groups in the alkyl loop. These polymers arc also amorphous. Because of the interring torsions, the alkyl substituents are expected to form a cylindrical shell around the chain. The thickness of the shell has been estimated from single-crystal x-ray data of the monomers. The conductivity decreases w ith an increase of the shell thickness. This indicates the importance of interchain hopping for this property. 

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