Interchain transport

The temperature dependence of conductivity chain axis [14]. Although oj /charge transport, is nearly identical in both cases (oj and charge transport properties. 

In a second step interchain coupling is taken into account. Interchain transport can now take place. Two limiting cases have to be considered. In the case of weak disorder (the chains are reasonably parallel to each other), interchain coupling, by reintroducing some three-dimensional features, can prevent one-dimensional effects, such as one-dimensional localization, which reduce conductivity. If Ae (the mean-square deviation of the on-site energy) is a measure of the disorder, the condition for the onedimensional localization to be removed is... 

Electrical conductivity in PPy involves the movement of positively charged carriers and/or electrons along polymer chains and the hopping of these carriers between chains. It is generally believed that the intrachain hopping resistance is much greater than the interchain transport resistance. 

Figure 10-2 7/t/e/chain charge mobility. Although the dopant counterion, ag., I (which also easts as I3" and Ij" ) has been omitted from these drawings, it may play a role in interchain transport. 

It is worthwhile, at this point, to examine in more detail the influence of interchain transport on the conductivity of PPy. The total resistivity of PPy, p = (l/(7), maybe defined as follows [15]... 

Figure 1.8 Interchain transport of solitons and bipolarons in (a) polyacetylene and...

It is well known that in an ideal one-dimensional conductor the transverse orbital motion is restricted, thus the carriers cannot make circular motion in the presence of a magnetic field. Hence, one could hardly expect any MC in an ideal one-dimensional condnctor. However, in the presence of any finite interchain transfer integral, as in several q-lD conductors, the MC can be used as a powerful tool to investigate the intrachain versus interchain transport. Nevertheless, the fine features in anisotropic MC can be made inconspicuous in the presence of disorder. 

In summary, using the electron—lattice dynamics theory, we have been able to explore the details of the intrachain polaron motion. In particular, we have shown that the velocity of the polaron can exceed the sound velocity of the system. This is achieved by the decoupling of acoustic phonons from the polaron. With this knowledge about the intrachain behavior of the polaron dynamics, we will now go on to discuss the interchain transport of polarons. 

Similar to the case of transition to supersonic velocities discussed above, this interchain transport process is also nonadiahatic. To pass through the barrier, the electron has to undergo an electronic transition from the polaron level localized to chain 1 to the TT -level localized to chain 2. The energy needed for this transition, the activation energy, is taken from the phonon system. Actually, the process is very similar to that treated by the Holstein theory discussed in Section 2.2 the electronic coupling between the chains is weak enough to force the electronic states to localize on individual chains. 

As indicated earlier, polymers have a semicrystalline structure that is compatible with a two-phase model of polymer conductivity. A model proposed by Epstein and co-workers [8] describes the polymer sample as a set of metallic islands embedded in the insulating matrix. Conductivity is controlled by hopping of charge carriers between metallic islands. Such a structure may be a result of nonuniform doping as well as of two-phase crystalline-amorphous morphology. Interchain transport is favorable for high-density crystalline packing of macromolecules because... 

We previously noted that both intrachain and interchain transport of carriers mdst be considered when examining the electronic conductivity of conjugated polymer materials. We now describe a theoretical model recently developed by Pearson and coworkers that can be used to examine the effect of polymer molar mass and polymer orientation on the conductivity behavior of conjugated polymer materials. 

In polymer films, there are generally crystallized and amorphous zones, as indicated hy the atomic force microscopy (AFM) image in Fig. 1.3h. Thus interchain transport is generally classified into two pathways (i) transport at ordered packing zones, which may adopt a hopping mechanism hke orderly packed small molecules (Fig. 1.3a, route 2) (ii) transport at loosely contacted zones, where carrier transport is slow (Fig. 1.3a, route 3). Thus ordered molecular packing in film will reduce the loosely contact zones, thereby improving interchain transport. 

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