Electronically conducting polymer conductivity models

Another model assumes that gel zones are formed by hydrated lead dioxide (PbO(OH)2) and act as bridging elements between the crystallite particles. Electrons can move along the polymer chains of this gel and so cause electronic conductivity between the crystalline zones 137],... 

Charge transfer kinetics for electronically conducting polymer formation, 583 Charge transport in polymers, 567 Chemical breakdown model for passivity, 236... 

Since model compounds reveal well-defined cyclic voltammograms for the Cr(CNR)g and Ni(CNR)g complexes (21) the origin of the electroinactivity of the polymers is not obvious. A possible explanation (12) is that the ohmic resistance across the interface between the electrode and polymer, due to the absence of ions within the polymer, renders the potentially electroactive groups electrochemically inert, assuming the absence of an electronic conduction path. It is also important to consider that the nature of the electrode surface may influence the type of polymer film obtained. A recent observation which bears on these points is that when one starts with the chromium polymer in the [Cr(CN-[P])6] + state, an electroactive polymer film may be obtained on a glassy carbon electrode. This will constitute the subject of a future paper. 

Fig. 10.2. One-dimensional semiconductor model of interacting 2/>z-electrons in polymer chain from C-C- bonds of alternating length (it-electron system of polyacetylene) [9] (a)-the configurations of chain with repeat union 2a (b)-energy band scheme for 2/>z-electrons G the gap between valent and conduction bands.

There are some (Heinze, 1996) to whom the polaron explanation of the ionic introduction of electronic conductivity in organic compounds is specious The roughness factor of 400 would limit the degree of penetration of ions into the interstices of the polymer. However, Li+ or even CIOJ is of course much smaller than the test molecules (large dye molecules) which are generally used to probe the real area. Thus, one might conceive of a model of the polymer that is all fibers, the intercalation being all pervasive. It is obvious that an Li+ ion adsorbed on the surface of a fiber will promote an electron that may indeed be free to move under a field, i.e., to conduct. 

Such models do not seem to explain the high specific conductivity observed in electronically conducting compounds. In an alkali metal, there is one conducting electron per atom. If some electronically conducting polymers are to conduct to within 1 or even 10% of this, it would seem to require 0.01 or 0.1 conductivity electrons per atom, and that is difficult to visualize as a consequence of surface adsorption of ions, which will seldom exceed 0 = 0.1 for surface occupancy. The mechanism by which such adsorption stimulates conductance inside the fibers has not yet appeared in understandable form. 

We can see that electronic conduction, ionic conduction and conduction in heterogeneous composites are all important in their own way in polymers, but they form three quite distinct subjects, and the latter two forms of conduction will therefore be treated separately in Chapter 8. Here we will discuss the basic models of electronic conduction in solid polymers. Materials will be discussed in the later chapters. 

When the polymer flhn is oxidized, its electronic conductivity can exceed the ionic conductivity due to mobile counterions. Then, the film behaves as a porous metal with pores of limited diameter and depth. This can be represented by an equivalent circuit via modified Randles circuits such as those shown in Figure 8.4. One Warburg element, representative of linear finite restricted diffusion of dopants across the film, is also included. The model circuit includes a charge transfer resistance, associated with the electrode/fllm interface, and a constant phase element representing the charge accumulation that forms the interfacial double... 

Within the alternative approach, the film is considered a porous medium [54, 94,114,119,121,122,127-129,148], Physically, it represents a porous membrane that includes a matrix formed by the conducting polymer and pores filled with an electrolyte. Mathematically, in this approach the film is modeled as a macroscop-ically homogeneous two-phase system consisting of an electronically conducting sohd phase and an ionically conducting electrolyte phase. Considering a planar geometry, each layer perpendicular to the electrode smface contains these two phases, and it can therefore be described at any point by two potentials that depend on the time and the spatial coordinates. 

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