Intra- and Interchain Charge Transport

The conductivity is a solid-state phenomenon, and, as pointed out already, conductivity is not a single chain phenomenon. The band-gap description of a conjugated chain is a one-dimensional model. Additionally, considerably interchain charge transport is necessary to describe a metal-like behavior in the highly doped three-dimensional sample and further transfer mechanisms across the polymer chains have to be discussed. What one actually needs to know in explaining conductivity of organic polymers is how the charge transport proceeds 

This complexity has led to a large number of theoretical considerations on the nature of the charge carriers and the mechanisms of transport [71, 83, 86, 90, 161-165]. 

1) the segregation between the rigid core of conjugated 7i-chains and the flexible alkyl chains, 

2) the formation of ordered layer structures with layer planes preferentially oriented perpendicular to the substrate. 

In such self-assembled structures the conductivity a as well as the charge carrier mobility n can be measured both parallel and perpendicular to the substrate. These studies nicely document how the structural organization of the chains increases both the anisotropy of the conductivity and of the charge-carrier mobility. 

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The electrical conductivity of a material is a macroscopic solid-state property since even in high molecular-weight polymers there is not just one conjugated chain which spans the distance between two electrodes. Then it is not valid to describe the conductivity by the electronic structure of a single chain only, because intra- and interchain charge transport are important. As with crystalline materials, some basic features of the microscopic charge-transport mechanism can be inferred from conductivity measurements [83]. The specific conductivity a can be measured as the resistance R of a piece of material with length d and cross section F within a closed electrical circuit,... 

Although the electrical conductivity of conducting polymers Is enabled by intra-chain transport, in order to avoid the localization inherent to one-dimensional systems, one must have the possibility of Interchain charge transfer.[1,3] The electrical transport becomes essentially three-dimensional (and thereby truly metallic) so long as there is a high probability that an electron will have diffused to a neighboring chain between defects on a single chain. For well-ordered crystalline material in which the chains have precise phase order, the interchain diffusion Is a coherent process. In this case, the condition for extended transport is that [1,3]... 

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