Connectedness criterion

Figure 1.5 Definition of the connectedness criterion (Equation 1.2) and its contribution to the percolation threshold as defined for mono-disperse hard-core rods.

Figure 4.9 Theoretical shifts of the percolation threshold due to changes in the inter-tube distance [f], or in the number of junctions of CNTs in two polymeric matrixes with different MWDs. Connectedness criterion [A] and CNT diameter [D] are as defined in Chapter 1. [Reprinted from reference 20, with permission from e-PoIymers],...

In this equation, the connectedness criterion [A] embraces the nature of the inter-tube junctions, as it describes the efficiency of electron tunneling between adjacent tubes. The value of A is set by the electron tunneling distance [f], the value of which presumably is influenced by the temperature and by the electronic states of the CNTs, the contact potential barrier, and the electrostatic... 

Scenario one In this scenario the hard-core diameter D is assumed to stay constant while the connectedness criterion A changes. In other words, the PEDOTiPSS layers are considered to be penetrable, which is reasonable considering the properties of the material. The original connectedness criterion value is defined as Ai = D + fi. The new value is defined as A2 = 2 + < pp where dpp = D + 8 and 6 is the thickness of the penetrable PEDOTiPSS layer. A schematic of scenario one is illustrated in Figure 6.6 along with the rewritten Equation 6.1. 

Scenario two We define as the diameter of a bare SWCNT and D2 as the new effective diameter of the SWCNT. The PEDOT PSS layer is now included in the hard-core diameter. This scenario describes the case in which the PEDOT PSS layer is taken to be an impenetrable layer, which simply increases the apparent hard-core diameter of the SWCNT. This would be a reasonable approximation if the mobility of the layer is low in the melt state [minimal flow]. The change in the percolation threshold is still viewed in terms on the SWCNTs themselves, and not in terms of the additional PEDOT PSS. For this reason, the original connectedness criterion remains unchanged. This situation is schematically illustrated in Figure 6.7, along with the Equation 6.1 rewritten for scenario two. 

This criterion of connectedness is particulaxiy appropriate for computer asristed implications. 

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