Distance charge hopping

Amino acid residue models such as a tyrosine residue model (p-cresol) lengthen remarkably the charge hopping distance, a phenomenon which can solve i he problem in the electrocatalysis mentioned in the above item 5) and enhance remarkably the catalytic activity. 

Regarding item 6) above on electrocatalysis, the coexistence of tyrosine residue model, p-cresol (p-Crej, enhanced remarkably the catalytic activity of Ru-red confined in a Nafion membrane coated on an electrode (Fig. 19.3).20) This was attributed to the nearly twofold lengthening of the charge hopping distance by p-cresol from 1.28 nm to 2.25nm). 

Schematic diagram depicting the factors causing the discrepancy between TFT and TOF mobilities. In (a), DOS of the organic material is broadened by the polar insulator surfece. In (b), the surface roughness of gate dielectric may affect charge hopping distances.

Figure 13-6. Electrocatalytic water oxidation utilizing a polymer-coated electrode as a ftmction of the Ru-red catalyst concentration confined in a Nafion membrane coated on an electrode. Applied potential 1.4 V vs. Ag-AgCl. (a) In the absence of amino acid model compound, (b) in the presence of 5.0 x 10" M p-cresol p-Cre), and (c) with toluene. The solid line is a simulated curve considering charge mediation, and the dashed lines are the calculated values without mediator. The dash-dotted curve (I) is a simulated curve in the presence of p-Cxt when and r

Pif) vs. r can be depicted as a function of c and is shown in Fig. 14-9. When assuming a charge-hopping distance r between molecules (center-to-center) within which charges can hop, the fraction of molecules that can accept charge Red is obtained by integration of the P r) function from s to r. The fraction of molecules that cannot accept charge is then represented by 1 - which is obtained as Eq. (14-13) [37,38]. 

For charge hopping, the distance is also an important parameter in addition to kc. A charge hopping distance between the [RuCbpyls] " complexes in the Nafion film was foimd to be 1.3 1.6 nm including the distance of the boimded motion of the complex that is dependent on the time scale of the reaction [42,43]. Here the boimded motion is a kind of local oscillation of the redox molecules in the incorporated matrix. 

In summary, the distance dependence of electron transport dynamics varies as r p, where r is the bridge length (or the number of bridge units in the case of a charge hopping process) and p is less than 2. Consequently, electron transport rates display a very weak dependence on bridge length. 

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