The Brown-Anson Model

Let us assume that the redox activity in a surface-deposited electroactive polymer film is quantified via the Nernst equation that is 

This expression can be written in a simpler form as follows. We set y = ln(b/a) and = nFlRT(E - E°) to obtain 

If interactions are present within the electroactive polymer, the Nernst equation is modified to read 

In the Brown-Anson approach, it is assumed that the degree of redox center interaction depends on the extent of film oxidation or reduction. We can write the Nernst equation in the following way  

In Eqn. 185 the interaction parameters r A, rsB, Tab, and i ba have been introduced, which quantify the interaction between redox sites. Note that r values can be negative or positive. If repulsive interactions operate, then r values are negative, whereas attractive interactions yield positive r values. Some authors use the opposite convention. We note that Eqn. 184 can be written as 

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This is the fundamental expression in the Brown-Anson model. 

FIGURE 1.35. Plot of the modified Nemst equation y = iO (see Eqn. 183) for an electroactive polymer film when redox site interactions are taken into account. Data points are recorded for a poly(thionine) film. The dashed line is computed from Eqn. 197 (the Brown-Anson model) with given by Eqn. 199. The full line is obtained from the Albery-Colby model, with i given by Eqn. 218. A good agreement between experiment and theory is obtained using the Albery-Colby model for a = 4.67. 

Figure2.17 Formal Os(lll)/Os(ll) redox potential as a function of the average fraction of oxidized osmium sites for Qai,= 1 mM (dashed lines) or 1.2 M (solid line). From the slope it is possible to predict the lateral interaction parameters in Brown and Anson model, Equation 2.8. Taken from Ref [120].

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