The Albery-Colby Model

This approach proposes that interactions between redox sites in the layer are responsible for the nonideal Nernstian behavior of 1, but it is assumed that these interactions do not depend on the degree of film oxidation or reduction. Instead it is assumed that each redox site has its own standard potential value and these values are distributed about the observed value Hence the heterogeneity of the layer is emphasised in this approach. The spread of standard potentials is assumed to be Gaussian. 

We consider a set of redox couples A/B with a single formal potential obeying the Nernst equation such that the mole fraction of couples Xj in this set is given by 

Summing over all possible sets of nonequivalent oxidized sites gives the total mole fraction of the oxidized form in the layer 

Now macroscopically the net observed behavior is given by the modified Nernst equation 

Replacing the summation over j with an integral over all values of 6j gives 

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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. 

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