Potential of the Osmium Redox Polymer

Although the mediator has already been specified as a cross-linked osmium redox polymer, there are many molecular strucmres that fulfill this requirement. The first engineering issue is to select the best available choice for the application. 

The driving force A et,c between the mediator and enzyme active site determines the rate of electron exchange between them. As described by Marcus in Equation 9.9, rates of electron transfer between species in solution are exponentially dependent on the free energy (potential) difference between the two species, which may be thought of as an overpotential [7,9,124]. If we neglect the quadratic term and assume d and / will be identical for similar redox polymers, we may collect constants and write a Tafel-like form of this equation (Equation 9.20)  

We can construct a one-dimensional model of a redox hydrogel-mediated enzyme film by performing a mass balance around the reduced mediator species, making use of the kinetic expression in Equation 9.12, resulting in Equation 9.21. 

Appropriate boundary conditions for the mediator at the electrode interface (x = 0) and electrolyte interface (x = (p) (Equation 9.22) are 

This is related to electrode potential through Equation 9.7. It is a reasonable assumption that oxygen concentration and enzyme concentration Cg are constants throughout the film. 

---